A new principle of enzyme catalysis: coupled vibrations facilitate conformational changes

The coupling between the molecular vibrations in chymotrypsinogen, alpha-chymotrypsin and tosyl-alpha-chymotrypsin, as expressed by the temperature factors of individual amino acid sidechains and by a flexibility parameter calculated from the masses and co-ordinates of the atoms, has been analyzed by calculation of the integral correlation coefficient, the autocorrelation coefficient, the Poincaré projection, the first Liapunov coefficient and the power spectra. The agreement between the results obtained with the temperature factors and the flexibility parameter as well as the correct display by the latter of known structural features support the validity of the approach. The localization and extent of the conformational change in the enzyme following its binding of a specific substrate is detected in the difference plot between the enzyme and the acylenzyme of the distribution of the flexibility parameter over the peptide chain. As many as about 70% of the aminoacids participate in this rearrangement. An attractor of low dimensionality, two, i.e. a limit cycle, is detected both in the total enzyme and in its domain which is mobilized by the specific substrate. A simple model based on a known prominent structural feature, which is common to the trypsin family of serine proteases, two extensive coaxial halfcylinders of beta-sheets, to which previously no mechanistic function could be assigned, is proposed to account for the role of the attractor in the catalytic process: (1) control of the entry of a specific substrate to the catalytic site by co-ordinated disentanglement of the interlocking sidechains; (2) correct positioning of the functional groups in the active site; (3) lowering of the activation energy of the formation of the transition state complex.