title: Analysis of diffusion in curved surfaces and its application to tubular membranes.
abstract: Diffusion of particles in curved surfaces is inherently complex compared with diffusion in a flat membrane, owing to the nonplanarity of the surface. The consequence of such nonplanar geometry on diffusion is poorly understood but is highly relevant in the case of cell membranes, which often adopt complex geometries. To address this question, we developed a new finite element approach to model diffusion on curved membrane surfaces based on solutions to Fick's law of diffusion and used this to study the effects of geometry on the entry of surface-bound particles into tubules by diffusion. We show that variations in tubule radius and length can distinctly alter diffusion gradients in tubules over biologically relevant timescales. In addition, we show that tubular structures tend to retain concentration gradients for a longer time compared with a comparable flat surface. These findings indicate that sorting of particles along the surfaces of tubules can arise simply as a geometric consequence of the curvature without any specific contribution from the membrane environment. Our studies provide a framework for modeling diffusion in curved surfaces and suggest that biological regulation can emerge purely from membrane geometry.
authors.affiliation: Department of Mathematics, Vanderbilt University, Nashville, TN 37232.
authors.forename: Colin James Stockdale
authors.initials: CJ
authors.lastname: Klaus
authors.affiliation: Department of Molecular Physiology and Biophysics, Vanderbilt University, Nashville, TN 37232.
authors.forename: Krishnan
authors.initials: K
authors.lastname: Raghunathan
authors.affiliation: Department of Mathematics, Vanderbilt University, Nashville, TN 37232 anne.kenworthy@vanderbilt.edu em.diben@vanderbilt.edu.
authors.forename: Emmanuele
authors.initials: E
authors.lastname: DiBenedetto
authors.affiliation: Department of Molecular Physiology and Biophysics, Vanderbilt University, Nashville, TN 37232 anne.kenworthy@vanderbilt.edu em.diben@vanderbilt.edu.|Department of Cell and Developmental Biology, Vanderbilt University School of Medicine, Nashville, TN 37232.
authors.forename: Anne K
authors.initials: AK
authors.lastname: Kenworthy
mesh_terms: D000465:Algorithms; D055592:Biophysical Phenomena; D002462:Cell Membrane / Q000378:metabolism; D003198:Computer Simulation; D004058:Diffusion; D057446:Hydrodynamics; D008566:Membranes / Q000378:metabolism; D008954:Models, Biological; D008962:Models, Theoretical; D012984:Software; D013329:Structure-Activity Relationship