Potential energy function structures

A particularly important application of molecular dynamics, often in conjunction with the simulated annealing method, is in the refinement of X-ray and NMR data to determine the three-dimensional structures of large biological molecules such as proteins. The aim of such refinement is to determine the conformation (or conformations) that best explain the experimental data. A modified form of molecular dynamics called restrained moleculai dynarrdcs is usually used in which additional terms, called penalty functions, are added tc the potential energy function. These extra terms have the effect of penalising conformations... 

Jones D T and J M Thornton 1996. Potential Energy Functions for Threading. Current Opinion in Structural Biology 6 210-216. 

A potential energy function is a mathematical equation that allows for the potential energy, V, of a chemical system to be calculated as a function of its tliree-dimensional (3D) structure, R. The equation includes terms describing the various physical interactions that dictate the structure and properties of a chemical system. The total potential energy of a chemical system with a defined 3D strucmre, V(R)iai, can be separated into terms for the internal, V(/ )i,iBmai, and external, V(/ )extemai, potential energy as described in the following equations. 

That stable nuclear structures should involve stable local structures about each of the inner-core spherons is a reasonable consequence of the mutual interdependence of structure and potential energy function and the short range of internucleonic forces. 

We now describe a relatively simple MD model of a low-index crystal surface, which was conceived for the purpose of studying the rate of mass transport (8). The effect of temperature on surface transport involves several competing processes. A rough surface structure complicates the trajectories somewhat, and the diffusion of clusters of atoms must be considered. In order to simplify the model as much as possible, but retain the essential dynamics of the mobile atoms, we will consider a model in which the atoms move on a "substrate" represented by an analytic potential energy function that is adjusted to match that of a surface of a (100) face-centered cubic crystal composed of atoms interacting with a Lennard-Jones... 

Figure 3.3 (a) The potential energy function assumed in the particle-in-a-one-dimensional-box model, (b) A wave function satisfying the boundary conditions, (c) An unacceptable wave function. (Reproduced with permission from P. A. Cox, Introduction to Quantum Theory and Atomic Structure, 1996, Oxford University Press, Oxford, Figure 2.6.)... 

Molecular dynamics calculations have been performed (35-38). One ab initio calculation (39) is particularly interesting because it avoids the use of pairwise potential energy functions and effectively includes many-body interactions. It was concluded that the structure of the first hydration shell is nearly tetrahedral but is very much influenced by its own solvation. 

The study of liquids near solid surfaces using microscopic (atomistic-based) descriptions of liquid molecules is relatively new. Given a potential energy function for the interaction between liquid molecules and between the liquid molecules and the solid surface, the integral equation for the liquid density profile and the liquid molecules orientation can be solved approximately, or the molecular dynamics method can be used to calculate these and many other structural and dynamic properties. In applying these methods to water near a metal surface, care must be taken to include additional features that are unique to this system (see later discussion). 

One of the important electrochemical interfaces is that between water and liquid mercury. The potential energy functions for modeling liquid metals are, in general, more complex than those suitable for modeling sohds or simple molecular liquids, because the electronic structure of the metal plays an important role in the determination of its structure." However, based on the X-ray structure of liquid mercury, which shows a similarity with the solid a-mercury structure, Heinzinger and co-workers presented a water/Hg potential that is similar in form to the water/Pt potential described earlier. This potential was based on quantum mechanical calculations of the adsorption of a water molecule on a cluster of mercury atoms. ... 

Although the potential energy functions can be made to reproduce thermodynamic solvation data quite well, they are not without problems. In some cases, the structure of the ion solvation shell, and in particular the coordination number, deviates from experimental data. The marked sensitivity of calculated thermodynamic data for ion pairs on the potential parameters is also a problem. Attempts to alleviate these problems by introducing polarizable ion-water potentials (which take into account the induced dipole on the water caused by the ion strong electric field) have been made, and this is still an active area of research. 

In principle, it is a simple matter to include solvent water molecules directly in MD simulations, since appropriate intermolecular potential energy functions for water are available (1Z 37,38) one would just surround the solute molecules with a sufficient number of water molecules to approximate a bulk solution. Unfortunately, a "sufficient number of water molecules might be enormous, since many of the effects of aqueous solvation are long range or are due to entropic contributions arising from "structuring of the solvent, which may be cooperative in nature. 

A short presentation of the Consistent Force Field is given, with emphasis on parametrization and optimization of energy function parameters. For best possible calculation of structure, potential energy functions with parameter values optimized on both structural and other properties must be used. Results from optimization with the Consistent Force Field on alkanes and ethers are applied to glucose, gentiobiose, maltose and cellobiose. Comparison is made with earlier and with parallel work. The meaning and use of conformational maps is discussed shortly. 

For maltose. Figure 3 shows that there are no significant differences between the geometric results found with the four rather different potential energy functions. The only discrepancy is the absence of minimum 1 in the map of French (18). Most crystal structure data fall within the valley joining the three upper points. 

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