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The stochastic behavior of a molecular switching circuit with feedback
Background: Using a statistical physics approach, we study the stochastic
switching behavior of a model circuit of multisite phosphorylation and
dephosphorylation with feedback. The circuit consists of a kinase and
phosphatase acting on multiple sites of a substrate that, contingent on its
modification state, catalyzes its own phosphorylation and, in a symmetric
scenario, dephosphorylation. The symmetric case is viewed as a cartoon of
conflicting feedback that could result from antagonistic pathways impinging on
the state of a shared component.
Results: Multisite phosphorylation is sufficient for bistable behavior under
feedback even when catalysis is linear in substrate concentration, which is the
case we consider. We compute the phase diagram, fluctuation spectrum and
large-deviation properties related to switch memory within a statistical
mechanics framework. Bistability occurs as either a first-order or second-order
non-equilibrium phase transition, depending on the network symmetries and the
ratio of phosphatase to kinase numbers. In the second-order case, the circuit
never leaves the bistable regime upon increasing the number of substrate
molecules at constant kinase to phosphatase ratio.
Conclusions: The number of substrate molecules is a key parameter controlling
both the onset of the bistable regime, fluctuation intensity, and the residence
time in a switched state. The relevance of the concept of memory depends on the
degree of switch symmetry, as memory presupposes information to be remembered,
which is highest for equal residence times in the switched states.
Reviewers: This article was reviewed by Artem Novozhilov (nominated by Eugene
Koonin), Sergei Maslov, and Ned Wingreen.Comment: Version published in Biology Direct including reviewer comments and
author responses, 28 pages, 7 figure
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