Potential energy functions, molecular dynamics

Molecular dynamics conceptually involves two phases, namely, the force calculations and the numerical integration of the equations of motion. In the first phase, force interactions among particles based on the negative gradient of the potential energy function U,... 

How can we apply molecular dynamics simulations practically. This section gives a brief outline of a typical MD scenario. Imagine that you are interested in the response of a protein to changes in the amino add sequence, i.e., to point mutations. In this case, it is appropriate to divide the analysis into a static and a dynamic part. What we need first is a reference system, because it is advisable to base the interpretation of the calculated data on changes compared with other simulations. By taking this relative point of view, one hopes that possible errors introduced due to the assumptions and simplifications within the potential energy function may cancel out. All kinds of simulations, analyses, etc., should always be carried out for the reference and the model systems, applying the same simulation protocols. 

The pressure often fluctuates much more than quantities such as the total energy in constant NVE molecular dynamics simulation. This is as expected because the pressure related to the virial, which is obtained as the product of the positions and the derivativ of the potential energy function. This product, rijdf rij)/drij, changes more quickly with than does the internal energy, hence the greater fluctuation in the pressure. 

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... 

Molecular Dynamics and Monte Carlo Simulations. At the heart of the method of molecular dynamics is a simulation model consisting of potential energy functions, or force fields. Molecular dynamics calculations represent a deterministic method, ie, one based on the assumption that atoms move according to laws of Newtonian mechanics. Molecular dynamics simulations can be performed for short time-periods, eg, 50—100 picoseconds, to examine localized very high frequency motions, such as bond length distortions, or, over much longer periods of time, eg, 500—2000 ps, in order to derive equiUbrium properties. It is worthwhile to summarize what properties researchers can expect to evaluate by performing molecular simulations ... 

Despite their simplicity, certainly compared to the all-atom potentials used in molecular dynamics studies, these contact energy functions enable the exploration of different interaction scenarios. This diversity is achieved by changing the heterogeneity of the sequence, by altering the number N of different types of residues that are being used. The most elementary lattice model involves only two types of monomers hydrophobic... 

The calculation of the potential of mean force, AF(z), along the reaction coordinate z, requires statistical sampling by Monte Carlo or molecular dynamics simulations that incorporate nuclear quantum effects employing an adequate potential energy function. In our approach, we use combined QM/MM methods to describe the potential energy function and Feynman path integral approaches to model nuclear quantum effects. 

Stanton, R. V., D. S. Hartsough, and K. M. Merz Jr. 1993. Calculation of Solvation Free Energies Using a Density Functional/Molecular Dynamics Coupled Potential. J. Phys. Chem. 97, 11868. 

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). 

In order to study the behavior of ions at the water/metal interface using the molecular dynamics method, the potential energy functions for the interaction between the ions and the water and between the ions and the metal surface must be specified. 

Figure 6. History of the Cremer-Pople pucker parameter 6 calculated from molecular dynamics simulation of fi-D-glucopyranose in the Cj conformation in vacutim using the Rasmussen potential energy function PEF422. This molecule underwent four transitions in conformation. (Reproduced with permission from Ref. 11. Copyright 1987 Elsevier Science Publishers.)...

The molecular dynamics unit provides a good example with which to outline the basic approach. One of the most powerful applications of modem computational methods arises from their usefulness in visualizing dynamic molecular processes. Small molecules, solutions, and, more importantly, macromolecules are not static entities. A protein crystal structure or a model of a DNA helix actually provides relatively little information and insight into function as function is an intrinsically dynamic property. In this unit students are led through the basics of a molecular dynamics calculation, the implementation of methods integrating Newton s equations, the visualization of atomic motion controlled by potential energy functions or molecular force fields and onto the modeling and visualization of more complex systems. 

The molecular potential energy is an energy calculated for static nuclei as a function of the positions of the nuclei. It is called potential energy because it is the potential energy in the dynamical equations of nuclear motion. 

To generate the potential energy function under which molecules move, for molecular dynamics or Monte Carlo calculations. 

To Generate the Potential Energy Function Under Which Molecules Move, for Molecular Dynamics or Monte Carlo Calculations... 

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