Multi-scale dynamical modelling of T-cell development from an early thymic progenitor state to lineage commitment

Abstract

Intrathymic development of committed pro-T-cells from multipotent hematopoietic precursors offers a unique opportunity to dissect the molecular circuitry establishing cell identity in response to environmental signals. This transition encompasses programmed shutoff of stem/progenitor genes, upregulation of T-cell specification genes, proliferation, and ultimately commitment. To explain these features in light of reported cis-acting chromatin effects and experimental kinetic data, we develop a three-level dynamic model of commitment based upon regulation of the commitment-linked gene Bcl11b. The levels are: (1) a core gene regulatory network architecture from transcription factor (TF) perturbation data, (2) a stochastically controlled chromatin-state gate, and (3) a single-cell proliferation model validated by experimental clonal growth and commitment kinetic assays. Using RNA-FISH measurements of genes encoding key TFs and measured bulk population dynamics, this single-cell model predicts state-switching kinetics validated by measured clonal proliferation and commitment times. The resulting multi-scale model provides a mechanistic framework for dissecting commitment dynamics.

Graphical Abstract

eTOC

Olariu et al. use computational modeling and live-cell developmental imaging to explain the kinetics of early T-cell developmental commitment. An integrated computational multi-scale model incorporating gene network architecture, single-cell RNA levels, chromatin state shifts and proliferation is developed, explored, and validated.

INTRODUCTION

Hematopoietic progenitors continually replenish the body’s supply of blood cells. While many of the molecular and cellular requirements of commitment to the various hematopoietic lineages have been studied in detail, how a single differentiating progenitor cell integrates multiple inputs into lineage decisions over time is less clear. Computational modelling approaches can provide new insights into the dynamics of this complex process.

T-cell development provides an excellent model system for studying lineage commitment from a multipotent progenitor. Small numbers of multipotent hematopoietic precursors migrate continuously from bone marrow into the thymus (Zietara et al., 2015; Zlotoff and Bhandoola, 2011) where they enter the T-cell developmental pathway, driven by Notch signalling and cytokines in the thymic microenvironment. Many of the important regulatory factors controlling T-lineage commitment are known (reviewed in (De Obaldia and Bhandoola, 2015; Yui and Rothenberg, 2014)), as well as their patterns of expression(David-Fung et al., 2009; Mingueneau et al., 2013; Zhang et al., 2012). Specific targets of several of these factors have been defined by perturbation studies, providing a strong basis for understanding the dynamic operation of an intrinsic gene regulatory network (GRN)(Anderson et al., 2002; Champhekar et al., 2015; Chen et al., 1995; Del Real and Rothenberg, 2013; Dionne et al., 2005; Franco et al., 2006; García-Ojeda et al., 2013; Germar et al., 2011; Hoogenkamp et al., 2007; Hosokawa et al., 2018; Kueh et al., 2016; Leddin et al., 2011; Li et al., 2010a; Li et al., 2010b; Longabaugh et al., 2017; Scripture-Adams et al., 2014; Taghon et al., 2007; Taghon et al., 2005; Weber et al., 2011; Xu et al., 2013; Zarnegar et al., 2010). However, the timing of observed transitions and the accompanying rapid proliferation leave open questions about how commitment decisions are made. In particular, recent experimental evidence has indicated a strong, rate-limiting role of cis-acting chromatin constraints in addition to the changes in trans-acting factors in controlling the timing of commitment (Ng et al., 2018). As a result, modelling the commitment process through a simple factor-target interaction approach alone is unrealistic. This work takes advantage of new and recently published experimental data to integrate these processes into a novel three-level model that explores the dynamics of T-cell commitment at both population and single-cell levels.

Early stages of T-cell development are well defined. Progenitor (pro-)T cells are CD4 and CD8 double negative (DN) and lack T-cell receptor expression. The Kit^high early thymic progenitors (ETP or DN1) proliferate before transitioning to DN2a, a step marked by CD25 surface expression, then upregulate Bcl11b and undergo Bcl11b-dependent T-lineage commitment (Fig. 1A)(Ikawa et al., 2010; Kueh et al., 2016; Li et al., 2010a; Li et al., 2010b; Yui et al., 2010). Expression of the zinc finger transcription factor (TF) Bcl11b not only alters many aspects of genomic activity and cell function (Avram and Califano, 2014; Hu et al., 2018; Kueh et al., 2016), but also correlates with the functional committed state of single DN2a cells (Kueh et al., 2016) and can thus serve as a proxy for commitment. After Bcl11b activation, Kit^high DN2a cells move through DN2b into the Kit^low DN3 stage, after which they can continue differentiation after rearranging a signalling competent T-cell receptor (Fig. 1A). A broad shift in expression of multiple regulatory genes occurs during commitment, and the stem/progenitor TFs expressed in DN1 and DN2 stages are generally extinguished (reviewed in (Rothenberg et al., 2016; Yui and Rothenberg, 2014)).

Fig. 1. Proliferation and developmental kinetics from multipotent DN1 progenitors to T-lineage committed cells.

A Schematic of T-cell development showing initial Notch-dependent stages after multipotent precursors immigrate to thymus. The most immature Kit^high Early T Precursors (ETP) are referred to here as DN1. At DN3, T-cell receptor gene rearrangement occurs, and all subsequent development depends on T-cell receptor expression and signaling. B Flow cytometry plots showing early T-cell developmental stages (DN1-DN4) and the gating strategies used for purifying progenitor DN1 cells, Kit^high and lacking CD25 and Bcl11b-YFP, for cell culture. C-E In vitro analysis of proliferation and development from DN1 cells. DN1 cells were purified from thymi of Bcl11b-YFP reporter mice, stained with a proliferation tracking dye, Cell Trace Violet (CTV), co-cultured with Notch ligand expressing OP9-DL1 stromal cells, and harvested for flow cytometric analysis on days 2-5. C Flow cytometry plots show the upregulation of CD25 followed by Bcl11b-YFP expression from days 2 to 5 (left), and the relationships between CD25 (middle) and Bcl11b-YFP (right) expression and the numbers of cell cycles each cell has experienced as determined by CTV levels (color coded by cell division as shown; see Fig. S1 for details). D Summary plots of the distributions of cell division numbers for cultured DN1 cells each day as measured by CTV. E Summary plots of the percentages of CD25-positive (blue) and of Bcl11b-YFP-positive cells (red) from each day. The histograms show mean and standard deviation of data from two experiments.

Computational modelling of GRNs represents an important starting point for studying mechanisms controlling cell-fate decisions (Olariu and Peterson, 2019). Our earlier dynamical models dealt, respectively, with the flux of T-cell progenitor populations through the DN1 to DN4 stages (Manesso et al., 2013), and with the transcriptional network for Bcl11b activation assuming deterministic, direct transcriptional regulation by positive regulators Notch, GATA3, and TCF-1 (Manesso et al., 2016). In (Ye et al., 2019) an exhaustive search of 3-gene network topologies characterized by four attractors was pursued, recovering the one employed in (Manesso et al., 2016). Interestingly, such motifs can generate step-wise commitment as in T-cell development. However, more recent empirical data have undermined basic assumptions of the deterministic direct model. First, we found that the roles of GATA3 and TCF1 are mostly required in a hit-and-run fashion, before Bcl11b is activated, in contrast to the roles of Runx1 and Notch signaling (Kueh et al., 2016). A simple combination of the earlier models, and evidence that all four known positive regulators are all active by DN1 stage, would predict Bcl11b to be turned on multiple cell cycles earlier than it is, well beyond the range of measurement error. This suggests that the deterministic assumptions about Bcl11b control itself were incorrect or incomplete.

Second, recent evidence implies that the timing discrepancy also reflects an intervening local, functionally important chromatin state change (epigenetic event). Extensive repression marks and methylation are removed from the Bcl11b locus during its activation (Ji et al., 2010; Li et al., 2013). This process can be rate limiting. Close analyses of cells with different fluorescent reporters in the two alleles of Bcl11b show that the two alleles within the same DN2 cell nucleus can become activated at different times, with discordances of several days (and cell cycles) despite exposure to the same TFs (Ng et al., 2018). Consequently, in the model proposed here, we have introduced an explicit stochastic timing event for epigenetic activation in addition to the initial trans-acting regulatory activity.

Altogether, we propose a three-stage dynamic model of early T-cell commitment from DN1 cells. The gene network aspects of the model take into account the unique linkage of commitment to Bcl11b activation, and encompass trans-acting and epigenetic levels of Bcl11b regulation to account for its proximal activation kinetics. Step 1 is a single cell GRN model based on previously published perturbation experiments with model parameters trained on new gene expression measurements from single molecule RNA-fluorescent in situ hybridization (smFISH). Step 2 is a collaborative epigenetic model to account for local chromatin constraints limiting Bcl11b activation, even after trans-factor requirements are met. At step 3, we embedded the two-step single-cell gene network model into a population growth model, trained with new cell culture dynamics data. Model predictions were confirmed by time-lapse imaging data from individual DN1 clones differentiating through commitment in vitro. The resulting multi-scale model closely represents measured early T-cell commitment kinetics and helps to elucidate required mechanisms controlling this process, enabling future dissection of the controllers of commitment.

RESULTS

Experimental Results – Training Data

Proliferation and Differentiation Kinetics from DN1 (ETP) to Commitment

To relate commitment rigorously to proliferation and to absolute time, we required new benchmark measurements linking cell proliferation and developmental kinetics of DN1 cell progeny through commitment. DN1 cells were purified from thymi of Bcl11b-YFP reporter mice (Kueh et al., 2016) (Fig. 1B) and then stained with Cell Trace Violet (CTV) dye that tracks each cell’s proliferation history through dilution. The cells were co-cultured with Notch-ligand-expressing OP9-DL1 stromal cells and growth-supporting cytokines, IL-7 and Flt3L, to promote T-lineage development (Yui et al., 2010). Parallel DN1 cultures were harvested daily, from days 2—5, and assessed by flow cytometry for total cell numbers, CTV-fluorescence intensity, the developmentally-regulated surface marker, CD25 (marking DN2 transition), and Bclllb-YFP, marking commitment (Fig. 1C). The number of divisions each cell had experienced was determined by flow cytometric measurement of residual CTV staining as calibrated in control cultures (Fig. S1). Numbers of cell divisions experienced by individual cells are highlighted by different colors on the flow cytometry plots (Fig. 1C) and as population distributions of cells with different numbers of cell divisions at each time (Fig. 1D).

Approximately 50% of DN1 cells had differentiated to DN2, marked by CD25 expression, by day 2 of culture, with further percentage increases over time (Fig. 1C, E). However, few if any committed Bcl11b-YFP⁺ cells appeared among the CD25⁺ cells until day 3, with percentages of YFP⁺CD25⁺ cells then increasing over time (Fig. 1C, E). CTV analysis at day 2 showed that cell division was not required for onset of CD25 expression (red dots=cells with 0 divisions), and that the most rapidly dividing cells were neither most nor least likely to turn on CD25. By days 4-5, however, CD25⁺ DN2 cells on average had divided more rapidly than cells remaining CD25⁻, as seen by the shift towards a larger population with the lowest CTV levels (turquoise or lilac) (Fig. 1C). Bcl11b-YFP was not expressed in any non-proliferating cells, and by days 4 and 5 the Bcl11b-YFP⁺ cells appeared to have proliferated more rapidly than cells remaining Bcl11b-YFP⁻, based on lower CTV levels for YFP⁺ cells (Fig. 1C). Overall, these results confirm that CD25 is expressed before Bcl11b-YFP (Fig. 1C, E) and that CD25 can be turned on in DN1s without cell division, while Bcl11b-YFP cannot be. Furthermore, more developmentally advanced cells in these cultures proliferated somewhat faster than those that were delayed.

Single Cell RNA-FISH Measurement of Key Transcription Factor Genes

Potential TF drivers of commitment include TCF1 (Tcf7, Gata3, and Runx1, which are necessary positive inputs for Bcl11b expression(Kueh et al., 2016), while PU.1 (Spi1) antagonizes developmental progression (Champhekar et al., 2015; Ungerbäck et al., 2018). To determine the normal ranges of expression of Spi1, Tcf7, Runx1 and Gata3 in individual T-cell precursors in developmental stages leading up to Bcl11b activation, for use in the model, DN thymocytes were purified from 5-week-old mice and analyzed by multiplex single molecule RNA-FISH (smFISH) (Fig. 2A,B) using gene-specific readout probes (STAR Methods). Developmental stages of individual cells were scored based on measured Kit, CD25 protein and mRNA levels. Absolute transcript counts showed that Runx1, Gata3, and Tcf7 expression was variable in DN1s, increasing up to 2x in DN2s (DN2 median transcript levels/cell: Tcf7≈40; Runx1≈12 Gata3≈8) (Fig. 2C). In contrast, Spi1 was highest in DN1 and DN2, and declined with further development, in accord with previous bulk population measurements (Mingueneau et al., 2013; Zhang et al., 2012). Bcl11b was not expressed in DN1s but turned on in CD25⁺ DN2s (median transcripts/cell≈15), remaining high into DN3 (Fig. 2C).

Fig. 2. Regulatory gene expression measurement by smFISH.

A Schematics of smFISH hybridizations. Primary probes were hybridized against mRNAs in immobilized DN cells in pools, and genes were detected with readout probes (Table S6) in groups of 4 genes, imaged and stripped with formamide before the second round of readout hybridizations. B Representative microscopy images. Each mRNA transcript was represented by a single dot under fluorescent microscopy, and the transcripts of each gene were counted (Tcf7, red; Gata3, magenta; Spi1, gray; Runx1, green) and assigned to individual cells that were categorized into DN1-DN2-DN3-DN4 by antibody stained surface markers Kit (red) and CD25 (encoded by Il2ra, green)). Scale bars in panels in B represent 10 μm. C Violin plots of transcript count distributions of Runx1, Gata3, Spi1 (PU.1), Tcf7 and Bcl11b in single cells, showing median and quartiles, in developmental stages DN1-DN3. n = 169.

These gene expression changes from DN1 to DN2 were used as input to the GRN model as an approximation for developmental changes in TF protein. The half-lives of these proteins can differ substantially; for example, PU.1 has a half-life at least 10x that of TCF1, Runx1, and Gata3 (Kueh et al., 2013; Manesso et al., 2016), and so their relative expression patterns were used, rather than absolute protein levels.

Modelling Results

Overview

As described earlier, a GRN model for Bcl11b activation during commitment must incorporate three separate aspects of control. First, four positive regulatory inputs, Notch signaling, TCF1, Gata3, and Runx1, are needed in the DN1-DN2a stages to make Bcl11b eligible for activation. Second, TCF1 and GATA3 work in a hit-and-run way and are dispensable for the final steps of Bcl11b induction, while Runx1 and Notch are still required (Kueh et al., 2016). Third, activation of each Bcl11b allele, in a cell fulfilling the eligibility requirements, still requires a slow stochastic epigenetic remodeling process (Ng et al., 2018). To accommodate these requirements, we separated an initial, transcriptionally driven specification process from a subsequent, epigenetic process.

Thus, we developed a three-level dynamic model. (1) In the specification level, network dynamics between Notch signaling, Runx1, Tcf7 (product of the Tcf7 gene, also called TCF1), Gata3, and an antagonistic regulator (possibly PU.1) determine cell permissiveness for Bcl11b activation, but act indirectly on Bcl11b via control of a critical, newly invoked function X, as described below. (2) In the stochastic level, the transition of Bcl11b from a closed to open state is influenced by the inhibitory function, X, balanced against the continuing positive drivers Runx1 and Notch signaling. (3) Finally, in the population level, to predict how these mechanisms generate observed population phenotypes, the single-cell processes are combined with a population growth model that accounts for the expansion of cells that have and have not yet activated Bcl11b. Model development and validation procedures are shown in Fig. 3.

Fig. 3. Modelling and experimental steps emphasizing predictions versus calibrations.

Level 1: With literature data and single cell experiments a GRN model is developed - both deterministic and stochastic versions. Level 2: The latter are augmented with an epigenetic model for Bcl11b expression. The resulting relative production rates of cells expressing Bcl11b are validated against bulk data. A population model is then developed using Cell Trace Violet experimental data. Level 3: This model is subsequently combined with the stochastic model from level 2 into a multi-level model that is validated against clonal imaging results.

Level 1: The Specification Gene Regulatory Network Architecture

For the first level of the single cell model we proposed a GRN architecture based upon gene expression, perturbation experiments, and literature (Table 1), describing the interplay between the T-cell specification regulatory genes Tcf7, Gata3, Runx1 and an opposing regulatory gene, which is here represented by Spi1 (Fig. 4A). However, these TFs alone could not account for the experimentally observed delay in Bcl11b upregulation (Kueh et al., 2016) because of the intervening cis-acting epigenetic process recently shown to be required (Ng et al., 2018). Therefore, rather than having these regulators control Bcl11b transcription directly, we proposed that their inputs collectively removed obstruction due to an antagonist of Bcl11b opening, X. X was defined as a composite of a slow initial chromatin opening mechanism and the actions of any additional DN1-specific antagonists of Bcl11b expression, still to be defined (Ng et al., 2018). Only X, Notch signaling, and Runx1 then propagate to the next, stochastic, epigenetic level.

TABLE 1:

Gene network and epigenetic model components and sources of evidence

Gene Regulatory Network Components
From	To	Effect	Evidence Type	References	Index
Notch	Runx1	Activate	Modest up-regulation in pro-T cells	(Del Real and Rothenberg, 2013)	1
Notch	Tcfl	Activate	Direct binding and activation	(Germar et al., 2011; Weber et al., 2011)	2
Notch	Gata3	Activate	Developmental activation requirements and protection from repression, but no direct binding evidence	(Hosoya-Ohmura et al., 2011; Schmitt et al., 2004; Taghon et al., 2005; Tydell et al., 2007)	3
Runx1	Runx1	Activate	Auto-regulation seen in HSC precursors in embryo (‘Cbfa2’); many binding sites; not certain in pro-T	(North et al., 1999)	4
Runx1	PU.1	Repress	Direct molecular evidence of repression through interaction sites	(Hoogenkamp et al., 2007; Hosokawa et al., 2018; Huang et al., 2008; Zarnegar et al., 2010)	5
PU.1	PU.1	Activate	Functionally only in myeloid cells, promoter activation and auto-regulation via cell cycle	(Chen et al., 1995; Kueh et al., 2013; Leddin et al., 2011)	6
PU.1	Tcf1	Repress	Functional perturbation; possibly indirect due to paucity of binding	(Champhekar et al., 2015; Del Real and Rothenberg, 2013; Franco et al., 2006)	7
PU.1	Gata3	Repress	Functional perturbation; dependent on absence of Notch signal	(Del Real and Rothenberg, 2013)	8
Notch	Repression of Gata3 by PU.1	Inhibit	Functional perturbation	(Del Real and Rothenberg, 2013)	9
PU.1	Ability of Notch to activate Tcf1	Inhibit	Functional perturbation	(Del Real and Rothenberg, 2013; Franco et al., 2006)	10
PU.1	Ability of Notch to activate Gata3	Inhibit	Functional perturbation	(Del Real and Rothenberg, 2013)	11
Tcf1	Gata3	Activate	Gain and loss of function perturbation in pro-T cells	(Weber et al., 2011)	12
Gata3	Tcf1	Activate	Genetic perturbation and retroviral interference	(García-Ojeda et al., 2013; Scripture-Adams et al., 2014)	13
Tcf1	X	Repress	Conjectural	Interpretation (Kueh et al., 2016; Ng et al., 2018)	14
Gata3	X	Repress	Conjectural	Interpretation (Kueh et al., 2016; Ng et al., 2018; Scripture-Adams et al., 2014)	15
Tcf1	Tcf1	Activate	Gain and loss of function perturbation in pro-T cells	(Weber et al., 2011)	16
X	Bcl11b	Repress	Epigenetic constraint on Bcl11b activation, apparently not relieved until after DN1 to DN2 transition	(Kueh et al., 2016; Ng et al., 2018)	17
Epigenetic Model Components
From	To	Effect	Evidence Type		References
Runx1	Bcl11b	Open	positively regulates Bcl11b expression amplitude at single-cell level based on gain and loss-of-function perturbation; direct DNA binding		(Guo et al., 2008; Hosokawa et al., 2018; Kueh et al., 2016)
Notch	Bcl11b	Open	accelerates and enhances frequency up-regulation from DN2; primes for activation in DN1		(Tydell et al., 2007), (Kueh et al., 2016)
X	Bcl11b	Close	conjectural based on stage-dependent prohibition and inter-allelic asynchrony		(Kueh et al., 2016), (Ng et al., 2018)

Fig. 4. Core circuit. Pseudo-time-series data, stochastic simulations and multi-level model results.

A GRN Topology. The interaction indices correspond to the rightmost column in Table 1. The arrows and thick red lines are positive and negative DNA regulations respectively. The thin red lines are PU.1 repression of Notch activation of Tcf1 and Gata3 and Notch inhibition of Pu.1 repression of Gata3. The dashed red line is the function X causing epigenetic repression of Bcl11b. B Pseudo-time-series (mean and standard deviation) obtained from ordering the clusters given by the Gaussian Mixture algorithm such that the Tcf7 and Bcl11b dynamics are similar to experimental behavior. Note the different y-axis scales. C Schematic representation of the epigenetic level model for the Bcl11b regulatory regions where Runx1 and Notch (blue and grey arrows) favor open DNA for transcription while X (green arrow) is keeping the Bcl11b regulatory regions closed. D Stochastic simulation results obtained from transcriptional level model. In the first plot the system stays in a state controlled by Pu.1 and X. In the second plot, the T-cell factors are switched on while Pu.1 and X are down-regulated. E Stochastic simulations obtained from the model including an epigenetic level. In the first plot, the Bcl11b regulatory region remains closed while in the second plot the regulatory region becomes open. F Predicted distribution (yellow) of the percentage of single-cell multi-level model simulations with the outcome of Bcl11b regulatory region open. G Predicted distribution (green) of the percentage of single cell model simulations where X activity levels have low values at time points corresponding to each day of the experiment (mean and standard deviations for 3 sets of 100 single cells model simulations). F-G The model predicts a clear delay between the X loss of activity and Bcl11b regulatory region opening (e.g. at day 2 almost 50% of cells have lost X while less of 10% are Bcl11b positive).

Specification Level: Deterministic model - Parameter Setting Based on Pseudo-Time-Series

To use the single cell FISH data for setting TF values in the GRN (Fig. 2), we created pseudo-time-series from DN1 through DN2, which show that in early DN1, expression of Tcf7 increases substantially and becomes predominant, while Bcl11b transcription begins only after a delay (200 arbitrary time units) (Fig. 4B). Gata3 expression slightly rises with increasing Tcf7 expression, along with Runx1. In contrast, expression of the opposing gene, Spi1 (PU.1), is fairly constant at a low level through these stages, turning off post-commitment (in DN3). For the following, note that PU.1 (Spi1) is the most prominent regulator in precommitment cells (Ungerbäck et al., 2018), but it is possible that another factor with a similar expression pattern to PU.1, or a complex of PU.1 with another factor, may be more directly involved than PU.1 alone in the initial restraint on Bcl11b activation. The model simulations below predict the dynamics of the functionally relevant factor whether or not it is PU.1 itself.

We developed the computational model for the level 1 specification GRN (Fig. 4A) using Shea-Ackers deterministic rate equations(Ackers et al., 1982) (see Methods). Initial conditions for Tcf7, Gata3, PU.1 and Runx1 were set equal to the “earliest” pseudo-time-series expression values, and the X function was assumed to be highly active initially. The model results show that the system, when exposed to external Notch signaling, moves towards a steady state where the T-cell factors are highly expressed, with a pronounced increase in Tcf7, while PU.1 and X activity levels descend towards low values. The GRN model parameters (Table S1), optimized to the pseudo-time-series, were picked and adjusted to accommodate the DN1 to DN2 transition shown by single cell RNA-FISH measurements (Fig. S2), and were then frozen throughout the rest of this work. While the marker CD25 plays an important role in interpreting the experimental results relative to the DN1-DN2 developmental transition, note that it is not a regulator and therefore was not explicitly included in these models.

Specification Level: Stochastic Model - Predicting Heterogeneity

Stochastic simulations (Gillespie, 1977) of the specification GRN model (Fig. 4A) in individual cells with the same parameters (Table S1) showed that noise could be a source of heterogeneity in DN1 cells, as not all simulations exhibited dynamic switching towards a steady state with high T-cell factors (Fig. 4D). Of note, this heterogeneity is not a predetermined outcome as the system could have been in a dynamical region with high synchronization. However, such synchronization was not observed when using realistic parameter values determined from the FISH data. Moreover, the stochastic simulations showed that GRN intrinsic noise alone sometimes led to delays of the switch towards T-cell commitment.

Level 2: Epigenetic Level Model

The second level of modelling was designed to account for the stochastic all-or-none activation timing observed for individual Bcl11b alleles, in terms of a simplified epigenetic model for the Bcl11b regulatory region with two possible states, open or closed (Fig. 4C). Published data showing the extent of epigenetic changes at the Bcl11b locus during commitment reveal multiple increases in DNA looping (Hu et al., 2018) and chromatin accessibility (Yoshida et al., 2019) over 1 Mb of DNA flanking the locus, as summarized in Fig. S3, along with published evidence for asynchronous activation of the two alleles in the same cells (Ng et al., 2018). Such state changes presumably are triggered by earlier TF actions, but substantially affect later TF actions. While the roles for Tcf7 and Gata3 become dispensable by the stage immediately before Bcl11b activation, positive influences from Notch signaling and Runx1 remain important. Notch signaling augments the likelihood of Bcl11b activation per unit time(Kueh et al., 2016), while Runx1 positively modulates expression levels (Kueh et al., 2016; Ng et al., 2018). Therefore, our model places these regulators in opposition to an epigenetic resistance function X, which represents a composite of repressive chromatin state and any additional repressive TFs not yet defined (Fig. 4A,C)

To account for the slow and potentially processive nature of this epigenetic transition, we used a model developed for calculating epigenetic activation as a function of the number of open (unmethylated) and closed (methylated) CpG dinucleotides at functional regulatory regions (Olariu et al., 2016) (see STAR Methods). Here, it could apply to other probabilistic, repressive local chromatin states as well as CpG methylation. Notch signaling and Runx1 levels obtained from stochastic GRN simulations serve as positive regulators for the probabilities that Bcl11b-regulating CpG sites (or equivalent chromatin features that are propagated by similar chromatin “reader-writer” mechanisms) become “open”, while X activity levels link to the probability of such CpGs remaining “closed”.

Merging Transcriptional with Epigenetic Levels - Predicting Time Delay Distributions

We next conducted stochastic simulations of the single cell multi-level model incorporating Bcl11b regulatory region state dynamics predicting that early T-cell progenitor cells are heterogeneous in their CpG methylation states(Li et al., 2013) or equivalent open/closed chromatin states in the Bcl11b regulatory regions. The simulations showed that the Bcl11b locus can remain closed or become opened depending on the status of these CpG (or equivalent) sites, as dictated by Notch signaling, Runx1 expression, and opposing X activity (Fig. 4D,E). The stochastic treatment of the epigenetic level predicted further delays in T-cell commitment. In an example when the switch was thrown by day 3 (i.e., Tcf7 and Gata3 becoming highly expressed while X activity drops), the corresponding stochastic simulation of Bcl11b status showed that the regulatory system only opens after day 4 (Fig. 4E, lower panels).

Three sets of 100 stochastic simulations of this multi-level model predicted that on days 2 and 3 <20% of cells would express Bcl11b, ~40% on day 4, and ~50% on day 5 (Fig. 4F). These predictions agree well with direct monitoring of Bcl11b-YFP during 5 days in DN1-derived populations going through commitment (Fig. 1E). The distributions of cell percentages with low X (Fig. 4G) are very similar to the distributions of CD25⁺ cells in experimental data (Fig. 1E), suggesting that loss of X activity might be correlated with CD25 expression, and consistent with the observation that Bcl11b expression follows CD25 upregulation. Thus, the two-level single-cell model shows that stochastic mechanisms controlling eligibility for chromatin opening downstream of the core GRN can account for the observed delays in T-cell progenitor commitment.

Single Cell Two-Level Model Predictions of Knock-Down Effects

The two-level model predicts the effects of knocking down Tcf7, Gata3 and Runx1, which typically fall to 15-25% of their original expression in RNA interference experiments. This corresponds to few molecular copies, thus requiring stochastic model simulations. When initialized in DN1 state, our model predicted that early knock-down of Tcf7, Gata3 or Runx1 would halt progression towards a state of high T-cell factors and low PU.1, resulting in a steady state with high PU.1 and low Tcf7, Gata3 and Runx1, keeping the Bcl11b locus closed (Fig. S4A). In contrast, model simulations of the Tcf7 or Gata3 knock-down starting after X is inactivated, predicted no continued requirement for Tcf7 or Gata3 (Fig. S4B). These predictions were consistent with experimental data showing that for eventual Bcl11b expression, Tcf7 and Gata3 have stage-dependent roles and are much more important in DN1 than in DN2 stage (Kueh et al., 2016). The concordance further supports the likelihood that X activity is lost after the DN1 to DN2 transition.

Level 3: Population Model

We next developed population models based upon the CTV cell culture data (Fig. 1). An initial hypothesis that cell cycle length might be independent of generation was clearly incorrect (Table S3). We then relaxed this assumption, allowing each cell to have its division time stochastically determined from a normal distribution with mean and variance depending upon cell generation (Fig. 5A). We chose the normal distribution for simplicity since the data would not disentangle this one from a more realistic long-tailed distribution. Normalized cell number distributions among different generations within simulated cell cultures up to day 5 were compared to the CTV data (Fig. 1D), allowing us to determine the cell cycle distribution parameters (Table S4). We monitored each cell generation, and calculated the fraction of cells in each generation for each day from 172 simulations (Fig. 5B), with resulting distributions very similar to experimental data (Fig. 1D).

Fig. 5. Full multi-scale model predictions for developmental dynamics starting from individual DN1 cells.

A Snapshots of proliferation and differentiation kinetics of a single modelled DN1 cell at five time points. Each time point shows: top left panel: X function activity (green) impacting the epigenetic behavior of the Bcl11b regulatory regions; bottom left: cells with opened/closed regions are in gold/black respectively; top right: Tcf7 expression which is predicted to be maximal during DN1-DN2a transition; bottom right: expression timeline of all genes for two selected cells; one non-switching and one switching to DN2a respectively. B Multi-scale model distributions of cell generations for each day. C-D Multi-scale model predictions of the average fraction of cells with low X (green) and cells with the Bcl11b regulatory region open (yellow) at simulation times corresponding to days 2 - 5 of CTV and single cell imaging experiments for epigenetic level model with 20 CpGs, and 500 CpGs respectively. E Model predictions on variability in proliferation kinetics between clones. F Multi-scale model predictions for the fraction of simulations versus required time to reach 50% Bcl11b regulatory region open in each run. The number of simulations reaching 50% at each day are shown on top. G Multi-scale model predictions for the fraction of simulations versus time to reach 50% X activity loss. Also shown are the number of simulations reaching 50% at each day. The statistics were calculated from 172 model simulations.

Full Multi-scale Model - Predicting Single Clone Developmental Dynamics

We next implemented the single-cell GRN model within the population mode to determine how cell proliferation affects population distributions of fate-committed T-cell versus non-committed cells. To take into account the impact of cell division on the Bcl11b locus epigenetic state, we used an advanced collaborative version of the epigenetic model with an intermediate state permitted between open and closed (STAR Methods). When the specification and epigenetic level models were embedded in this full three-level model, we found that a higher epigenetic barrier was required than in the two-level version, in order to match observed kinetics of Bcl11b activation. Even though the two-level model with 20 CpG sites gave very good results, when invoking the full multi-scale model, which takes into account the population growth, the observed kinetics were not matched (Fig 5C), and the number of CpG sites needed to be increased to 500 before results similar to observed data were achieved (Fig. 5D; FIG. S7G–I). In fact, this is consistent with the very extended potential regulatory regions associated with the Bcl11b gene(Hu et al., 2018; Li et al., 2013). Thus, at the population level, the most proliferative cells generate most of the Bcl11b positive cells, and this population bias towards proliferation of the most advanced cells initially underestimates the resistance to turning on Bcl11b, which is apparent at the single cell level.

Full Multi-scale Model - Predicting Interclonal Kinetic Diversity

We computed the fraction of cells for which the Bcl11b regulatory region reached the open state in 172 simulations starting with one cell proliferating for five days. The model predicted that no cell has the Bcl11b regulatory region open at day 2, while at day 3 roughly 8% are open, increasing to 47% at day 4 and 60% at day 5 (Fig. 5D). Our multi-scale model also predicts that X activity is lost in ~50% of the cells by day 2, and the proportion lacking X gradually increases, reaching >70% by day 5 (Fig. 5D).

The multi-scale model predicted variability in proliferation kinetics among simulated single cell clones (Fig. 5E). The cell count increases over time for all clones. However, the cell numbers at each day of the experiment varied between clones (Fig. 5E). Furthermore, the model predicted that the clones would not turn on Bcl11b and/or lose X activity in a fully synchronized way. Predictions indicated that 10/172 in silico “clones” produced 50% of Bcl11b⁺ cells as early as day 3, with others delaying until day 4, 5 or even later (Fig. 5F). Similar results were obtained from monitoring the proportion of clones reaching 50% of cells without X activity (i.e., 95 of the simulated clones lost X activity at day 2 while 13 turned off X at day 5)(Fig. 5G).

Experimental Results – Validating Data

Clonal Kinetic Analysis of Differentiation from DN1

Finally, the multi-scale model predictions were tested by direct longitudinal imaging of DN1-derived T-lineage clones, through the DN1 to DN2 transition and upregulation of Bcl11b (Fig. 6). Data in Fig. 1 had already shown population level results, but because DN1s divide at different rates, output populations become dominated over time by progeny of the most rapidly proliferating input cells. By direct clonal monitoring, we could determine how well the 3-level model predicted the distribution of behaviors corresponding to our model simulations, starting with single clone founders and including cell divisions, GRN states, and Bcl11b epigenetic dynamics.

Fig. 6. Kinetic analysis of proliferation and differentiation for individual DN1 clones.

A DN1 clonal imaging. Thymic DN1 cells were purified from mice homozygous for mTomato and the nuclear Bcl11b-YFP reporter, added to microwells pre-seeded with OP9-DL1 stroma, and cultured with cytokines IL-7 and Flt3L and CD25-AlexaFluor647 antibodies (marking progression to DN2). Individual microwells with one DN1 cell were imaged daily from day 0 to 6 or 7. B False-color merged images of one DN1 clone for days 0 to 5: mTomato (gray), surface CD25 (magenta), and nuclear Bcl11b-YFP (cyan). Exposures were adjusted to allow visualization of cells in all channels. Scale bar in B represents 100 μm. C Higher magnification merged false-color images of selected cells from two DN1 clones showing the kinetics of CD25 (magenta) and Bcl11b-YFP (cyan) expression. Scale bars in C represent 10 μm. D Combined fractions of cells expressing CD25 and Bcl11b-YFP, alone or together over time. n = 67 (including 62 T-lineage clones, 2 non-T clones, 3 non-clonal wells). E Cell numbers counted from daily images of 62 clonal T-lineage wells. F (Left) Timing of CD25 and Bcl11b-YFP expression scored as days until >50% of cells in individual clones were CD25⁺ (n=62 clones) or Bcl11b-YFP⁺ (n = 58), and the difference in time between the two events for the clones that turned on both markers (n=58). (Right) The difference in cell cycles for individual clones between 50% of cells turning on CD25 and 50% turning on Bcl11b-YFP (n=58). Each symbol represents a single clone. Means and standard deviations are indicated with lines. G The probability of a clone reaching 50% Bcl11b-YFP⁺ on each day predicted by the multi-scale model simulations compared directly to the results obtained from the DN1 clone experimental data. The Kullback-Leibler divergence calculated between them has a very low value, confirming the similarity.

To determine the heterogeneity of DN1 cells and to resolve at a clonal level how consistently Bcl11b activation relates to absolute time or cell cycles, individual thymic DN1s were co-cultured with OP9-DL1 stroma in microwells and microscopically imaged over time(Kueh et al., 2016) (Fig. 6A). The DN1s were purified from thymi of mice with constitutively expressed membrane-(m)Tomato, for cell segmentation and counts, as well as the nuclear Bcl11b-YFP reporter gene, and plated into microwells pre-seeded with OP9-DL1 cells. Microwells verified to start with single live DN1 cells were imaged daily for 6-7 days to determine clonal expansion and onsets of surface CD25 and nuclear Bcl11b-YFP expression for cells within individual clones. Merged false-color images of microwells in mTomato, CD25-AlexaFluor647, and Bcl11b-YFP fluorescence channels over time, are shown in Fig. 6B from one representative clone of 64 clones imaged. Two of 64 DN1 clones generated only non-T cell lineage cells, possibly granulocytes, but the remainder turned on CD25 and most turned on Bcl11b-YFP within 7 days indicating that they were indeed in the T-lineage (Fig. S5). Fluorescence thresholds for determining CD25 and Bcl11b-YFP positivity were calculated using background fluorescence estimates (Fig. S6A). Higher magnification images for cells from two representative clones from days 1-6 (Fig. 6C) show that surface CD25 (magenta) was turned on by day 1-3, with nuclear Bcl11b-YFP⁺ cells (cyan) appearing in some cells by day 4 or 5.

Differentiation dynamics of CD25 and Bcl11b expression for all imaged wells combined are shown in Fig. 6D, demonstrating comparable overall dynamics to bulk DN1 cultures (Fig. 1E), and confirming that CD25 is turned on before Bcl11b. Based on cell counts, individual clones achieved similar proliferation rates in most cases, but with different lag times (Fig. 6E), reflecting heterogeneity within the starting DN1 population, similar to model predictions (Fig. 5E). At early timepoints, cells that remained DN1 had proliferated less than the CD25⁺ DN2s (Fig. S6B), in agreement with CTV data (Fig. 1C).

Wide variability in the timing of CD25 and Bcl11b-YFP expression between clones was observed (Figs. 6F, S5), and CD25 up-regulation was not synchronous for progeny within some clones (Fig. S5), hinting at a stochastic element even in the early transition to DN2. Because of this asynchrony in expression of both CD25 and Bcl11b within clones, CD25 and Bcl11b positivity for each clone was scored as the time at which at least 50% of cells within a clone were CD25⁺ or Bcl11b⁺ (Fig. 6F). These results show that most clones became >50% CD25⁺ at days 1-2, although 22% of clones waited until days 3-5, while clones became ≥50% Bcl11b-YFP⁺ between days 3 and 7, with most doing so on days 4-5 (Fig. 6F, S5).

These clonal data allow us to test the determinism of commitment, whether cells are programmed to turn on Bcl11b after a fixed period of time or fixed number of cell cycles after making the DN1-DN2 transition. Fig. 6F shows the differences observed for individual clones between the times when ≥50% of cells were scored as CD25⁺ and when ≥50% were scored as Bcl11b-YFP⁺, in elapsed time and in estimated cell cycles. The results showed that the intervals between entering the DN2 state (CD25⁺) and commitment (Bcl11b-YFP⁺) were highly variable both in absolute times and in cell cycles, taking from <1 to >5 days and from 1 to 7 cell divisions. Furthermore, Bcl11b-YFP was not turned on synchronously within a clone, generally requiring 2-3 days from expression in the first cells to expression in 100% of the cells (e.g. Figs. 6C, top row, day 4; S5). Thus, daughter cells from individual DN1 cells are not only heterogeneous in their clonal founders’ differentiation states, but also show a large stochastic element in timing of Bcl11b up-regulation even after entering the DN2 state(Ng et al., 2018).

The Bcl11b expression dynamics in these clonal cultures appear to be in close accord with our multi-scale model predictions (Fig. 6F, 5D), so to compare the model predictions directly with the experimental data, in Fig. 6G we show the probability distributions of reaching 50% Bcl11b-YFP⁺ predicted by model simulations with the experimental results (Fig. 5F). These distributions appear to be very similar and the Kullback-Leibler divergence value calculated between them has a very low value of 0.0407 (a value of 0 indicates that the two distributions are identical). Furthermore, rates of CD25 expression gave comparable dynamics to the loss of X activity predicted by the model (Fig. 6D, 5D), suggesting a potential relationship between these parameters.

Thus, DN1 clonal heterogeneity in differentiation potential and stochasticity in the execution of commitment dynamics, as predicted by the three-level model, was validated by the kinetics and the intra-and inter-clonal variation revealed by experimental clonal monitoring.

DISCUSSION

We have developed, explored and validated an integrated computational multi-scale model for early T-cell development and commitment kinetics. Commitment of multipotent precursors to the T-cell fate is particularly accessible for modelling because, at the single-cell level, commitment corresponds to Bcl11b activation. The model explains commitment kinetics in terms of the gene network circuitry controlling Bcl11b expression by incorporating results from both single cell and population-level experiments elucidating the process on different scales. Although the process has a core of classic transcriptional circuitry, the output of the process was recently shown to be substantially modulated by epigenetic resistance to transition (Ng et al., 2018), and, as shown here, by nonuniform cell proliferation as differentiation proceeds. A transcriptional gene network model optimized to ignore these additional factors would necessarily be inaccurate. Thus, after a transcriptional first level, our model has built in a second level of stochastic epigenetic control to predict chromatin opening. Finally, the two-step gene control model is integrated into a cell growth population model to predict how the internal molecular events generate measured population behavior.

The model delivers several validations and predictions using transcriptional and population model parameters set by fitting gene network parameters to experimental RNA expression data and population growth parameters to experimental proliferation data.

• DN1 population developmental heterogeneity can arise solely from GRN noise, although we cannot rule out an additional role for external noise.

• The heterogeneous delay in lineage commitment marked by Bcl11b expression, arises from both GRN and epigenetic variability.

• Effects of knock-down of Tcf7 and Gata3 are substantially different before and after X downregulation, consistent with experimentally observed differences between effects of disrupting these inputs at DN1 and DN2 stages.

• DN1 single clone commitment and proliferation kinetics resulting from GRN, epigenetic, and population dynamics are validated by clonal cell cultures.

• The high Bcl11b epigenetic barrier is partly masked by bulk population growth.

Computational models for epigenetics and GRNs have been proposed in the context of pluripotency acquisition through cell reprogramming (Artyomov et al., 2010; Olariu et al., 2016). Multi-scale modelling approaches, unifying observations from the intra-cellular to cell population scale, have also been used to model heterogeneity and function of mature peripheral T-cells, reviewed in (Carbo et al., 2014). Whereas other hematopoietic stem cell commitment processes have been subject to mathematical model investigations (reviewed in (Olariu and Peterson, 2019)), few attempts have been made for early lymphocyte development (Collombet et al., 2017; Manesso et al., 2016). The choice to use continuous-valued rather than Boolean transcriptional models here has the advantage of avoiding discretizing the data in instances when experimental real-valued gene expression levels are relevant for the problem studied, as in this case. Whereas a Boolean approach could probe larger networks than that modeled here (reviewed in (Olariu and Peterson, 2019)), previous investigations of important regulators of Bcl11b enable us to focus on a few key genes only.

Importantly, our model incorporates the complex molecular mechanisms shown recently to be involved in Bcl11b activation including the four known positive regulators, and the additional, slow epigenetic step that creates a stochastic delay in Bcl11b activation, long after the positive regulators are present. This level of control is probably not unique to Bcl11b regulation but has been demonstrated in particular depth for developmental activation of this gene (Ng et al., 2018). The design of the stochastic epigenetic level of the network is novel, incorporating some features not usually included in GRNs, in order to encompass the known mechanisms involved. Published experimental measurements indicate that a default repressive chromatin state is probably a major contributor to the stochastic timing of activation, with a delay from the activation of one allele to the other - a measure of noise in time to relieve an epigenetic barrier - on the order of days (Ng et al., 2018). We designed this negative function (X) to oppose the stepwise chromatin opening that is a prerequisite for Bcl11b activation. This strongly affects the predicted developmental timing control in the model as it does in experimental observation. For parsimony, we have proposed an architecture in which the positive regulators in the first transcriptional layer of the model work toward down-regulating X, leaving the second stochastic layer to determine when Bcl11b will respond by activation. In the complete three-layer implementation of the model, the predicted kinetics of X downregulation in individual clones match well with the observed kinetics of DN1 to DN2 developmental progression before Bcl11b activation in individual clones, as detected by the cell surface marker CD25. Similar timing of X downregulation and DN1 to DN2 progression would also fit the distinct effects of Tcf7 or Gata3 knockdown before and after X downregulation (in silico) and before and after DN1 to DN2 transition (in vitro), thus explaining the experimental observation that Bcl11b is activated only after DN1 to DN2 progression, despite the presence of all its positive regulators in DN1 stage.

In this model X is a composite function, not a single undefined regulatory gene. As Bcl11b starts out in an epigenetically silent state inherited from hematopoietic stem cells, X measures the resistance to the opening of relevant cis-regulatory elements at each allele of the locus. In the stochastic level of the model, we have taken the balance of Notch signals and Runx1 against decreasing X to drive a stepwise epigenetic opening process that we have modelled analogously to the removal of methylated CpGs. While demethylation may be part of this process, the use of this formalism is more abstract here and indicates the stochastic but neighbor-biased and progressive nature that is shared by demethylation with other epigenetic opening processes.

In different DN1 clones progressing toward T-cell commitment, the timing of CD25 expression (DN1 to DN2 transition, approximating X downregulation) is quite heterogeneous, confirming DN1 cell heterogeneity(Manesso et al., 2013; Yui and Rothenberg, 2014). If this were reflecting a pipeline of distinct developmental substages within DN1, then the cells might actually be starting with different initial regulatory states. However, stochastic simulations of the GRN controlling the first steps in T-cell commitment show that the switch towards a state with low X-levels does not occur in a synchronized manner between model simulations with identical initial conditions. This suggests that GRN intrinsic noise could be another source of heterogeneity in timing of the loss of X. The explicitly stochastic basis of progressive locus opening that follows X downregulation, in the epigenetic level of the model, is further supported by the high variability of Bcl11b activation timing in different clones even after they transition to DN2.

The very similar results obtained from the single cell model and clonal cell cultures suggest a high level of heterogeneity in critical GRN components during the DN1 to DN2 stages. The experimental and model population kinetics show an additional level of proliferative heterogeneity between these stages that is apparent at the single cell level, but much less apparent in bulk populations. The general increase in proliferation rate as cells transition to DN2 not only biases population phenotypes to favor the fastest-differentiating clones, but also might feed-back on the network by dilution of inherited proteins affecting the potential speed of epigenetic changes (Haerter et al., 2014; Kueh et al., 2013). The need to invoke a Bcl11b-regulating function, X, in the GRN and epigenetic models, to achieve proper model behavior, calls for identifying critical cis-as well as trans-acting GRN elements. Work to identify these factors, is currently underway.

In summary, this new model, that integrates three distinct types of mechanistic control, provides a quantitative understanding of commitment kinetic requirements of early T-cell precursors and a valuable in si/ico tool to help investigate new regulatory factors and processes and their roles in lineage commitment.

STAR METHODS

RESOURCE AVAILABILITY

Lead Contact

Further information and requests for algorithms and code should be directed to and will be fulfilled by the Lead Contact Carsten Peterson (carsten@thep.lu.se).

Materials Availability

Requests for animals, experimental resources and reagents should be directed to and will be fulfilled by the Corresponding Author for the experimental work, Ellen V. Rothenberg (evroth@its.caltech.edu). All genotypes of mice used in this study were crossed from strains available from Jackson Laboratories, or from strains reported previously by the Rothenberg lab (Kueh et al., 2016), which are available upon reasonable request from Dr. Rothenberg with a minimal standard MTA. Cell lines generated in this study were derived from OP9-DL1 stock originally provided by J. C. Zúñiga-Pflücker, Sunnybrook Research Institute, University of Toronto. They are available on request with an MTA from Dr. Rothenberg and an MTA from Dr. Zúñiga-Pflücker.

Data and Code Availability

All mathematical models were coded in Matlab version 9..3.0.713579 R (2017b), The Mathworks, Inc. Available at https://www.mathworks.com and in Python – Python Software Foundation. Python Language Reference, version 2.7. Available at http://www.python.org. The ordinary differential equations were solved using Runge-Kutta methods encoded both in Python (SciPy: Open source scientific tools for Python. Available at https://www.scipy.org) and Matlab (ode45 function). The stochastic simulations were done using the Gillespie algorithm implemented from scratch. All model implementations was done from scratch and the code is available upon request from the corresponding author.

The clustering algorithm we used is from Scikit-learn: Machine Learning in Python available at https://scikit-learn.org/stable/

The limited memory algorithm for bound constrained optimization L-BFGS-B is available at https://docs.scipy.org/doc/scipy/reference/optimize.minimize-lbfgsb.html

EXPERIMENTAL MODEL AND SUBJECT DETAILS

Animals

Mice of a variety of genotypes were used exclusively as sources of primary cells to be analyzed ex vivo in these studies. C57BL/6J, B6.Bcl11b^yfp/yfp (Bcl11btm1.1Evr) reporter mice (Kueh et al., 2016), and B6.129(Cg)-Gt(ROSA)26Sor^{{tm4(ACTB-tdTomato,-EGFP)}/J mice expressing ubiquitous membrane Tomato (Jackson Laboratory) were bred, crossed, and maintained in the Caltech Lab Animal Resources Facility under specific pathogen-free conditions in accordance with protocols reviewed and approved by the Animal Care and Use Committee at California Institute of Technology.

C57BL/6J (B6) mice (bred from stock originally from Jackson Laboratories) were used for multiplex single-molecule FISH. B6Bcl11tb^yfp/yfp reporter (Kueh et al., 2016) mice were used to track the kinetics of Bcl11b upregulation in vitro in bulk studies shown in Fig. 1. B6.ROSA26-mTom;Bcl11b-YFP mice for clonal imaging analysis were generated by crossing and backcrossing B6.129(Cg)-Gt(ROSA)26Sor^{tm4(ACTB-tdTomato,-EGFP)Luo}/J mice, which express ubiquitous membrane Tomato (Jackson Laboratories), with the B6.Bcl11b^yfp/yfp reporter mice until both loci were homozygous. These animals were then used for clonal imaging analyses. Note that the Bcl11b^yfp allele is a nondisruptive insertion of an internal ribosome entry site (IRES)-mCitrine (YFP) reporter into the 3’ untranslated region of the last Bcl11b exon, which allows fully normal expression of the Bcl11b protein from the same allele.

All adult animals used were mice between 4 and 8 weeks of age, and all experiments were performed with samples consisting of cells pooled from multiple age- and sex-matched animals. Animals used for these experiments were bred and maintained at the Animal Facilities at California Institute of Technology under conventional Specific Pathogen-Free conditions, and animal protocols were reviewed and approved by the Institute Animal Care and Use Committee of the California Institute of Technology (Protocol #1445-18G). To maximize both thymus population sizes and fertility of the mice in the colony, care was taken to protect these animals from stress throughout their lifetimes to the greatest extent possible.

Cell lines

To provide a microenvironment that supports T-lineage differentiation in vitro, we co-cultivated primary cells with the OP9-DL1 stromal cell line (Schmitt and Zúñiga-Pflücker, 2002), which were obtained from Dr. Zúñiga-Pflücker (Sunnybrook Research Institute, University of Toronto) and maintained in our laboratory as described in the original reference. Details of the differentiation cultures vary with individual experimental designs, and are given below under Method Details.

METHOD DETAILS

DN thymocyte purification

Single cell suspensions were made from thymuses from 4-6-week-old mice. Thymuses were removed, passed through sterile metal meshes and collected in 1X Hanks Balanced Salt Solution supplemented with 0.5 % fraction V bovine serum albumin, 10mM Hepes buffer (Gibco), 5mM MgCl₂, and DNAseI. After pelleting, the cells were resuspended in a cocktail of biotinylated antibodies to deplete unwanted cells: CD8α (53-6.7), TCRγδ (GL3), TCRβ (572597), Gr1 (R86.8C5), Ter119 (Ter119), NK1.1 (PK136), CD11b, and CD11c (N418), after which the cells were incubated with streptavidin-coated magnetic beads and then passed through a magnetic column (Miltenyi Biotec). The eluted DN cells were either used directly for RNA-FISH analysis or further purified by staining with fluorescent antibodies to CD44, Kit, CD25 and then sorting on a BD Biosciences FACSAria or FACSAriaFusion or a Sony SY3200 Cell Sorter in the Caltech Flow Cytometry Facility. For bulk cultures or clonal imaging, DN1 cells were sorted as CD44high Kit^high CD25-negative Bcl11b-YFP-negative cells. Note that for simplicity, throughout this paper, we use “DN1” to refer to the Kit^high subset of CD44⁺ CD25⁺ cells that contains the T-cell precursor function, also known as ETP.

Single Molecule Multiplex Fluorescent in situ Hybridization (sm-FISH)

Probe design and synthesis

The gene-specific primary probes for each gene tested were designed as previously described(Shah et al., 2016), with some modifications: each probe comprised a mRNA-complementary 35-mer sequence plus a shorter “gene handle” sequence that was shared by all probes against the same gene. All probes were blasted against the mouse transcriptome and expected copy numbers of off-target probe hits were calculated using predicted RNA counts in the ENCODE database for murine thymocytes. BLAST hits on any sequences other than the target gene with a 15-nt match were considered off-target hits. Any probe that hit an expected total off-target copy number exceeding 500 in count table was dropped. Probes were sequentially dropped from genes until any off-target gene was hit by no more than 6 probes from the entire pool. At this stage, all of the “viable” candidate probes for each gene had been identified. For the final probe set (Table S6), the best possible subset from the viable probes for each gene was selected such that none of the final probes used were within 2-nt bases of each other on the target mRNA sequence, with no-overlapping hybridization regions and GC-content close to 55%. Primary probes were synthesized and amplified from array-synthesized oligo-pool as previously described(Shah et al., 2016). The readout oligos against specific gene handles on primary probes were ordered from IDT (Integrated DNA Technologies, Coralville, Iowa) with 5’-amino modification and were coupled with NHS (N-hydroxysuccinimide)-ester labelled fluorescent dyes (Alexa 488, 594, 647 (Thermo Fisher Scientific) and Cy3B (GE Healthcare)) and purified through HPLC.

smFISH experiment and image acquisition

First, the isolated cells were spun onto an aminosilane modified coverslip, crosslinked with 4 % Formaldehyde (ThermoScientific 28908) in 1X PBS for 10min, and permeabilized in 70 % EtOH overnight at 4C. Samples were imaged first to record the surface antibody signals, followed by briefly bleaching away antibody signals through incubation in 0.1 % NaBH₄ (Sigma 452882) in 1XPBS for 10 min. Then, the samples were 1) hybridised overnight at 37° C with primary mRNA probes at 1 nM each oligo concentration in 50% Hybridization Buffer (50% HB: 2X SSC (saline sodium citrate, Invitrogen 15557-036), 50% (v/v) Formamide (Ambion AM9344), 10 % Dextran Sulfate (Sigma D8906) in Ultrapure water (Invitrogen 10977-015)); then 2) washed in 50 % Wash Buffer [2X SSC, 50 % (v/v) Formamide, 0.1 % Triton-X 100 (Sigma X-100)] for 20 minutes, followed by incubation in 2X SSC for 10 minutes. The samples were then 3) incubated with fluorophore-coupled readout oligos, in 30 % Hybridization buffer (30% HB: 2X SSC, 30% (v/v) Formaldehyde, 10% Dextran Sulfate in Ultrapure water) at concentrations of 10 nM each oligonucleotide for 30 minutes; this was followed by 4) 5 minutes wash in 30 % Wash Buffer (2X SSC, 30 % Formamide (v/v), 0.1 % Triton-X 100 (Sigma X-100)), 3 minute wash in 2X SSC and DAPI staining. We then 5) proceeded to imaging of this round of hybridization as described below. After image acquisition, 6) the samples were incubated with 70% formamide with 1x PBS at room temperature for 30 minutes, followed by 3 rounds of washing in 1x PBS for 5 minutes each round. The procedures 3)-6) were then repeated with a set of gene-specific readout oligos until the completion of measurements of all genes of interest, as illustrated in Fig. 2A.

Samples were imaged in an anti-bleaching buffer (20 mM Tris-HCl, 50 mM NaCl, 0.8 % glucose, saturated Trolox (Acros Organics 218940050), pyranose oxidase (OD405 = 0.05) (Sigma P4234), and catalase at a dilution of 1/1000 (Sigma C3155)) with the microscope (Olympus IX81) equipped with a confocal scanner unit (Yokogawa CSU-W1), a CCD camera (Andor iKon-M 934), 100x oil objective lens (Olympus NA 1.4), and a motorised stage (ASI MS2000). Lasers from CNI and filter sets from Semrock were used. Snapshots were acquired with 0.5 μm z steps for more than 10 positions per sample.

The cells were segmented and categorised according to surface antibodies, and dots representing individual mRNA molecules were assigned to individual cells as shown in Fig. 2B.

Bulk cell cultures

For experiments on developmental kinetics DN1 cells were cultured on OP9-DL1 stromal cells as previously described (Kueh et al., 2016; Yui et al., 2010) in αMEM medium supplemented with L-glutamine, penicillin, streptomycin (OP9 culture medium) and IL-7 (5 ng/ml) and Flt3L (10 ng/ml). For tracking proliferation in bulk cultures, FACS purified DN1 cells were stained in 5 μM Cell Trace Violet (Molecular Probes) for 7 minutes at 37°C in HBSS and washed 2X with whole medium before being plated in 96-well OP9-DL1 cocultures. Cells were incubated at 37°C 7% CO₂, harvested on days 2, 3, 4, and 5 by vigorous pipetting, and evaluated for developmental status by staining with antibodies, CD25 and Kit for development and CD45 to separate developing cells from stroma, plus a viability dye, 7AAD. The cells were then analyzed for expression of these markers plus Bcl11b-YFP using a Miltenyi MACSQUANT flow cytometer. Analysis was carried out using FlowJo software (Treestar). CTV measurements of cell division histories were calibrated using total DN (DN1—4) cultures on OP9-DL1 stroma (Fig. S1).

Clonal Image Analysis

Specialty biological inputs

To follow the kinetics of development and proliferation in individual DN1-derived clones by microscopic imaging, several technical problems had to be solved. First, to allow for accurate identification and segmentation of developing cells of varying shapes and sizes on a background layer of OP9-DL1 stroma, we needed to use cells purified from B6.R26m^mTom/mTom Bcl11b^yfp/yfp J mice expressing ubiquitous membrane Tomato (Jackson Laboratory) as well as an mCitrine yellow fluorescent reporter for Bcl11b expression, as described above. For imaging, we used animals in which both fluorescent reporter loci were homozygous (B6.ROSA26-mTom;Bcl11b-YFP mice).

To enable the use of the Bcl11b-YFP reporter for imaging the commitment status of individual T-cell precursors developing on an OP9-DL1 stromal layer, GFP had to be removed from the original OP9-DL1 stromal cells to reduce spectral interference (Schmitt and Zúñiga-Pflücker, 2002). To do this, we designed guide RNAs targeting GFP and electroporated them along with a CRISPR puromycin plasmid v2.0 (Plasmid # 62988, Addgene) into OP9-DL1-GFP cells using the Lonza Nucleofector Kit. After puromycin selection, different clones were analyzed for GFP expression and one clone found to be completely negative for GFP (OP9-DL1-delGFP1) which was selected for use in imaging.

Imaging culture conditions

Developing T-cells are extremely active in motility, so individual DN1 cells had to be confined in wells for imaging. We used a protocol similar to our previous experiments with DN2 cells (Kueh et al., 2016), but we found that the background of the clear wells was too high in the fluorescence channels used in these experiments, so black microwells were substituted. Black 8mm circular poly (dimethyl siloxane) PDMS micromeshes with over 150 microwells punched/micromesh, each approximately 250_μM wide × 100 μM deep, were custom fabricated by Microsurfaces (Australia). One day before the start of co-culture and imaging these micro meshes were adhered to each of 2-4 (macro)wells of a 24-well glass-bottom plate (P24G-1.0-13-F) (MatTek, Ashland, CA), sterilized with ethanol, and washed in accordance with manufacturer’s instructions, and then seeded with 5,000 OP9-DL1-delGFP stromal cells. Cultures were carried out in OP9 culture medium prepared as previously described except for the omission of pH indicator, phenol red, from the medium, which gives background fluorescence, and with the addition of 10mM Hepes buffer to stabilize the pH of the wells during imaging. On the first day of culture the following were added to the medium: 10 ng/ml Flt3L, 5 ng/ml IL-7, and 0.05 μg/ml anti-CD25-AlexaFluor647 antibody (BioLegend) for detection of CD25 surface expression. DN cells were isolated from B6.ROSA26-mTom/Bcl11b-YFP mice and DN1 cells were FACS-purified as described above. 1,500 sorted DN1 cells were added to each well of the 24-well plate which had the microwells pre-seeded with OP9-DL1-delGFP. The cells were allowed to recover for at least one-hour at 37C, 7% CO₂, before transfer to the fluorescence microscope.

Imaging data collection

Imaging was carried out with a Leica 6000 wide-field fluorescence microscope with Metamorph software and an incubation chamber pre-set to 37C, 7 % CO₂. Each microwell was briefly checked using the 40X objective, which allowed imaging of one entire microwell, for mTomato-positive cells. Microwells with 1 or 2 cells had their X-Y stage positions marked. All marked microwells were imaged daily using differential interference contrast (DIC) and three fluorescence channels: 504 excitation-542 filter for YFP, 560-607 for mTomato, and 650-684 for CD25-AlexaFluor647. Wells found to have one mTomato positive cell on either day 1 or 2 and cells present throughout the culture period were selected to further analysis. mTomato-positive cells were segmented and analyzed using Fiji (ImageJ) and by hand to obtain cell area and CD25 and Bcl11b-YFP fluorescence data. For each cell, total fluorescence was calculated by multiplying mean fluorescence by area. Because microwells became quite crowded by late time points (days 6-7), and cell clumps were very difficult to segment, all cells were counted but only a subset of the distinguishable cells were segmented and sampled to obtain fluorescence data for the well. Fifty background fluorescence sample cells were taken and the mean total fluorescence for CD25 and Bcl11b-YFP plus 3 standard deviations was used to set the thresholds for determination of positive vs. negative cells (Fig. S6).

Modelling: Pseudo-time series

From the single cell FISH data, pseudo-time-series were created by clustering the data and ordering the clusters, assuming that the cells measured are in states distributed over the whole-time intervals of both stages DN1 and DN2. The data points were first classified into clusters with a Gaussian-Mixture algorithm (Pedregosa et al., 2011), assuming that they follow several Gaussian distributions with individual parameters. Moreover, the number of data points in each cluster should be similar in order to regard all data with the same significance. The mean expression and standard deviation of all data points in a cluster were then computed for each gene and used to arrange the clusters in time. The cluster order was set by the fact that both Tcf7 and Bcl11b expression levels are known to increase during cell commitment (Tydell et al., 2007; Zhou et al., 2010). We considered the relative values of gene expression levels with respect to the maximum level at each stage to prohibit Tcf7 from dictating the order of the clusters alone, since its absolute expression is higher than Bcl11b expression. For each cluster, expression values of Tcf7 and Bcl11b were added. Finally, the clusters were ordered such that this sum is increasing and placed equidistantly on an arbitrary time axis.

Single Cell Model: Transcription factor Level

For the circuit in Fig. 4A we obtained the following set of rate equations from a thermodynamic approach(Ackers et al., 1982). The equations describe the dynamics of T-cell specific genes Tcf7, Gata3 and Runx1 along with gene opposing the T-cell fate PU.1 and X function, with concentration levels denoted as: [T], [G], [R], [P] and [X]. The Notch signaling activity is denoted as N.

$$\frac{\partial \left[R\right]}{\partial t}=\frac{p_1\left[R\right]+p_{2}N}{1+p_1\left[R\right]+p_{2}N}-{\gamma }_R\left[R\right]$$

$$\frac{\partial \left[T\right]}{\partial t}=\frac{p_3\left[T\right]+p_4\left[G\right]+\frac{p_{5}N}{p_6+\left[P\right]}}{1+p_3\left[T\right]+p_4\left[G\right]+p_{5}N+p_7\left[P\right]}-{\gamma }_T\left[T\right]$$

$$\frac{\partial \left[G\right]}{\partial t}=\frac{p_8\left[T\right]+\frac{p_{9}N}{p_{10}+\left[P\right]}}{1+p_8\left[T\right]+p_{9}N+p_{11}\left[P\right]}-{\gamma }_G\left[G\right]$$

$$\frac{\partial \left[P\right]}{\partial t}=\frac{p_{12}\left[P\right]}{1+p_{12}\left[P\right]+p_{13}\left[R\right]\left[G\right]\left[T\right]}-{\gamma }_P\left[P\right]$$

$$\frac{\partial \left[X\right]}{\partial t}=\frac{1}{1+p_{14}\left[T\right]+p_{15}\left[G\right]}-{\gamma }_X\left[X\right]$$

$$\frac{\partial N}{\partial t}=\frac{p_{16}}{1+N}$$

We considered that repression of PU.1 by the T-cell specific factors follows AND logic i.e. Runx1, Tcf7 and Gata3 all need to be present for active repression of PU.1. This accounts for the experimentally observed increases in PU.1 expression upon deletion or downregulation of any one of these regulators (see Table 1 for references). We modelled the Notch activity such that the N levels increase throughout the simulations, however, parameter p₁₆ values were chosen to be very low to assure only a slight increase of the Notch activity, avoiding a jump to infinity. PU.1 limits the up-regulation of Tcf7 and Gata3 by Notch signaling. This was modelled by dividing the Notch activation term, in the nominator of the rate equations of Tcf7 and Gata3, by a linear term including PU.1 expression level. The rest of interactions in the model follow a standard Shea-Ackers formalism implementation. The parameters p_i with i=1:15 except p₆, p₁₀, which are part of implementation of PU.1 impeding the Notch positive regulation of Tcf7 and Gata3, correspond to binding affinities, while γ parameters model the decay rates linked to the half-lives of the respective molecules. The parameter values (Table S1) were chosen such as the resulting expression levels dynamics for all the genes in the network are within the range levels of genes expression observed in the single cell FISH experiments (Fig. S2). It should be noted that parameters p₁₄ and p₁₅ were estimated from FISH expression data of candidate genes for X function. The model parameters were optimized (see details below) from the pseudo-time-series data using simulated annealing, genetic algorithms and a bound constrained optimization algorithm (L-BFGS-B)(Byrd et al., 1995). From optimization solutions (Raue et al., 2013) we picked one that with minor adjustment including rounding accommodated the DN1 to DN2 transition shown by RNA-FISH measurements (Fig. 2C). The determined parameters exhibit robustness, see below. .

Single Cell Model: Parameter Optimization Details

The cost function of the model parameter set p measuring the squared difference between the pseudo-time-series data D and model simulated concentration values of the genes in the network, all grouped under variable M has the following expression:

$$S\left(p\right)={\sum _k\sum _{i=1}^n\left(D_{k,j}-M_{k,j}\left(p\right)\right)}^{2}wherek=\left[R\right],\left[T\right],\left[G\right],\left[P\right]$$

n is the number of data points for each gene in the pseudo-time-series data, genes Tcf7, Gata3 and Runx1 along with gene opposing the T-cell fate PU.1, concentration levels were denoted as: [T], [G], [R], [P].

S(p), or rather its -log likelihood counterpart, was minimized with respect to the model parameters when we used the bound constrained optimization algorithm (LBFGS-B)(Byrd et al., 1995). This was done 100 times with different initializations from the parameter space by Latin Hypercube sampling (Raue et al., 2013) with most solutions having similar levels for the cost function value. From the optimization outcomes we picked a solution, denoted preferred, that respected the experimentally observed transition from DN1 to DN2 (Fig. 2C). The picked solution was used as input further in the work, even though it had somewhat higher cost function value compared to other solutions (Fig. S7C). The rounded values of optimized parameters are shown in Table S1. The set of parameters that we picked (agreeing both with pseudo-time-series data and experimentally observed DN1 to DN2 transition in Fig. 2C) has most of the values within the distribution of the values of parameters obtained from 100 optimization runs (Fig. S7D). We also estimated the model prediction bounds using methods inspired from the Matlab Curve Fitting Toolbox functions. We found that, for the set of parameters that we used throughout this work, the model prediction bounds are within the experimental data levels, see Fig. S2. The prediction bounds for many of the other parameter sets either diverged or vanished. In order to compare properties among parameter sets that yielded different types of prediction bounds, we manually categorized the prediction bounds depending on their behavior. Fig. S7E shows the distribution of the sums of the absolute values of the components of the Jacobian, from which the prediction bounds are calculated, for each category. The preferred parameter set ends up in the ‘OK’ prediction bounds cluster. There is also a clear separation between the three main cases. Fig. S7F shows the component of the Jacobian that corresponds to each parameter, plotted against the parameter value. The preferred parameter set clearly lies close to zero in most cases. One should keep in mind that the fitting is not performed on original data but rather on pseudo time series. These originate from clustering procedures and do not yield unique results -- “horizontal” errors from the time ordering are hard to estimate.

Robustness Analysis

We also performed robustness analysis by calculating the robustness indexes given by

$$R_p^M=\frac{\delta M\left(x\right)/M\left(x\right)}{\delta p/p}$$

where p are the varied parameters, δp is the change in p, i.e. increased/decreased by 1%, 2%, 5% and 10% of its value, M(x) is the model output with unperturbed parameters with x representing the gene expression levels and δM(x) is the change of M(x) due to change δp in p. In Fig. S7B robustness coefficients are shown when all model parameters simultaneously are varied with 1%, 2%, 5% and 10% respectively. The robustness coefficients are lower than the perturbation level, increasing with the level of perturbation, leading to the conclusion that the model is robust.

The deterministic and stochastic simulation results presented in Figs. 4, 5, S2, S4 were obtained using the parameter values shown in Tables S1, S2, S4, S5. Among the parameters, the decay rates are given in real units, whereas the other parameters cannot be tied with experimental numbers as there are overall implicit constants multiplying the ratios appearing on the right-hand side of the rate equations.

It should be noted that we consider the starting state of the system to correspond to an uncommitted early progenitor cell with high expression levels of PU.1 and X activity along with Runx1 being expressed and low expression levels of Tcf7, Gata3. In actual DN1-DN2a stage cells, note that several other progenitor-specific transcription factors in addition to PU.1 are still expressed until commitment, but the network connections of these factors to Tcf7, Gata3, Runx1 and Notch signaling have not yet been studied in depth (Yui and Rothenberg, 2014). Thus, it is possible that PU.1 is not the only factor involved in antagonizing GATA3, Tcf7 and Notch, and further work should define better the roles of other genes in this initial period.

Single Cell Model: Epigenetic Level

We implemented a simplified computational model for Bcl11b regulatory system transition from chromatin closed to open state. The epigenetic level model is linked to the transcription level model through the fact that the expression of Runx1 and X and level of activity of Notch signaling (outputs of transcription level model) serve as inputs to the Bcl11b regulatory system model. We consider that Runx1 along with Notch signaling activity push towards an open Bcl11b regulatory system state thus the probability of achieving this state is direct proportional to Runx1 and Notch levels. X activity is considered to help maintain a closed state of the Bcl11b regulatory system, dictating the probability of the regulatory region to be closed. We initially put forward a very simplified model in which we considered the size of the Bcl11b regulatory system to have a finite low number of CpG sites i.e. 20. This was chosen to make sure that the simulations were very fast, but that we considered enough CpG sites so that the transitions between the opened and closed states are not instant and not completely controlled by noise. The amount of existing CpG sites in one of the states influences negatively the amount of CpG sites in the other state, because of the finite total number of CpG sites. We conducted a stochastic implementation of the simplified model for epigenetic state evolution of Bcl11b regulatory region governed by thefollowing master equation:

$$\frac{\partial B_{open}}{\partial t}=p_{17}R+p_{18}N-p_{19}{B}_{closed}$$

$$\frac{\partial B_{closed}}{\partial t}=p_{20}X-p_{21}{B}_{open}$$

where N denotes Notch signaling activity, R represents the expression level of Runx1 and X is the X activity level. The model parameter values are shown in Table S2.

The initial conditions for stochastic simulations of the epigenetic level model consider the Bcl11b regulatory system to be in closed state i.e. the number of closed CpG sites is greater than the number of sites considered to be open. In some simulations the Bcl11b regulatory system becomes open i.e. the number of opened CpG sites becomes and remains greater than the number of closed CpG sites during simulation time.

Multi-scale model of proliferation and gene expression

Multi-scale Model: Population Level

To analyze the effects of cell proliferation on the population scale gene expression we devised a model in which we can track the gene expression and division history of each individual cell. The model is an extension of in house developed framework, written in C++ and used previously in the context of cell-based simulations (Krupinski et al., 2012). We have implemented mechanical interactions between cells for the sole purpose of displaying the evolution of cells in a simple way. Each cell in the model contains a copy of a gene network presented in Single Cell Model (both transcription and epigenetic levels) and evolves its gene expression levels independently from other cells by a stochastic Gillespie simulation(Gillespie, 1977). Cell cycle length for each cell is also a stochastic variable and chosen from a normal distribution. The cell divisions are assumed to be symmetric such that the daughter cells inherit the mother cell content, but then evolve independently. Since we assume that the presented network describes transition from DN1 to DN2a cell state in the multi-cell simulations we turn on the network in its initial state between day 1 and day 2 while the start of the simulation at day 0 corresponds to introduction of a single DN1 clone to the well.

We constructed a unified model of cell proliferation consistent with the data by assuming that the cell cycle length is a function of the cell generation. The parameters of the cell cycle length normal distributions were chosen independently for each cell based on its generation and fitted globally to the CTV data in Table S4.

Population Model - Details

In order to take population dynamics into account in a multi-level model, we developed population models with parameters extracted from the CTV data. As CTV staining intensity provides information about the number of divisions that an individual cell has gone through, it allows us to build generation profiles for each of the assessed cell type groups (DN1 and DN2a) and at different time points of measurements. These profiles exhibit dispersion of the generation distributions in time.

A simplified model.

To assess if this dispersion can be explained by proliferation, which is uniform for all generations, we first developed a population proliferation model in which the division rate of a cell does not depend on its generation.

A three-parameter model was employed that gave the best fit of the predicted to measured cell numbers with the substantial different average relative error at the points of measurement. The prediction of DN1 cell numbers differed on average from experimental values by 16.9% at day 2 and by 5.3% at day 3 (Table S3). At day 2 in both groups of cells we observed a large proportion (above 50%) of the cell population not dividing between measurements. At day 3 this proportion was lowered to about 20%, with most of the cells (around 50%) having divided twice. This demonstrates that the cells after sorting and seeding into the cell plate culture experienced an initial slowdown in proliferation rate to a value smaller than 1/24h but recovering to the rate of about 1/12h at later times.

The results of this simple population model of cell proliferation suggest that the dispersion of the cell proportions among different generations is not uniform either between different cell types (DN1 or DN2a) or for different measurement time points (day 2, day 3) within the same cell group.

In order to estimate the cell cycle lengths in a population of immature thymocytes as they progress through their development, we first devised a simple population model of cell division fitted to experimental CTV data. This “null model” assumes that a cell can divide between measurement time points from 0 to 3 times. This assumption matches our observations from confocal imagining of the cell cultures. The proportions of the cells in the population undergoing 1 to 3 divisions are denoted a, b and c respectively. These parameters have to satisfy the relation a+b+c < 1. The proportion of cells not dividing between measurements points is given by 1-a-b-c, which exhausts all the cases considered in the model. We also hypothesize in this “null model” that these proportions are uniform through all the cell generations in the population. Correctness of this working hypothesis will be assessed from the results of the model. This means that number of cells in generation $G_i^{n+1}$ at time t_n+1 is given in terms of generations at previous time t_n by

$$G_i^{n+1}=\left(1-a-b-c\right)G_i^n+2a{G}_{i-1}^n+4b{G}_{i-2}^n+8c{G}_{i-3}^n$$

Measuring the goodness of the fit to CTV data is given by the relative error (Table S3).

This demonstrates that the cells after seeding into the cell plate culture experience initial slowdown in proliferation rate to a value smaller than 1/24h recovering the rate of about 1/12h at later times.

The results and the outputs of this population “null model” of cell proliferation suggest that the dispersion of the cell proportions among different generations is not uniform either between different cell types (DN1 or DN2a) or for different measurement time points (day 2, day 3) within the same cell group.

The CTV data provides complete untruncated distributions of generations 0 to 6 for two groups of cells (DN1 and DN2a cells) for days 2, 3 and 4. This allows us to predict with the model distributions at day 3 given data at day 2 and to predict distributions at day 4 given data at day 3. Comparison of these predictions to the actual data gives us best fit parameters of population level cell proliferation at given time point (Table S4). In this way the dispersion of cell proportions among different generations can be included. These parameters were found by global minimization of the normalized mean error measure between predicted and measured cell numbers in generations.

Multiscale Model: Epigenetic Level

In order to take into account the effect of cell division on the amounts of epigenetic factors inside a cell, we implemented a Bcl11b regulation region epigenetic model where the regulatory system can be open, close or at an intermediate state corresponding, in a CpG site methylation model, to the methylated, unmethylated and hemi-methylated states (Fig. S7G). This type of collaborative model was proposed in(Haerter et al., 2014; Olariu et al., 2016) and used here to simulate the opening and closing of the Bcl11b regulation region. In the model the CpG sites can be methylated (M) -- closed state, hemi-methylated (H) -- intermediate state or unmethylated (U) -- open state. Transition rate constants depend on the level of X activity, expression level of Runx1 as well as Notch signaling activity. The arrows labelled with α to ε indicate reactions that require a mediator nearby (e.g. the α arrow defines a transition from U to H in the presence of a mediator in state M).

The collaborative model is described be the following set of equations:

$$\frac{\partial U}{\partial t}=\left(k_{2}N+k_3\left[R\right]\right)H-k_1\left[X\right]U+HU-UM$$

$$\frac{\partial H}{\partial t}=k_1\left[X\right]U+\left(k_{2}N+k_3\left[R\right]\right)M-\left(k_1\left[X\right]+k_{2}N+k_3\left[R\right]\right)H+UM+MU-HU-HM-HH$$

$$\frac{\partial M}{\partial t}=k_1\left[X\right]H-\left(k_{2}N+k_3\left[R\right]\right)M+HM+HH-MU$$

The parameter values are shown in Table S5.

When we simulate division in the multi-scale model, two new Gillespie simulations are started. In the absence of X, and in response to Runx1 (R) and Notch signals (N), the states of the mother cell Bcl11b regulatory region CpG sites are transferred to the daughters following the rule: M -> H, H -> 50% H + 50% U, U -> U (Haerter et al., 2014). It should be noted that when the collaborative model was used, the Bcl11b regulatory system had to be of a size of minimum 500 CpG sites, Fig. S7H,I. The results shown in Fig. 5D were obtained only if the regulatory region of Bcl11b went through epigenetic events corresponding to demethylation of at least 500 CpG sites. Note that the real Bcl11b gene includes multiple methylated CpG islands in the gene body and also possesses extended enhancers spread over more than 850 million bp of DNA (Fig. S3)(Hu et al., 2018; Li et al., 2013), so this constraint is quite likely to be biologically meaningful.

Multi-scale Model: Parameters Collaborative Epigenetic Model

Since the previously presented “simple” population based model assumed cell cycle lengths independent from cell generations and required different parameter sets for each data time point, we wanted to see if now we can construct unified model of cell proliferation consistent with the data by assuming that the cell cycle length is a function of the cell generation. As such, the parameters of the cell cycle length normal distributions were chosen independently for each cell based on its generation and fitted globally to the CTV data in Table S4. In order to take into account, the effect of cell division on the amounts of epigenetic factors inside a cell, we implemented a Bcl11b regulation region collaborative epigenetic model Fig. S7G with parameters shown in Table S5.

We considered the number of CpG sites of Bcl11b regulatory region to be also a model parameter and identified that at least 500 CpG sites have to be considered for the collaborative model. This result originates from analyzing the impact of noise when the number of CpG sites were varied (Supplementary Fig. S7H). For low number of CpG sites the noise has a larger impact. Therefore, we conclude that a minimal number of 500 CpG sites is required for observing a stable switch. We observed larger fluctuations at the steady states for a low number of CpG sites (see error bars Fig S7I) and also that the fraction of unmethylated sites in steady state decreases with higher CpG number. These results are not strongly affected by our choice of parameter values for the DNA methylation collaborative model (see Fig. S7G).

This result is in good agreement with experimental findings in Fig. S3 showing that the Bcl11b regulatory region includes >30 stage-specifically opening elements spread over >1 Mb of gene desert, many of which loop to the promoter once Bcl11b is activated. Not shown, over 30 of them bind Runx1 and multiple elements bind GATA3, Notch/RBPJ, and/or TCF1, although this can be seen from genome browser analysis of published datasets. Only the elements in the vicinity of the “Major Peak” enhancer (magenta highlight, Fig. S3) have been functionally analyzed so far (Ng et al., 2018; Isoda et al., 2017; Li et al., 2013), and those results plus newer work by Hosokawa et al. (2020) indicate that more than this one regulatory element is involved in the full extent of Bcl11b regulation. It would be realistic to say that this large genomic region contains at least 500 functionally relevant CpG dinucleotides.

QUANTIFICATION AND STATISTICAL ANALYSIS

Experimental data: Cell trace violet experimental data shown in Fig. 1 are from two independent experiments as described in the text and figure legend. FISH transcript count distributions in Fig. 2 show median and quartiles from 169 cells. Clonal imaging data shown in Fig. 6 are from images of 62 clonal T-lineage wells, which were individually tracked as shown in Fig. S5. Means and standard deviations are shown, as described in the text and figure legend. Fluorescence thresholds for the imaging data were determined by using the average + 3 standard deviations of background values taken from 50 samples, as described in the legend for Fig. S6.

The statistical tests used are indicated in the individual figure legends.

The modelling results shown in Figs. 1, 4 and 5 along with the ones in the Figs. S2, S4 and S7 were obtained using Matlab version 9..3.0.713579 R (2017b), The Mathworks, Inc. Available at https://www.mathworks.com.

Supplementary Material

2

TABLE S6: Supplementary Dataset Table S6.xlsx

Table of Probe Sequences for smFISH, related to Figure 2 and STAR Methods. Sequences are shown for the primary probe pool, the secondary readout probe pool, and the hybridization chain reaction (HCR) probes. This table is available as an excel file.

Highlights.

• A multi-level dynamical model is developed for the commitment of T-cell precursors

• It links gene networks, single-cell RNA analysis, chromatin changes and cell division

• It provides quantitative understanding of commitment kinetic requirements

• The model predictions are verified against new clonal and real-time imaging data.