Stochastic resetting and applications Evans, Martin R; Majumdar, Satya N; Schehr, Grégory
Journal of physics. A, Mathematical and theoretical,
05/2020, Letnik:
53, Številka:
19
Journal Article
Recenzirano
Odprti dostop
In this topical review we consider stochastic processes under resetting, which have attracted a lot of attention in recent years. We begin with the simple example of a diffusive particle whose ...position is reset randomly in time with a constant rate r, which corresponds to Poissonian resetting, to some fixed point (e.g. its initial position). This simple system already exhibits the main features of interest induced by resetting: (i) the system reaches a nontrivial nonequilibrium stationary state (ii) the mean time for the particle to reach a target is finite and has a minimum, optimal, value as a function of the resetting rate r. We then generalise to an arbitrary stochastic process (e.g. Lévy flights or fractional Brownian motion) and non-Poissonian resetting (e.g. power-law waiting time distribution for intervals between resetting events). We go on to discuss multiparticle systems as well as extended systems, such as fluctuating interfaces, under resetting. We also consider resetting with memory which implies resetting the process to some randomly selected previous time. Finally we give an overview of recent developments and applications in the field.
Diffusion with stochastic resetting Evans, Martin R; Majumdar, Satya N
Physical review letters,
2011-Apr-22, Letnik:
106, Številka:
16
Journal Article
Recenzirano
Odprti dostop
We study simple diffusion where a particle stochastically resets to its initial position at a constant rate r. A finite resetting rate leads to a nonequilibrium stationary state with non-Gaussian ...fluctuations for the particle position. We also show that the mean time to find a stationary target by a diffusive searcher is finite and has a minimum value at an optimal resetting rate r*. Resetting also alters fundamentally the late time decay of the survival probability of a stationary target when there are multiple searchers: while the typical survival probability decays exponentially with time, the average decays as a power law with an exponent depending continuously on the density of searchers.
Bacterial growth environment strongly influences the efficacy of antibiotic treatment, with slow growth often being associated with decreased susceptibility. Yet in many cases, the connection between ...antibiotic susceptibility and pathogen physiology remains unclear. We show that for ribosome‐targeting antibiotics acting on Escherichia coli, a complex interplay exists between physiology and antibiotic action; for some antibiotics within this class, faster growth indeed increases susceptibility, but for other antibiotics, the opposite is true. Remarkably, these observations can be explained by a simple mathematical model that combines drug transport and binding with physiological constraints. Our model reveals that growth‐dependent susceptibility is controlled by a single parameter characterizing the ‘reversibility’ of ribosome‐targeting antibiotic transport and binding. This parameter provides a spectrum classification of antibiotic growth‐dependent efficacy that appears to correspond at its extremes to existing binary classification schemes. In these limits, the model predicts universal, parameter‐free limiting forms for growth inhibition curves. The model also leads to non‐trivial predictions for the drug susceptibility of a translation mutant strain of E. coli, which we verify experimentally. Drug action and bacterial metabolism are mechanistically complex; nevertheless, this study illustrates how coarse‐grained models can be used to integrate pathogen physiology into drug design and treatment strategies.
Synopsis
Fast‐growing E. coli cells are found to be more susceptible to reversibly‐binding ribosome‐targeting antibiotics while the opposite is true for irreversibly‐binding antibiotics. A coarse‐grained model explains this growth‐dependent susceptibility.
Fast‐growing cells are more susceptible to reversibly‐binding antibiotics while slow‐growing cells are more susceptible to irreversibly‐binding antibiotics.
This can be explained by a simple model, combining drug transport and binding with physiological constraints linking growth rate to ribosome abundance and synthesis.
The model highlights a combination of parameters that can be used to characterize growth‐dependent susceptibility and generates non‐trivial predictions for the drug susceptibility of a translation‐mutant strain.
The study illustrates how coarse‐grained models can be used to integrate pathogen physiology into drug design and treatment strategies.
Fast‐growing E. coli cells are found to be more susceptible to reversibly‐binding ribosome‐targeting antibiotics while the opposite is true for irreversibly‐binding antibiotics. A coarse‐grained model explains this growth‐dependent susceptibility.
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