Limited searching in the conformational space is one of the major obstacles for investigating protein dynamics by numerical approaches. For this reason, classical all-atom molecular dynamics (MD) simulations of proteins tend to be confined to local energy minima, particularly when the bulk solvent is treated explicitly. To overcome this problem, we have developed a novel replica exchange protocol that uses modified force-field parameters to treat interparticle nonbonded potentials within the protein and between protein and solvent atoms, leaving unperturbed those relative to solvent-solvent interactions. We have tested the new protocol on the 18-residue-long tip of the P domain of calreticulin in an explicit solvent. With only eight replicas, we have been able to considerably enhance the conformational space sampled during a 100 ns simulation, compared to as many parallel classical molecular dynamics simulations of the same length or to a single one lasting 450 ns. A direct comparison between the various simulations has been possible thanks to the implementation of the weighted histogram analysis method, by which conformations simulated with modified force-field parameters can be assigned different weights. Interatom, inter-residue distances in the structural ensembles obtained with our novel replica exchange approach and by classical MD simulations compare equally well with those derived from NMR data. Rare events, such as unfolding and refolding, occur with reasonable statistical frequency. Visiting of conformations characterized by very small Boltzmann weights is also possible. Despite their low probability, such regions of the conformational space may play an important role in the search for local potential-energy minima and in dynamically controlled functions.

Proteins have a complex free-energy landscape because of their rich topology and the nature of their nonbonded interaction potential. This has important consequences because the roughness of the landscape affects the ease with which a chain folds and also determines the dynamic behavior of the folded structure, thus influencing its functional and stability properties. A detailed description of the free-energy landscape is therefore of paramount importance for a quantitative understanding of the relationships between structure, dynamics, stability, and functional behavior of proteins. The free-energy landscape of a protein is a high-dimensional hypersurface, difficult to rationalize. Therefore, achieving its detailed graphical representation in a way that goes beyond the familiar funnel-like free-energy model is still a big challenge. We describe here an approach based on global structural parameters that allows a two-dimensional representation of the free-energy landscape from simulated atomic trajectories. As shown in this and in the accompanying article, our representation of the landscape, combined with other conformational analyses, provides valuable information on its roughness and on how atomic trajectories evolve with time.

We report the low temperature carbon monoxide recombination kinetics after photolysis and the temperature dependence of the visible absorption spectra of the isolated alpha SH-CO and beta SH-CO subunits from human hemoglobin A in ethylene glycol/water and in glycerol/water mixtures. Kinetic measurements on sperm whale (Physeter catodon) myoglobin and previously published optical spectroscopy data on the latter protein and on human hemoglobin A, in both solvents, (Cordone, L., A. Cupane, M. Leone, E. Vitrano, and D. Bulone. 1988. J. Mol. Biol. 199:312-218) are taken as reference. Low temperature flash photolysis data are analyzed within the multiple substates model proposed by Frauenfelder and co-workers (Austin, R. H., K. W. Beeson, L. Eisenstein, H. Frauenfelder, and I. C. Gunsalus. 1975. Biochemistry. 14:5355-5373). Within this model a distribution of activation enthalpies for ligand binding accounts for the structural heterogeneity of the protein, while the preexponential factor, containing also the entropic contribution to the free energy of the process, is considered to be constant for all conformational substates. Optical spectra are deconvoluted in gaussian components and the temperature dependence of the moments of the resulting bands is analyzed, within the harmonic Frank-Condon approximation, to obtain information on the stereodynamic properties of the heme pocket. The kinetic and spectral parameters thus obtained are found to be protein dependent also with respect to their sensitivity to changes in the composition of the external medium. A close correlation between the kinetic and spectral features is observed for the proteins examined under all experimental conditions studied. The results reported are discussed in terms of differences in the heme pocket structure and in the conformational heterogeneity among the various proteins, as related to their different capability to accommodate constraints imposed by the external medium.

The study of the thermal evolution of the Soret band in heme proteins has proved to be a useful tool to understand their stereodynamic properties; moreover, it enables one to relate protein matrix fluctuations and functional behavior when carried out in combination with kinetic experiments on carbon monoxide rebinding after flash photolysis. In this work, we report the thermal evolution of the Soret band of deoxy, carbonmonoxy, and nitric oxide derivatives of the cooperative homodimeric Scapharca inaequivalvis hemoglobin in the temperature range 10-300 K and the carbon monoxide rebinding kinetics after flash photolysis in the temperature range 60-200 K. The two sets of results indicate that Scapharca hemoglobin has a very rigid protein structure compared with other hemeproteins. This feature is brought out i) by the absence of nonharmonic contributions to the soft modes coupled to the Soret band in the liganded derivatives, and ii) by the almost "in plane" position of the iron atom in the photoproduct obtained approximately 10(-8) s after dissociating the bound carbon monoxide molecule at 15 K.