Surface-constrained solvent model

Subtilisin, 170 active site of, 171,173 autocorrelation function of, 216, 216 potential surfaces for, 218 site-specific mutations, 184, 185, 187-188 Sugars, see Oligosaccharides Surface-constrained solvent model, 125... 

G. King and A. Warshel, J. Chem. Phys., 91, 3647 (1989). A Surface Constrained All-Arom Solvent Model for Effective Simulations of Polar Solutions. 

A drastic reduction has been introduced by King and Warshel with their SCAAS (surface constrained all atoms solvent) model. In this model the space is divided into three regions by two concentric spherical surfaces. The outer region is treated as a continuum dielectric, the inner sphere contains M and some solvent molecules (water), the intermediate layer has a thickness sufficient to contain a layer of solvent molecules. Water molecules in both internal regions are described as dipoles. The position and the orientation of such dipoles describe a solvent coordinate Q, which is coupled to a spatial coordinate R to describe a reaction in a 2D space. MD simulations are used to define the time-dependence of both coordinates (Q(r)> and / (/)). This model introduces new and important features in the area of QM/MM methods, but little attention is paid to boundary conditions. 

The Cooper-Mann theory of monolayer transport was based on the model of a sharply localized interfacial region in which ellipsoidal molecules were constrained to move. The surfactant molecules were assumed to be massive compared with the solvent molecules that made up the substrate and a proportionate part of the interfacial region. It was assumed that the surfactant molecules had many collisions with solvent molecules for each collision between surfactant molecules. A Boltzmann equation for the singlet distribution function of the surfactant molecules was proposed in which the interactions between the massive surfactant molecules and the substrate molecules were included in a Fokker-Planck term that involved a friction coefficient. This two-dimensional Boltzmann equation was solved using the documented techniques of kinetic theory. Surface viscosities were then calculated as a function of the relevant molecular parameters of the surfactant and the friction coefficient. Clearly the formalism considers the effect of collisions on the momentum transport of the surfactant molecules. 

The particular model used in the original simulation i- of this reaction was that of a Cl + CI2 like reaction as modeled by a LEPS potential energy surface. The barrier for this symmetric reaction was normally taken to be 20 kcal/mol (—33 kT at room temperature). Other simulations used 10 and 5 kcal/mol barriers. The reactants were placed in either a 50 or 100 atom solvent (Ar in the earliest simulations Ar, He, or Xe in the later work) with periodic truncated octahedron boundary conditions. To sample the rare reactive events, as described previously, this system was equilibrated with the Cl—Cl—Cl reaction coordinate constrained at its value at the transition state dividing surface (specifically, the value of the antisymmetric stretch coordinate was set equal to zero). From symmetry arguments, this constraint is the appropriate one (except in the rare case where the solvent stabilizes the transition state sufficiently such that a well is created at the top of the gas phase barrier). For each initial configuration, velocities were chosen for all coordinates from a Boltzmann distribution and molecular dynamics run for 1 ps both forward and backward in time. 

For the problem of random copolymers, unlike the situation discussed in the previous section, the randomness is now not in the medium, but in the SAW itself. One of the simpler cases is when there are two types of monomer, say A and B. Typically one has a fraction p of A-type monomers, and a fraction (1 — p) of B-type monomers. One usually assumes that the monomers are randomly distributed and constrained only by the value of p. An excellent contemporary review of this topic can be found in [2]. More generally, one can consider the case with k types of monomer, denoted m, .. , ruk, where the state of the polymer, modelled by an n-step SAW, is given by an n-tuple a = ai,..., an, where a G mi,..., TTifc. The values of a are taken from some distribution, appropriately chosen to model the problem at hand. In [2] three representative situations are discussed. The first is adsorption of a copolymer onto a surface, the second is the localization of a copolymer at an interface between two immiscible liquids, and the third is the temperature- or solvent-induced coil-ball collapse of a copolymer. We discuss these three representative problems below. 

A central result of the discussion in the last chapter was the strong influence of finite-size effects on the freezing behavior of flexible polymers constrained to regular lattices. Thus, (unphysical) lattice effects interfere with (physical) finite-size effects and the question remains what polymer crystals of small size could look like. Since all effects in the freezing regime are sensitive to system or model details, this question cannot be answered in general. Nonetheless, it is obvious that the surface exposed to a different environment, e.g., a solvent, is relevant for the formation of the whole crystalhne or amorphous stmcture. This is true for any physical system. If a system tries to avoid contact with the environment (a polymer in bad solvent or a set of mutually attracting particles in vacuum), it will form a shape with a minimal surface. A system that can be considered as a continuum object in an isotropic environment, like a water droplet in the air, will preferably form a spherical shape. 

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