Spatial Cycling of Rab GTPase, Driven by the GTPase Cycle, Controls Rab's Subcellular Distribution.

Rab GTPases (>60 members in humans) function as master regulators of intracellular membrane trafficking. Correct and specific localization of Rab proteins is required for their function. How the distinct spatial distribution of Rab GTPases in the cell is regulated remains elusive. To globally assess the subcellular localization of Rab1, we determined kinetic parameters of two pathways that control the spatial cycles of Rab1, i.e., vesicular transport and GDP dissociation inhibitor (GDI)-mediated recycling. We demonstrate that the switching between GTP and GDP binding states, which is governed by guanine nucleotide exchange factors (GEFs), GTPase-activating proteins (GAPs), GDI, and GDI displacement factor (GDF), is a major determinant of Rab1's ability to effectively cycle between cellular compartments and eventually its subcellular distribution. In silico perturbations of vesicular transport, GEFs, GAPs, GDI, and GDF using a mathematical model with simplified cellular geometries showed that these regulators play an important role in the subcellular distribution and activity of Rab1.

Turing instabilities in a mathematical model for signaling networks.

GTPase molecules are important regulators in cells that continuously run through an activation/deactivation and membrane-attachment/membrane-detachment cycle. Activated GTPase is able to localize in parts of the membranes and to induce cell polarity. As feedback loops contribute to the GTPase cycle and as the coupling between membrane-bound and cytoplasmic processes introduces different diffusion coefficients a Turing mechanism is a natural candidate for this symmetry breaking. We formulate a mathematical model that couples a reaction-diffusion system in the inner volume to a reaction-diffusion system on the membrane via a flux condition and an attachment/detachment law at the membrane. We present a reduction to a simpler non-local reaction-diffusion model and perform a stability analysis and numerical simulations for this reduction. Our model in principle does support Turing instabilities but only if the lateral diffusion of inactivated GTPase is much faster than the diffusion of activated GTPase.

Phase-field modeling of the dynamics of multicomponent vesicles: Spinodal decomposition, coarsening, budding, and fission.

We develop a thermodynamically consistent phase-field model to simulate the dynamics of multicomponent vesicles. The model accounts for bending stiffness, spontaneous curvature, excess (surface) energy, and a line tension between the coexisting surface phases. Our approach is similar to that recently used by Wang and Du [J. Math. Biol. 56, 347 (2008)] with a key difference. Here, we concentrate on the dynamic evolution and solve the surface mass conservation equation explicitly; this equation was not considered by Wang and Du. The resulting fourth-order strongly coupled system of nonlinear nonlocal equations are solved numerically using an adaptive finite element numerical method. Although the system is valid for three dimensions, we limit our studies here to two dimensions where the vesicle is a curve. Differences between the spontaneous curvatures and the bending rigidities of the surface phases are found numerically to lead to the formation of buds, asymmetric vesicle shapes and vesicle fission even in two dimensions. In addition, simulations of configurations far from equilibrium indicate that phase separation via spinodal decomposition and coarsening not only affect the vesicle shape but also that the vesicle shape affects the phase separation dynamics, especially the coarsening and may lead to lower energy states than might be achieved by evolving initially phase-separated configurations.

Spiral growth and step edge barriers.

The growth of spiral mounds containing a screw dislocation is compared to the growth of wedding cakes by two-dimensional nucleation. Using phase field simulations and homoepitaxial growth experiments on the Pt(111) surface we show that both structures attain the same large scale shape when a significant step-edge barrier suppresses interlayer transport. The higher vertical growth rate of the spiral mounds on Pt(111) reflects the different incorporation mechanisms for atoms in the top region and can be formally represented by an enhanced apparent step-edge barrier.