A Generalized Langevin Approach to Modeling Protein Migration

The KRas protein, while being vital for relaying signals to cell nuclei for functions such as cell growth and division, has also been implicated in roughly 30% of all human cancers in its mutated form (e.g., 95% of pancreatic cancer and 45% colorectal cancers). KRas is known to assemble into nanoclusters on the plasma membrane, and understanding the connection between the formation of these nanoclusters and potentially oncogenic signaling pathways is an open question in cancer research. While molecular dynamics (MD) simulations are used to investigate the dynamics of KRas at the atomic scale, the time- and length-scales required for nanocluster formation in the protein-membrane-cytosol system are often unattainable. Here, we propose a generalized Langevin model to describe the migration of KRas (and other proteins) along the membrane, thus mitigating many of the computational constraints of traditional MD simulations. An approximate memory kernel is constructed from MD, where the non-Markovian fluctuations are mapped onto an auxiliary Ornstein-Uhlenbeck process. Simulation results are compared to MD data, and applications to KRas nanoclusters are discussed.