Theoretical analysis of Nucleosome mediated Epigenetics

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  1. Simulation Window: Shows the state of the individual histones. The visual update of the histones depend on the "update speed" buttons in panel 2. If both buttons are inactive (blue) every update will be seen as a small animation. If one or both buttons are pressed, this window is updated every N,100 or Nx100 updates .

    A histone can be changed manually. By clicking on a histone a green box will appear in the top right corner from where the histone can be changed to either of the 3 states.

  2. Timeseries: This panel shows the timeseries of the methylated and/or acethylated state.

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  3. Probability plot: Shows the probability distribution of (M-A). Under the plot there are two buttons. The left button resets the probability data only, and the right gives an option to view the data either as log or normal.
  4. Standard control window:
    Left from top:
    • Pause/Start (Pauses/restarts)
    • Reset (resets all)
    • The dimension of recruitment can be chosen here. There are 3 values: 3d/1d/"pow. law." 1d and "pow. law." will give access to the advanced (red-colored) panel 5 under the button.
      Default is 3d, in which recruitment happens with equal probability along the Region.
    Right from top:
    • F - recruit to noise ration α/(1-α)
    • N - system size, can take values between 2 and 120
    • Assymetry - activates assymetry that is controlled from panel 6.
    • Cell division - activates cell division that is controlled from panel 7
    Middle: Shows the status of the simulation - N, F and how long it time it has gathered data.
  5. Dimension: This panel is active when the dimension is 1d or power law.
    For 1d there are two options:
    • a standard 1d, where the recruitment only can happen by neighboring nucleosomes
    • and an advanced 1d where nucleosomes can act at two distances (with equal probability) specified by the user.
    Under powerlaw the powerlaw can be specified.
  6. Assymetry: This panel is active when the assymetry button from panel 5 is pressed.
    There are two types of assymetry: Type1 affects both recruitive moves: U->A and M->U, while Type2 only affects the move U->A. The assymmetry can be any number larger than 0.
  7. Cell division: This panel is active when the Cell div form panel 5 is pressed.
    Here there is a choise of the number of updates that should happen between cell divisions, and the distribution of the new nucleosomes added after cell-division.

Philosophy

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