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

Reconstitution and Characterization of Budding Yeast γ-Tubulin Complex

Nucleation of microtubules is central to assembly of the mitotic spindle, which is required for each cell division. γ-Tubulin is a universal component essential for microtubule nucleation from centrosomes. To elucidate the mechanism of microtubule nucleation in budding yeast we reconstituted and characterized the yeast γ-tubulin complex (Tub4p complex) produced in insect cells. The recombinant complex has the same sedimentation coefficient (11.6 S) as the native complex in yeast cell extracts and contains one molecule of Spc97p, one molecule of Spc98p, and two molecules of Tub4p. The reconstituted Tub4p complex binds preformed microtubules and has a low nucleating activity, allowing us to begin a detailed analysis of conditions that enhance this nucleating activity. We tested whether binding of the recombinant Tub4p complex to the spindle pole body docking protein Spc110p affects its nucleating activity. The solubility of recombinant Spc110p in insect cells is improved by coexpression with yeast calmodulin (Cmd1p). The Spc110p/Cmd1p complex has a small sedimentation coefficient (4.2 S) and a large Stokes radius (14.3 nm), indicative of an elongated structure. The Tub4p complex binds Spc110p/Cmd1p via Spc98p and the K(d) for binding is 150 nM. The low nucleation activity of the Tub4p complex is not enhanced when it is bound to Spc110p/Cmd1p, suggesting that it requires additional components or modifications to achieve robust activity. Finally, we report the identification of a large 22 S Tub4p complex in yeast extract that contains multimers of Spc97p similar to γ-tubulin ring complexes found in higher eukaryotic cells

Dendritic Fibroblasts in Three-dimensional Collagen Matrices

Cell motility determines form and function of multicellular organisms. Most studies on fibroblast motility have been carried out using cells on the surfaces of culture dishes. In situ, however, the environment for fibroblasts is the three-dimensional extracellular matrix. In the current research, we studied the morphology and motility of human fibroblasts embedded in floating collagen matrices at a cell density below that required for global matrix remodeling (i.e., contraction). Under these conditions, cells were observed to project and retract a dendritic network of extensions. These extensions contained microtubule cores with actin concentrated at the tips resembling growth cones. Platelet-derived growth factor promoted formation of the network; lysophosphatidic acid stimulated its retraction in a Rho and Rho kinase-dependent manner. The dendritic network also supported metabolic coupling between cells. We suggest that the dendritic network provides a mechanism by which fibroblasts explore and become interconnected to each other in three-dimensional space