George Oster

Two theoretical formalisms are widely used in modeling mechanochemical systems such as protein motors: continuum Fokker-Planck models and discrete kinetic models. Both have advantages and disadvantages. Here we present a “finite volume” procedure to solve Fokker-Planck equations. The procedure relates the continuum equations to a discrete mechanochemical kinetic model while retaining many of the features of the continuum formulation. The resulting numerical algorithm is a generalization of the algorithm developed previously by Fricks, Wang, and Elston through relaxing the local linearization approximation of the potential functions, and a more accurate treatment of chemical transitions. The new algorithm dramatically reduces the number of numerical cells required for a prescribed accuracy. The kinetic models constructed in this fashion retain some features of the continuum potentials, so that the algorithm provides a systematic and consistent treatment of mechanical-chemical responses such as load-velocity relations, which are difficult to capture with a priori kinetic models. Several numerical examples are given to illustrate the performance of the method.

... complex systems. We shall not deal to any great extent with linear graph theory since it is adequately treated in the technical literature (Berge, 1962; Berge & Ghouila-Houri, 1965; Harary, 1969; Seshu & Reed, 1961). The example ...

Myxococcus xanthus is a Gram-negative, soil-dwelling bacterium that glides on surfaces, reversing direction approximately once every 6 min. Motility in M. xanthus is governed by the Che-like Frz pathway and the Ras-like Mgl pathway, which together cause the cell to oscillate back and forth. Previously, Igoshin et al. (2004) suggested that the cellular oscillations are caused by cyclic changes in concentration of active Frz proteins that govern motility. In this study, we present a computational model that integrates both the Frz and Mgl pathways, and whose downstream components can be read as motor activity governing cellular reversals. This model faithfully reproduces wildtype and mutant behaviors by simulating individual protein knockouts. In addition, the model can be used to examine the impact of contact stimuli on cellular reversals. The basic model construction relies on the presence of two nested feedback circuits, which prompted us to reexamine the behavior of M. xanthus cells. We performed experiments to test the model, and this cell analysis challenges previous assumptions of 30 to 60 min reversal periods in frzCD, frzF, frzE, and frzZ mutants. We demonstrate that this average reversal period is an artifact of the method employed to record reversal data, and that in the absence of signal from the Frz pathway, Mgl components can occasionally reverse the cell near wildtype periodicity, but frz- cells are otherwise in a long nonoscillating state.

ABSTRACT By combining the physics of gels with the hydrodynamics of two-phase fluids, we construct a set of equations that describe the hydration dynamics of polyelectrolyte gels. Numerical solutions to these equations are consistent with previous theory and experiments on gel swelling, but extend the physics to include the flow of the fluid solvent as well as treating the fluid and solvent equally. We use our equations to derive the effective diffusion constants for neutral and charged spherically distributed gels in terms of more microscopic paramters. We then solve the novel probelm of calculating the swelling of an isotropic, spherical gel with a permeable boundary condition and compare these results to previous experimetns on swelling gels.

ABSTRACT Crawling eukaryotic cells play many roles in biology. White blood cells chemotactically track down pathogens. Fibroblasts crawl and pull skin back together during wound healing. Cancer cells become metastatic and migrate to other points in the body. Therefore, understanding the physical mechanism driving crawling motility is very important. In crawling cells, a polymer meshwork, usually composed of actin filaments, provides both the structural integrity of the cell and is reponsible for the force production during migration. We present a theory that describes the dynamics of this actin gel and apply it to the crawling motility of nematode sperm cells. This model maintains the shape of the cell during crawling as occurs during the migration of Ascaris suum spermatozoa and also produces forces comparable to what has been measured in other crawling cells.