Explicit factorization of external coordinates in constrained Statistical Mechanics models

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.Comment: 22 pages, 2 figures, LaTeX, AMSTeX. v2: Introduccion slightly extended. Version in arXiv is slightly larger than the published on

Design of HIV-1-PR inhibitors which do not create resistance: blocking the folding of single monomers

One of the main problems of drug design is that of optimizing the drug--target interaction. In the case in which the target is a viral protein displaying a high mutation rate, a second problem arises, namely the eventual development of resistance. We wish to suggest a scheme for the design of non--conventional drugs which do not face any of these problems and apply it to the case of HIV--1 protease. It is based on the knowledge that the folding of single--domain proteins, like e.g. each of the monomers forming the HIV--1--PR homodimer, is controlled by local elementary structures (LES), stabilized by local contacts among hydrophobic, strongly interacting and highly conserved amino acids which play a central role in the folding process. Because LES have evolved over myriads of generations to recognize and strongly interact with each other so as to make the protein fold fast as well as to avoid aggregation with other proteins, highly specific (and thus little toxic) as well as effective folding--inhibitor drugs suggest themselves: short peptides (or eventually their mimetic molecules), displaying the same amino acid sequence of that of LES (p--LES). Aside from being specific and efficient, these inhibitors are expected not to induce resistance: in fact, mutations which successfully avoid their action imply the destabilization of one or more LES and thus should lead to protein denaturation. Making use of Monte Carlo simulations within the framework of a simple although not oversimplified model, which is able to reproduce the main thermodynamic as well as dynamic properties of monoglobular proteins, we first identify the LES of the HIV--1--PR and then show that the corresponding p--LES peptides act as effective inhibitors of the folding of the protease which do not create resistance

Bending of the calmodulin central helix: A theoretical study

The crystal structure of calcium-calmodulin (CaM) reveals a protein with a typical dumbbell structure. Various spectroscopic studies have suggested that the central linker region of CaM, which is α-helical in the crystal structure, is flexible in solution. In particular, NMR studies have indicated the presence of a flexible backbone between residues Lys 77 and Asp 80. This flexibility is related directly to the function of the protein because it enables the N- and C-terminal domains of the protein to move toward each other and bind to the CaM-binding domain of a target protein. We have investigated the flexibility of the CaM central helix by a variety of computational techniques: molecular dynamics (MD) simulations, normal mode analysis (NMA), and essential dynamics (ED) analysis. Our MD results reproduce the experimentally determined location of the bend in a simulation of only the CaM central helix, indicating that the bending point is an intrinsic property of the α-helix, for which the remainder of the protein is not important. Interestingly, the modes found by the ED analysis of the MD trajectory are very similar to the lowest frequency modes from the NM analysis and to modes found by an ED analysis of different structures in a set of NMR structures. Electrostatic interactions involving residues Arg 74 and Asp 80 seem to be important for these bending motions and unfolding, which is in line with pH-dependent NMR and CD studies