Mathematical analysis of G1/S sub-networks in hematopoietic proliferation: Sequential and lineage-specific activation

Summary

Commitment to the cell division cycle constrains other fate choices at the single-cell level. Hence the molecular network controlling the G1/S transition must be coordinated with developmental phases. Healthy hematopoiesis relies on shifts in cell cycle dynamics that balance proliferation and differentiation of hematopoietic stem cells and lineage progenitors, offering an ideal model system to study this coordination. Using computational analysis of published single-cell transcriptomics profiles of human bone marrow and mathematical modeling, we demonstrate that variations in the expression of cyclin D- and cyclin E-centered sub-modules of the G1/S network carve out distinct trajectories from G1 to S, explaining the distinct proliferation properties of hematopoietic cell types evolving in the same microenvironment. We map 68 hematopoietic cell types to specific model parameters, and identify their individual route through G1/S. This theoretical work provides mechanistic insight into hematopoietic proliferation that could guide experimental testing and the design of more nuanced cell cycle-targeting pharmacological strategies.

Graphical abstract

Highlights

• •The expression of 24 G1/S genes identifies hematopoietic cell types
• •Cyclin D, Cyclin E, and CDKN modules are sequentially expressed during differentiation
• •Three main routes from G1 to S, depending on lineage and developmental stage
• •Mathematical method to analyze G1/S commitment in homogeneous cell subsets

Cell biology; mathematical biosciences; systems biology

Introduction

In all eukaryotic species, cells commit to division by activating a large transcriptional program at the G1/S transition of the cell division cycle (reviewed in Bertoli et al.¹). The molecular network that controls this transcriptional burst is highly conserved—from plants,² to yeasts,³ and mammals.¹ The regulation of the cell cycle, and the G1/S commitment point in particular, is among the most extensively studied pathways in cell biology, owing to its central relevance in cancer and regenerative medicine. Over the past 70 years, intensive research has identified the key proteins and their interactions that together form the G1/S network. Although the network architecture is well described, it is far less understood from a functional perspective: in particular, it is not known which upstream signals trigger the activation of the G1/S transcriptional program; nor can we explain why cells that cohabit the same microenvironment, and are therefore exposed to the same external stimuli, exhibit markedly different proliferation activity.

Under normal physiological conditions, once G1/S transcription is fully activated, the cell cycle most often completes.⁴ Consequently, the G1 phase represents a time window during which a cell can opt for other cell fate choices like quiescence^5,6 or differentiation,⁷ and extending the duration of G1 phase increases the odds that other developmental decisions are made at the molecular level.^8,9 How are cell division, quiescence, and differentiation coordinated by the G1/S network? This is the central question motivating this work.

To study how cell fate decisions are coordinated, the hematopoietic system is an ideal model: each day, the bone marrow produces ∼284 billion new hematopoietic cells, accounting for ∼86% of total cellular turnover in the human body.^10,11 This output originates from a small population of hematopoietic stem cells (HSCs). To sustain the lifelong hematopoiesis, most HSCs are dormant in cell-cycle quiescence (G0 phase), i.e., have a low proliferation rate that protects them from functional exhaustion and cellular insults.¹² A subset of HSCs, however, differentiates into multipotent progenitors (MPPs), which further give rise to lineage-committed progenitors.¹³ Progenitor populations are characterized by a fast proliferation,¹⁴ which supports their self-renewal and the maintenance of stem cell identity.^15,16 In response to differentiation cues, lineage-committed progenitors evolve toward terminally differentiated cells that display a low intrinsic proliferation rate, although some cell types, such as naive and memory B and T cells, can re-enter the cell cycle upon contact with an antigen.¹⁷ Hence, cell cycle activity evolves along the hematopoietic differentiation paths, raising the possibility that G1/S modulations may contribute to the acquisition of differentiation biases.

Before committing to further differentiation, cells sense differentiation cues and make cell fate choices during G1,¹⁸ the duration of which varies depending on the cell type and environmental context.¹⁹ Increased G1 duration delays cell cycle progression and increases cells’ exposure to differentiation cues. In contrast, a short G1 drives the rapid proliferation of progenitors and uncouples cells from extrinsic signals. Thus, the G1/S checkpoint not only serves as a gate to proliferation but also constrains alternative fate choices. Interestingly, changes in cell cycle duration alone can shift developmental trajectories.¹⁸ For instance, increased cell cycle speed in megakaryocytic-erythroid progenitors (MEPs) is sufficient to promote their differentiation toward erythroid progenitors (ERPs) rather than toward megakaryocytic progenitors (MkP).²⁰ Similarly, a slower cell cycle in fetal liver hematopoietic progenitors promotes myelomonocytic over B cell fate.²¹ Thus, cell cycle duration, and G1 duration in particular, plays a role in lineage specification.

Across kingdoms of life, passage through G1/S is orchestrated at the transcriptional level by the E2F family of transcription factors: in plants, E2Fa-c, reviewed in²²; in yeast, SBF/MBF, reviewed in³ across evolution; and in mammals, E2F1-3, reviewed in.²³ In G1, E2Fs are kept inactive through high affinity binding of Retinoblastoma (RB) family proteins (Rbr in plants, Whi5 in yeast, and RB1/RBL1-2 in mammals).^22,24,25,26 In late G1, RB-like proteins are heavily phosphorylated by cyclin dependent kinases (CDKs, CDK2-4-6 in mammals). The intrinsic kinase activity of endogenous CDKs is very low but is boosted upon binding to G1 cyclins (Cln1-3 in yeast, cyclins D1-3 and E1-2 in mammals²⁷). RB phosphorylation disrupts RB-E2F complexes, releasing active E2Fs that transcribe genes required for progression into S-phase. Among E2F targets are the CCNE1 and CCNE2 (cyclin E1 and E2), CDK2 (cyclin-dependent kinase 2), and CDC25A (cell division cycle 25A) genes, that further activate CDKs and complete RB phosphorylation in a positive feedback loop.^24,28,29 In human, the activity of Cyclin-CDK complexes is balanced by cyclin-dependent kinase inhibitors (encoded by CDKN genes). The proteins p16 (CDKN2A) and p15 (CDKN2B) specifically inhibit CDK4/6, while p21 (CDKN1A), p27 (CDKN1B), and, in certain tissue contexts p57 (CDKN1C) also inhibit CDK2 and may also play an activatory role by assisting in the assembly of CycD-CDK4/6 complexes. Dysfunctional CDKN2A/B locus is the 2^nd most common genetic alteration found in cancer and is also very frequent in hematological malignancies.³⁰

The consensus chain of events that lead to full G1/S commitment is the following: first, mitogenic signals and/or growth factors induce the transcription of cyclin D1-3 genes.^31,32,33,34 This promotes assembly of CycD-CDK4/6 complexes, which initiate RB phosphorylation. Partial RB phosphorylation reduces E2F inhibition, which induces low-level transcription of cyclin E and other activators, thereby activating the positive feedback loop that leads to full RB phosphorylation, E2F release, and G1/S activation via transcription of E2F targets. In this paradigm, absence of either CycD-CDK4/6 or CycE-CDK2 would prevent full RB phosphorylation and E2F activation (see Hume et al.³⁵ and discussion therein), keeping E2F in an intermediate state of moderate activity³⁶ that is insufficient to pass G1/S. However, some cell types proliferate despite minimal expression of CycD-CDK4/6-related genes, possibly because RB hyperphosphorylation is in some contexts already achieved at cell birth.³⁷ Likewise, the existence of cancer cells resistant to CDK4/6 inhibition challenges this canonical model and demonstrates the existence of alternative routes through G1/S.^38,39

We hypothesize that different hematopoietic cell types employ distinct strategies within the G1/S molecular network to pass the transition. This idea is supported by the fact that while certain cell types degrade RB during G1 phase to elicit E2F activation (e.g., in hTERT-immortalized human mammary epithelium cells⁴⁰), and depend on CDK activity, others pass G1/S without RB degradation (e.g., hTERT-immortalized human retina epithelial cells^41,42), indicating a plethora of strategies cells can employ to activate E2F and commit to division. We hypothesize that, due to the large variability in gene expression patterns and proliferation rates across hematopoietic cell types, the hematopoietic system encloses the different transition dynamics encoded within the G1/S network.

To test this hypothesis, we leveraged the best-resolved transcriptomics atlas of healthy human hematopoiesis published to date,¹³ which provides a detailed snapshot of the relative expression of core G1/S regulators across different cell types. We integrated this data into a dynamical mathematical model of the G1/S transition, that enabled to predict the proliferative potential of each cell type and provided a mechanistic basis for how different cell types navigate the G1/S transition. Our analysis identified 3 major routes for the G1/S transition, and the hematopoietic cell types that elicit each route. Since the different routes through G1/S are based on distinct G1/S core regulatory proteins, our model explains the differential sensitivity of hematopoietic cell types to specific drugs (e.g., CDK4/6 inhibitors). We envision our model could serve as a guide for further experimental and pre-clinical investigation and, on the longer term, the design of more nuanced, personalized cell cycle-targeting pharmacological strategies and rational drug combinations.⁴³

Results

Expression patterns of the 24 genes defining the core G1/S network recapitulate the diversity of immune cell types and of their proliferative properties

To explore how the expression of the core G1/S regulatory genes (Figure 1; Table 1; STAR Methods) varies across hematopoietic cell types and relates to their differential proliferation, we utilized the comprehensive human hematopoiesis atlas published by Zhang et al.¹³ As this scRNA-seq macro-dataset integrates datasets from several experiments, we minimized batch effects by focusing our analysis on the Hay et al.⁴⁴ dataset that encompasses scRNA-seq profiles from ∼100k cells from the bone marrow (BM) of 8 healthy adult donors.

Figure 1.

A mathematical model for the G1/S transition

Schematics of the G1/S network model.

Molecular species and complexes are shown as ellipses and rectangles, respectively, framed in green or red depending on whether they are in active or inactive form. Dashed circles represent upstream mitogenic inputs that influence commitment to cell-cycle entry. Black ellipses represent proteins whose activity toward the G1/S transition is not accounted for in the model, when they are not part of complexes. Arrows indicate all biochemical reactions included in the model, with the corresponding rate/coefficient shown on the side of the arrow. Blue arrows indicate synthesis/degradation reactions, black arrows complex binding/dissociation, red arrows complex/protein inactivation, and green arrows complex/protein activation. Dashed green arrows represent indirect activation that stems from the competition for shared CDK inhibitor proteins, and modulate the rates f₁₃ and f₁₄. “nP” diamonds represent activation functions that are governed by multi-site phosphorylation, multiplying the corresponding rate by a Hill function of the activatory factor (see “STAR Methods” and “supplemental methods”). See also Figures S1–S6.

Table 1.

G1/S genes

HGNC symbol	Description	Ensembl gene ID	Entrez gene ID	Chromosome	Start position	End position	Strand
CCND1	cyclin D1	ENSG00000110092	595	11	69641156	69654474	1
CCND2	cyclin D2	ENSG00000118971	894	12	4269771	4305353	1
CCND3	cyclin D3	ENSG00000112576	896	6	41934934	42050357	−1
CCNE1	cyclin E1	ENSG00000105173	898	19	29811991	29824312	1
CCNE2	cyclin E2	ENSG00000175305	9134	8	94879770	94896678	−1
CDC25A	cell division cycle 25A	ENSG00000164045	993	3	48157146	48188417	−1
CDK2	cyclin-dependent kinase 2	ENSG00000123374	1017	12	55966781	55972789	1
CDK4	cyclin-dependent kinase 4	ENSG00000135446	1019	12	57747727	57756013	−1
CDK6	cyclin-dependent kinase 6	ENSG00000105810	1021	7	92604921	92836573	−1
CDKN1A	cyclin-dependent kinase inhibitor 1A	ENSG00000124762	1026	6	36676460	36687397	1
CDKN1B	cyclin-dependent kinase inhibitor 1B	ENSG00000111276	1027	12	12685498	12722369	1
CDKN1C	cyclin-dependent kinase inhibitor 1C	ENSG00000129757	1028	11	2883213	2885775	−1
CDKN2A	cyclin-dependent kinase inhibitor 2A	ENSG00000147889	1029	9	21967752	21995301	−1
CDKN2B	cyclin-dependent kinase inhibitor 2B	ENSG00000147883	1030	9	22002903	22009305	−1
CDKN2C	cyclin-dependent kinase inhibitor 2C	ENSG00000123080	1031	1	50960745	50974634	1
CDKN2D	cyclin-dependent kinase inhibitor 2D	ENSG00000129355	1032	19	10566460	10569059	−1
CDKN3	cyclin-dependent kinase inhibitor 3	ENSG00000100526	1033	14	54396849	54420218	1
E2F1	E2F transcription factor 1	ENSG00000101412	1869	20	33675477	33686385	−1
E2F2	E2F transcription factor 2	ENSG00000007968	1870	1	23506438	23531233	−1
E2F3	E2F transcription factor 3	ENSG00000112242	1871	6	20401879	20493714	1
MYC	MYC proto-oncogene, bHLH transcription factor	ENSG00000136997	4609	8	127735434	127742951	1
RB1	RB transcriptional corepressor 1	ENSG00000139687	5925	13	48303744	48599436	1
RBL1	RB transcriptional corepressor like 1	ENSG00000080839	5933	20	36996349	37095997	−1
RBL2	RB transcriptional corepressor like 2	ENSG00000103479	5934	16	53433977	53491648	1

List of G1/S regulatory genes accounted for in this study (core G1/S network, see Figure 1).

Since cells that pass the G1/S checkpoint typically complete the cell cycle and divide,⁴ we used the expression of essential S, G2 and M phase genes (Table S2,^45,46) to define a propensity to divide coefficient (P_d, ranging from 0 to 1) for each of the 68 cell types (Methods). Throughout the manuscript, P_d will be our readout for proliferation. This data-inferred P_d was homogeneous across donors but strongly differed across the different cell types, highlighting erythroid-primed megakaryocyte-erythroid progenitors (MEP-Eryth-1), late erythroid progenitors (ERPs) and erythroblasts, progenitor B (pro-B) cells, and late monocyte-dendritic progenitors (MDPs) as the most proliferative hematopoietic cell types in the adult human bone marrow (Figure 2A; Table S1). We partitioned hematopoietic cell types into 5 categories (mostly quiescent, low proliferation, mid, high and very high proliferation) using the Jenks algorithm. The P_d evolved similarly along most branches of the hematopoietic tree, with HSCs and early progenitors showing rather low P_d (∼0.05–0.2, quiescent/low proliferation), later progenitors showing much higher P_d (0.25–1), and finally terminally differentiated cells showing very low P_d (0–0.1; Figures 2B and 2C).

Figure 2.

The propensity to divide evolves non-monotonically along branches of the hematopoietic tree, consistently across donors

(A) Bar chart shows the propensity to divide score (P_d) in developmentally ordered hematopoietic cell types from the adult bone marrow,⁴⁴ scRNA-seq annotated by Zhang et al.¹³. For each cell type, individual bars represent the donors, highlighting low inter-donor variability in P_d. Coarse cell type annotations (Level 1¹³) are indicated in bold. Dashed lines indicate P_d categories (Jenks breaks).

(B) UMAP representation of the dataset at single-cell resolution (1 dot = 1 cell, see “STAR Methods”) captures hematopoietic lineage relationships and highlights differentiation trajectories. Cell types are color-coded as in A).

(C) UMAP (panel B) colored by P_d scores illustrates how the proliferative potential evolves during hematopoiesis. See also Figures S12–S14 and Tables S1 and S2.

Since the G1/S checkpoint gates proliferation, we hypothesized that the regulation of the G1/S regulatory genes (Table 1) is consistent within cell types and forms lineage-specific expression patterns that reflect, or even explain, the distinct proliferative properties along the hematopoietic tree (Figure 2).

To test this hypothesis, we aggregated cells from the same donor-cell type combination to form pseudobulk expression profiles and performed unsupervised principal component analysis (PCA) clustering based on the expression of the 24 core G1/S genes (Table 1). Because small gene sets can resolve only broad immune cell type classes,⁴⁷ we used the coarser (“Level 1”) annotations from Zhang et al. (Figure 2A) encompassing 24 cell types (see “STAR Methods”) to enable meaningful interpretation of the resulting clustering patterns.

The expression profiles of the G1/S gene set—despite its narrow mechanistic focus—clustered the 24 cell types (Figure 3A, left) nearly as effectively as the 24 most highly variable genes (HVGs) of the dataset (Figure 3A, middle right), and way better than 24 randomly selected genes (Figure 3A, right), as quantified by the clustering performance metrics Adjusted Silhouette Width (ASW), Adjusted Rand Index (ARI) and Normalized Mutual Information (NMI)⁴⁸ (Figure 3B, right). In comparison, a list of 24 genes coding for receptors sensing bone marrow niche signals (Table S3)^13,49 performed only slightly better than the 24 G1/S genes in the task of clustering cell types across the 8 donors (Figure 3A, middle left).

Figure 3.

The expression of 24 core G1/S genes accurately segregates hematopoietic cell types and captures their propensity to divide

(A) PCA of pseudobulk samples (i.e., aggregated cells from each cell type and donor) based on the expression of 24 G1/S (Table 1), receptors for bone marrow (BM) niche signals (Table S3), HVGs and random genes. Each dot represents one donor/cell type combination (n = 8 donors, 24 cell types).

(B) Same PCA plots as in A) recolored according to the propensity to divide score P_d of each pseudobulk sample. See also Table S3.

(C) Clustering performance for each 24 genes set.

The variation in proliferative potential was best captured by the G1/S genes-based PCA, compared to HVG or hematopoietic receptors: the lead principal component (PC1) segregated well highly proliferative cell types (PC1 > 2.5) from less proliferative stem cells and early progenitors (0 < PC1 < 2.5), and terminally differentiated populations (PC1 < 0) (Figure 3B, left). In contrast, PC2 mainly distinguished different branches of the hematopoietic tree, indicating the existence of distinct structures within the G1/S network that would both affect hematopoietic proliferation and lineage identity.

Taken together, the expression pattern of the sole 24 core G1/S genes is sufficient to define hematopoietic cell types across all lineages, beyond inter-donor variability. This compact and interpretable gene set captures both lineage distinctions and proliferative dynamics of hematopoietic cells. This observation also supports the use of the core 24 G1/S genes for further mechanistic analysis of differential G1/S regulation across the hematopoietic tree.

Three gene modules within the G1/S network are sequentially expressed along differentiation paths

The ability of G1/S genes to cluster diverse hematopoietic cell types effectively indicated the presence of distinct gene signatures within this core G1/S network which would be expressed in a lineage- and differentiation-stage specific way. This motivated us to interrogate whether co-expressed gene modules exist within the G1/S network and display distinct expression patterns along hematopoietic lineage trajectories.

To identify co-expressed G1/S genes, we computed gene-gene Pearson correlations across the cell type∗donor space. We used the fine annotation level that distinguishes 68 bone marrow hematopoietic cell types (Figure 2) to increase the number of samples from which correlations are calculated, thereby improving the correlation estimates.

The resulting correlogram highlighted 3 gene groups with strong intra-group correlations and varying degrees of inter-group correlations (Figure 4A; Table S4). We refer to these 3 groups as functional “modules” within the G1/S network: a “Cyclin D module” encompassing CCND1, CCND2, CDK6, MYC, and E2F3; a “Cyclin E module” consisting of CCNE1, CCNE2, CDK2, CDKN3, CDC25A (activator of CycE-Cdk2 complexes), E2F1, E2F2, RBL1, CDK4, and CDKN2C; and a “Inhibitors” module comprising of RB1, RBL2, other CDKN genes (CDKN1A, CDKN1B, CDKN1C, CDKN2A, CDKN2B, and CDKN2D) and, surprisingly, CCND3.

Figure 4.

Three distinct G1/S network sub-modules are sequentially activated during hematopoietic differentiation

(A) Hierarchical clustering of G1/S gene-gene Pearson correlations across all cell types (n = 8 donors, pseudobulk) identifies three distinct co-regulated gene groups: Cyclin D, Cyclin E, and Inhibitors module.

(B) Ternary plot shows pseudobulk samples positioned according to their relative expression of Cyclin D, Cyclin E, and Inhibitor module (one dot = aggregated cells from one cell type and donor). Top: cell types colored by their propensity to divide P_d; middle top, middle bottom, and bottom: lineage-specific G1/S module activity carves out a landscape through which hematopoietic cells traverse as they differentiate. Arrows illustrate differentiation trajectories.

(C) Single-cell UMAP representation of the dataset (from Figure 2) highlights the sequential activation of Cyclin D, Cyclin E, and Inhibitors module along the hematopoietic tree. See also Figures S10–S14, S16, and Table S4.

Intra-module correlations were strongest in the Cyclin E module, followed by the Inhibitors module and weaker, but still positive, in the Cyclin D module. The Cyclin D module showed consistent positive correlations with the Cyclin E module and negative correlations with the Inhibitors module. Interestingly, the Cyclin E module also correlated positively with the Inhibitors module at some developmental stages (Figure S11). Coarse cell type annotation tended to reduce the amplitude of both intra-module and inter-module correlations for the Cyclin D module, reducing the ability to segregate it from the Cyclin E module (Table S4, compare Hay et al.⁴⁴ data with resolutions of 68, 24 and 9 cell types). E2F1 and E2F2 were co-expressed with the Cyclin E module, while E2F3 clustered into the Cyclin D module. We note that CDK4, which functionally should belong to the Cyclin D module, clustered within the Cyclin E module. However, CDK4 expression showed strong correlations with all genes of the Cyclin D module as well, falling therefore in between these two modules.

We next assessed whether these 3 modules show distinct expression patterns across the hematopoietic tree. To examine how each cell type balances the expression between the 3 modules, we computed a “module score” for each cell type-donor sample (“STAR Methods”) and projected these in barycentric coordinates (Figure 4B). Cell types expressing predominantly Cyclin D, Cyclin E, or Inhibitors module aligned with low, high/very high, and very low propensity to divide (Figure 4B top).

The Cyclin D module dominated the expression of G1/S regulatory genes at the root of the hematopoietic tree (HSCs and MPPs), while the Cyclin E module dominated in strongly proliferating early to mid-stage progenitors. Interestingly, the gene most strongly correlated with the proliferative P_d score across all cell types was CDKN3—a Cyclin E module gene and known CDK inhibitor (Figure S10). In contrast, the Inhibitors module was strongly expressed in the quiescent, terminally differentiated cells across all lineages (Figure 4B). Terminally differentiated cells from distinct lineages expressed distinct subsets of the Inhibitors module: T/NK cells expressed CDKN1B, RBL2, CCND3, and CDKN2A at high levels, while B cells expressed also CDKN2D, CDKN1A, and RB1 strongly. Dendritic cells rather expressed CDKN2D, CDKN1A, and RB1 at high levels, while monocytes expressed CDKN2B and CDKN1C in addition (Figure S11).

Developmental transitions often coincided with shifts in module dominance, exemplified by the expression or shutdown of specific genes (Figure S11): for example, HSCs/CLPs express CDKN2 family inhibitors at very low levels, while these inhibitors become strongly up-regulated in B-lymphoid progenitors (pro-B). In parallel, a strong CDK2 up-regulation and a down-regulation of CDK4/6 drives the developmental trajectory of pro-B cells toward the “Cyclin E−Inhibitors” wall (Figure 4B, bottom triangle). Overlaying the modules’ activity to the hematopoietic landscape with single-cell resolution (UMAP, Figure 2B) confirmed these trends at the single-cell level (Figure 4C). We confirmed these results in three independent healthy human cohorts: 4 adult bone marrow donors¹³ (Figure S12), 3 fetal bone marrow donors⁵⁰ (Figure S13), and 10 adult bone marrow donors⁵¹ (Figure S14A).

In conclusion, both in healthy adult and fetal hematopoiesis, a sequential gene activation of three G1/S sub-modules marks hematopoietic differentiation: each branch of the hematopoietic tree begins with stem or stem-like cells with low propensity to divide that express predominantly the Cyclin D module genes; then these cells evolve to more proliferative progenitors that rely on the Cyclin E module, until Inhibitors dominate the expression of G1/S regulators and terminal differentiation is reached (Figures S11–S14). The module sequence—Cyclin D, Cyclin E, and finally Inhibitors—is consistent across hematopoietic lineages, while variations in the expression of the modules’ individual genes defined lineage identity.

To further understand the functional consequences on the G1/S transition of the uncovered hematopoietic G1/S gene expression dynamics, we sought to develop a mathematical model of the G1/S network that connects G1/S genes’ expression to E2F/CDK activation and the propensity to divide.

A mathematical model of the G1/S transition across distinct hematopoietic cell types

To design a model able to capture proliferation properties of all hematopoietic cell types, we curated known interactions between the 24 G1/S genes’ products from the literature and assembled them into a protein interaction network (Figure 1). Our model includes one generic representative for E2F transcription factors (“E2F”), RB-like proteins (“RB”), D-type cyclins (“CycD”), and E-type cyclins (“CycE”). Moreover, the effects of CDK inhibitor proteins were incorporated through modulations of specific parameters (see “STAR Methods” for details). This modeling framework can be readily extended to explicitly model the individual proteins rather than the generic representatives.

We described time-dependent changes in protein concentrations (via synthesis and degradation), assembly into complexes, and activation or inactivation using a system of ordinary differential equations (ODEs) based on mass action kinetics. We accounted for protein synthesis, degradation, activation, inactivation reactions, as well as binding and unbinding into complexes that can be activated or inactivated. Activation functions, such as the activation of CDC25A by CycE-CDK2 and the breakdown of the RB-E2F complex by CDK activity, were modeled as Hill functions, to provide more flexibility in describing how outputs respond to inputs. The model’s outputs that are solved for are the concentrations of 15 interacting molecular species: MYC, free CycD ([CyD]^F), free CycE ([CyE]^F), RB-free E2F ([E2F]^F), active and inactive CDC25A ([CDC25A]^A and [CDC25A]^I), unbound inactive CDKs ([CDK2]^I, [CDK4]^I, [CDK6]^I), active and inactive CycE-CDK2 complexes (${\left[Cy{k}_{E/2}\right]}^A$ and ${\left[Cy{k}_{E/2}\right]}^I$), active and inactive CycD-CDK4 complexes (${\left[Cy{k}_{D/4}\right]}^A$ and ${\left[Cy{k}_{D/4}\right]}^I$), and CycD-CDK6 complexes (${\left[Cy{k}_{D/6}\right]}^A$ and ${\left[Cy{k}_{D/6}\right]}^I$). Their inter-dependent dynamics are governed by a set of 38 model parameters: 26 kinetic rate parameters, 3 Hill exponents, 4 threshold concentrations, and 5 total protein concentrations for RB, E2F, and CDKs (Table 2). Full model equations are provided in supplemental methods, and default parameter values are listed in Table 2. Model construction and criteria for the choice of the default parameters are explained in the STAR Methods section.

Table 2.

Model parameters and steady-state meta-parameters

Model parameters	Default values	Rationale
[CDK2]tot	300 nM	measurements in yeast
[CDK4]tot	300 nM	measurements in yeast
[CDK6]tot	400 nM	measurements in yeast
[RB0]	100 nM	measurements in yeast and human cells
[E2F0]	50-400 nM (default: 200 nM)	measurements in yeast
GF0	1 nM	does not have direct influence; combines with f1, f9, and f10 coefficients
M0	1 nM	does not have direct influence; combines with f1, f9, and f10 coefficients
f1	0.00580000 s−1	balanced by u1, sets the steady-state MYC level; together, u1/f1 combine with f2 and f3 → without loss of generality, one can choose f1 = u1 with u1 defined with measurements of MYC half-life
f2	0.00002750 s−1	balanced by u2, sets the CycE steady-state level that depends on MYC only (E2F-independent); chosen to be low
f5	0.00011000 s−1	balanced by u2, sets the CycE steady-state level that depends on E2F; chosen to be high enough so that maximal E2F activation provides efficient CycE synthesis
f3	0.00019300 s−1	balanced by u3, sets the CDC25A steady-state level that depends on MYC only (E2F-independent); chosen to be low
f8	0.00038600 s−1	balanced by u3, sets the CDC25A steady-state level that depends on E2F; chosen to be high enough so that maximal E2F activation provides efficient CDC25A synthesis
f9	0.00112000 s−1	chosen to yield low CycD concentration, according to unpublished observations (f9/u4 = 2)
f10	0.00168000 s−1	chosen to yield low CycD concentration, according to unpublished observations (f10/u4 = 3, so [CycD] = 5 nM)
u1	0.00058000 s−1	fast MYC synthesis and degradation (see also f1)
u2	0.00056000 s−1	fast CycE synthesis and degradation (see also f2)
u3	0.00027700 s−1	fast CDC25A protein turnover (see also f3)
u4	0.00056000 s−1	fast CycD protein turnover (see also f9, f10)
f4	0.14285714 nM−1s−1	CycE CDK2 binding rate; to be balanced with d1
f11	0.10000000 nM−1s−1	CycD CDK4/6 binding rate; to be balanced with d2
d5	0.10000000 nM−1s−1	RB dephosphorylation rate; chosen fast (second scale), to be balanced with f15
d1	100 s−1	CycE CDK2 dissociation rate; to be balanced with f4
d2	100 s−1	CycD-CDK4/6 dissociation rate; to be balanced with f11
f15	15 s−1	maximal RB phosphorylation rate; chosen so that when CDK activation is maximal, and both RB and E2F concentrations are in the 100 nM range, the RB-E2F dissociation Kd is quite larger than RB and E2F concentrations such that the complex is unstable → f15/d5 > 300 nM → f15 = 300∗d5
f6	50 s−1	balanced with d3; needs to be large enough so that the CDC25A-driven feedback loop matters in CycE-CDK2 activation
f7	100 s−1	balanced with u3 and d6; needs to be large enough so that the CDC25A-driven feedback loop matters in CycE-CDK2 activation
f13	15 s−1	balanced with d3; needs to be large enough if one wants CycE-CDK2 to activate independent of CDC25A as well
f14	15 s−1	balanced with d4; needs to be large enough if one wants CycD-CDK4/6 to be activated
d3	5 s−1	see above
d4	5 s−1	see above
d6	10 s−1	CDC25A (spontaneous) inactivation rate, to be balanced with f7 (see above)
p1	3	number of critical phosphosites on CDK2 unknown, between 1 and 5
p2	2	2 critical phosphosites on CDC25A substrate
p3	7	7 critical phosphosites at least on RB1 substrate
Co1	50 nM	critical active CDC25A concentration for CycE-CDK2 activation; must be more than the basal level of active CDC25A, but less than the maximal level
Co2	30 nM	critical active CycE-CK2 concentration for CDC25A activation; must be more than the basal level of active CycE-CDK2, but less than the maximal level
Co3	50 nM	critical active Cyc-CDK concentration for full E2F activation; must be more than the basal level of active Cyc-CDK, but less than the maximal level
C3	10 nM	threshold concentration of Cyc-CDK complexes, above which they compete for p27 inhibition; has to be chosen in the range of p27 concentration (5–20 nM, our unpublished measurements)

META-PARAMETERS	Min value ([E2F0] = 50 nM)	Mid value ([E2F0] = 100 nM)	Large value ([E2F0] = 400 nM)
K1	1.39350181	2.78700361	11.14801444
K2	0.13935018	–	–
K3	10	–	–
K5	9.99972301	–	–
K8	0.01492537	–	–
K9	0.00497512	–	–
K10	0.01403061	0.02806122	0.11224490
K11	0.00070153	–	–
K12	35	–	–
K13	0.5	1	4
K14	1,5	–	–
K15	14	–	–
K16	6	–	–
K17	30	–	–
f13/d3	3	–	–
f6/d3	10	–	–

Critical parameters and functions for steady-state analysis ([E2F0] = 100 nM)	Min value (fraction of E2F active Y = 0)	Mid value (fraction of E2F active Y = 50%)	Large value (fraction of E2F active Y = 100%)
K6	0.00070104	0.01451826	0.02795859
K7	0.00701039	0.14518258	0.27958589
Critical parameter 1 = (K1∗Y + K2)∗K5/(1 + K5)	0.12668166	1.39349830	2.66031493
Critical parameter 2 = K3∗(K6+K7)/(1 + K6+K7)	0.07652416	1.37708649	2.35207662

Default model parameter values (first table), with rationales provided for the parameter choices. Meta-parameters that characterize the model’s steady state(s) are shown in the second table “meta-parameters” for 3 different values of the total E2F concentration (50 nM: lower than RB concentration; 100 nM: equal to RB concentration; 400 nM: 4-fold the total RB concentration). The third table indicates critical parameters for the bistability analysis (Figures S5 and S6), calculated for the default parameters (including a total E2F concentration of 100 nM) but for 3 different fractions of E2F activation (0%, 50%, and 100%). The values shown for K₆, K₇, and the two critical parameters $K_3\ast \frac{K_7+K_{6\mathrm{mod}}}{1+K_7+K_{6\mathrm{mod}}}$ and $\left(K_1\frac{{\left[E2F\right]}^F}{\left[E2F_0\right]}+K_2\right)*\frac{K_5}{1+K_5}$ are to be used together with Figure S5 to visualize the model’s steady state(s).

We first solved both the model dynamics (time-dependent variations) and its steady state computationally, using respectively Runge-Kutta integration and a robust fixed point algorithm (Table S5,⁵²). With default parametrization (Table 2) and across random initial conditions, the model solutions consistently converged over time toward one of two discrete steady states: a “low activity” state (Figure 5A), or a “high activity” state (Figure 5B). The low-activity state was characterized by RB-bound E2F, low CDK activity, low concentrations of CycE and CDC25A, and inactive (“off”) Hill functions. In contrast, the high-activity state showed RB-free E2F, elevated CDK2 activity, over 10-fold higher CycE and CDC25A concentrations, and active (“on”) Hill functions. The convergence toward one or the other steady state depended on initial conditions: simulations beginning in a state with elevated CycD/CycE pools, some active Cyc-CDK complexes and/or active CDC25A resumed convergence toward fully active state, while simulations beginning with inactive Cyc-CDK complexes and without pre-existing CycD/E or CDC25A pools converged to the inactive steady state (Table S6). Both steady states were dynamically stable in the Lyapunov sense (Table S7), as perturbation of the steady-state variables by ±20% of their value resulted in re-convergence to the same state. Thus, under default parameters, the G1/S transition exhibited robust bistability.

Figure 5.

Our mathematical model predicts a bistable G1/S transition

Each panel shows the simulated time course (x axis, in seconds) in protein concentration changes of the core G1/S protein/protein complexes (y axis, concentration in nM) or Hill function activation (in arbitrary units). Time courses were simulated under different initial conditions, to produce convergence toward the low activity steady state (A) or the high activity steady state (B). All timecourses were simulated under the default parametrization (Table 2). See also Figure S7 and Tables S5, S6, and S7.

In summary, numerical simulations of the model using the default parameters set (Table 2) generated time courses for the concentrations of G1/S proteins that evolved toward a low-activity state where the cell is not engaged in the G1/S transition or a high-activity state where E2F is activated and G1/S transcription is expected, committing the cell to division. Both states are stable to small perturbation (±20%), showing that the network structure protects cells from molecular noise. Transition from the low activity state to the high activity state therefore requires stronger perturbation, reflecting the binary decision a cell faces—whether to remain in a non-dividing state, or commit to cell cycle entry. However, the default model parameters likely correspond to one cell type. Since different hematopoietic cell types expressed different levels of G1/S genes (Figures 3, 4, and S11–S14), translating to different model parameter regimes, we next sought to gain mechanistic insight into how the 38 model parameters influence the model outputs. In this purpose, we performed a partial analytical resolution of the model’s steady state.

Steady-state analysis reveals 3 routes through the G1/S transition

E2F1-3 are together essential, at least in mouse embryo fibroblasts⁵³; however, ectopic E2F activation is insufficient to induce S-phase in the absence of CycE,⁵⁴ and leukemia cell proliferation is reduced in vivo by CDK4/6 inhibition.⁴³ Hence, both CDK activity and E2F activity (at least to a minimal level, and depending on the cellular context) are required to pass the G1/S transition, although both are intricately linked.⁵⁵

In an attempt to solve analytically the steady-state equations (supplemental methods, Equations 1–6), we therefore first focused on analyzing E2F activation (supplemental methods, Equation 1). In the steady state, the fraction of active E2F, i.e., the ratio of the RB-free E2F concentration [E2F]^F to the total concentration [E2F₀] is given by:

$$Y=\frac{{\left[E2F\right]}^F}{\left[E2F_0\right]}=\frac{-\left(1-K_{13}+K_{14}X\right)+\sqrt{{\left(1-K_{13}+K_{14}X\right)}^2+4\ast K_{13}\ast K_{14}X}}{2K_{13}}\text{.}$$ (Equation 1)

The meta-parameter $K_{13}=\frac{\left[E2F_0\right]}{\left[R{B}_0\right]}$ is the ratio of total E2F protein pool over the total RB protein pool. The meta-parameter $K_{14}=\frac{f_{15}}{d_5\left[R{B}_0\right]}$ is the ratio of the maximal rate of RB-E2F dissociation (f₁₅, corresponding to E2F activation, and that is achieved for complete RB phosphorylation), to the spontaneous RB-E2F binding rate d₅[RB₀], that corresponds to E2F inactivation and is proportional to RB concentration. Because during the G1 and G1/S phases, RB phosphorylation is dependent on the concentration of catalytically active Cyc-CDK complexes, K₁₄ is modulated by the fraction of phosphorylated RB-E2F complexes, which is assumed a Hill function of the total CDK activity (methods⁵⁶):

$$X=\frac{{\left(\frac{{\left[Cy{k}_{E/2}\right]}^A+{\left[Cy{k}_{D/4}\right]}^A+{\left[Cy{k}_{D/6}\right]}^A}{C{o}_3}\right)}^{p_3}}{1+{\left(\frac{{\left[Cy{k}_{E/2}\right]}^A+{\left[Cy{k}_{D/4}\right]}^A+{\left[Cy{k}_{D/6}\right]}^A}{C{o}_3}\right)}^{p_3}}\in \left[0,1\right]\text{.}$$

Here, the parameter Co₃ is a threshold of active CDK concentration above which it efficiently catalyzes RB phosphorylation.

Plotting the active E2F fraction Y as a function of K₁₃ and K₁₄X revealed three principal ways by which maximal E2F activation can be achieved (Figure S1): very large K₁₃ (i.e., large excess of E2F vs. RB), very large K₁₄ (e.g., low RB concentration leading to unstable RB-E2F complexes); or K₁₄ of order 1 or more, and maximal CDK activation X = 1. While the first two conditions might be achieved independently of any other model parameter, the third condition requires to fully solve the model for CDK activation (supplemental methods).

In total, we identified 6 distinct routes for E2F activation, and the triggering of the G1/S transition.

• •Route 1: E2F accumulation-driven G1/S transition. When the total E2F concentration [E2F₀] greatly exceeds the total RB concentration [RB₀], we have K₁₃≫1 and a large fraction of the E2F pool is active, without further requirement for an increase in CDK activity (Figure S1, bottom arrow). Thus, this route of E2F activation is independent of all other parameters.
• •Route 2: CycD-driven G1/S transition. Even without strong E2F accumulation (relative to RB), a sufficient rise in the concentration of active CycD-CDK4 (${\left[Cy{k}_{D/4}\right]}^A$) or CycD-CDK6 complexes (${\left[Cy{k}_{D/6}\right]}^A$) increases the fraction of phosphorylated RB, which in turn activates the E2F pool, provided that, overall K₁₄X > 1. The higher K₁₄ (e.g., low RB concentration), the less CDK activity X is required for E2F activation. Enhanced CycD-CDK4/6 activity, eliciting Route 2, can be achieved either via high CDK4/6 and CycD expression which directly increases the number of complexes (route 2a, Methods), or via sequestering by CycE-CDK2 of the common CDK inhibitor p27 which leads to CycD-CDK4/6 de-repression (route 2b). Route 2 does not require CycE-CDK2 activity, although CycE-CDK2 complexes may get activated downstream, as a consequence of E2F activation.
• •Route 3: CycE-driven G1/S transition. In the more general case where CycD-CDK4/6 activity is insufficient on its own to fully activate E2F, CycE-CDK2 activity is required. Our model shows that an active CycE-CDK2 pool ${\left[Cy{k}_{E/2}\right]}^A$ can accumulate through a positive feedback loop in which E2F stimulates CycE synthesis (Figures S5 and S6). This can occur through 3 sub-mechanisms: either with (route 3a) or without (route 3b) contribution from CDC25A, and/or via sequestering of p27 by inactive CycD-CDK4/6 complexes, leading to CycE-CDK2 de-repression (route 3c).

We identified 16 meta-parameters, defined in supplemental methods and calculated in Table 2, whose value ranges determine which of the three G1/S routes defined above is triggered, as demonstrated mathematically in supplemental methods (Figures S1–S6). Under the default parametrization, the meta-parameters K₁₃ and K₁₄ were of order of magnitude 1, leading to a CDK-dependent E2F activation, excluding Route 1. Furthermore, the meta-parameters capturing CycD-dependent CycD-CDK4/6 binding and activation (K₈ and K₉, supplemental methods Equation 5) were much smaller than 1, making the residual CycD-CDK4/6 activity insufficient for E2F activation, also excluding Route 2. Instead, E2F activation under the default conditions required both the two critical conditions $\frac{K_7+K_{6\mathrm{mod}}}{1+K_7+K_{6\mathrm{mod}}}>\frac{1}{K_3}$ and $\frac{K_5}{1+K_5}>\frac{1}{K_1\frac{{\left[E2F\right]}^F}{\left[E2F_0\right]}+K_2}$ to be satisfied for higher E2F activity. Those conditions lead to a bistable, CycE-CDK2/CDC25A driven, steady state (route 3, Figures S5 and S6A).

E2F activation in the steady state was robust to variations in most individual meta-parameters over 4 orders of magnitude, as revealed by a comprehensive parameter space analysis (Figure S7). This robustness most likely stems from the strong redundancy built in the G1/S network, which offers multiple activation routes for both E2F and/or CDK activation (routes 1, 2a-b, and 3a-b-c). Small values of one activatory meta-parameter—which would block one activation route—could be compensated by large values of other activatory meta-parameters, that enabled other activation routes. Thus, our analysis demonstrated that cells can preserve G1/S transition competence despite experiencing significant variations in molecular inputs. The analysis of correlations between meta-parameter values and model outputs (Figure S9) revealed that active CycD-CDK4/6 correlated positively with inactive CycE-CDK2 and vice-versa, indicating the relevance of the mechanism of competition for p27 across the whole meta-parameter space.

Since the meta-parameters depended on expression of the G1/S genes, hematopoietic transitions along the lineages are accompanied by changes in G1/S meta-parameters that may alter the dynamical modes through which different cell types pass the G1/S transition.

G1/S gene expression patterns elicit distinct G1/S routes in distinct hematopoietic cell types

Having identified, in the mathematical analysis of our model, different routes to pass the G1/S transition that used either CycD and/or CycE and E2F or even E2F alone, we sought to predict whether those routes correspond to how distinct hematopoietic cell types pass the transition.

With default parameters, the model predicts low Cyclin D expression, low CycD-CDK4/6 activity (Figure 5), little competition for p27 and a fully active CycE-CDK2/CDC25A feedback loop (route 3a, Figure S6A). To identify a cell type that matched those characteristics and may exemplify the default parameters, we looked for a cell type with low CCND and CDK4/6 expression, high E2F and RB expression, and that relies on Cyclin E module for proliferation (on the Cyclin E module-Inhibitors module wall on Figure 4). We identified pro-B cells with such characteristics, and grouped pro-B-early-cycling, pro-B-cycling-1, 2 and transitional pro-B1 to reduce inter cell type variability in the pro-B pool (methods). The mRNA concentrations of the 24 G1/S genes in other cell types were normalized to that of the pro-B group, and those normalized mRNA concentrations were used to rescale the corresponding model parameter(s) in other cell types proportionally, in order to model that cell type (STAR Methods, Table S8). For instance, the total CDK2 concentration in the model was rescaled to ${\left[CDK2\right]}_{celltypeX}^{tot}={\left[CDK2\right]}_{default\mathit{(}pro-B\mathit{)}}^{tot}\ast \frac{mRNAcon{c}_{celltypeX}}{mRNAcon{c}_{pro-B}}$.

All 68 cell types were modeled this way (Table S8), and we emphasized on ERP-7, pre-DC-1, HSC/MPP (HSC-2 + MPP-1 + MPP-2) and MEP-1 cells to illustrate our results. For each cell type, the meta-parameters were re-calculated from the rescaled model parameters, and the G1/S route was identified based on those meta-parameter values, as analyzed in supplemental methods (Table S9). All 5 highlighted cell types showed K₁₃, K₁₄ > 1 and a total CDK content larger than Co₃, showing a priori potential for all G1/S routes.

While cycling pro-B cells were predicted to pass G1/S via route 3, ERP cells showed a fully active CycD-CDK4/6 with a strong contribution of the competition for p27 (route 2b), in addition to active CycE-CDK2. MEP-1 cells showed a E2F/RB ratio larger than 1, suggestive of route 1, yet also exhibited partial activation of both CycE-CDK2 and CycD-CDK4/6, alongside effects from the competition for p27 (route 1/3c). In contrast, pre-DC-1 and HSC/MPP cells showed a predicted monostable steady state, where the CDC25-CycE feedback loop (Figure S5) was turned « off » (Figure S6D) and CycE-CDK2 activation was not rescued by the competition for p27 (unlike Figure S6F). In HSC/MPP cells, very low RB expression yielded a large $K_{14}=\frac{f_{15}}{d_5\left[R{B}_0\right]}$ coefficient, ensuring minimal CDK activity (provided in those cells by CycD-CDK4/6 complexes, route 2a). In pre-DC-1 cells, high CycD expression was sufficient to provide CycD-CDK4/6 activation, despite a low E2F/RB ratio. Hence, our model predicts that evolution of G1/S gene expression across the hematopoietic tree primes distinct cell types for different routes through the G1/S transition.

The total amount of E2F is a key pivotal parameter that affects G1/S commitment across G1/S routes

Our analysis of the parameter space (Figure S7; K₁₃ plot) and global sensitivity analysis (Figure S9; highest correlation of active E2F with K₁₃) indicated that the fraction of active E2F, our readout for the G1/S transition, depends more strongly on total E2F concentration than on any other parameter. This dependency holds across the entire parameter space and thus applies across all G1/S routes. In line with this result, we recently have shown that in yeast, accumulation of the E2F functional analog SBF to a threshold level during G1 was necessary to enable the G1/S transition.^56,57,58 Motivated by these experimental findings, we next examined how varying total E2F concentration influences the steady-state levels of the model variables. Keeping other meta-parameters fixed at default values, we found a sharp transition in Cyc-CDK activity: below the threshold [E2F₀] ≤ 0.85∗[RB₀], Cyc-CDK activity remained low, while above this threshold, a high activity was observed (Figure 6A). Notably, the concentration of active CycE-CDK2 was much more sensitive to E2F levels than to the concentration of CycD-CDK4/6 complexes.

Figure 6.

E2F accumulation leads to a sharp G1/S transition, triggered by a dynamical instability

(A) Steady-state concentrations (y axis, in nM) or fraction of activated complexes (as indicated) as a function of total E2F concentration (x axis, in nM). Default total RB concentration is 100 nM.

(B) Sensitivity analysis of the steady-state concentrations (model outputs, in columns) in response to a 1% change of the meta-parameters (rows), normalized to this change (see “STAR Methods”), at the tipping point (in A) where [E2F]^tot = 85 nM.

(C) Propensity to divide P_d as a function of the average E2F mRNA abundance per cell (left) or of the average concentration of E2F mRNAs per cell, computed as the average single-cell concentration per cell type for each donor (STAR Methods). Color-coded according to cell types. See also Figures S7–S9 and Table S8. RNAs concentrations and renormalization of default parameters, related to Figures 6 and 7, Table S9. Route through G1/S for pro-B, ERP-7, pre-DC-1, HSPC, and MEP-1 cells, related to Figure 6, Table S10. Modeling CycE expression, E2F/Cyc-CDK activation, and Pd for 68 cell types, related to Figures 6 and 7.

At this tipping point, the model outputs—including the fractions of active E2F, active and inactive CycE-CDK2 complexes, and active CDC25A—became hypersensitive to very small changes in two meta-parameters K₈ and K₁₀. A mere 1% change in either meta-parameter values yields about 25% change in output values (sensitivity analysis, Figure 6B). As K₈ and K₁₀ represent, respectively, the activation rate of CycD-CDK4/6 complexes and the E2F-dependent CycE synthesis rate, this result indicates a dynamical instability that appears when sufficient E2F is accumulated: small fluctuations in CycE synthesis or CycD-CDK4/6 activation strongly affect the model’s activation. Sensitivity to CycD-CDK4/6 accumulation and activation was much lower, and restricted to E2F activation for [E2F₀] ≤ 0.85∗[RB₀]; and for [E2F₀] > 0.85∗[RB₀] the system’s steady state was almost insensitive to fluctuations in meta-parameters, emphasizing the robustness of the transition (Figure S8).

The pattern where E2F accumulation to a threshold—0.85 times the amount of RB for default parameters—was driving the model to a bistable state, hypersensitive to small fluctuations in CycE synthesis or CycD-CDK4/6 activation, was not encountered in all cell types. Modeled erythroid progenitors (such as ERP-7) or erythroblasts, for instance, showed full E2F activation even at very low total E2F concentrations, due to the excessive CycD-CDK4/6 activity. Likewise, in HSCs, E2F activation did not require strong E2F accumulation, possibly due to very low RB levels; however, high E2F concentration was required to activate CycE-CDK2.

B lymphoid opt for E2F-driven proliferation while MEP/ERP undergo CDK-driven proliferation

Our mathematical model identified the total pool of E2F as a pivotal parameter controlling the G1/S transition across routes, prompting us to examine whether E2F expression levels correlate with the propensity to divide across hematopoietic cell types. Because some cell types, such as late erythroid and B-cell progenitors, express preferentially the Cyclin E module (with E2F1-2), while others, such as HSC/MPPs and earliest myeloid progenitors (MultiLin-GMP), favor the Cyclin D module (including E2F3) (Figures 4 and S11–S14), we considered the summed expression of E2F1-3 (total E2F) in order to enable comparisons across cell types (STAR Methods). We then plotted the propensity to divide P_d for each cell type against total E2F per cell (Figure 6C, left).

The positive correlation between the propensity to divide P_d and total E2F transcript abundance per cell type was strong (r = 0.79, p < 0.01, Pearson test, Figure 6C, left), with highest amounts in late ERP, erythroblasts, MkP-late, pro-B-cycling-1, and transitional-B-1 cells. However, significant dispersion appeared among cell types with mid-to-high E2F values—suggesting that additional factors beyond E2F transcript abundance contribute to P_d in this range.

Since differences in sequencing depth are mitigated by the use of pseudobulk samples, we hypothesized that this dispersion may essentially originate from large differences in the total RNA content across cell types, that would affect E2F RNA content. Therefore, we normalized the E2F counts to the total RNA content in each cell, defining a E2F concentration per cell (STAR Methods). This normalization revealed that P_d scales with E2F concentration only in cell types with low P_d and E2F (r = 0.41, p < 0.01, Pearson test, Figure 6C, right). In contrast, cell types with high P_d displayed either moderate E2F concentration (MEPs and ERPs) or very large E2F concentration (pro-B cells). These results suggest that while a minimum E2F concentration is required for proliferation, exceeding this threshold does not further enhance P_d.

Our model predicted that, as an alternative to E2F driven G1/S commitment (route 1, and to a lesser extent route 3), cell could pass through G1/S by relying on excessive CDK activity (route 2; Figure S1). To test this, we plotted P_d for each donor/cell type pseudobulk sample against the total CDK concentration.

Overall, P_d correlated positively with CDK concentration, but certain cell types with mid/high P_d had low CDK concentrations (0–0.5) and instead had a E2F/RB ratio ≥1 (Figure 7A). Thus, as for E2F, once a minimal CDK concentration is reached, the correlation between CDK concentration and P_d is weak. This trend was particularly evident in erythroid progenitor cell types (ERP-1 to ERP-8), which showed a rather high variability in P_d despite quite similar total CDK concentrations, indicating that in these cells, other factors dominate the G1/S transition.

Figure 7.

Pro-B cells, late MDP/pre-DC cells, and Erythroblasts opt for E2F-driven proliferation whereas MEP/ERP cells rely on CDK-driven proliferation

(A) Propensity to divide P_d (y axis) as a function of CDK mRNA concentration (x axis), color-coded by cell type (left, as on panel D) or by the total E2F/RB ratio (right).

(B) Total CycE protein concentration predicted by the model (y axis, nM) as a function of the mean CCNE1/2 transcript concentration (normalized UMI counts) in erythroid progenitor developmental stages (y axis), demonstrating a strong correlation. Color-coded by average P_d.

(C) Average propensity to divide P_d,model predicted by the model (y axis) versus P_d estimated from scRNA-seq profiles (x axis), across 68 hematopoietic cell types (color coded). Vertical green line indicates the limit P_d for mostly quiescent and low proliferation categories (Figure 2, Jenks breaks).

(D) Barchart showing model predicted cell type dependent sensitivities to 98% CDK4/6 inhibition, expressed as Residual P_d (P_d in CDKi treated cells normalized to P_d with full CDK4/6 activity for the same cell type).

(E) Ternary plot showing pseudobulk samples (from D), positioned according to their relative expression of Cyclin D, Cyclin E, and Inhibitor module (one dot = aggregated cells from one cell type, all donors). Top: samples colored by cell type types as in D); bottom: samples colored by their model predicted residual P_d following 98% CDK4/6 inhibition (data from D). See also Figure S14 and Tables S8 and S10.

Since ERP cells express both CycD and CDK4/6 at high level (Table S8 and Figures S11–S14), we hypothesized that in these cells, the limiting factor is rather the CycE-CDK2 activity, that requires CycE synthesis (under the control of E2F). To test this hypothesis, we compared the model-predicted CycE levels against the total CCNE1-2 expression in individual ERP stages and colored them according to their propensity to divide (Figure 7B). The correlation between model-predicted CycE synthesis and CCNE1-2 expression in primary ERP cells was very high (r = 0.86, p < 0.01, Pearson test), confirming that higher CycE levels associate with higher P_d in ERPs. Hence, although ERPs express Cyclin D module genes at very high levels, the limiting factor for them to pass G1/S is CycE synthesis.

To integrate the contributions of both E2F- and CDK-driven mechanisms, we defined a unified model-based propensity to divide predicted by the model P_d,model as the geometric mean of the total pool of active E2F and active CDK in the steady state (STAR Methods). This definition captures all routes of G1/S activation. Solving the model across all 68 hematopoietic cell types yielded predicted proliferation propensities (Table S10), which correlated well with the scRNA-seq data derived P_d, especially for low and mid proliferative cell types (r = 0.72, p < 0.01, Pearson test, Figure 7C). The correlation was weaker in highly proliferative cell types, indicating that once minimal levels of E2F and CDK activity are attained, the propensity to divide is modulated by additional factors—either not included in our model, or whose nature and quantitative effect are cell type-dependent.

In summary, the proliferation of hematopoietic cell types relies either on a sufficiently large E2F/RB ratio or elevated CDK expression, consistent with the model prediction of E2F-driven (route 1 and to a lesser extent route 3) or CDK-driven (route 2) G1/S transition routes. This is captured by our model-derived propensity to divide P_d,model. Once the inter-dependent E2F and CDK thresholds are met, the proliferative potential is further shaped by additional, potentially lineage-specific regulatory inputs.

The G1/S network shapes cell type dependent sensitivity to CDK4/6 inhibition

CDK4/6 inhibitors (CDKi), such as palbociclib, ribociclib, and abemaciclib, are FDA approved drugs against breast cancer, also used in small cell lung cancer treatment to protect patients from chemotherapy induced hematologic toxicities.⁵⁹ They are currently being tested in clinical trials against leukemia.^43,60 To rationalize the use of CDKi and anticipate their impact on hematopoiesis, we applied our model (STAR Methods) to predict how CDKi influence the propensity to divide P_d across cell types.

Our model predicted that HSPCs (e.g., HSC/MPP, LMPP-1, and Multilin-2) and early lymphoid progenitors (CLP, early cycling pro-B cells) are strongly affected by CDKi, with P_d attenuation of ∼85%–99%. In contrast, granulocyte-myeloid and megakaryocyte-erythroid lineage-committed progenitors (MultiLin-GMP, MEP-Erythroid, MkP, and ERPs) showed only ∼50% P_d reduction or even less, indicating a predicted resistance of those cells to CDK4/6 inhibition (Figure 7D). Notably, MEP-1 cells—the earliest megakaryocyte-primed progenitors—were much less affected than MEP-2, the earliest erythrocyte progenitors, indicating that CDK4/6 inhibition may facilitate the proliferation of megakaryocyte progenitors over erythrocyte progenitors. Overall, cell types that positioned closer to the Cyclin D-Cyclin E axis or the Cyclin E node in the ternary plot (Figure 7E) tended to be more resistant to CDK4/6 inhibition.

Published evidence of lineage specific proliferation responses to CDK4/6 inhibition across clinical trials,^60,61 xenograft models,^59,62 ex vivo assays,^20,63,64 and cell lines⁵⁹ were all qualitatively, and often quantitatively, captured by our model (Table 3). Thus, the modular organization of the G1/S network encodes differential sensitivity of distinct hematopoietic cell types to CDK4/6 inhibitors.

Table 3.

Model predicts the differential response to CDK4/6 inhibition of distinct hematopoietic cell types reported in published experiments

References	Context (in vitro, in vivo, primary, cell lines …)	CDK4/6 inhibition treatment	Phenotype	Model prediction (from Figures 7D and 7E)	Additional interpretation or observation points
Ettl61	in vivo, human, CDK4/6i clinical trial against metastatic breast cancer	palbociclib, ribociclib, abemaciclib, clinical dose	neutropenia in 40%–80% of patients, attributed to lack of neutrophil progenitors proliferation	Pd is reduced by about 50% in neutrophils progenitors (MultiLin-GMP, pre-Neu, ImmNeu-1)	–
Johnson et al.59	in vivo, mouse model, CDK4/6i used to protect HSCs from DNA-damaging chemotherapy against small cell lung cancer	palbociclib, clinical dose, 48 h	HSC and MPP proliferation very strongly affected by CDKi; lineage-committed progenitors less affected, with strongest effects in CMP/CLP compared to GMP and MEP	Pd reduced by 99% in HSC and MPP-1, 80% in MPP-2, then only 60%–80% in LMPP (lymphoid-myeloid primed progenitor) and 83% in CLP; CMP not captured in Hay et al.44 dataset because very rare; in contrast, Pd reduced by only 45%–58% in GMP and 40%–50% in MEP-1, MkP, and ERP	–
Hu et al.63	ex vivo, human, CD34+ HSPCs differentiated into myeloid, erythroid, and megakaryocytes on plates	palbociclib, 10 nM–10 μM, 5 days	erythroid lineage 3–4 times more affected by CDKi than megakaryocyte and myeloid	Pd is 3–4 times more reduced in MEP-2 (erythrocyte lineage progenitor) compared to MEP-1 (megakaryocyte lineage progenitor) and MultiLin-GMP (myeloid progenitors)	–
Lu et al.20	ex vivo, human, CD34-selected primary granulocyte colony-stimulating factor (G-CSF) mobilized peripheral blood cells	palbociclib, 100–500 nM, 72 h treatment	reduced MEP proliferation and promotion of megakaryocyte lineage over erythrocyte lineage	Pd reduced in both MEP-1 and MEP-2, but 3–4 times more in MEP-2 (erythrocyte lineage progenitor) compared to MEP-1 (megakaryocyte lineage progenitor)	–
Maurer et al.62	in vivo, CDK4 or CDK6 deficient mice (not both repressed simultaneously)	genetic suppression of CDK4/6	reduced counts of CD11+ granulocytes; reduced erythropoiesis overall (RBC counts) but increased fraction of cells committed to erythroid lineage	Pd reduced upon CDKi in granulocyte progenitors and erythroid progenitors, in line with lower cell counts; yet, erythroid lineage is the less affected lineage, in line with increased fraction of erythroid-committed cells	the interpretation of cell fraction data is complex. The post-CDKi cell type fractions depend both on the relative Pd with/without CDKi, the cell type fractions before treatment, and which cell type is a precursor of which other (since low Pd of a progenitor affects the fraction of all the cell types downstream on the hematopoietic tree
Raetz et al.60	in vivo, children/young adult ALL, patients with relapsed/refractory ALL (heavily pre-treated)	palbociclib, clinical dose, 21 days, supplemented with standard ALL chemotherapy for last 18 days	50% B-ALL and 42% T-ALL patients show complete response	CDKi strongly reduces Pd in CLP (83%), but much less so in pro-B-1, pro-B-early and pro-B-cycling-1 (3%–42%)	ALL often derives from lymphoid progenitors displaying more stem cell like features (i.e., partially reverting their development, see “discussion”) → they are closer to CDKi sensitive CLP than CDKi resistant later progenitors, e.g., pro-B. This could explain the positive response to CDKi in ALL therapy.
Wang et al.64	in vitro, venetoclax-resistant and sensitive cell lines and primary AML cells (ex vivo)	palbociclib, 2.5 μM, 24 h treatment, without or with venetoclax-azacitidine chemotherapy	CDKi reduces cell counts of AML cell lines by only 15%–20% in most lines and primary AML cells compared to control; not due to apoptosis → due to impaired proliferation; CDKi induced Pd reduction increases to 30%–50% in presence of Ven/Aza	Pd reduction (at the cell population level, integrating all bone marrow cells from AML donors) ranges from 10% to 20%, to 50% or even 80%–100% in more sensitive samples; AML cells resist CDKi more than most healthy cell types	–

Table summarizing the proliferative response of multiple hematopoietic cell types to CDK4/6 inhibition in a range of biological contexts, ranging from CDKi clinical trials against breast cancer or acute lymphoid leukemia (ALL) to CDK4/6 deficient mice xenografts, ex vivo CDKi treatment of primary CD34⁺ enriched bone marrow samples, or leukemia cells or healthy and leukemia cell lines. For each experiment, the phenotype (differential proliferation of distinct hematopoietic cell type) is compared to the prediction of our model (Figure 7D).

The modular structure of the G1/S network is perturbed in AML

We next sought to test whether our model describes situations where the modular structure of the G1/S network would be disrupted. In this purpose, we analyzed cells from donors with acute myeloid leukemia (AML).⁵¹ We first confirmed that in the healthy (control) donors from the Lasry et al. cohort,⁵¹ the 24 G1/S genes were expressed in modules, sequentially across the hematopoietic tree, consistent with all other hematopoiesis datasets analyzed (Figure S14A). In malignant cells, however, this coherence was disrupted (Figure S14B). Relative to total RNA expression, AML cells from both adult and pediatric donors showed inconsistent regulation within each module: in the Cyclin D module, AML cells upregulated CDK6 and E2F3 while downregulated CCND1; in the Cyclin E module, AML cells upregulated CDK2 and downregulated CCNE1; and in the Inhibitors module, they upregulated CDKN2A and CDKN2C and downregulated CCND3, CDKN1B, and RBL2 (Figures S14B and S14C). The variability in G1/S gene expression was increased, especially in adult AML samples. Thus, AML cells used alternative routes through G1/S, where G1/S modules are “mixed up.”

Consequently, malignant cells occupied their own niches within the ternary plots representing cell types as a function of their relative expression of the 3 G1/S modules. Compared to cells collected from healthy donors (Figure S14D, right, altogether: green dots, and segregated by cell types: other dots), malignant cells from pediatric AML donors shifted mainly toward the Cyclin D node (Figure S14E). Cells from adult AML donors spreaded over a much broader region, indicating a greater heterogeneity of G1/S transcriptional states in adult AML (Figure S14E). Non-malignant microenvironmental cells in both age groups moved rather toward the center of the ternary plot. As for healthy cells, malignant cells closer to the middle of the Cyclin D-Cyclin E axis or to the Cyclin E node displayed the highest P_d (Figure S14D).

Clonal selection is expected from CDK4/6 inhibition in AML

To gain clinically relevant insight, we used our model to predict how AML cells respond to CDK4/6 inhibitors. In this purpose, we used transcriptome- and protein-based annotations of cancer cell subsets, mapped to the closest healthy cell types, as provided by Lasry et al.⁵¹ (see “STAR Methods”).

Model predicted P_d correlated well with the data inferred P_d (Pearson r = 0.62, restricted to low-mid P_d range; Figure S14F), demonstrating that our model also captures the alternative, perturbed routes through G1/S taken by malignant cells. Simulating CDK4/6 inhibition with a 98% activity reduction revealed a heterogeneity in P_d suppression, both across donors and across malignant cells’ subsets within a donor (Figure S14G). For instance, all subsets from pediatric donor 003 showed a strong reduction in P_d, whereas from the pediatric donor 005, only the LymP-like subset of cancer cells responded strongly, while MPP-like and GMP-like subsets remained resistant (Table S10). The differential responses to CDKi of cancer cell subsets could be anticipated from their position in our ternary plot showing the relative usage of Cyclin D, Cyclin E, and Inhibitors modules (Figure S14G). Reducing CDK4/6 activity by only 95% barely affected the P_d response to CDKi in almost all cancer cell subsets, while a milder reduction to 80% CDK4/6 activity still affected many cancer cell subsets as much as 98% CDKi (Table S10). Hence, efficient suppression of cell proliferation is predicted across a range of pharmacological inhibition levels.

AML is most often polyclonal,^65,66 i.e., distinct genetic clones may give rise to transcriptionally distinct subsets of malignant cells, similar to those defined by Lasry et al. and analyzed above. In this context, differential CDKi sensitivity would drive clonal selection upon CDKi treatment: clones localizing near the Cyclin D-Cyclin E axis or close to the Cyclin E node in the ternary plot representation (Figure S14G) would continue to proliferate substantially more than other clones despite CDK4/6 inhibition.

Taken together, our mathematical model offers a conceptual tool to predict patient-specific responses, as well as a mechanistic framework to anticipate clonal selection upon CDKi in AML.

The routes through G1/S are elicited by G1-dependent concentration of distinct G1/S activators/inhibitors across cell types

For most genes, mRNA production and degradation rates are coordinated with cell size to maintain mRNA concentration homeostasis—a phenomenon known as size-scaling.⁶⁷ However, some G1/S regulators exhibit nonlinear scaling: while mRNAs of certain G1/S activators were accumulating faster relative to cell size (super-scaling), the opposite was true for G1/S repressors (sub-scaling⁶⁸). Differential scaling of G1/S activators/repressors with respect to cell growth in G1 was also reported at the protein level.^40,56,69,70 This differential scaling effect shifts the balance between protein concentrations of G1/S activators and repressors, increasing the likelihood that cells proceed through G1/S as they become bigger in G1 phase.

Since UMI-based scRNA-seq data accurately reflect total transcript abundances per cell, and these correlate with cell size,^39,71 we utilized the here analyzed human bone marrow dataset (Hay et al.⁴⁴) to assess whether differential size-scaling effects could drive the G1/S transition also in human hematopoietic cells. For this purpose, we calculated the single-cell RNA concentrations of the 24 G1/S genes and binned the cells according to their total RNA, used here as a proxy for cell size. Then, we computed for each gene the average RNA concentration within each bin. We focused on example cell types for which the model suggested distinct routes through G1/S: HSC/MPPs and pre-DC-1 (route 2a), ERP-7 and ERP-8 (route 2b), and pro-B-1 cells (route 3).

Variability in RNA content was observed across cell types, with pro-B-1 cells having the lowest total RNA content, followed by HSC-2, MPP-2, pre-DC-1, and finally ERP-7/8 cells that showed the highest transcript abundance, but within cell types the total RNA content was more evenly distributed (Figure S15A). Thus, to align the different cell types by cell cycle phase, we binned cells separately within each type. We then examined the expression pattern of canonical S/G2/M markers—MKI67 (marker of proliferation Ki-67), TOP2A (topoisomerase 2A), H4C3 (H4 clustered histone 3), and TUBB (tubulin). The concentration of these post-G1/S markers rose beyond the fourth bin, indicating that the first 3–4 size bins were predominantly populated with cells in G1 and G1/S phases (Figure S15B).

In ERP-7 and ERP-8 cells—locating at the top of the Cyclin D/Cyclin E module wall (Figure 4), and predicted to utilize CycD-CDK4/6 driven G1/S route 2b—CCNE1 concentration super-scaled with cell size (Figure 8, in red), indicating that late ERP stages might need to accumulate enough CycE to pass the transition. This observation is in line with the strong correlation between CCNE concentration across ERP developmental stages at the population (cell type)-level and their propensity to divide (Figure 7B). In contrast, genes from the Inhibitors module, such as RB and CDKNs, as well as E2F (data not shown) and CDK4 concentrations remained mostly constant across the first 4 size bins, indicating size-independent expression in G1 and early S phase. Hence, although ERP cells expressed Cyclin D module genes at a much higher level than most other cell types, they might rely on CycE-CDK2 activation to pass the G1/S transition.

Figure 8.

Cell type-specific differential scaling of G1/S regulators during G1 growth elicit distinct transition mechanisms in B lymphoid progenitors and late ERP

Single-cell gene concentration averaged over all cells of a given type across donors (y axis) as a function of their total RNA content (proxy for cell size, x axis), color-coded according to cell types. Curves represent 3rd-order polynomial fits and error bars indicate mean ± SEM. See also Figure S15.

In pro-B-1 cells, which are predominant Cyclin E and Inhibitors module users with minor contribution of Cyclin D module (Figure 4), and are predicted G1/S route 3 users, CDKN1B mRNA concentration rapidly declined with increasing cell size (Figure 8, blue), indicating a potential reduction of p27 protein levels during G1. This sub-scaling of CDKN1B suggests a progressive release of CDK repression when G1 cells grow. In parallel, CDK4 gene expression super-scaled with size. Thus, although pro-B cells express Cyclin E module genes at a much higher level than most other cell types (Figures 4 and S11), they might rely on CycD-CDK4 activation to pass the G1/S transition. In line with this observation, the pro-B type with the highest P_d—pro-B-early cycling—exhibited a larger contribution of Cyclin D module than other pro-B subtypes, while still maintaining a relatively high Cyclin E module expression (Figures 4 and S11). Given the relatively low expression of CCND and CDK4/6 genes at the population level, CycD-CDK4/6 activity might represent the limiting factor to pass G1/S in pro-B cells.

HSC-2 cells, that displayed a low E2F/RB ratio at the pseudobulk level (Table S8) showed RB1 expression slightly decreasing in the first 4 size bins, while MPP-2 cells, that displayed a pseudobulk E2F/RB ratio around 1 (Figure 7B), did not (Figure S15); likewise, pre-DC-1 cells, that showed low CDK expression (but mostly active due to high CycD as predicted by our model, Table S9), had an unfavorable E2F/RB ratio at the peudobulk level (Table S8) but showed an increase in E2F transcription in the first 3 bins (Figure S15). This data indicates that HSC-2 and pre-DC-1, which need to increase their E2F/RB ratio, may use differential scaling of E2F and RB1 gene expression⁶⁸ during G1 as a tool to pass the G1/S transition. However, in those cell types, the data was very variable, possibly due to the small number of cells scored overall, and to the fact that a dominant fraction of those cells is not cycling, introducing a major component to mRNA expression variability that is not associated with the cell cycle.

In summary, analysis of concentration changes of G1/S regulators in relation to cells’ total mRNA content uncovers a subtle regulatory layer that may not be evident at the population level. G1 hematopoietic cells may rely on cell type-specific size scaling of G1/S regulators to coordinate their division rate with their developmental phase. While gene expression patterns at the population level reflect cell type’s overall “priming” to proliferate (P_d), and to pass the G1/S transition through a specific route, the actual commitment to divide at the single-cell level may be triggered by scaling-induced shifts in the concentration of key activators and inhibitors, which can be captured in our model through cell size-dependent protein concentrations (e.g., Figure 6A, for E2F).

Sequential expression of Cyclin D, Cyclin E, and CDKN modules along differentiation trajectories across human tissues

Finally, to assess whether our findings extend beyond hematopoiesis, we tested whether the sequential expression of G1/S modules also operates in other tissues representing epithelial, nervous, and connective tissue types.

We first verified that genes from the Cyclin D, Cyclin E, and Inhibitors modules remain strongly co-expressed across these cell types from other tissues (Table S4). While the intra-module correlations remained strong across tissues (mean Pearson r coefficient of 0.2–0.5 for Cyclin D, 0.4–0.7 for Cyclin E, slightly weaker for Inhibitors), the inter-modules correlations were more variable. Thus, non-hematopoietic cell types tended to use Cyclin D and Cyclin E modules concomitantly or did not co-express Cyclin E and Inhibitors modules, reducing the contrast ratio between modules’ correlations (STAR Methods).

In the adult small intestine epithelium,⁷² epithelial stem cells strongly expressed Cyclin D module genes, and displayed low to mid P_d similar to HSCs (Figure S16A). Cyclin E module expression peaked in transit-amplifying cells (TAs), which are fast proliferating progenitors located in the basal epithelial layer and giving rise to enterocytes, Goblet cells, enteroendocrine cells, Paneth cells, and Tuft cells in the small intestine. The Cyclin E module remained highly expressed in Goblet progenitors, while the Cyclin D module expression declined. The Inhibitors module was most strongly expressed in terminally differentiated cells, especially in Paneth cells, BEST4 entero/colonocytes, enterocytes, enteroendocrine cells, and Goblet cells. Thus, the G1/S gene expression signatures also discriminated intestine epithelial cell types, and the sequential Cyclin D, Cyclin E, and Inhibitors expression along differentiation trajectories was also found in the small intestine.

Likewise, our analysis of a trachea epithelium scRNA-seq dataset⁷³ highlighted that proliferating basal epithelium cells comprised of distinct subpopulations: one with high Cyclin D module expression and low to mild P_d, and one with high Cyclin E module expression and high P_d (Figure S16B). Inhibitors module was enriched in more differentiated cell types such as mucus secretory or ciliated cells.

The Cyclin D-Cyclin E-Inhibitors sequence was also manifest in steady-state (4 months old) human brain organoids derived from induced pluripotent stem cells (iPSCs),⁷⁴ although we identified substantial Cyclin D module expression in later progenitors. Stem cells, such as slowly proliferating ventricular radial glia, displayed high Cyclin D module expression (Figure S16C, top row). Cyclin E module expression was restricted to the fast proliferating, lineage committed progenitors: a subset of ventricular radial glia (vRGC), at the base of the neurogenesis tree (Figure S16C, bottom row), in which the Cyclin D module expression was also strong; and a subset of outer radial glia cells (oRGCs), which derive from vRGC and from which originate neurons from outer brain layers (Figure S16C, top row), in which the Cyclin D module expression was weak (oRGCs are more committed than vRGCs). G1/S Inhibitors were more expressed in neural layers 2–6, and caudal ganglionic eminence (CGE) inhibitory neurons, although with low expression contrast across cell types. Surprisingly, the Cyclin D module genes were also highly expressed in later progenitors (post Cyclin E expression), such as the inhibitory neuron progenitors (INP) or intermediate progenitors (IPs) on the outer layer neuron lineage. This resurgence of Cyclin D expression did not correlate with a rise in P_d, possibly due to the relatively high concomitant expression of Inhibitors, which directly counteract CycD-CDK4/6-based G1/S activation.

Last, we examined the expression patterns of G1/S regulatory modules in subcutaneous adipose tissue, using the annotations and pseudotime ordering of the differentiation states along the adipocyte lineage from PDGFRA positive adipose stem and progenitor cells (ASPCs), provided by authors.⁷⁵ Cyclin D module expression peaked in ASPC1, the multipotent cells at the top of the differentiation cascade. ASPC1 cells also showed some Cyclin E module expression, consistent with their rather high P_d when compared to stem cells and early progenitors from the other tissues analyzed. Cyclin E module expression and P_d both peaked coincidentally in the adipose fate committed progenitors “ASPC2,” where the expression of the Inhibitors module was also high. The latter was also strongly expressed in classical adipocytes, at the bottom of the differentiation cascade, although those cells preserved mild Cyclin D/Cyclin E module expression and showed measurable P_d.

In summary, the Cyclin D-Cyclin E-Inhibitors expression sequence paradigm was generally conserved across human tissues and tissue types, although isolated cell types (e.g., neuron precursors) showed alternative G1/S expression patterns.

Discussion

Despite half a century of intense research on the cell cycle mechanisms, since Leland Hartwell and co-workers identified the first cell cycle genetic mutants in budding yeast, it is still unknown how cells take the decision to divide at the molecular level.

In this work, we combine two complementary computational approaches, data-driven and model-driven, to gain mechanistic insight into the G1/S transition across cell types, using the healthy hematopoietic system as a model. Our theoretical work bridges the gap between previous “generic” mathematical models of the G1/S transition, that do not include cell type differences and therefore are unable to probe the different routes through which different cell types pass G1/S,^35,76 and data-only based studies (e.g., Riba et al.⁷⁷ and Sukys and Grima⁷⁸) that account for distinct cell cycle gene expression across cell types but lack the theoretical framework to functionally link gene expression patterns to proliferation. To the best of our knowledge, our model is the first mathematical model of cell cycle commitment parametrized with RNA seq data across donor-derived primary cells at distinct developmental stages.

We restricted our transcriptomics data analysis to the expression of 24 genes encoding for the core G1/S regulators. We show that this shortlist is sufficient to define/cluster hematopoietic cell types across all lineages and capture their propensity to divide—beyond inter-donor variability and without accounting for additional cell type markers, such as lineage-specific receptors. Thus, despite its narrow mechanistic focus, the set of 24 core G1/S regulators appears as an efficient discriminator of hematopoietic cell identity. Expression patterns highlighted 3 distinct modules within the G1/S network, encompassing respectively cyclin D-related genes, cyclin E-related genes, and G1/S inhibitory genes. These modules are sequentially expressed along hematopoietic developmental trajectories: Cyclin D in slightly proliferative HSCs and early multipotent progenitors, Cyclin E in highly proliferative lineage-biased progenitors, and Inhibitors in quiescent terminally differentiated cells respectively, along all hematopoietic lineages. The concordant upregulation of the Inhibitors module with Cyclin E module in proliferative lymphoid and myeloid progenitor cells may seem counter-intuitive (Figures 4B and S11). Yet, 70 years ago in his seminal work,⁷⁹ Alan Turing already remarked that robust switch-like systems based on feedback regulation require both strong activation and strong inhibition. In our analysis, no cell type was found on the Cyclin D module-Inhibitors module axis (Figure 4B). This absence stems from the fact that cyclin D expression is not dependent on a (E2F-dependent) positive feedback loop; hence, cyclin D activators and inhibitors act in opposition to each other—unlike activators and inhibitors of the Cyclin E module, which work in concert.

Integrating the transcriptomics data into a mathematical model constructed from known interactions between the core G1/S regulators reveals that modules’ expression profiles project the G1/S network into distinct functional modes that correspond to a continuum of routes through the G1/S transition, that we classified in 6 broad categories. Moreover, cell growth during G1 leads to size-dependent changes in the mRNA concentration of key G1/S regulators, which could—in a cell type-specific manner—trigger commitment to the given G1/S route for which the cell is primed.

Despite its simplicity, our model estimated the propensity to divide in 68 hematopoietic cell types and in several cancer cell subsets from multiple donors relatively well. We speculate that this heterogeneity in how the G1/S transition is wired across hematopoietic cell types provides means for healthy cells to react differentially to the same chemical stimulation within the same bone marrow microenvironment, to adjust G1 duration to developmental needs. To predict how the different routes through G1/S specifically affect developmental states, our model would need to be coupled with a model for cell differentiation, such as that proposed by Cho et al.⁸⁰ In this work, cell division is modeled at a coarse, phenomenological level, accounting for the proliferation rate and division symmetry. Including such an approach is a key pre-requisite to make testable predictions on lineage commitment from our model. Without it, our conclusions on how the G1/S regulation impacts differentiation remain speculative.

Integration of our results to current knowledge and new hypotheses raised by this work

The existence of multiple routes through G1/S has been known for a long time, although G1/S plasticity is often attributed to cancer cells.^38,81,82 Our work demonstrates that, in the healthy hematopoietic system, a variety of routes through G1/S is captured quantitatively by a unified model based on just 24 G1/S regulators.

The Skotheim laboratory found that increasing RB1 dosage increases cell size at the G1/S transition almost linearly.⁴⁰ In our model, although cell size is not explicitly represented, increasing RB1 concentration led to an almost linear increase in the concentration of the critical amount of E2F required to elicit the transition, when pro-B cells were simulated (as a “reference,” with default parameters). Hence, for this cell type, RB1 dosage—in fact, the E2F/RB ratio—is a critical parameter constraining the G1/S transition, paralleling the experimental findings.⁴⁰ Notably, those experiments were performed under CDK4/6 inhibition, placing the cells into a regulatory mode resembling the type 1/3 routes observed in pro-B cells. However, when we simulated erythroid progenitors (ERP-7/8)—where high concentration of CycD-CDK4/6 is found—with increasing amounts of RB1, the dynamics of the G1/S transition were much less modified. These results align with recent data showing that RB1 downregulation during G1 is only essential in cells born with low CycD-CDK4/6 activity, while cells born with high CDK activity could commit to division without the need to reduce their RB1 pool.⁸³ Hence, as captured by our model, elevated enough E2F/RB1 ratio or CDK activity can function as independent but not mutually exclusive routes through the G1/S checkpoint, characterizing distinct cell types.

Consistent with our predictions, HSCs rely on the Cyclin D module (i.e., CCND1-2 and CDK6) to pass the G1/S transition,³⁸ corresponding to route 2. From a kinetics perspective, route 2 does not require time-consuming synthesis and accumulation of E2F, cyclin E and CDC25A (both under E2F control), and therefore, allows for a shorter G1 phase. This prediction is supported by Mende et al.¹⁹ who demonstrated that short G1 duration is critical for preserving stemness in human HSCs and progenitor cells (HSPCs). Conversely, re-directing the G1/S dynamics to the Cyclin E module (route 3) leads to a reduction in stemness and loss of functional HSPCs. Likewise, our model predicts that MEP-1 progenitors (MkP precursors,¹³) require more E2F accumulation to fully activate CycE-CDK2 than MEP-2 (ERP precursors,¹³), predictive of a longer G1 phase. This prediction aligns with the results published by Lu et al., who showed that overexpressing both CDK4/cyclin D1 and CDK2/cyclin E in MEPs results in a shorter G1 phase and evolution of MEPs toward the erythroid lineage, rather than megakaryocytic lineage.²⁰ Conversely, pharmacological inhibition of CDK4/6 with palbociclib—which shifts cells from route 2 to route 3 in our theoretical work—prolonged the G1 duration in MEPs and promoted their differentiation toward megakaryocytes.

Leukemic cells can derive from HSC or multipotent progenitors, or from lineage committed progenitors.^13,84 Leukemic cells tend to overexpress CDK6 and CCND2, both belonging to the Cyclin D module, in AML and B-acute lymphoid leukemia (B-ALL).⁸³ Hence, CDK4/6 inhibitors—such as palbociclib, ribociclib, and abemaciclib—that are FDA-approved anti-cancer drugs used in the clinics to treat breast cancer, are currently tested in trials against leukemia.⁴³ In the Zhang et al. hematopoietic atlas,¹³ AML leukemia stem cells aligned with early progenitors such as MPP-2, MPP-MEP, LMPP-1, MDP-2 or MultiLin-GMP-2, all of which show high CDK6 and CCND2 expression (Figure S11) and locate on the Cyclin D-Cyclin E module axis (Figure 4B). When we model these cell types, they pass G1/S through route 2, characterized by constitutive E2F activity driven by elevated CycD-CDK activity. In this context, further CycE-CDK2 activation is possible upon accumulation of E2F, which increases CycE synthesis as in ERPs (Figure 7B). In the light of our results, leukemic cells may undergo partial reversal of their development, as they turn from a progenitor state (Cyclin E module user) into a more HSPC profile (Cyclin D module user). Thus, according to our model, CDK4/6 inhibitors may impair leukemic cells while providing a competitive growth advantage to healthy cells that operate on the Cyclin E module-Inhibitors module axis (Figure 4B), including pro-B, pre-DC, and Mono-2 cells. This differential sensitivity to the drug may underlie the observed benefit of inhibiting CDK4/6 in T-ALL and B-ALL mouse models.⁴³

Moreover, our model’s steady state—particularly the fraction of activated E2F and Cyc-CDK complexes—is poorly sensitive to changes in most meta-parameter values, indicating that the G1/S network is very robust to perturbation, such as fluctuations in protein expression or signaling. This robustness is conferred by the E2F-CycE-CDC25A positive feedback loops, which buffer against molecular noise. In contrast, the Cyclin D module responds linearly to perturbation. As a result, in the absence of additional mutations such as CDKN2A or RB1, lymphoblastic leukemia cells (Cyclin D module users) are predicted to be more sensitive than healthy lymphoid progenitors (Cyclin E module users) to perturbations in the environment. This vulnerability could explain the strong selective pressure for mutations in CDKN2A and RB1—two of the most frequently inactivated cell cycle genes in leukemia.⁸⁵ CDKN2A loss of function dopes the Cyclin D route for G1/S activation (route 2), while RB1 loss of function elicits the routes 1 and 3 by increasing the model meta-parameters K₁₃ and K₁₄. Hence, simultaneous CDKN2A and RB1 mutation provides leukemic cells with plasticity for G1/S commitment, as all routes through G1/S get promoted, and the theoretical benefit of inhibiting CDK4/6 may be circumvented in leukemia.

Indeed, in other cancers the promising therapeutic effects of CDK4/6 inhibition are counterbalanced by the development of resistance to these drugs, which limits long-term efficacy.³⁹ MCF-7 breast cancer cells treated with Palbociclib resumed growth following a 2-step process where RB was first degraded, followed by c-MYC-mediated E2F activation. The rapid degradation or RB upon CDK4/6 inhibition may be explained by the removal of CDK4-mediated hypophosphorylation of RB, that protects it from degradation.⁸³ In parallel, c-MYC activation promotes CDC25A synthesis and enables cells to bypass CDK4/6 inhibition through activation of the CycE-CDK2/CDC25A positive feedback (route 3). Hence, blocking route 2 via CDK4/6 inhibition is counterbalanced by c-MYC dependent increased activation of route 3. Our model explains therefore the strong correlation between patients’ c-MYC levels and their (poor) survival outcomes following CDK4/6 inhibition. In Kim et al.,³⁹ it was suggested that restoring RB levels via proteasome inhibition could prevent relapse following CDK4/6 inhibition. Our model supports this hypothesis, predicting that increasing RB1 levels alters routes 1 and 3. Consistently, single breast tumor cells with elevated levels of E2F1, RB1 and CDK2—key components of the Cyclin E module, priming to use routes 1 and 3—tend to show stronger resistance to Palbociclib,⁸⁶ emphasizing the plasticity of the G1/S network.

CDK2 inhibition has also been tested in vitro against cancer cells and is currently investigated in clinical trials against leukemia.^87,88 However, resistance mechanisms have also emerged. Treatment of breast cancer cell line MCF10A with the PF3600 inhibitor—selective for CDK2 at low concentrations (25–100 nM) and also targeting CDK4/6 at higher doses (500 nM)—led to a rapid decline in CDK2 activity. However, the initial drop was transient: within 1–2 h, a compensatory CycD-CDK4/6 activation (route 2) recovered the CDK2 activity, allowing cells to complete the cell cycle. Our model provides a mechanistic explanation for this adaptive response: CDK2 inhibition is equivalent to an increase in the CycE-CDK2 de-activation rate d₃, reducing K₆ and K₇ and therefore moving the blue curve downward on Figure S5. Additional accumulation of E2F may compensate for this effect, by re-increasing K₆ and K₇, unless partial E2F activation is further compromised by additional inhibition of CDK4/6, as achieved with concomitant Palbociclib treatment in Arora et al.⁸⁸ Measuring E2F total expression and activation following CDK2 inhibition in MCF10A cells would test this hypothesis.

In summary, our model provides a quantitative analysis of the different routes that cells can take through the G1/S transition. Based on our analysis of hematopoietic cells, we propose that differential wiring of the G1/S network across cell types provides a means for the cells to react differentially to the same biochemical environmental stimulation—being it growth signals from the bone marrow microenvironment, or pharmacological interventions—and enables cells to adjust their G1 duration according to their developmental stage. We find that, although 6 different routes to pass G1/S can be distinguished, those are largely overlapping and provide a continuum of mechanisms. This work demonstrates that the commitment to division must be tackled at the systems level, and that one may never find a single mechanism of G1/S commitment. Our model is able to correctly recapitulate the wealth of propensities to divide across the hematopoietic tree, as well as in AML samples, and to predict how cells would react to perturbation. Hence, by quantifying the RNA or ideally the absolute protein concentrations of the 24 core G1/S regulators, patient-specific renormalization of model parameters could enable tailored predictions of the efficacy of CDK or E2F inhibition strategies.

Limitations of the study

This work is a theoretical study, wherein we used computational analysis of scRNA-seq data from primary human tissues and integrated these data into a mechanistic mathematical model to gain functional insight. While our model predictions were confirmed by the reanalysis of existing datasets, they remain to be validated through dedicated experiments.

Our model is parametrized by protein concentrations, protein synthesis and degradation rates, complex binding/unbinding rates, and multi-site phosphorylation rates as the main post-translational modification. Although we derived those parameters with great care from published data (STAR Methods) and our own measurements,⁸⁹ many were measured only indirectly or outside of the hematopoietic context. As a simplified mathematical representation of biological reality, the model does not include alternative RNA splicing, protein isoforms, or other signal-mediated regulatory layers that can affect the outcome of the G1/S transition. Despite these limitations, our model reproduced many published datasets at a semiquantitative level (Figure 7; Table 3; Figures S12F and S14F), suggesting that it captures the essence of G1/S control.

While our model is based on protein concentrations, it was fed with parameters deduced from mRNA measurements. For a given cell type—in contexts where protein translation and degradation rates are not modulated by external factors—it can be assumed that RNA concentration is proportional to the protein concentration.⁹⁰ Hence, comparisons of mRNA concentrations between small and large cells of the same type, that reflect different growth stages in G1, can be reasonably converted at the protein level in the model parametrization, although translation and degradation rates may evolve in G1 for some genes.⁹¹ However, these rates do vary between different hematopoietic cell types: for example, the rather slow-proliferating HSCs have typically low translation rates while the fast-proliferating erythroid progenitors are translationally very active.⁹² These differences could explain discrepancies between our model predicted P_d and the scRNA-seq-derived P_d across different cell types. Moreover, recent proteomics studies indicate that for proteins that super-scale with size, enhanced translation—rather than increased transcription—is driving their accumulation.⁹¹ In contrast, protein sub-scaling in fast-growing hematopoietic cells is predominantly a result of dilution effects, rather than active degradation.⁹³ Thus, our observed transcriptional upregulation of some G1/S activators in small to medium-sized cells may translate to even stronger changes in protein concentrations. Consistent with this, the scRNA-seq data-derived P_d typically exceeded the model predicted P_d in fast proliferating erythroid-lineage cells, suggesting that we under-estimated the G1/S (activatory) proteins concentrations in ERP/erythroblast cells.

Because our mathematical model is based on protein concentrations, and scRNA-seq data was used to model multiple cell types or samples, it was needed to map RNA concentrations to protein concentrations. In the adult bone marrow samples, this was achieved by mapping the default model parameters (for which the model predicts an essentially Cyclin E module-driven G1/S transition) to the gene expression profile of a cell type which was also predominantly expressing the Cyclin E module (pro-B cells). Applying our framework to other RNA-seq datasets requires identifying within each dataset a reference cell population with a similar G1/S genes’ expression pattern as the pro-B cells, which may not always be achievable.

It is noteworthy that neither our transcriptomics analysis approach, which quantified S/G2/M mRNAs at the population (cell-type) level, nor our modeling approach, which predicted E2F and Cyc-CDK activation at the single-cell level but without a definite readout for cytokinesis, did quantify cell proliferation as such directly. Hence, moderately high levels of a given gene in the transcriptomics analysis might originate from either very high levels of the gene in a small fraction of the cells, or moderately high levels in most cells, or anything in between, making the mapping of cell types to model G1/S routes via renormalized gene expression debatable. However, both approaches converged in that if the model predicts for a given cell type a low P_d, it implies that it does not predict strong E2F/CDK activation when provided with typical gene expression values for this cell type and, therefore, that this cell type is not “primed” for G1/S activation, indicating a low P_d in vivo.

Likewise, due to several interdependent feedback loops, there are threshold effects taking place (e.g., for full activation of the Cyclin E module). Hence, a model simulation parametrized by the “average cell” of a sample where G1/S activation variables are below threshold will predict a very low P_d. Yet, owing to biological variability in gene expression across cells, some individual cells within the experimental sample might be above threshold, pass G1/S, express S/G2/M genes, and therefore contribute to an increase in data inferred P_d. The opposite applies to samples where G1/S activation variables are above threshold, when averaged over all cells: here, the model would predict a high P_d although a substantial fraction of the cells might be below threshold and therefore not contribute to data inferred P_d. These effects limit the accuracy of our model predictions. Despite the model simplicity, predicted and data inferred propensities to divide correlated rather well (Figures 7C, S12F, and S14F), and the predicted cell type dependent response to CDK4/6 inhibition (Figure 7D) was in very good agreement with published data (Table 3).

We stress that model predictions of the cells’ response to perturbation (e.g., effects of CDK4/6 inhibition) were validated by semiquantitative data only, from manually curated published experiments, rather than a comprehensive scRNA-seq dataset of the perturbed system (here, bone marrow sample ± CDK4/6 inhibitor). Such data were unfortunately unavailable at the time when this work was finalized and were out of reach of our own experimental capabilities.

To define our model, we have focused on the 24 proteins that constitute the core of the G1/S network. This gene subset clusters hematopoietic cell types and their P_d in PCA as efficiently as hematopoietic receptors, or as the most variable genes, demonstrating (1) that there is a strong correlation between G1/S properties and cellular identity along the hematopoietic tree and (2) that these 24 genes capture the essence of the G1/S transition in hematopoietic cells. Yet, we did not include other factors that may play a direct mechanistic role on the transition, such as other E2Fs and/or their dimerization partners.⁹⁴

Our current G1/S transition model does not account for genes’ specificities within the Cyclin D or E2F families. However, CCND1-3 genes and E2F1-3 genes had distinct expression patterns across cell types. E2F3—together with CCND1-2, CDK6, and MYC—was upregulated in stem and early progenitor cells, whereas E2F1-2 dominated in later developmental stages (Figure S11). Interestingly, CCND3 concentrations were highest in fast-proliferating pro-B stages as well as several differentiated lymphoid cells, such as plasma B cells, T, and NK cells—which, unlike other mature blood cells, can re-enter the cell cycle massively upon contact with an antigen. Cyclin D3 governs proliferation of B and T cells outside the bone marrow, such as of mature B cells in germinal centers of lymph nodes,⁹⁵ and of late T cell progenitors in the thymus (thymocytes⁹⁶). These findings suggest that emerging roles of specific E2F and Cyclin D genes⁹⁷ might need to be included into a refined version of the model.

Resource availability

Lead contact

Requests for further information and resources should be directed to and will be fulfilled by the lead contact, Dr. Sylvain Tollis (quantcellbiolconsulting@gmail.com).

Materials availability

No biological material was generated in the course of this study.

Data and code availability

• •This paper analyzes existing, publicly available data, accessible at Synapse (syn18659336, syn53237600,⁴⁴ and syn53222756¹³); the Gene Expression Omnibus (GEO) (GSE185381⁵¹ and GSE134174⁷³); Zenodo (https://zenodo.org/records/7083558)⁷⁴; the CZ CELLxGENE portal (https://cellxgene.cziscience.com/collections/ba84c7ba-8d8c-4720-a76e-3ee37dc89f0b)⁷⁵; the Human Developmental Cell Atlas (https://developmental.cellatlas.io/studies/fetal-bone-marrow/dataset/65/cherita)⁵⁰; and the Gut Cell Survey web portal (https://www.gutcellatlas.org/pangi.html#datasets).⁷²
• •All original code has been deposited on Zenodo. MATLAB scripts for mathematical model simulations are available at https://doi.org/10.5281/zenodo.17549225. Python/R scripts for custom transcriptomics data analyses are available at https://doi.org/10.5281/zenodo.17700000 and on GitHub: https://github.com/andreahanel/2025_G1S_cellcycle_hematopoiesis.
• •Any additional information required to reanalyze the data reported in this article is available from the lead contact upon request.

Acknowledgments

We warmly thank Dr. Gerardo Aquino for his careful and critical reading of the manuscript. We also thank the reviewers for their very constructive comments, which lead us to improve our work. We acknowledge the Bioinformatics Center at the University of Eastern Finland for access to computing facilities. This work was funded by the Academy of Finland (grant #350887 to S.T.) and the Sigrid Jusélius Foundation (grant #220196 to S.T.). A.H. conducted this project with personal funding from the Instrumentarium Science Foundation (grant #220006) and Finnish Cultural Foundation (grant #00240437) independent of the author’s primary research work. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Author contributions

Conceptualization, S.T. and A.H.; methodology, S.T., A.H, and A.A.; software, A.A., S.T., and A.H.; formal analysis, A.A., A.H., and S.T.; writing – original draft preparation, S.T., A.H., and A.A.; writing – review and editing, all authors; funding acquisition, S.T. and A.H. All authors have read and agreed to the published version of the manuscript.

Declaration of interests

The authors declare no competing interests.

STAR★Methods

Key resources table

REAGENT or RESOURCE	SOURCE	IDENTIFIER
Deposited data
Healthy adult bone marrow dataset (n = 8)	Hay et al.44	syn18659336; annotations from syn53237600
Healthy adult bone marrow dataset (n = 4)	Zhang et al.13	syn53222756
Healthy fetal bone marrow dataset	Jardine et al.50	https://developmental.cellatlas.io/studies/fetal-bone-marrow/dataset/65/cherita
Healthy and AML bone marrow dataset	Lasry et al.51	GSE185381
Adult small intestine dataset	Oliver et al.72	https://www.gutcellatlas.org/pangi.html#datasets
Trachea epithelium dataset (non-smokers)	Goldfarbmuren et al.73	GSE134174
Subcutaneous adipose tissue dataset	Lazarescu et al.75	https://cellxgene.cziscience.com/collections/ba84c7ba-8d8c-4720-a76e-3ee37dc89f0b
Human brain organoids dataset	Li et al.74	https://zenodo.org/records/7083558
Analysis code generated for this manuscript	This study	Zenodo archive: https://zenodo.org/records/17549225; https://zenodo.org/records/17700000; Github: https://github.com/andreahanel/2025_G1S_cellcycle_hematopoiesis
Software and algorithms
Python v3.12.3	Python Software Foundation	https://www.python.org/
R v4.3.1 and v4.3.3	R Core Team	https://www.R-project.org/
Scanpy v1.10.4	Wolf et al.98	https://github.com/scverse/scanpy
Seurat v4.4.0	Butler et al.99	https://github.com/satijalab/seurat
Anndata v0.7.5.6	Wolf et al.98	https://github.com/dynverse/anndata/
Biomart v2.58.0	Durinck et al.100	https://doi.org/10.18129/B9.bioc.biomaRt
Decoupler v1.8.0	Badia-I-Monpel et al.101	https://github.com/scverse/decoupler
EdgeR v3.42.4	Chen et al.102	https://doi.org/10.18129/B9.bioc.edgeR
rstatix v0.7.2	Kassambara103	https://github.com/kassambara/rstatix
Delve benchmark	Ranek et al.104	https://github.com/jranek/delve_benchmark
scDEED v0.1.0	Xia et al.105	https://github.com/JSB-UCLA/scDEED
Harmony v1.2.3	Korsunsky et al.106	https://github.com/immunogenomics/harmony
classInt v0.4.11	Bivand107	https://github.com/r-spatial/classInt/
AUCell v1.22.0	Aibar et al.108	https://doi.org/10.18129/B9.bioc.AUCell
scib v1.1.7	Luecken et al.48	https://github.com/theislab/scib
corrplot v0.95	Wei and Simko109	https://github.com/taiyun/corrplot
ggtern v3.5.0	Hamilton et al.110	https://doi.org/10.32614/CRAN.package.ggtern
ComplexHeatmap v2.18.0	Gu111	https://doi.org/10.18129/B9.bioc.ComplexHeatmap
MATLAB 2024b	Mathworks	https://www.mathworks.com

Method details

G1/S genes

Throughout the manuscript, we consider a core subset of 24 genes/proteins that are the most direct regulators of the G1/S transition. The list of G1/S genes was assembled from various literature sources and include: the activating E2F transcription factors (E2F1-3); E2F repressors RB1, RBL1 and RBL2 genes; CDKs relevant to E2F de-repression, i.e., CDK2/4/6, and their activators cyclins D1-3 (CCND1-3 genes) and cyclins E1-2 (CCNE1-2); 8 CDKN genes coding from CDK inhibitory proteins (CDKN1A-C, CDN2A-D, and CDKN3); and finally, the CDC25A phosphatase that activates CDK2-CycE complexes, and the c-MYC transcription factor that partially controls CDC25A and cyclin E expression, independent of E2F. The 24 genes listed above (3 activating E2F, 3 repressing RB-like, 3 CDK, 5 cyclins, 8 CDKN, CDC25A and MYC) are the basis of our mathematical model and are referred to as the “G1/S genes” in the transcriptomics data analysis detailed below and throughout the manuscript (Table 1).

Single cell transcriptomics data curation

Healthy adult bone marrow single cell RNA sequencing (scRNA-seq) data⁴⁴ was downloaded from synapse (syn18659336) as a h5ad object, and updated with cell type annotation from¹³ downloaded from syn53237600. Six other human cohorts were used for the validation and extension of our results: 4 adults bone marrow donors¹³; 3 fetal bone marrow donors⁵⁰; 10 healthy adult bone marrow donors, 18 and 19 donors respectively with adult and pediatric Acute Myeloid Leukemia (AML⁵¹); 32 healthy adult small intestine donors,⁷² 7 trachea epithelium donors (never-smokers),⁷³ and 5 subcutaneous adipose tissue donors.⁷⁵ In addition, we used scRNA-seq data from cells collected from human brain organoids.⁷⁴ For all those datasets, the data was processed using the toolkits Scanpy (v1.10.4)⁹⁸ in Python (v3.12.3) and Seurat (v.4.4.0),⁹⁹ with anndata (v.0.7.5.6) in R (v.4.3.1 and 4.3.3). For the Hay et al.⁴⁴ dataset, gene annotation was updated based on ENSG IDs to Ensembl version 113 (release October 2024)¹¹² via Biomart in R (v.2.58.0).¹⁰⁰ In case of duplicated gene identifiers, the version with the higher gene count and lower Entrez gene ID was kept.

Data processing

We used the finest cell type annotation provided by Zhang and co-authors (“Level 3”,¹³) for the Hay et al.⁴⁴ dataset to process the single cell data and create pseudobulk samples. To focus on high-quality hematopoietic cells, we filtered out stromal cells and excluded cells with a mitochondrial read fraction >10% (1117 cells) as recommended in Osorio and Cai.¹¹³ Moreover, we removed outlier cells with a log-library size or log-transformed number of expressed genes exceeding >5 median absolute deviations from the median of the given cell type. Then we aggregated read counts from cells from the same donor-cell type combination with Decoupler (version 1.8.0)¹⁰¹ to form pseudobulk samples. Samples formed from <10 cells or <50,000 read were removed as recommended.¹¹⁴ Furthermore, cell types present in <5 donors were excluded from the dataset. This procedure selected 68 cell types out of the 89 annotated by Zhang et al., totalizing 95,685 single cells and 501 pseudobulk samples (Table S1). For the coarse level pseudobulk analysis, we utilized “Level 1” annotation of the same dataset provided by Zhang et al. to form pseudobulk samples. For Principal Component Analysis (PCA) analysis, we further reduced the number of cell types to 24, i.e., the number of core G1/S genes, by excluding the cell types with the lowest number of donors (Ba/Ma/Eo).

For validation cohorts, we used author-provided QC-filtered data objects. The X. Zhang et al. (n = 4) dataset¹³ was further restricted to the 68 types that we analyzed in this work. Non-hematopoietic cell types were excluded from other hematopoiesis datasets. For the Lasry et al. healthy cohort analysis (n = 10),⁵¹ ‘Broad_cell_identity’ was used as cell type label due to the relatively low sequencing depth in this dataset (Figure S14D). For the AML cohort analysis, we utilized authors’ segregation of malignant from microenvironmental cells, and authors’ phenotyping of malignant cells to their closest healthy counterpart (termed “cancer cell subsets” in this work). Cells were aggregated per cell type/subset, per donor, or per cell type∗donor combination (as indicated on Figure S14). To test model predictions with robust AML data, we focused on analyzing the 6 most frequently found cancer cell subsets per AML age group (pediatric/adult AML), 4 of which were common to both age groups, yielding in total 8 AML cell subsets: HSC-like, MPP-like, MEP-like, Erythrocyte-like, Granulocyte-like, CD14⁺ monocytes-like, GMP-like and HLA-II+ monocytes-like. We selected from each age group and each subset the three samples (donors) with the highest number of cells.

Data normalization and RNA concentration estimate

For sample level analysis, to normalize pseudobulk samples for both the coarse (Level 1) and fine (Level 3) annotation levels, library sizes (i.e., total RNA count per pseudobulk sample) were adjusted by the TMM method, and counts per million (CPM) and log2-CPM counts were calculated for each gene using the cpm (log = FALSE or log = TRUE) function in EdgeR (v.3.42.4).¹⁰²

For per cell RNA concentration estimates in cell types, for each gene G and donor-cell type sample S, we calculated the average of single cell-level normalized expression values (i.e., gene UMI counts divided by total UMI per cell, scaled to 10,000):

$$Concentration\left(geneG\right)=\frac{\sum _{cells\in sample}\left(\frac{RawcountsofG\in cell}{TotalRNA\in cell}\ast 10000\right)}{Numberofcells\in sample}$$

To calculate average concentration of E2F (E2F1+E2F2+E2F3), CDK (CDK2+CDK4+CDK6), RB (RB1+RBL1+RBL2), and CCNE (CCNE1+CCNE2) (Figures 6 and 7), raw UMI counts of individual genes (e.g., E2F1+E2F2+E2F3) were summed per cell prior to normalization.

Average cellular transcript abundance of E2F per cell type was calculated by summing raw UMI counts of E2F1+E2F2+E2F3, divided by the number of cells per individual donor-cell type combination (i.e., “absolute scaling” in³⁹).

For model predictions of P_d in healthy hematopoietic cell types,^13,44 per cell RNA concentrations of the 24 G1/S genes were averaged across donors to obtain one value per cell type (Table S8). This approach is reasonable due to the very low variability of G1/S gene expression across healthy donors (Figures S11, S12E, and S14A). For model predictions of AML samples,⁵¹ we retained the donor resolution due to the higher gene expression variability across patients. To mitigate noise from the relatively low sequencing depth of this dataset, we used RNA concentrations at the donor∗cancer cell subset level. Expression levels of selected G1/S genes in AML donors were compared to healthy donors using a one-sided Wilcoxon test (rstatix v0.7.2).¹⁰³ Comparisons with p < 0.05 were considered significant.

Single cell level visualization tools

To visualize the structure of the Hay et al.⁴⁴ hematopoietic transcriptome dataset, we generated a UMAP (Uniform Manifold Approximation and Projection) representation of the single cell data following a standard processing pipeline for dimensionality reduction: first, gene expression was normalized to the cell’s total RNA counts (i.e., library size) and multiplied by 10,000, followed by log1p transformation via the function NormalizeData, and finally z-scored with ScaleData in Seurat. Then, the top 4000 genes with highest feature importance were detected by a Random Forest classifier (implemented in Delve benchmark¹⁰⁴), and used to compute principal components (PCs) via the RunPCA function. Finally, the top 30 PCs were used to produce the UMAP plot using RunUMAP (method = uwot) in Seurat. For a faithful representation of the data, the hyperparameters of the UMAP were optimized with scDEED package (v.0.1.0).¹⁰⁵ The resulting UMAP (Figure 2B) where our 68 hematopoietic cell types align along developmental trajectories, was used as a backbone for overlaying various scores (see below), providing an overview of how the different scores vary along developmental trajectories across the hematopoietic tree.

UMAP coordinates for validation cohorts were retrieved from authors’ data objects or re-calculated after removing off target cell types (e.g., non-hematopoietic cells in hematopoiesis datasets). For the fetal bone marrow, data was processed and UMAPs generated following authors’ script.⁵⁰ PCs were corrected for batch effects using Harmony (version 1.2.3).¹⁰⁶ To process the small intestine epithelium data,⁷² the neighborhood graph was computed with the top 30 Harmony-corrected PCs (correcting for “donorID_unified”, theta = 2) with 23 nearest neighbors, and the UMAP generated with a minimum distance of 0.21. For the trachea epithelium data,⁷³ the neighborhood graph was calculated with the top 30 Harmony-corrected PCs (“donor”, theta = 2) with 30 nearest neighbors, and the UMAP made with a minimum distance of 0.4.

Propensity to divide from transcriptomics data

The propensity to divide P_d was defined based on the mRNA counts of genes that are expressed specifically after the G1/S transition, i.e., during the S, G2, and M phases of the cell cycle. S/G2/M genes were obtained from Macosko et al. (clusters 6-7-8, 277 genes in total,⁴⁵). This list was intersected with the list of universally essential genes, i.e., genes whose knock-out suppresses viability across 10 different cell lines,⁴⁶ to derive a list of 29 core S/G/2M genes whose expression specifically after the G1/S transition is required across all viable cell types (Table S2).

At the pseudobulk (cell type-donor combination) level, P_d was calculated as follows.

• 1.For each S/G2/M-specific gene G, and each pseudobulk sample S, we calculated the mean G expression per cell:

$$Gpc\left(S\right)=\frac{\sum _{cells\in sampleS}\left(RawcountsofG\in cell\right)}{Numberofcells\in sampleS}$$

• 2.To balance each gene’s G contribution to the score, we z-scored each G mean expression across samples:

$$ZGpc\left(S\right)=\frac{Gpc\left(S\right)-\mu \left(G\right)}{\sigma \left(G\right)}$$

where μ(G) and σ(G) are the mean and standard deviation of gene G’s expression across all samples.

• 3.We then calculated the average z-scores across all the genes G of the S/G2/M gene list, for each pseudobulk sample S:

$$⟨ZGpc⟩\left(S\right)=\frac{\sum _{G\in SG2Mgenes}ZGpc\left(S\right)}{NumberofSG2Mgenes}$$

• 4.Finally, the average Z-scores of all samples were rescaled to the |0–1] interval via:

$$P_d=\frac{⟨ZGpc⟩\left(S\right)-\min \left(⟨ZGpc⟩\left(S\right)\right)}{\max \left(⟨ZGpc⟩\left(S\right)\right)-\min \left(⟨ZGpc⟩\left(S\right)\right)}$$

where min(⟨ZGpc⟩(S)) and max(⟨ZGpc⟩(S)) are respectively the smallest and largest average Z score across all pseudobulk samples S. For each relevant dataset, P_d values were segregated into 5 categories using Jenks natural breaks implemented in classInt (v.0.4.11,¹⁰⁷ see Figure 2A and S12A, S12F, S13A, and S14F).

At the single cell level, for visualization purposes, P_d was estimated using the AUCell algorithm (v.1.22.0), which uses a ranking-based approach to calculate the enrichment of a gene list relative to other genes expressed in the same cell.¹⁰⁸ The list of 29 S/G2/M specific genes was used as an input to AUCell.

Principal Component Analysis, correlation analysis and definition of Cyclin D, Cyclin E and inhibitors modules

Principal Component Analysis (PCA) was performed using z-scored log2-CPM counts obtained from coarse-level (level 1) pseudobulk samples. P_d was calculated for those samples as described above for the fine-level analysis, and overlaid on the PCA plots. To evaluate how well different cell types separate in the PCA space, we utilized clustering performance metrics Adjusted Silhouette Width (ASW), Adjusted Rand Index (ARI) and Normalized Mutual Information (NMI)⁴⁸ in scib (v.1.1.7).

Gene-gene correlograms were plotted from the Pearson correlation coefficients of z-scored log2-CPM counts between any pair of genes, across all the 68 level 3 pseudobulk samples, using the corrplot package (v.0.95,¹⁰⁹). Genes were ordered using hierarchical clustering. The statistical significance of gene-gene correlations across the pseudobulk samples was assessed with the cor.mtest function, and a confidence level of 0.99. We adjusted the p-values for multiple hypothesis testing using the Benjamini-Hochberg correction method, and considered correlations with FDR<0.01 as significant. Correlogram highlighted different patterns of correlation for cyclin D related genes, cyclin E related genes and G1/S inhibitor genes, from which we derived 3 modules (see results). For a better visualization of the shared correlations, CDK4 has been swapped with CDKN2C to highlight its unique position, as CDK4 correlated strongly both with Cyclin D and Cyclin E modules (Table S4). We quantified genes’ clustering into modules using the adjusted contrast ratio metric, defined as the average intra-module Pearson correlation minus the average inter-module correlation divided by 2 (Table S4).

To position pseudobulk samples according to how they express the three modules, we used barycentric coordinates. Specifically, for each sample (donor-cell type), TMM-adjusted CPM counts per module were z-scored, averaged, and min-max scaled as done in steps 2–4 for P_d calculation. Finally, scaled module scores were divided by the sum of the 3 scores for the same sample, ensuring that once re-normalized, Cyclin D module score + Cyclin E module score + Inhibitors module = 1, prior to conversion to barycentric coordinates and ternary plotting using ggtern (v.3.5.0) package.¹¹⁰ To visualize the overall expression of Cyclin D, Cyclin E and Inhibitors modules at the single cell level, we scored the enrichment of each module using the AUCell tool, as described above for the propensity to divide. Heatmaps were generated with ComplexHeatmap (v.2.18.0)¹¹¹ with z-scored log2-CPM expression values clipped to ∣z∣ ≤ 2 to prevent extreme values skewing the visualization.

Interactions amongst the G1/S regulatory proteins: construction of the G1/S molecular network

Interactions between the 24 core G1/S genes defined above were pulled from the literature. The mechanisms of action of CDKN gene products differ in that CDK4/6 specific inhibitors (INK4 family, CDKN2 genes) alter the structure of the Cyclin-binding pocket on CDK4/6, preventing the formation of the CycD-CDK4/6 complexes specifically, while CDKNs of the Cip/Kip family (CDKN1 gene products) can bind to an already formed Cyc-CDK complex, rather inhibiting its catalytic activity.¹¹⁵ The mechanism of CycE-CDK2 inhibition by CDKN3 is less clear. The expression of E-type cyclins is under control of E2F, producing a positive feedback loop where a small pool of active E2F transcribe CCNE1-2 genes, increasing CycE-CDK2 activity which phosphorylates more RB-like proteins, increasing the overall level of E2F activity. In addition to CycE, E2F also induces expression of CDC25A,¹¹⁶ a phosphatase with documented activating effect on CDK2.⁴ The phosphatase function of CDC25A is activated by CycE-CDK2,¹¹⁷ establishing another positive feedback loop within the G1/S network. We note that the CDC25A gene is a transcriptional target of c-MYC independent of E2F,¹¹⁸ making c-MYC a core element of the G1/S network. c-MYC expression is, itself, responsive to mitogenic signals,¹¹⁹ while D-type cyclins expression also responds to a range of growth factors,^{31,32,33,34,120} coupling the cell cycle trigger to the environment.

Simplification of the G1/S network and mathematical description

To simplify the network and its mathematical description, we chose to represent explicitly E2F1-3 as a single E2F factor, RB-like proteins as a single RB transcriptional repressor, cyclins E1-2 as a single CycE, cyclins D1-3 as a single CycD, and to include the effect of CDK inhibitor proteins in the model parameters describing the binding of CycD to CDK4/6 (for CDKN2 gene products) and describing the activation of CycD-CDK4/6 and CycE-CDK2 complexes (for CDKN1 gene products). While CDKN1A,C inhibits only CycE-CDK2, CDKN1B can also impact CycD-CDK4/6, prompting us to include potential differential inhibition of CycE-CDK2 and CycD-CDK4/6 complexes by CDKN. Therefore, the corresponding parameters in the model can vary independent of each other. In summary, our model includes explicitly 9 protein factors: E2F, RB, CycD, CycE, CDK2, CDK4, CDK6, CDC25A and (c-)MYC, that represent 16 proteins of the core G1/S network, and includes implicitly 8 CDK inhibitor proteins whose effects are captured by changes in model kinetic parameters d₃ and d₄ (see below and supplementary methods).

Total concentrations of proteins with long half-lives (CDK2, CDK4, CDK6, E2F, RB, several hours)¹²¹ were assumed constant and considered as model parameters, i.e., external inputs to the G1/S network. Binding/unbinding reactions were assumed to satisfy mass-action kinetics. Moreover, we chose to describe explicitly active and inactive forms of the complexes. Under those constraints, the full dynamics of the CDK2, CDK4, CDK6, E2F and RB sub-network is captured by 10 ordinary differential equations (ODEs) for the concentrations of 10 molecular species: unbound (inactive) CDK2-4-6 ([CDK2-4-6]^I), cyclin-bound but inactive CycE-CDK2 (shortened as ${\left[Cy{k}_{E/2}\right]}^I$) and CycD-CDK4/6 (shortened as ${\left[Cy{k}_{D/4-6}\right]}^I$), cyclin-bound and catalytically active CycE-CDK2 (shortened as ${\left[Cy{k}_{E/2}\right]}^A$) and CycD-CDK4/6 (shortened as ${\left[Cy{k}_{D/4-6}\right]}^A$), and finally RB-free E2F ([E2F]^F). Those 10 ODEs are provided as supplementary methods.

In contrast, total concentrations of CycD, CycE, CDC25A and (c-)MYC were assumed to be time-dependent variables, and their synthesis/degradation rates were also included in the model, in addition to their binding/dissociation to/from other factors, and their activation/inactivation. CycD synthesis was put under control of mitogens and growth factors; MYC synthesis was assumed to respond to mitogens; CycE and CDC25A synthesis were assumed to be stimulated by both active (RB-free) E2F and MYC.^122,123 Degradation rates were deduced from proteins half-lives as measured with SILAC proteomics¹²¹ or biochemical experiments (CDC25A,¹²⁴: MYC;^125,126). Cyclins were degraded only in the free state, but not while bound to CDKs, in line with the observation that subunits of protein complexes tend to be degraded at similar rates (the degradation rate of the Cyc-CDK complex).^121,127 Hence, binding to CDKs stabilizes cyclins, as reflected by the very long CycE half-life in S-phase cells.¹²⁸ Synthesis/degradation of CycD, CycE, CDC25A and (c-)MYC yielded 4 more ODEs, coupled to the binding/dissociation ODEs (supplementary methods).

Our model also describes explicitly the activation of CDC25A (via CycE-CDK2 phosphorylation¹¹⁷), activation of CDK2 (via CDC25A dephosphorylation at tyrosine 14 and threonine 15 ¹¹⁷), and activation of E2F (via a Cyc-CDK multi-site phosphorylation-dependent dissociation rate of the RB-E2F complex), and the corresponding spontaneous deactivation reactions. The effect of multi-site phosphorylation on protein activity is complex, due to non-trivial conformational changes that follow each phosphorylation event and that may affect other putative phosphorylation sites. In this work, we consider the general framework of the Hill functions to model phosphorylation-dependent activation functions: $activation=\frac{{\left(\frac{\left[kinase,phosphatase\right]}{Co}\right)}^p}{1+{\left(\frac{\left[kinase,phosphatase\right]}{Co}\right)}^p}$ where the Hill threshold Co parametrizes the typical concentration range of the kinase/phosphatase that is required to elicit the activation, and the Hill exponent p parametrizes the sensitivity of the full activation to kinase/phosphatase concentration. p scales as the number of phosphorylation sites that need to be independently processed to elicit full activation (number of critical phosphosites).⁵⁶

Finally, p27 (CDKN1B gene product) binds to and inhibits both CycE-CDK2 and CycD-CDK4/6 complexes.¹²⁹ Hence, Cyc-CDK complexes may compete for p27 and an increase in the concentration of inactive CycD-CDK4/6 (a fraction of which is p27-bound) leads to a decrease in the pool of available p27 and therefore an increase in CycE-CDK2 activation.¹²⁹ Our model accounts for this competition by using a ${\left[Cy{k}_{D/4-6}\right]}^I$ dependent activation rate of CycE-CDK2, and a ${\left[Cy{k}_{E/2}\right]}^I$ dependent activation rate of CycD-CDK4/6. All model equations are detailed in supplementary methods, and feature 15 variables and 38 parameters.

Model parameters

Concentrations were expressed in nM. In the absence of proteome-wide measurements of absolute protein concentrations at the subcellular level in single human cells, we used different strategies to parametrize absolute total concentrations in our model. First, we used quantitative proteomics data¹³⁰ to get an estimate of the order of magnitude of the G1/S proteins concentrations. In Ref.¹³⁰, absolute protein counts are reported for various cell lines (A549, Hep-G2, PC-3 and U87MG) and range from about 3.000–5.000 copies of RBL1-2, 20.000–40.000 copies of RB1, 10.000–100.000 copies for CDK4 and CDK6, to 45.000–200.000 copies of CDK2 depending on cell types. Using an average volume of about 5 pL for those cell types we found the correspondence 30.000 copies ↔ 10 nM. Rieckmann and co-authors also measured RB1, RBL1-2, CDK2-4-6 copy numbers using spiked-in proteomics on primary human immune cells, in basal state and following immune activation.¹³¹ They reported basal levels around 10.000–30.000 copies per cell depending on the proteins (with CDK2 and CDK6 more expressed than RBLs and CDK4) in most immune cells, and those number very multiplied several fold upon activation. CycD2-3 and E2F3 expression was measured in just a few cell types to <10.000 copies per cell, indicating that total CycD levels are at least 2- to 3-fold less than RB1. E2F1-2 were not reported. Of course, those values are averaged over a cell population and, importantly, over sub-cellular localizations, so that proteins with a much predominant nuclear localization (e.g., RB1) would show 5- to 10-fold larger nuclear concentration, since the nucleus is 5–10 times smaller than the cell. This rough analysis, though, informed that RB1 should be present at a typical concentration of 70–100 nM, 6–7 more than RBL1-2, and that CDKs should be presents at slightly larger concentrations (2- to 3-fold). Concentrations of MYC, Cyclins and CDC25A were not reported in quantitative proteomics datasets providing absolute values, possibly because of low expression levels. Those concentrations, while roughly estimated based on ad hoc conversion of quantitative proteomics data, were in reasonably good agreement with concentrations of homologs of these proteins in budding yeast, determined accurately using single live cell quantitative microscopy (Number and Brightness, N&B).⁵⁶ In this work, the yeast RB1 (Whi5) was quantified at 100 nM, and cyclins were expressed at 5 nM in early G1 and 5–15 nM in late G1 phase, at the transition. Our own N&B measurements in a NALM-6 pre-B leukemia cell model yielded an RB1 nuclear concentration of about 100 nM and a very low p27 concentration (typically 10 nM⁸⁹), indicating that p27 may be in stoichiometric default compared to Cyc-CDK complexes. Since no data was found for the absolute concentration of mammalian E2F1-3, we decided to keep the total concentration of E2F as a tunable parameter (see below, steady-state analysis), and as a default value, chose [E2F]^tot = [RB1]^tot = 100 nM. Protein degradation rates were fixed to: CycD, 30 min¹²⁷; CDC25A, 60 min¹²⁴; MYC, 28 min^125,126; CycE, 30 min¹²⁷ Synthesis rates were adjusted to provide steady-state concentrations that fall in the range defined above.

For activation functions, Hill thresholds Co_1,2,3 were chosen in the range of actual concentrations of the relevant proteins in the G1/S network (see steady-state analysis), and the Hill exponents were chosen as the number of critical phosphorylation sites on the substrates RB1 (p₃ = 7), CDC25A (p₂ = 2) and CDK2 (p₁ = 1–5 as the number of critical CDK2 sites on CDC25A is unknown, default p₁ = 3).

Cyc-CDK complex binding/unbinding dynamics were assumed to be in the millisecond (ms) range, to promote a fast activation of the targets when enough Cyc-CDK complexes are present. Binding rates were adjusted to yield ms dynamics even in the presence of low cyclin concentrations. The default parameters that were used unless otherwise specified are listed in Table 2.

Model parameters for cell types other than default

The default model parameters above produced dynamics where the Cyclin E module dominates E2F activation. We matched those dynamics with that of pro-B cells, and grouped pro-B-early-cycling, pro-B-cycling-1, 2 and transitional pro-B1 to reduce inter cell type variability in the pro-B pool. For all the 24 G1/S genes, the average mRNA concentration (see above) was averaged over the 4 pro-B types above. Then, for all other cell types, a fold-enrichment relative to the pro-B group was calculated for each gene G as:

$$F{E}_{celltypeX}\left(G\right)=\frac{mRNAconc{\left(G\right)}_{celltypeX}}{mRNAconc{\left(G\right)}_{pro-B}}$$

Fold-enrichments were then averaged over CCND genes, CCNE genes, RB genes, E2F genes CDKN2 genes and CDKN1A,C genes to match the generic variables of the model. Finally, the model parameters that reflect the expression levels of those genes were renormalized based on the FE for each gene/cell type. Specifically, to model a cell type X, we updated model parameters as:

$$f_9\left(celltypeX\right)=f_9\ast F{E}_{celltypeX}\left(CCND\right)\text{;}$$

$$f_1\left(celltypeX\right)=f_1\ast F{E}_{celltypeX}\left(MYC\right)\text{;}$$

[E2F]^tot(celltypeX) = [E2F]^tot∗FE_celltypeX(E2F) and similarly for other total concentrations (RB, CDKs);

$$C_3\left(celltypeX\right)=C_3\ast F{E}_{celltypeX}\left(CDKN1B\right),\text{for}\mathrm{p}27\text{;}$$

d₄(celltypeX) = d₄∗FE_celltypeX(CDKN2), as CDKN2 concentrations influence CycD-CDK4/6 inactivation; and.

d₃(celltypeX) = d₃∗FE_celltypeX(CDKN1), as CDKN1 concentrations influence CycE-CDK2 inactivation.

This data is reported in Table S8 for all cell types. To model cancer cell subsets,⁵¹ the same procedure was used, and the LymP cell type (where the Cyclin E module dominates E2F activation) from healthy donors of the same cohort was chosen as default cell type and used to renormalize model parameters for other samples as above (Table S8).

Model analysis

Analytical resolution (partial) of steady-state equations and definition of the propensity to divide: as detailed in the supplemental information (Figures S1–S6), in the steady state the model ODEs reduce to a closed system of only 6 algebraic equations coupling 6 variables: $\raisebox{1ex}{${\left[E2F\right]}^F$}\!\left/ \!\raisebox{-1ex}{$\left[E2F_0\right]$}\right.$, the fraction of active E2F; $\raisebox{1ex}{${\left[CDC25A\right]}^A$}\!\left/ \!\raisebox{-1ex}{$C{o}_1$}\right.$, the concentration of active CDC25A relative to the threshold for CycE-CDK2 activation; $\raisebox{1ex}{${\left[Cy{k}_{E/2}\right]}^I$}\!\left/ \!\raisebox{-1ex}{${\left[CDK2\right]}^{tot}$}\right.$, the fraction of catalytically inactive CycE-CDK2 complexes, relative to the total CDK2 concentration; $\raisebox{1ex}{${\left[Cy{k}_{E/2}\right]}^A$}\!\left/ \!\raisebox{-1ex}{${\left[CDK2\right]}^{tot}$}\right.$ the fraction of catalytically active CycE-CDK2 complexes, relative to the total CDK2 concentration; $\raisebox{1ex}{${\left[Cy{k}_{D/4}\right]}^I$}\!\left/ \!\raisebox{-1ex}{${\left[CDK4\right]}^{tot}$}\right.$, the fraction of inactive CycD-CDK4 complexes, relative to the total CDK4 concentration; and $\raisebox{1ex}{${\left[Cy{k}_{D/4}\right]}^A$}\!\left/ \!\raisebox{-1ex}{${\left[CDK4\right]}^{tot}$}\right.$, the fraction of catalytically active CycD-CDK4 complexes, relative to the total CDK4 concentration. Those 6 steady state equations are parametrized by 16 meta-parameters, that combine one or several kinetic rates and other model parameters such that constant protein concentrations (e.g., CDKs, RB, E2F, Table 2). For the default parameters (pro-B cells, Table 2), the model was bistable (Figures S5 and S6), i.e., two stable steady-state solutions co-existed and transitions between them were dynamically possible, following adequate stimuli. One state showed low activity (E2F mostly RB-bound, low CDK activity, low CDC25A concentration), and the other higher activity (E2F free, high CDK activity, high CDC25A concentration). This knowledge guided the numerical resolution of the equations presented below.

Numerical resolution of the steady state equations: steady state equations (Equations 1, 2, 3, 4, 5, and 6, supplementary methods) were solved numerically using a fixed point methodology.⁵² Briefly, a vector variable x is a fixed point of a function F if F(x) = x, which is the form of Equations 1, 2, 3, 4, 5, and 6. The fixed point algorithm choses arbitrary starting values for the variables, and iteratively modifies them using Equations 1, 2, 3, 4, 5, and 6, until the relative change between variables’ values between 2 iterations is less than a chosen tolerance (here 10⁻⁶). The algorithm was written in MATLAB 2024b (Mathworks). Computations were run on a Lenovo 81WB laptop equipped with IntelCore I5 10210U CPU (1.6 GHz) and 8 Gb physical RAM. The algorithm was robust to changes in the starting values for the variables (Table S5).

Time-dependent simulations of the model: to generate full time-dependent solutions of the model ODEs, we implemented dynamical numerical simulations with the Ode45 solver in MATLAB R2024b, that operates a Runge Kutta integration algorithm.⁵² In presence of a bistable steady state, dynamical simulations were performed starting from two types of initial state: either “inactive”, where all proteins whose total concentration is known were assumed inactive and unbound, and all proteins whose concentrations evolve in the model (CycE, CycD, CDC25A and MYC) were assumed to be absent; or “active”, where all the E2F pool was assumed RB-free, CycD, CycE, CDC25A and MYC concentration were fixed to 20–200 nM and most CDKs were cyclin-bound. The first and second sets of initial conditions converged respectively to the “low activity” and “high activity” steady states. We generated 1000 timecourses with random initial conditions and all converged to either of the steady states (Table S6).

Stability analysis: we performed Lyapunov stability analysis using 100 randomized initial conditions picked in a ±20% neighborhood of each steady state separately, and running the time-dependent simulations as described above. Convergence after 50.000 s is reported in Table S7.

Parameter space analysis: a comprehensive numerical analysis of the effect of parameters on model outputs was performed using the 16 meta-parameters and steady state equations. 678978 parameter sets were randomly generated, using for each parameter 10^(−2+4∗r) where r is a random number, uniformly distributed on [0,1] (with the exception of K₉, that was randomly sampled on [0,1]). Hence, all meta-parameters but K₉ varied between 0.01 and 100. The steady state was computed for the 6 variables defined above for each parameter set, using low activity initial conditions, generating a (16 + 6)∗678978 data matrix. For each meta-parameter, the fraction of active E2F and meta-parameter value were co-binned and the resulting 3D histogram was represented as colour-coded 2D plots (Figure S7).

Sensitivity analysis: we performed local sensitivity analysis (SA,¹³²) to assess the effects of each meta-parameter individually on model output variables. We proceeded as follows: first, we computed the relative deviation in the steady state values of the biochemical variables $\left(S{S}_{new}-S{S}_{default}\right)/S{S}_{default}$ caused by a 1% change in one meta-parameter kp; then, we normalized this deviation to the relative change in this meta-parameter to its default value¹³²: $sensitivity=\frac{\raisebox{1ex}{$\left(S{S}_{new}-S{S}_{default}\right)$}\!\left/ \!\raisebox{-1ex}{$S{S}_{default}$}\right.}{\raisebox{1ex}{$\left(k{p}_{new}-k{p}_{default}\right)$}\!\left/ \!\raisebox{-1ex}{$k{p}_{default}$}\right.}$

To prevent biases in sensitivity that would arise from widely different physiological ranges of distinct parameters, we converted most meta-parameters to log scale prior to calculation of the relative change, following what was done in parameter space analysis. This analysis was performed for 4 different total E2F concentrations.

Global sensitivity analysis (GSA): we used Pearson correlation coefficients (PCC,¹³³) to capture linear trends between the 6 model outputs and the 16 meta-parameters. Specifically, pairwise Pearson correlations were computed between variables/meta-parameter, meta-parameter/meta-parameter and variable/variable pairs across the 678978 simulated samples (see above, parameter space analysis), and the correlation matrix was clustered using hierarchical clustering (clustergram function in MATLAB 2024b, Pearson’s R coefficient and associated p-value, Figure S9).

Model predicted propensity to divide

Due to the existence of multiple routes through G1/S, showing distinct requirements for E2F activation and CDK activation, we defined the propensity to divide for each cell type as the geometric mean of the total pool of active (RB-unbound) E2F and the total pool of active CDK (in the model, CDK2+CDK4 explicitly accounted for):

$$P_{d,model}=\sqrt{{\left[E2F\right]}^F\ast \left({\left[Cy{k}_{E/2}\right]}^A+{\left[Cy{k}_{D/4}\right]}^A\right)}\text{.}$$

Pearson’s correlation between data derived P_d and model predicted P_d was calculated for samples classified by Jenks natural breaks algorithm into the low Pd category.

Modeling CDK4/6 inhibition

CDK4/6 inhibitors such as palbociclib, ribociclib, and abemaciclib (referred to as CDKi throughout the manuscript) inhibit CDK4/6 kinase activity by binding to the ATP binding pocket of the enzymes. The affinity of CDKi to CDKs is very strong, with a dissociation constant K_d in the 10–40 nM range.¹³⁴ In cells, CDK4/6 concentrations are estimated over several hundreds nM (see model parameters in Table 2), while CDKi at clinical dosage reach micromolar range,¹³⁴ i.e., order(s) of magnitude above the K_d. Under these conditions, we estimate the fraction of free CDK4/6 to only a few percent. Accordingly, we have set by default the residual CDK activity in in silico CDKi treated cells to 2%, by turning the CDK4/6 activation rate f₁₄ to 0.02∗f₁₄ in model simulations and P_d calculations. When indicated, residual activities of 5% or 20% have been considered, using similar re-scaling of f₁₄.

Published: November 29, 2025

Supplemental information

Table S1. Samples information, related to Figure 2

Information about the pseudobulk samples from (Hay et al.⁴⁴), with annotations from Zhang et al.,¹³ including the propensity to divide P_d calculated for each cell type/donor (see also Figure 2).

Table S2. S/G2/M genes, related to Figure 2

List of genes expressed during the S/G2/M phases, derived from Bertomeu et al.⁴⁶ and Macosko et al.⁴⁵, used to calculate the propensity to divide.

Table S3. Hematopoietic receptors genes, related to Figure 3

List of 24 genes encoding for receptors sensing bone marrow niche signals, derived from De Jong et al.⁴⁹ and Zhang et al.¹³ (surface protein data).

Table S4. Correlated expression among the G1/S genes, related to Figure 4

Correlation matrix underlying the correlograms Figure 4A, Figures S12C, S13C, and S14A, showing the definition of the Cyclin D, Cyclin E, and Inhibitors modules. Correlation matrices are provided for all datasets analyzed in this study under different tabs.

Table S5. Robustness of the fixed-point algorithm for steady state resolution, related to Figure 5

Table presenting the steady-state values of the model variables, ${\left[Cy{k}_{E/2}\right]}^I$, ${\left[Cy{k}_{E/2}\right]}^A$, ${\left[Cy{k}_{D/4}\right]}^I$, ${\left[Cy{k}_{D/4}\right]}^A$, [CDC25A]^I, and [CDC25A]^A in the steady state and with default parameters, as calculated by the fixed point algorithm for 1,000 different sets of starting values for the algorithm. The algorithm robustly converged toward one of the two steady states.

Table S6. Dynamical bistability of the model, related to Figure 5

Table presenting the steady-state values (as measured after 70.000 s of time-dependent simulation) of the 15 molecular species included in the full dynamical model, simulated with default parameters, with 100 different sets of randomly selected initial conditions for the 15 variables at t = 0. The table shows that after 70.000 s the model converges toward one of the two steady states, demonstrating bistability sensitive to initial conditions.

Table S7. Dynamical stability of each steady state, related to Figure 5

Table presenting the Lyapunov stability analysis of the bistable model with default parameters. From the low activity steady state (first tab) and the high activity steady state (second tab), model variables were randomly perturbed by ± 20% and the ODE model was solved for 50.000 s until the concentrations of the 15 molecular species were recorded. The operation was repeated 100 times. All variables re-converged to their original steady-state values before the perturbation.

Table S8. RNAs concentrations and renormalization of default parameters, related to Figures 6 and 7

Table showing per cell RNA concentration estimates (STAR Methods) averaged across donors, defining the mean RNA concentration per cell for each G1/S gene in the 68 cell types in Hay et al.⁴⁴ and in Zhang et al.¹³ datasets used for model predictions (columns B→BQ). For Lasry et al.⁵¹ dataset, sample-level concentrations (STAR Methods) and authors’ provided cell type annotations were used. Data for pro-B-cycling-1, pro-B-cycling-2, pro-B-early-cycling, and transitional-B-1 that showed similar gene expression profiles by Pearson correlations were averaged to create a « pro-B » cell type that matched the default model parameters. For G1/S route analysis (Table S9), an HSC-MPP group including HSC-2, MPP-1, and MPP-2 was also created by averaging RNA concentrations over those 3 cell types, to reduce variability due to low cell counts. The RNA concentration of each gene in ERP-7, pre-DC-1, HSC-MPP, and MEP-1 was normalized to RNA concentration of the same gene in the pro-B group (columns BZ→CC) for comprehensive analysis of the G1/S transition modes in those cell types (Table S9). Then RNA concentrations were normalized to the pro-B group for all cell types (columns CE→ET) yielding RNA fold-enrichment scores (STAR Methods). Those scores were further averaged within groups of genes represented by a unique generic gene in the model (i.e., CCND, CCNE, E2F, RB, CDKN2, and CDKN1A-C) in order to rescale model parameters to model each cell type (STAR Methods). First tab: HCA data⁴⁴; second tab: validation data¹³; third tab: AML data,⁵¹ showing LymP healthy and 48 malignant cell subsets (used in Figures S14F and S14G).

Table S9. Route through G1/S for pro-B, ERP-7, pre-DC-1, HSPC, and MEP-1 cells, related to Figure 6

Table showing the meta-parameters (columns B→Q), steady-state values of the model’s output variables (columns S→Z) and critical parameters that depends on those outputs (columns AA→AF) for pro-B, ERP-7, pre-DC-1, HSC-MPP, and MEP-1 cells. From those values, the route for G1/S activation is derived, from Figures S1, S5, and S6.

Table S10. Modeling CycE expression, E2F/Cyc-CDK activation, and P_d for 68 cell types, related to Figures 6 and 7

Table showing the model-predicted steady-state values for the total concentrations of CycE, active E2F, active CycE-CDK2 + CycD-CDK4 complexes and active CycE-CDK2 + CycD-CDK4 + CycD-CDK6 complexes from which the propensity to divide P_d is calculated (column F). First tab: 68 healthy cell types⁴⁴; second tab: the same cell types, in response to 98% inhibition of CDK4/6; third tab: validation data, 68 healthy cell types¹³; tabs 4–7: 48 malignant cell subsets mapped to the closest healthy types by Lasry et al., with full CDK4/6 activity (tab 4), 98%, 95% and 80% CDK4/6 inhibition (tabs 5–7, respectively); tab 8: comparison of the response of cancer cells’ model predicted P_d to different efficiencies of CDK inhibition.