Strain in the folding nucleus of chymotrypsin inhibitor 2

Double Mutant of Chymotrypsin Inhibitor 2 Stabilized through Increased Conformational Entropy

The conformational heterogeneity of a folded protein can affect not only its function but also stability and folding. We recently discovered and characterized a stabilized double mutant (L49I/I57V) of the protein CI2 and showed that state-of-the-art prediction methods could not predict the increased stability relative to the wild-type protein. Here, we have examined whether changed native-state dynamics, and resulting entropy changes, can explain the stability changes in the double mutant protein, as well as the two single mutant forms. We have combined NMR relaxation measurements of the ps-ns dynamics of amide groups in the backbone and the methyl groups in the side chains with molecular dynamics simulations to quantify the native-state dynamics. The NMR experiments reveal that the mutations have different effects on the conformational flexibility of CI2: a reduction in conformational dynamics (and entropy estimated from this) of the native state of the L49I variant correlates with its decreased stability, while increased dynamics of the I57V and L49I/I57V variants correlates with their increased stability. These findings suggest that explicitly accounting for changes in native-state entropy might be needed to improve the predictions of the effect of mutations on protein stability.

Water's Variable Role in Protein Stability Uncovered by Liquid-Observed Vapor Exchange NMR

Water is essential to protein structure and stability, yet our understanding of how water shapes proteins is far from thorough. Our incomplete knowledge of protein-water interactions is due in part to a long-standing technological inability to assess experimentally how water removal impacts local protein structure. It is now possible to obtain residue-level information on dehydrated protein structures via liquid-observed vapor exchange (LOVE) NMR, a solution NMR technique that quantifies the extent of hydrogen-deuterium exchange between unprotected amide protons of a dehydrated protein and D₂O vapor. Here, we apply LOVE NMR, Fourier transform infrared spectroscopy, and solution hydrogen-deuterium exchange to globular proteins GB1, CI2, and two variants thereof to link mutation-induced changes in the dehydrated protein structure to changes in solution structure and stability. We find that a mutation that destabilizes GB1 in solution does not affect its dehydrated structure, whereas a mutation that stabilizes CI2 in solution makes several regions of the protein more susceptible to dehydration-induced unfolding, suggesting that water is primarily responsible for the destabilization of the GB1 variant but plays a stabilizing role in the CI2 variant. Our results indicate that changes in dehydrated protein structure cannot be predicted from changes in solution stability alone and demonstrate the ability of LOVE NMR to uncover the variable role of water in protein stability. Further application of LOVE NMR to other proteins and their variants will improve the ability to predict and modulate protein structure and stability in both the hydrated and dehydrated states for applications in medicine and biotechnology.

Synergistic stabilization of a double mutant in chymotrypsin inhibitor 2 from a library screen in E. coli

Most single point mutations destabilize folded proteins. Mutations that stabilize a protein typically only have a small effect and multiple mutations are often needed to substantially increase the stability. Multiple point mutations may act synergistically on the stability, and it is often not straightforward to predict their combined effect from the individual contributions. Here, we have applied an efficient in-cell assay in E. coli to select variants of the barley chymotrypsin inhibitor 2 with increased stability. We find two variants that are more than 3.8 kJ mol-1 more stable than the wild-type. In one case, the increased stability is the effect of the single substitution D55G. The other case is a double mutant, L49I/I57V, which is 5.1 kJ mol-1 more stable than the sum of the effects of the individual mutations. In addition to demonstrating the strength of our selection system for finding stabilizing mutations, our work also demonstrate how subtle conformational effects may modulate stability.

Global analysis of protein stability by temperature and chemical denaturation

The stability of a protein is a fundamental property that determines under which conditions, the protein is functional. Equilibrium unfolding with denaturants requires preparation of several samples and only provides the free energy of folding when performed at a single temperature. The typical sample requirement is around 0.5-1 mg of protein. If the stability of many proteins or protein variants needs to be determined, substantial protein production may be needed. Here we have determined the stability of acyl-coenzyme A binding protein at pH 5.3 and chymotrypsin inhibitor 2 at pH 3 and pH 6.25 by combined temperature and denaturant unfolding. We used a setup where tryptophan fluorescence is measured in quartz capillaries where only 10 μl is needed. Temperature unfolding of a series of 15 samples at increasing denaturant concentrations provided accurate and precise thermodynamic parameters. We find that the number of samples may be further reduced and less than 10 μg of protein in total are needed for reliable stability measurements. For assessment of stability of protein purified in small scale e.g. in micro plate format, our method will be highly applicable. The routine for fitting the experimental data is made available as a python notebook.

Using contact statistics to characterize structure transformation of biopolymer ensembles

As a unique subset of functional polymers, many biopolymers have a set of well-defined three-dimensional (3D) structural characteristics that can be described by spatial contacts between monomers. Statistical analysis of the contacts has been extremely productive in characterizing the biopolymer structural ensemble, such as for 3D chromosome structures. Often, native contacts and compartment structures are the focus of the studies, while the generic polymer aspect, such as the overall decaying of contacts with increasing sequence distance, is analyzed separately or preemptively removed. Here, we explore insights that can be gained by performing "compartment analysis" that keeps the distance decay, which we believe is particularly useful for characterizing the structure transformation of biopolymers. We tested contact analysis on several such transformations under physical perturbation or biological processes, including (1) unfolding of proteins induced by thermal denaturation, (2) chromosome conformation transition during the cell cycle, and (3) chromosome unpacking by physicochemical perturbations. Useful score functions were developed to further quantitatively characterize the transformation judging from the contact analysis. We also find that the sinusoidal undertone of eigenvector patterns (the "unwanted," low frequency signal, in contrast to the detailed A/B compartment) that had previously been attributed to biological effects of centromere proximal and distal interactions may in fact reflect a universal feature of polymers that have relatively weaker long-range contacts.

Intrinsic Disorder in a Well-Folded Globular Protein

The folded structure of the heterodimeric sweet protein monellin mimics single-chain proteins with topology β1-α1-β2-β3-β4-β5 (chain A: β3-β4-β5; chain B: β1-α1-β2). Furthermore, like naturally occurring single-chain proteins of a similar size, monellin folds cooperatively with no detectable intermediates. However, the two monellin chains, A and B, are marginally structured in isolation and fold only upon binding to each other. Thus, monellin presents a unique opportunity to understand the design of intrinsically disordered proteins that fold upon binding. Here, we study the folding of a single-chain variant of monellin (scMn) using simulations of an all heavy-atom structure-based model. These simulations can explain mechanistic details derived from scMn experiments performed using several different structural probes. scMn folds cooperatively in our structure-based simulations, as is also seen in experiments. We find that structure formation near the transition-state ensemble of scMn is not uniformly distributed but is localized to a hairpin-like structure which contains one strand from each chain (β2, β3). Thus, the sequence and the underlying energetics of heterodimeric monellin promote the early formation of the interchain interface (β2-β3). By studying computational scMn mutants whose "interchain" interactions are deleted, we infer that this energy distribution allows the two protein chains to remain largely disordered when this interface is not folded. From these results, we suggest that cutting the protein backbone of a globular protein between residues which lie within its folding nucleus may be one way to construct two disordered fragments which fold upon binding.

Investigation of an anomalously accelerating substitution in the folding of a prototypical two-state protein

The folding rates of two-state single-domain proteins are generally resistant to small-scale changes in amino acid sequence. For example, having surveyed here over 700 single-residue substitutions in 24 well-characterized two-state proteins, we find that the majority (55%) of these substitutions affect folding rates by less than a factor of 2, and that only 9% affect folding rates by more than a factor of 8. Among those substitutions that significantly affect folding rates, we find that accelerating substitutions are an order of magnitude less common than those that decelerate the process. One of the most extreme outliers in this data set, an arginine-to-phenylalanine substitution at position 48 (R48F) of chymotrypsin inhibitor 2 (CI2), accelerates the protein's folding rate by a factor of 36 relative to that of the wild-type protein and is the most accelerating substitution reported to date in a two-state protein. In order to better understand the origins of this anomalous behavior, we have characterized the kinetics of multiple additional substitutions at this position. We find that substitutions at position 48 in CI2 fall into two distinct classes. The first, comprising residues that ablate the charge of the wild-type arginine but retain the hydrophobicity of its alkane chain, accelerate folding by at least 10-fold. The second class, comprising all other residues, produces folding rates within a factor of two of the wild-type rate. A significant positive correlation between hydrophobicity and folding rate across all of the residues we have characterized at this position suggests that the hydrophobic methylene units of the wild-type arginine play a significant role in stabilizing the folding transition state. Likewise, studies of the pH dependence of the histidine substitution indicate a strong correlation between folding rate and charge state. Thus, mutations that ablate the arginine's positive charge while retaining the hydrophobic contacts of its methylene units tend to dramatically accelerate folding. Previous studies have suggested that arginine 48 plays an important functional role in CI2, which may explain why it is highly conserved despite the anomalously large deceleration it produces in the folding of this protein.

Characterization of protein-folding pathways by reduced-space modeling

Ab initio simulations of the folding pathways are currently limited to very small proteins. For larger proteins, some approximations or simplifications in protein models need to be introduced. Protein folding and unfolding are among the basic processes in the cell and are very difficult to characterize in detail by experiment or simulation. Chymotrypsin inhibitor 2 (CI2) and barnase are probably the best characterized experimentally in this respect. For these model systems, initial folding stages were simulated by using CA-CB-side chain (CABS), a reduced-space protein-modeling tool. CABS employs knowledge-based potentials that proved to be very successful in protein structure prediction. With the use of isothermal Monte Carlo (MC) dynamics, initiation sites with a residual structure and weak tertiary interactions were identified. Such structures are essential for the initiation of the folding process through a sequential reduction of the protein conformational space, overcoming the Levinthal paradox in this manner. Furthermore, nucleation sites that initiate a tertiary interactions network were located. The MC simulations correspond perfectly to the results of experimental and theoretical research and bring insights into CI2 folding mechanism: unambiguous sequence of folding events was reported as well as cooperative substructures compatible with those obtained in recent molecular dynamics unfolding studies. The correspondence between the simulation and experiment shows that knowledge-based potentials are not only useful in protein structure predictions but are also capable of reproducing the folding pathways. Thus, the results of this work significantly extend the applicability range of reduced models in the theoretical study of proteins.

Mutations in alpha-helical solvent-exposed sites of eglin c have long-range effects: evidence from molecular dynamics simulations

Eglin c is a small protease inhibitor whose structural and thermodynamic properties have been well studied. Previous thermodynamic measurements on mutants at solvent-accessible positions in the protein's helix have shown the unexpected result that the data could be best fit by the inclusion of residue- and position-specific parameters to the model. To explore the origins of this surprising result, long molecular dynamics simulations in explicit solvent have been performed. These simulations indicate specific long-range interactions between the solvent-exposed residues in the eglin c alpha-helix and binding loop, an unexpected observation for such a small protein. The residues involved in the interaction are on opposite sides of the protein, about 25 A apart. Simulations of alanine substitutions at the solvent-exposed helix positions, arginine 22, glutamic acid 23, threonine 26, and leucine 27, show both small and large perturbations of eglin c dynamics. Two mutations exhibit large impacts on the long-range helix-loop interactions. Previous stability measurements (Yi et al., Biochemistry 2003;42:7594-7603) had indicated that an alanine substitution at position 27 was less stabilizing than at other solvent-exposed positions in the helix. The L27A mutation effects observed in these simulations suggest that the position-dependent loss of stability measured in wet bench experiments is derived from changes in dynamics that involve long-range interactions; thus, these simulations support the hypothesis that solvent-exposed positions in helices are not always equivalent.

Topological determinants of protein folding

The folding of many small proteins is kinetically a two-state process that represents overcoming the major free-energy barrier. A kinetic characteristic of a conformation, its probability to descend to the native state domain in the amount of time that represents a small fraction of total folding time, has been introduced to determine to which side of the free-energy barrier a conformation belongs. However, which features make a protein conformation on the folding pathway become committed to rapidly descending to the native state has been a mystery. Using two small, well characterized proteins, CI2 and C-Src SH3, we show how topological properties of protein conformations determine their kinetic ability to fold. We use a macroscopic measure of the protein contact network topology, the average graph connectivity, by constructing graphs that are based on the geometry of protein conformations. We find that the average connectivity is higher for conformations with a high folding probability than for those with a high probability to unfold. Other macroscopic measures of protein structural and energetic properties such as radius of gyration, rms distance, solvent-accessible surface area, contact order, and potential energy fail to serve as predictors of the probability of a given conformation to fold.

Probing the energy landscape of protein folding/unfolding transition states

Previous molecular dynamics (MD) simulations of the thermal denaturation of chymotrypsin inhibitor 2 (CI2) have provided atomic-resolution models of the transition state ensemble that is well supported by experimental studies. Here, we use simulations to further investigate the energy landscape around the transition state region. Nine structures within approximately 35 ps and 3 A C(alpha) RMSD of the transition state ensemble identified in a previous 498 K thermal denaturation simulation were quenched under the quasi-native conditions of 335 K and neutral pH. All of the structures underwent hydrophobically driven collapse in response to the drop in temperature. Structures less denatured than the transition state became structurally more native-like, while structures that were more denatured than the transition state tended to show additional loss of native structure. The structures in the immediate region of the transition state fluctuated between becoming more and less native-like. All of the starting structures had the same native-like topology and were quite similar (within 3.5 A C(alpha) RMSD). That the structures all shared native-like topology, yet diverged into either more or less native-like structures depending on which side of the transition state they occupied on the unfolding trajectory, indicates that topology alone does not dictate protein folding. Instead, our results suggest that a detailed interplay of packing interactions and interactions with water determine whether a partially denatured protein will become more native-like under refolding conditions.

Constructing, verifying, and dissecting the folding transition state of chymotrypsin inhibitor 2 with all-atom simulations

Experimentally, protein engineering and phi-value analysis is the method of choice to characterize the structure in folding transition state ensemble (TSE) of any protein. Combining experimental phi values and computer simulations has led to a deeper understanding of how proteins fold. In this report, we construct the TSE of chymotrypsin inhibitor 2 from published phi values. Importantly, we verify, by means of multiple independent simulations, that the conformations in the TSE have a probability of approximately 0.5 to reach the native state rapidly, so the TSE consists of true transition states. This finding validates the use of transition state theory underlying all phi-value analyses. Also, we present a method to dissect and study the TSE by generating conformations that have a disrupted alpha-helix (alpha-disrupted states) or disordered beta-strands 3 and 4 (beta-disrupted states). Surprisingly, the alpha-disrupted states have a stronger tendency to fold than the beta-disrupted states, despite the higher phi values for the alpha-helix in the TSE. We give a plausible explanation for this result and discuss its implications on protein folding and design. Our study shows that, by using both experiments and computer simulations, we can gain many insights into protein folding.

Redesigning the hydrophobic core of a model beta-sheet protein: destabilizing traps through a threading approach

An off-lattice 46-bead model of a small all-beta protein has been recently criticized for possessing too many traps and long-lived intermediates compared with the folding energy landscape predicted for real proteins and models using the principle of minimal frustration. Using a novel sequence design approach based on threading for finding beneficial mutations for destabilizing traps, we proposed three new sequences for folding in the beta-sheet model. Simulated annealing on these sequences found the global minimum more reliably, indicative of a smoother energy landscape, and simulated thermodynamic variables found evidence for a more cooperative collapse transition, lowering of the collapse temperature, and higher folding temperatures. Folding and unfolding kinetics were acquired by calculating first-passage times, and the new sequences were found to fold significantly faster than the original sequence, with a concomitant lowering of the glass temperature, although none of the sequences have highly stable native structures. The new sequences found here are more representative of real proteins and are good folders in the T(f) > T(g) sense, and they should prove useful in future studies of the details of transition states and the nature of folding intermediates in the context of simplified folding models. These results show that our sequence design approach using threading can improve models possessing glasslike folding dynamics.

Use of a quantitative structure-property relationship to design larger model proteins that fold rapidly

A quantitative structure-property relationship (QSPR) was used to design model protein sequences that fold repeatedly and relatively rapidly to stable target structures. The specific model was a 125-residue heteropolymer chain subject to Monte Carlo dynamics on a simple cubic lattice. The QSPR was derived from an analysis of a database of 200 sequences by a statistical method that uses a genetic algorithm to select the sequence attributes that are most important for folding and a neural network to determine the corresponding functional dependence of folding ability on the chosen attributes. The QSPR depends on the number of anti-parallel sheet contacts, the energy gap between the native state and quasi-continuous part of the spectrum and the total energy of the contacts between surface residues. Two Monte Carlo procedures were used in series to optimize both the target structures and the sequences. We generated 20 fully optimized sequences and 60 partially optimized control sequences and tested each for its ability to fold in dynamic MC simulations. Although sequences in which either the number of anti-parallel sheet contacts or the energy of the surface residues is non-optimal are capable of folding almost as well as fully optimized ones, sequences in which only the energy gap is optimized fold markedly more slowly. Implications of the results for the design of proteins are discussed.

A simple model for calculating the kinetics of protein folding from three-dimensional structures

An elementary statistical mechanical model was used to calculate the folding rates for 22 proteins from their known three-dimensional structures. In this model, residues come into contact only after all of the intervening chain is in the native conformation. An additional simplifying assumption is that native structure grows from localized regions that then fuse to form the complete native molecule. The free energy function for this model contains just two contributions-conformational entropy of the backbone and the energy of the inter-residue contacts. The matrix of inter-residue interactions is obtained from the atomic coordinates of the three-dimensional structure. For the 18 proteins that exhibit two-state equilibrium and kinetic behavior, profiles of the free energy versus the number of native peptide bonds show two deep minima, corresponding to the native and denatured states. For four proteins known to exhibit intermediates in folding, the free energy profiles show additional deep minima. The calculated rates of folding the two-state proteins, obtained by solving a diffusion equation for motion on the free energy profiles, reproduce the experimentally determined values surprisingly well. The success of these calculations suggests that folding speed is largely determined by the distribution and strength of contacts in the native structure. We also calculated the effect of mutations on the folding kinetics of chymotrypsin inhibitor 2, the most intensively studied two-state protein, with some success.

Exploring structures in protein folding funnels with free energy functionals: the transition state ensemble

We use free energy functionals that account for the partial ordering of residues in the transition state ensemble to characterize the free energy surfaces for fast folding proteins. We concentrate on chymotrypsin inhibitor and lambda-repressor. We show how the explicit cooperativity that can arise from many body forces, such as side-chain ordering or hydrophobic surface burial, determines the crossover from folding with a large delocalized nucleus and the specific small classical nucleus of the type envisioned in nucleation growth scenarios. We compare the structural correlations present in the transition state ensemble obtained from free energy functionals with those inferred from experiment using extrathermodynamic free energy relations for folding time obtained via protein engineering kinetics experiments. We also use the free energy functionals to examine both the size of barriers and multidimensional representations of the free energy profiles in order to address the question of appropriate reaction coordinates for folding.

Satisfying turns in folding transitions

Protein engineering studies show that conformations in the folding transition state ensemble can be structurally polarized. In two SH3 beta-sheet domains, the formation of hydrophobic contacts goes hand in hand with the formation of the solvated distal loop beta-turn, while large parts of the molecule remain unstructured in the ensemble.

Protein design: a perspective from simple tractable models

Recent progress in computational approaches to protein design builds on advances in statistical mechanical protein folding theory. Here, the number of sequences folding into a given conformation is evaluated and a simple condition for a protein model's designability is outlined.

How evolution makes proteins fold quickly

Sequences of fast-folding model proteins (48 residues long on a cubic lattice) were generated by an evolution-like selection toward fast folding. We find that fast-folding proteins exhibit a specific folding mechanism in which all transition state conformations share a smaller subset of common contacts (folding nucleus). Acceleration of folding was accompanied by dramatic strengthening of interactions in the folding nucleus whereas average energy of nonnucleus interactions remained largely unchanged. Furthermore, the residues involved in the nucleus are the most conserved ones within families of evolved sequences. Our results imply that for each protein structure there is a small number of conserved positions that are key determinants of fast folding into that structure. This conjecture was tested on two protein superfamilies: the first having the classical monophosphate binding fold (CMBF; 98 families) and the second having type-III repeat fold (47 families). For each superfamily, we discovered a few positions that exhibit very strong and statistically significant "conservatism of conservatism"-amino acids in those positions are conserved within every family whereas the actual types of amino acids varied from family to family. Those amino acids are in spatial contact with each other. The experimental data of Serrano and coworkers [Lopez-Hernandez, E. & Serrano, L. (1996) Fold. Des. (London) 1, 43-55]. for one of the proteins of the CMBF superfamily (CheY) show that residues identified this way indeed belong to the folding nucleus. Further analysis revealed deep connections between nucleation in CMBF proteins and their function.

The sequences of small proteins are not extensively optimized for rapid folding by natural selection

The thermodynamic stabilities of small protein domains are clearly subject to natural selection, but it is less clear whether the rapid folding rates typically observed for such proteins are consequences of direct evolutionary optimization or reflect intrinsic physical properties of the polypeptide chain. This issue can be investigated by comparing the folding rates of laboratory-generated protein sequences to those of naturally occurring sequences provided that the method by which the sequences are generated has no kinetic bias. Herein we report the folding thermodynamics and kinetics of 12 heavily mutated variants of the small IgG binding domain of protein L retrieved from high-complexity combinatorial libraries by using a phage-display selection for proper folding that does not discriminate between rapidly and slowly folding proteins. Although the stabilities of all variants were decreased, many of the variants fold faster than wild type. Taken together with similar results for the src homology 3 domain, this observation suggests that the sequences of small proteins have not been extensively optimized for rapid folding; instead, rapid folding appears to be a consequence of selection for stability.