Biophysics

Protein-driven lipid domain nucleation in biological membranes

Raft formation in cellular membranes is still a controversial topic. In this paper, we introduce two models to simulate the aggregation of sterol-sphingolipid-protein rafts. The first model is a tunable Ising model with Kawasaki dynamics to simulate a two-component lipid mixture and a third component representing a protein that induces raft formation. We perform an extensive analysis of sizes of the cluster around the third particle and its dynamics. Additionally, we identify a dependency between the cluster size and the diffusion constant that implies that the diffusion has a variable and a constant part depending on the cluster size. The approach of this finding is motivated by the process of Brownian motion. Furthermore, examining the angle- and distance-dependent distribution of raft lipids around the protein relative to its movement direction, we ascertain that the cluster around the protein follows the protein. The second model is a three-dimensional molecular dynamics model that builds a stable two-component bilayer membrane with three different phases (unstable, liquid, gel) and it works without explicit solvent particles. Also, this model of a mixed two-component lipid bilayer membrane is extended with a third particle to include a protein. In the analysis, we display the time scales that are needed to equilibrate the protein in the generated cluster, the averaged cluster size and its fluctuation. In addition, we investigate the dynamics of the protein and note that the movement of the protein is sub-diffusive on a long time scale if the membrane is in the fluid as well as in the liquid phase. Moreover, we detect that around the cluster of the protein there is a significantly lower density of raft-lipids than in the rest of the system. Finally, we compare the two theoretical models each to each.

This paper presents the results of my master thesis, I submitted in June 2017 with the title "Statistical Physics of Raft formation in Cell Membranes". S. Zapperi was my supervisor.

Research Project: Repelling Asymmetric Simple Exclusion Process

Kinesins are motor proteins that are able to move on microtubules (MT) by the energy gained from the hydrolysis of adenosine triphosphate (ATP). They are involved in different cellular processes. Until recently, the belief prevailed that kinesins move only in one direction either to the plus- or minus-end of the MT. Recent studies show that kinesin-5 Cut-7 motors can reverse their direction. The direction reversal occurs in in crowed regions due to steric interaction. We introduce a model called the "repelling asymmetric simple exclusion process" (RASEP) which is a specific case of the asymmetric simple exclusion process (ASEP). In our model, motors move on a discrete, filamentous structure in a preferred direction as long as there is no hindrance. If the motors cannot move in the preferred direction and if the is no hindrance in the other direction, motor make a backwards-step. We perform a extensive analysis of the model with open on closed boundary conditions. In the first, we investigate current and density depending on the in- and out- rates at the boundaries (see figure above) and find a current-density relation. In the second, we investigate temporal evolution of density steps. Further, we categorize the evolution behavior in six types.