Investigation of Mechanical Properties of Asymmetric Lipid Bilayers via Coarse-Grained Simulation

Cellular bilayer membranes consist of a diverse array of lipids and proteins. In many cases, the two constituent leaflets of the membrane are known to differ in their

composition. However, existing theoretical treatments of membranes have mostly avoided this added level of complexity. In this thesis we use theory and computational

methods to explore the relationship between asymmetry, thermodynamics, and mechanical properties of lipid bilayer membranes. We review the experimental evidence for membrane asymmetry in cells and present an overview of recently developed techniques for creating model asymmetric bilayers. Measurements on these systems have yielded some unexpected results for their material properties, namely, a relatively high bending stiffness compared to their symmetric counterparts. We clarify the distinction between leaflets composition and leaflets

stress as two sources of asymmetry in bilayers and develop a theoretical framework for analyzing their interplay in determining the meta-stable equilibrium state of the

membrane. We consider the implications for residual stress born by membranes with externally-imposed zero-curvature constraint, for instance, through periodic boundary

conditions during simulations. We use coarse-grained molecular dynamics simulations of buckled membranes of

MARTINI lipids to show how asymmetry in leaflet tension, or \differential stress", can cause a significant increase in bending rigidity of the membrane if this asymmetry exceeds a certain critical threshold. We use this observation to explain experimental results and, by inspecting lipid order in the bilayer, attribute stiffening to the formation

of highly-ordered domains in the compressed lea

et of the differentially-stressed membrane. We investigate the effect of system parameters such as temperature, lipid

type, and size on the stiffening transition and consider their implications. Some pitfalls of using the buckling method for measuring the bending modulus of asymmetric membranes are also examined. We investigate the role of cholesterol in bilayer asymmetry and, using a simple theoretical model, argue that the relatively rapid flip-flop rate of cholesterol does not necessarily eliminate differential stress. In fact, we show that there are circumstances where addition of cholesterol to the system can generate stress asymmetry. We present evidence from simulations supporting our claim and address conflicting claims from other works on the matter. Finally, we take a closer look at the coexistence of ordered and disordered phases in the compressed leaflet of an asymmetric bilayer. We use a Hidden Markov Model

to classify phases and discuss barrier-crossing issues pertaining to the formation of the ordered phase.