Investigation of Elastic Properties of Lipids and Proteins using Computer Simulations

The elastic properties of biological materials play an important role in many biomechanical functions. As a result, a large effort has gone into understanding these properties through the creation of theoretical frameworks and the measurement of the parameters entering such theories. With the improvement of computer hardware and software, computational studies now work alongside experimental techniques to probe the mechanics of biomaterials. In this thesis, we will look at three different ways that computational work to improve our understanding of the elastic properties of biomaterials: (1) developing methods to measure important material parameters, (2) test theories and provide data to refine theories, and (3) develop new computational models to investigate the properties of biomaterials. In Chapter 2, we discuss a method of measuring the bending modulus of lipid bilayers in the fluid-phase by simulating buckled membranes. This method is computationally efficient and can be applied to lipid models of a wide range of resolution, using both implicit or explicit solvent. After showing how Helfrich theory [1], a standard theory of membrane elasticity, predicts the shape of the buckles as well as the stress-strain relation, we apply the method to three different coarse-grained models: a low resolution implicit solvent model, a medium resolution implicit solvent model, and a medium resolution explicit solvent model. In Chapter 3, we try to apply the method from Chapter 2 to membranes in the gel-phase. We find that Helfrich theory fails to accurately describe both the shape and stress-strain relation of the buckles. Drawing inspiration from the shapes of the simulated buckles, we present a modification of Helfrich theory that incorporates curvature softening and show that this theory does describe both the shape and stress of the gel-phase buckles. Unexpectedly, the buckles exhibit negative compressibility. In Chapter 4, we apply the new theory to the fluid-phase buckles studied in Chapter 2. The large fluctuations of the membranes makes the error in our measurement of the shapes too large to draw proper conclusions from the shape, but we are able to fit the theory directly to the stress-strain relation from the simulations. The results show that there is a small amount of curvature softening at large curvatures, and this has a small effect on the bending modulus of the lipids. In Chapter 5, we switch our focus to the study of elastic networks, a way of investigating the fluctuations of biomolecules such as globular proteins and folded RNA structures. Specifically, we study a technique to create course-grained elastic networks from a high resolution model without the need to run a reference simulation. We show that the choice of which particles to remove upon coarse-graining determines the ability of the elastic network to reproduce the fluctuations of the high resolution model, with a good choice of particles leading