Potential Of The Mean Force Research Articles

Influence of the shell thickness and charge distribution on the effective interaction between two like-charged hollow spheres.

The mean-force and the potential of the mean force between two like-charged spherical shells were investigated in the salt-free limit using the primitive model and Monte Carlo simulations. Apart from an angular homogeneous distribution, a discrete charge distribution where point charges localized on the shell outer surface followed an icosahedral arrangement was considered. The electrostatic coupling of the model system was altered by the presence of mono-, trivalent counterions or small dendrimers, each one bearing a net charge of 9 e. We analyzed in detail how the shell thickness and the radial and angular distribution of the shell charges influenced the effective interaction between the shells. We found a sequence of the potential of the mean force similar to the like-charged filled spheres, ranging from long-range purely repulsive to short-range purely attractive as the electrostatic coupling increased. Both types of potentials were attenuated and an attractive-to-repulsive transition occurred in the presence of trivalent counterions as a result of (i) thinning the shell or (ii) shifting the shell charge from the outer towards the inner surface. The potential of the mean force became more attractive with the icosahedrally symmetric charge model, and additionally, at least one shell tended to line up with 5-fold symmetry axis along the longest axis of the simulation box at the maximum attraction. The results provided a basic framework of understanding the non-specific electrostatic origin of the agglomeration and long-range assembly of the viral nanoparticles.

Reorientation Dynamics of Chromophores in Photosensitive Polymers by Means of Coarse-Grained Modeling.

We study the photoisomerization of azobenzene chromophores embedded into a polymer matrix by using coarse-grained simulations. Two types of beads are considered: t- and c-beads, which are rich in trans and cis isomers, respectively. Simulations combine deterministic (molecular dynamics) and stochastic (random-type switching) parts. The ratio between the characteristic times for photoinduced reorientation and for orientation relaxation is tuned to be of the order found in experiments. The essential features of the phenomenon: 1) the existence of a stationary state, and 2) anisotropic distribution of the orientations of t-beads (orientation hole-burning effect), are reproduced. We study population dynamics of c-beads and the strength of the orientation hole burning, depending on the illumination wavelength and its intensity. The form of the reorientation potential of the mean force acting on the t-beads is analyzed and its use is validated.

Removal of a hazardous heavy metal from aqueous solution using functionalized graphene and boron nitride nanosheets: Insights from simulations

A computer simulation was performed to investigate the removal of Zn2+ as a heavy metal from aqueous solution using the functionalized pore of a graphene nanosheet and boron nitride nanosheet (BNNS). The simulated systems were comprised of a graphene nanosheet or BNNS with a functionalized pore containing an aqueous ionic solution of zinc chloride. In order to remove heavy metal from an aqueous solution using the functionalized pore of a graphene nanosheet and BNNS, an external voltage was applied along the z-axis of the simulated box. For the selective removal of zinc ions, the pores of graphene and BNNS were functionalized by passivating each atom at the pore edge with appropriate atoms. For complete analysis systems, we calculated the potential of the mean force of ions, the radial distribution function of ion–water, the residence time of ions, the hydrogen bond, and the autocorrelation function of the hydrogen bond.

Alkane separation using nanoporous graphene membranes.

We studied the permeability of graphene sheets with designed nanopores using the classical molecular dynamics. To characterize the energy profile for transmission we calculated the potential of the mean force. A high selectivity for methane + butane mixture with the hydrogen-passivated pore diameter of 0.32 nm was found where the volume exclusion mechanism governs the separation process. In the case of a slightly larger pore diameter of 0.64 nm the same alkane mixture separates completely unexpectedly: a larger butane molecule permeates much faster than a small methane one. The blocking effect of the permeation path by a larger mixture component when it worked like a cork was also observed. This is a promising perspective for using graphene to design intelligent membranes which can maintain a constant composition of mixtures in the permeable area.

The influence of cholesterol on interactions and dynamics of ibuprofen in a lipid bilayer

In this work, molecular dynamics (MD) simulations with atomistic details were performed to examine the influence of the cholesterol on the interactions and the partitioning of the hydrophobic drug ibuprofen in a fully hydrated 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) bilayer. Analysis of MD simulations indicated that ibuprofen molecules prefer to be located in the hydrophobic acyl chain region of DMPC/cholesterol bilayers. This distribution decreases the lateral motion of lipid molecules. The presence of ibuprofen molecules in the bilayers with 0 and 25mol% cholesterol increases the ordering of hydrocarbon tails of lipids whereas for the bilayers with 50mol% cholesterol, ibuprofen molecules perturb the flexible chains of DMPC lipids which leads to the reduction of the acyl chain order parameter. The potential of the mean force (PMF) method was used to calculate the free energy profile for the transferring of an ibuprofen molecule from the bulk water into the DMPC/cholesterol membranes. The PMF studies indicated that the presence of 50mol% cholesterol in the bilayers increases the free energy barrier and slows down the permeation of the ibuprofen drug across the DMPC bilayer. This can be due to the condensing and ordering effects of the cholesterol on the bilayer.

Dynamics of ions in the selectivity filter of the KcsA channel

The statistical and dynamical properties of ions in the selectivity filter of the KcsA ion channel are considered on the basis of molecular dynamics (MD) simulations of the KcsA protein embedded in a lipid membrane surrounded by an ionic solution. A new approach to the derivation of a Brownian dynamics (BD) model of ion permeation through the filter is discussed, based on unbiased MD simulations. It is shown that depending on additional assumptions, ion's dynamics can be described either by under-damped Langevin equation with constant damping and white noise or by Langevin equation with a fractional memory kernel. A comparison of the potential of the mean force derived from unbiased MD simulations with the potential produced by the umbrella sampling method demonstrates significant differences in these potentials. The origin of these differences is an open question that requires further clarifications.

Excited-State Tautomerization of 7-Azaindole in Nonpolar Solution: A Theoretical Study Based on Liquid-Phase Potential Surfaces of Mean Force.

Excited state tautomerization of a 7-azaindole (7AI) complex with one methanol molecule in heptane was studied using variational transition state theory including multidimensional tunneling (VTST/MT) with the dielectric continuum model for the solvent effect. Electronic structures and energies for reactants and transition state (TS) in solution were computed at the complete active space self-consistent field (CASSCF) level with second-order multireference perturbation theory (MRPT2) to take into consideration of dynamic electron correlation. The polarizable continuum model using the integral equation formalism (IEFPCM) and the SMD model were used for the excited-state solvent effect. Excited-state surfaces of potential of the mean force in solution were generated for the first time at the MRPT2//SMD/CASSCF(10,9)/6-31G(d,p) level. The position of TS on the reaction coordinate substantially depended on the dynamic electron correlation. The two protons in the excited-state tautomerization were transferred in a concerted but asynchronous process. Calculated HH/DD kinetic isotope effect (KIE) and the ratio of Arrhenius pre-exponential factors, A(HH)/A(DD), agreed very well with the corresponding experimental values. The shape of the adiabatic energy surfaces in the excited-state strongly depended on the position of isotopes due to the asynchronicity of the reaction path, and the tunneling effect was essential for reproducing experimental KIEs. The pyrrolic proton moved a twice longer distance by tunneling than the hydroxyl proton in the most probable tunneling path at 292 K. This study strongly suggests that the mechanism of the excited-state double proton transfer in heptane is triggered by proton transfer from the pyrrolic nitrogen of 7AI to alcohol (protolytic pathway), rather than by proton transfer from alcohol to the pyridine nitrogen of 7AI (solvolytic pathway).

Time scale separation leads to position-dependent diffusion along a slow coordinate

When there is a separation of time scales, an effective description of the dynamics of the slow variables can be obtained by adiabatic elimination of fast ones. For example, for anisotropic Langevin dynamics in two dimensions, the conventional procedure leads to a Langevin equation for the slow coordinate that involves the potential of the mean force. The friction constant along this coordinate remains unchanged. Here, we show that a more accurate, but still Markovian, description of the slow dynamics can be obtained by using position-dependent friction that is related to the time integral of the autocorrelation function of the difference between the actual force and the mean force by a Kirkwood-like formula. The result is generalized to many dimensions, where the slow or reaction coordinate is an arbitrary function of the Cartesian coordinates. When the fast variables are effectively one-dimensional, the additional friction along the slow coordinate can be expressed in closed form for an arbitrary potential. For a cylindrically symmetric channel of varying cross section with winding centerline, our analytical expression immediately yields the multidimensional version of the Zwanzig-Bradley formula for the position-dependent diffusion coefficient.

Computational analysis of aspartic protease plasmepsin II complexed with EH58 inhibitor: a QM/MM MD study

Plasmepsin (PM) II is one of four enzymes in the food vacuole of Plasmodium falciparum. It has become an attractive target for combating malaria through research regarding its importance in the P. falciparum metabolism and life cycle, making it the target of choice for structure-based drug design. This paper reports the results of hybrid quantum mechanics / molecular mechanics (QM/MM) molecular dynamics (MD) simulations employed to study the details of the interactions established between PM II and N-(3-{(2-benzo[1, 3]dioxol-5-yl-ethyl)[3-(1-methyl-3-oxo-1,3-dihydro-isoindol-2-yl) propionyl]-amino}-1-benzyl-2-(hydroxyl-propyl)-4-benzyloxy-3,5dimethoxy-benzamide (EH58), a well-known potent inhibitor for this enzyme. Electrostatic binding free energy and energy terms decomposition have been computed for PM II complexed with the EH58 inhibitor. The results reveal that there is a strong interaction between Asp34, Val78, Ser79, Tyr192 and Asp214 residues and the EH58 inhibitor. In addition, we have computed the potential of the mean force (PMF) profile in order to assign the protonation state of the two catalytic aspartates in PM II-EH58 complex. The results indicate that the protonation of Asp214 favors a stable active site structure, which is consistent with our electrostatic binding free energy calculation and with previous published works.

Far-from-equilibrium measurements of thermodynamic length

Thermodynamic length is a path function that generalizes the notion of length to the surface of thermodynamic states. Here, we show how to measure thermodynamic length in far-from-equilibrium experiments using the work fluctuation relations. For these microscopic systems, it proves necessary to define the thermodynamic length in terms of the Fisher information. Consequently, the thermodynamic length can be directly related to the magnitude of fluctuations about equilibrium. The work fluctuation relations link the work and the free-energy change during an external perturbation on a system. We use this result to determine equilibrium averages at intermediate points of the protocol in which the system is out of equilibrium. This allows us to extend Bennett's method to determine the potential of the mean force, as well as the thermodynamic length, in single-molecule experiments.

Self-Alignment of Co Adatoms on In Atomic Wires by Quasi-One-Dimensional Electron-Gas-Meditated Interactions

Low-density Co atoms are found to self-align on the Si(111)-(4 x 1)-In surface in the direction of In atomic wires at incommensurate adsorption sites. Indirect interaction between a pair of Co adatoms is investigated through a site distribution function of adatoms determined with scanning tunneling microscopy. In the direction of self-alignment, the potential of the mean force between two Co adatoms is long-range and oscillatory with multiple frequencies, which correlate strongly to the electronic scattering vectors of the surface-state bands at the Fermi level. We thus attribute the Co-Co interaction to that mediated by a quasi-one-dimensional electron gas confined within the In atomic wires.

Role of Collective Interactions in Self‐Assembly of Charged Particles at Liquid Interfaces

AbstractCharged nano‐colloidal particles self‐assemble and display ordered arrays or other structures at liquid interfaces. We used Monte Carlo (MC) simulations to examine the effect of long‐range repulsive collective inter‐particle interactions on structural—transitions from liquid‐like to crystal‐like. We used the asymptotic pair interaction potential proposed by Hurd (J. Phys. A. Math Gen 18, L1055 (1985)), which includes both the screened Coulombic contribution and the dipole‐dipole interaction. The effects of the collective inter‐particle interactions on the interfacial 2‐D colloid structure formation were quantified by the radial distribution function and the potential of the mean force. The MC simulations agreed with the experimentally observed particle structural transitions at both the air‐water and oil‐water interfaces. The effects of the particle charge and interfacial coverage on the 2‐D structure formation were analyzed. The significance of the results lies in their potential applications in inducing 2‐D structural transitions in interfacial colloids to form ordered structures; this controls the emulsion and foam stability, and aids in the fabrication of patterned materials with desirable properties.

Ornstein–Zernike equations for highly asymmetric mixtures: confronting the no-solution challenge

The question of the absence of a solution to the Ornstein–Zernike integral equations for the pair structure of asymmetric binary mixtures is discussed. The behaviour of a recently proposed closure with a reduced no-solution domain in the case of highly asymmetric hard sphere mixtures is considered. The modifications that are required to treat non-hard-sphere interactions are examined. A possible implementation of the same strategy is illustrated for the potential of the mean force for solvophilic macroparticles in a Lennard–Jones fluid.

Defect structures and three‐body potential of the mean force for nanoparticles in a nematic host

AbstractWe have investigated the defect structures and potential of mean force (PMF) of three colloidal spheres immersed in a nematic liquid crystal (for linear and equilateral‐triangular configurations), using a coarse‐grained theory for the tensor order parameter. At large separations, each sphere is surrounded by an equatorial Saturn ring defect; at short separations, the theory predicts a drastic reorganization of the disclination lines: additional disclination rings are observed in planes perpendicular to the original ones. For both types of configurations, the PMF is attractive and always greater than a pairwise sum of binary PMFs. Comparing the PMFs of linear and equilateral‐triangular configurations, we have found the triangular configuration to be more stable than the linear configuration. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 1033‐1040, 2005

One-Dimensional Reaction Coordinate and the Corresponding Potential of Mean Force from Commitment Probability Distribution

In general, finding a one-dimensional representation of the kinetics of a high-dimensional system is a great simplification for the study of complex systems. Here, we propose a method to obtain a reaction coordinate whose potential of the mean force can reproduce the commitment probability distribution from the multidimensional surface. We prove that such a relevant one-dimensional representation can be readily calculated from the equilibrium distribution of commitment probabilities, which can be obtained with simulations. Also, it is shown that this representation is complementary to a previously proposed one-dimensional representation based on a quadratic approximation of the potential energy surface. The usefulness of the method is examined with dynamics in a two-dimensional system, showing that the one-dimensional surface thus obtained can predict the existence of an intermediate and the occurrence of path switching without a priori knowledge of the morphology of the original surface. The applicability of the method to more complex and realistic reactions such as protein folding is also discussed.

Molecular dynamics simulation of liquid N2O42NO2 by orientation-sensitive pairwise potential. III. Reaction dynamics.

The dissociation and association dynamics of N2O4 [see text] 2NO2 in liquid state are studied by classical molecular dynamics simulations of reactive liquid NO2. An OSPP+LJ potential between NO2 molecules, which is a sum of an orientation-sensitive pairwise potential (OSPP) between N-N atoms proposed in Paper I [J. Chem. Phys. 115, 10852 (2001)] and Lennard-Jones potentials between N-O and O-O atoms, has been used in the simulation. The reaction dynamics is studied as a function of well depth De and anisotropy factors of the OSPP potential: Atheta (0< or =Atheta< or =1) for the rocking angle and Atau (0< or =Atau< or =0.5) for the torsional angle of relative NO2-NO2 orientation. The lifetime tauD of initially prepared NO2 dimers is found to increase as De increases, Atheta increases, and Atau decreases. Dissociation and association dynamics are studied in detail around the extreme limit of pure NO2-dimer liquid: De=0.12 x 10(-18) J, Atheta=0.5, and Atau=0.1, which has been found to reproduce both the observed liquid phase equilibrium properties and Raman band shapes of the dissociation mode very well. The dissociation dynamics from microscopic reaction trajectories is compared with the potential of the mean force (PMF) as a function of the N-N distance R. The PMF of reactive liquid NO2 shows a transition state barrier at R=2.3-2.5 A, and NO2-trimer structure is found to be formed at the barrier. Two types of dissociation of the NO2 dimer-the dissociation by collisional activation of the reactive mode to cross the dissociation limit and the NO2-mediated dissociation via bond transfer-are studied. The latter needs less free energy and is found to be much more probable. The dissociation trajectories and PMF in reactive liquid NO2 are compared with those of a reactive NO2 pair in inert solvent N2O4.

Monte Carlo Simulation of the Mean Force between Two Like-Charged Macroions with Simple 1:3 Salt Added

The mean force and the potential of the mean force between two like- harged macroions with monovalent counterions and added simple 1:3 salt described within the primitive model and confined in a cylindrical cell have been investigated by Monte Carlo simulations. Without additional salt, a strongly repulsive mean force was obtained at all macroion separations, consistent with a stable solution of macroions. At a trivalent counterion-to-macroion charge ratio of 0.4, the mean force became attractive at short separations but still possessed a substantial repulsion at longer separations. However, at a stoichiometric amount of trivalent counterions, no long-range repulsion remained and the attraction became substantial (approximate to5kT attraction at a short separation). In excess of salt, the magnitude of the attractive mean force was reduced. The attractive component of the mean force originates from spatial correlations between counterions residing near different macroions and is not captured by mean-field theories such as the Poisson-Boltzmann equation or any of its simplific tions. The observed sequence of mean forces is consistent with recent experimental observations on an aqueous solution of sodium dodecyl sulfate micelles as Al(NO3)(3) was added. (Less)

Interaction forces between particles containing grafted or adsorbed polymer layers

The interaction forces between particles containing grafted or adsorbed polymer layers have been investigated using rheological and surface force measurements. Polystyrene latex dispersions with grafted poly(ethylene oxide) (PEO) chains ( M=2000) were used for the rheological measurements. Results were also obtained for latex dispersions stabilised with adsorbed graft copolymers of poly(methyl methacrylate–methacrylic acid) with methoxy capped PEO chains ( M=750). The relative viscosity η r –volume fraction ϕ curves for the latex dispersions with grafted PEO chains were established for three particle radii of 77.5, 306 and 502 nm. For comparison the η r – ϕ curve was calculated using the Dougherty–Krieger equation. This allows one to obtain the adsorbed layer thickness δ as a function of ϕ. The results showed a decrease of δ with increase of ϕ, which was attributed to the interpenetration and/or compression of the PEO chains on increasing ϕ. Viscoelastic measurements as a function of ϕ showed a change from predominantly viscous to predominantly elastic response at a critical volume fraction, which indicated the onset of the strong steric repulsion when the polymer layers begin to overlap. A similar trend was obtained with the latex particles containing adsorbed graft copolymer layers. A scaling law was used to fit the elastic part of the log G′−log ϕ curve (where G′ is the elastic modulus). This fit could be used to estimate the compressibility of the PEO chains. The correlation of the rheology of concentrated sterically stabilised dispersions with interparticle interactions was investigated by measuring the energy–distance curves for the graft copolymer that was adsorbed on smooth mica sheets. Using de Gennes scaling theory, it was possible to calculate the energy of interaction between the polymer layers. The high frequency modulus of the latex dispersions was obtained as a function of the volume fraction and the results were compared with those calculated from the potential of the mean force. The trends in the variation of the modulus with volume fraction were similar for the experimental rheological results and those calculated using the directly measured interaction forces. The above results demonstrated the powerful use of rheological measurements for studying the interaction between sterically stabilised dispersions in concentrated systems.

Thermodynamic, structural, and dynamic study of the N–H⋯OC hydrogen bond association in aqueous solution

A molecular dynamics simulation of an infinitely dilute aqueous solution of the formamide–formaldehyde complex was carried out using an ab initio 12-6-1 potential to describe the solute–solvent interaction. The solute–solvent interaction energy is used to evaluate the enthalpies and free energies associated with the solvation process. The conclusion is that the surrounding aqueous medium hinders the formation of the complex compared with the same process in gas phase, with a value of ΔG as=−3.59 kJ mol −1 and K as=3.8×10 −2 M −1 being found for the association energy and equilibrium constant, respectively. The potential of the mean force created with the two-solute approximation presents the double minimum, which is typical of these molecular associations that contain the contact solutes and solvent-separated solutes configurations. The structure of water surrounding the complex shows a minor coordination of solvent molecules when a hydrogen bond is formed, and a slight increase of the R H⋯O inter-molecular distance is produced by the aqueous medium. Finally, the dynamics of the complex in solution was studied via the mean square displacement and time correlation functions, which allow us to deduce the diffusion coefficient, reorientation time, and frequencies associated with translational and rotational movements of the bonding hydrogen.

Use of umbrella sampling in the calculation of the potential of the mean force for silicon surface oxidation

In order to establish the growth model of silicon oxide films within the thin regime, the potential energy surface was calculated for the reactions that may take place in the initial oxidation of the hydrogen-terminated silicon surface. Particularly, in order to take into account the effect of temperature, which is one of the important process parameters, the umbrella sampling technique was employed. The activation free energy for the oxidation of complete hydrogen-terminated Si surface and that for the desorption of hydrogen from the Si surface are both calculated to be 50 kcal mol −1 at 700 K. The following oxidation at the hydrogen-defect site created by the desorption, which may be regarded as the oxidation of the clean surface, also requires 50 kcal mol −1 of activation free energy. However, the insertion of oxygen to form a precursor is the rate determining step in the oxidation of hydrogen-terminated surface, while the oxygen migration from the precursor to form a stable oxide is the one in the oxidation of hydrogen-defect site. The activation free energy for the oxidation of partially oxidized site is 40 kcal mol −1, hence the preoxidation by the activated oxygen species may accomplish the selective oxidation prior to the hydrogen desorption.