Biology – Quantitative Biology – Quantitative Methods
Scientific paper
2005-12-15
J. Comp. Chem. 27 (2006) 1748-1755
Biology
Quantitative Biology
Quantitative Methods
22 pages, 2 figures, LaTeX, AMSTeX. v2: Introduccion slightly extended. Version in arXiv is slightly larger than the published
Scientific paper
10.1002/jcc.20499
If a macromolecule is described by curvilinear coordinates or rigid constraints are imposed, the equilibrium probability density that must be sampled in Monte Carlo simulations includes the determinants of different mass-metric tensors. In this work, we explicitly write the determinant of the mass-metric tensor G and of the reduced mass-metric tensor g, for any molecule, general internal coordinates and arbitrary constraints, as a product of two functions; one depending only on the external coordinates that describe the overall translation and rotation of the system, and the other only on the internal coordinates. This work extends previous results in the literature, proving with full generality that one may integrate out the external coordinates and perform Monte Carlo simulations in the internal conformational space of macromolecules. In addition, we give a general mathematical argument showing that the factorization is a consequence of the symmetries of the metric tensors involved. Finally, the determinant of the mass-metric tensor G is computed explicitly in a set of curvilinear coordinates specially well-suited for general branched molecules.
Calvo Ivan
Echenique Pablo
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