ATTRACTOR CONTROL OF THE BINDING OF DIGOXIN TO A SPECIFIC ANTIBODY

The characteristics of attractor control of the changes in the molecul ar vibrations of a protein have previously been detected when an enzym e (chymotrypsin) reacted with a specific substrate and when myoglobin interacted with oxygen. Similar studies have now been carried out on t he binding of a hapten, digoxin, to an antibody. The temperature facto rs of the F-ab-fragment of a specific anti-digoxin antibody with and w ithout the bound antigen were used in this analysis. The integral corr elation function of the difference in the temperature factor between t he 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, t he former under the control of 11 +/- 1 factors and the latter by 12 /- 2 factors. This result was corroborated by Poincare plots showing t he cross-section of attractors and by a positive Liapunov exponent. Th e power spectrum was, as expected, broad, but the autocorrelation func tion showed only significant damping in the case of the L-chain. The s pacing of the temperature factors resembled a ''Devil's Staircase'' su ggesting the operation of a stochastic attractor. Its dimension, which was determined by the methods of the correlation between the step-gap lengths and that of the Farey tree was found to be near one. Repetiti on of the calculation using data for the second antigen-antibody compl ex in the unit cell yielded similar results. However, the dimensions o f 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, p robably reflecting the lower degree of order of the latter. In all cas es, the saturation of the integral correlation coefficient with increa sing 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 b y integration of equations of atomic movement to the prediction of fol ding pathways since the stochastic element in the dynamics can elimina te leading equations in the set, thus influencing the folding pathway. (C) 1997 Academic Press Limited.