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This work considers an expansion of a dense monolayer of cells: a collective multicellular phenomenon, where cells divide, grow, and maintain contacts with their neighbors. During migration, cells display complex behavior, adjusting both their division rate and their growth after division to the local mechanical environment. Experimental observations show that cells near the edge of the expanding monolayer are larger and move faster than cells deep inside the colony. To explain these observations and describe cell migration patterns, we formulate a spatio-temporal theoretical model for multicellular dynamics in terms of the cell area distribution; the model includes cell growth after division and effective pressure. Numerical simulations of the model predict both the speed of invasion and the width of the outer proliferative rim; these predictions are in a good agreement with experimental observations. Theoretical analysis yields the equation for density of cells and reveals a novel type of propagating front with compact support. The velocity of front propagation (monolayer expansion) is derived analytically and its dependence on all the relevant parameters is determined. [ABSTRACT FROM AUTHOR]

Analyses have disagreed on whether the velocity u T of bulk advancement of a Huygens front in turbulence vanishes or remains finite in the limit of vanishing local front propagation speed u 0 . Here, a connection to the large-deviation statistics of log-correlated random processes enables a definitive determination of the correct small- u 0 asymptotics. This result reconciles several theoretical and phenomenological perspectives with the conclusion that u T remains finite for vanishing u 0 , which implies a propagation anomaly akin to the energy-dissipation anomaly in the limit of vanishing viscosity. Various leading-order structural properties such as a novel u 0 dependence of a bulk length scale associated with front geometry are predicted in this limit. The analysis involves a formal analogy to random advection of diffusive scalars. [ABSTRACT FROM AUTHOR]

We consider a system of N particles with a stochastic dynamics introduced by Brunet and Derrida (Phys. Rev. E 70:016106, ). The particles can be interpreted as last passage times in directed percolation on {1,..., N} of mean-field type. The particles remain grouped and move like a traveling front, subject to discretization and driven by a random noise. As N increases, we obtain estimates for the speed of the front and its profile, for different laws of the driving noise. As shown in Brunet and Derrida (Phys. Rev. E 70:016106, ), the model with Gumbel distributed jumps has a simple structure. We establish that the scaling limit is a Lévy process in this case. We study other jump distributions. We prove a result showing that the limit for large N is stable under small perturbations of the Gumbel. In the opposite case of bounded jumps, a completely different behavior is found, where finite-size corrections are extremely small. [ABSTRACT FROM AUTHOR]

We present a discrete stochastic model which represents many of the salient features of the biological process of wound healing. The model describes fronts of cells invading a wound. We have numerical results in one and two dimensions. In one dimension we can give analytic results for the front speed as a power series expansion in a parameter, p, that gives the relative size of proliferation and diffusion processes for the invading cells. In two dimensions the model becomes the Eden model for p ≈ 1. In both one and two dimensions for small p, front propagation for this model should approach that of the Fisher-Kolmogorov equation. However, as in other cases, this discrete model approaches Fisher-Kolmogorov behavior slowly. [ABSTRACT FROM AUTHOR]

We study reaction-diffusion systems where diffusion is by jumps whose sizes are distributed exponentially. We first study the Fisher-like problem of propagation of a front into an unstable state, as typified by the A+B → 2A reaction. We find that the effect of fluctuations is especially pronounced at small hopping rates. Fluctuations are treated heuristically via a density cutoff in the reaction rate. We then consider the case of propagating up a reaction rate gradient. The effect of fluctuations here is pronounced, with the front velocity increasing without limit with increasing bulk particle density. The rate of increase is faster than in the case of a reaction-gradient with nearest-neighbor hopping. We derive analytic expressions for the front velocity dependence on bulk particle density. Computer simulations are performed to confirm the analytical results. [ABSTRACT FROM AUTHOR]