Macromolecular structures algorithms

Notwithstanding the algorithmic developments described in preceding sections, and the laudable efforts by the simulation community to achieve full exploitation of available parallel hardware, the problem identified earlier remains, in macromolecular structures at least that is, the current time and spatial scales are in many instances inappropriate for the target physical questions. Because information spanning several orders of magnitude beyond the currently accessible picosecond-nanosceond time frame is needed from MD simulations, the development of more effective multiple-time-scale MD methods is seen as crucial. 

Molecular dynamics (MD), Monte Carlo, energy minimization, and related algorithms are used for refining macromolecular structures, using data from x-ray crystallography and NMR. MD can also be employed to simulate macromolecular motions over timescales ranging from femtoseconds to nanoseconds (1). 

This is the simplest version of the cooperative algorithm. It has minimum assumptions concerning types of moves and has no limits in complexity of the macromolecular structures. Moreover, it represents probably the most plausible dynamics on the local scale. 

Conformational Sampling Conformational Search Proteins Distance Geometry Theory, Algorithms, and Chemical Applications Macromolecular Structures Determined using NMR Data NMR Refinement Simulated Anneeding. 

There are several reasons that Newton-Raphson minimization is rarely used in mac-romolecular studies. First, the highly nonquadratic macromolecular energy surface, which is characterized by a multitude of local minima, is unsuitable for the Newton-Raphson method. In such cases it is inefficient, at times even pathological, in behavior. It is, however, sometimes used to complete the minimization of a structure that was already minimized by another method. In such cases it is assumed that the starting point is close enough to the real minimum to justify the quadratic approximation. Second, the need to recalculate the Hessian matrix at every iteration makes this algorithm computationally expensive. Third, it is necessary to invert the second derivative matrix at every step, a difficult task for large systems. 

Transferred electron density fragments obtained by AFDF method can provide excellent approximations. One such approach, formulated in terms of transferability of fragment density matrices within the AFDF framework is a tool that has been suggested as an approach to macromolecular quantum chemistry [114, 115, 130, 142-146] and to a new density fitting algorithm in the crystallographic structure refinement process [161]. 

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