Surface fluctuating hydrodynamics methods for the drift-diffusion dynamics of particles and microstructures within curved fluid interfaces

Rower, David A.; Padidar, Misha; Atzberger, Paul J.

doi:10.1016/j.jcp.2022.110994

Cited by 10 publications

(2 citation statements)

References 79 publications

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“…A detailed study of biophysical transport applicable to curved membranes was carried out in a few recent works [52][53][54][55][56][57][58]. In particular [52,53] generalized the pioneering works of Saffman and Delbrück [39,40] for curved surfaces of static geometry.…”

Section: Introductionmentioning

confidence: 99%

Vortex flows and streamline topology in curved biological membranes

Samanta

Oppenheimer

2021

Physics of Fluids

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When considering flows in biological membranes, they are usually treated as flat, though more often than not, they are curved surfaces, even extremely curved, as in the case of the endoplasmic reticulum. Here, we study the topological effects of curvature on flows in membranes. Focusing on a system of many point vortical defects, we are able to cast the viscous dynamics of the defects in terms of a geometric Hamiltonian. In contrast to the planar situation, the flows generate additional defects of positive index. For the simpler situation of two vortices, we analytically predict the location of these stagnation points. At the low curvature limit, the dynamics resemble that of vortices in an ideal fluid, but considerable deviations occur at high curvatures. The geometric formulation allows us to construct the spatio-temporal evolution of streamline topology of the flows resulting from hydrodynamic interactions between the vortices. The streamlines reveal novel dynamical bifurcations leading to spontaneous defect-pair creation and fusion. Further, we find that membrane curvature mediates defect binding and imparts a global rotation to the many-vortex system, with the individual vortices still interacting locally.

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Section: Introductionmentioning

confidence: 99%

Vortex flows and streamline topology in curved biological membranes

Samanta

Oppenheimer

2021

Physics of Fluids

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“…Methods modeling at the level of particles include Monte-Carlo (MC) Methods and Kinetic MC (KMC) in [20][21][22][23][24][25][26], Molecular Dynamics (MD) studies in [27][28][29], and Coarse-Grained (CG) Models in [30,31]. Some work has been done on hybrid discrete-continuum approaches for membranes in [32][33][34][35][36][37][38], and taking into account geometric effects in [35,39], and through point-cloud representations in [26,[40][41][42][43].…”

Section: Introductionmentioning

confidence: 99%

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

Tran¹,

Blanpied²,

Atzberger³

2021

Preprint

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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.

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On differences between deterministic and statistical models of the interphase region

Wacławczyk

2022

Acta Mech. Sin.

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Surface fluctuating hydrodynamics methods for the drift-diffusion dynamics of particles and microstructures within curved fluid interfaces

Cited by 10 publications

References 79 publications

Vortex flows and streamline topology in curved biological membranes

Vortex flows and streamline topology in curved biological membranes

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

On differences between deterministic and statistical models of the interphase region

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