A method for constrained energy minimization of macromolecules

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Abstract
Two algorithms for the local energy minimization of the structure of macromolecules in the presence of constraints are proposed. They are a combination of the method of steepest descents and the method of conjugate gradients with the procedure SHAKE, by which distance constraints can be satisfied. The two algorithms are tested by applying them to a small protein, the bovine pancreatic trypsin inhibitor (BPTI), and compared with the penalty function method for conserving constraints. The efficiency of the proposed methods depends on the level of interdependence of the constraints. For bond‐length constraints, the use of SHAKE is superior to the penalty function method. However, when bond‐angle constraints are included, SHAKE is more efficient only if the curvature of the penalty function is considerably greater than that of the potential function being minimized. The results indicate that with bond‐length constraints the minimization behavior is similar to that without constraints. However, the simultaneous application of bond‐length and bond‐angle constraints appears to confine the molecule to a very limited part of configuration space, very different from the part covered by an unconstrained minimization. This conclusion calls into question energy minimizations of protein systems in which only the dihedral angles are allowed to vary.

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