The distribution shown in Figure 7 indicates that the population is not uniform. While most of the population is in the starting low state with each of the corresponding epigenetic marks set accordingly, a significant number of cells have one of those marks changed in at least one of the two copies of the NANOG gene, and a much smaller number has two or even all three changed in at least one of the copies. The cells occupy this distribution of states due to finite, non-zero rates for flipping epigenetic marks and flipping them back. Stochastic events are responsible for which cells are in which state at any point in time. Once a steady-state distribution is reached, individual cells continue to change state, but the distribution is invariant. Thus, whereas stochastic events drive the system to its steady state, the steady-state distribution is deterministic and a characteristic of the modeled cell population. We Ginsenoside-Ro hypothesized that the different subpopulations in the steadystate distribution could have different reprogramming dynamics, because some were further along the reprogramming pathway than others. Sharp Amikacin hydrate differences in reprogramming time could give the appearance of an elite subpopulation especially primed for reprogramming. Fundamentally, however, the cells are equally capable of interconverting among the same set of states, and emerging differences are due to the state each cell happened to be in at the time the induction protocol was initiated. To explore the effect of pre-existing states on reprogramming dynamics, each of the eight substates was used to start sets of simulations under induction conditions. Simulations were run for all models, and results for the distribution of reprogramming times are given in Figure 8. .gif)
Distinct subpopulations can have significantly different reprogramming times. This is especially true of the Cooperative model variants and particularly those with slow steps. Subpopulations starting further along the reprogramming pathway tended to complete the process more quickly than those beginning more distant from the final state. When one or more slow steps was present, substates after the last slow step reprogrammed much faster than those before. While terms such as “elite” may be applied to these subpopulations to indicate that they respond more quickly to induction protocols than other cells, for the case described here all cells are equally capable of reprogramming. The faster time scale available to these cells suggests it may be advantageous to isolate and induce only them, or even to search for methods to accelerate slow steps either to prepare cells for induction or to apply concomitant with induction. Understanding the influence of mechanisms and kinetics in accelerating particular reactions is especially relevant, considering the evidence that suggests some of the cells that do not reprogram in the initial weeks of the protocols are relatively stable in partially reprogrammed states. Characterization of these cells revealed that the promoters of key genes of the reprogramming circuitry remained heavily methylated and some of the necessary histone modifications have not happened. Regarding our work, Figure 9D shows that a dominant slow step can cause cells to remain in the same state most of time until reprogramming, and the black line in Figure 6D shows that only 20% of cells collected at day 14 would have reprogrammed; by implication, those that did not reprogram would not have done so because of the slow step keeping them in their unreprogrammed state.