The stability of spherocyte membranes: Theoretical study

¹ School of Ophthalmology and Optometry, Eye Hospital, School of Biomedical Engineering, Wenzhou Medical University - Wenzhou 325027, China
² Wenzhou Institute, University of Chinese Academy of Sciences - Wenzhou 325001, China
³ Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology Cambridge, MA 02139, USA
⁴ Institute of Theoretical Physics, the Chinese Academy of Sciences - Beijing 100190, China
⁵ Department of Chemistry, Massachusetts Institute of Technology - Cambridge, MA 02139, USA
⁶ Singapore-MIT Alliance for Research and Technology (SMART) - Singapore, 138602

^(a) muwh@wibe.ac.cn, whmu@mit.edu

Received: 30 July 2019
Accepted: 13 November 2019

Abstract

Human red blood cell (RBC) membranes are typically biconcave-shaped under physiological conditions, and membranes of other shapes, such as spherical, are also observed in pathological RBCs. It has been suggested that there is a relationship between the RBC membrane's material properties, morphologies and physiological functions. The present work studies how various factors affect the morphologies of the RBC membrane based on a free energy functional in continuum elasticity descriptions. In particular, the instability conditions of a diseased spherocyte's spherical shape is obtained explicitly, which determines the region in the phase diagram constructed by two dimensionless state variables defined by elastic moduli, osmotic pressure, etc., in which the spherocyte's membrane can exist in a stable form. In this phase diagram, each point represents the statistical results for a large number of samples observed in recent experiments. Within this stable region of spherocyte's membrane, the spherical RBC membrane is in the global minimal state whereas in the adjacent region on the other side of the boundary, the echinocyte's membrane corresponds to the global minimal state. Our results could be used as a theoretical guide for clinical applications in related diseases, such as malaria, and are in quantitative agreement with recent dynamic optical measurements on the morphological transition of the RBC membrane (see Park Y. et al. Proc. Natl. Acad. Sci. U.S.A., 107 (2010) 6731).