Molecular Modeling of Proteins: A Strategy for Energy Minimization by Molecular Mechanics in the AMBER Force Field

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Abstract
Energy minimization is an important step in molecular modeling of proteins. In this study, we sought to develop a minimization strategy which would give the best final structures with the shortest computer time in the AMBER force field. In the all-atom model, we performed energy minimization of the melittin (mostly α-helical) and cardiotoxin (mostly β-sheet and β-turns) crystal structures by both constrained and unconstrained pathways. In the constrained path, which has been recommended in the energy minimization of proteins, hydrogens were relaxed first, followed by the side chains of amino acid residues, and finally the whole molecule. Despite the logic of this approach, however, the structures minimized by the unconstrained path fit the experimental structures better than those minimized by constrained paths. Moreover, the unconstrained path saved considerable computer time. We also compared the effects of the steepest descents and conjugate gradients algorithms in energy minimization. Previously, steepest descents has been used in the initial stages of minimization and conjugate gradients in the final stages of minimization. We therefore studied the effect on the final structure of performing an initial minimization by steepest descents. The structures minimized by conjugate gradients alone resembled the structures minimized initially by the steepest descents and subsequently by the conjugate gradients algorithms. Thus an initial minimization using steepest descents is wasteful and unnecessary, especially when starting from the crystal structure. Based on these results, we propose the use of an unconstrained path and conjugate gradients for energy minimization of proteins. This procedure results in low energy structures closer to the experimental structures, and saves about 70–80% of computer time. This procedure was applied in building models of lysozyme mutants. The crystal structure of native T4 lysozyme was mutated to three different mutants and the structures were minimized. The minimized structures closely fit the crystal structures of the respective mutants (< 0.3 Å root-mean-square, RMS, deviation in the position of all heavy atoms). These results confirm the efficiency of the proposed minimization strategy in modeling closely related homologs. To determine the reliability of the united atom approximation, we also performed all of the above minimizations with united atom models. This approximation gave structures with similar but slightly higher RMS deviations than the all-atom model, but gave further savings of60-70% in computer time. However, we feel further investigation is essential to determine the reliability of this approximation. Finally, to determine the limitation of the procedure, we built the melittin molecule interactively in an α-helical conformation and this model showed an RMS deviation greater than 2.8 Å when compared to the melittin crystal structure. This model was minimized by various strategies. None of the minimized structures converged towards the crystal structure. Thus, although the proposed method seems to give valid structures starting from closely related crystal structures, it cannot predict the native structure when the starting structure is far from the native structure. From these results, we recommend the use of the proposed strategy of minimizing by an unconstrained path using the conjugate gradients algorithm, but only for modeling of closely related structural homologs of proteins.