Membrane Elasticity and Mediated Interactions in Continuum Theory: A Differential Geometric Approach

Part of the Handbook of Modern Biophysics book series (HBBT)


Biomembranes are fantastically complex systems [1–4]: hundreds of different lipid and protein species self-assemble into a large two-dimensional aggregate of locally complex and laterally inhomogeneous structure, and a globally potentially daunting topology. Thermal motion of this elastically soft system contributes prominently to its properties, and active processes constantly drive it away from equilibrium. How can we ever hope to learn something quantitative about such a complicated thing? The route to success lies — as so often in physics — in the observation that we can frefectly well described by an effective Hamiltonian, whose small number of phenomenological parameters depend on — and can in principle be determined from — the underlying microscopic physics. Yet, establishing this micro–macro relation is not prerequisite to a successful ing steps can be performed, thus constructing a hierarchy of scales with much beautiful physics in the different tiers. For instance, the laws of quantum mechanics explain everything about water that we need to know — e.g., how water structure and hydrogen bonds give rise to many of water’s anomalies — but we can often just describe it effectively as a substance with some measurable material parameters, such as density, heat of vaporization, melting point, and compressibility. And even of these parameters many become irrelevant if we’re only interested in large-scale fluid motion, for which density and viscosity are often the only relevant properties. Having gotten so used to this separability, we sometimes even forget that the success of physics as a science rests entirely on it. If phenomena on different scales could not be disentangled, we would for instance not be able to describe the motion of the liquid in a stirred cup of coffee without a thorough appreciation of its atomic structure. Or, maybe we’d even need to understand quarks? Or strings? The fact that for all intents and purposes we can master our surrounding world quite well, without knowing what the ultimate structure of matter and the form of a Grand Unified Theory is, provides a vivid proof for the power of scale separation.


Stress Tensor Curvature Tensor Grand Unify Theory Riemann Tensor Membrane Elasticity 
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Copyright information

© Humana Press 2009

Authors and Affiliations

  1. 1.Department of PhysicsCarnegie Mellon UniversityPennsylvaniaUSA

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