Vesicle Translocation into Closed Constrictions as a Function of Molecular Motor Parameters

TL;DR

This paper develops a simplified stochastic model of vesicle transport driven by molecular motors into dendritic spines, revealing how spine geometry and motor parameters influence translocation probability and timing, with implications for understanding brain disorders.

Contribution

The authors simplify an existing agent-based model by neglecting second-order moments, enabling direct computation of vesicle translocation times based on geometry and motor parameters.

Findings

Thinner dendritic spines reduce vesicle translocation probability.

Cell can partially compensate for spine geometry changes by adjusting motor parameters.

Model aligns with biological observations linking spine morphology to brain disorders.

Abstract

We study the dynamics of molecular motor-driven transport into dendritic spines, which are bulbous intracellular compartments in neurons that play a key role in transmitting signals between neurons. We further develop a stochastic model of vesicle transport in [Park, Singh, and Fai, SIAM J. Appl. Math. 82.3 (2022), pp. 793--820] by showing that second-order moments may be neglected. We exploit this property to significantly simplify the model and confirm through numerical simulations that the simplification retains key behaviors of the original agent-based myosin model of vesicle transport. We use the simplified model to explore the vesicle translocation time and probability through dendritic spines as a function of molecular motor parameters, which was previously not practically possible. Relevance to Life Sciences: We find that thinner dendritic spine geometry can greatly reduce the probability of vesicle translocation to the post-synaptic density. The cell may alter molecular motor parameters to compensate, but only to a point. These findings are consistent with the biological literature, where brain disorders are often associated with an excess of long, thin dendritic spines. Mathematical Content: We use a moment-generating function to deduce that second-order moments in motor attachment times may be neglected, and therefore the first-order moment is a sufficient approximation. Using only the mean attachment times and neglecting the variance yields a tractable master equation from which vesicle mean first passage times may be computed directly as a function of geometry and molecular motor parameters.