Mechanics and Thermodynamics of Differentially Stressed Lipid Membranes: Theory and Coarse-Grained Simulation

Biological lipid membranes are almost universally asymmetric. While asymmetry in the form of composition difference between the two membrane leaflets has been studied since the 1970s, the possibility of a difference in tension between the two leaflets has been largely neglected historically. This asymmetric tension state has become known as differential stress, and recent molecular dynamics (MD) simulation studies have shown that sufficiently high differential stress leads to stiffening of single-component membranes. This thesis aims to further shed light on the impact of differential stress upon the mechanical and thermodynamic properties of lipid bilayers by leveraging ultra-coarse-grained (CG) MD simulations in conjunction with theoretical modeling. In pursuit of this goal, we develop new simulation methodologies and employ them to gain novel insights, as well as pave the way for potential future investigations of asymmetric membranes. Chapter 1 introduces the reader to lipid membranes, along with the necessary elastic theory and simulation background. 

In Chapter 2, we examine the difficulties of simulating differentially stressed membranes in the ultra-CG Cooke lipid model. We present a modification of this model which allows for the simulation of general asymmetric membranes, and is stable even in the presence of differential stress. This model is then used to make novel measurements of monolayer properties, including a higher order correction to the monolayer area elastic modulus.

Chapter 3 examines the thermodynamics of the recently uncovered stiffening transition of bilayers subject to sufficient differential stress. We present a phenomenological free energy for the main phase transition of a lipid monolayer and use it to produce asymmetric bilayer phase diagrams which predict the formation of stable gel domains within the compressed leaflet of the membrane. We compare our model to results of MD simulations of differentially stressed membranes using two CG models: the newly modified Cooke model of Chapter 1, and the Martini lipid model. The results are found to be in good agreement with the theory when amended with suitable finite-size corrections. 

Finally, in Chapter 4 we explore new boundary conditions for the simulation of asymmetric bilayers. In order to simulate membranes which are simultaneously able to relax both their area and curvature, we are forced to abandon the usual fully periodic boundary conditions and simulate semi-periodic membrane strips with open edges. In order to prevent the loss of membrane asymmetry, we introduce nano-scale “sticky tape” to prevent lipid flip-flop over the membrane’s open edge. We then show that these edge adhesives successfully allow for the simulation of curvature-relaxed membranes in the CG model presented in Chapter 1 with minimal impact to the fluid properties. Additionally, we are able to exploit this new ensemble to measure the location of the monolayer neutral surface, an important elastic material property for fluid membranes.