The intricate geometry of cytoskeletal networks and internal membranes causes the space available for diffusion in cytoplasm to be convoluted, thereby affecting macromolecule diffusivity. We present a first systematic computational study of this effect by approximating intracellular structures as mixtures of random overlapping obstacles of various shapes. Effective diffusion coefficients are computed using a fast homogenization technique. It is found that a simple two-parameter power law provides a remarkably accurate description of effective diffusion over the entire range of volume fractions and for any given composition of structures. This universality allows for fast computation of diffusion coefficients, once the obstacle shapes and volume fractions are specified. We demonstrate that the excluded volume effect alone can account for a four-to-sixfold reduction in diffusive transport in cells, relative to diffusion in vitro. The study lays the foundation for an accurate coarse-grain formulation that would account for cytoplasm heterogeneity on a micron scale and binding of tracers to intracellular structures.

An algorithm is presented for solving a diffusion equation on a curved surface coupled to diffusion in the volume, a problem often arising in cell biology. It applies to pixilated surfaces obtained from experimental images and performs at low computational cost. In the method, the Laplace-Beltrami operator is approximated locally by the Laplacian on the tangential plane and then a finite volume discretization scheme based on a Voronoi decomposition is applied. Convergence studies show that mass conservation built in the discretization scheme and cancellation of sampling error ensure convergence of the solution in space with an order between 1 and 2. The method is applied to a cellbiological problem where a signaling molecule, G-protein Rac, cycles between the cytoplasm and cell membrane thus coupling its diffusion in the membrane to that in the cell interior. Simulations on realistic cell geometry are performed to validate, and determine the accuracy of, a recently proposed simplified quantitative analysis of fluorescence loss in photobleaching. The method is implemented within the Virtual Cell computational framework freely accessible at www.vcell.org.

In living cells, the cytoskeleton connects to the extracellular environment through focal adhesions, multimolecular structures that can sense applied force. A model is presented that for the first time explains why the focal adhesions tend to high-curvature regions at the cell periphery. It is based on experimental evidence for positive feedback between adhesion formation and assembly of actomyosin bundles (stress fibers). The model predicts that the focal adhesions propagate by treadmilling with a velocity proportional to the integrin diffusion coefficient.

The availability of quantitative experimental data on the kinetics of actin assembly has enabled the construction of many mathematical models focused on explaining specific behaviors of this complex system. However these ad hoc models are generally not reusable or accessible by the large community of actin biologists. In this work, we present a comprehensive model that integrates and unifies much of the in vitro data on the components of the dendritic nucleation mechanism for actin dynamics. More than 300 simulations have been run based on compartmental and three-dimensional spatial versions of this model. Several key findings are highlighted, including an explanation for the sharp boundary between actin assembly and disassembly in the lamellipodia of migrating cells. Because this model, with the simulation results, is "open source", in the sense that it is publicly available and editable through the Virtual Cell database (http://vcell.org), it can be accessed, analyzed, modified, and extended.

The Virtual Cell (VCell) is a general computational framework for modeling physico-chemical and electrophysiological processes in living cells. Developed by the National Resource for Cell Analysis and Modeling at the University of Connecticut Health Center, it provides automated tools for simulating a wide range of cellular phenomena in space and time, both deterministically and stochastically. These computational tools allow one to couple electrophysiology and reaction kinetics with transport mechanisms, such as diffusion and directed transport, and map them onto spatial domains of various shapes, including irregular three-dimensional geometries derived from experimental images. In this article, we review new robust computational tools recently deployed in VCell for treating spatially resolved models.