BIOPHYSICAL THEORY AND MODELING |
Reaction coordinates for the flipping of genetic switches
Marco J. Morelli 1, Sorin Tanase-Nicola 1, Rosalind J Allen 2 and Pieter Rein ten Wolde 1*
1 FOM Institute for Atomic and Molecular Physics
2 School of Physics, University of Edinburgh
* To whom correspondence should be addressed. E-mail: tenwolde{at}amolf.nl.
Submitted on July 4, 2007
Revised on August 12, 2007
Accepted on 13 December 2007
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Abstract |
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We present a detailed analysis, based on the Forward Flux Sampling (FFS) simulation method, of the switching dynamics and stability of two models of genetic toggle switches, consisting of two mutually-repressing genes encoding transcription factors (TFs); in one model (the exclusive switch), the two transcription factors mutually exclude each other's binding, while in the other model (general switch) the two transcription factors can bind simultaneously to the shared operator region. We assess the role of two pairs of reactions that in uence the stability of these switches: TF-TF homodimerisation and TF-DNA association/dissociation. In both cases, the switch ipping rate increases with the rate of TF dimerisation, while it decreases with the rate of TF-operator binding. We factorise the flipping rate k into the product of the probability p(q*) of finding the system at the dividing surface (separatrix)between the two stable states, and a kinetic prefactor R. In the case of the exclusive switch, the rate of TF-operator binding affects both p(q*) d R, while the rate of TF dimerisation affects only R. The general switch displays a higher ipping rate than the exclusive switch, and both TF-operator binding and TF dimerisation affect k, R and p(q*) To elucidate this, we analyze the transition state ensemble (TSE). For the exclusive switch, the TSE is strongly affected by the rate of TF-operator binding, but unaffected by varying the rate of TF-TF binding. Thus, varying the rate of TFoperator binding can drastically change the pathway of switching, while changing the rate of dimerisation changes the switching rate without altering the mechanism. The switching pathways of the general switch are highly robust to changes in the rate constants of both TF-operator and TF-TF binding, even though these rate constants do affect the flipping rate; this feature is unique for non-equilibrium systems.
Key Words:
genetic switches, modeling, rare events, systems biology
