Potential of mean force surface

BM Pettitt, M Karplus. The potential of mean force surface for the alanine dipeptide in aqueous solution A theoretical approach. Chem Phys Lett 121 194-201, 1985. 

The vacuum potential results, corresponding to the limit of zero viscosity, are shown in Fig. 41a. At zero viscosity, the dihedral angle 41 oscillates with a period of approximately 0.63 ps. When the conditions are changed to represent water at 300 K (i.e., the solvent-modified potential-of-mean-force surface is used and r) = 1.0 cP), the dominant effect is that the dihedral motion has a periodicity of about 3.7 ps (see Fig. 41b). The solvent influence observed in these simulations is consistent with an earlier molecular dynamics study of... 

In the equilibrium solvation path (ESP) approximation [74, 76], ve first find a potential of mean force surface for the primary subsystem in the presence of the secondary subsystem, and then we finish the calculation using this free energy surface. Notice a critical difference from the SES in that now we find the MEP on U rather than V, and we now find solute vibrational frequencies using U rather than V. 

Chemical reaction dynamics is an attempt to understand chemical reactions at tire level of individual quantum states. Much work has been done on isolated molecules in molecular beams, but it is unlikely tliat tliis infonnation can be used to understand condensed phase chemistry at tire same level [8]. In a batli, tire reacting solute s potential energy surface is altered by botli dynamic and static effects. The static effect is characterized by a potential of mean force. The dynamical effects are characterized by tire force-correlation fimction or tire frequency-dependent friction [8]. 

Potential functions induced-dipole terms, 84-85 minimization, 113-116 nonbonded interactions, 84-85 Potential of mean force, 43, 144 Potential surfaces, 1,6-11, 85, 87-88, 85 for amide hydrolysis, 176-181,178,179, 217-220, 218... 

In Section IV.B the energy of an ion was calculated by a simple version of the quasichemical approximation. The same procedure can be used to calculate the potential of mean force 0pinfW of an ion [18], which is the average potential that the ion experiences as a function of its position x in the direction perpendicular to the surface. This consists of two... 

It may come as a surprise to some that two commensurate surfaces withstand finite shear forces even if they are separated by a fluid.31 But one has to keep in mind that breaking translational invariance automatically induces a potential of mean force T. From the symmetry breaking, commensurate walls can be pinned even by an ideal gas embedded between them.32 The reason is that T scales linearly with the area of contact. In the thermodynamic limit, the energy barrier for the slider to move by one lattice constant becomes infinitely high so that the motion cannot be thermally activated, and hence, static friction becomes finite. No such argument applies when the surfaces do not share a common period. 

We determined the free energy barrier for dissociation by defining a free energy surface for the oxygen-hydrogen distances, viz. W(r) = k T In [g(ROH)L where W(r) is the free energy surface (potential of mean force). The results are shown in Figure 11. 

The issue of contact vs. noncontact adsorption and the location of the adsorbed ion relative to the surface is best handled by an examination of the ion potential of mean force. If we denote by P(z) the probability density for finding an ion at a position z relative to a planar interface, then the free energy profile (or the potential of mean force) is given by... 

Here Vij denotes the distance between atoms i and j and g(i) the type of the amino acid i. The Leonard-Jones parameters Vij,Rij for potential depths and equilibrium distance) depend on the type of the atom pair and were adjusted to satisfy constraints derived from as a set of 138 proteins of the PDB database [18, 17, 19]. The non-trivial electrostatic interactions in proteins are represented via group-specific dielectric constants ig(i),g(j) depending on the amino-acid to which atom i belongs). The partial charges qi and the dielectric constants were derived in a potential-of-mean-force approach [20]. Interactions with the solvent were first fit in a minimal solvent accessible surface model [21] parameterized by free energies per unit area (7j to reproduce the enthalpies of solvation of the Gly-X-Gly family of peptides [22]. Ai corresponds to the area of atom i that is in contact with a ficticious solvent. Hydrogen bonds are described via dipole-dipole interactions included in the electrostatic terms... 

In general terms, the interactions between the colloidal particles with surfaces covered by adsorbed biopolymer layers can be described qualitatively and quantitatively using the appropriate expression for the potential of mean force W(r). Extending the formalism of equation (3.2), at least four separate contributions to W(r) can contribute to the total free energy of interaction between a pair of colloidal particles in the aqueous dispersion medium (a biopolymer solution) (Snowden et al, 1991 Dickinson, 1992 Israelachvili, 1992 Vincent, 1999 de Kruif, 1999 Praus-nitz, 2003) ... 

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