Single-molecule Diffusion in Biological Membranes: Modeling, Analysis, and Image Processing

Abstract

Biological membranes consist of various types of lipids and proteins. At physiological temperature, these molecules interact with each other and diffuse laterally in the membrane driven by thermal fluctuation. Because of the complex composition of the system, membranes are thought to be heterogeneous at different length scales and timescales. Motions of individual molecules are also expected to be beyond simple Brownian diffusion. Experimentally, it has been extremely challenging to measure these putative membrane structures and single-molecule diffusion because of the fluidic nature of the membrane. Recent development of high-speed and high-precision optical measurement provides the opportunity to peek at the single-molecule dynamics with unprecedented clarity. While it is exciting to see a large amount of data become available, it calls for new ways of data analysis in order to truly understand the underlying principles of this complex random system. Through proper data analysis, ideally, a clean mathematical model that considers the stochastic properties of the system could be established. In this talk, I will introduce the longstanding puzzles of biological membranes and show the recent data acquired by our state-of-the-art measurements. I will then introduce the existing math models of anomalous diffusion and explain the need of new methods for data analysis and modeling. Finally, I will show the importance of image processing in our data analysis.