Empirical energy function

The effective moment of inertia / and the friction coefficient / could easily be estimated. The force constant k associated with the relative motion of the lobes was determined from an empirical energy function. To do so, the molecule was opened in a step-wise fashion by manipulating the hinge region and each resulting structure was energy minimized. Then, the interaction energy between the two domains was measured, and plotted versus 0. 

Figure 2-108 shows the correspondence between a histogram and the derived empirical energy function for the torsion angle fragment C-N H)-C(H)(H -C. 

Bryant S H and C E Lawrence 1993. An Empirical Energy Function for Threading Protein Sequences Through the Folding Motif. Proteins Structure, Punction and Genetics 16 92-112. 

Suppose we are using an empirical energy function such as the following to describe the inter- and intramolecular interactions in our ethanol/ethane thiol system ... 

Empirical energy functions can fulfill the demands required by computational studies of biochemical and biophysical systems. The mathematical equations in empirical energy functions include relatively simple terms to describe the physical interactions that dictate the structure and dynamic properties of biological molecules. In addition, empirical force fields use atomistic models, in which atoms are the smallest particles in the system rather than the electrons and nuclei used in quantum mechanics. These two simplifications allow for the computational speed required to perform the required number of energy calculations on biomolecules in their environments to be attained, and, more important, via the use of properly optimized parameters in the mathematical models the required chemical accuracy can be achieved. The use of empirical energy functions was initially applied to small organic molecules, where it was referred to as molecular mechanics [4], and more recently to biological systems [2,3]. 

SH Bryant, CE Lawrence. An empirical energy function for threading protein sequence thi-ough the folding motif. Pi-otems Struct Eunct Genet 16 92-112, 1993. 

Krieger E, Darden T, Nabuurs SB, Finkelstein A, Vriend G. Making optimal use of empirical energy functions force-field parameterization in crystal space. Proteins 2004 57 678-83. 

A. D. MacKerell, J. Wiorkiewicz-Kuczera, and M. Karplus, An all-atom empirical energy function for the simulation of nucleic acids, J. Am. Chem. Soc. 117 11946 (1995). 

Using Atomic Charges to Construct Empirical Energy Functions for Molecular Mechanics/Molecular Dynamics Calculations... 

The potential energy of the system U(q) can be determined from the solution of the corresponding quantum-mechanical problem for electrons (in this case, it is called first-principles MD), or by using empirical energy functionals (they will be discussed in detail below). 

At present, simulations with the MD method using a first-principles energy functional can be performed for relatively small systems that contain several hundreds of atoms. Therefore, for the simulation of larger systems, one should use empirical energy functionals. 

As in the MD method, PES for KMC can be derived from first-principles methods or using empirical energy functionals described above. However, the KMC method requires the accurate evaluation of the PES not only near the local minima, but also for transition regions between them. The corresponding empirical potentials are called reactive, since they can be used to calculate parameters of chemical reactions. The development of reactive potentials is quite a difficult problem, since chemical reactions usually include the breaking or formation of new bonds and a reconfiguration of the electronic structure. At present, a few types of reactive empirical potentials can semi-quantitatively reproduce the results of first-principles calculations these are EAM and MEAM potentials for metals and bond-order potentials (Tersoff and Brenner) for covalent semiconductors and organics. 

The empirical energy functions used to compute MIFs can consist of the sum of one or more terms. In the GRID program, the energy function is given by the following terms ... 

B. von Freyberg and W. Braun, /. Comput. Chem., 14, 510 (1933). Minimization of Empirical Energy Functions in Proteins Including Hydrophobic Surface Area Effects. 

L. Nilsson and M. Karplus,/. Comput. Chem., 7,59 (1986). Empirical Energy Functions for Energy Minimization and Dynamics of Nucleic Acids. 

Sanders C. R., and Schwonek, J. P. (1993). An Approximate Model and Empirical Energy Function for Solute Interactions with a Wat -niosphatidylcholine Interface. Biophys. J. 65, 1207-1218. 

Another aspect of enzyme function, which can be readily studied by methods based on empirical energy functions, are large scale atomic displacements, such as domain motions and conformational transitions of loops. The energy as a function of the relative positions of domains or loops can be obtained through several techniques... 

Since the first work describing a molecular dynamics simulation of a small protein was published (McCammon et al. 1977), there has been explosive growth in research concerned with theoretical studies of proteins and enzymes (McCammon and Harvey 1987 Brooks, et al 1988 Warshel 1991). Most of the studies have used empirical energy functions. This chapter describes the nature of the empirical energy function, its use in molecular mechanics calculations and molecular dynamics simulations and... 

MacKerell, A. D., Wiokiewicz-Kuczera, J. and Karplus, M. (1995) An All-Atom Empirical Energy Function for the Simulation of Nucleic Acids,/. dm. Chem. Soc. 117, 11946-11975. 

Nilsson, L. and Karplus, M. (1986) Empirical energy functions for energy minmization and dynamics of nucleic acids, J. Comput. Chem. 7, 591-616. 

Empirical energy functions were originally developed for energy minimization and molecular dynamics studies of macromolecular structure and function (see [31], for an introduction). The parameters of the empirical potential energy Echem are inferred from experimental as well as theoretical investigations, in particular, vibrational spectroscopy and small-molecule crystallography [25-30],... 

---