Abstract. Angular self-organization of the actin cytoskeleton is modeled as a process of instant changing of filament orientation in the course of specific actin-actin interactions. These interactions are modified by cross-linking actin-binding proteins. This problem was raised first by Civelekoglu and Edelstein-Keshet [Bull. Math. Biol., 56 (1994), pp. 587–616]. When restricted to a two-dimensional configuration, the mathematical model consists of a single Boltzmann-like integrodifferential equation for the one-dimensional angular distribution. Linear stability analysis, asymptotic analysis, and numerical results reveal that at certain parameter values of actin-actin interactions, spontaneous alignment of filaments in the form of unipolar or bipolar bundles or orthogonal networks can be expected.

this paper, we consider local and non-local spatially explicit mathematical models for biological phenomena. We show that, when rate di!erences between fast and slow local dynamics are great enough, non-local models are adequate simpli"cations of local models. Non-local models thus avoid describing fast processes in mechanistic detail, instead describing the e!ects of fast processes on slower ones. As a consequence, non-local models are helpful to biologists because they describe biological systems on scales that are convenient to observation, data collection, and insight. We illustrate these arguments by comparing local and non-local models for the aggregation of hypothetical organisms, and we support theoretical ideas with concrete examples from cell biology and animal behavior. ( 2001 Academic Press 1. Introduction Biological interactions occur at speci"c locations and frequentl

This paper introduces a one-dimensional, partial integro-differential model for bacterial aggregation. Integro-differential equation is derived from a chemotactic partial differential system, and stability and numerical analyses are applied to study pattern formation. We demonstrate that an interplay between positive and negative chemotaxis can generate both periodic patterns and aggregation. In the limit of slow diffusion we use a Lagrangian approach to derive a gradient system and analyze periodic peak-like patterns. We discuss the possibility of existence of other types of patterns, and the applicability of the model to the pattern formation in bacterial swarms, in particular the rippling phenomenon in Myxobacteria. 1 Introduction Pattern formation is an intriguing widespread phenomenon in nature, particularly in biology. In this paper we are concerned with patterns evolving in populations of microorganisms, phenomena that have been studied extensively. The spatio-temporal patte...