Protein folding function

Abstract. A smooth empirical potential is constructed for use in off-lattice protein folding studies. Our potential is a function of the amino acid labels and of the distances between the Ca atoms of a protein. The potential is a sum of smooth surface potential terms that model solvent interactions and of pair potentials that are functions of a distance, with a smooth cutoff at 12 Angstrom. Techniques include the use of a fully automatic and reliable estimator for smooth densities, of cluster analysis to group together amino acid pairs with similar distance distributions, and of quadratic progrmnming to find appropriate weights with which the various terms enter the total potential. For nine small test proteins, the new potential has local minima within 1.3-4.7A of the PDB geometry, with one exception that has an error of S.SA. 

While this is disappointing, the nonuniqueness theorem also shows that if some empirical potential is able to predict correct protein folds then many other empirical potentials will do so, too. Thus, the construction of empirical potentials for fold prediction is much less constrained than one might think initially, and one is justified in using additional qualitative theoretical assumptions in the derivation of an appropriate empirical potential function. 

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. 

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. 

Ithough knowledge-based potentials are most popular, it is also possible to use other types potential function. Some of these are more firmly rooted in the fundamental physics of iteratomic interactions whereas others do not necessarily have any physical interpretation all but are able to discriminate the correct fold from decoy structures. These decoy ructures are generated so as to satisfy the basic principles of protein structure such as a ose-packed, hydrophobic core [Park and Levitt 1996]. The fold library is also clearly nportant in threading. For practical purposes the library should obviously not be too irge, but it should be as representative of the different protein folds as possible. To erive a fold database one would typically first use a relatively fast sequence comparison lethod in conjunction with cluster analysis to identify families of homologues, which are ssumed to have the same fold. A sequence identity threshold of about 30% is commonly... 

Bryngelson J D, J N Onuchic, N D Socci and P G Wolynes 1995. Funnels, Pathways, and the Energy Landscape of Protein Folding A Synthesis. Proteins Structure, Function and Genetics 21 167-195. 

Maiorov V N and G M Crippen 1994. Learning About Protein Folding via Potential Functions. Proteins Structure, Function and Genetics 20 167-173. 

Noncovalent Forces Stabilizing Protein Structure. Much of protein engineering concerns attempts to alter the stmcture or function of a protein in a predefined way. An understanding of the underlying physicochemical forces that participate in protein folding and stmctural stabilization is thus important. 

Through combined effects of noncovalent forces, proteins fold into secondary stmctures, and hence a tertiary stmcture that defines the native state or conformation of a protein. The native state is then that three-dimensional arrangement of the polypeptide chain and amino acid side chains that best facihtates the biological activity of a protein, at the same time providing stmctural stabiUty. Through protein engineering subde adjustments in the stmcture of the protein can be made that can dramatically alter its function or stabiUty. 

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. 

L Rychlewski, B Zhang, A Godzik. Fold and function predictions for Mycoplasma genitalmm proteins. Fold Des 3 229-238, 1998. 

S Vajda, M Sippl, J Novotny. Empirical potentials and functions for protein folding and binding. Cuit Opm Struct Biol 7 228-228, 1997. 

How does the GroEL-GroES complex function as a chaperone to assist protein folding Although several aspects of the mechanism are not clear, the main features of the functional cycle are known. The first step is the... 

The first requirement for threading is to have a database of all the known different protein folds. Eisenberg has used his own library of about 800 folds, which represents a minimally redundant set of the more than 6000 structures deposited at the Protein Data Bank. Other groups use databases available on the World Wide Web, where the folds are hierarchically ordered according to structural and functional similarities, such as SCOP, designed by Alexey Murzin and Cyrus Chothia in Cambridge, UK. 

Srinivasan, R., and Rose, G. D., 1995. LINUS A hierarchic procedure to predict the fold of a protein. Proteins Structure, Function and Genetics 22 81-99. 

In order to make as much data on the structure and its determination available in the databases, approaches for automated data harvesting are being developed. Structure classification schemes, as implemented for example in the SCOP, CATH, andFSSP databases, elucidate the relationship between protein folds and function and shed light on the evolution of protein domains. 

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