Post-translational modifications of the histone proteins in the chromosomes are an important factor in epigenetic control as specific regions of DNA in the chromatin are expressed , depending on the particular modification states of the histone proteins. We study the stochastic dynamics of histone protein states, taking into account a non-local feedback mechanism where modified nucleosomes recruit enzymes that diffuse to nearby nucleosomes. We formulate the master equation as a quantum many-body variational problem and employ a Hartree ansatz to obtain a system of coupled nonlinear difference equations . Multiple stable histone states appear in a parameter regime whose size increases with increasing number of modification sites , and multistability is possible even if the non-local feedback term is weak compared to local processes. Increasing the number of independent modification sites exponentially increases the number of stable histone states. We discuss the role of the spatial dependence due to the non-local feedback mechanism , and we consider the effects of spatially heterogeneous enzymatic activity  .
Post-translational modifications of histone proteins are an important factor in epigenetic control that serve to regulate transcription , depending on the particular modification states of the histone proteins. We study the stochastic dynamics of histone protein states, taking into account a feedback mechanism where modified nucleosomes recruit enzymes that diffuse to adjacent nucleosomes. We map the system onto a quantum spin system whose dynamics is generated by a non-Hermitian Hamiltonian. Making an ansatz for the solution as a tensor product state leads to nonlinear partial differential equations that describe the dynamics of the system . Multiple stable histone states appear in a parameter regime whose size increases with increasing number of modification sites . We discuss the role of the spatial dependance , and we consider the effects of spatially heterogeneous enzymatic activity . Finally, we consider multistability in a model of several types of correlated post-translational modifications .
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the histone proteins in the chromosomes
histone proteins
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as specific regions of DNA in the chromatin are expressed
that serve to regulate transcription
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non-local
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nearby
adjacent
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formulate the master equation as a quantum many-body variational problem and employ a Hartree ansatz to obtain a system of coupled nonlinear difference equations
map the system onto a quantum spin system whose dynamics is generated by a non-Hermitian Hamiltonian. Making an ansatz for the solution as a tensor product state leads to nonlinear partial differential equations that describe the dynamics of the system
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, and multistability is possible even if the non-local feedback term is weak compared to local processes. Increasing the number of independent modification sites exponentially increases the number of stable histone states.
.
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dependence due to the non-local feedback mechanism
dependance
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. Finally, we consider multistability in a model of several types of correlated post-translational modifications