Potential Of Average Force Research Articles

Structural Basis and Mechanism for Vindoline Dimers Interacting with α,β-Tubulin.

Vinblastine and its derivatives used in clinics as antitumor drugs often cause drug resistance and some serious side effects; thus, it is necessary to study new vinblastine analogues with strong anticancer cytotoxicity and low toxicity. We designed a dimer molecule using two vindoline-bonded dimer vindoline (DVB) and studied its interaction with α,β-tubulin through the double-sided adhesive mechanism to explore its anticancer cytotoxicity. In our work, DVB was docked into the interface between α-tubulin and β-tubulin to construct a complex protein structure, and then it was simulated for 100 ns using the molecular dynamics technology to become a stable and refined complex protein structure. Based on such a refined structure, the quantum chemistry at the level of the MP2/6-31G(d,p) method was used to calculate the binding energies for DVB interacting with respective residues. By the obtained binding energies, the active site residues for interaction with DVB were found. Up to 20 active sites of residues within α,β-tubulin interacting with DVB are labeled in β-Asp179, β-Glu207, β-Tyr210, β-Asp211, β-Phe214, β-Pro222, β-Tyr224, and β-Leu227 and α-Asn249, α-Arg308, α-Lys326, α-Asn329, α-Ala333, α-Thr334, α-Lys336, α-Lys338, α-Arg339, α-Ser340, α-Thr349, and α-Phe351. The total binding energy between DVB and α,β-tubulin is about −251.0 kJ·mol–1. The sampling average force potential (PMF) method was further used to study the dissociation free energy (ΔG) along the separation trajectory of α,β-tubulin under the presence of DVB based on the refined structure of DVB with α,β-tubulin. Because of the presence of DVB within the interface between α- and β-tubulin, ΔG is 252.3 kJ·mol–1. In contrast to the absence of DVB, the separation of pure β-tubulin needs a free energy of 196.9 kJ·mol–1. The data show that the presence of DVB adds more 55.4 kJ·mol–1 of ΔG to hinder the normal separation of α,β-tubulin. Compared to vinblastine existing, the free energy required for the separation of α,β-tubulin is 220.5 kJ·mol–1. Vinblastine and DVB can both be considered through the same double-sided adhesive mechanism to give anticancer cytotoxicity. Because of the presence of DVB, a larger free energy is needed for the separation of α,β-tubulin, which suggests that DVB should have stronger anticancer cytotoxicity than vinblastine and shows that DVB has a broad application prospect.

A Didactic Model of Macromolecular Crowding Effects on Protein Folding

A didactic model is presented to illustrate how the effect of macromolecular crowding on protein folding and association is modeled using current analytical theory and discrete molecular dynamics. While analytical treatments of crowding may consider the effect as a potential of average force acting to compress a polypeptide chain into a compact state, the use of simulations enables the presence of crowding reagents to be treated explicitly. Using an analytically solvable toy model for protein folding, an approximate statistical thermodynamic method is directly compared to simulation in order to gauge the effectiveness of current analytical crowding descriptions. Both methodologies are in quantitative agreement under most conditions, indication that both current theory and simulation methods are capable of recapitulating aspects of protein folding even by utilizing a simplistic protein model.

MOLECULAR-STATISTICAL DESCRIPTION OF NONUNIFORMLY DEFORMED SPECIMENS. 2. CALCULATION OF THE DISTRIBUTION FUNCTIONS OF MOLECULES AND VACANCIES IN A ONE-DIMENSIONAL UNIFORMLY DEFORMED STATISTICAL EXTENSION-COMPRESSION MODEL

Within the framework of a two-level molecular-statistical study of the thermodynamic and mechanical properties of condensed systems, a one-dimensional statistical model of uniform extension and compression of a crystal with vacancies has been developed. The micro- and macrostructures of the model are described using correlative distribution functions of real molecules (particles of the r (real) type) and vacancies, account of which is carried out using a subsystem of fictitious particles (quasiparticles of the f (fictitious) type) that do not interact with the molecules and with each other. A nonlinear integral equation for the average-force potentials which determine the single- and two-particle correlative functions of the two-component statistical system of real and fictitious particles has been obtained. The analytical solution of the integral equation has been found within the framework of a modified approach due to the vacancies of the Gauss approximation.

Interaction and stability of adsorbed ferritin clusters on hydrophobic quartz surfaces

Ferritin adsorption on a hydrophobic quartz surface was measured at different bulk concentrations and adsorption times. The initial slope of the isotherms increases with increasing bulk concentration. The pair correlation function, g( r), was obtained from the spatial distribution of adsorbed ferritin molecules on a quartz surface. The potential of average force was found to be around 1.4 kT, and clusters that are kept together by this potential are found to be stable only for less than a second. Ferritin molecules adsorbed on a hydrophobic quartz surface at low concentration (1 mg l −1) were found to interact at distances up to 5 radii. A theoretical model describing the kinetics of adsorption, desorption and cluster dissociation on an ideal surface was also derived.

Statistical-Mechanical Model for Calculating Equilibrium Properties of Systems Composed of Interacting Ellipsoidal Molecules at a Solid Surface

Abstract We have proposed a statistical-mechanical theory of a nematic liquid crystal composed of ellipsoidal molecules interacting through angle-dependent nonseparable potentials in contact with a solid interacting surface. The theory takes into account pair intermolecular correlations. Within the framework of the theory the concept of an average force potential is used to develop a truncation procedure for arbitrary equation of the chain. The closed system of integral equations for average force potential is similar to that used by Brook-Levinson and Zakharov for uniform nematic phase. These equations are solved numerically and results are given for the cubic closed packing ellipsoidal molecules interacting through Berne–Pechukas potentials. Although the calculations have been made for the nematic liquid crystal, the general approach can be applied to any liquid crystalline phase.

Ion–ion correlations in polyelectrolyte solutions: Hard sphere counterions

The intimately related mechanisms of macroion screening and ion–ion correlations in electrolyte solutions are investigated with the aim to explore the simplest theoretical estimations of the latter on the former. The Poisson–Boltzmann theory of macroion screening in electrolyte solutions was developed under two important assumptions. Specifically, the correlated motion of the mobile ions is ignored by identifying the mean field electrostatic potential with the potential of average force and, moreover, only point charges are considered so that finite size effects are not accounted for. Utilizing the generalized van der Waals free energy density functional formulation for inhomogeneous fluids, we obtain simple corrections to the Poisson–Boltzmann result where both these mechanisms are treated in local and nonlocal approximations. By incorporating a somewhat more realistic short range repulsive interaction, the asymptotic instability encountered in the point particle case is avoided and self-consistent density profiles can be computed. Nonlocal approximations are shown to be thermodynamically consistent in terms of the contact theorem for the osmotic pressure, and excellent agreement with Monte Carlo simulation is achieved even at high electrostatic coupling and with large particles.

Temperature-dependent potentials in the theory of rubber elasticity

The new theory that aims to replace the classical theory of rubber elasticity is discussed. It is pointed out that the potential used in this theory to describe the effect of a deformation of the rubber is a potential of average force. As a result, it depends on the temperature. When this is taken into account, the objections raised against the classical theory can be shown to be invalid and the results of the new theory become identical with those of the classical one

Structure and elastic constants for systems composed of ellipsoidal molecules interacting through angle-dependent nonseparable pair potentials

We present results for the Frank elastic constants and the order parameters of nematic liquid crystals obtained from a recently developed theory which is based on the method of conditional distribution. Within the framework of the method the concept of the average force potentials is used to develop a truncation procedure for an arbitrary equation of the chain. A closed system of integral equations for the average force potential is formulated. These equations are solved numerically. Qualitative features exhibited by our calculation for the nematics are in agreement with the experiment.

Statistical-mechanical study of the translational self-diffusion coefficients for systems composed of ellipsoidal molecules interacting through angle-dependent nonseparable pair potentials

The self-diffusion coefficients for systems composed of ellipsoidal molecules interacting through angle-dependent nonseparable potentials have been studied by the method of conditional distribution, proposed by Rott. Within the framework of the method the concept of an average force potential is used to develop a truncation procedure for an arbitrary equation of the chain. The closed system of integral equations for the average force potential is similar to that used by Brook-Levinson and Zakharov.

Statistical mechanical theory of polar fluids for all densities

We present results for the structure and thermodynamics of a polar fluid obtained from a recently developed theory which is based on the method of conditional distribution. Within the framework of the method the concept of the average force potentials is used to develop a truncation procedure for an arbitrary equation of the chain. A closed system of integral equations for the average force potential is formulated. The Helmholtz free energy, the pressure, structural properties and the static dielectric constant are calculated in terms of the binary distribution function. We compare our results with experimental data and find that the theory gives realistic results. Comparisons are also made for self-diffusion coefficients obtained from molecular dynamics simulations.

A statistical-mechanical study of the pair correlations for a liquid with non-central forces

The Helmholtz free energy and pair correlations for liquids composed of nonspherical molecules have been studied by the method of conditional distribution, proposed by Rott. Within the framework of the method the concept of an average force potential is used to develop a truncation procedure for an arbitrary equation of the chain. The closed system of integral equations for the average force potential is similar to that used by Belov and Brook-Levison for monatomic fluids.

The potential of average force between two ions at infinite dilution in a solvent of polarizable hard spheres

The potential of average force between two ions at infinite dilution in a solvent of polarizable hard spheres is considered. The ions are treated as hard spheres with point charges and the solvent molecules are treated as polarizable hard spheres. The diameter of ions may be different than the diameter of polarizable particles. The potential of average force rises near contact much more steeply than the primitive model would permit and also has maxima and minima vanishing at larger distances, in semiquantitative agreement with the similar results of Patey and Valleau. The oscillating character of the potential of average force is due above all to the oscillations of the radial distribution function between the ion and polarizable hard sphere.

Potential of average force between two ions in a solvent of polarizable hard spheres

A method of obtaining the potential of average force between two ions immersed in a polarizable hard sphere fluid is described. The ions and the solvent particles may have different hard sphere diameters. For large values of the reduced polarizability of the solvent particles, α*, the potential of average force rises near contact much more steeply than the primitive model would permit and also has maxima and minima vanishing at larger distances, in semiquantitative agreement with the similar results of Patey and Valleau. The oscillating character of the potential of average force is due above all to the oscillations of the radial distribution function between the ion and polarizable hard sphere.

Potentials of average force for an interaction site model of aqueous alcohols: a molecular model for the hydrophobic bond

An interaction site model with simple square-well potentials of average force is shown, to accurately fit experimental second osmotic virial coefficients for a number of aqueous alcohol systems. The model takes into account the nonspherical structure of the alcohol molecules, includes all important orientational effects, and considers all interactions of the sites

The irreducible three-body interaction between three ions in a solvent

The irreducible potential of average force between three ions in a dipolar solvent is found for an equilateral triangular configuration. The interaction falls off asymptotically as R −4 at large distances.

Truncation procedure for high order reduced distribution functions

The concept of the average force potentials is used to develop the truncation procedure for an arbitrary equation of the chain. The closed system of integral equations for the average force potentials is formulated. In the case when the truncation approximation involves the four-particle distribution function the expression for the configurational integral is derived. The internal energy and the pressure calculated in terms of the binary distribution function are thermodynamically compatible.

Solute interactions in dilute solutions. Part 2.—A statistical mechanical study of the hydrophobic interaction

The aqueous solution properties of aliphatic alcohols have been analysed in terms of pairwise hydrophobic interactions. The potential of average force W(r) was obtained as the sum of the vacuum potential U(r), calculated by a Monte Carlo method, and a simple solvent free energy A(r). Using published osmotic coefficient data, it has been found unexpectedly that the well depth of W(r) is shallower than that of U(r). The pair correlation function g(r), obtained from W(r) by the hypernetted chain approximation has been used to derive the energy, entropy and volume changes associated with the hydrophobic interaction. The results are not compatible with the conventional model of the hydrophobic association. Alternative models are discussed and the results are compared with those from earlier theoretical treatments.

Diffraction corrections to the equilibrium properties of the classical electron gas. Pair correlation function

We perform a systematic study of the diffraction corrections (h/≠0) in the high-temperature range (kBT≳1 Ry) for the pair correlation function of the one-component classical electron gas with a neutralizing background, up to the third-order in the plasma parameter Λ=e2/kBTλD. This program is achieved through the effective interaction Vee(r) = (e2/r)(1−e−cr) with c ∼ (thermal De Broglie wavelength)−1, allowing for a straightforward and tractable generalization of the one-component classical plasma model. The nodal expansion of the potential of average force is performed order-by-order with finite Mayer-Salpeter diagrams. The classical results of De Witt (second-order) and Cohen–Murphy (third-order) are recovered in the h/→0 limit. The resummation to all orders of the bubble diagrams gives access to the short-range behavior of the pair correlation function, which is found similar with the Monte-Carlo results.

Asymptotic behavior of equilibrium pair correlations in a dense electron gas

The nodal expansion of the potential of average force is worked out systematically by iterating all the nonconvolution compact graphs from the order at which they appear first to infinity. For this purpose, we perform an exhaustive study of the asymptotic behavior of the bridge (without articulation points) graphs, and show that they decrease as $\frac{\ensuremath{\beta}{e}^{\ensuremath{-}\ensuremath{\alpha}r}}{r}$, with $\ensuremath{\alpha}>1$ and $r$ in units of the Debye length ${\ensuremath{\lambda}}_{D}$. We demonstrate that the asymptotic ${w}_{2}(r)$ expansion is obtained from the resummation of the longest convolution chains [$l\ensuremath{\ge}2(n\ensuremath{-}1)$] with $n\ensuremath{-}1$ two-bubbles and $0\ensuremath{\le}c\ensuremath{\le}n$ Debye lines, which allow for a systematic improvement of the usual hypernetted-chain (HNC) approximation with the replacement of one, two, or more two-bubbles by bridge graphs. Substantial simplification of the final expression is achieved with the aid of the $n$-bubble sum which decreases asymptotically faster than the Debye line. The onset of short-range order is shown to arise at the critical value ${\ensuremath{\Lambda}}_{c}=4.247$ of the plasma parameter $\ensuremath{\Lambda}=\frac{{e}^{2}}{{k}_{B}}T{\ensuremath{\lambda}}_{D}$ in excellent agreement with the Del Rio-DeWitt calculations.

Polymers at Interfaces and the Interactions in Colloidal Dispersions

Abstract Solutions of different polymers in the same solvent are incompatible as a rule and show phase separation when they are mixed. If incompatibility is also to be observed in systems where one of the polymer components is replaced by colloidal particles, sterically stabilized by a cover of polymer chains, will be discussed in this lecture. After a discussion of the applicability of statistical thermodynamical criteria for colloid stability we focus attention on the potential of average force between two particles, V(r), and the second virial coefficient, B2. First it is shown from general arguments that V(r) and B2 always decrease in magnitude upon addition of particles identical to the particle pair considered. The decrease is particularly large for high molecular weight polymers. Subsequently, the analysis is extended, with the help of simple models, to mixtures of polymer colloid and polymer. It is predicted that B2 should decrease and may become negative when the molecular weight and concentration of the polymer are sufficiently large. For high molecular weight polymer this is of the order of a per cent or less. More polymer is needed for low molecular weights. The destabilization is intimately connected with the expulsion of polymer from the interstitial spaces between approaching particles because of “volume restriction”- and “osmotic” effects. The predictions are in accordance with some experiments that were available. Finally the applicability of light scattering as an experimental tool in these stability problems is stressed. Results are also given of the incompatibility of two polymers in a single solvent in which one of the polymers is masked i.e. does not scatter light.