• Corpus ID: 238259766

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

@article{Tran2021DriftDiffusionDA,
  title={Drift-Diffusion Dynamics and Phase Separation in Curved Cell Membranes and Dendritic Spines: Hybrid Discrete-Continuum Methods},
  author={P. D. Tran and Thomas A. Blanpied and Paul J. Atzberger},
  journal={ArXiv},
  year={2021},
  volume={abs/2110.00725}
}
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… 
First-Passage Time Statistics on Surfaces of General Shape: Surface PDE Solvers using Generalized Moving Least Squares (GMLS)
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Using Dynkin’s formula, numerical methods for computing statistics of stochastic processes on surfaces of general shape with drift-diffusion dynamics are developed and how FPTs are influenced by the surface geometry, drift dynamics, and spatially dependent diffusivities are performed.

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