We are continuing our studies of the folding properties of single-domain proteins using ? simple statistical-mechanical models. In these models it is assumed that the folding ? properties of a protein are determined entirely by the intramolecular interactions present ? in its native folded conformation. Proteins are represented as chains of monomer units ? (corresponding to amino acid residues) each of which has only two possible ? conformational states, the """"""""native"""""""" state, corresponding to the conformation assumed by ? the unit in the native structure of the chain, and the """"""""random-coil"""""""" state, which ? encompasses all non-native conformations. The structural states of a polypeptide chain ? are then defined by the sequence of native/random-coil states of these monomers. The ? stability of any such state of the chain is determined by the offsetting effects of the ? destabilizing entropy losses associated with fixing monomers in the native conformation, ? and the stabilizing native non-bonding contacts between different parts of the chain. The ? map of native contacts is derived from the X-ray crystallographic or NMR-derived ? structure of the corresponding protein. In the simplest picture, a state with a specified ? sequence of native/random-coil monomers may only form those native contacts that ? connect parts of the chain lying in the same contiguous stretch of native monomers. In a ? more complete picture, contacts are also possible between parts of the chain separated by ? intervening stretches of non-native monomers and induce an additional destabilizing ? entropy loss by constraining the ends of the loops of random-coil chain formed by these ? non-native stretches. For a model protein of a given length and a specified set of ? structurally-derived native contacts, it is possible in principle to explicitly construct all ? possible sequences of monomer native/random-coil states. For specified values for the ? entropy losses of fixing a single unit in the native conformation and of closing loops of ? non-native chain, and for the energy of the intra-chain contacts, it is possible to compute ? the stabilities of all such sequences and thereby compute a model partition function of the ? chain. The intractably large number of states that arises from complete enumeration of ? the possible combinations of monomer states for typical chain lengths has motivated the ? calculation of partition functions in the so-called """"""""single-sequence"""""""", """"""""double-sequence"""""""", ? and """"""""triple-sequence"""""""" approximations, in which only states which have at most one, two, ? or three contiguous stretches of native monomers, respectively, are included. These ? partition functions are used to compute the free energy for a given chain as a function of ? a single reaction coordinate defined for each state as either the total number of native ? monomers or the fraction of native contacts formed in that state; this """"""""reaction free-? energy surface"""""""" provides the basis for modeling the equilibrium and kinetic folding ? properties of the chain. In work reported in previous years, we used a """"""""combinatorial ? modeling"""""""" procedure within this framework to identify which among a wide variety of ? possible model assumptions and features consistently produce the most accurate ? descriptions of the measured folding properties of a set of two-state proteins. More ? recently, we have been using the best-performing of these models to directly analyze an ? extensive set of equilibrium and kinetic measurements performed in our own laboratory ? of the folding of the single alpha-helical protein villin. Among the measurements being ? modeled is the equilibrium temperature dependence of the UV circular dichroism, which ? reflects the extent of alpha-helix formation concomitant with the folding process; in our ? model the helical content of each state of the protein chain is simply the combined ? lengths of contiguous stretches of native monomers in parts of the sequence that are ? helical in the native state. We also analyze both the equilibrium temperature dependence ? and the T-jump kinetics of the UV fluorescence, which probes the formation of locally ? compact protein structures through the degree of quenching of the fluorescence of the ? single tryptophan sidechain by contact with residues elsewhere in the chain; model states ? in which the fluorescence is quenched are precisely those in which a native contact ? between the tryptophan and the quenching residue(s) is formed. Most recently we have ? incorporated into our analysis the model-based calculation of heat-capacity changes of ? villin as temperature is varied through the thermal folding/unfolding transition, in order ? to analyze differential scanning calorimetry measurements (in collaboration with the ? group of Jose M. Sanchez-Ruiz of the University of Granada in Spain). Preliminary ? results indicate that our simple model picture for the enumeration and stabilities of the ? various states of the protein chain, combined with a straightforward prescription for ? computing the spectroscopic properties of the individual states, describes quite well the ? equilibrium and kinetic spectroscopic measurements of the folding properties of this ? protein. ? In keeping with our interest in developing and exploiting new methods for probing the ? structural dynamics of macromolecules, we are collaborating with Philip Anfinrud's ? group in the Laboratory of Chemical Physics in the development of new algorithms for ? the analysis of Laue (i.e., polychromatic illumination) diffraction data acquired in time-? resolved X-ray crystallographic studies of proteins. These algorithms include efficient ? procedures for the assignment of Miller indices to observed reflections, the integration of ? intensities to produce structure factors for these reflections, and the scaling of the ? resulting sets of structure factors from multiple images onto a common intensity scale. ? We have also created a fundamentally new prescription for extracting more accurate ? structure-factor information from the distributions of pixel intensities within the ? individual spots in a Laue diffraction image, based on a model description of the ? distribution of mosaic structures actually present in the crystal.
| Henry, Eric R; Bettati, Stefano; Hofrichter, James et al. (2002) A tertiary two-state allosteric model for hemoglobin. Biophys Chem 98:149-64 |
| Eaton, W A; Munoz, V; Hagen, S J et al. (2000) Fast kinetics and mechanisms in protein folding. Annu Rev Biophys Biomol Struct 29:327-59 |
| Eaton, W A; Henry, E R; Hofrichter, J et al. (1999) Is cooperative oxygen binding by hemoglobin really understood? Nat Struct Biol 6:351-8 |
