Experimental Phi Values Research Articles

Validation of the Conservation and Robustness of Folding Initiation Sites in Evolutionarily Related Proteins

Despite the recent progress in the protein folding field, how a given amino acid sequence folds into its unique structure is still unclear. According to KA Scott et. al., for Immunoglobulin and Fibronectin-like fold, which are evolutionarily unrelated but have the same topology, share a folding mechanism consisting of 4 key residues and their peripheral residues. However, there are also some cases that two evolutionarily related proteins have different folding mechanisms (for example, PDZ2 and PDZ3 whose sequence identity is nearly 30%). In this study, we aim to investigate whether such folding segments (i.e., folding initiation sites playing important roles for the folding from the denatured state to the transition state) really exist in evolutionarily related proteins by our sequence analysis methods and validate the results with the experimental phi values that provide a degree of the contribution for the structural formation in the transition state for each residue. Our sequence analysis methods are based on the inter-residue average distance statistics and already applied to several proteins, like leghemoglobin, FABP, azurin, and TIM-barrel proteins; they returned reasonable results with HD exchange experiments or phi-value analyses. According to the current study, for the Ferredoxin-like proteins we treat here, the predicted folding initiation sites have good agreements with experimental phi values, and the application to their evolutionarily related proteins returns a suggestion that the location of folding initiation sites are more conservative than sequence. In addition to these analyses, we also investigate the robustness of folding initiation sites by comparing the results of our analyses between naturally evolved proteins, which are under the pressure of nature, and artificially evolved proteins, which are not under the pressure of nature. The details will be reported in the conference.

Comparison of transition states obtained upon modeling of unfolding of immunoglobulin-binding domains of proteins L and G caused by external action with transition states obtained in the absence of force probed by experiments

We have studied the extent of coincidence of the pathway of unfolding of protein globules upon experimental modeling of protein unfolding caused by external actions and denaturants. To this end, we compared experimental Phi-values reported in the literature and Phi-values obtained by us upon modeling of unfolding of immunoglobulin-binding domains of proteins L and G caused by external actions at a constant rate. A comparison of the results of calculation with the experimental data shows that the folding pathways for protein L coincide, while those for protein G do not coincide despite structural similarity of these proteins.

Probing the free energy landscape of the FBP28WW domain using multiple techniques

The free-energy landscape of a small protein, the FBP 28 WW domain, has been explored using molecular dynamics (MD) simulations with alternative descriptions of the molecule. The molecular models used range from coarse-grained to all-atom with either an implicit or explicit treatment of the solvent. Sampling of conformation space was performed using both conventional and temperature-replica exchange MD simulations. Experimental chemical shifts and NOEs were used to validate the simulations, and experimental phi values both for validation and as restraints. This combination of different approaches has provided insight into the free energy landscape and barriers encountered by the protein during folding and enabled the characterization of native, denatured and transition states which are compatible with the available experimental data. All the molecular models used stabilize well defined native and denatured basins; however, the degree of agreement with the available experimental data varies. While the most detailed, explicit solvent model predicts the data reasonably accurately, it does not fold despite a simulation time 10 times that of the experimental folding time. The less detailed models performed poorly relative to the explicit solvent model: an implicit solvent model stabilizes a ground state which differs from the experimental native state, and a structure-based model underestimates the size of the barrier between the two states. The use of experimental phi values both as restraints, and to extract structures from unfolding simulations, result in conformations which, although not necessarily true transition states, appear to share the geometrical characteristics of transition state structures. In addition to characterizing the native, transition and denatured states of this particular system in this work, the advantages and limitations of using varying levels of representation are discussed.

Protein folding by zipping and assembly.

How do proteins fold so quickly? Some denatured proteins fold to their native structures in only microseconds, on average, implying that there is a folding "mechanism," i.e., a particular set of events by which the protein short-circuits a broader conformational search. Predicting protein structures using atomically detailed physical models is currently challenging. The most definitive proof of a putative folding mechanism would be whether it speeds up protein structure prediction in physical models. In the zipping and assembly (ZA) mechanism, local structuring happens first at independent sites along the chain, then those structures either grow (zip) or coalescence (assemble) with other structures. Here, we apply the ZA search mechanism to protein native structure prediction by using the AMBER96 force field with a generalized Born/surface area implicit solvent model and sampling by replica exchange molecular dynamics. Starting from open denatured conformations, our algorithm, called the ZA method, converges to an average of 2.2 A from the Protein Data Bank native structures of eight of nine proteins that we tested, which ranged from 25 to 73 aa in length. In addition, experimental Phi values, where available on these proteins, are consistent with the predicted routes. We conclude that ZA is a viable model for how proteins physically fold. The present work also shows that physics-based force fields are quite good and that physics-based protein structure prediction may be practical, at least for some small proteins.

Unfolding transition state and intermediates of the tumor suppressor p16INK4a investigated by molecular dynamics simulations

The ankyrin repeat is one of the most common protein motifs and is involved in protein-protein interactions. It consists of 33 residues that assume a beta-hairpin helix-loop-helix fold. Mutagenesis and kinetic experiments (Phi-value analysis of the folding transition state) have shown that the tumor suppressor p16(INK4a), a four-repeat protein, unfolds sequentially starting from the two N-terminal repeats. Here, the flexibility of p16(INK4a) at room temperature and its unfolding mechanism at high temperature have been investigated by multiple molecular dynamics runs in explicit water for a total simulation time of 0.65 micros. The transition state ensemble (TSE) of p16(INK4a) was identified by monitoring both the deviation from the experimental Phi values and sudden conformational changes along the unfolding trajectories. Conformations in the TSE have a mainly unstructured second repeat whereas the other repeats are almost completely folded. A rigid-body displacement of the first repeat involving both a rotation and translation is observed in all molecular dynamics simulations at high temperature. The Trp(15), Pro(75), and Ala(76) side-chains are more buried in the TSE than the native state. The sequential unfolding starting at the second repeat is in agreement with the mutagenesis studies whereas the displacement of the first repeat and the presence of nonnative interactions at the TSE are simulation results which supplement the experimental data. Furthermore, the unfolding trajectories reveal the presence of two on-pathway intermediates with partial alpha-helical structure. Finally, on the basis of the available experimental and simulation results we suggest that in modular proteins the shift of the folding TSE toward the native structure upon reduction of the number of tandem repeats is consistent with the Hammond effect.

Transition State Contact Orders Correlate with Protein Folding Rates

We have used molecular dynamics simulations restrained by experimental phi values derived from protein engineering experiments to determine the structures of the transition state ensembles of ten proteins that fold with two-state kinetics. For each of these proteins we then calculated the average contact order in the transition state ensemble and compared it with the corresponding experimental folding rate. The resulting correlation coefficient is similar to that computed for the contact orders of the native structures, supporting the use of native state contact orders for predicting folding rates. The native contacts in the transition state also correlate with those of the native state but are found to be about 30% lower. These results show that, despite the high levels of heterogeneity in the transition state ensemble, the large majority of contributing structures have native-like topologies and that the native state contact order captures this phenomenon.

Loop‐closure events during protein folding: Rationalizing the shape of Φ‐value distributions

In the past years, the folding kinetics of many small single-domain proteins has been characterized by mutational Phi-value analysis. In this article, a simple, essentially parameter-free model is introduced which derives folding routes from native structures by minimizing the entropic loop-closure cost during folding. The model predicts characteristic folding sequences of structural elements such as helices and beta-strand pairings. Based on few simple rules, the kinetic impact of these structural elements is estimated from the routes and compared to average experimental Phi-values for the helices and strands of 15 small, well-characterized proteins. The comparison leads on average to a correlation coefficient of 0.62 for all proteins with polarized Phi-value distributions, and 0.74 if distributions with negative average Phi-values are excluded. The diffuse Phi-value distributions of the remaining proteins are reproduced correctly. The model shows that Phi-value distributions, averaged over secondary structural elements, can often be traced back to entropic loop-closure events, but also indicates energetic preferences in the case of a few proteins governed by parallel folding processes.

A critical assessment of the topomer search model of protein folding using a continuum explicit‐chain model with extensive conformational sampling

Recently, a series of closely related theoretical constructs termed the "topomer search model" (TSM) has been proposed for the folding mechanism of small, single-domain proteins. A basic assumption of the proposed scenarios is that the rate-limiting step in folding is an essentially unbiased, diffusive search for a conformational state called the native topomer defined by an overall native-like topological pattern. Successes in correlating TSM-predicted folding rates with that of real proteins have been interpreted as experimental support for the model. To better delineate the physics entailed, key TSM concepts are examined here using extensive Langevin dynamics simulations of continuum C(alpha) chain models. The theoretical native topomers of four experimentally well-studied two-state proteins are characterized. Consistent with the TSM perspective, we found that the sizes of the native topomers increase with experimental folding rate. However, a careful determination of the corresponding probabilities that the native topomers are populated during a random search fails to reproduce the previously predicted folding rates. Instead, our results indicate that an unbiased TSM search for the native topomer amounts to a Levinthal-like process that would take an impossibly long average time to complete. Furthermore, intraprotein contacts in all four native topomers considered exhibit no apparent correlation with the experimental phi-values determined from the folding kinetics of these proteins. Thus, the present findings suggest that certain basic, generic yet essential energetic features in protein folding are not accounted for by TSM scenarios to date.

Three-body interactions improve the prediction of rate and mechanism in protein folding models.

Here we study the effects of many-body interactions on rate and mechanism in protein folding by using the results of molecular dynamics simulations on numerous coarse-grained Calpha-model single-domain proteins. After adding three-body interactions explicitly as a perturbation to a Gō-like Hamiltonian with native pairwise interactions only, we have found (i) a significantly increased correlation with experimental phi values and folding rates, (ii) a stronger correlation of folding rate with contact order, matching the experimental range in rates when the fraction of three-body energy in the native state is approximately 20%, and (iii) a considerably larger amount of three-body energy present in chymotripsin inhibitor than in the other proteins studied.

Comparison of the Transition States for Folding of Two Ig-like Proteins from Different Superfamilies

In the "fold approach" proteins with a similar fold but different sequences are compared in order to investigate the relationship between native state structure and folding behaviour. Here we compare the properties of the transition states for folding of TI I27, the 27th immunoglobulin domain from human cardiac titin, and that of TNfn3, the third fibronectin type III domain from human tenascin. Experimental phi-values were used as restraints in molecular dynamics simulations to determine the structures that make up the transition state ensembles (TSEs) for folding of the two proteins. The restrained simulations that we present allow a detailed structural comparison of the two TSEs to be made. Further calculations show explicitly that for both proteins the formation of the interactions involving the residues in the folding nucleus is sufficient for the establishment of the topology of the Ig-like fold. We found that, although the folding nuclei of the two proteins are similar, the packing of the folding nucleus of TI I27 is much tighter than that of TNfn3, reflecting the higher experimental phi-values and beta(T) (Tanford Beta) of TI I27. These results suggest that the folding nucleus can be significantly deformed to accommodate extensive sequence variation while conserving the same folding mechanism.

Molecular dynamics simulations of protein folding from the transition state.

Putative transition-state ensemble (TSE) conformations of src SH3 were identified by monitoring the deviation from the experimental phi values along molecular dynamics (MD) simulations of unfolding. Sixty MD trajectories (for a total of about 7 micros) were then started from the putative TSE. About one-half of the 60 runs reached the folded state while unfolding was observed in the remaining half of the runs. This result validates phi-value analysis as an approach to obtain structural information on the transition state. It also demonstrates that an atomic resolution description of the TSE can be extracted from MD simulations. All conformations in the TSE have the central three-stranded beta-sheet formed in agreement with experimental data. An elongation of strand beta 2 as well as non-native side-chain interactions between the diverging turn and the distal hairpin are observed. The simulation results indicate that the tight packing of the side chains between the diverging turn and the distal hairpin is a necessary condition for rapid folding. Contacts between residues in the most structured element of the TSE, the central beta-sheet, are kinetically more important than those between the N- and C-terminal strands.

Transition states and the meaning of Phi-values in protein folding kinetics.

What is the mechanism of two-state protein folding? The rate-limiting step is typically explored through a Phi-value, which is the mutation-induced change in the transition state free energy divided by the change in the equilibrium free energy of folding. Phi-values ranging from 0 to 1 have been interpreted as meaning the transition state is denatured-like (0), native-like (1) or in-between. But there is no classical interpretation for the experimental Phi-values that are negative or >1. Using a rigorous method to identity transition states via an exact lattice model, we find that nonclassical Phi-values can arise from parallel microscopic flow processes, such as those in funnel-shaped energy landscapes. Phi < 0 results when a mutation destabilizes a slow flow channel, causing a backflow into a faster flow channel. Phi > 1 implies the reverse: a backflow from a fast channel into a slow one. Using a 'landscape mapping' method, we find that Phi correlates with the acceleration/deceleration of folding induced by mutations, rather than with the degree of nativeness of the transition state.