The nature of phospholipid membranes repulsion at nm-distances

Why hydrophobic membranes repel at small distances? 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 favor 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 nm-size bodies in water arising from long-range correlations between the water molecules.
More details can be found here:

arXiv:0908.0632 [pdf, other]

The nature of phospholipid membranes repulsion at nm-distances

Authors: P. O. Fedichev, L.I. Menshikov

Molecular polarization on a polar liquid interface: the structure of a water surface

The orientations of water molecules within the liquid depend on interplay of long-range dipole-dipole interaction and short range hydrogen-bonding interactions. At room temperature water is in paraelectric (disordered) phase and thus average dipole moment of any large enough fraction of the liquid vanishes.

This observation is not necessarily true at the liquid boundary. Since no molecules "like" to point at a hydrophobic interface direction (this would imply many uncompensated hydrogen bonds), most of the molecules orient along the liquid surface, the boundary between the liquid and a hydrophobic may become polarized (become essentially ferroelectric). Practically this amounts to a formation of stable network of hydrogen bonds on the interface.

The solution corresponding to such polarized boundary can be obtained in the very latest "incarnation" of the QUANTUM water model (See the attached figures). The first one demonstrates the density of the liquid starting from the gas phase on the left (model liquid density 0.3) and to the liquid phase (model density 1). The transition between the two phases is similar to that in classical model of van der Waals liquid.

The second graph corresponds to the polarization density (mean dipole moment of a liquid volume). Comparing the two graphs we see that the interface is indeed polarized and the polarization decays quickly into the bulk both of the gas and the liquid phase and, as the detailed calculation shows, contributes to the surface tension coefficient considerably.

In short we observe that depending on the ordering state of the water layer next to a molecular surface the effective surface tension may be different by a large number. Another observation suggests that the water density depletion next to a fully hydrophobic (and thus ordering) surface can be large (up to 30-50%)

New Quantum Water Model helps find stable ss DNA conformation in solution

ss DNA Molecular dynamics trajectory using the latest Quantum force field helps to find a perfectly stable conformation of the biomolecule in solution. The outcome of the simulation is very reasonable, given the fact that ss DNA (such as telomers) tend indeed to form such loops (see the Figure on the right). The Figure shows the structure of a DNA quadruplex formed by telomere repeats. The conformation of the DNA backbone diverges significantly from the typical helical structure

How much water is in a Generalized Born protein?

Born approximation is a weapon of choice for a (relatively) fast calculation of solvation energies in modeling. Although the approach is conceptually simple, it can not be correctly derived from first principles (i.e. does not correspond to a solution of electrostatic problem in a strict or even variational sense).

In practice applications of Generalized Born models are further complicated by various approximations for calculating volume (or surface) integrals, removing atom overlaps etc. What remains left is some sort of approximation to molecular volume (surface) and the so called Born Radii for every atom.

Each of the Born radii quantitatively shows a degree to which an atom is "buried" within the protein. The presented graph gives a simple idea to a which extent GB can even be used for description of solvation energies of a simple, model spherical protein containing approx. 1000 atoms of carbon.

The red squares give the dependence of the Born Radii on the atom positions. The points are obtained using our own implementation of AGBNP, one of the best realizations of GB procedures available in the literature.

The yellow curve represents exact result for a spherical protein, where GB and exact analytical expressions coinside. As one can see, AGBNP result fails to grow inwards and saturates at a very small value at r=0.

The reason for this behaviour is two-fold: first AGBNP is based on the so-called Coulomb approximation and thus can not be exact. Indeed, Coulomb approximation fails at the protein boundary and gives d(Born Radius)/dr twice as large as the exact result. This is a true problem, but it can not explain fundamentally wrong results in the protein center!

The other problem of AGBNP (and in fact any GB model), is that the model implies a certain approximation for molecular surface and the surface may have water filled cavities inside the protein! The cavities represent (within the same model) a medium with high dielectric constant and decrease the value of the Born radii.

To check the last assumption we searched for the water filled cavities removed them (to a certain adjustable extent). The result is represented by the blue circles and shows a clear improvement towards reproducing the exact analytical result.

Conclusion? Dry your protein up before even attempting to use GB approximation to get a good solvation energy for a large molecule!

Video recorded from "Water as a ferroelectric..." presentation at MIPT, November 5th, 2008

Water as a ferroelectric: anomalous properties, long range order and interactions of nano-particles in solution (in Russian)

Making a good water model: Molecules do conformationally change when cross from a gas to water solution

Solvation energy calculation is absolutely crucial for a successful binding free energy (IC50) determination. Quantum Pharmaceuticals develops aqueous solvation models and tests them against available experimental data to validate the theoretical approaches.

The graph on the left represents two types of solvation energy calculations compared with experiments. The first series (small circles) are the energy differences on solvation for a set of molecules without conformational changes taken into account. The second set (large squares) is obtained after a single optimization run.

The correlation with the experiment clearly improves after conformational changes calculations. Apparently this does not only mean that the model is good, it also means that the molecules do change structure when inserted into water from the gas phase.

The nature of percolation phase transition in films of hydration water around immersed bodies.

In a set of molecular dynamics calculations (MD) the percolation phase transition in water layer absorbed on a body surface was revealed at definite temperature. Below this temperature the infinite network of unbroken hydrogen bonds exists. Above it this network decays on islands. This conclusion corresponds also with measurements of conduction of moisture contained disperse materials as quartz, for example: the conductivity drops almost to zero value while heating the specimens up to definite temperature. It is known that the water conductance dominates by the “estafette” mechanism in which protons are transferred over the hydrogen bonds. The breakdown of network means the conductivity drop. These phenomena are explained in the paper in frames of early published continuous vector model of polar liquids. It is shown that the immersed bodies are surrounded by the ferroelectric film, in which the dipole moments of water molecules are ordered, arranged in one direction parallel to the interface. It is the physics behind above mentioned MD results. In addition of our previous papers the stability of this ferroelectric order is proved. The character of phase transition to the paraelectric phase is discussed and its temperature is estimated that is in agreement with MD results. Below the critical temperature the polarization vector field contains the structures as “vortex-antivortex pairs”. These pairs dissociate above this temperature that means the order breaking. The boundary conditions for the polarization vector field of molecular dipole moments are derived that is necessary to enclose the vector model equations.

Reference: accepted for publication to Journal of Structual Chemistry (Russian Journal of), 2008

Spontaneous polarization of a polar liquid next to nano-scale impurities

Numerous properties of water are determined by the hydrogen bonds between its molecules. Water does not form hydrogen bonds with hydrophobic materials, henceforth, dipole moments of its molecules are arranged mainly parallel to the interfaces with such substances. According to molecular dynamics calculations (MD) at such orientation molecules save the maximal number of hydrogen bonds: three of fourth. It is shown in this Letter that in the layer of water or ice next to surface the long-range order spontaneously forms: remaining parallel to the surface dipole moment vectors arrange in one direction. Some fraction of dipole moments form the vortex structures on the surface. At low temperatures the ordered state has small admixture of vortex-antivortex pairs. The interaction energy of vortexes in this pairs arises proportional to the distance between them. A definite temperature the phase transition takes place: pairs suffer the dissociation, the molecular dipole moments order disappears. This conclusion agrees with he results of MD calculations, in which the percolation phase transition was revealed in the hydrogen bond network of water molecules absorbed on a surface.

The spontaneous polarization of liquid induced by the immersed in it nano-size bodies (proteins, peptides, …) results in the additional long-range interaction between them that depends on their relative orientation. Polarization of liquid in this case looks like that presented in Fig.1 in agreement with MD. All mentioned MD results can not be explained in frames of standard continuous scalar theory of water. These phenomena were analyzed here in frames of continuous vector model of polar liquids applications of which looks like promising to speed the simulations of macromolecular complexes.

Reference: arXiv:cond-mat/0601129 [ps, pdf, other]

Title: Long-Range Order and Interactions of Macroscopic Objects in Polar Liquids

Authors: P.O. Fedichev, L.I. Men'shikov

Comments: 11 pages, 6 figures

Subjects: Soft Condensed Matter (cond-mat.soft); Chemical Physics (physics.chem-ph); Biomolecules (q-bio.BM)

Accepted for publication in Journal of Physical Chemistry A (Russian Journal of), 2009

Ferro-electric phase transition in a polar liquid and the nature of lambda-transition in supercooled water

Water is a major and all-important example of a strongly interacting polar liquid. Dielectric properties of water surrounding nano-scale objects pose a fundamentally important problem in physics, chemistry, structural biology and in silica drug design. The issue of temperature dependence of dielectric constant, the role of fluctuations and a possibility of a ferro-electric phase transition in a polar liquid is fairly old . It attracted a new attention when a new phase transition (so called lambda-transition) was observed in supercooled water at critical temperatures between T_{c}=228K and T_{c}=231.4K . Isothermal compressibility, density, diffusion coefficient, viscosity and static dielectric constant \epsilon and other quantities diverge as T_{c} is approached, which is signature of a second order phase transition. The singularity of \epsilon is a feature of a ferro-electric transition . However, given a complexity of interactions between water molecules, the physical picture behind this phenomenon is not entirely clear . In the phase transition is explained as a formation of a rigid network of hydrogen bonds. On the other hand a ferro-electric hypothesis was also proposed and supported by molecular-dynamics simulations (MD). For example, a ferro-electric liquid phase was observed in a model of the so called ``soft spheres'' with static dipole moments . In fact, the existence of a ferro-electric phase appears to be model independent: domains where formed both in MD calculations with hard spheres with point dipoles and with soft spheres with extended dipoles .

In the our latest publication, Ferro-electric phase transition in a polar liquid and the nature of lambda-transition in supercooled water, we develop two related approaches 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 sufficiently 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 demonstrate that the ferro-electric transition is a sound physical explanation behind the experimentally observed \lambda-transition in supercooled water. Finally we discuss dielectric properties, the role of fluctuations and establish connections with earlier phenomenological models of polar liquids.

Reference: arXiv:0808.0991 [ps, pdf, other]

Title: Ferro-electric phase transition in a polar liquid and the nature of \lambda-transition in supercooled water

Authors: P.O. Fedichev, L.I. Menshikov

Comments: 4 pages, 1 eps figure

Subjects: Statistical Mechanics (cond-mat.stat-mech); Soft Condensed Matter (cond-mat.soft)