Protein folding energy

Oliveberg, M., Wolynes, P.G. The experimental survey of protein-folding energy landscapes. Q. Rev. Biophys. 2005, 38, 245-88. 

Wolynes, P., Z. Euthey-Schulten, and J. Onuchic, Fastfolding experiments and the topography of protein folding energy landscapes. Chem Biol, 1996. 3(6) p. 425-32. 

Wolynes, P.G., Luthey-Schulten, Z Onuchic, J.N. (1996) Fast-folding Experiments and the Topography of Protein Folding Energy Landscapes. Chem. Biol. 3 425-432. 

MES)==10 These results suggest tliat C(MES) grows (in all likelihood) only as In N with N. Thus tlie restriction of compactness and low energy of tlie native states may impose an upper bound on tlie number of distinct protein folds. 

Onuohio J N, Luthey-Sohulten Z A and Wolynes P G 1997 Theory of protein folding An energy landsoape perspeotive Ann. Rev. Phys. Chem. 48 545-600... 

Bryngelson J D, Onuchic J N, Socci N D and Wolynes P G 1995 Funnels, pathways, and the energy landscape of protein folding a synthesis Profe/ns 21 167-95... 

Keywords, protein folding, tertiary structure, potential energy surface, global optimization, empirical potential, residue potential, surface potential, parameter estimation, density estimation, cluster analysis, quadratic programming... 

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. 

One drawback to a molecular dynamics simulation is that the trajectory length calculated in a reasonable time is several orders of magnitude shorter than any chemical process and most physical processes, which occur in nanoseconds or longer. This allows yon to study properties that change w ithin shorter time periods (such as energy finctnations and atomic positions), but not long-term processes like protein folding. 

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. 

Fig. 10.27 Schematic representation of the energy landscape for protein folding. (Figure adapted from Onuchic ] N, Z Luthcy-Schulten and P Wolynes 1997. Theory of Protein Folding The Energy Landscape Perspective. Annual Reviews in Physical Chemistry 48 545-600.)...

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. 

Eisenberg D and A D McLachlan 1986. Solvation Energy in Protein Folding and Binding. Nature 319 199-203. 

Measuring Protein Sta.bihty, Protein stabihty is usually measured quantitatively as the difference in free energy between the folded and unfolded states of the protein. These states are most commonly measured using spectroscopic techniques, such as circular dichroic spectroscopy, fluorescence (generally tryptophan fluorescence) spectroscopy, nmr spectroscopy, and absorbance spectroscopy (10). For most monomeric proteins, the two-state model of protein folding can be invoked. This model states that under equihbrium conditions, the vast majority of the protein molecules in a solution exist in either the folded (native) or unfolded (denatured) state. Any kinetic intermediates that might exist on the pathway between folded and unfolded states do not accumulate to any significant extent under equihbrium conditions (39). In other words, under any set of solution conditions, at equihbrium the entire population of protein molecules can be accounted for by the mole fraction of denatured protein, and the mole fraction of native protein,, ie. 

For any given protein, the number of possible conformations that it could adopt is astronomical. Yet each protein folds into a unique stmcture totally deterrnined by its sequence. The basic assumption is that the protein is at a free energy minimum however, calometric studies have shown that a native protein is more stable than its unfolded state by only 20—80 kj/mol (5—20 kcal/mol) (5). This small difference can be accounted for by the favorable... 

More traditional applications of internal coordinates, notably normal mode analysis and MC calculations, are considered elsewhere in this book. In the recent literature there are excellent discussions of specific applications of internal coordinates, notably in studies of protein folding [4] and energy minimization of nucleic acids [5]. 

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. 

M Levitt. Protein folding by constrained energy minimization and molecular dynamics. J Mol Biol 170 723-764, 1983. 

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