Mechanics of Biological Membranes in the Presence of Proteins and Implications for Their Thermal Fluctuations Behavior

Abstract

Abstract Pure lipid bilayers are frequently used to mimic membranes that enclose living cells. However, real biological membranes are highly heterogeneous and have a complex structure. The so-called Helfrich Hamiltonian is frequently used to characterize the mechanical behavior of such membranes. Thermal fluctuations and, in general, statistical mechanics are used to explain a variety of cellular behaviors, but are very difficult to carry out in the case heterogeneous membranes. We propose to use a homogenized Hamiltonian that accounts for the presence of proteins to simplify the statistical mechanics analysis of realistic biological membranes. We recognize that (i) the effective Hamiltonian structure itself may be different from what is used for a homogeneous lipid bilayer and (ii) experimental evidence indicates that rigid proteins may introduce both stiffening and softening in the membrane. We consider generalized boundary conditions at the protein–lipid interface within the Helfrich Hamiltonian as a simple route to capture the protein membrane specificity and to account for both softening and stiffening due to rigid proteins. We postulate that real biological membranes require an effective elastic energy form that is far more complex than what is conventionally used and also propose to add a nonlocal elastic energy functional. The new augmented Helfrich Hamiltonian, in a mean-field setting, accounts for the presence of proteins by capturing their short- and long-range effects. Finally, by using the developed effective field theory, we present statistical mechanics results that illustrate the effect of proteins on the interaction between fluctuating membranes.