# Drift-Diffusion Dynamics and Phase Separation in Curved Cell Membranes and Dendritic Spines: Hybrid Discrete-Continuum Methods Source: [Drift-Diffusion Dynamics and Phase Separation in Curved Cell Membranes and Dendritic Spines: Hybrid Discrete-Continuum Methods]() Collection index: [llms.txt]() Data updated: 2025-10-25T04:23:25.234Z Authors: Patrick D. Tran, Thomas A. Blanpied, Paul J. Atzberger Published: 2021-10-02T04:52:18.000Z ## 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. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()