Quantitative criteria for native energetic heterogeneity influences in the prediction of protein folding kinetics.
ABSTRACT: Energy landscape theory requires that the protein-folding mechanism is generally globally directed or funneled toward the native state. The collective nature of transition state ensembles further suggests that sufficient averaging of the native interactions can occur so that the knowledge of the native topology may suffice for predicting the mechanism. Nevertheless, while simple homogeneously weighted native topology-based models predict the folding mechanisms for many proteins, for other proteins knowledge of the native topology, by itself, seems not to suffice in determining the folding mechanism. Simulations of proteins with differing topologies reveal that the failure of homogeneously weighted topology-based models can, however, be completely understood within the framework of a funneled energy landscape and can be quantified by comparing the fluctuation of entropy cost for forming contacts to the expected fluctuations in contact energy. To be precise, we find the transition state ensembles of proteins with all-alpha topologies, which are more uniform in the specific entropy cost of contact formation, have transition state ensembles that are more readily perturbed by differences in energetic weights than are the transition state ensembles of proteins with significant amounts of beta-structure, where the specific entropy costs of contact formation are more widely distributed. This behavior is consistent with a random-field Ising model analogy that follows from the free energy functional approach to folding.
Project description:Simulations based on perfectly funneled energy landscapes often capture many of the kinetic features of protein folding. We examined whether simulations based on funneled energy functions can also describe fluctuations in native-state protein ensembles. We quantitatively compared the site-specific local stability determined from structure-based folding simulations, with hydrogen exchange protection factors measured experimentally for ubiquitin, chymotrypsin inhibitor 2, and staphylococcal nuclease. Different structural definitions for the open and closed states based on the number of native contacts for each residue, as well as the hydrogen-bonding state, or a combination of both criteria were evaluated. The predicted exchange patterns agree with the experiments under native conditions, indicating that protein topology indeed has a dominant effect on the exchange kinetics. Insights into the simplest mechanistic interpretation of the amide exchange process were thus obtained.
Project description:The energy landscape approach has played a fundamental role in advancing our understanding of protein folding. Here, we quantify protein folding energy landscapes by exploring the underlying density of states. We identify three quantities essential for characterizing landscape topography: the stabilizing energy gap between the native and nonnative ensembles ?E, the energetic roughness ?E, and the scale of landscape measured by the entropy S. We show that the dimensionless ratio between the gap, roughness, and entropy of the system ?=?E/(?E?(2S)) accurately predicts the thermodynamics, as well as the kinetics of folding. Large ? implies that the energy gap (or landscape slope towards the native state) is dominant, leading to more funneled landscapes. We investigate the role of topological and energetic roughness for proteins of different sizes and for proteins of the same size, but with different structural topologies. The landscape topography ratio ? is shown to be monotonically correlated with the thermodynamic stability against trapping, as characterized by the ratio of folding temperature versus trapping temperature. Furthermore, ? also monotonically correlates with the folding kinetic rates. These results provide the quantitative bridge between the landscape topography and experimental folding measurements.
Project description:We study the folding mechanism of a three-helix bundle protein at atomic resolution, including effects of explicit water. Using replica exchange molecular dynamics we perform enough sampling over a wide range of temperatures to obtain the free energy, entropy, and enthalpy surfaces as a function of structural reaction coordinates. Simulations were started from different configurations covering the folded and unfolded states. Because many transitions between all minima at the free energy surface are observed, a quantitative determination of the free energy barriers and the ensemble of configurations associated with them is now possible. The kinetic bottlenecks for folding can be determined from the thermal ensembles of structures on the free energy barriers, provided the kinetically determined transition-state ensembles are similar to those determined from free energy barriers. A mechanism incorporating the interplay among backbone ordering, sidechain packing, and desolvation arises from these calculations. Large Phi values arise not only from native contacts, which mostly form at the transition state, but also from contacts already present in the unfolded state that are partially destroyed at the transition.
Project description:We explore the hypothesis that the folding landscapes of membrane proteins are funneled once the proteins' topology within the membrane is established. We extend a protein folding model, the associative memory, water-mediated, structure, and energy model (AWSEM) by adding an implicit membrane potential and reoptimizing the force field to account for the differing nature of the interactions that stabilize proteins within lipid membranes, yielding a model that we call AWSEM-membrane. Once the protein topology is set in the membrane, hydrophobic attractions play a lesser role in finding the native structure, whereas polar-polar attractions are more important than for globular proteins. We examine both the quality of predictions made with AWSEM-membrane when accurate knowledge of the topology and secondary structure is available and the quality of predictions made without such knowledge, instead using bioinformatically inferred topology and secondary structure based on sequence alone. When no major errors are made by the bioinformatic methods used to assign the topology of the transmembrane helices, these two types of structure predictions yield roughly equivalent quality structures. Although the predictive energy landscape is transferable and not structure based, within the correct topological sector we find the landscape is indeed very funneled: Thermodynamic landscape analysis indicates that both the total potential energy and the contact energy decrease as native contacts are formed. Nevertheless the near symmetry of different helical packings with respect to native contact formation can result in multiple packings with nearly equal thermodynamic occupancy, especially at temperatures just below collapse.
Project description:The energy landscape theory provides a general framework for describing protein folding reactions. Because a large number of studies, however, have focused on two-state proteins with single well-defined folding pathways and without detectable intermediates, the extent to which free energy landscapes are shaped up by the native topology at the early stages of the folding process has not been fully characterized experimentally. To this end, we have investigated the folding mechanisms of two homologous three-state proteins, PTP-BL PDZ2 and PSD-95 PDZ3, and compared the early and late transition states on their folding pathways. Through a combination of Phi value analysis and molecular dynamics simulations we obtained atomic-level structures of the transition states of these homologous three-state proteins and found that the late transition states are much more structurally similar than the early ones. Our findings thus reveal that, while the native state topology defines essentially in a unique way the late stages of folding, it leaves significant freedom to the early events, a result that reflects the funneling of the free energy landscape toward the native state.
Project description:Guided by recent experimental results suggesting that protein-folding rates and mechanisms are determined largely by native-state topology, we develop a simple model for protein folding free-energy landscapes based on native-state structures. The configurations considered by the model contain one or two contiguous stretches of residues ordered as in the native structure with all other residues completely disordered; the free energy of each configuration is the difference between the entropic cost of ordering the residues, which depends on the total number of residues ordered and the length of the loop between the two ordered segments, and the favorable attractive interactions, which are taken to be proportional to the total surface area buried by the ordered residues in the native structure. Folding kinetics are modeled by allowing only one residue to become ordered/disordered at a time, and a rigorous and exact method is used to identify free-energy maxima on the lowest free-energy paths connecting the fully disordered and fully ordered configurations. The distribution of structure in these free-energy maxima, which comprise the transition-state ensemble in the model, are reasonably consistent with experimental data on the folding transition state for five of seven proteins studied. Thus, the model appears to capture, at least in part, the basic physics underlying protein folding and the aspects of native-state topology that determine protein-folding mechanisms.
Project description:The loss of conformational entropy is a major contribution in the thermodynamics of protein folding. However, accurate determination of the quantity has proven challenging. We calculate this loss using molecular dynamic simulations of both the native protein and a realistic denatured state ensemble. For ubiquitin, the total change in entropy is T?STotal = 1.4 kcal?mol(-1) per residue at 300 K with only 20% from the loss of side-chain entropy. Our analysis exhibits mixed agreement with prior studies because of the use of more accurate ensembles and contributions from correlated motions. Buried side chains lose only a factor of 1.4 in the number of conformations available per rotamer upon folding (?U/?N). The entropy loss for helical and sheet residues differs due to the smaller motions of helical residues (T?Shelix-sheet = 0.5 kcal?mol(-1)), a property not fully reflected in the amide N-H and carbonyl C=O bond NMR order parameters. The results have implications for the thermodynamics of folding and binding, including estimates of solvent ordering and microscopic entropies obtained from NMR.
Project description:Characterization of the folding transition-state ensemble and the denatured-state ensemble is an important step toward a full elucidation of protein folding mechanisms. We report herein an investigation of the free-energy landscape of FSD-1 protein by a total of four sets of folding and unfolding molecular dynamics simulations with explicit solvent. The transition-state ensemble was initially identified from unfolding simulations at 500 K and was verified by simulations at 300 K starting from the ensemble structures. The denatured-state ensemble and the early-stage folding were studied by a combination of unfolding simulations at 500 K and folding simulations at 300 K starting from the extended conformation. A common feature of the transition-state ensemble was the substantial formation of the native secondary structures, including both the alpha-helix and beta-sheet, with partial exposure of the hydrophobic core in the solvent. Both the native and non-native secondary structures were observed in the denatured-state ensemble and early-stage folding, consistent with the smooth experimental melting curve. Interestingly, the contact orders of the transition-state ensemble structures were similar to that of the native structure and were notably lower than those of the compact structures found in early-stage folding, implying that chain and topological entropy might play significant roles in protein folding. Implications for FSD-1 folding mechanisms and the rate-limiting step are discussed. Analyses further revealed interesting non-native interactions in the denatured-state ensemble and early-stage folding and the possibility that destabilization of these interactions could help to enhance the stability and folding rate of the protein.
Project description:The rate-limiting step in the formation of the native dimeric state of human Cu, Zn superoxide dismutase (SOD1) is a very slow monomer folding reaction that governs the lifetime of its unfolded state. Mutations at dozens of sites in SOD1 are known to cause a fatal motor neuron disease, amyotrophic lateral sclerosis, and recent experiments implicate the unfolded state as a source of soluble oligomers and histologically observable aggregates thought to be responsible for toxicity. To determine the thermodynamic properties of the transition state ensemble (TSE) limiting the folding of this high-contact-order ?-sandwich motif, we performed a combined thermal/urea denaturation thermodynamic/kinetic analysis. The barriers to folding and unfolding are dominated by the activation enthalpy at 298 K and neutral pH; the activation entropy is favorable and reduces the barrier height for both reactions. The absence of secondary structure formation or large-scale chain collapse prior to crossing the barrier for folding led to the conclusion that dehydration of nonpolar surfaces in the TSE is responsible for the large and positive activation enthalpy. Although the activation entropy favors the folding reaction, the transition from the unfolded state to the native state is entropically disfavored at 298 K. The opposing entropic contributions to the free energies of the TSE and the native state during folding provide insights into structural properties of the TSE. The results also imply a crucial role for water in governing the productive folding reaction and enhancing the propensity for the aggregation of SOD1.
Project description:The molecular mechanism of a reaction in solution is reflected in its transition-state ensemble and transition paths. We use a Bayesian formula relating the equilibrium and transition-path ensembles to identify transition states, rank reaction coordinates, and estimate rate coefficients. We also introduce a variational procedure to optimize reaction coordinates. The theory is illustrated with applications to protein folding and the dipole reorientation of an ordered water chain inside a carbon nanotube. To describe the folding of a simple model of a three-helix bundle protein, we variationally optimize the weights of a projection onto the matrix of native and nonnative amino acid contacts. The resulting one-dimensional reaction coordinate captures the folding transition state, with formation and packing of helix 2 and 3 constituting the bottleneck for folding.