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MATHEMATICAL MODELS OF MEMBRANES

This paper outlines molecular dynamics simulations and their limitations when modeling large-scale shape dynamics of cellular membranes. We explore concepts from differential geometry and cellular-mechanics to describe cellular membranes in terms of Helfrich’s equation of generalized shape energy, which provides the theoretical framework for understanding shape changes in liposome vesicles. We present an outline of the derivation of Helfrich’s shape equation in order to illustrate how these equations can be used to model largescale shape changes in biological cells. We conclude by discussing biological applications of the equations in modeling red blood cell shape.