WKB study of fluctuations and activation in nonequilibrium dissipative steady states

The distributions of many proteins in rod-shaped bacteria are far from homogeneous. Often they accumulate at the cell poles or in the cell centre. At the same time, the copy number of proteins in a single cell is relatively small making the patterns noisy. To explore limits to protein patterns due to molecular noise, we studied a generic mechanism for spontaneous polar protein assemblies in rod-shaped bacteria, which are based on cooperative binding of proteins to the cytoplasmic membrane. For mono-polar assemblies, we find that the switching time between the two poles increases exponentially with the cell length and with the protein number. This feature could be beneficial to organelle maintenance in ageing bacteria.

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“…Note, that variations of C 0 and M 0 are not independent as C 0 + M 0 = 1/L. From the above expression follows that 25) and similarly…”

Section: Galerkin Approximation For the Fokker-planck Equationmentioning

confidence: 87%

Effects of molecular noise on bistable protein distributions in rod-shaped bacteria

2014

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“…The idea of energy is considerably more subtle than it sometimes seems, if systems are dissipative, nonlinear, and open, thus violating, in many respects, the assumptions made in elementary treatments of thermodynamics or mechanics. Consideration of the mechanics of nonlinear mechanical systems containing just a few components, like a driven dissipative pendulum (Ben- Jacob, Bergman, Matkowsky & Schuss, 1982;Kupferman, Kaiser, Schuss & Ben-Jacob, 1992), shows the need for careful thought and mathematical treatment before extending the laws of thermodynamics to nonequilibrium nonlinear systems.…”

Section: Poisson's Equation In Semiconductorsmentioning

confidence: 99%

Computing the Field in Proteins and Channels

Eisenberg¹

1996

Journal of Membrane Biology

242

237

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“…Fig. 3 in [73]). As discussed above, the linear relation between and v h can be calculated perturbatively for small and reads v h = / √ 32.…”

Section: Phase Approximationmentioning

confidence: 99%

Theory of pattern forming systems under traveling-wave forcing

et al. 2007

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The response of pattern forming systems to external forcing either spatial or temporal has received much attention for several decades. Combined spatio-temporal forcing has only been introduced recently, in particular in the form of a spatially resonant traveling-wave forcing [S. Rüdiger, D.G. Míguez, A.P. Muñuzuri, F. Sagués, J. Casademunt, Phys. Rev. Lett. 90 (2003) 128301]. Since then, both a series of experiments, in the context of Turing patterns in reaction-diffusion systems, and the development of the corresponding generic theory, have unveiled a wealth of new and unexpected phenomena. In this article we review these phenomena, we provide a unified and comprehensive description of them, and extend the theoretical analysis to new situations. We formulate the generic amplitude equations for different orders of spatial resonance for 1d and 2d patterns (stripes and hexagons). We identify and describe in detail the autonomous dynamical system which underlies the phenomenon of traveling-stripe resonance. For 1d we focus on localized solutions (kinks and pulses), their dynamics and their interaction for both 1:1 and 2:1 resonance. Specifically, we discuss the effect of wave-number mismatch (inexact resonance) combined with the non-gradient dynamics induced by the motion of the forcing, resulting in non-trivial interactions and complex spatio-temporal dynamics. Analytical results in the phase approximation are obtained, while numerical techniques are used to study the complete problem. We show that defect interaction is oscillatory with distance, allowing for the existence of locked chaotic wave trains. In 2d we discuss the modulational instabilities of striped patterns and focus mostly on the emergence of hexagons induced by traveling stripe forcing, for exact 1:1 resonance. In this case, we examine in detail the complex bifurcation scenario beyond primary instabilities. We finally discuss the problem of traveling-wave forcing in the context of a specific system, the photosensitive CDIMA reaction, where most experiments have been carried out. We compare experiments and theoretical predictions and propose other experimental systems where the study could be extended. Finally, we review related work by other authors and discuss possible further developments and open questions which hold the promise of new interesting findings.

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WKB study of fluctuations and activation in nonequilibrium dissipative steady states

Cited by 9 publications

References 40 publications

Effects of molecular noise on bistable protein distributions in rod-shaped bacteria

Effects of molecular noise on bistable protein distributions in rod-shaped bacteria

Computing the Field in Proteins and Channels

Theory of pattern forming systems under traveling-wave forcing

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