Optimized potential energy functions

Optimized Potential Energy Functions in Conformational Anafysis of Saccharides... 

RASMUSSEN AND FABRICIUS Optimized Potential Energy Functions... 

Table II. Glucose in an Optimized Potential Energy Function PEFAC2 and Comparisons with Non-Optimized Functions (7-8. 10)...

PEF95SAC optimized potential energy function for alcohols and carbohydrates. J. Carbohydr. Chem. 16, 751-772. 

Murrell JN, Carter S, Halonen LO, Frequency optimized potential energy functions for the ground-state surfaces of HCN and HCP, J Mol Spectrosc 93,307-316 (1982)... 

Equations (l)-(3) in combination are a potential energy function that is representative of those commonly used in biomolecular simulations. As discussed above, the fonn of this equation is adequate to treat the physical interactions that occur in biological systems. The accuracy of that treatment, however, is dictated by the parameters used in the potential energy function, and it is the combination of the potential energy function and the parameters that comprises a force field. In the remainder of this chapter we describe various aspects of force fields including their derivation (i.e., optimization of the parameters), those widely available, and their applicability. 

A number of more general force fields for the study of small molecules are available that can be extended to biological molecules. These force fields have been designed with the goal of being able to treat a wide variety of molecules, based on the ability to transfer parameters between chemical systems and the use of additional terms (e.g., cross terms) in their potential energy functions. Typically, these force fields have been optimized to... 

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. 

Potential Energy Functions and Parameters. The second point is the importance of non-bonded interactions. The program was developed to optimize also on unit cell dimensions in addition to the usual conformational properties, because this gives the possibility of optimizing on properties that are very sensitive to non-bonded interactions. 

We can state, in conclusion, that optimization of the potential energy function parameters on experimental data of small model compounds has led to a parameter set that gives an overall improvement of the accuracy of postdiction and, by implication, of the validity of prediction. The improvement is most marked in the most flexible substance. 

Schlenkrich, M., Brickmann, J., MacKerell Jr., A. D., and Karplus, M. (1996) An empirical potential energy function for phospholipids criteria for parameter optimization and application. In Biological membranes a molecular perspective from computational and experiment, Merz Jr., K. M. and Roux, B. (eds.), Birkhauser, Boston, 31-81. 

Before we go on to consider functional forms for all of the components of a molecule s total steric energy, let us consider the limitations of Eq. (2.2) for bond stretching. Like any truncated Taylor expansion, it works best in regions near its reference point, in this case req. Thus, if we are interested primarily in molecular structures where no bond is terribly distorted from its optimal value, we may expect Eq. (2.2) to have reasonable utility. However, as the bond is stretched to longer and longer r, Eq. (2.2) predicts the energy to become infinitely positive, which is certainly not chemically realistic. The practical solution to such inaccuracy is to include additional terms in the Taylor expansion. Inclusion of the cubic term provides a potential energy function of the form... 

Therefore, two parts of any molecular mechanics package that have a direct influence on a particular optimized structure, i. e., on the nuclear coordinates of a specific energy minimum on the calculated potential energy surface, are the mathematical functions and the corresponding parameters. The potential energy functions and the force field parameters are interrelated and, therefore, the parameters may not, in general, be transferred from one force field into another. 

A vast amount of empirical molecular potential energy functions and a series of corresponding programs (molecular mechanics and consistent force field programs) are available (for recent reviews see 203 205)). Unfortunately these energy functions are always the result of optimization on a rather limited group of compounds. No... 

In conventional MM the potential energy function (PEF) is parameterized and these optimized parameters are called force-field parameters. Such methods are widely applied in the studies of nucleic acids, proteins, their complexes and other biomolecular systems. A typical, simple force field of a molecular system is defined by the following equation ... 

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