Solvation energy contribution to protein-ligand binding conceptually consists of two different contributions. The first one is collective in nature, comes from the long range interaction of the molecules charges with polar water molecules. The other comes mostly from the short range interactions of the molecules in question with the adjacent layer of the water molecules.

The long range part can be, to a certain extent, be modeled within a continuous electrostatics framework. Recently we have posted a number of improvements to commonly used Generalized Born models. Let us show that GB models may naturally have a good built-in approximation for the surface accessible area for the non-polar contribution calculations.

To do that we take  FSBE model as the example and suggest the following equation for the surface area of a molecule:



where is a coefficient, are the surface tensions associated with the atom types, are the radii of the ions and are the Born radii defined according to the model settings, e.g.



The results of the model surface area differences for 230 protein ligand complexes (the model vs. exact surface data) are presented on the graph. The numbers show an impressive correlation with .

The surface area requires the same power of the Born radii for the evaluation and thus can be implemented both numerically accurate and computationally efficient.

P.O. Fedichev, L.I. Menshikov
(Submitted on 7 Aug 2008 (v1), last revised 20 Dec 2009 (this version, v3))
We develop a series of approximations to calculate free energy of a polar liquid. We show that long range nature of dipole interactions between the molecules leads to para-electric state instability at low temperatures and to a second-order phase transition. We establish the transition temperature, T_{c}, both within mean field and ring diagrams approximation and show that the ferro-electric transition may play an important role explaining a number of peculiar properties of supercooled water, such as weak singularity of dielectric constant as well as to a large extent anomalous density behavior. Finally we discuss the role of fluctuations, shorter range forces and establish connections with phenomenological models of polar liquids.
Comments: 5 pages, 1 eps figure, density anomaly at T=4C analysis added
Subjects: Statistical Mechanics (cond-mat.stat-mech); Soft Condensed Matter (cond-mat.soft)
Cite as: arXiv:0808.0991v3 [cond-mat.stat-mech]

P. O. Fedichev, L.I. Menshikov
(Submitted on 5 Aug 2009 (v1), last revised 14 Dec 2009 (this version, v2))
We apply recently developed phenomenological theory of polar liquids to calculate the repulsive pressure between two hydrophilic membranes at nm-distances. We find that the repulsion does show up in the model and the solution to the problem fits the published experimental data well both qualitatively and quantitatively. Moreover, we find that the repulsion is practically independent on temperature, and thus put some extra weight in favour of the so called hydration over entropic hypothesis for the membranes interactions explanation. The calculation is a good proof of concept example a continuous water model application to non-trivial interactions on -size bodies in water arising from long-range correlations between the water molecules.
Comments: 4 pages, 1 png figure, massive update
Subjects: Soft Condensed Matter (cond-mat.soft); Materials Science (cond-mat.mtrl-sci)
Cite as: arXiv:0908.0632v2 [cond-mat.soft]

The talk "Water as a segnetoelectric, anomalous properties and interactions of molecular sized objects at nm-distances" (in Russian).



The talk was a part of IAChPhys seminar held at the Institute of Molecular Physics, Russian Research Center "Kurchatov Institute". The talk in part mirrored the last year presentation at MIPT (Moscow) and contained all the new stuff we developed over the last year: the nature of phospholipid membranes repulsion at nm-distances, Molecular polarization on a polar liquid interface: the structure of a water surface, The nature of percolation phase transition in films of hydration water around immersed bodies (see publications on polar liquids for more info).

Up to now, there have been at least two schools of thoughts among those trying to calculate electrostatics part of solvation energies. Half of the folks believe that only an exact solution of the Poisson equation can be better than the solution of the Poisson equation. The other half believes that though the exact solution of the Poisson equation can be obtained, it is too slow and numerically unstable. Here in Quantum we attempt to give Generalized Born models almost infinite credit of trust and push for a direct link between the Poisson equation solutions and Generalized Born models.

The missing link between the two worlds is established by the equation linking the Born radii with the water polarization charges on a molecular interface. If the surface charges are then interpreted on their own, we can calculate the solvation energy using its direct definition, rather than an approximate Born formula. The question is of course if it all works in real life.

To proof the concept we attempted the calculation of the solvation energies for about 580 proteins from our Quantum Pharmaceuticals target list of proteins with available 3D structure. The results obtained with 4 different types of Surface Charges Generalized Born (SCGB) models are compared with the Surface Electrostatics solutions of the Poisson eqaution and are summarized below:

Here the surface electrostatics solvation energies are measured along the horizontal axis, the vertical axis is used for the SCGB solvation energies values. The green dots represent SCGB model with FSBE radii, yellow and red dots are SCGB models with respectively. All the three models give exact solvation energies for an arbitrary system of charges within a shpere and cope fairly well with the realistic proteins. SCGB with standard CFA Born radii (the blue dots) are completely off. Given tremendous speed advantage of SCGB models over SE we end up with an approximation worth to be employed!