Thermodynamic hierarchy and local energetics of folded proteins

Thermodynamics of protein folding using a modified Wako-Saitô-Muñoz-Eaton model

Herein, we propose a modified version of the Wako-Saitô-Muñoz-Eaton (WSME) model. The proposed model introduces an empirical temperature parameter for the hypothetical structural units (i.e., foldons) in proteins to include site-dependent thermodynamic behavior. The thermodynamics for both our proposed model and the original WSME model were investigated. For a system with beta-hairpin topology, a mathematical treatment (contact-pair treatment) to facilitate the calculation of its partition function was developed. The results show that the proposed model provides better insight into the site-dependent thermodynamic behavior of the system, compared with the original WSME model. From this site-dependent point of view, the relationship between probe-dependent experimental results and model's thermodynamic predictions can be explained. The model allows for suggesting a general principle to identify foldon behavior. We also find that the backbone hydrogen bonds may play a role of structural constraints in modulating the cooperative system. Thus, our study may contribute to the understanding of the fundamental principles for the thermodynamics of protein folding.

Probing local structural fluctuations in myoglobin by size-dependent thiol-disulfide exchange

All proteins undergo local structural fluctuations (LSFs) or breathing motions. These motions are likely to be important for function but are poorly understood. LSFs were initially defined by amide hydrogen exchange (HX) experiments as opening events, which expose a small number of backbone amides to (1)H/(2)H exchange, but whose exchange rates are independent of denaturant concentration. Here, we use size-dependent thiol-disulfide exchange (SX) to characterize LSFs in single cysteine-containing variants of myoglobin (Mb). SX complements HX by providing information on motions that disrupt side chain packing interactions. Most importantly, probe reagents of different sizes and chemical properties can be used to characterize the size of structural opening events and the properties of the open state. We use thiosulfonate reagents (126-274 Da) to survey access to Cys residues, which are buried at specific helical packing interfaces in Mb. In each case, the free energy of opening increases linearly with the radius of gyration of the probe reagent. The slope and the intercept are interpreted to yield information on the size of the opening events that expose the buried thiol groups. The slope parameter varies by over 10-fold among Cys positions tested, suggesting that the sizes of breathing motions vary substantially throughout the protein. Our results provide insight to the longstanding question: how rigid or flexible are proteins in their native states?

Equilibrium unfolding thermodynamics of beta2-microglobulin analyzed through native-state H/D exchange

The exchange rates for the amide hydrogens of beta(2)-microglobulin, the protein responsible for dialysis-related amyloidosis, were measured under native conditions at different temperatures ranging from 301 to 315 K. The pattern of protection factors within different regions of the protein correlates well with the hydrogen-bonding pattern of the deposited structures. Analysis of the exchange rates indicates the presence of mixed EX1- and EX2-limit mechanisms. The measured parameters are consistent with a two-process model in which two competing pathways, i.e., global unfolding in the core region and partial openings of the native state, determine the observed exchange rates. These findings are analyzed with respect to the amyloidogenic properties of the protein.

Solvation and desolvation effects in protein folding: native flexibility, kinetic cooperativity and enthalpic barriers under isostability conditions

As different parts of a protein chain approach one another during folding, they are expected to encounter desolvation barriers before optimal packing is achieved. This impediment originates from the water molecule's finite size, which entails a net energetic cost for water exclusion when the formation of compensating close intraprotein contacts is not yet complete. Based on recent advances, we extend our exploration of these microscopic elementary desolvation barriers' roles in the emergence of generic properties of protein folding. Using continuum Gō-like C(alpha) chain models of chymotrypsin inhibitor 2 (CI2) and barnase as examples, we underscore that elementary desolvation barriers between a protein's constituent groups can significantly reduce native conformational fluctuations relative to model predictions that neglected these barriers. An increasing height of elementary desolvation barriers leads to thermodynamically more cooperative folding/unfolding transitions (i.e., higher overall empirical folding barriers) and higher degrees of kinetic cooperativity as manifested by more linear rate-stability relationships under constant temperature. Applying a spatially non-uniform thermodynamic parametrization we recently introduced for the pairwise C(alpha) potentials of mean force, the present barnase model further illustrates that desolvation is a probable physical underpinning for the experimentally observed high intrinsic enthalpic folding barrier under isostability conditions.

From discrete protein kinetics to continuous Brownian dynamics: a new perspective

This article presents a comparative analysis of two sets of data from recent experiments on kinetics of (i) protein unfolding by mechanical force and (ii) channel gating with membrane electric potential. Both situations necessitate a continuous Brownian-dynamic view of protein conformational kinetics. We show that the discrete approach traditional to biochemical kinetics is insufficient for understanding dynamics of protein molecules in an aqueous solution or lipid membrane with varying conditions under which the major activation barrier can disappear. A semiquantitative analysis based on Brownian dynamics in a continuous energy landscape offers a more comprehensive description for motions of biological macromolecules.

Ensemble modulation as an origin of denaturant-independent hydrogen exchange in proteins

Native state hydrogen exchange (HX) has become a powerful tool for the analysis of conformational states that exist under native conditions. However, the interpretation of HX data in terms of conformational fluctuations is still controversial. In particular, it has been shown that many residues display exchange behavior that is independent of denaturant concentration. It has been postulated that this lack of denaturant dependence results from local fluctuations that do not expose appreciable amounts of buried surface area. Here, we use a general thermodynamic description of HX to explore the different possibilities for this behavior. We find that the denaturant dependence seen in HX experiments under native conditions is not a de facto indication of the amount of surface area exposure required for exchange. Instead, this behavior results from the relatively homogenous character of the conformational ensemble that exists under native conditions and the non-specific nature of denaturant effects. Furthermore, a comparison of the HX behavior from a stabilized mutant of Staphylococcal nuclease (SNase) with that predicted for the wild-type SNase from the COREX algorithm suggests that denaturant-independent exchange of many residues is consistent with significant (approximately 10 %) surface area exposure for this protein.

Hydrogen exchange kinetics of proteins in denaturants: a generalized two-process model

The recent progress in measurements on the amide hydrogen exchange (HX) in proteins under varying denaturing conditions, both at equilibrium and in transient relaxation, necessitates the development of a unifying theory which quantitatively relates the HX rates to the conformational energetics of the proteins. We present here a comprehensive kinetic model for the site-specific HX of proteins under varying solvent denaturing conditions based on the two-state protein folding model. The generalized two-process model considers both conformational fluctuations and residual protections, respectively, within the folded and unfolded states of a protein, as well as a global kinetic folding-unfolding transition between the two states. The global transition can be either rapid or slow, depending on the solvent condition for the protein. This novel model is applicable to the traditional equilibrium HX measurements in both EX2 and EX1 regimes, and also the recently introduced transient pulse-labeling HX experiments. A set of simple analytical equations is provided for quantitative interpretation of experimental data. The model emphasizes the use of full time-course of bi-exponential HX kinetics, rather than fitting time-course data to single rate constants, to obtain quantitative information about fluctuating conformers within the folded and unfolded states of proteins. This HX kinetic model naturally unfolds into a simple two-state and two-stage kinetic interpretation for protein folding. It suggests that the various observed intermediates of a protein can be interpreted as dominant isomers of either the folded or the unfolded state under different solvent conditions. This simple, minimalist's view of protein folding is consistent with various recent experimental observations on folding kinetics by HX.

Hydrogen exchange in ribonuclease A and ribonuclease S: evidence for residual structure in the unfolded state under native conditions

Two-dimensional NMR spectroscopy has been used to monitor the exchange of backbone amide protons in ribonuclease A (RNase A) and its subtilisin-cleaved form, ribonuclease S (RNase S). Exchange measurements at two different pH values (5.4 and 6.0) show that the exchange process occurs according to the conditions of the EX2 limit. Differential scanning calorimetry measurements have been carried out in 2H2O under conditions analogous to those used in the NMR experiments in order to determine the values of DeltaCp, DeltaHu and Tm, corresponding to the thermal denaturation of both proteins. For the amide protons of a large number of residues in RNase A, the free energies at 25 degreesC for exchange competent unfolding processes are much lower than the calorimetric denaturation free energies, thus showing that exchange occurs through local fluctuations in the native state. For 20 other protons, the cleavage reaction had approximately the same effect on the exchange rate constants than on the equilibrium constant for unfolding, indicating that those protons exchange by global unfolding. There is a good agreement between the residues to which these protons belong and those involved in the putative folding nucleation site identified by quench-flow NMR studies. The unfolding free energies of the slowest exchanging protons, DeltaGex, as evaluated from exchange data, are much larger than the calorimetric free energies of unfolding, DeltaGu. Given the agreement between DeltaDeltaGex(A-S), the difference in free energy from exchange for a given proton of the two proteins, and DeltaDeltaGu(A-S), the difference in the calorimetric free energy of the two proteins, the discrepancy indicates that the intrinsic exchange rates in the unfolded state of those protons cannot be approximated by those measured in short unstructured peptides and, consequently, exchange for those protons in RNase A and S must occur through a rather structured denatured state.

Hydrogen exchange and protein folding

Amide hydrogen-deuterium exchange is a sensitive probe of the structure, stability and dynamics of proteins. The significant increase in the number of small, model proteins that have been studied has allowed a better understanding of the structural fluctuations that lead to hydrogen exchange. Recent technical advances enable the methodology to be applied to the study of protein-protein interactions in much larger, more complex systems.