Real 3D stochastic particle (H+) simulations

The control and regulation of the intracellular pH is of pivot-al importance for every living organism. To keep the pHi at a constant level, the cell can bind or release protons from molecular binding sites. This process is called H+ buffering. Buffering was so far often measured in equilibrium, but the dynamic development over time has not been considered. We recently developed a new dynamic buffering concept, which considers both the amplitude and the time course of H+ buffering. To gain more knowledge about the dynamics of proton buffering we set up a mathematical model of the processes involved in H+ buffering. Since we have not found any adequate and efficient tool which allows the in-silico simulation of reaction-diffusion processes in cells with complex three-dimensional geometries, we developed a method which is based on a stochastic approach (in contrast to the common PDE solvers), and which consists of a combination of a Monte Carlo particle simulation and an additional Importance Sampling step, which allows the in-finite reuse of already sampled paths. This additional step makes the method extremely efficient. Simulations can be done by factors faster than real-time. We used this tool to simulate the pH dynamics in an oocyte and in an astro-cyte-like shape of model cell with a highly complex geometry. The computation time was compared with a state of the art partial differential equation (PDE) solver.