Stochastic transitions in a bistable reaction system on the membrane

Kochańczyk, Marek; Jaruszewicz, Joanna; Lipniacki, Tomasz

doi:10.1098/rsif.2013.0151

Cited by 15 publications

(14 citation statements)

References 62 publications

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“…All of the considered models introduced hereafter are analyzed by means of spatial kinetic Monte Carlo (KMC) simulations [37,38], Molecules are placed on discrete sites of a two-dimensional triangular lattice which forms a square domain with periodic boundary conditions. The molecules diffuse freely by hopping to adjacent empty lattice sites.…”

Section: A Numerical Methodsmentioning

confidence: 99%

Effective reaction rates in diffusion-limited phosphorylation-dephosphorylation cycles

et al. 2015

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We investigate the kinetics of the ubiquitous phosphorylation-dephosphorylation cycle on biological membranes by means of kinetic Monte Carlo simulations on the triangular lattice. We establish the dependence of effective macroscopic reaction rate coefficients as well as the steady-state phosphorylated substrate fraction on the diffusion coefficient and concentrations of opposing enzymes: kinases and phosphatases. In the limits of zero and infinite diffusion, the numerical results agree with analytical predictions; these two limits give the lower and the upper bound for the macroscopic rate coefficients, respectively. In the zero-diffusion limit, which is important in the analysis of dense systems, phosphorylation and dephosphorylation reactions can convert only these substrates which remain in contact with opposing enzymes. In the most studied regime of nonzero but small diffusion, a contribution linearly proportional to the diffusion coefficient appears in the reaction rate. In this regime, the presence of opposing enzymes creates inhomogeneities in the (de)phosphorylated substrate distributions: The spatial correlation function shows that enzymes are surrounded by clouds of converted substrates. This effect becomes important at low enzyme concentrations, substantially lowering effective reaction rates. Effective reaction rates decrease with decreasing diffusion and this dependence is more pronounced for the less-abundant enzyme. Consequently, the steady-state fraction of phosphorylated substrates can increase or decrease with diffusion, depending on relative concentrations of both enzymes. Additionally, steady states are controlled by molecular crowders which, mostly by lowering the effective diffusion of reactants, favor the more abundant enzyme.

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Section: A Numerical Methodsmentioning

confidence: 99%

Effective reaction rates in diffusion-limited phosphorylation-dephosphorylation cycles

et al. 2015

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“…In this case, the front can be established in the opening called axon hilock, as in the solution shown in Fig 2E (subpanel E2). As demonstrated in [ 34 ], polarizing traveling fronts can arise also due to stochastic fluctuations, which occur more eagerly in narrow parts of the domain.…”

Section: Discussionmentioning

confidence: 99%

Polarization of concave domains by traveling wave pinning

2017

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Pattern formation is one of the most fundamental yet puzzling phenomena in physics and biology. We propose that traveling front pinning into concave portions of the boundary of 3-dimensional domains can serve as a generic gradient-maintaining mechanism. Such a mechanism of domain polarization arises even for scalar bistable reaction-diffusion equations, and, depending on geometry, a number of stationary fronts may be formed leading to complex spatial patterns. The main advantage of the pinning mechanism, with respect to the Turing bifurcation, is that it allows for maintaining gradients in the specific regions of the domain. By linking the instant domain shape with the spatial pattern, the mechanism can be responsible for cellular polarization and differentiation.

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“…In this subsection we analyze events of switching between metastable states in a bistable reaction-diffusion system that has been analyzed previously by means of on-lattice kinetic Monte Carlo simulations in Ref. [21]. The system contains autophosphorylating bisphosphorylatable kinases K and phosphatases P, that react as follows:…”

Section: State-to-state Transition Rates In a Bistable Systemmentioning

confidence: 99%

Sampling rare events in stochastic reaction-diffusion systems within trajectory looping

2018

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In bistable reaction-diffusion systems, transitions between stable states typically occur on timescales orders of magnitude longer than the chemical equilibration time. Estimation of transition rates within explicit Brownian dynamics simulations is computationally prohibitively costly. We present a method that exploits a single trajectory, generated by a prior simulation of diffusive motions of molecules, to sample chemical kinetic processes on timescales several orders of magnitude longer than the duration of the diffusive trajectory. In this approach, we "loop" the diffusive trajectory by transferring chemical states of the molecules from the last to the first time step of the trajectory. Trajectory looping can be applied to enhance sampling of rare events in biochemical systems in which the number of reacting molecules is constant, as in cellular signal transduction pathways. As an example, we consider a bistable system of autophosphorylating kinases, for which we calculate state-to-state transition rates and traveling wave velocities. We provide an open-source implementation of the method.

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Stochastic transitions in a bistable reaction system on the membrane

Cited by 15 publications

References 62 publications

Effective reaction rates in diffusion-limited phosphorylation-dephosphorylation cycles

Effective reaction rates in diffusion-limited phosphorylation-dephosphorylation cycles

Polarization of concave domains by traveling wave pinning

Sampling rare events in stochastic reaction-diffusion systems within trajectory looping

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