Insights into the cell fate decision-making processes from chromosome structural reorganizations

Abstract

The cell fate decision-making process, which provides the capability of a cell transition to a new cell type, involves the reorganizations of 3D genome structures. Currently, the high temporal resolution picture of how the chromosome structural rearrangements occur and further influence the gene activities during the cell-state transition is still challenging to acquire. Here, we study the chromosome structural reorganizations during the cell-state transitions among the pluripotent embryonic stem cell, the terminally differentiated normal cell, and the cancer cell using a nonequilibrium landscape-switching model implemented in the molecular dynamics simulation. We quantify the chromosome (de)compaction pathways during the cell-state transitions and find that the two pathways having the same destinations can merge prior to reaching the final states. The chromosomes at the merging states have similar structural geometries but can differ in long-range compartment segregation and spatial distribution of the chromosomal loci and genes, leading to cell-type-specific transition mechanisms. We identify the irreversible pathways of chromosome structural rearrangements during the forward and reverse transitions connecting the same pair of cell states, underscoring the critical roles of nonequilibrium dynamics in the cell-state transitions. Our results contribute to the understanding of the cell fate decision-making processes from the chromosome structural perspective.

I. INTRODUCTION

The cell fate decision-making process, often in the form of the cell-state transition, provides the capacity of the cells to acquire new fates; thus, it is the most fundamental cell event for the development of multicellular organisms. As a typical pathological cell-state transition process, the transformation of the normal cell to the cancer cell is central to the initiation and progression of a tumor. Despite the versatility of the cell-state transitions, the processes that establish the connections between two distinct cell types are generally recognized to be governed by the underlying gene regulatory networks.^1,2 As the scaffold for the genome function, the chromosome folds into a nonrandom 3D structural organization to underpin the desired gene expressions. Thus, the chromosome often exhibits the cell-type-specific structural characteristics that, in turn, influence function.³ During the transition, cells undergo phenotypic and functional switching, involving an interactive combination of large-scale chromosome structural rearrangements and specific gene expression pattern adaptations toward the destined cell state.⁴ It has been recognized that the 3D chromosome structural dynamics should play an indispensable role in cell development⁵ and carcinogenesis.⁶ However, the spatial reorganization of the chromosome structure during the cell fate decision-making process is still challenging to be characterized in the experiments, which are often confronted with difficulties in covering the large spatiotemporal scales of the chromosome systems in the cell nucleus. This impedes our understanding of the cell-state transition from the chromosome structural perspective.

Currently, chromosome structural determination is largely performed by the Hi-C experiments, which use proximity ligation to capture the 3D organizational structures of the chromosomes.^7,8 Hi-C experiments measure the frequencies of the contacts formed by all chromosomal loci pairs across the genome, often resulting in an ensemble-averaged contact map. Careful analysis of the Hi-C contact map revealed that the chromosome folds into a hierarchical organization from the spatially segregated multi-megabase compartments^7,8 to the self-interacting sub-megabase topologically associating domains (TADs).^9,10 These two chromosome structural features have been acknowledged to have functional implications in helping to shape gene expressions.^11–14 A compartment in the chromosome can be classified into A and B types, associated with open, gene-rich euchromatin and closed, gene-poor heterochromatin, respectively.^7,8,15 TAD exhibits to have a higher propensity to form intradomain contacts than interdomain contacts, thus contributing to the regulation of the gene expressions by restricting interactions of cis-regulatory sequences to their target genes.¹⁶ Even though our knowledge of the chromosome 3D structure and its potential roles in gene regulation has been significantly increased by the Hi-C techniques, the measurement only provides the static description of one cell state; thus, dynamical changes of the chromosome structure during the transition between two cell states are still inaccessible.

Recently, 4D nucleome methods were in rapid development, aiming to map the structure and dynamics of the chromosome both in space and time, simultaneously.¹⁷ As an extension of Hi-C on the temporal dimension, the time-course Hi-C experiments provide the time-dependent dynamical changes of the genome structures during different cellular processes.^18–21 However, in light of the increasing experimental evidence that the cell-state transitions exhibit switching dynamics between two stable cell states,^22–25 the time-course experiments, which can only be undertaken at a limited number of discrete time points and lacks a continuous picture, may bypass the critical points for the cell-state transition. Noteworthy, in a Hi-C experiment, the cross-linked chromosome is digested into fragments using certain specific restriction enzymes;^7,8 thus, the 4D data provide the measurements from the independent cell pools sampled at the specified time points rather than constantly tracking the chromosome structural changes during the cellular processes. In other words, the time-course Hi-C experiment does not provide real-time measurements, rather it measures the ensemble-averaged characteristics at the designated time points of the transition. More importantly, given the fact that the cell-state transitions at the single-cell level are highly stochastic,^18,26,27 the time-course data measured at certain time points inevitably contain the temporal heterogeneity of the cell states from different stages of the transition, thus giving rise to the difficulties in characterizing the intermediate states.^28,29

Here, from the theoretical aspects, we applied the landscape-switching model to study the chromosome structural reorganizations during the cell-state transitions among the embryonic stem cell (ESC), the differentiated normal, and cancer cells.^30–34 The ESC is a pluripotent cell that can differentiate into any cell type derived from the three germ layers. The model contains two steps and is described briefly in the following. First, we developed a coarse-grained chromosome model and adopted the data-driven modeling strategy using the maximum entropy principle to reproduce the experimental Hi-C data in simulations of the chromosome structures for these three cell states, respectively.^35–37 This leads to three energy landscapes for describing the chromosome structures at these three cell states, respectively. Second, we performed the landscape-switching simulations that implemented an instantaneous switch of the energy landscape from one cell state to the other to trigger the cell-state transitions. The post-switching relaxation process is referred to as the transition process. Overall, there are six transition processes in the system, including the ESC differentiation to the normal cell and the cancer cell, the reprogramming of the normal cell and the cancer cell to the ESC, and the cancer cell formation from the normal cell and the cancer cell reversion to the normal cell. Hence, the system presents a complete circuitry of cell fate decision-making processes, including the normal and pathological developments of cells.

Noteworthy, cells may go through multiple intermediates to accomplish the state transition processes. For instance, the ESC initially differentiates to multipotent progenitor cells followed by further specific developmental processes to the terminally differentiated cells. The landscape-switching model has approximated the multi-step complex process into a one-step transition, based on the following two facts. First, in the context of Waddington's developmental landscape,³⁸ the cell developmental system possesses multiple stable cell states as the coexisting attractors, so the cell developmental process is directed by these stable cell states, whereas stochastic fluctuations and regulations drive the transitions between the coexisting attractors.³⁹ The cell progenitors often show multipotency and a high tendency to differentiate to the destined cells; thus, they are less stable than the ESC, normal, and cancer cells. Second, the cell-state transitions among the stable attractors were experimentally found to exhibit switching phenotypic behaviors.^22–25 Theoretical studies that used bistable switches to model the transitions between two cell states were widely found to be capable of capturing many characteristics of the cell-state transition in reality.^39–43 In addition, it has been well recognized that although individual epigenetic modifications can occur frequently, the switching of the cell states can only be realized by the cooperative changes of histone states at a global scale.^44,45

In addition, cells often undergo multiple cell cycles to accomplish the cell developmental process. Our approach focuses on slow cell differentiation, reprogramming, cancer formation, and reversion dynamics while averaging out the fast cell cycle dynamics. The rationale is based on the following three facts. First, our data-driven model does not intend to describe the details of the molecular processes that account for the chromosome structural organizations, instead, it provides an experimentally consistent description of the chromosome structural ensemble at the interphase of the cells. The ensemble is then adapted to the one at the interphase of the destined cell fate after the state transition by the landscape-switching simulation. Second, there are two types of chromosome structural dynamics involved in the cell-state transitions, namely, the cyclic structural (de)condensation in the cell cycle and structural reorganization in the interphase when the cell converts to the new fate. It has been revealed that the chromosome forms a highly condensed, uniformly cylinder-like structure at the mitotic phase, regardless of the cell type.⁴⁶ On the contrary, the chromosome at the interphase of the cell is cell-type-specific, underpinning the desired gene expression pattern. In this respect, the chromosome structural reorganizations during the cell-state transition can be regarded as a combination of the nonspecific cell-cycle-dependent (de)condensation and the specific cell-fate-dependent structural reorganizations. Our approach is devised to focus on the specific chromosome structural reorganizations during the cell-state transitions. Third, cells spend most of the time residing in the interphase (usually more than 90% of the time in the interphase) in the fast cell cycle. In contrast, the cell developmental processes are very slow and can take several days or even months/years. There is a clear separation in the timescales between the slow cell developmental process and the fast cell cycle process. To study the dynamics of a complex system (cell-state transition process) containing both fast (cell cycle) and slow (cell-fate-switching) degrees of freedom while the primary interest is focused on the slow dynamics such as differentiation, it is a practically useful and also widely used approach that the fast dynamics can be separated and averaged out when the timescale of the fast dynamics is significantly shorter than that of the slow dynamics.⁴⁷ Through this approximation, the process can be simplified into an effective picture of chromosome structural reorganizations at the interphase of the cell during the cell-state transition (Fig. S1), in line with the description led by our model.

Our simulations provided quantified pathways of chromosome structural reorganizations during the cell fate decision-making processes. From the chromosome structural perspective, we observed early bifurcation events in the ESC differentiation to the normal and cancer cell, in line with the previous theoretical studies^39,48 and experimental observations.⁴⁹ For the two processes having the same destination, the chromosome structural (de)compaction pathways can merge at certain stages, after which the chromosome has to undergo further structural compaction in accompany by arranging the chromosome contacts and spatially positioning the chromosome loci, to reach the final states. Detailed structural analyses revealed that chromosomes during cell reprogramming can reach over-expanding structures, which are even more open than those at the ESC. The over-expanding chromosome structures observed in the normal and cancer cell reprogramming processes are different, reminiscent of the cell-type-specific cell reprogramming routes identified in experiments.^50,51 We further showed that the chromosomes at the merging states of the compaction pathways for forming cancer cells from the ESC and the normal cell have substantially different structures in terms of the compartments and radial distributions of the loci. This implies the complex and multiple-route characteristics of cancer formation. By analyzing the processes connecting the same pair of cell states with opposite directions, namely, the differentiation/reprogramming and the cancer formation/reversion, we found the non-overlapping forward and reverse pathways. Since chromosome structure participates in the regulation of gene expression, the irreversibility in the chromosome structural reorganization pathways may suggest distinct gene activities during forward and reverse cell-state transition processes. This observation can be further attributed to the consequence of the nonequilibrium landscape-switching model, reflecting the nonequilibrium nature of the cell-state transition processes.⁵² Our study presents a computational framework to study the chromosome structural reorganizations during the cell fate decision-making processes and contributes to our understanding of the structure-function relationship at the chromosomal level.

II. METHODS

A. Hi-C data

The Hi-C data of the ESC and the normal cell (IMR90, the human fetal lung cell) were downloaded from the Gene Expression Omnibus (GEO) repository archives with accession number GSE35156.⁹ The Hi-C data of the cancer cell (A549, the human lung carcinoma cell) was obtained from the ENCODE project with GEO accession number GSE105600.⁵³ All the replicates in each dataset of Hi-C data were used and proceeded to the Hi-C Pro software using the standard pipeline.⁵⁴ All the Hi-C contact maps were built at 100 kb resolution after iterative correction and eigenvector decomposition (ICE) normalization.⁵⁵ A further normalization process was performed to convert the Hi-C contact frequencies into the contact probabilities, which range from 0 to 1. This was practically done by assuming that the neighboring beads, which are usually detected to possess the highest contact frequencies, are always in the contacts with a contact probability equal to 1.^35,36,56,57 Here, we focused on the long arm of chromosome 14 (20.5–106.1 Mb).

We note that for one cell line, there may be alternative Hi-C datasets available. To see how the selected Hi-C datasets may influence the simulation results, we downloaded one additional Hi-C dataset for the ESC (GSE52457),⁵⁸ the IMR90 cell (GSE63525),⁸ and the A549 cell (GSE92819),⁵⁹ respectively, and generated the Hi-C contact maps using the procedure described above. We made comparisons of these Hi-C contact maps to the corresponding ones used in our study, in terms of the contact map, TAD insulation score, and compartment profiles (Fig. S11). For the ESC, we also generated the Hi-C contact maps for the two replicates in one Hi-C dataset and performed the comparisons. We found that the Hi-C data from two different datasets or two replicates within one dataset are highly correlated. Therefore, we speculate that the results of our simulations, which used the data-driven modeling strategy based on the Hi-C contact map at the first step, will not change significantly if another Hi-C dataset is used.

B. Polymer model

The chromosome is described by a “beads-on-a-string” polymer model. Each bead, representing a 100 kb DNA segment, is connected by pseudo bonds to the neighboring beads. Thus, the system has a total of 857 beads. The potential of the polymer model is expressed as follows:

$$V_{\text{Polymer}}=V_{\text{Bonds}}+V_{\text{Angles}}+V_{\text{sc}}+V_{\mathrm{C}}.$$

For the bond potential $V_{\text{Bonds}}$, which acts on the neighboring beads, we used a modified finitely extensible nonlinear elastic (FENE) potential to describe the bond stretching.⁶⁰ An additional repulsive potential was added between the neighboring beads to avoid spatial overlap.⁶¹ The angle potential for the three consecutive beads $V_{\text{Angles}}$ was added to take into account the stiffness of the chain at the local range.^35,62 We used the soft-core potential $V_{\text{sc}}$ to describe the interactions between the non-bonded beads;⁶² thus, the chain-crossing event was allowed in the simulations, aiming to mimic the effects of the topoisomerases on unknotting the DNA molecules in the cell nucleus.^27,63 Finally, spherical confinement $V_{\mathrm{C}}$ with radius R_C was added to mimic the volume fraction of the chromosome inside the cell nucleus at 10%.³⁵ The polymer potential $V_{\text{Polymer}}$ leads to a typical homopolymer model and finally generates an equilibrium globule chromosome ensemble, which has no TAD and compartment formation.³¹ Details of the polymer model can be found in the supplementary material and our previous work.^30–32,34

C. Maximum entropy principle simulation

The data-driven modeling process was undertaken by incorporating the Hi-C data into the polymer model, so the potential of the chromosome at one cell state $V(\mathit{r}|\mathit{Cell})$ is expressed as follows:

$$V(\mathit{r}|\mathit{Cell})=V_{\text{Polymer}}+V_{\text{Hi}‐\mathrm{C}},$$

where $V_{\text{Hi}‐\mathrm{C}}$ is the potential representing the experimental Hi-C data restraints. We used the maximum entropy principle for the data-driven modeling, aiming to generate a chromosome ensemble that can reproduce the experimental Hi-C data associated with a minimal bias by maximizing the entropy of the system. In accordance with the maximum entropy principle,⁶⁴ $V_{\text{Hi}‐\mathrm{C}}$ should be in the linear form of the experimental observables, i.e., the contact probabilities in Hi-C data, expressed as follows:

$$V_{\text{Hi}‐\mathrm{C}}=\sum _{i,j}{\alpha }_{ij}{P}_{ij},$$

where P_ij is the contact probability between the chromosomal loci i and j, and the prefactor α_ij represents the strength. α_ij was practically determined by multiple iterations that eventually fit the simulated contact map to the experimental one.^35–37

We performed the maximum entropy principle simulations for the ESC, the normal cell, and the cancer cell, respectively. The simulations lead to three data-driven potentials in the forms of $V(\mathit{r}|\mathit{ESC}),\hspace{0.17em}V(\mathit{r}|\mathit{normal})$, and $V(\mathit{r}|\mathit{cancer})$. These three potentials generated three heterogeneous chromosome structural ensembles at the ESC, the normal cell, and the cancer cell, respectively.^31,32 We further referred to the potential obtained from the maximum entropy principle simulation as the effective equilibrium landscape that governs the chromosome structural dynamics within on cell state.^30–32

D. Landscape-switching model

To explore the chromosome structural reorganizations during the cell-state transitions, we used the landscape-switching model developed in our previous work.^30–34 First, we performed two independent sets of molecular dynamics (MD) simulations with chromosomes under the potentials of two distinct cell states, respectively. After a long duration of simulations when the systems became steady, we triggered the cell-state transition by switching these two potentials (landscapes). From the biological perspective, the switching implementation occurs abruptly to recapitulate the bistable switch between the two gene expression states of two stable cell states in cell development.^22,23,65 From the physical perspective, the intra-landscape motions within one cell state are often much faster than the inter-landscape hopping events (waiting for hopping) between two cell states in a cell-state transition. In this regard, the cell-state transition process, which requires a significant amount of energy input, can be approximately described by the nonequilibrium nonadiabatic process,^66,67 which is qualified using the landscape-switching model.⁶⁸

In this study, the landscape-switching model was applied to studysix cell-state transition processes indicated in Fig. 1(a), including the ESC differentiation to the normal cell through the simulations of $V(\mathit{r}|\mathit{ESC})\to V(\mathit{r}|\mathit{normal})$ and to the cancer cell through the simulations of $V(\mathit{r}|\mathit{ESC})\to V(\mathit{r}|\mathit{cancer})$, the reprogramming from the normal cell through the simulations of $V(\mathit{r}|\mathit{normal})\to V(\mathit{r}|\mathit{ESC})$ and from the cancer cell through the simulations of $V(\mathit{r}|\mathit{cancer})\to V(\mathit{r}|\mathit{ESC})$, the cancer formation from the normal cell through the simulations of $V(\mathit{r}|\mathit{normal})\to V(\mathit{r}|\mathit{cancer})$ and the cancer reversion to the normal cell through the simulations of $V(\mathit{r}|\mathit{cancer})\to V(\mathit{r}|\mathit{normal})$. All the trajectories of the relaxation processes in the landscape-switching model simulations were collected and analyzed for describing the chromosome structural reorganizations during the cell-state transition processes.

FIG. 1.

Chromosome structural reorganizations during the cell-state transitions among the ESC, the normal cell and the cancer cell. (a) The six cell-state transition processes associated with chromosome structural reorganizations. The chromosome contact maps of the ESC, the normal cell and the cancer cell, as well as the processing states during the transitions at four time points (0.1τ, 1τ, 10τ, and 100τ) are shown. τ is the reduced time unit (see Sec. II). For the ESC, the normal and the cancer cell, the ideograms of the chromosome segment used in our study (chr14: 20.5–106.1 Mb) are annotated by the compartment status at the corresponding cell state. The percentages in the parentheses near the ideograms are the populations of the compartment A (red) and B (blue) in the chromosome segment. The correlation maps between the time-evolving chromosome contact maps of two transitions during (b) the ESC differentiation to the normal cell (Diff_N) and the cancer cell (Diff_C), (c) reprogramming from the normal cell (Repr_N) and the cancer cell (Repr_C) to the ESC, (d) transitions for forming the normal cell from the ESC (differentiation, Diff_N) and the cancer cell (cancer reversion, Cancer_R), (e) transitions for forming the cancer cell from the ESC (differentiation, Diff_C) and the normal cell (cancer formation, Cancer_F). The comparison between process “A” at time $t^A=I$ and process “B” at time $t^B=J$ is made by calculating the coefficient of determination $R^2(I,J)$ between the contact probability P_ij formed by the chromosomal loci i and j: $R^2(I,J)=1-\sum _{i,j}{[P_{ij}(t^A=I)-P_{ij}(t^B=J)]}^2/\sqrt{\sum _{i,j}{[P_{ij}(t^A=I)-〈P_{ij}(t^A=I)〉]}^2\sum _{i,j}{[P_{ij}(t^B=J)-〈P_{ij}(t^B=J)〉]}^2}$. $R^2(I,J)$, which measures the similarity of two chromosome contact maps at time $t^A=I$ of process A and $t^B=J$ of process B ( $R^2(I,J)$ = 1 corresponds to the identical contact maps with $P_{ij}(t^A=I)$ =  $P_{ij}(t^B=J)$ and the deviation of $R^2(I,J)$ from 1 indicates that degree of difference between these two contact maps.), is shown by 2D plot colored from blue to red, at the upper panels in (b)–(e). At the lower panels in (b)–(e), the cell states “J” are selected to be either the initial states (solid lines) or the final states (dashed lines) to represent how the chromosomes dynamically deviate from the initial structures and establish the final structures, simultaneously.

E. Physical units of model and simulation

We used Gromacs (version 4.5.7)⁶⁹ with PLUMED plugin (version 2.5.0)⁷⁰ to perform all the simulations. Reduced units were used throughout the simulations. The time unit is τ and the length unit is σ, which dictates the diameter of the bead in our chromosome polymer model. To estimate the physical length of our chromosome model, we compared the pairwise distance of two chromosomal loci in the chromosome ensemble at the normal cell between the simulations and the genomic-scale single-cell imaging experiments,⁷¹ resulting in σ = 277 nm (Fig. S2). As noted elsewhere, the bead in our model at the 100 kb resolution approximately represents the 30-nm chromatin fiber,^36,72 of which the length has been reported to be $\sim 300$ nm.⁷³ Therefore, our estimation of σ is in reasonably good agreement with the above facts.

We further estimated the physical timescale of our simulation by comparing the diffusion properties of the bead in our model with that from experiments. The experimental measurement of the mean squared displacement (MSD) of the chromosome loci in HeLa cells at $0.5\hspace{0.17em}\mathrm{s}$ is in the range of 0.01–0.015 $\mu {\mathrm{m}}^2$.⁷⁴ From the MSD calculation results present in our previous studies,^31,32 we estimated τ in the range of 8.3–12.5 s. We found that the magnitudes of the time unit estimated in our simulations are close to those found previously using a similar chromosome polymer model.^35,75 Considering that there should be quantitative differences in diffusion coefficients of the chromosomal loci in different types of cells, the estimation of τ presented here may be quite rough. On the other hand, due to the essence of the landscape-switching model, which abruptly switches the potential of the chromosome dynamics, the timescale estimated within one cell state may not be directly linked to the real reaction rates or waiting time of the cell-state transition processes. In other words, the timescale of the landscape-switching model is a parameter of the model. This parameter can be further calibrated with the experimental measurements when the experimental data are available. Thus, the time during the cell-state transition indicates the stage of the process rather than revealing the actual kinetic timescale of the process.

F. Quantities and order parameters

To quantitatively describe the geometry of the chromosome structure, we introduced the radius of gyration R_g and aspheric quantity Δ. These two quantities can be determined by the inertia tensor T,⁷⁶ expressed as follows:

$$\mathit{T}=\left[\begin{array}{ccc}{{\mathit{r}}_{\mathit{x}}{\mathit{r}}_{\mathit{x}}}^T& {{\mathit{r}}_{\mathit{x}}{\mathit{r}}_{\mathit{y}}}^T& {{\mathit{r}}_{\mathit{x}}{\mathit{r}}_{\mathit{z}}}^T\\ {{\mathit{r}}_{\mathit{y}}{\mathit{r}}_{\mathit{x}}}^T& {{\mathit{r}}_{\mathit{y}}{\mathit{r}}_{\mathit{y}}}^T& {{\mathit{r}}_{\mathit{y}}{\mathit{r}}_{\mathit{z}}}^T\\ {{\mathit{r}}_{\mathit{z}}{\mathit{r}}_{\mathit{x}}}^T& {{\mathit{r}}_{\mathit{z}}{\mathit{r}}_{\mathit{y}}}^T& {{\mathit{r}}_{\mathit{z}}{\mathit{r}}_{\mathit{z}}}^T\end{array}\right],$$

where ${\mathit{r}}_{\mathit{x}},\hspace{0.17em}{\mathit{r}}_{\mathit{y}}$, and ${\mathit{r}}_{\mathit{z}}$ are the row vectors for the spatial positions of the chromosomal loci shifted by the corresponding means. The eigenvalues λ_k (k = 1, 2, and 3) of T correspond to the squares of the extension lengths along the three principal axes. Thus, R_g is expressed as follows:

$$R_g=\sqrt{tr\mathit{T}}=\sqrt{\sum _{k=1}^3}{\lambda }_k,$$

and Δ is expressed as follows:

$$\Delta =\frac{3}{2}\frac{\sum _{k=1}^3{({\lambda }_k-〈\lambda 〉)}^2}{{(tr\mathit{T})}^2}.$$

R_g measures the level of chromosome compaction and deviation of Δ from 0 indicates the extent of anisotropy.

The radial gene density distribution $\rho {(r)}^{\mathit{gene}}$ was used to describe the spatial distribution of the loci in the chromosome with the expression as follows:

$$\rho {(r)}^{\mathit{gene}}=\frac{n{(r)}^{\mathit{gene}}}{4\pi r^2\Delta r},$$

where r is the distance to the center of the spherical confinement, which has a radius of R_C, $n{(r)}^{\mathit{gene}}$ is the number of the genes found in the spherical shell between r and $r+\Delta r$, and the denominator calculates the volume of the spherical shell.

G. Identification of TADs and compartments

TAD structures were described by the insulation score, which was previously used to determine the boundaries of the TADs.⁷⁷ The same sliding space as used in the original study (500 × 500 kb) was used to calculate the insulation score from the chromosome contact map. In general, the valley/minimum of the insulation score profile indicates a strong local insulation tendency to form the TAD boundary (Fig. S4).⁷⁷ The compartment profiles were calculated from the enhanced contact probability $P_{\text{obs}}$/ $P_{\hspace{0.17em}\text{exp}}$,⁷ which is the ratio between the observed contact probability $P_{\text{obs}}$ and expected contact probability $P_{\hspace{0.17em}\text{exp}}$ at the 1 Mb resolution. Then the principal component analysis (PCA) was performed on the enhanced contact probability matrix after the ICE normalization.⁵⁵ The first principles component (PC1) was used to represent the compartment profile. Since the direction of the PC1 value is arbitrary, we assigned the A/B compartment annotation in the chromosome at the ESC, the normal cell, and the cancer cell based on the associated gene density with the positive values (compartment A) to the gene-rich regions and the negative values (compartment B) to the gene-poor regions (Fig. S12).

For the state during the transition processes, we calculated the $P_{\text{obs}}$/ $P_{\hspace{0.17em}\text{exp}}$ and obtained the PC1 at the particular time point during the landscape-switching model simulations. Then, the direction of the PC1 was assigned by minimizing the differences to the PC1 of the state at the previous time step via calculating the correlation coefficient with the positive and negative signs of the PC1. Through this, we performed the compartment annotation assignment in the chromosome at each state during the simulations progressively, and eventually determined the compartment profiles for all the states during the cell-state transition processes (Fig. S5). We applied this strategy based on the assumption that the chromosome structural reorganizations should be smooth and continuous during the cell-state transitions.

III. RESULTS

A. Dynamical chromosome structural reorganizations during differentiation, reprogramming, and cancer processes

We chose the IMR90 and A549 cell lines to represent the differentiated normal and cancer cells in human lungs, respectively. We focused on the long arm of chromosome 14 (20.5–106.1 Mb), rather than the whole genome or one intact chromosome due to the following reasons. First, we aimed to study intra-chromosome dynamics. Given the fact that there are well-established chromosome territories,⁷⁸ the effects of inter-chromosome interactions on the chromosome structures can be approximately averaged and modeled as spatial confinement, which was widely used in previous studies.^{35,56,62,79–82} Second, Hi-C data often have poor quality around the centromeres and telomeres. The human chromosome 14 is acrocentric, and the long arm of chromosome 14 has a comparable length with the full chromosome 17, thus it is sufficiently long to represent a complete chromosome associated with good quality Hi-C data. Third, the chromosome segment used in this study does not contain any type of chromosomal abnormalities in cancer (A549) cell.^83,84 The chromosomal abnormalities, including chromosome deletion, duplication, inversion, substitution, and translocation, are related to the (ex)changes of the DNA elements in the cancer genome.⁸⁵ These complex processes cannot be realized by molecular dynamics (MD) simulations.

At the first step of our approach, we integrated the experimental Hi-C data into a coarse-grained chromosome model using the maximum entropy principle and performed the data-driven simulations of chromosome dynamics at the ESC, the cancer cell, and the normal cell, respectively (see Sec. II). The chromosome structural ensembles obtained from the simulations were verified by comparing the simulated Hi-C contact maps with the experimental ones, showing high consistency for all these three cells.^31,32 Furthermore, we benchmarked our simulation results with the experimental single-cell imaging data for the IMR90 cell.⁷¹ The overall good agreements between the simulations and experiments confirm the validity of the chromosome structural ensembles predicted by the data-driven modeling based on ensemble-average Hi-C data (Fig. S2).⁹

It has been demonstrated that the potential generated by the data-driven simulation is also capable of capturing the characteristics of the chromosome kinetics in one cell state, including the sub-diffusivity, spatial coherence, and viscoelasticity of the chromosome motions.^{30–32,75,82} In this regard, the potential can be regarded as an effective energy landscape that accounts for both the chromosome structure and dynamics within one cell state.^86–88 To bridge the two landscapes during the cell-state transition, the landscape-switching model implements an energy excitation of the system to switch from one landscape to the other. This implementation breaks the detailed balance of the system and drives the system out of equilibrium. The model not only echoes the switching dynamics and nonequilibrium essence of the cell-state transition from the biological and physical aspects,^22–25,52 but also significantly accelerates the process in silico, thus making it possible to study the slow and large-scale chromosome structural reorganizations during the cellular processes by MD simulations.

We calculated the chromosome contact map evolving with time during the landscape-switching model simulations of the six cell-state transitions [Fig. 1(a)]. We observed that the chromosome dynamically rearranges its structure during the cell-state transition in terms of gradually adapting the contact map from the initial cell state toward the final cell state. It is an intuitive observation, as the landscape after the switching implementation provides strong driving forces to guide the chromosomes to reorganize their structures toward the ones at the final cell state. Recent experiments found that the cell-state transitions can be incomplete with gene expressions slightly deviated from those at the final cell state.^89–92 This may be due to the insufficiently long timescales adopted in the experimental measurements. To see whether our landscape-switching simulations converged at the final cell states, we examined the trajectories by projecting onto the geometrical quantities of the chromosome structures and the contact maps at various ranges (Fig. S3). Our results show that the chromosome structures can readily reach the ones at the final cell state at the end of all the landscape-switching simulations for the cell-state transition processes. This suggests that our landscape-switching simulations were performed sufficiently long so that the cell-state transition processes were accomplished within the simulations.

Interestingly, it appears that the evolutions of the contact maps do not follow the same routes for the forward and reverse transitions between any pair of cell states [Fig. 1(a)]. This indicates that although the forward and reverse cell-state transition processes can be realized by reversible switching of the landscapes at the initial and final cell states, the pathways of the transitions in opposite directions are irreversible from the chromosome structural perspective. The irreversibility of the pathways at the chromosome structural level may have further implications on the irreversible gene regulation pathways that in turn control the nonequilibrium cell fate decision-making processes.⁹³

Intuitively, the differentiation processes starting from the ESC should bifurcate during the transitions toward the normal and the cancer cell, while the processes for reprogramming the normal cell and the cancer cell, the processes for forming the normal cell from the ESC and the cancer cell, and the processes for forming the cancer cell from the ESC and the normal cell should merge during the transitions toward the final cell states. To gain insights into how the bifurcation and merging of the pathways occur from the chromosome structural perspective, we calculated the correlation coefficient of determination R² between the two contact maps in time [Figs. 1(b)–1(e)]. For differentiation, the two transitions toward the normal and cancer cells (Diff_N and Diff_C) bifurcate at $\sim 1\tau$ [Fig. 1(b), upper panel, τ is the reduced time unit, see Sec. II], where the chromosome has different structures from that at the ESC and also deviates from those at the final cell states [Fig. 1(b), lower panel].

For reprogramming, it appears that the two pathways of the normal and cancer cells transition to the ESC (Repr_N and Repr_C) start to merge at $\sim 0.1\tau$ with high values of R² [Fig. 1(c), upper panel]. At $\sim 0.1\tau$, the chromosomes have different contact formations from either the ESC and final state [Fig. 1(c), lower panel]. It is worth noting that our previous work identified an over-expanding chromosome structure with respect to the one at the ESC during the normal cell reprogramming to the ESC.³¹ Here, we also observed a similar over-expanding chromosome structure during the cancer cell reprogramming to the ESC with a more sparse contact map at $1\tau$ than the one at the ESC [Fig. 1(a)]. The results imply that the over-expanding chromosome structure may be universal during reprogramming.

For forming the normal cell from the ESC differentiation (Diff_N) and the cancer cell reversion (Cancer_R), we found that the chromosomes during these two transitions become structurally similar at $\sim 1\tau$ [Fig. 1(d), upper panel], where the chromosomes have accomplished significant structural rearrangements for forming the normal cell [Fig. 1(d), lower panel]. However, a considerable number of the chromosome contact charges after $1\tau$ were still observed during the Diff_N to make the chromosome gradually deviate from the ESC. A similar observation can be found in forming the cancer cell by the ESC differentiation (Diff_C) and the cancer cell formation process (Cancer_F) [Fig. 1(e)]. The contact maps of the two pathways become similar at $\sim 1\tau$, where the chromosomes with different structures from those at the ESC still have to undergo a certain degree of structural arrangements in order to form the structures at the cancer cell.

B. Quantified chromosome compaction and decompaction pathways during differentiation, reprogramming, and cancer processes

It has been assumed that chromosome compaction has implications on transcriptional activities by regulating the accessibility to the transcription factors and DNA interactions.^94,95 The open chromosome structure is a signature of pluripotency,⁹⁶ and different levels of chromosome compaction may be associated with different developmental stages.⁹⁷ MD simulation can provide the 3D chromosome structural information in addition to the 2D chromosome contact map, thus it can be used to dissect the chromosome compaction and decompaction during the differentiation, reprogramming, and cancer processes. We introduced two reaction coordinates to describe the geometry of the chromosome structure. The radius of gyration R_g is used to quantify the level of the chromosome compaction and the aspherical shape parameter Δ is used to measure the extent of anisotropy with deviation from 0 as an indication of deviation from a perfect sphere (see Sec. II).⁷⁶ We projected the trajectories onto these two reaction coordinates and calculated the average pathways for chromosome compaction and decompaction during the cell-state transitions [Figs. 2(a)–2(d)].

FIG. 2.

Quantified pathways for chromosome structural shape changing during the differentiation, reprogramming and cancer processes. The pathways are shown for (a) differentiation, (b) reprogramming, (c) forming the normal cell, and (d) forming the cancer cell. The individual pathway is shown as the average of all the simulation trajectories of the corresponding transition projected onto the radius of gyration (R_g) and aspherical parameter (Δ). The arrows indicate the directions of the transitions. The states representing the bifurcation points in (a) and the merging points in (b)–(d) of the two pathways are shown in squares and diamonds, and denoted in accordance with the names of the corresponding transitions with a superscript “S.” The chromosome contact maps at (e) the bifurcation points and (f)–(h) the merging points are plotted and compared through the coefficient of determination R².

We found that the chromosomes monotonically compact their structures during the ESC differentiation toward the normal and cancer cells [Fig. 2(a)]. Our results resonate with the experimental observations that the chromosome with widely dispersed open euchromatin at the ESC promotes hyperactive transcriptional activities^96,98 and the chromosome compaction correlates with a reduction in transcriptional activity upon differentiation.^97,99 Furthermore, the quantified chromosome structural shape-changing pathways undergo the same route toward the normal and cancer cells at the early stages of the processes with the bifurcation points observed at 8τ ( ${\text{Diff}}_N^S$) and 8τ ( ${\text{Diff}}_C^S$), respectively. From the chromosome contact formation perspective, we found that the bifurcation of the two differentiation processes starts at $\sim 1\tau$ [Fig. 1(b)], earlier than that based on the chromosome structural shape-changing pathways [Fig. 2(a)]. Further comparisons on the chromosome contact maps between the bifurcation states of the ${\text{Diff}}_N^S$ and ${\text{Diff}}_C^S$ show clear differences [Fig. 2(e)]. These features indicate that the chromosomes during the differentiation perform cell-type-specific rearrangements on the contact maps based on the destined cells at the very beginning of the processes, while the chromosome compaction pathways exhibit to undergo the same route for a relatively long duration during differentiation to different types of cells.

Interestingly, we observed the non-monotonic processes of the chromosome decompaction followed by compaction during the reprogramming of the normal and cancer cells to the ESC [Fig. 2(b)]. The over-expanding chromosome structures were found with similar geometric shapes occurring at the same time points ( $2\tau$) in these two transitions, leading to the merging points on the reprogramming pathways (denoted as ${\text{Repr}}_N^S$ and ${\text{Repr}}_C^S$). The chromosome contact maps for these two states at the merging points are highly similar [Fig. 2(f)], suggesting a common state formed for the chromosome rearranging its structure during the reprogramming of different cell states. Then, the chromosome undergoes slight compaction to establish the chromosome shape at the ESC through the merging pathways with mild adaptions of the contact map toward the one at the ESC [Fig. 1(c), after $2\tau$]. From the chromosome structural perspective, these two reprogramming processes use different routes to form similar over-expanding chromosome structures, implying that the reprogramming pathways are cell-type-specific at the early stages, in line with previous experiments.^50,51

From the chromosome structural shape-changing pathways, we can see that the two processes of forming the normal cell by the ESC differentiation and the cancer reversion also merge prior to reaching the final state [Fig. 2(c)]. The merging states occur at time points 8τ and 5τ for the ${\text{Diff}}_N^S$ and ${\text{Cancer}}_R^S$ respectively, and show highly similar chromosome contact maps [Fig. 2(g)]. A similar observation was observed for forming the cancer cell from the ESC and the normal cell, where the merging states with similar chromosome structure geometries and contact maps were identified [Figs. 2(d) and 2(h), ${\text{Diff}}_{\mathrm{C}}^S$ at 8τ and ${\text{Cancer}}_F^S$ at 7τ]. Noteworthy, the bifurcation states for the ESC differentiation coincidently correspond to the merging states in cancer formation and reversion processes (the ${\text{Diff}}_{\mathrm{N}}^S$ and ${\text{Diff}}_{\mathrm{C}}^S$). In addition, we found that the transitions between the normal and cancer cells are made up of an initial chromosome structure decompaction followed by compaction [Figs. 2(c) and 2(d), dashed lines]. The chromosomes at the merging states exhibit to have more open structures than those at both the normal and cancer cells. Our observations resonate with a recent super-resolution imaging experiment, where Xu et al. detected universal chromosome decompaction across different cell types in the early stages of carcinogenesis.¹⁰⁰ The non-monotonic chromosome structural pathways of the cancer process have been found to open the chromosome structure and increase the similarity of the chromosome structures to the ones at the ESC during the transition,³² thus potentially contributing to the increase in the cell stemness.^101,102 The late stages of the cancer processes share similar routes with the chromosome compaction pathways during the ESC differentiation.

C. Chromosome structures at the bifurcation and merging states during cell-state transitions

Chromosomes at the bifurcation and merging states of two structural compaction pathways during the cell-state transitions show similar levels of structural compaction and asphericity. Nevertheless, these features gained from the global view of the chromosome structural geometry do not always lead to similar chromosome structural organizations at the bifurcations and merging states. For instance, as shown in Fig. 2(e), we observed significantly different contact maps formed at the bifurcation states of the two differentiation pathways. To dissect the chromosome structural formations at the bifurcation and merging states, we made further comparisons based on the chromosome contact maps among these states and the ESC, normal, and cancer cells. In Figs. 2(f)–2(h) and 3(a), we found that the contact maps at the merging states of two chromosomes (de)compaction pathways are highly similar with R² all equal to 0.99. In addition, the chromosomes at the merging state exhibit to have a more similar contact map with the one at the final state than the initial state. This indicates that the chromosome has accomplished a large proportion of designated structural changes at the merging state prior to reaching the final state.

FIG. 3.

Characteristics of the chromosome structures at the bifurcation and merging states during the cell-state transitions. Chromosome structural similarities among the bifurcation states, merging states, ESC, normal and cancer cells in terms of the (a) contact map, (b) TADs, and (c) compartments. For TAD, R² is calculated based on the insulation score.⁷⁷ For compartment, R² is calculated based on the compartment profile.⁷ The calculation procedures of TAD insulation score and compartment profile can be found in Sec. II. The radial probability distribution of the chromosomal loci at (d) the bifurcation states of the differentiation, (e) the merging states of the reprogramming, (f) the merging states of forming the normal cells, and (g) the merging states of forming the cancer cells. In each panel, the blue, red and cyan lines represent the average radial position of the chromosomal locus at the ESC, the normal and cancer cells. The bold line colored in accordance with the corresponding bifurcation/merging state represents the average radial position of the chromosomal locus and the compartment status of the locus is shown at the right side (red for compartment A, blue for compartment B). r is the distance to the center of the spherical confinement and R_C is the radius of the spherical confinement. The correlation coefficient of the average radial position of the chromosomal locus among the states during (h) the differentiation, (i) the reprogramming, (j) the formation of the normal cells, and (k) the formation of the cancer cells.

We further calculated the insulation score and compartment profile from the contact map to investigate the chromosome structures from the perspective of the local TADs and long-range compartments, respectively. These two types of chromosome organization characteristics at different hierarchical levels have been recognized to have implications on transcriptional activities.^7,8,15,16 We found that TADs and compartments dynamically change during the cell-state transitions (Figs. S4 and S5). The formations of the TAD structures in the chromosomes at the merging states are very similar and almost the same as the ones at the destined cell states from the insulation score analysis [Figs. 3(b) and S6A]. On the other hand, the chromosomes at the merging states for forming the normal cell ( ${\text{Diff}}_{\mathrm{N}}^S$ and ${\text{Cancer}}_{\mathrm{R}}^S$) and for forming the cancer cell ( ${\text{Diff}}_{\mathrm{C}}^S$ and ${\text{Cancer}}_{\mathrm{F}}^S$) have similar structural shapes, but the insulation score profiles are not strongly correlated [Fig. 3(b)]. It is due to the fact that there are differences in the TAD structural formation at the ${\text{Diff}}_{\mathrm{N}}^S$ and ${\text{Diff}}_{\mathrm{C}}^S$, representing the bifurcation states for the differentiation. It is worth noting that during our simulations, we did not detect substantial changes in the TAD insulation score in all six cell-state transitions (Fig. S4). The observation resonates with the experimental evidence that the TAD features are mostly conserved in mammals across different cell types and species.^9,103 We speculate that the moderate chromosome structural changes at the TAD level may have limited effects on the cell-state transitions, as increasing experimental evidence found that the disruptions of the TAD organizations only have minor influences on the gene expressions.^104,105

For compartments, we found strong correlations of the signals at the merging states of forming the normal cell ( ${\text{Diff}}_{\mathrm{N}}^S$ and ${\text{Cancer}}_{\mathrm{R}}^S$). In contrast, the compartment profiles are quite different at the Repr_N and Repr_C representing the merging states for reprogramming processes from the normal and cancer cells, and at the ${\text{Diff}}_{\mathrm{C}}^S$ and ${\text{Cancer}}_{\mathrm{F}}^S$ representing the merging states for the cancer cell formation processes [Figs. 3(c) and S6B]. The significantly different compartment profiles between the bifurcation states of the differentiation with R² lower than 0 imply that the chromosomes at the ${\text{Diff}}_{\mathrm{N}}^S$ and ${\text{Diff}}_{\mathrm{C}}^S$ have substantially different compartment segregation patterns. The results based on the TADs and compartments at merging states suggest the different rates of rearranging the chromosome structures at different structural levels during the cell-state transitions. At the merging states, the structures of TADs at the final cell states are well established, while the structures of compartments at the final cell states are only partially formed.

The location of the chromosomal locus is thought to correlate with the gene activity, likely due to the fact that the spatial position preference of the locus is driven by compartment segregation.^78,106,107 Here, we calculated the radial distribution of the chromosomal loci at the ESC, the normal and cancer cells, as well as at the bifurcation and merging states of the chromosome (de)compaction pathways. We found that the radial distributions of the chromosomal loci in the ESC are more dispersed and homogeneous than the ones in the normal cell (Fig. S7). In addition, the radial distribution of the chromosomal loci in the normal cell is strongly correlated with the associated compartment status, namely, the loci within the compartments A and B are preferentially located at the surface and the interior of the chromosome, respectively. These observations are in line with the experimental evidence that a more homogenous and open chromatin structure was detected in the pluripotent cells than the differentiated cells,^97,98,108 and the gene-rich chromosomal loci tend to lie at the periphery of the chromosome territory.¹⁰⁹

The chromosomes at the bifurcation states of the differentiation have significant differences in the radial distributions of the loci [Figs. 3(d) and 3(h)], suggesting again that the ${\text{Diff}}_N^S$ and ${\text{Diff}}_C^S$ are distinct states on the ESC developmental paths. At the merging states of the reprogramming, the chromosomal loci exhibit to be localized at the surface of the chromosome [Fig. 3(e)]. However, the radial distributions of the loci at these two states are different as each partially retains the characteristics of the one at the corresponding initial cell state [Fig. 3(i)]. This observation underscores the fact that the chromosome structural rearrangement pathways of the reprogramming should be cell-type-specific. For the merging states on the pathways of forming the normal cell, we found that the chromosomal loci tend to locate at the positions of the final cell, in particular for the loci in compartment A [Fig. 3(f)]. The average radial positions of the chromosomal loci at the merging states of the ${\text{Diff}}_N^S$ and ${\text{Cancer}}_R^S$ are very similar and strongly correlated with the ones at the normal cells [Fig. 3(j)]. Thus, the transition processes after the merging points are mostly related to the relocation of the loci in compartment B toward the final positions at the normal cells. This corresponds to further compaction of the chromosomes by establishing the structures of compartment B in the chromosomes. For the merging states on the pathways of forming the cancer cell, we found that the radial distributions of the chromosomal loci are quite different in these two states [Fig. 3(g)], though the average radial positions of the chromosomal loci appear to be mildly correlated in these two states [Fig. 3(k)]. This observation suggests that ${\text{Diff}}_C^S$ and ${\text{Cancer}}_F^S$ are different states from the chromosome structural perspective.

D. Irreversible chromosome (de)compaction pathways during cell-state transitions

Cell reprogramming is often considered the reverse process of cell differentiation. However, whether these two processes undergo the same route, albeit in opposite directions, to accomplish the cell-state transitions, remains elusive.¹¹⁰ We presented the quantified chromosome compaction and decompaction pathways during the differentiation and reprogramming [Figs. 4(a) and 4(b)]. We found that the two pathways connecting the same pair of the ESC and the differentiated cells never overlap. In particular, the chromosomes undergo monotonic compaction during differentiation and the degree of the chromosome structural asphericity increases first followed by the decrease during both of the transitions to the normal cell and the cancer cell. On the contrary, during both the reprogramming processes from the normal cell and the cancer cell, the non-monotonic chromosome decompaction followed by compaction pathways was observed, and the asphericity of the chromosome structure appears to decrease monotonically. The observation indicates that reprogramming does not proceed in reverse order of the differentiation, consistent with the recent findings based on the Hi-C studies.^20,111

FIG. 4.

Quantified irreversible pathways for chromosome structural rearrangements during the differentiation, reprogramming and cancer processes. (a)–(c) Chromosome compaction and decompaction pathways during the cell-state transitions projected onto R_g and Δ. (d)–(f) Spatial redistribution of genes during the cell-state transitions. (top) Principal component analysis (PCA) plots of the radial gene density distribution $\rho {(r)}^{\mathit{gene}}$ pathways at the first two principal components (PCs) during the cell-state transitions. (middle and bottom) Profiles of the $\rho {(r)}^{\mathit{gene}}$ evolving during the cell-state transitions. $\rho {(r)}^{\mathit{gene}}$ at the ESC, the normal cell and the cancer cell are shown as the thick lines. In each panel, the arrows indicate the directions of the transition processes. On the quantified pathways, four typical time points in the trajectories are additionally shown as squares ( $\square$, t = 0.1τ), circles ( $◯$, t = 1τ), triangles ( $△$, t = 10τ), and diamond ( $\diamond$, t = 100τ). Time is in the logarithmic scale.

Similar observations can be found for the processes of cancer cell formation and reversion [Fig. 4(c)]. Although the chromosomes show an initial chromosome decompaction followed by compaction during both processes, the two quantified pathways do not overlap, suggesting the irreversibility of the chromosome structural reorganization pathways in the cancer-related cell-state transitions. From the physical perspective, the irreversible pathways originate from the landscape-switching model, which breaks the detailed balance of the system by implementing an instantaneous energy excitation to switch the landscape, and further reflects the nature of the high nonequilibrium cellular processes.⁵²

E. Irreversible pathways of spatially repositioning genes in chromosomes during cell-state transitions

Genes were previously found to have a preferential spatial location at the periphery of the chromosome territories,¹¹² where they can be easily accessible to the transcription machinery.^78,109 To see the potential roles of the irreversible pathways in affecting the transcriptional activities, we calculated the radial distribution of the gene density evolving during the cell-state transitions [Figs. 4(d)–4(f)]. We drew the PCA plots for the radial distribution of the gene density evolving during the cell-state transitions. On the PCA plots, we can see that the ESC, the normal cell, and the cancer cell are clearly separated. PC1 associated with an overwhelming weight captures the predominant difference of the ESC from the normal and cancer cells, thus it likely corresponds to the direction of differentiation. On the other hand, PC2 captures the difference between the normal cell and the cancer cell, albeit with a small weight, thus it potentially describes the features of canceration.

The pathways for the differentiation and reprogramming do not overlap [Figs. 4(d) and 4(e)], indicating that the chromosomes use different ways to spatially redistribute the genes during the forward and reverse processes. In particular, the ESC differentiation processes reposition the genes located at the surface toward the interior of the chromosomes, thus this may contribute to a reduction of transcriptional activities. Conversely, during the reprogramming processes, there can be even more genes located at the chromosome surface when the chromosomes possess the over-expanding structures than they are at the ESC. The over-expanding chromosome structure, which has an open, loosely formed structural organization associated with genes predominantly located at the periphery of the chromosome territories, may suggest an increase in transcriptional activities with respect to the ESC.

We also found that the positions of the genes change through different routes during the cancer formation and reversion processes [Fig. 4(f)]. Nevertheless, the gene radial distribution profiles change in a similar two-step manner during both transitions. The profile adapts toward the one at the ESC initially, followed by establishing the one at the final cell state. These non-monotonic chromosome structural rearrangements represented by the chromosome (de)compaction and genes repositioning during the cancer processes imply that there may also be increase-followed-by-decrease changes in the transcriptional activities, leading to an elevated cell stemness at the transient states during the cancer-related cell-state transitions.³²

IV. DISCUSSION AND CONCLUSIONS

In this work, we used a nonequilibrium landscape-switching model to study the chromosome structural reorganizations during the transitions between two different cell states among the ESC, the normal cell, and the cancer cell. The ideal way to validate the landscape-switching model is to compare our simulation predictions with the experimental Hi-C data during the transitions. We note that there are Hi-C data available at four ESC-derived cell lineages at the early stages of the ESC developmental processes, namely, the mesendoderm (ME) cell, mesenchymal stem (MS) cell, neural progenitor (NP) cell, and trophoblast-like (TB) cell.⁵⁸ In this study, we used the IMR90 cell derived from mesoderm, as the normal cell. Thus, only the ME cell can be deemed as an intermediate state in the differentiation process of the ESC to the IMR90 cell, while the other three cells differentiate toward the other tissues or organisms. By comparing the simulated chromosome contact maps during the ESC differentiation processes with the experimental Hi-C data of these four cell lines, we found that the MS, NP, and TB cell states are located far away from the simulation pathways, echoing the evidence that these three cell lines are not on the differentiation path (Fig. S8). In contrast, we found that the ME cell is located at the early stages of the simulation pathways. However, this observation may partially be attributed to the high similarity of the Hi-C data between the ESC and ME cell. In this regard, further critical assessments of our simulation results should be made when the Hi-C data at other intermediate states of the transitions are available.

As our simulation approaches were devised to simulate the structural changes of the chromosome during the cell-state transition processes, we did not obtain the trajectories of the transcriptional activity. Here, to see how the transcriptional activity changes among the ESC, normal cells, and cancer cells, we analyzed the RNA-seq data of these three cells and further made comparisons among them (Fig. S13). Overall, the trends of the whole gene expressions on the chromosome segment focused on this study are similar for the ESC, normal, and cancer cells (Fig. S13A). More genes are having low expression levels in the normal cell than those in the cancer cell and ESC, suggesting that there are more transcriptional activities in the cancer cell and the ESC than those in the normal cell (Fig. S13B). In other words, when the normal cell undergoes reprogramming in forming the ESC or tumorigenesis in forming the cancer cell, a large number of genes switch from low expression levels to high expression levels or from inactive to active state. In addition, we found that the switching between compartments A and B can contribute to the changes in the gene expression levels during the cell-state transitions between the ESC and the normal cell, as well as between the ESC and the cancer cell (Fig. S13C). For the ESC switching to the normal cell, the gene expressions are overall weakened, with the median and mean values of the changes in the gene expression level at the individual locus level all lower than 0. In particular, the decrease of the expression levels for the genes involved in the compartment A to B switching is more than those involved in the compartment B to A switching. The results suggest that the genes in compartment B have lower preferences to be expressed than those in compartment A. Similar observations can be found for the transition between the ESC and the cancer cell. Overall, the gene expression levels for the transition of the ESC to the normal cell and to the cancer cell show a general decrease. The results indicate that the gene expressions in the ESC have the highest level among these three cells, consistent with the fact that open chromosome indicates high pluripotency.⁹⁶

Noteworthy, our landscape-switching model differs from the recently developed data-driven chromosome modeling methods based on the time-course Hi-C experimental data.^113,114 Using MD simulations, these studies constructed the smooth trajectories for describing the chromosome structural reorganizations during the cell-state transitions by gradually establishing the connections between the discrete time points, where the Hi-C data are available. However, the time-course Hi-C data at each time point likely contains the heterogeneity of cells from different states, due to the high stochasticity of cell dynamics^18,26,27 and the switch-like cell-state transitions.^22–25 In this regard, the results of the chromosome structural ensemble evolution obtained from a completely data-driven approach should be associated with changing the populations of different cell states during the transitions of a massive population of cells, resulting in a mixture between temporal heterogeneity and cell-state switching.^28,29 In contrast, our model implements the switch of the landscape to trigger the cell-state transitions for all the individual simulations simultaneously. The results reflect the underlying chromosome structural rearrangements purely led by switching of the cell fate, thus providing an effective way to characterize the chromosome structures at the intermediate states during the transition.^28–30 In addition, our model assumes that the dynamics of the cell-state transitions are strongly driven by the destined cell states. However, the switch of the landscape does not lead to synchronous structural reorganizations for all the chromosomal loci. As demonstrated in Fig. 3, different loci along the chromosome can use different rates to adapt their spatial positions at the bifurcation/merging state from the ones at the initial cell state toward the ones at the final cell state. The results indicate that although the model changes the landscape or interactions globally by a sudden switch, the structural reorganizations of the chromosome at different regions can proceed asynchronously. The continuous chromosome structural changes are then described by the MD simulation trajectories.

Our study focused on the long arm of chromosome 14, where no chromosome abnormalities were found in the cancer cell used here.^83,84 To see whether the results obtained here apply to the other chromosomes, we calculated the contact probability P(l) decaying with the genomic distance l for the chromosome segment used in our study, and further compared it to the other chromosomes. P(l) describes the strengths of the chromosome interactions at different genomic distances, thus dictating the polymer structural state of the chromosome.¹¹⁵ P(l) was previously used to quantify the chromosome models at different states.^46,116–118 For cell-state transitions, we found that the results from P(l) on describing the differentiation, reprogramming and cancer processes, are very similar to those from the contact map (Fig. S9). In addition, we observed the similar trends of P(l) for chromosomes 1 to 14, as well as their changes among the ESC, the normal cell, and the cancer cell (Fig. S10). Since our simulation potentials are rendered by the Hi-C data through the maximum entropy principle, this observation may suggest similar characteristics of the data-driven energy landscapes for chromosomes 1 to 14 and their relationships among these three cells. However, for the small chromosomes 15 to 22, the probability curves vs genomic distance P(l) are separated from the chromosomes to the chromosome segment used in this study for the ESC, the normal, and cancer cells. This implies that the results may change when applying our model to study the autosomes 15 to 22. The haplotype-resolved high-resolution Hi-C data has shown that the structural organizations of the two homologous chromosomes of the autosomes (chromosomes 1 to 22) are very similar.⁵⁸ Further applications of our approach to the sex-chromosomes may have to additionally take into account different molecular interactions that lead to the allele-specific structural organizations in the active and inactive chromosomes X, as well as the chromosome Y.⁵⁷ Therefore, these features indicate that our simulation results based on the long arm of chromosome 14 may be extended to chromosomes 1 to 14 as long as there are no chromosome abnormalities.

Based on the chromosome structural reorganization pathways from our simulations, we can draw a full picture of the cell-state transitions among the ESC, the normal cell, and the cancer cell (Fig. 5). The monotonic chromosome compaction during the ESC differentiation involves two types of chromosome structural rearrangements that occur simultaneously, including the structural deviation from the ones at the pluripotent state and structural adaptation toward the final states. The latter form, which contributes to the bifurcation of the pathways toward different differentiated cell states, occurs at the early stages of ESC differentiation. Early bifurcation events during the pluripotent cell differentiation to different cell types were also observed by the previous theoretical and experimental studies.^39,48,49

FIG. 5.

Scheme illustrating the six cell-state transition processes among the ESC, the normal cell and the cancer cell involved with the bifurcation and merging states from the chromosome structural perspective. The vertical arrow from top to bottom indicates the level of the chromosome compaction.

Starting from different differentiated cell states, the chromosomes during reprogramming can form similar structural geometries, resulting in the merging states prior to the ESC. At the merging states, the chromosomes are similar in contact maps and TADs but differ in compartments and spatial distributions of the loci. Our simulation results are in excellent agreement with the Hi-C experiments, where reprogramming processes of four somatic cell types were found to undergo different paths to establish the ESC-like states with distinguishable cell-type chromosome structural differences before reaching the final, identical pluripotent state.⁵⁰ In addition, a recent experimental study on characterizing the transcriptional dynamics of different somatic cells reprogramming to the pluripotent cells also found that the processes strongly depend on the cell types.⁵¹ This provides a demonstration of the cell-type-specific reprogramming processes at the gene expression level. Furthermore, we found that the non-monotonic chromosome structural reorganization pathways during the reprogramming observed in our simulations resonate with a recent experimental study, where Cacchiarelli et al. characterized the transcriptional and epigenomic changes during the reprogramming at a high temporal resolution and uncovered a subpopulation of cells with the pre-implantation-like characteristics.¹¹⁹ During the pre-implantation stages, the chromosome undergoes structural reorganization to establish the transition from the totipotent toward the pluripotent state.^5,120 Studies on the two-cell-embryo-like cells, which possess higher potency for development than the ESC, detected more relaxed chromosome structures with increased chromatin accessibility, compared to the ESC.^121–123 This implies a chromosome compaction process during the pre-implantation stages, verifying our simulation predictions of the over-expanding chromosome structures and further chromosome compaction to the ones at the ESC.

Interestingly, the two processes of forming the cancer cell from the ESC and the normal cell do not share the chromosome structural reorganization pathways, in contrast with the processes of forming the normal cell. Despite showing similar chromosome geometries, contact maps, and TAD structures, the chromosomes at the compaction merging states of the ${\text{Diff}}_{\mathrm{C}}^S$ and ${\text{Cancer}}_{\mathrm{F}}^S$ have large differences in the compartment formation and the spatial distribution of the chromosomal loci. Further changing the compartment status with spatial repositioning of the chromosome loci/genes from the ${\text{Diff}}_{\mathrm{C}}^S$ and ${\text{Cancer}}_{\mathrm{F}}^S$ toward the cancer cell is indispensable and undergoes different pathways for the differentiation and cancer formation processes. Therefore, our results show multiple routes for forming the cancer cell from the chromosome structural perspective. The results here focused on the chromosome structural reorganizations resonate with our recent theoretical work using the gene regulatory network, which revealed the global mechanisms of cancer with multiple states and paths, underlining the complexity of cancer at the gene expression level.¹²⁴

Currently, our model has three prominent limitations that can be improved. First, the cell-state transition was considered as a bi-switch process connecting the initial and final stable state in our study, while the (meta)stable intermediate states may exist in reality. To overcome this, the intermediate states with available experimental Hi-C data can be added into the model, so that there will be stepwise landscape-switching simulations among the multistable cell states to construct the transition process. Second, the model does not explicitly take into account the cell-cycle process, due to the lack of experimental Hi-C data on all the phases of the cell cycle for making up the cell-state transitions and the unclear relationship between the cell cycle and the cell-state transition. Delineating the quantitative relation between the cell cycle and the cell-state transitions can help improvements on our model by introducing the cell-cycle processes,^125,126 where the chromosome (de)condensation can be described by the landscape-switching simulations.³⁰ Third, to reduce the computational demands, our chromosome model was built on a coarse-grained level with implicit treatments of proteins, so the microscopic molecular-level processes, such as the loop extrusion and the DNA-binding of the transcriptional factors, were not captured. We foresee that the chromosome models taking into account the binding of proteins to the specific sites in chromatins at a finer resolution can be devised,^116,127,128 and subsequently implemented into the landscape-switching model in future studies.

In summary, we implemented a nonequilibrium landscapes-switching model into the MD simulations and studied the chromosome structural rearrangements during the differentiation, reprogramming, and cancer processes. We identified the chromosome compaction bifurcation and merging states for the cell-state transitions, and characterized the chromosome structures at these states in terms of TADs, compartments, and radial distributions of the loci. Another prominent observation gained from this approach is the irreversibility in the chromosome structural reorganization pathways of the cell-state transitions. From the physical perspective, the irreversibility reflects the nature of the high nonequilibrium cell dynamics; thus, it should be the common theme in the diverse cellular processes.⁵² Our study provides useful insights into the understanding of the cell fate decision-making processes from the chromosomal structural perspective.

SUPPLEMENTARY MATERIAL

See the supplementary material for additional methods and figures.

AUTHOR DECLARATIONS

Conflict of Interest

The authors have no conflicts to disclose.

Author Contributions

Xiakun Chu: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Resources (equal); Software (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Jin Wang: Conceptualization (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Project administration (equal); Resources (equal); Supervision (equal); Validation (equal); Writing – original draft (equal); Writing – review & editing (equal).

DATA AVAILABILITY

The data that support the findings of this study are available from the corresponding author upon reasonable request.