The folding and unfolding of a three-helix bundle protein were explored with molecular-dynamics simulations, cluster analysis, and weighted-histogram techniques. The folding-unfolding process occurs by means of a "folding funnel," in which a uniform and broad distribution of conformational states is accessible outside of the native manifold. This distribution narrows near a transition region and becomes compact within the native manifold. Key thermodynamic steps in folding include initial interactions around the amino-terminal helix-turn-helix motif, interactions between helices I and II, and, finally, the docking of helix III onto the helix I-II subdomain. A metastable minimum in the calculated free-energy surface is observed at approximately 1.5 times the native volume. Folding-unfolding thermodynamics are dominated by the opposing influences of protein-solvent energy, which favors unfolding, and the overall entropy, which favors folding by means of the hydrophobic effect.

A comparison between two methods for combining data from molecular simulations to generate free energy surfaces for physical and chemical processes is presented. The conventional "splicing" method is compared with a recently introduced histogram-based technique for the calculation of the free energy surface for folding a short peptide in vacuo. We present an extension of the weighted histogram analysis method, described recently by Kumar et al. (J. Comput. Chem. 1992,13,1101-1021), which is specialized to the case of constant-temperature simulations and generalized to multiple dimensions. Our data indicate that both methods produce identical results, at the qualitative level, for the folding free energy surface. However, the constant-temperature weighted histogram analysis equations we present here yield a smoother surface, incorporate all of the data from the simulations, and are generalized to multiple dimensions. We propose that these equations will provide a general framework for the calculation of free energy surfaces in multiple dimensions.

The multidimensional free energy surface for a small fast folding helical protein is explored based on first-principle calculations. The model represents the 46-residue segment from fragment B of staphylococcal protein A. The relationship between collapse and tertiary structure formation, and the order of collapse and secondary structure formation, are investigated. We find that the initial collapse process gives rise to a transition state with about 30% of the native tertiary structure and 50-70% of the native helix content. We also observe two distinct distributions of native helix in this collapsed state (R g Ϸ 12 Å), one with about 20% of the native helical hydrogen bonds, the other with near 70%. The former corresponds to a local minimum. The barrier from this metastable state to the native state is about 2 k B T. In the latter case, folding is essentially a downhill process involving topological assembly. In addition, the order of formation of secondary structure among the three helices is examined. We observe cooperative formation of the secondary structure in helix I and helix II. Secondary structure in helix III starts to form following the formation of certain secondary structure in both helix I and helix II. Comparisons of our results with those from theory and experiment are made.The process of protein organization from the random coil manifold of states to a specific native structure remains an intriguing problem in molecular biology. Because of the vast conformational space available to the protein chain, the time it would require to locate its unique structure by a random search would be astronomical. Different ways of overcoming this search problem have been proposed. Some models such as the framework model (1) and the diffusion-collision model (2) focus on the formation of secondary structural elements followed by their assembly. Others such as the hydrophobic collapse model (3) emphasize the formation of tertiary structure accompanying secondary structure formation. More recently, a theoretical model based on a statistical landscape analysis has been proposed (4). According to this theory, folding can be described by the descent of the folding chain down a folding funnel, with local roughness reflecting the potential for transient trapping in local minima and the overall slope of the funnel representing the thermodynamic drive to the native state. The bottleneck to folding in this funnel picture is the confluence of multiple delocalized ''nuclei'' at a transition point (the transition state). While the folding funnel model incorporates many aspects of the other folding models, a fully unified view of protein folding has yet to be developed. For example, it is unclear from these models how much secondary structure, resembling that in the native state, is present in the unfolded state. Nor is the degree of similarity between the transition state and the native state well understood. Further, the order of collapse and secondary structure formation is still under debate. Because of the very...

The use of luciferase reporters has become a precise, noninvasive, high-throughput method for real-time monitoring of promoter activity in living cells, especially for rhythmic biological processes such as circadian rhythms. We developed a destabilized firefly luciferase as a reporter for rhythmic promoter activity in both the cell division and respiratory cycles of the budding yeast Saccharomyces cerevisiae in which real-time luminescence reporters have not been previously applied. The continuous output of light from luciferase reporters allowed us to explore the relationship between the cell division cycle and the yeast respiratory oscillation, including the observation of responses to chemicals that cause phase shifting of the respiratory oscillations. Destabilized firefly luciferase is a good reporter of cell cycle position in synchronized or partially synchronized yeast cultures, in both batch and continuous cultures. In addition, the oxygen dependence of luciferase can be used under certain conditions as a genetically encodable oxygen monitor. Finally, we use this reporter to show that there is a direct correlation between premature induction of cell division and phase resetting of the respiratory oscillation under the continuous culture conditions tested.circadian rhythms ͉ luciferase reporter ͉ metabolic cycle ͉ Saccharomyces ͉ ultradian rhythms