Stem cell regeneration is a vital biological process in self-renewing tissues, governing development and tissue homeostasis. Gene regulatory network dynamics are pivotal in controlling stem cell regeneration and cell type transitions. However, integrating the quantitative dynamics of gene regulatory networks at the single-cell level with stem cell regeneration at the population level poses significant challenges. This study presents a computational framework connecting gene regulatory network dynamics with stem cell regeneration through a data-driven formulation of the inheritance function. The inheritance function captures epigenetic state transitions during cell division in heterogeneous stem cell populations. Our scheme allows the derivation of the inheritance function based on a hybrid model of cross-cell-cycle gene regulation network dynamics. The proposed scheme enables us to derive the inheritance function based on the hybrid model of cross-cell-cycle gene regulation network dynamics. By explicitly incorporating gene regulatory network structure, it replicates cross-cell-cycling gene regulation dynamics through individual-cell-based modeling. The numerical scheme holds the potential for extension to diverse gene regulatory networks, facilitating a deeper understanding of the connection between gene regulation dynamics and stem cell regeneration.
The cell states were obtained by solving the SDE model (2.7) with initial conditions randomly distributed over 0 < Xi(0) < 2. (b). Epigenetic state of cells derived from a single cell after 15 divisions. The cell states were obtained by solving the hybrid model (2.13), with initially a single cell having random gene expression states 0 < Xi(0) < 2. (c). Same as (b) with symmetric division ( > 2) and different distributions for the parameter i. (d). Same as (b) with asymmetric division ( < 2) and different distributions for the parameter i. Here, the epigenetic states are represented by x = log(X(t) + 1)|(t)=T1 . In (a), no cell division was considered, and different external perturbation strengths were applied. In (b)-(d), cell division was considered, with = 0.5 and different parameters for the distribution of i (refer to (2.12)). The values of and are shown in the figure; the parameters 1 = 2 = 3 = 0.3; the conditional pers
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12) was set as = 0.5; the cell cycling parameters were T = 50, T1 = 25, T2 = 8; other parameters were the same as in Figure 5.
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14 in defining the distribution of the coefficient i. Fixing = 0.4, we adjusted to reflect symmetry division (10 to 1000), resulting in a decreased variance of i. The distribution of epigenetic states in Figure 6 appears independent of the parameter . Similarly, varying to reflect asymmetric division (ranging from 1 to 0.01) yields consistent distributions of epigenetic states at the 15th cycle, as shown in Figure 6d. These results suggest that the distribution of the epigenetic states of a cell clone remains insensitive to the variance of i in cell division. For subsequent discussions below, we focused on the method of obtaining the inheritance function through simulation data, with fixed values of = 0.5, = 60, and = 0.4.
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3.2. Data-driven inheritance function In Figure 6, we have demonstrated the variability of epigenetic states in individual cells originating from a single cell. The variability reflects the stochastic changes in cell states during cell division. To derive the inheritance function p(x, y) based on the gene regulation dynamics (2.13), we tracked the process of cell division through numerical simulations. We recorded the state of the mother cells (y) and the daughter In our simulations, we initiated 106 cells. For each cell, we simulated the model for 3 cell cycles, considering all cells at the second cycle as mother cells and denoting cells (x) following each cell division event. their epigenetic states as y. For each mother cell with state y, we paired it with the epigenetic state x of
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