Guiding the search for a protein's maximum rate of folding

Scaling Laws for Protein Folding under Confinement

Spatial confinement significantly affects protein folding. Without the confinement provided by chaperones, many proteins cannot fold correctly. However, the quantitative effect of confinement on protein folding remains elusive. In this study, we observed scaling laws between the variation in folding transition temperature and the size of confinement, (Tf - Tfbulk)/Tfbulk ∼ L-ν. The scaling exponent v is significantly influenced by both the protein's topology and folding cooperativity. Specifically, for a given protein, v can decrease as the folding cooperativity of the model increases, primarily due to the heightened sensitivity of the unfolded state energy to changes in cage size. For proteins with diverse topologies, variations in topological complexity influence scaling exponents in multiple ways. Notably, v exhibits a clear positive correlation with contact order and the proportion of nonlocal contacts, as this complexity significantly enhances the sensitivity of entropy loss in the unfolded state. Furthermore, we developed a novel scaling argument yielding 5/3 ≤ ν ≤ 10/3, consistent with the simulation results.

Backbone Modification in a Protein Hydrophobic Core

Targeted protein backbone modification can recreate tertiary structures reminiscent of folds found in nature on artificial scaffolds with improved biostability. Incorporation of altered monomers in such entities is typically limited to sites distant from the hydrophobic core to avoid potential disruptions to folding. This is limiting, as it is advantageous in some applications to incorporate artificial connectivity at buried sites. Here, we report an examination of protein backbone modification targeted specifically to hydrophobic core positions and its impacts on tertiary folded structure and fold stability. Different artificial monomer types are placed at core, core-flanking, or solvent-exposed positions in a compact three-helix protein. Effects on structure and folding energetics are assessed by NMR spectroscopy and biophysical methods. Results show that artificial residues can be well accommodated in the hydrophobic core of a defined tertiary fold, with effects on stability only modestly larger than identical changes at solvent-exposed sites. Collectively, these results provide new insights into folding behavior of protein-like artificial chains as well as strategies for the design of such molecules.

Targeting the protein folding transition state by mutation: Large scale (un)folding rate accelerations without altering native stability

Proteins are constantly undergoing folding and unfolding transitions, with rates that determine their homeostasis in vivo and modulate their biological function. The ability to optimize these rates without affecting overall native stability is hence highly desirable for protein engineering and design. The great challenge is, however, that mutations generally affect folding and unfolding rates with inversely complementary fractions of the net free energy change they inflict on the native state. Here we address this challenge by targeting the folding transition state (FTS) of chymotrypsin inhibitor 2 (CI2), a very slow and stable two-state folding protein with an FTS known to be refractory to change by mutation. We first discovered that the CI2's FTS is energetically taxed by the desolvation of several, highly conserved, charges that form a buried salt bridge network in the native structure. Based on these findings, we designed a CI2 variant that bears just four mutations and aims to selectively stabilize the FTS. This variant has >250-fold faster rates in both directions and hence identical native stability, demonstrating the success of our FTS-centric design strategy. With an optimized FTS, CI2 also becomes 250-fold more sensitive to proteolytic degradation by its natural substrate chymotrypsin, and completely loses its activity as inhibitor. These results indicate that CI2 has been selected through evolution to have a very unstable FTS in order to attain the kinetic stability needed to effectively function as protease inhibitor. Moreover, the CI2 case showcases that protein (un)folding rates can critically pivot around a few key residues-interactions, which can strongly modify the general effects of known structural factors such as domain size and fold topology. From a practical standpoint, our results suggest that future efforts should perhaps focus on identifying such critical residues-interactions in proteins as best strategy to significantly improve our ability to predict and engineer protein (un)folding rates.

Computational Design of Homotetrameric Peptide Bundle Variants Spanning a Wide Range of Charge States

With the ability to design their sequences and structures, peptides can be engineered to realize a wide variety of functionalities and structures. Herein, computational design was used to identify a set of 17 peptides having a wide range of putative charge states but the same tetrameric coiled-coil bundle structure. Calculations were performed to identify suitable locations for ionizable residues (D, E, K, and R) at the bundle's exterior sites, while interior hydrophobic interactions were retained. The designed bundle structures spanned putative charge states of -32 to +32 in units of electron charge. The peptides were experimentally investigated using spectroscopic and scattering techniques. Thermal stabilities of the bundles were investigated using circular dichroism. Molecular dynamics simulations assessed structural fluctuations within the bundles. The cylindrical peptide bundles, 4 nm long by 2 nm in diameter, were covalently linked to form rigid, micron-scale polymers and characterized using transmission electron microscopy. The designed suite of sequences provides a set of readily realized nanometer-scale structures of tunable charge that can also be polymerized to yield rigid-rod polyelectrolytes.

Can glycine betaine denature proteins?

Glycine betaine (GB) is a naturally occurring osmolyte that has been widely recognized as a protein protectant. Since GB consists of a methylated ammonium moiety, it can engage in strong cation-π interactions with aromatic amino acid sidechains. We hypothesize that such specific binding interactions would allow GB to decrease the stability of proteins that are predominantly stabilized by a cluster of aromatic amino acids. To test this hypothesis, we investigate the effect of GB on the stability of two β-hairpins (or mini-proteins) that contain such a cluster. We find that for both systems the stability of the folded state first decreases and then increases with increasing GB concentration. Such non-monotonic dependence not only confirms that GB can act as a protein denaturant, but also underscores the complex interplay between GB's stabilizing and destabilizing forces toward a given protein. While stabilizing osmolytes all have the tendency to be excluded from the protein surface which is the action underlying their stabilizing effect, our results suggest that in order to quantitatively assess the effect of GB on the stability of any given protein, specific cation-π binding interactions need to be explicitly considered. Moreover, our results show, consistent with other studies, that cation methylation can strengthen the respective cation-π interactions. Taken together, these findings provide new insight into the mechanism by which amino acid-based osmolytes interact with proteins.

Effect of Mutations on the Global and Site-Specific Stability and Folding of an Elementary Protein Structural Motif

Understanding the folding mechanism of proteins requires detailed knowledge of the roles of individual amino acid residues in stabilization of specific elements and local segments of the native structure. Recently, we have utilized the combination of circular dichroism (CD) and site-specific ¹³C isotopically edited infrared spectroscopy (IR) coupled with the Ising-like model for protein folding to map the thermal unfolding at the residue level of a de novo designed helix-turn-helix motif αtα. Here we use the same methodology to study how the sequence of local thermal unfolding is affected by selected mutations introduced into the most and least stable parts of the motif. Seven different mutants of αtα are screened to find substitutions with the most pronounced effects on the overall stability. Subsequently, thermal unfolding of two mutated αtα sequences is studied with site-specific resolution, using four distinct ¹³C isotopologues of each. The data are analyzed with the Ising-like model, which builds on a previous parametrization for the original αtα sequence and tests different ways of incorporating the amino acid substitution. We show that for both more and less stable mutants only the adjustment of all interaction parameters of the model can yield a satisfactory fit to the experimental data. The stabilizing and destabilizing mutations result, respectively, in a similar increase and decrease of the stability of all probed local segments, irrespective of their position with respect to the mutation site. Consequently, the relative order of their unfolding remains essentially unchanged. These results underline the importance of the interconnectivity of the stabilizing interaction network and cooperativity of the protein structure, which is evident even in a small motif with apparently noncooperative, heterogeneous unfolding. Overall, our findings are consistent with the native structure being the dominant factor in determining the folding mechanism, regardless of the details of its overall or local thermodynamic stabilization.

Protein folding, misfolding and aggregation: The importance of two-electron stabilizing interactions

Proteins associated with neurodegenerative diseases are highly pleiomorphic and may adopt an all-α-helical fold in one environment, assemble into all-β-sheet or collapse into a coil in another, and rapidly polymerize in yet another one via divergent aggregation pathways that yield broad diversity of aggregates’ morphology. A thorough understanding of this behaviour may be necessary to develop a treatment for Alzheimer’s and related disorders. Unfortunately, our present comprehension of folding and misfolding is limited for want of a physicochemical theory of protein secondary and tertiary structure. Here we demonstrate that electronic configuration and hyperconjugation of the peptide amide bonds ought to be taken into account to advance such a theory. To capture the effect of polarization of peptide linkages on conformational and H-bonding propensity of the polypeptide backbone, we introduce a function of shielding tensors of the C^α atoms. Carrying no information about side chain-side chain interactions, this function nonetheless identifies basic features of the secondary and tertiary structure, establishes sequence correlates of the metamorphic and pH-driven equilibria, relates binding affinities and folding rate constants to secondary structure preferences, and manifests common patterns of backbone density distribution in amyloidogenic regions of Alzheimer’s amyloid β and tau, Parkinson’s α-synuclein and prions. Based on those findings, a split-intein like mechanism of molecular recognition is proposed to underlie dimerization of Aβ, tau, αS and PrP^C, and divergent pathways for subsequent association of dimers are outlined; a related mechanism is proposed to underlie formation of PrP^Sc fibrils. The model does account for: (i) structural features of paranuclei, off-pathway oligomers, non-fibrillar aggregates and fibrils; (ii) effects of incubation conditions, point mutations, isoform lengths, small-molecule assembly modulators and chirality of solid-liquid interface on the rate and morphology of aggregation; (iii) fibril-surface catalysis of secondary nucleation; and (iv) self-propagation of infectious strains of mammalian prions.

Globular Protein Folding In Vitro and In Vivo

In vitro, computational, and theoretical studies of protein folding have converged to paint a rich and complex energy landscape. This landscape is sensitively modulated by environmental conditions and subject to evolutionary pressure on protein function. Of these environments, none is more complex than the cell itself, where proteins function in the cytosol, in membranes, and in different compartments. A wide variety of kinetic and thermodynamics experiments, ranging from single-molecule studies to jump kinetics and from nuclear magnetic resonance to imaging on the microscope, have elucidated how protein energy landscapes facilitate folding and how they are subject to evolutionary constraints and environmental perturbation. Here we review some recent developments in the field and refer the reader to some original work and additional reviews that cover this broad topic in protein science.

When fast is better: protein folding fundamentals and mechanisms from ultrafast approaches

Protein folding research stalled for decades because conventional experiments indicated that proteins fold slowly and in single strokes, whereas theory predicted a complex interplay between dynamics and energetics resulting in myriad microscopic pathways. Ultrafast kinetic methods turned the field upside down by providing the means to probe fundamental aspects of folding, test theoretical predictions and benchmark simulations. Accordingly, experimentalists could measure the timescales for all relevant folding motions, determine the folding speed limit and confirm that folding barriers are entropic bottlenecks. Moreover, a catalogue of proteins that fold extremely fast (microseconds) could be identified. Such fast-folding proteins cross shallow free energy barriers or fold downhill, and thus unfold with minimal co-operativity (gradually). A new generation of thermodynamic methods has exploited this property to map folding landscapes, interaction networks and mechanisms at nearly atomic resolution. In parallel, modern molecular dynamics simulations have finally reached the timescales required to watch fast-folding proteins fold and unfold in silico. All of these findings have buttressed the fundamentals of protein folding predicted by theory, and are now offering the first glimpses at the underlying mechanisms. Fast folding appears to also have functional implications as recent results connect downhill folding with intrinsically disordered proteins, their complex binding modes and ability to moonlight. These connections suggest that the coupling between downhill (un)folding and binding enables such protein domains to operate analogically as conformational rheostats.

Web-based computational chemistry education with CHARMMing II: Coarse-grained protein folding

A lesson utilizing a coarse-grained (CG) G-like model has been implemented into the CHARMM INterface and Graphics (CHARMMing) web portal (www.charmming.org) to the Chemistry at HARvard Macromolecular Mechanics (CHARMM) molecular simulation package. While widely used to model various biophysical processes, such as protein folding and aggregation, CG models can also serve as an educational tool because they can provide qualitative descriptions of complex biophysical phenomena for a relatively cheap computational cost. As a proof of concept, this lesson demonstrates the construction of a CG model of a small globular protein, its simulation via Langevin dynamics, and the analysis of the resulting data. This lesson makes connections between modern molecular simulation techniques and topics commonly presented in an advanced undergraduate lecture on physical chemistry. It culminates in a straightforward analysis of a short dynamics trajectory of a small fast folding globular protein; we briefly describe the thermodynamic properties that can be calculated from this analysis. The assumptions inherent in the model and the data analysis are laid out in a clear, concise manner, and the techniques used are consistent with those employed by specialists in the field of CG modeling. One of the major tasks in building the G-like model is determining the relative strength of the nonbonded interactions between coarse-grained sites. New functionality has been added to CHARMMing to facilitate this process. The implementation of these features into CHARMMing helps automate many of the tedious aspects of constructing a CG G model. The CG model builder and its accompanying lesson should be a valuable tool to chemistry students, teachers, and modelers in the field.

Microsecond folding experiments and simulations: a match is made

For the past two decades, protein folding experiments have been speeding up from the second or millisecond time scale to the microsecond time scale, and full-atom simulations have been extended from the nanosecond to the microsecond and even millisecond time scale. Where the two meet, it is now possible to compare results directly, allowing force fields to be validated and refined, and allowing experimental data to be interpreted in atomistic detail. In this perspective we compare recent experiments and simulations on the microsecond time scale, pointing out the progress that has been made in determining native structures from physics-based simulations, refining experiments and simulations to provide more quantitative underlying mechanisms, and tackling the problems of multiple reaction coordinates, downhill folding, and complex underlying structure of unfolded or misfolded states.

Using thioamides to site-specifically interrogate the dynamics of hydrogen bond formation in β-sheet folding

Thioamides are sterically almost identical to their oxoamide counterparts, but they are weaker hydrogen bond acceptors. Therefore, thioamide amino acids are excellent candidates for perturbing the energetics of backbone-backbone H-bonds in proteins and hence should be useful in elucidating protein folding mechanisms in a site-specific manner. Herein, we validate this approach by applying it to probe the dynamic role of interstrand H-bond formation in the folding kinetics of a well-studied β-hairpin, tryptophan zipper. Our results show that reducing the strength of the peptide's backbone-backbone H-bonds, except the one directly next to the β-turn, does not change the folding rate, suggesting that most native interstrand H-bonds in β-hairpins are formed only after the folding transition state.

An induced fit mechanism regulates p53 DNA binding kinetics to confer sequence specificity

The p53 tumour suppressor gene, the most frequently mutated gene in human cancer, encodes a transcription factor that contains sequence-specific DNA binding and homo-tetramerization domains. Interestingly, the affinities of p53 for specific and non-specific DNA sites differ by only one order of magnitude, making it hard to understand how this protein recognizes its specific DNA targets in vivo. We describe here the structure of a p53 polypeptide containing both the DNA binding and oligomerization domains in complex with DNA. The structure reveals that sequence-specific DNA binding proceeds via an induced fit mechanism that involves a conformational switch in loop L1 of the p53 DNA binding domain. Analysis of loop L1 mutants demonstrated that the conformational switch allows DNA binding off-rates to be regulated independently of affinities. These results may explain the universal prevalence of conformational switching in sequence-specific DNA binding proteins and suggest that proteins like p53 rely more on differences in binding off-rates, than on differences in affinities, to recognize their specific DNA sites.

Infrared study of the folding mechanism of a helical hairpin: porcine PYY

The helical hairpin motif plays a key role as a receptor site in DNA binding and protein-protein interactions. Thus, various helical hairpins have recently been developed to assess the factors that control the DNA and/or protein binding affinities of this structural motif and to form synthetic templates for protein and drug design. In addition, several lines of evidence suggest that rapid acquisition of a helical hairpin structure from the unfolded ensemble may guide the rapid formation of helical proteins. Despite its importance as a crucial structural element in protein folding and binding, the folding mechanism of the helical hairpin motif has not been thoroughly studied. Herein, we investigate the structural determinants of the folding kinetics of a naturally occurring helical hairpin (porcine PYY) that is free of disulfide bonds and metal ion-induced cross-links using an infrared temperature-jump technique. It is found that mutations in the turn region predominantly increase the barrier of folding irrespective of the temperature, whereas the effect of mutations that perturb the hydrophobic interactions between the two helices is temperature-dependent. At low temperatures, deletion of hydrophobic side chains is found to predominantly affect the unfolding rate, while the opposite is observed at high temperatures. These results are interpreted in terms of a folding mechanism in which the turn is formed in the transition state and also based on the assumption that cross-strand hydrophobic contacts exist in the thermally unfolded state of PYY.

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.

Folding simulations of a de novo designed protein with a betaalphabeta fold

betaalphabeta structural motifs are commonly used building blocks in protein structures containing parallel beta-sheets. However, to our knowledge, no stand-alone betaalphabeta structure has been observed in nature to date. Recently, for the first time that we know of, a small protein with an independent betaalphabeta structure (DS119) was successfully designed in our laboratory. To understand the folding mechanism of DS119, in the study described here, we carried out all-atom molecular dynamics and coarse-grained simulations to investigate its folding pathways and energy landscape. From all-atom simulations, we successfully observed the folding event and got a stable folded structure with a minimal root mean-square deviation of 2.6 A with respect to the NMR structure. The folding process can be described as a fast collapse phase followed by rapid formation of the central helix, and then slow formation of a parallel beta-sheet. By using a native-centric Gō-like model, the cooperativity of the system was characterized in terms of the calorimetric criterion, sigmoidal transitions, conformation distribution shifts, and free-energy profiles. DS119 was found to be an incipient downhill folder that folds more cooperatively than a downhill folder, but less cooperatively than a two-state folder. This may reflect the balance between the two structural elements of DS119: the rapidly formed alpha-helix and the slowly formed parallel beta-sheet. Folding times estimated from both the all-atom simulations and the coarse-grained model were at microsecond level, making DS119 another fast folder. Compared to fast folders reported previously, DS119 is, to the best of our knowledge, the first that exhibits a parallel beta-sheet.

Infrared signature and folding dynamics of a helical beta-peptide

Synthetic foldamers consisting of beta-amino acids offer excellent model systems for examining the effect of backbone flexibility on the dynamics of protein folding. Herein, we study the folding-unfolding kinetics of a beta-peptide that folds into a 14-helical structure in water. We find that the T-jump induced relaxation kinetics of this peptide occur on the nanosecond time scale and are noticeably slower than those of alanine-based alpha-helical peptides, and additionally, the relaxation rates show a weaker dependence on temperature. These differences appear to indicate that the folding energy landscapes of these peptides are different. In addition, we find that the amide I' band of this beta-peptide exhibits a sharp feature at approximately 1612 cm(-1), which we believe is a distinct infrared reporter of 14-helix.

Challenges in the computational design of proteins

Protein design has many applications not only in biotechnology but also in basic science. It uses our current knowledge in structural biology to predict, by computer simulations, an amino acid sequence that would produce a protein with targeted properties. As in other examples of synthetic biology, this approach allows the testing of many hypotheses in biology. The recent development of automated computational methods to design proteins has enabled proteins to be designed that are very different from any known ones. Moreover, some of those methods mostly rely on a physical description of atomic interactions, which allows the designed sequences not to be biased towards known proteins. In this paper, we will describe the use of energy functions in computational protein design, the use of atomic models to evaluate the free energy in the unfolded and folded states, the exploration and optimization of amino acid sequences, the problem of negative design and the design of biomolecular function. We will also consider its use together with the experimental techniques such as directed evolution. We will end by discussing the challenges ahead in computational protein design and some of their future applications.

Characterization of the cofactor-induced folding mechanism of a zinc-binding peptide using computationally designed mutants

Metals are the most commonly encountered protein cofactors, and they play important structural and functional roles in biology. In many cases, metal binding provides a major driving force for a polypeptide chain to fold. While there are many studies on the structure, stability, and function of metal-binding proteins, there are few studies focusing on understanding the kinetic mechanism of metal-induced folding. Herein, the Zn(2+)-induced folding kinetics of a small zinc-binding protein are studied; the CH1(1) peptide is derived from the first cysteine/histidine-rich region (CH1 domain) of the protein interaction domains of the transcriptional coregulator CREB-binding protein. Computational design is used to introduce tryptophan and histidine mutations that are structurally consistent with CH1(1); these mutants are studied using stopped-flow tryptophan fluorescence experiments. The Zn(2+)-induced CH1(1) folding kinetics are consistent with two parallel pathways, where the initial binding of Zn(2+) occurs at two sites. However, the initially formed Zn(2+)-bound complexes can proceed either directly to the folded state where zinc adopts a tetrahedral coordination or to an off-pathway misligated intermediate. While elimination of those ligands responsible for misligation simplifies the folding kinetics, it also leads to a decrease in the zinc binding constant. Therefore, these results suggest why these nonnative zinc ligands in the CH1(1) motif are conserved in several distantly related organisms and why the requirement for function can lead to kinetic frustration in folding. In addition, the loop closure rate of the CH1(1) peptide is determined based on the proposed model and temperature-dependent kinetic measurements.

Probing possible downhill folding: native contact topology likely places a significant constraint on the folding cooperativity of proteins with approximately 40 residues

Experiments point to appreciable variations in folding cooperativity among natural proteins with approximately 40 residues, indicating that the behaviors of these proteins are valuable for delineating the contributing factors to cooperative folding. To explore the role of native topology in a protein's propensity to fold cooperatively and how native topology might constrain the degree of cooperativity achievable by a given set of physical interactions, we compared folding/unfolding kinetics simulated using three classes of native-centric C(alpha) chain models with different interaction schemes. The approach was applied to two homologous 45-residue fragments from the peripheral subunit-binding domain family and a 39-residue fragment of the N-terminal domain of ribosomal protein L9. Free-energy profiles as functions of native contact number were computed to assess the heights of thermodynamic barriers to folding. In addition, chevron plots of folding/unfolding rates were constructed as functions of native stability to facilitate comparison with available experimental data. Although common Gō-like models with pairwise Lennard-Jones-type interactions generally fold less cooperatively than real proteins, the rank ordering of cooperativity predicted by these models is consistent with experiment for the proteins investigated, showing increasing folding cooperativity with increasing nonlocality of a protein's native contacts. Models that account for water-expulsion (desolvation) barriers and models with many-body (nonadditive) interactions generally entail higher degrees of folding cooperativity indicated by more linear model chevron plots, but the rank ordering of cooperativity remains unchanged. A robust, experimentally valid rank ordering of model folding cooperativity independent of the multiple native-centric interaction schemes tested here argues that native topology places significant constraints on how cooperatively a protein can fold.

Heterogeneity even at the speed limit of folding: large-scale molecular dynamics study of a fast-folding variant of the villin headpiece

We have performed molecular dynamics simulations on a set of nine unfolded conformations of the fastest-folding protein yet discovered, a variant of the villin headpiece subdomain (HP-35 NleNle). The simulations were generated using a new distributed computing method, yielding hundreds of trajectories each on a time scale comparable to the experimental folding time, despite the large (10,000 atom) size of the simulation system. This strategy eliminates the need to assume a two-state kinetic model or to build a Markov state model. The relaxation to the folded state at 300 K from the unfolded configurations (generated by simulation at 373 K) was monitored by a method intended to reflect the experimental observable (quenching of tryptophan by histidine). We also monitored the relaxation to the native state by directly comparing structural snapshots with the native state. The rate of relaxation to the native state and the number of resolvable kinetic time scales both depend upon starting structure. Moreover, starting structures with folding rates most similar to experiment show some native-like structure in the N-terminal helix (helix 1) and the phenylalanine residues constituting the hydrophobic core, suggesting that these elements may exist in the experimentally relevant unfolded state. Our large-scale simulation data reveal kinetic complexity not resolved in the experimental data. Based on these findings, we propose additional experiments to further probe the kinetics of villin folding.

The effect of charge-charge interactions on the kinetics of alpha-helix formation

The formation of the monomeric alpha-helix represents one of the simplest scenarios in protein folding; however, our current understanding of the folding dynamics of the alpha-helix motif is mainly based on studies of alanine-rich model peptides. To examine the effect of peptide sequence on the folding kinetics of alpha-helices, we studied the relaxation kinetics of a 21-residue helical peptide, Conantokin-T (Con-T), using time-resolved infrared spectroscopy in conjunction with a laser-induced temperature jump technique. Con-T is a neuroactive peptide containing a large number of charged residues that is found in the venom of the piscivorous cone snail Conus tulipa . The temperature-jump relaxation kinetics of Con-T is distinctly slower than that of previously studied alanine-based peptides, suggesting that the folding time of alpha-helices is sequence-dependent. Furthermore, it appears that the slower folding of Con-T can be attributed to the fact that its helical conformation is stabilized by charge-charge interactions or salt bridges. Although this finding contradicts an earlier molecular dynamics simulation, it also has implications for existing models of protein folding.

Statistical theory for protein ensembles with designed energy landscapes

Combinatorial protein libraries provide a promising route to investigate the determinants and features of protein folding and to identify novel folding amino acid sequences. A library of sequences based on a pool of different monomer types are screened for folding molecules, consistent with a particular foldability criterion. The number of sequences grows exponentially with the length of the polymer, making both experimental and computational tabulations of sequences infeasible. Herein a statistical theory is extended to specify the properties of sequences having particular values of global energetic quantities that specify their energy landscape. The theory yields the site-specific monomer probabilities. A foldability criterion is derived that characterizes the properties of sequences by quantifying the energetic separation of the target state from low-energy states in the unfolded ensemble and the fluctuations of the energies in the unfolded state ensemble. For a simple lattice model of proteins, excellent agreement is observed between the theory and the results of exact enumeration. The theory may be used to provide a quantitative framework for the design and interpretation of combinatorial experiments.

Fluorescence correlation spectroscopic study of serpin depolymerization by computationally designed peptides

Members of the serine proteinase inhibitor (serpin) family play important roles in the inflammatory and coagulation cascades. Interaction of a serpin with its target proteinase induces a large conformational change, resulting in insertion of its reactive center loop (RCL) into the main body of the protein as a new strand within beta-sheet A. Intermolecular insertion of the RCL of one serpin molecule into the beta-sheet A of another leads to polymerization, a widespread phenomenon associated with a general class of diseases known as serpinopathies. Small peptides are known to modulate the polymerization process by binding within beta-sheet A. Here, we use fluorescence correlation spectroscopy (FCS) to probe the mechanism of peptide modulation of alpha(1)-antitrypsin (alpha(1)-AT) polymerization and depolymerization, and employ a statistical computationally-assisted design strategy (SCADS) to identify new tetrapeptides that modulate polymerization. Our results demonstrate that peptide-induced depolymerization takes place via a heterogeneous, multi-step process that begins with internal fragmentation of the polymer chain. One of the designed tetrapeptides is the most potent antitrypsin depolymerizer yet found.

Computational protein design: structure, function and combinatorial diversity

Computational protein design has blossomed with the development of methods for addressing the complexities involved in specifying the structure, sequence and function of proteins. Recent applications include the design of novel functional membrane and soluble proteins, proteins incorporating non-biological components and protein combinatorial libraries.

Infrared Study of the Effect of Hydration on the Amide I Band and Aggregation Properties of Helical Peptides

The amide I' band of a polypeptide is sensitive not only to its secondary structure content but also to its environment. In this study we show how degrees of hydration affect the underlying spectral features of the amide I' band of two alanine-based helical peptides. This is achieved by solubilizing these peptides in the water pool of sodium bis(2-ethylhexyl)sulfosuccinate reverse micelles with different water contents or w0 values. In agreement with several earlier studies, our results show that the amide I' band arising from a group of dehydrated helical amides is centered at approximately 1650 cm-1, whereas hydration shifts this frequency toward lower wavenumbers. More importantly, temperature-dependent infrared studies further show that these helical peptides undergo a thermally induced conformational transition in reverse micelles of low w0 values (e.g., w0=6), resulting in soluble peptide aggregates rich in antiparallel beta-sheets. Interestingly, however, increasing w0 or water content leads to an increase in the onset temperature at which such beta-aggregates begin to form. Therefore, these results provide strong evidence suggesting that dehydration facilitates aggregate formation and that removal of water imposes a free energy barrier to peptide association and aggregation, a feature that has been suggested in recent simulation studies focusing on the mechanism of beta-amyloid formation.

Probing the folding intermediate of Rd-apocyt b562 by protein engineering and infrared T-jump

Small proteins often fold in an apparent two-state manner with the absence of detectable early-folding intermediates. Recently, using native-state hydrogen exchange, intermediates that exist after the rate-limiting transition state have been identified for several proteins. However, little is known about the folding kinetics from these post-transition intermediates to their corresponding native states. Herein, we have used protein engineering and a laser-induced temperature-jump (T-jump) technique to investigate this issue and have applied it to Rd-apocyt b(562) , a four-helix bundle protein. Previously, it has been shown that Rd-apocyt b(562) folds via an on-pathway hidden intermediate, which has only the N-terminal helix unfolded. In the present study, a double mutation (V16G/I17A) in the N-terminal helix of Rd-apocyt b(562) was made to further increase the relative population of this intermediate state at high temperature by selectively destabilizing the native state. In the circular dichroism thermal melting experiment, this mutant showed apparent two-state folding behavior. However, in the T-jump experiment, two kinetic phases were observed. Therefore, these results are in agreement with the idea that a folding intermediate is populated on the folding pathway of Rd-apocyt b(562) . Moreover, it was found that the exponential growth rate of the native state from this intermediate state is roughly (25 microsec)(-1) at 65 degrees C.

Ab initio folding of albumin binding domain from all-atom molecular dynamics simulation

Ab initio folding with all-atom model remains to be a difficult task even for small proteins. In this report, we conducted an accumulated 24 mus simulations on the wild type and two mutants of albumin binding domain (ABD) using the AMBER FF03 all-atom force field and a generalized-Born solvation model. Folding events have been observed in multiple trajectories, and the best folded structures achieved root-mean-square deviation (RMSD) of 2.0 A. The folding of this three-helix bundle protein followed a diffusion-collision process, where substantial formation of the individual helices was critical and preceded the global packing. Owing to the difference in the intrinsic helicity, helix I formed faster than the other two helices. The order of the formation of helices II and III varied in different trajectories, indicating heterogeneity of the folding process. The slightly shifted boundaries of the helical segments had direct impact on the global packing, suggesting room for improvement on the simulation force field and solvation model.

Tuning lambda6-85 towards downhill folding at its melting temperature

The five-helix bundle lambda6-85* is a fast two-state folder. Several stabilized mutants have been reported to fold kinetically near-downhill or downhill. These mutants undergo a transition to two-state folding kinetics when heated. It has been suggested that this transition is caused by increased hydrophobicity at higher temperature. Here we investigate two histidine-containing mutants of lambda6-85* to see if a weaker hydrophobic core can extend the temperature range of downhill folding. The very stable lambdaHA is the fastest-folding lambda repressor to date (k(f)(-1) approximately k(obs)(-1)=2.3 micros at 44 degrees C). It folds downhill at low temperature, but transits back to two-state folding at its unfolding midpoint. lambdaHG has a weakened hydrophobic core. It is less stable than some slower folding mutants of lambda6-85*, and it has more exposed hydrophobic surface area in the folded state. This mutant nonetheless folds very rapidly, and has the non-exponential folding kinetics of an incipient downhill folder even at the unfolding midpoint (k(m)(-1) approximately 2 micros, k(a)(-1)=15 micros at 56 degrees C). We also compare the thermodynamic melting transition of lambdaHG with the nominal two-state folding mutant lambdaQG, which has a similar melting temperature. Unlike lambdaQG, lambdaHG yields fluorescence wavelength-dependent cooperativities and probe-dependent melting temperatures. This result combined with previous work shows that the energy landscapes of lambda repressor mutants support all standard folding mechanisms.

Ultrafast and downhill protein folding

Ultrafast folding proteins have served an important role in benchmarking molecular dynamics simulations and testing protein folding theories. These proteins are simple enough and fold fast enough that realistic simulations are possible, which facilitates the direct comparison of absolute folding rates and folding mechanisms with those observed experimentally. Such comparisons have achieved remarkable success, but have also revealed the shortcomings that remain in experiment, theory and simulation alike. Some ultrafast folding proteins may fold without encountering an activation barrier (downhill folding), allowing the exploration of the molecular timescale of folding and the roughness of the energy landscape. The biological significance of ultrafast folding remains uncertain, but its practical significance is crucial to progress in understanding how proteins fold.

Criteria for downhill protein folding: Calorimetry, chevron plot, kinetic relaxation, and single-molecule radius of gyration in chain models with subdued degrees of cooperativity

Recent investigations of possible downhill folding of small proteins such as BBL have focused on the thermodynamics of non-two-state, "barrierless" folding/denaturation transitions. Downhill folding is noncooperative and thermodynamically "one-state," a phenomenon underpinned by a unimodal conformational distribution over chain properties such as enthalpy, hydrophobic exposure, and conformational dimension. In contrast, corresponding distributions for cooperative two-state folding are bimodal with well-separated population peaks. Using simplified atomic modeling of a three-helix bundle-in a scheme that accounts for hydrophobic interactions and hydrogen bonding-and coarse-grained C(alpha) models of four real proteins with various degrees of cooperativity, we evaluate the effectiveness of several observables at defining the underlying distribution. Bimodal distributions generally lead to sharper transitions, with a higher heat capacity peak at the transition midpoint, compared with unimodal distributions. However, the observation of a sigmoidal transition is not a reliable criterion for two-state behavior, and the heat capacity baselines, used to determine the van't Hoff and calorimetric enthalpies of the transition, can introduce ambiguity. Interestingly we find that, if the distribution of the single-molecule radius of gyration were available, it would permit discrimination between unimodal and bimodal underlying distributions. We investigate kinetic implications of thermodynamic noncooperativity using Langevin dynamics. Despite substantial chevron rollovers, the relaxation of the models considered is essentially single-exponential over an extended range of native stabilities. Consistent with experiments, significant deviations from single-exponential behavior occur only under strongly folding conditions.

Sub-microsecond protein folding

We have investigated the structure, equilibria, and folding kinetics of an engineered 35-residue subdomain of the chicken villin headpiece, an ultrafast-folding protein. Substitution of two buried lysine residues by norleucine residues stabilizes the protein by 1 kcal/mol and increases the folding rate sixfold, as measured by nanosecond laser T-jump. The folding rate at 300 K is (0.7 micros)(-1) with little or no temperature dependence, making this protein the first sub-microsecond folder, with a rate only twofold slower than the theoretically predicted speed limit. Using the 70 ns process to obtain the effective diffusion coefficient, the free energy barrier height is estimated from Kramers theory to be less than approximately 1 kcal/mol. X-ray crystallographic determination at 1A resolution shows no significant change in structure compared to the single-norleucine-substituted molecule and suggests that the increased stability is electrostatic in origin. The ultrafast folding rate, very accurate X-ray structure, and small size make this engineered villin subdomain an ideal system for simulation by atomistic molecular dynamics with explicit solvent.

Limitations of yeast surface display in engineering proteins of high thermostability

Engineering proteins that can fold to unique structures remains a challenge. Protein stability has previously been engineered via the observed correlation between thermal stability and eukaryotic secretion level. To explore the limits of an expression-based approach, variants of the highly thermostable three-helix bundle protein alpha3D were studied using yeast surface display. A library of alpha3D mutants was created to explore the possible correlation of protein stability and fold with expression level. Five efficiently expressed mutants were then purified and further studied biochemically. Despite their differences in stability, most mutants expressed at levels comparable with that of wild-type alpha3D. Two other related sequences (alpha3A and alpha3B) that form collapsed, stable molten globules but lack a uniquely folded structure were similarly expressed at high levels by yeast display. Together these observations suggest that the quality control system in yeast is unable to discriminate between well-folded proteins of high stability and molten globules. The present study, therefore, suggests that an optimization of the surface display efficiency on yeast may yield proteins that are thermally and chemically stable yet are poorly folded.

T-jump infrared study of the folding mechanism of coiled-coil GCN4-p1

Partially folded intermediates have been frequently observed in equilibrium and kinetic protein folding studies. However, folding intermediates that exist at the native side of the rate-limiting step are rather difficult to study because they often evade detection by conventional folding kinetic methods. Here, we demonstrated that a laser-induced temperature-jump method can potentially be used to identify the existence of such post-transition or hidden intermediates. Specifically, we studied two cross-linked variants of GCN4-p1 coiled-coil. The GCN4 leucine zipper has been studied extensively and most of these studies have regarded it as a two-state folder. Our static circular dichroism and infrared data also indicate that the thermal unfolding of these two monomeric coiled-coils can be adequately described by an apparent two-state model. However, their temperature-jump-induced relaxation kinetics exhibit non-monoexponential behavior, dependent upon sequence and temperature. Taken together, our results support a folding mechanism wherein at least one folding intermediate populates behind the main rate-limiting step.

High-resolution x-ray crystal structures of the villin headpiece subdomain, an ultrafast folding protein

The 35-residue subdomain of the villin headpiece (HP35) is a small ultrafast folding protein that is being intensely studied by experiments, theory, and simulations. We have solved the x-ray structures of HP35 and its fastest folding mutant [K24 norleucine (nL)] to atomic resolution and compared their experimentally measured folding kinetics by using laser temperature jump. The structures, which are in different space groups, are almost identical to each other but differ significantly from previously solved NMR structures. Hence, the differences between the x-ray and NMR structures are probably not caused by lattice contacts or crystal/solution differences, but reflect the higher accuracy of the x-ray structures. The x-ray structures reveal important details of packing of the hydrophobic core and some additional features, such as cross-helical H bonds. Comparison of the x-ray structures indicates that the nL substitution produces only local perturbations. Consequently, the finding that the small stabilization by the mutation is completely reflected in an increased folding rate suggests that this region of the protein is as structured in the transition state as in the folded structure. It is therefore a target for engineering to increase the folding rate of the subdomain from approximately 0.5 micros(-1) for the nL mutant to the estimated theoretical speed limit of approximately 3 micros(-1).

Advances in computational protein design

Computational protein design continues to experience a variety of methodological advances. Several improvements have been suggested for the objective functions used to quantify sequence/structure compatibility. Disparate design strategies based upon dead-end elimination, simulated annealing and statistical design have each recently yielded striking successes involving de novo designed proteins with sizes on the order of 100 residues or greater. Such methods may be used to design new proteins, as well as to redesign natural proteins to facilitate structural and biophysical studies.