Theoretical analysis of Nucleosome mediated Epigenetics

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Chromosomal regions can adopt stable and heritable alternative states resulting in bistable gene expression without changes to the DNA sequence. Such epigenetic control is often associated with alternative covalent modifications of histones. The stability and heritability of the states is thought to involve positive feedback where modified nucleosomes recruit enzymes that similarly modify nearby nucleosomes. We developed a simplified stochastic model for dynamic nucleosome modification based on the silent mating-type region of the yeast Schizosaccharomyces pombe. We show that the mechanism can indeed give strong bistability that is resistant both to high noise due to random gain or loss of nucleosome modifications, and also to the random partitioning upon DNA replication. However, robust bistability required
  1. cooperativity, the activity of more than one modified nucleosome, in the modification reactions; and
  2. that nucleosomes occasionally stimulate modification beyond their neighbour nucleosomes,
arguing against a simple continuous spreading of nucleosome modification.

Algorithm: The stochastic simulation is carried out by iterating the following process of attempted modification of a nucleosome.

  • Step 1: A random nucleosome n1 to be modified is selected from among the N nucleosomes. With probability α a positive feedback (recruited) conversion of n1 is attempted (Step 2A), OR (with probability 1-α a noisy change of n1 is attempted (Step 2B).
  • Step 2A: - Recruited conversion: A second random nucleosome n2 is selected from anywhere within the region and if n2 is in either the M or the A state, n1 is changed one step towards the state of n2. That is, if n2 is M, then n1 is changed A->U or U->M; if n2 is A, then n1 is 10 changed M->U or U->A. If n1 and n2 are in the same state, or if n2 is a U, then no changes are performed.
  • Step 2B: - Noisy conversion:. Nucleosome n1 is changed one step towards either of the other types (i.e. no direct A . M interconversions) with a probability 1/3 or is left unchanged.

α is found from F=α/(1-α) reflecting that our key controll parameter F is the ratio of recruitment attempts to noise attempts.

The dynamics of the system is illustrated in the figure. In the bi-stable system the majority of nucleosomes are maintained for a longer periode in either the M or the A state.

The log of the probility of being in a state is - to a rough approximation - inversely proportional to an effective potential. A bi-stable system requires of the potential that there are two minima and a barrier between them. A barrier at M=A means that it is difficult to maintain a state with equally many M and A's: In our real system an excess of either M or A will be selfampifying due to the positive feedback. To get from one minima (state) to the other, the barrier has to be crossed, and this process is drive by fluctuations in recruitment and noise (including cell-division). The rate of going from the A to the M state (or vice verca) is propotional to exp(ΔV) and thus the stability will grow exponentially with the height of the barrier ΔV.

[1] I. B. Dodd, M. A. Micheelsen, K. Sneppen and G. Thon. (2007)
Theoretical Analysis of Epigenetic Cell Memory by Nucleosome Modification.
Cell, 129 , pp 813-822