Active Brownian Particles. From Individual to Collective Stochastic Dynamics

We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of such self-propelled entities in the framework of statistical mechanics. Examples of such active units in complex physico-chemical and biological systems are chemically powered nano-rods, localized patterns in reaction-diffusion system, motile cells or macroscopic animals. Based on the description of individual motion of point-like active particles by stochastic differential equations, we discuss different velocity-dependent friction functions, the impact of various types of fluctuations and calculate characteristic observables such as stationary velocity distributions or diffusion coefficients. Finally, we consider not only the free and confined individual active dynamics but also different types of interaction between active particles. The resulting collective dynamical behavior of large assemblies and aggregates of active units is discussed and an overview over some recent results on spatiotemporal pattern formation in such systems is given.Comment: 161 pages, Review, Eur Phys J Special-Topics, accepte

Extracellular Signal-regulated Kinase Mediates Phosphorylation of Tropomyosin-1 to Promote Cytoskeleton Remodeling in Response to Oxidative Stress: Impact on Membrane Blebbing

Oxidative stress induces in endothelial cells a quick and transient coactivation of both stress-activated protein kinase-2/p38 and extracellular signal-regulated kinase (ERK) mitogen-activated protein kinases. We found that inhibiting the ERK pathway resulted, within 5 min of oxidative stress, in a misassembly of focal adhesions characterized by mislocalization of key proteins such as paxillin. The focal adhesion misassembly that followed ERK inhibition with the mitogen-activated protein kinase kinase (MEK) inhibitor PD098059 (2′-amino-3′-methoxyflavone) or with a kinase negative mutant of ERK in the presence of H(2)O(2) resulted in a quick and intense membrane blebbing that was associated with important damage to the endothelium. We isolated by two-dimensional gel electrophoresis a PD098059-sensitive phosphoprotein of 38 kDa that we identified, by mass spectrometry, as tropomyosin-1. In fact, H(2)O(2) induced a time-dependent phosphorylation of tropomyosin that was sensitive to inhibition by PD098059 and UO126 (1,4-diamino-2,3-dicyano-1,4-bis[2-aminophenylthio]butanediane). Tropomyosin phosphorylation was also induced by expression of a constitutively activated form of MEK1 (MEK(CA)), which confirms that its phosphorylation resulted from the activation of ERK. In unstimulated cells, tropomyosin-1 was found diffuse in the cells, whereas it quickly colocalized with actin and stress fibers upon stimulation of ERK by H(2)O(2) or by expression of MEK(CA). We propose that phosphorylation of tropomyosin-1 downstream of ERK by contributing to formation of actin filaments increases cellular contractility and promotes the formation of focal adhesions. Incidentally, ML-7 (1-[5iodonaphthalene-1-sulfonyl]homopiperazine, HCl), an inhibitor of cell contractility, inhibited phosphorylation of tropomyosin and blocked the formation of stress fibers and focal adhesions, which also led to membrane blebbing in the presence of oxidative stress. Our finding that tropomyosin-1 is phosphorylated downstream of ERK, an event that modulates its interaction with actin, may lead to further understanding of the role of this protein in regulating cellular functions associated with cytoskeletal remodeling