Evidence of quasi-linear gas transport through sperm whale myoglobin.

The diffusion of molecular oxygen or its isosteric analogue, carbon monoxide, from the surface of myoglobin to its deeply imbedded haem appears to represent one of the simplest protein functions. Hence, it was chosen for the study of the possible role of a global controlling effect like an attractor. However, whereas the six statistical criteria of the classical non-linear dynamic analysis for the existence of an attractor in myoglobin were fulfilled and invariant to the Fourier transformation, the properties of this attractor were not as simple as anticipated. The parameters were tested and confirmed by alternative approaches, the interpoint distance method of Judd and Fourier transformation. If the diffusion were approximately linear, the order of the attractor would be expected to be near one. However, a clearly higher value, 1.46+/-0.03, was found, indicating the existence of additional steps. Later, the latter were identified as a 90 degrees rotation of CO followed by a translocation by 0.4 A to a transient pocket. These additional steps may explain the high number of regulatory factors found, 10+/-1. The autocorrelation function was damped with a correlation length of at least 20 residues. The Poincaré plot showed a dense domain compatible with the cross-section of a quasi-spherical attractor. The first Lyapunov exponent, lambda(1), was clearly positive. The Hurst fractal coefficient was 1.90+/-0.22, indicating a clear departure from simple linear diffusion.