Post-transcriptional regulation in the nucleus and cytoplasm: study of mean time to threshold (MTT) and narrow escape problem

Computational methods and diffusion theory in triangulation sensing to model neuronal navigation

Computational methods are now recognized as powerful and complementary approaches in various applied sciences such as biology. These computing methods are used to explore the gap between scales such as the one between molecular and cellular. Here we present recent progress in the development of computational approaches involving diffusion modeling, asymptotic analysis of the model partial differential equations, hybrid methods and simulations in the generic context of cell sensing and guidance via external gradients. Specifically, we highlight the reconstruction of the location of a point source in two and three dimensions from the steady-state diffusion fluxes arriving to narrow windows located on the cell. We discuss cases in which these windows are located on the boundary of a two-dimensional plane or three-dimensional half-space, on a disk in free space or inside a two-dimensional corridor, or a ball in three dimensions. The basis of this computational approach is explicit solutions of the Neumann-Green's function for the mentioned geometry. This analysis can be used to design hybrid simulations where Brownian paths are generated only in small regions in which the local spatial organization is relevant. Particle trajectories outside of this region are only implicitly treated by generating exit points at the boundary of this domain of interest. This greatly accelerates the simulation time by avoiding the explicit computation of Brownian paths in an infinite domain and serves to generate statistics, without following all trajectories at the same time, a process that can become numerically expensive quickly. Moreover, these computational approaches are used to reconstruct a point source and estimating the uncertainty in the source reconstruction due to an additive noise perturbation present in the fluxes. We also discuss the influence of various window configurations (cluster vs uniform distributions) on recovering the source position. Finally, the applications in developmental biology are formulated into computational principles that could underly neuronal navigation in the brain.

Microdomain [Ca(2+)] Fluctuations Alter Temporal Dynamics in Models of Ca(2+)-Dependent Signaling Cascades and Synaptic Vesicle Release

Ca(2+)-dependent signaling is often localized in spatially restricted microdomains and may involve only 1 to 100 Ca(2+) ions. Fluctuations in the microdomain Ca(2+) concentration (Ca(2+)) can arise from a wide range of elementary processes, including diffusion, Ca(2+) influx, and association/dissociation with Ca(2+) binding proteins or buffers. However, it is unclear to what extent these fluctuations alter Ca(2+)-dependent signaling. We construct Markov models of a general Ca(2+)-dependent signaling cascade and Ca(2+)-triggered synaptic vesicle release. We compare the hitting (release) time distribution and statistics for models that account for [Ca(2+)] fluctuations with the corresponding models that neglect these fluctuations. In general, when Ca(2+) fluctuations are much faster than the characteristic time for the signaling event, the hitting time distributions and statistics for the models with and without Ca(2+) fluctuation are similar. However, when the timescale of Ca(2+) fluctuations is on the same order as the signaling cascade or slower, the hitting time mean and variability are typically increased, in particular when the average number of microdomain Ca(2+) ions is small, a consequence of a long-tailed hitting time distribution. In a model of Ca(2+)-triggered synaptic vesicle release, we demonstrate the conditions for which [Ca(2+)] fluctuations do and do not alter the distribution, mean, and variability of release timing. We find that both the release time mean and variability can be increased, demonstrating that Ca(2+) fluctuations are an important aspect of microdomain Ca(2+) signaling and further suggesting that Ca(2+) fluctuations in the presynaptic terminal may contribute to variability in synaptic vesicle release and thus variability in neuronal spiking.