Molecular function conjugate gradient method

Energy minimization methods that exploit information about the second derivative of the potential are quite effective in the structural refinement of proteins. That is, in the process of X-ray structural determination one sometimes obtains bad steric interactions that can easily be relaxed by a small number of energy minimization cycles. The type of relaxation that can be obtained by energy minimization procedures is illustrated in Fig. 4.4. In fact, one can combine the potential U r) with the function which is usually optimized in X-ray structure determination (the R factor ) and minimize the sum of these functions (Ref. 4) by a conjugated gradient method, thus satisfying both the X-ray electron density constraints and steric constraint dictated by the molecular potential surface. 

Conjugate gradients A mathematical first-order procedure to minimize a function such as a potential energy function used in molecular mechanics. The conjugate gradients method is the method of choice to energy minimize large... 

Figure 5 Optimization of the objective function in Modeller. Optimization of the objective function (curve) starts with a random or distorted model structure. The iteration number is indicated below each sample structure. The first approximately 2000 iterations coiTespond to the variable target function method [82] relying on the conjugate gradients technique. This approach first satisfies sequentially local restraints, then slowly introduces longer range restraints until the complete objective function IS optimized. In the remaining 4750 iterations, molecular dynamics with simulated annealing is used to refine the model [83]. CPU time needed to generate one model is about 2 mm for a 250 residue protein on a medium-sized workstation.

Payne, M.C. Teter, M.P. Allan, D.C. Arias, T.A. Joannopoulos, J.D. Iterative minimization techniques for ab inito total-energy calcrJations molecular dynamics and conjugate gradients. Rev. Mod. Phys. 1992, 64, 1045 Pickett, W. Pseudopotential methods in condensed matter applications, Corn-put. Phys. Rep. 1989, 9, 115 Beck, T.L. REal-space mesh techniques in density-functional theoryRev. Mod. Phys. 2000, 72, 1041-1080 Chelikowsky, J.R. The pseudopotential-density functional method applied to nanostructures. Physica D 2000, 33, R33. 

---