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).

There is no need to explain how important are electrostatics interactions in Biology. Unfortunately electrostatics forces are long range and the interactions led by the interaction of molecular charges with each other and the charges of the water molecules are hard to calculate fast and accurately. On the other hand, continuous electrostatics is fast and simple. Moreover, electrostatic energy of a system of charges in a solute can be approximately calculated within the sol called Generalized Born approximation (GB). It's not accurate, it's wrong but it's fast! That's why we decided to walk an extra mile to see how far we can take GB seriously.

Generalized Born calculation for a system of charges placed at the positions proceeds as follows. The solvation energy is given by the approximate (e.g. variational)Kirkwood-like anzatz:

where is a carefully chosen variational function. The classic approximation (often called the Coulomb Field Approximation, or CFA) is given by



where the integration is assumed either over the macromolecule excluded volume or over the water-macromolecule interface . This approximation is known to fail miserably even for a single charge within a sphere. The surface integral implementations of Born radii calculations are more stable than the volume integration and we'll stick to the surface integral formalism.

Is there an approximate giving the exact solution at least in a simple geometry? It turns out the answer is "yes" and in fact there are three different ways to get right. One is similar to CFA and reads:

Two more approximations are given by the generic formula:



with . It's easy to check by a direct calculation that all the tree suggested expressions for the Born radii give the same EXACT result for any system of charges placed at positions within a sphere of a radius .

In practice it means that there are at least 3 different GB approaches capable to recover Kirkwood's result for the solvation energy of a spherical protein with charged groups inside. Which of the approximation works better for an arbitrary (not spherical geometry)? Remains to be seen in our future posts.

Solvation energy is one of the major contribution to binding energy of a ligand to a biologically active protein and is the contribution mostly responsible for the protein selectivity. Although nothing can, probably, better approximate the interaction with water molecules than a sufficiently long molecular dynamics run in an all-atom force field, out of necessity we decided to try our best in ascribing as much physical meaning to Generalized Born models as it can be possibly made.

To do that (see our recent "Fast Surface Based Electrostatics for biomolecules modeling" preprint) we start from the classic GB approximate expression for the solvation energy and re-interpret it as a direct definition of the reaction field potential:

Here are the charges of the atoms, are the charges positions and are the Born radii. This is enough to establish the water polarization charge density at the molecule boundary at a point , no matter which specific approach for the Born radii calculation is chosen:



Therefore, the polarization charge density can be a sanity check both for the direct reaction field potential interpretation and for an estimate of the Born radii calculation accuracy. The obvious requirement is the overall neutrality of the combined molecule and water system: . Below we provide the calculations of the total water polarization charges vs. the macromolecule charge using our FSBE algorithm for roughly 430 different macromolecules from a pdb databank:



Well, it does not look good at all. The results on the graph above show not a correlation, but rather a distribution. The total water polarization charge anti-correlates with the macromolecule charge (as it should), though not ideally. This is a common deficiency of all Generalized Born models, but one. In fact it is possible to construct an approximation for the Born radius and enforce the neutrality at once. We will discuss it in our future posts.