Activation in Vesicle-Mediated Signaling Shaped by Batch Arrival Statistics

TL;DR

This paper presents an exact mathematical framework for understanding how stochastic vesicle release and degradation influence activation timing in cellular communication, highlighting the importance of arrival statistics beyond mean rates.

Contribution

It introduces a full probability distribution solution for batch arrival-degradation models, revealing how arrival variability affects activation kinetics in vesicle-mediated signaling.

Findings

Activation timing depends on arrival event statistics, not just mean rates.

Different arrival processes with same mean can produce distinct activation behaviors.

The framework can incorporate vesicle depletion effects.

Abstract

Vesicle-mediated secretion of ions or molecules is a central mechanism of cellular communication, for example in processes such as neurotransmission or hormone release. These events are inherently stochastic: vesicle fusions lead to bursts of variable sizes, releasing discrete packets of transmitters that are subsequently cleared or degraded. The dynamics break time-reversal symmetry due to the interplay of spontaneous bursts and continuous degradation. Using generating functions and a recursion relation, we derive an exact solution for the full time-dependent probability distribution of a general batch arrival-degradation model. This framework also enables a full analysis of first-passage times to a concentration threshold representing downstream activation. We show that activation kinetics are not determined by mean dynamics alone, but depend sensitively on the temporal statistics of arrival events, batch-size variability, and degradation. In particular, different arrival processes with identical mean rates can lead to qualitatively distinct first-passage behavior, reflecting the role of time-asymmetric fluctuations. We also discuss extensions incorporating vesicle depletion. Our results provide a transparent link between stochastic release dynamics and activation timing in vesicle-mediated signaling.