Statistical thermodynamic basis in drug-receptor interactions: double annihilation and double decoupling alchemical theories, revisited

Alchemical theory is emerging as a promising tool in the context of molecular dynamics simulations for drug discovery projects. In this theoretical contribution, I revisit the statistical mechanics foundation of non covalent interactions in drug-receptor systems, providing a unifying treatment that encompasses the most important variants in the alchemical approaches, from the seminal Double Annihilation Method by Jorgensen and Ravimohan [W.L. Jorgensen and C. Ravimohan, J. Chem. Phys. 83,3050, 1985], to the Gilson's Double Decoupling Method [M. K. Gilson and J. A. Given and B. L. Bush and J. A. McCammon, Biophys. J. 72, 1047 1997] and the Deng and Roux alchemical theory [Y. Deng and B. Roux, J. Chem. Theory Comput., 2, 1255 2006]. Connections and differences between the various alchemical approaches are highlighted and discussed, and finally placed into the broader context of nonequilibrium thermodynamics.Comment: 25 pages, 4 figure

Convergent expansions for Random Cluster Model with q>0 on infinite graphs

In this paper we extend our previous results on the connectivity functions and pressure of the Random Cluster Model in the highly subcritical phase and in the highly supercritical phase, originally proved only on the cubic lattice $\Z^d$, to a much wider class of infinite graphs. In particular, concerning the subcritical regime, we show that the connectivity functions are analytic and decay exponentially in any bounded degree graph. In the supercritical phase, we are able to prove the analyticity of finite connectivity functions in a smaller class of graphs, namely, bounded degree graphs with the so called minimal cut-set property and satisfying a (very mild) isoperimetric inequality. On the other hand we show that the large distances decay of finite connectivity in the supercritical regime can be polynomially slow depending on the topological structure of the graph. Analogous analyticity results are obtained for the pressure of the Random Cluster Model on an infinite graph, but with the further assumptions of amenability and quasi-transitivity of the graph.Comment: In this new version the introduction has been revised, some references have been added, and many typos have been corrected. 37 pages, to appear in Communications on Pure and Applied Analysi

The analyticity region of the hard sphere gas. Improved bounds

We find an improved estimate of the radius of analyticity of the pressure of the hard-sphere gas in $d$ dimensions. The estimates are determined by the volume of multidimensional regions that can be numerically computed. For $d=2$, for instance, our estimate is about 40% larger than the classical one.Comment: 4 pages, to appear in Journal of Statistical Physic

On Lennard-Jones type potentials and hard-core potentials with an attractive tail

We revisit an old tree graph formula, namely the Brydges-Federbush tree identity, and use it to get new bounds for the convergence radius of the Mayer series for gases of continuous particles interacting via non absolutely summable pair potentials with an attractive tail including Lennard-Jones type pair potentials