Protein folding calculation

In another study of protein structure, Cox and Johnston3 analyzed how the choice of GA parameters affects the quality of the GA search. This sort of approach was also adopted by Djurdjevic and Biggs,4 who presented a detailed study of how evolutionary algorithms can be used, in combination with a full atomistic protein ab initio model, for fold prediction and, like Cox and Johnston, considered the influence of the different values of parameters on the success of their protein folding calculations. 

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 techniques listed above are dynamical simulations. It is also possible to use bead interaction potentials for strictly thermodynamic calculations. For example, the following steps have been used for protein-folding problems ... 

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. 

Because protein ROA spectra contain bands characteristic of loops and turns in addition to bands characteristic of secondary structure, they should provide information on the overall three-dimensional solution structure. We are developing a pattern recognition program, based on principal component analysis (PCA), to identify protein folds from ROA spectral band patterns (Blanch etal., 2002b). The method is similar to one developed for the determination of the structure of proteins from VCD (Pancoska etal., 1991) and UVCD (Venyaminov and Yang, 1996) spectra, but is expected to provide enhanced discrimination between different structural types since protein ROA spectra contain many more structure-sensitive bands than do either VCD or UVCD. From the ROA spectral data, the PCA program calculates a set of subspectra that serve as basis functions, the algebraic combination of which with appropriate expansion coefficients can be used to reconstruct any member of the... 

To illustrate these methods, we consider the main biological problems that have motivated their development. The problems that have received the most attention are the receptor-ligand binding problem [12-16] and the calculation of proton binding affinities (pKa shifts) [17-20], The methods described can also be applied to many related problems, such as redox protein behavior, protein-protein association, protein folding, or membrane insertion. 

The use of the term ab initio in the context of protein folding should not be confused with its use to describe ab initio quantum chemistry calculations. In both cases, ab initio is meant to convey the idea of from first principles, but die starting point and theoretical framework are different for each. 

Comparison of the experimental potential in a crystal and the theoretical potential for an isolated molecule is an excellent test for the transferability of theoretical isolated molecule densities to problems such as molecular packing and protein folding. A systematic study of this kind was done on L-alanine. Figure 8.3 shows a comparison between theory and experiment for a plane containing the C—N bond in this molecule. The comparison is with the 6-3IG basis set of double-zeta-plus-polarization quality. The agreement of experiment with more modest basis-set calculations was found to be inferior, which gives confidence in the experimental results. Both in the plane shown, and in the plane of the carboxyl... 

It is hard to believe that, in order to see how the enzyme works, or how the protein folds up, one must view the movie in its entirety. It is more plausible that there are only a few interesting parts, during which the system passes through critical bottlenecks in its configuration space the rest of the time being spent exploring large, equilibrated reservoirs between the bottlenecks. If the trajectory calculation were... 

Transition state theory (Chapter 2, section A) was derived for chemical bonds that obey quantum theory. An equation analogous to that for transition state theory may be derived even more simply for protein folding because classical low energy interactions are involved and we can use the Boltzmann equation to calculate the fraction of molecules in the transition state i.e., = exp(— AG -D/RT), where A G D is the mean difference in energy between the conformations at the saddle point of the reaction and the ground state. Then, if v is a characteristic vibration frequency along the reaction coordinate at the saddle point, and k is a transmission coefficient, then... 

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