title: Geometric localization of thermal fluctuations in red blood cells.
abstract: The thermal fluctuations of membranes and nanoscale shells affect their mechanical characteristics. Whereas these fluctuations are well understood for flat membranes, curved shells show anomalous behavior due to the geometric coupling between in-plane elasticity and out-of-plane bending. Using conventional shallow shell theory in combination with equilibrium statistical physics we theoretically demonstrate that thermalized shells containing regions of negative Gaussian curvature naturally develop anomalously large fluctuations. Moreover, the existence of special curves, "singular lines," leads to a breakdown of linear membrane theory. As a result, these geometric curves effectively partition the cell into regions whose fluctuations are only weakly coupled. We validate these predictions using high-resolution microscopy of human red blood cells (RBCs) as a case study. Our observations show geometry-dependent localization of thermal fluctuations consistent with our theoretical modeling, demonstrating the efficacy in combining shell theory with equilibrium statistical physics for describing the thermalized morphology of cellular membranes.
authors.affiliation: Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53706; artio.evans@gmail.com.
authors.forename: Arthur A
authors.initials: AA
authors.lastname: Evans
authors.affiliation: Department of Applied Physics, Indian School of Mines Dhanbad, Jharkhand 826004, India.|Quantitative Light Imaging Laboratory, Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, IL 61801.
authors.forename: Basanta
authors.initials: B
authors.lastname: Bhaduri
authors.affiliation: Quantitative Light Imaging Laboratory, Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, IL 61801.
authors.forename: Gabriel
authors.initials: G
authors.lastname: Popescu
authors.affiliation: Department of Physics and Astronomy, University of California, Los Angeles, CA 90095.|Department of Chemistry and Biochemistry, University of California, Los Angeles, CA 90095.|Department of Biomathematics, University of California, Los Angeles, CA 90095.
authors.forename: Alex J
authors.initials: AJ
authors.lastname: Levine
mesh_terms: D003198:Computer Simulation; D004548:Elasticity; D004912:Erythrocytes; D006801:Humans; D008051:Lipid Bilayers; D008433:Mathematics; D008962:Models, Theoretical; D013314:Stress, Mechanical
chemical_list: D008051:Lipid Bilayers
keywords: geometric mechanics; membrane fluctuations; red blood cells; shell structures; thermal fluctuations