Attractor control of the binding of digoxin to a specific antibody.

The characteristics of attractor control of the changes in the molecular vibrations of a protein have previously been detected when an enzyme (chymotrypsin) reacted with a specific substrate and when myoglobin interacted with oxygen. Similar studies have now been carried out on the binding of a hapten, digoxin, to an antibody. The temperature factors of the Fab-fragment of a specific anti-digoxin antibody with and without the bound antigen were used in this analysis. The integral correlation function of the difference in the temperature factor between the free and the loaded state of the antigen binding site indicated the existence of a regular attractor of the dimension 4.0+/-0.1 in the light chain and one of the dimension 5.7+/-0.7 in the heavy chain, the former under the control of 11+/-1 factors and the latter by 12+/-2 factors. This result was corroborated by Poincaré plots showing the cross-section of attractors and by a positive Liapunov exponent. The power spectrum was, as expected, broad, but the autocorrelation function showed only significant damping in the case of the L-chain. The spacing of the temperature factors resembled a "Devil's Staircase" suggesting the operation of a stochastic attractor. Its dimension, which was determined by the methods of the correlation between the step-gag lengths and that of the Farey tree was found to be near one. Repetition of the calculation using data for the second antigen-antibody complex in the unit cell yielded similar results. However, the dimensions of the attractors in the second complex (6.0+/-0.1 for the L- and 7.6+/-0.1 for the H-chain) are somewhat larger than that of the first, probably reflecting the lower degree of order of the latter. In all cases, the saturation of the integral correlation coefficient with increasing number of phase-space dimensions strongly indicates the existence of an attractor. The evidence of attractors in the molecular dynamics of proteins raises doubt about the value of trajectories calculated by integration of equations of atomic movement of the prediction of folding pathways since the stochastic element in the dynamics can eliminate leading equations in the set, thus influencing the folding pathway.