Exploring the relationship between funneled energy landscapes and two-state protein folding

Transition paths, diffusive processes, and preequilibria of protein folding

Fundamental relationships between the thermodynamics and kinetics of protein folding were investigated using chain models of natural proteins with diverse folding rates by extensive comparisons between the distribution of conformations in thermodynamic equilibrium and the distribution of conformations sampled along folding trajectories. Consistent with theory and single-molecule experiment, duration of the folding transition paths exhibits only a weak correlation with overall folding time. Conformational distributions of folding trajectories near the overall thermodynamic folding/unfolding barrier show significant deviations from preequilibrium. These deviations, the distribution of transition path times, and the variation of mean transition path time for different proteins can all be rationalized by a diffusive process that we modeled using simple Monte Carlo algorithms with an effective coordinate-independent diffusion coefficient. Conformations in the initial stages of transition paths tend to form more nonlocal contacts than typical conformations with the same number of native contacts. This statistical bias, which is indicative of preferred folding pathways, should be amenable to future single-molecule measurements. We found that the preexponential factor defined in the transition state theory of folding varies from protein to protein and that this variation can be rationalized by our Monte Carlo diffusion model. Thus, protein folding physics is different in certain fundamental respects from the physics envisioned by a simple transition-state picture. Nonetheless, transition state theory can be a useful approximate predictor of cooperative folding speed, because the height of the overall folding barrier is apparently a proxy for related rate-determining physical properties.

Protein structure and dynamics studied by mass spectrometry: H/D exchange, hydroxyl radical labeling, and related approaches

Mass spectrometry (MS) plays a central role in studies on protein structure and dynamics. This review highlights some of the recent developments in this area, with focus on applications involving the use of electrospray ionization (ESI) MS. Although this technique involves the transformation of analytes into highly nonphysiological species (desolvated gas-phase ions in the vacuum), ESI-MS can provide detailed insights into the solution-phase behavior of proteins. Notably, the ionization process itself occurs in a structurally sensitive manner. An increased degree of solution-phase unfolding is correlated with a higher level of protonation. Also, ESI allows the transfer of intact noncovalent complexes into the gas phase, thereby yielding information on binding partners, stoichiometries, and even affinities. A particular focus of this article is the use of hydrogen/deuterium exchange (HDX) methods and hydroxyl radical (.OH) labeling for monitoring dynamic and structural aspect of solution-phase proteins. Conceptual similarities and differences between the two methods are discussed. We describe a simple method for the computational simulation of protein HDX patterns, a tool that can be helpful for the interpretation of isotope exchange data recorded under mixed EX1/EX2 conditions. Important aspects of .OH labeling include a striking dependence on protein concentration, and the tendency of commonly used solvent additives to act as highly effective radical scavengers. If not properly controlled, both of these factors may lead to experimental artifacts.

Nonadditive interactions in protein folding: the zipper model of cytochrome C

Hydrogen exchange experiments (Krishna et al. in J. Mol. Biol. 359:1410, 2006) reveal that folding-unfolding of cytochrome c occurs along a defined pathway in a sequential, stepwise manner. The simplified zipper-like model involving nonadditive coupling is proposed to describe the classical "on pathway" folding-unfolding behavior of cytochrome c. Using free energy factors extracted from HX experiments, the model can predict and explain cytochrome c behavior in spectroscopy studies looking at folding equilibria and kinetics. The implications of the proposed model are discussed for such problems as classical pathway vs. energy landscape conceptions, structure and function of a native fold, and interplay of secondary and tertiary interactions.

A Minimalist Model for Exploring Conformational Effects on the Electrospray Charge State Distribution of Proteins

The electrospray ionization (ESI) charge state distribution of proteins is highly sensitive to the protein structure in solution. Unfolded conformations generally form higher charge states than tightly folded structures. The current study employs a minimalist molecular dynamics model for simulating the final stages of the ESI process in order to gain insights into the physical reasons underlying this empirical relationship. The protein is described as a string of 27 beads ("residues"), 9 of which are negatively charged and represent possible protonation sites. The unfolded state of this bead string is a random coil, whereas the native conformation adopts a compact fold. The ESI process is simulated by placing the protein inside a solvent droplet with a 2.5 nm radius consisting of 1600 Lennard-Jones particles. In addition, the droplet contains 14 protons which are modeled as highly mobile point charges. Disintegration of the droplet rapidly releases the protein into the gas phase, resulting in average charge states of 4.8+ and 7.4+ for the folded and unfolded conformation, respectively. The protonation probabilities of individual residues in the folded state reveal a characteristic pattern, with values ranging from 0.2 to 0.8. In contrast, the protonation probabilities of the unfolded protein are more uniform and cover the range from 0.8 to 1.0. The origin of these differences can be traced back to a combination of steric and electrostatic effects. Residues exhibiting a small accessible surface area are less likely to capture a proton, an effect that is exacerbated by partial electrostatic shielding from nearby positive residues. Conversely, sites that are sterically exposed are associated with electrostatic funnels that greatly increase the likelihood of protonation. Unfolding enhances the steric and electrostatic exposure of protonation sites, thereby causing the protein to capture a greater number of protons during the droplet disintegration process.

Gas-Phase Interference-Free Analysis of Protein Ion Charge-State Distributions: Detection of Small-Scale Conformational Transitions Accompanying Pepsin Inactivation

Analysis of protein ion charge-state distributions in electrospray ionization (ESI) mass spectra has become an indispensable tool in the studies of protein dynamics. However, applications of this technique have been thus far limited to detection of large-scale conformational transitions, which typically change the extent of multiple charging in a very significant way. However, more subtle conformational changes often elude detection, since the resulting changes of the extent of multiple charging are often smaller than the charge-state shifts caused by other external factors. Proton-transfer reactions involving protein ions and residual solvent molecules are the major extrinsic factors causing changes of charge-state distributions unrelated to conformational transitions. Since the extent of such reactions depends on the amount of various solvent components transferred to the ESI interface, profound changes of solvent composition may affect protein ion charge-state distributions not only by affecting protein higher order structure in solution but also through modulation of the efficiency of proton-transfer reactions in the gas phase. Here we demonstrate that it is possible to choose experimental conditions in such a way that the influence of gas-phase ion chemistry on protein ion charge-state distributions is not altered over a wide pH range. This methodology (gas-phase interference-free analysis of protein ion charge-state distributions, or GIFPICS) is sensitive enough to allow detection of pepsin inactivation under mildly acidic conditions. Pepsin is active and tightly folded in its native strongly acidic environment. Inactivation of pepsin at mildly acidic pH is not accompanied by global unfolding, as spectroscopic measurements suggest the protein remains compact. GIFPICS provides a means to observe this small-scale conformational transition that does not result in protein unfolding and may in fact elude detection by traditional spectroscopic techniques.