| The problems covered in this dissertation fall into two main categories in theoretical biophysics. The first three chapters following the Introduction address problems related to the physics of cell membranes and the final two chapters deal with non-equilibrium transport in biology. In Chapter 2, we explore the equilibrium mechanics of a binary lipid membrane that wraps around a spherical or a cylindrical particle. One of the lipid membrane components induces a positive intrinsic spontaneous curvature, while the other induces a negative local curvature. We determine the parameter regimes in which particle wrapping is efficient. This model is directly applicable to the study of invagination of clathrin coated pits and receptor-induced viral endocytosis. In Chapter 3, we present a model of pathway selection in viral entry. Some types of enveloped viruses, which have a lipid membrane, can enter cells via either endocytosis, or by direct fusion of their lipid envelope with the cell membrane, and one pathway is often more infective than the other. We determine the parameter regimes in which one entry pathway is favored over the other. In Chapter 4, we consider the mechanics of pulling a ligand that is bound to an integral membrane receptor. As the ligand is pulled, the membrane and the underlying cytoskeleton can deform before either the membrane delaminates from the cytoskeleton or the ligand detaches from the receptor. Depending on the pulling velocity, a membrane tether of varying length may form before the receptor-ligand bond breaks. We obtain the probability of tether formation and the mean tether length at the moment of ligand detachment as a function of system parameters. Our results are applicable to AFM studies of cellular adhesion molecules, and leukocyte rolling. In Chapter 5, we investigate the dynamics of a one-dimensional asymmetric exclusion process with Langmuir kinetics and a fluctuating wall. We find the parameter regimes in which the wall acquires a steady state position. In other regimes, the wall will either drift to the left and fall off the lattice at the injection site, or drift indefinitely to the right. Our results are applicable to protein transport along microtubules, and to mRNA translation. In Chapter 6, we propose a time-dependent mechanism of chemotaxis in which a self-propelled particle (e.g., a cell) releases a chemical that diffuses to fixed particles (targets) and signals the production of a second chemical by these targets. The particle then moves up concentration gradients of this second chemical. In the presence of multiple targets, target selection depends on the strength and, interestingly, on the frequency of probe chemical release. |
