Model reduction for Ca²+ -induced vesicle fusion dynamics

Abstract

In this work, we adapt an established model for the Ca²+ -induced fusion dynamics of synaptic vesicles and employ a lumping method to reduce its complexity. In the reduced system, sequential Ca²+ -binding steps are merged to a single releasable state, while keeping the important dependence of the reaction rates on the local Ca²+ concentration. We examine the feasibility of this model reduction for a representative stimulus train over the physiologically relevant site-channel distances. Our findings show that the approximation error is generally small and exhibits an interesting nonlinear and non-monotonic behavior where it vanishes for very low distances and is insignificant at intermediary distances. Furthermore, we give expressions for the reduced model's reaction rates and suggest that our approach may be used to directly compute effective fusion rates for assessing the validity of a fusion model, thereby circumventing expensive simulations.