Rotational Drift-Diffusion of Proteins in Dynamic Bilayer Lipid Membranes

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Surrounding living cells and many subcellular compartments are membranes, which allow the passage of certain information and materials but block some others. Membranes deform at different magnitudes, sometimes drastically, during this selective transport, and the processes are facilitated and regulated by various protein complexes. Proteins accomplish regulation through attaching to or residing in membranes at specific locations. Understanding and quantifying the number and orientation of these membrane proteins on dynamically deforming membranes is essential for developing medications and therapeutic strategies to facilitate or suppress membrane transport. By integrating mathematical modeling and computational simulations, this research will examine (1) how the rotation and translation of proteins leads to the deformation of bilayer membranes; (2) how deformation leads proteins to stay at specific positions and orientations; and (3) how these interactions are related to protein structure and membrane composition. This investigation aims to provide reliable models and efficient algorithms for protein-membrane interactions and related biomedical applications.The bilayer membranes in cells are highly dynamic, heterogeneous environments with multiple critical biological functions, many of which are regulated by specific proteins through various protein-membrane interactions. The rotational and translational localizations of membrane proteins are the major driving mechanism of membrane morphological changes. Yet quantification of these localizations in dynamical bilayer membranes remains mathematically and computationally challenging. This research strives to introduce principal directions and curvature to account for orientation-dependent localization in membranes and the resulting membrane deformation. Surface drift-diffusion equations with integer and fractional orders will be derived for low and high protein densities. Through integrating mathematical and computational investigation of these equations, the research will generate a predictive model for the dynamics of bilayer membranes with surface protein flows.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.