Measuring Gaussian Rigidity Using Curved Substrates

Physical Review Letters, vol. 125, pp. 188002

Abstract

The Gaussian (saddle splay) rigidity of fluid membranes controls their equilibrium topology but is notoriously difficult to measure. In lipid mixtures, typical of living cells, linear interfaces separate liquid ordered (LO) from liquid disordered (LD) bilayer phases at subcritical temperatures. Here, we consider such membranes supported by curved substrates that thereby control the membrane curvatures. We show how spectral analysis of the fluctuations of the LO-LD interface provides a novel way of measuring the difference in Gaussian rigidity between the two phases. We provide a number of conditions for such interface fluctuations to be both experimentally measurable and sufficiently sensitive to the value of the Gaussian rigidity, while remaining in the perturbative regime of our analysis.

Authors 4

1. Piermarco Fonda Aachen Instituut-Lorentz

   Leiden University · Max Planck Institute of Colloids and Interfaces

   Affiliation as printed

   Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, Netherlands

   Theory & Bio-Systems, Max Planck Institute of Colloids and Interfaces, Am Mühlenberg 1, 14476 Potsdam, Germany

2. Sami C. Al-Izzi

   Centre National de la Recherche Scientifique · Université Paris Sciences et Lettres · UNSW Sydney · University of Warwick · EMBL Australia · Institut Curie

   Affiliation as printed

   Department of Mathematics, University of Warwick, Coventry CV4 7AL, United Kingdom

   Institut Curie, PSL Research University, CNRS, Physical Chemistry Curie, F-75005, Paris, France

   School of Physics & EMBL-Australia node in Single Molecule Science, University of New South Wales, 2052 Sydney, Australia

3. Luca Giomi Aachen Instituut-Lorentz

   Leiden University

   Affiliation as printed

   Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, Netherlands

4. Matthew S. Turner

   Kyoto University · University of Warwick

   Affiliation as printed

   Centre for Complexity Science, University of Warwick, Coventry CV4 7AL, United Kingdom

   Department of Chemical Engineering, University of Kyoto, Kyoto 615-8510, Japan

   Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom