arXiv subjects

Joseph W. Baron

Publications and source records attributed to Joseph W. Baron.

22 records · Page 2Linked to original sources

arXiv2020

Effective diffusion coefficients in reaction-diffusion systems with anomalous transport

We show that the Turing patterns in reaction systems with subdiffusion can be replicated in an effective system with Markovian cross-diffusion. The effective system has the same Turing instability as the original system, and the same patterns. If particles are short-lived, the transient dynamics are captured as well. We use the cross-diffusive system to define effective diffusion coefficients for the system with anomalous transport, and we show how they can be used to efficiently describe the Turing instability. We also demonstrate that the mean squared displacement of a suitably defined ensemble of subdiffusing particles grows linearly with time, with a diffusion coefficient which agrees with our earlier calculations. We verify these deductions by numerically integrating both the fractional reaction-diffusion equation and its normally diffusing counterpart. Our findings suggest that cross-diffusive behaviour can come about as a result of anomalous transport.

nlin.PS↗

arXiv2019

Intrinsic noise, Delta-Notch signalling and delayed reactions promote sustained, coherent, synchronised oscillations in the presomitic mesoderm

Using a stochastic individual-based modelling approach, we examine the role that Delta-Notch signalling plays in the regulation of a robust and reliable somite segmentation clock. We find that not only can Delta-Notch signalling synchronise noisy cycles of gene expression in adjacent cells in the presomitic mesoderm (as is known), but it can also amplify and increase the coherence of these cycles. We examine some of the shortcomings of deterministic approaches to modelling these cycles and demonstrate how intrinsic noise can play an active role in promoting sustained oscillations, giving rise to noise-induced quasi-cycles. Finally, we explore how translational/transcriptional delays can result in the cycles in neighbouring cells oscillating in anti-phase and we study how this effect relates to the propagation of noise-induced stochastic waves.

q-bio.SC↗

arXiv2019

Stochastic fluctuations and quasi-pattern formation in reaction-diffusion systems with anomalous transport

Many approaches to modelling reaction-diffusion systems with anomalous transport rely on deterministic equations and ignore fluctuations arising due to finite particle numbers. Starting from an individual-based model we use a generating-functional approach to derive a Gaussian approximation for this intrinsic noise in subdiffusive systems. This results in corrections to the deterministic fractional reaction-diffusion equations. Using this analytical approach, we study the onset of noise-driven quasi-patterns in reaction-subdiffusion systems. We find that subdiffusion can be conducive to the formation of both deterministic and stochastic patterns. Our analysis shows that the combination of subdiffusion and intrinsic stochasticity can reduce the threshold ratio of the effective diffusion coefficients required for pattern formation to a greater degree than either effect on its own.

cond-mat.stat-mech↗

arXiv2016

Sojourn times and fixation dynamics in multi-player games with fluctuating environments

We study evolutionary multi-player games in finite populations, subject to fluctuating environments. The population undergoes a birth-death process with absorbing states, and the environment follows a Markovian process, resulting in a fluctuating payoff matrix for the evolutionary game. Our focus is on the fixation or extinction of a single mutant in a population of wildtypes. We show that the nonlinear nature of fitnesses in multi-player games gives rise to an intricate interplay of selection, genetic drift and environmental fluctuations. This generates effects not seen in simpler two-player games. To analyse trajectories towards fixation we analytically calculate sojourn times for general birth-death processes in populations of two types of individuals and in fluctuating environments.

q-bio.PE↗