Two-dimensional distributions of activation enthalpy and entropy from kinetics by the maximum entropy method

The maximum entropy method (MEM) is used to numerically invert the kinetics of ligand rebinding at low temperatures to obtain the underlying two-dimensional distribution of activation enthalpies and entropies, g(H,S). A global analysis of the rebinding of carbon monoxide (CO) to myoglobin (Mb), monitored in the Soret band at temperatures from 60 to 150 K, is performed using a Newton-Raphson optimization algorithm. The MEM approach describes the data much better than traditional least-squares analyses, reducing chi 2 by an order of magnitude. The MEM resolves two barrier distributions suggestive of rebinding to different bound conformations of MbCO, the so-called A1 and A3 substates, whose activation barriers have been independently estimated from kinetics monitored in the infrared. The distribution corresponding to A3 possesses higher activation entropies, also consistent with infrared measurements. Within an A substate, correlations of S and H are recovered qualitatively from simulated data but can be difficult to obtain from experimental data. When the rebinding measured at 60 K is excluded from the inversion, two peaks are no longer clearly resolved. Thus, data of very high quality are required to unambiguously determine the kinetic resolvability of subpopulations and the shape of the barrier distribution for a single A substate.