Results with Hard-Sphere Potential

These computations, with a hard-sphere potential, were extended to helical pentapeptide and hexapeptide structures of the type gly-X4 and gly-X5 in order to determine the additional steric restrictions which arise 

It should be recalled that, as mentioned in Section II, equations exist to convert n, hto f , p and vice versa. These relations exist, independent of the question as to whether or not sterio overlaps occur at any given values of f and ip. Leach et al. (1966b, c) have shown that, in general, there are 

Because of the variations which occur in the arrangement of the hydrogen bonds, as described in the previous paragraph, the (n,h) and SR nomenclature for classifying various types of helices do not always coincide. Thus, whenever observed structures are said to have an a- 

In light of the above discussion on helical structures, let us consider the results of Leach etal. (1966b) in which steric overlaps in gly-X4 and gly-X5 were examined over the plane. In addition to the steric requirement, Leach et al. (1966b) introduced simplified and rather arbitrary criteria 

A comparison of the maps of Figs. 15 and 16 illustrates similar additional steric restrictions on a poly-L-alanine chain, as one passes from a dipeptide (Fig. 15) to helical structures (Fig. 16). Further discussion of steric effects in small polypeptide structures can be found in the recent review of Ramachandran and Sasisekharan (1968). 

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To compare molecular theoretical and molecular dynamics results, we have chosen the same wall-particle potential but have used the 6 - oo fluid particle potential. Equation 14, Instead of the truncated 6-12 LJ potential. This Is done because the molecular theory Is developed In terms of attractive particles with hard sphere cores. The parameter fi n Equation 8 Is chosen so that the density of the bulk fluid In equilibrium with the pore fluid Is the same, n a = 0.5925, as that In the MD simulations. 

When (r) is a hard-sphere potential of diameter d, use of the OZ equation (2.27) plus (2.94) and (2.95), with t>(12) adjusted inside the core region rordered approximation (LOGA). The further approximation that Cq(12) is equal to zero for r>[Pg.216]

Smith and Henderson (5) have inverted G(s) analytically for 1 < x < 5. For the hard-sphere potential, these PY results for A, P, and g(r) are in good agreement with computer simulations. 

Repulsive interactions are important when molecules are close to each other. They result from the overlap of electrons when atoms approach one another. As molecules move very close to each other the potential energy rises steeply, due partly to repulsive interactions between electrons, but also due to forces with a quantum mechanical origin in the Pauli exclusion principle. Repulsive interactions effectively correspond to steric or excluded volume interactions. Because a molecule cannot come into contact with other molecules, it effectively excludes volume to these other molecules. The simplest model for an excluded volume interaction is the hard sphere model. The hard sphere model has direct application to one class of soft materials, namely sterically stabilized colloidal dispersions. These are described in Section 3.6. It is also used as a reference system for modelling the behaviour of simple fluids. The hard sphere potential, V(r), has a particularly simple form ... 

The results for the chemical potential determination are collected in Table 1 [172]. The nonreactive parts of the system contain a single-component hard-sphere fluid and the excess chemical potential is evaluated by using the test particle method. Evidently, the quantity should agree well with the value from the Carnahan-Starling equation of state [113]... 

Fig. 6. Excess chemical potential of hard-sphere solutes in SPC water as a function of the exclusion radius d. The symbols are simulation results, compared with the IT prediction using the flat default model (solid line). (Hummer et al., 1998a)...

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