Energy functions, conformational

D. Shalloway, Application of the renormalization group to deterministic global minimization of molecular conformation energy functions. Journal of Global Optimization 2 (1992), 281. 

The vrork reported here has beat carried out in the context of a program to develop reliable conformational energy functions for polysaccharides in solution U, ). A quite satisfactory model for aqueous amylosic chains has been developed details are reported at length elsevdtere P, ). Here procedures... 

Figure 6. An energy surface as in Figure 2, but based on alternative assumptions about skeletal geometry and conformational energy functions as described in the text...

If the core structure is accurate enough, the above closure methods generally yield reasonable conformations for short loops (up to six or seven residues) that are relatively well determined by conditions of correct covalent bonding to the rest of the chain, and the correct packing of side chains. By contrast, the conformation of longer loops (n > 7) is heavily affected by nonbonded interactions, as well as solvation and entropic effects. Conformational energy functions without... 

Free Energy Function The conformational free energy was estimated by the following energy expression ... 

C.D. Maranas, IP. Androulakis and C.A. Floudas, A deterministic global optimization approach for the protein folding problem, pp. 133-150 in Global minimization of nonconvex energy functions molecular conformation and protein folding (P. M. Pardalos et al., eds.), Amer. Math. Soc., Providence, RI, 1996. 

G. Ramachandran and T. Schlick. Beyond optimization Simulating the dynamics of supercoiled DNA by a macroscopic model. In P. M. Pardalos, D. Shal-loway, and G. Xue, editors. Global Minimization of Nonconvex Energy Functions Molecular Conformation and Protein Folding, volume 23 of DIM ACS Series in Discrete Mathematics and Theoretical Computer Science, pages 215-231, Providence, Rhode Island, 1996. American Mathematical Society. 

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... 

The most ambitious approaches to the protein folding problem attempt to solve it from firs principles (ab initio). As such, the problem is to explore the coirformational space of th molecule in order to identify the most appropriate structure. The total number of possibl conformations is invariably very large and so it is usual to try to find only the very lowes energy structure(s). Some form of empirical force field is usually used, often augmente with a solvation term (see Section 11.12). The global minimum in the energy function i assumed to correspond to the naturally occurring structure of the molecule. 

PC Model has some features that are not found in many other molecular mechanics programs. This is one of the few programs that outputs the energy given by the force field and the heat of formation and a strain energy. Atom types for describing transition structures in the MMX force field are included. There is a metal coordination option for setting up calculations with metal atoms. There are also molecular similarity and conformation search functions. 

K. Rasmussen, in G. Berthier and co-workers, eds., Eecture Notes in Chemisty, Vol. 27, Potential Energy Functions in Conformational Analysis, Springer-Vedag, Berlin, 1985. 

Equations (5)-(8) assume that the energy functions (7 and Ub operate on the same conformation space i.e., A and B must have the same number N of degrees of freedom. In practice, this almost always implies that A and B have the same number of atoms or particles. Most biochemical changes of interest (e.g., point mutations of a protein) do not obey this requirement, but they can often be made to do so artificially through the use of dummy atoms (see below). 

The problem of finding conformations of the molecule that satisfy the experimental data is then that of finding conformations that minimize a hybrid energy function i,ybiM, which contains different contributions from experimental data and the force field (see below). These contributions need to be properly weighted with respect to each other. However, if the chosen experimental upper and lower bounds are wide enough to avoid any geometrical inconsistencies between the force field and the data, this relative weight does not play a predominant role. 

Finding the minimum of the hybrid energy function is very complex. Similar to the protein folding problem, the number of degrees of freedom is far too large to allow a complete systematic search in all variables. Systematic search methods need to reduce the problem to a few degrees of freedom (see, e.g.. Ref. 30). Conformations of the molecule that satisfy the experimental bounds are therefore usually calculated with metric matrix distance geometry methods followed by optimization or by optimization methods alone. 

RJ Petrella, T Lazardis, M Karplus. Protein sidecham conformer prediction A test of the energy function. Folding Des 3 353-377, 1998. 

K Yue, KA Dill. Folding proteins with a simple energy function and extensive conformational searching. Protein Sci 5 254-261, 1996. 

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