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Modeling the dynamics of bivalent histone modifications.

Ku WL, Girvan M, Yuan GC, Sorrentino F, Ott E - PLoS ONE (2013)

Bottom Line: It is generally agreed that bivalent domains play an important role in stem cell differentiation, but the underlying mechanisms remain unclear.Here we formulate a mathematical model to investigate the dynamic properties of histone modification patterns.We then illustrate that our modeling framework can be used to capture key features of experimentally observed combinatorial chromatin states.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics, University of Maryland, College Park, Maryland, United States of America ; Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland, United States of America.

ABSTRACT
Epigenetic modifications to histones may promote either activation or repression of the transcription of nearby genes. Recent experimental studies show that the promoters of many lineage-control genes in stem cells have "bivalent domains" in which the nucleosomes contain both active (H3K4me3) and repressive (H3K27me3) marks. It is generally agreed that bivalent domains play an important role in stem cell differentiation, but the underlying mechanisms remain unclear. Here we formulate a mathematical model to investigate the dynamic properties of histone modification patterns. We then illustrate that our modeling framework can be used to capture key features of experimentally observed combinatorial chromatin states.

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Average final fraction of  nucleosomes vs. the number of initial  nucleosomes.The average final fraction of  nucleosomes is plotted as a function of  (the number of initial  nucleosomes) for (, ) being (0.003, 0.0015)(red) and (0.005, 0.0025)(blue). These levels of  nucleosomes are computed by averaging the final number of  nucleosomes in the simulations over 2000 runs.
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pone-0077944-g005: Average final fraction of nucleosomes vs. the number of initial nucleosomes.The average final fraction of nucleosomes is plotted as a function of (the number of initial nucleosomes) for (, ) being (0.003, 0.0015)(red) and (0.005, 0.0025)(blue). These levels of nucleosomes are computed by averaging the final number of nucleosomes in the simulations over 2000 runs.

Mentions: Finally, we also studied the effects of varying the number of nucleosomes in the initial condition on the above simulations. Using the same parameters values as above, we plot (Fig. 5) the final average fraction of nucleosome at the end of the final simulated cell cycle (10 cell cycles) as function of the initial number of nucleosomes which are taken to occupy the nucleosome sites in the center of the lattice. As shown in Fig. 5, the average fraction of final nucleosomes initially increases with increasing . We observe that past (i.e., ) the value is essentially constant up to with nucleosomes spanning the whole lattice. For a given , each simulation can be categorized into two groups, (1) the final spatial average level of nucleosomes is approximately equal to the corresponding large limiting value, or (2) all nucleosomes vanish. Thus at low , the value plotted on the vertical axis of Fig. 5 can be thought of as the limiting larger- value (basically the value at ) multiplied by the fraction of runs in category (1). In the early stage of a simulation, the spreading of histone marks compete with the loss of histone marks via histone turnover. If either type of mark is lost totally, it cannot recover (i.e., the run is in category 2). On the other hand, we find that histone marks do not die out if there are enough of them on the lattice (the run is then in category 1). As a result, the average fraction of nucleosomes is larger with larger , and with smaller and (compare the red and blue plots in Fig. 5). The above simulations suggest that in order for states to form when and are small, a sufficient number of initial nucleosomes is required. Taken together, these results have shown that the formation of bivalent domains undergoes two distinct phases: expansion and stabilization. In the expansion phase, the border of bivalent domains expands to neighboring nucleosomes. The expansion process is relatively fast (10 nucleosomes per cell-cycle in our simulation) but quite noisy. As a result, only a sparse subset of nucleosomes are marked with the state. During the stabilization phase, the nucleosome state configuration is further refined and eventually reaches an equilibrium. Even then, the state of individual nucleosomes is still highly dynamic and equilibrium is only reached in the statistical sense.


Modeling the dynamics of bivalent histone modifications.

Ku WL, Girvan M, Yuan GC, Sorrentino F, Ott E - PLoS ONE (2013)

Average final fraction of  nucleosomes vs. the number of initial  nucleosomes.The average final fraction of  nucleosomes is plotted as a function of  (the number of initial  nucleosomes) for (, ) being (0.003, 0.0015)(red) and (0.005, 0.0025)(blue). These levels of  nucleosomes are computed by averaging the final number of  nucleosomes in the simulations over 2000 runs.
© Copyright Policy
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC3815350&req=5

pone-0077944-g005: Average final fraction of nucleosomes vs. the number of initial nucleosomes.The average final fraction of nucleosomes is plotted as a function of (the number of initial nucleosomes) for (, ) being (0.003, 0.0015)(red) and (0.005, 0.0025)(blue). These levels of nucleosomes are computed by averaging the final number of nucleosomes in the simulations over 2000 runs.
Mentions: Finally, we also studied the effects of varying the number of nucleosomes in the initial condition on the above simulations. Using the same parameters values as above, we plot (Fig. 5) the final average fraction of nucleosome at the end of the final simulated cell cycle (10 cell cycles) as function of the initial number of nucleosomes which are taken to occupy the nucleosome sites in the center of the lattice. As shown in Fig. 5, the average fraction of final nucleosomes initially increases with increasing . We observe that past (i.e., ) the value is essentially constant up to with nucleosomes spanning the whole lattice. For a given , each simulation can be categorized into two groups, (1) the final spatial average level of nucleosomes is approximately equal to the corresponding large limiting value, or (2) all nucleosomes vanish. Thus at low , the value plotted on the vertical axis of Fig. 5 can be thought of as the limiting larger- value (basically the value at ) multiplied by the fraction of runs in category (1). In the early stage of a simulation, the spreading of histone marks compete with the loss of histone marks via histone turnover. If either type of mark is lost totally, it cannot recover (i.e., the run is in category 2). On the other hand, we find that histone marks do not die out if there are enough of them on the lattice (the run is then in category 1). As a result, the average fraction of nucleosomes is larger with larger , and with smaller and (compare the red and blue plots in Fig. 5). The above simulations suggest that in order for states to form when and are small, a sufficient number of initial nucleosomes is required. Taken together, these results have shown that the formation of bivalent domains undergoes two distinct phases: expansion and stabilization. In the expansion phase, the border of bivalent domains expands to neighboring nucleosomes. The expansion process is relatively fast (10 nucleosomes per cell-cycle in our simulation) but quite noisy. As a result, only a sparse subset of nucleosomes are marked with the state. During the stabilization phase, the nucleosome state configuration is further refined and eventually reaches an equilibrium. Even then, the state of individual nucleosomes is still highly dynamic and equilibrium is only reached in the statistical sense.

Bottom Line: It is generally agreed that bivalent domains play an important role in stem cell differentiation, but the underlying mechanisms remain unclear.Here we formulate a mathematical model to investigate the dynamic properties of histone modification patterns.We then illustrate that our modeling framework can be used to capture key features of experimentally observed combinatorial chromatin states.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics, University of Maryland, College Park, Maryland, United States of America ; Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland, United States of America.

ABSTRACT
Epigenetic modifications to histones may promote either activation or repression of the transcription of nearby genes. Recent experimental studies show that the promoters of many lineage-control genes in stem cells have "bivalent domains" in which the nucleosomes contain both active (H3K4me3) and repressive (H3K27me3) marks. It is generally agreed that bivalent domains play an important role in stem cell differentiation, but the underlying mechanisms remain unclear. Here we formulate a mathematical model to investigate the dynamic properties of histone modification patterns. We then illustrate that our modeling framework can be used to capture key features of experimentally observed combinatorial chromatin states.

Show MeSH