PROTEIN MOLECULAR-DYNAMICS CONSTRAINED TO SLOW MODES - THEORETICAL APPROACH BASED ON A HIERARCHY OF LOCAL MODES WITH A SET OF HOLONOMIC CONSTRAINTS - THE METHOD AND ITS TESTS ON CITRATE SYNTHASE

We present a new approach for theoretical simulation of protein dynamics constrained to slow modes in order to allow for an increase of the integration time step by an order of magnitude. It consists in building a hierarchy of internal vectors, according to the tree principle (generalization of Jacobi coordinates), and in using their polar coordinates, referred for each vector to the two vectors immediately lower in the tree, as local modes. Then the higher frequency modes are either fixed to their equilibrium values (holonomic constraints) or, as regards the cyclic coordinates which have no equilibrium value, affected with a friction coefficient. Conditions in the design of the tree are derived which allow the holonomic constraints to be applied as a correction after each step without needing an iteration. The method is tested on citrate synthase, a dimeric enzyme with 2 X 437 residues. The CHARMM-20 programs were used for topology, energy calculation, and basic dynamics. Comparisons between exact dynamics, 1-fs time step, and constrained dynamics, 8-fs time step, are presented in terms of the variations of some randomly chosen unconstrained coordinates along a 2.8-ps run, and in terms of statistics on average values and RMS fluctuations of all unconstrained coordinates in the same time lag. Finally, prospects for improvement and extension of this method are discussed.