Functionals linear in curvature and statistics of helical proteins

Abstract

The effective free energy of globular protein chain is considered to be a functional defined on smooth curves in three dimensional Euclidean space. From the requirement of geometrical invariance, together with basic facts on conformation of helical proteins and dynamical characteristics of the protein chains, we are able to determine, in a unique way, the exact form of the free energy functional. Namely, the free energy density should be a linear function of the curvature of curves on which the free energy functional is defined. We briefly discuss the possibility of using the model proposed in Monte Carlo simulations of exhaustive searching the native stable state of the protein chain. The relation of this model to the rigid relativistic particles and strings is also considered.

18 pages, LaTeX2e, no figures, no tables; the title is changed slightly, the explanations are added concerning the physical content of the approach; the list of references is enlarged

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Cited by in corpus (7)

• Force and moment balance equations for geometric variational problems on curves
• Rigid particle revisited: extrinsic curvature yields the Dirac equation
• Variational analysis of inextensible elastic curves
• Lagrangian Curves in Affine Symplectic 4-space
• Spectral analysis of protein backbone geometry reveals abrupt helix--coil boundaries
• External field influence on semiflexible macromolecules: geometric coupling
• On the use of the Rotation Minimising Frame for Variational Systems with Euclidean Symmetry