Drift-Diffusion Dynamics and Phase Separation in Curved Cell Membranes and Dendritic Spines: Hybrid Discrete-Continuum Methods

TL;DR

This paper introduces hybrid stochastic methods to study protein drift-diffusion and phase separation in curved cell membranes and dendritic spines, highlighting the influence of geometry on biological processes.

Contribution

The authors develop novel hybrid discrete-continuum numerical methods for modeling protein dynamics in complex membrane geometries, applicable to dendritic spines and reaction-diffusion systems.

Findings

Protein organization is affected by spine neck size.

Geometry influences phase separation and reaction-diffusion patterns.

Methods enable detailed investigation of protein kinetics in curved membranes.

Abstract

We develop methods for investigating protein drift-diffusion dynamics in heterogeneous cell membranes and the roles played by geometry, diffusion, chemical kinetics, and phase separation. Our hybrid stochastic numerical methods combine discrete particle descriptions with continuum-level models for tracking the individual protein drift-diffusion dynamics when coupled to continuum fields. We show how our approaches can be used to investigate phenomena motivated by protein kinetics within dendritic spines. The spine geometry is hypothesized to play an important biological role regulating synaptic strength, protein kinetics, and self-assembly of clusters. We perform simulation studies for model spine geometries varying the neck size to investigate how phase-separation and protein organization is influenced by different shapes. We also show how our methods can be used to study the roles of geometry in reaction-diffusion systems including Turing instabilities. Our methods provide general approaches for investigating protein kinetics and drift-diffusion dynamics within curved membrane structures.