Hammond Behavior Research Articles

A structurally heterogeneous transition state underlies coupled binding and folding of disordered proteins

Many intrinsically disordered proteins (IDPs) attain a well-defined structure in a coupled folding and binding reaction with another protein. Such reactions may involve early to late formation of different native structural regions along the reaction pathway. To obtain insights into the transition state for a coupled binding and folding reaction, we performed restrained molecular dynamics simulations using previously determined experimental binding Φb values of the interaction between two IDP domains: the activation domain from the p160 transcriptional co-activator for thyroid hormone and retinoid receptors (ACTR) and the nuclear co-activator binding domain (NCBD) of CREB-binding protein, each forming three well-defined α-helices upon binding. These simulations revealed that both proteins are largely disordered in the transition state for complex formation, except for two helices, one from each domain, that display a native-like structure. The overall transition state structure was extended and largely dynamic with many weakly populated contacts. To test the transition state model, we combined site-directed mutagenesis with kinetic experiments, yielding results consistent with overall diffuse interactions and formation of native intramolecular interactions in the third NCBD helix during the binding reaction. Our findings support the view that the transition state and, by inference, any encounter complex in coupled binding and folding reactions are structurally heterogeneous and largely independent of specific interactions. Furthermore, experimental Φb values and Brønsted plots suggested that the transition state is globally robust with respect to most mutations but can display more native-like features for some highly destabilizing mutations, possibly because of Hammond behavior or ground-state effects.

Extracting the Hidden Distributions Underlying the Mean Transition State Structures in Protein Folding.

The inherent conflict between noncovalent interactions and the large conformational entropy of the polypeptide chain forces folding reactions and their mechanisms to deviate significantly from chemical reactions. Accordingly, measures of structure in the transition state ensemble (TSE) are strongly influenced by the underlying distributions of microscopic folding pathways that are challenging to discern experimentally. Here, we present a detailed analysis of 150,000 folding transition paths of five proteins at three different thermodynamic conditions from an experimentally consistent statistical mechanical model. We find that the underlying TSE structural distributions are rarely unimodal, and the average experimental measures arise from complex underlying distributions. Unfolding pathways also exhibit subtle differences from folding counterparts due to a combination of Hammond behavior and native-state movements. Local interactions and topological complexity, to a lesser extent, are found to determine pathway heterogeneity, underscoring the importance of the balance between local and nonlocal energetics in protein folding.

Exploring the folding pathway of green fluorescent protein through disulfide engineering.

We have introduced two disulfide crosslinks into the loop regions on opposite ends of the beta barrel in superfolder green fluorescent protein (GFP) in order to better understand the nature of its folding pathway. When the disulfide on the side opposite the N/C-termini is formed, folding is 2× faster, unfolding is 2000× slower, and the protein is stabilized by 16 kJ/mol. But when the disulfide bond on the side of the termini is formed we see little change in the kinetics and stability. The stabilization upon combining the two crosslinks is approximately additive. When the kinetic effects are broken down into multiple phases, we observe Hammond behavior in the upward shift of the kinetic m-value of unfolding. We use these results in conjunction with structural analysis to assign folding intermediates to two parallel folding pathways. The data are consistent with a view that the two fastest transition states of folding are "barrel closing" steps. The slower of the two phases passes through an intermediate with the barrel opening occurring between strands 7 and 8, while the faster phase opens between 9 and 4. We conclude that disulfide crosslink-induced perturbations in kinetics are useful for mapping the protein folding pathway.

The free energy landscape of small molecule unbinding.

The spontaneous dissociation of six small ligands from the active site of FKBP (the FK506 binding protein) is investigated by explicit water molecular dynamics simulations and network analysis. The ligands have between four (dimethylsulphoxide) and eleven (5-diethylamino-2-pentanone) non-hydrogen atoms, and an affinity for FKBP ranging from 20 to 0.2 mM. The conformations of the FKBP/ligand complex saved along multiple trajectories (50 runs at 310 K for each ligand) are grouped according to a set of intermolecular distances into nodes of a network, and the direct transitions between them are the links. The network analysis reveals that the bound state consists of several subbasins, i.e., binding modes characterized by distinct intermolecular hydrogen bonds and hydrophobic contacts. The dissociation kinetics show a simple (i.e., single-exponential) time dependence because the unbinding barrier is much higher than the barriers between subbasins in the bound state. The unbinding transition state is made up of heterogeneous positions and orientations of the ligand in the FKBP active site, which correspond to multiple pathways of dissociation. For the six small ligands of FKBP, the weaker the binding affinity the closer to the bound state (along the intermolecular distance) are the transition state structures, which is a new manifestation of Hammond behavior. Experimental approaches to the study of fragment binding to proteins have limitations in temporal and spatial resolution. Our network analysis of the unbinding simulations of small inhibitors from an enzyme paints a clear picture of the free energy landscape (both thermodynamics and kinetics) of ligand unbinding.

Temperature-Dependent Hammond Behavior in a Protein-Folding Reaction: Analysis of Transition-State Movement and Ground-State Effects

Characterization of the transition-state ensemble and the nature of the free-energy barrier for protein folding are areas of intense activity and some controversy. A key issue that has emerged in recent years is the width of the free-energy barrier and the susceptibility of the transition state to movement. Here we report denaturant-induced and temperature-dependent folding studies of a small mixed α–β protein, the N-terminal domain of L9 (NTL9). The folding of NTL9 was determined using fluorescence-detected stopped-flow fluorescence measurements conducted at seven different temperatures between 11 and 40 °C. Plots of the log of the observed first-order rate constant versus denaturant concentration, “chevron plots,” displayed the characteristic V shape expected for two-state folding. There was no hint of deviation from linearity even at the lowest denaturant concentrations. The relative position of the transition state, as judged by the Tanford β parameter, β T, shifts towards the native state as the temperature is increased. Analysis of the temperature dependence of the kinetic and equilibrium m values indicates that the effect is due to significant movement of the transition state and also includes a contribution from temperature-dependent ground-state effects. Analysis of the Leffler plots, plots of Δ G ‡ versus Δ G°, and their cross-interaction parameters confirms the transition-state movement. Since the protein is destabilized at high temperature, the shift represents a temperature-dependent Hammond effect. This provides independent confirmation of a recent theoretical prediction. The magnitude of the temperature-denaturant cross-interaction parameter is larger for NTL9 than has been reported for the few other cases studied. The implications for temperature-dependent studies of protein folding are discussed.

Point Mutations in Membrane Proteins Reshape Energy Landscape and Populate Different Unfolding Pathways

Using single-molecule force spectroscopy, we investigated the effect of single point mutations on the energy landscape and unfolding pathways of the transmembrane protein bacteriorhodopsin. We show that the unfolding energy barriers in the energy landscape of the membrane protein followed a simple two-state behavior and represent a manifestation of many converging unfolding pathways. Although the unfolding pathways of wild-type and mutant bacteriorhodopsin did not change, indicating the presence of same ensemble of structural unfolding intermediates, the free energies of the rate-limiting transition states of the bacteriorhodopsin mutants decreased as the distance of those transition states to the folded intermediate states decreased. Thus, all mutants exhibited Hammond behavior and a change in the free energies of the intermediates along the unfolding reaction coordinate and, consequently, their relative occupancies. This is the first experimental proof showing that point mutations can reshape the free energy landscape of a membrane protein and force single proteins to populate certain unfolding pathways over others.

Ionic-Strength-Dependent Effects in Protein Folding: Analysis of Rate Equilibrium Free-Energy Relationships and Their Interpretation

The traditional approach to studying protein folding involves applying a perturbation, usually denaturant or mutation, and determining the effect upon the free energy of folding, DeltaG0, and the activation free energy, DeltaG(not equal). Data collected as a function of the perturbation can be used to construct rate equilibrium free-energy relationships, which report on the development of interactions in the transition state for folding. We examine the use of the ionic-strength-dependent rate equilibrium free-energy relationship in protein folding using the N-terminal domain of L9, a small alpha-beta protein, as a model system. Folding is two-state for the range of ionic strength examined, 0.045-1.52 M. The plot of DeltaG(not equal) versus DeltaG0 is linear (r2= 0.918), with a slope equal to 0.45. The relatively low value of the slope indicates that the ionic-strength-dependent interactions are modestly developed in the transition state. The slope is, however, greater than that of a plot of DeltaG(not equal) versus DeltaG0 constructed by varying pH, thus demonstrating directly that ionic-strength-dependent studies probe more than simple electrostatic interactions. Potential transition movement was probed by analysis of the denaturant, ionic strength cross-interaction parameters. The values are small but nonzero and positive, suggesting a small shift of the transition state toward the native state as the protein is destabilized, i.e., Hammond behavior. The complications that arise in the interpretation of ionic-strength-dependent rate equilibrium free-energy relationships are discussed, and it is concluded that the ionic-strength-dependent studies do not provide a reliable indicator of the role of electrostatic interactions. Complications include incomplete screening of electrostatic interactions, specific ion binding, Hofmeister effects, and the potential presence of electrostatic interactions in the denatured state ensemble.

Kinetic Definition of Protein Folding Transition State Ensembles and Reaction Coordinates

Using distributed molecular dynamics simulations we located four distinct folding transitions for a 39-residue ββαβ protein fold. To characterize the nature of each room temperature transition, we calculated the probability of transmission for 500 points along each free energy barrier. We introduced a method for determining transition states by employing the transmission probability, P trans, and determined which conformations were transition state ensemble members ( P trans ≈ 0.5). The transmission probability may be used to characterize the barrier in several ways. For example, we ran simulations at 82°C, determined the change in P trans with temperature for all 2,000 conformations, and quantified Hammond behavior directly using P trans correlation. Additionally, we propose that diffusion along P trans may provide the configurational diffusion rate at the top of the barrier. Specifically, given a transition state conformation x 0 with estimated P trans = 0.5, we selected a large set of subsequent conformations from independent trajectories, each exactly a small time δt after x 0 (250 ps). Calculating P trans for the new trial conformations, we generated the P( P trans| δt = 250 ps) distribution that reflected diffusion. This approach provides a novel perspective on the diffusive nature of a protein folding transition and provides a framework for a quantitative study of activated relaxation kinetics.

Shape of the Free Energy Barriers for Protein Folding Probed by Multiple Perturbation Analysis

The characterization of the free energy barriers has been a major goal in studies on the mechanism of protein folding. Testing the effect of mutations or denaturants on protein folding reactions revealed that transition state movement is rare, suggesting that folding barriers are robust and narrow maxima on the free energy landscape. Here we demonstrate that the application of multiple perturbations allows the observation of small transition state movements that escape detection in single perturbation experiments. We used tendamistat as a model protein to test the broadness of the free energy barriers. Tendamistat folds over two consecutive transition states and through a high-energy intermediate. Measuring the combined effect of temperature and denaturant on the position of the transition state in the wild-type protein and in several mutants revealed that the early transition state shows significant transition state movement. Its accessible surface area state becomes more native-like with destabilization of the native state by temperature. To the same extent, the entropy of the early transition state becomes more native-like with increasing denaturant concentration, in accordance with Hammond behavior. The position of the late transition state, in contrast, is much less sensitive to the applied perturbations. These results suggest that the barriers in protein folding become increasingly narrow as the folding polypeptide chain approaches the native state.

An Extension of the Hammond Postulate. Structural Effects on the Classification of Chemical Reactions

Combination of the reaction energy, a thermodynamic index, with structural descriptors, such as the force constants associated with the reactant and products potential wells, allows us to define a new index that quantifies the position of the transition state and classifies reactions in terms of their Hammond or anti-Hammond character. Switching from the classical restricted Hammond behavior to a general behavior, in which the position of the transition state is not only conditioned by energy comparisons, occurs through adding a new term accounting for the structural effects in the potential-energy function. It is shown that these effects strongly influence the position of transition states but leave the barrier height practically unchanged. Analysis of 27 chemical reactions of different types, such as rotational isomerizations, SN2, and intramolecular reordering reactions, provides strong support to the model presented here.

Hammond Behavior versus Ground State Effects in Protein Folding: Evidence for Narrow Free Energy Barriers and Residual Structure in Unfolded States

Apparent transition state movement upon mutation or changes in solvent conditions is frequently observed in protein folding and is often interpreted in terms of Hammond behavior. This led to the conclusion that barrier regions in protein folding are broad maxima on the free energy landscape. Here, we use the concept of self-interaction and cross-interaction parameters to test experimental data of 21 well-characterized proteins for Hammond behavior. This allows us to characterize the origin of transition state movements along different reaction coordinates. Only one of the 21 proteins shows a small but coherent transition state movement in agreement with the Hammond postulate. In most proteins the structure of the transition state is insensitive to changes in protein stability. The apparent change in the position of the transition state upon mutation, which is frequently observed in φ-value analysis, is in most cases due to ground-state effects caused by structural changes in the unfolded state. This argues for significant residual structure in unfolded polypeptide chains of many proteins. Disruption of these residual interactions by mutation often leads to decreased folding rates, which implies that these interactions are still present in the transition state. The failure to detect Hammond behavior shows that the free energy barriers encountered by a folding polypeptide chain are generally rather narrow and robust maxima for all experimentally explorable reaction coordinates.

Non-linear rate-equilibrium free energy relationships and Hammond behavior in protein folding

Non-linear rate-equilibrium relationships upon mutation or changes in solvent conditions are frequently observed in protein folding reactions and are usually interpreted in terms of Hammond behavior. Here we first give a general overview over the concept of transition state movements in chemical reactions and discuss its application to protein folding. We then show examples for genuine Hammond behavior and for apparent transition state movements caused by other effects like changes in the rate-limiting step of the folding reaction or ground state effects, i.e. structural changes in either the native state or the unfolded state. These examples show that apparent transition state movements can easily be mistaken for Hammond behavior. We describe experimental tests using self- and cross-interaction parameters to distinguish between structural changes in a single transition state following Hammond behavior and apparent transition state movements caused by other effects.

A model-independent, nonlinear extrapolation procedure for the characterization of protein folding energetics from solvent-denaturation data.

We have characterized the guanidine-induced denaturation of hen egg white lysozyme within the 30-75 degrees C temperature range on the basis of equilibrium fluorescence measurements, unfolding assays, kinetic fluorescence measurements, and differential scanning calorimetry. Analysis of the guanidine denaturation profiles according to the linear extrapolation method yields values for the denaturation Gibbs energy which are about 15 kJ/mol lower than those derived from differential scanning calorimetry. Our results strongly suggest that this discrepancy is not due to deviations from the two-state denaturation mechanism. We propose a new method for the determination of denaturation Gibbs energies from solvent-denaturation data (the constant-delta G extrapolation procedure). It employs several solvent-denaturation profiles (obtained at different temperatures) to generate the protein stability curve at zero denaturant concentration within the -8 to 8 kJ/mol delta G range. The method is model-independent and provides a practical, nonlinear alternative to the commonly employed linear extrapolation procedure. The application of the constant-delta G method to our data suggests that the guanidine-concentration dependence of the denaturation Gibbs energy is approximately linear over an extended concentration range but, also, that strong deviations from linearity may occur at low guanidine concentrations. We tentatively attribute these deviations to the abrupt change of the contribution to protein stability that arises from pairwise charge-charge electrostatic interactions. This contribution may be positive, negative, or close to zero, depending on the pH value and the charge distribution on the native protein surface [Yang, A.-S., & Honig, B. (1993) J. Mol. Biol. 231, 459-474], which may help to explain why disparate effects have been found when studying protein denaturation at low guanidine concentrations. Kinetic m values for lysozyme denaturation depend on temperature, in a manner which appears consistent with Hammond behavior.

Nonlinear free energy relationships in Arc repressor unfolding imply the existence of unstable, native-like folding intermediates.

Under strongly denaturing conditions, the logarithm of the rate constant for dissociation/unfolding of the wild-type Arc dimer varies in a nonlinear fashion with denaturant concentration. To assess the unfolding/dissociation behavior under conditions favoring the native structure, we mixed Arc variants labeled with fluorescence acceptor or donor groups and used energy transfer to monitor the increase in heterodimer with time. Under the conditions of this experiment, the rate at which the heterodimer concentration approaches its equilibrium value is determined by rate of dissociation and unfolding of the protein. Using this method and traditional denaturant-jump experiments, rate constants for unfolding/dissociation were determined over a wide range of stabilizing and destabilizing conditions. In each case examined, plots of log(ku) versus denaturant showed significant curvature under strongly denaturing conditions, even though other kinetic experiments indicates that the unfolding/dissociation reactions remain largely two-state. This curvature can be explained most readily by a series of unstable intermediates in the unfolding pathway, with denaturant-induced changes in the kinetic step that is rate-limiting. Alternatively, curvature might result from Hammond behavior in which the structure of the transition state becomes more native-like as the stability of native Arc decreases with increasing denaturant.

Exploring the energy surface of protein folding by structure-reactivity relationships and engineered proteins: Observation of Hammond behavior for the gross structure of the transition state and anti-Hammond behavior for structural elements for unfolding/folding of barnase

The structure of alpha-helix 1 (residues 6-18) in the transition state for the unfolding of barnase has been previously characterized by comparing the kinetics and thermodynamics of folding of wild-type protein with those of mutants whose side chains have been cut back, in the main, to that of alanine. The structure of the transition state has now been explored further by comparing the kinetics and thermodynamics of folding of glycine mutants with those of the alanine mutants at solvent-exposed positions in the alpha-helices of barnase. Such "Ala-->Gly scanning" provides a general procedure for examining the structure of solvent-exposed regions in the transition state. A gradual change of structure of the transition state was detected as helix 1 becomes increasingly destabilized on mutation. The extent of change of structure of helix 1 in the transition state for the mutant proteins was probed by a further round of Ala-->Gly scanning of those mutants. Destabilization of the helix 1 was found to cause the overall transition state for unfolding to become closer in structure to that of the folded protein. This is analogous to the conventional Hammond effect in physical-organic chemistry whereby the transition state moves parallel to the reaction coordinate with change in structure. But, paradoxically, the structure of helix 1 itself becomes less folded in the transition state as helix 1 becomes destabilized. This is analogous, however, to the rarer anti-Hammond effect in which there is movement perpendicular to the reaction coordinate. These observations are rationalized by plotting correlation diagrams of degree of formation of individual elements of structure against the degree of formation of overall structure in the transition state. There is a relatively smooth movement of the degree of compactness in the transition state against changes in activation energy on mutation that suggests a smooth movement of the transition state along the energy surface on mutation rather than a switch between two different parallel pathways. The results are consistent with the transition state having closely spaced energy levels. Helix 1, which appears to be an initiation point and forms early in the folding of wild-type protein, may be radically destabilized to the extent that it forms late in the folding of mutants. The order of events in folding may thus not be crucial.