Is protein folding rate dependent on number of folding stages? Modeling of protein folding with ferredoxin-like fold

Statistical analysis of protein folding rates has been done for 84 proteins with available experimental data. A surprising result is that the proteins with multi-state kinetics from the size range of 50–100 amino acid residues (a.a.) fold as fast as proteins with two-state kinetics from the same size range. At the same time, the proteins with two-state kinetics from the size range 101–151 a.a. fold faster than those from the size range 50–100 a.a. Moreover, it turns out unexpectedly that usually in the group of structural homologs from the size range 50–100 a.a., proteins with multi-state kinetics fold faster than those with two-state kinetics. The protein folding for six proteins with a ferredoxin-like fold and with a similar size has been modeled using Monte Carlo simulations and dynamic programming. Good correlation between experimental folding rates, some structural parameters, and the number of Monte Carlo steps has been obtained. It is shown that a protein with multi-state kinetics actually folds three times faster than its structural homologs.     

NMR and temperature-jump measurements of de novo designed proteins demonstrate rapid folding in the absence of explicit selection for kinetics

We address the importance of natural selection in the origin and maintenance of rapid protein folding by experimentally characterizing the folding kinetics of two de novo designed proteins, NC3-NCAP and ENH-FSM1. These 51 residue proteins, which adopt the helix-turn-helix homeodomain fold, share as few as 12 residues in common with their most closely related natural analog. Despite the replacement of up to 3/4 of their residues by a computer algorithm optimizing only thermodynamic properties, the designed proteins fold as fast or faster than the 35,000 s(-1) observed for the closest natural analog. Thus these de novo designed proteins, which were produced in the complete absence of selective pressures or design constraints explicitly aimed at ensuring rapid folding, are among the most rapidly folding proteins reported to date.     

Proteome Folding Kinetics Is Limited by Protein Halflife

How heterogeneous are proteome folding timescales and what physical principles, if any, dictate its limits? We answer this by predicting copy number weighted folding speed distribution – using the native topology – for E.coli and Yeast proteome. E.coli and Yeast proteomes yield very similar distributions with average folding times of 100 milliseconds and 170 milliseconds, respectively. The topology-based folding time distribution is well described by a diffusion-drift mutation model on a flat-fitness landscape in free energy barrier between two boundaries: i) the lowest barrier height determined by the upper limit of folding speed and ii) the highest barrier height governed by the lower speed limit of folding. While the fastest time scale of the distribution is near the experimentally measured speed limit of 1 microsecond (typical of barrier-less folders), we find the slowest folding time to be around seconds (8 seconds for Yeast distribution), approximately an order of magnitude less than the fastest halflife (approximately 2 minutes) in the Yeast proteome. This separation of timescale implies even the fastest degrading protein will have moderately high (96%) probability of folding before degradation. The overall agreement with the flat-fitness landscape model further hints that proteome folding times did not undergo additional major selection pressures – to make proteins fold faster – other than the primary requirement to “sufficiently beat the clock” against its lifetime. Direct comparison between the predicted folding time and experimentally measured halflife further shows 99% of the proteome have a folding time less than their corresponding lifetime. These two findings together suggest that proteome folding kinetics may be bounded by protein halflife.     

Engineering strand-specific DNA nicking enzymes from the type IIS restriction endonucleases BsaI, BsmBI, and BsmAI

To determine the extent to which protein folding rates and free energy landscapes have been shaped by natural selection, we have examined the folding kinetics of five proteins generated using computational design methods and, hence, never exposed to natural selection. Four of these proteins are complete computer-generated redesigns of naturally occurring structures and the fifth protein, called Top7, has a computer-generated fold not yet observed in nature. We find that three of the four redesigned proteins fold much faster than their naturally occurring counterparts. While natural selection thus does not appear to operate on protein folding rates, the majority of the designed proteins unfold considerably faster than their naturally occurring counterparts, suggesting possible selection for a high free energy barrier to unfolding. In contrast to almost all naturally occurring proteins of less than 100 residues but consistent with simple computational models, the folding energy landscape for Top7 appears to be quite complex, suggesting the smooth energy landscapes and highly cooperative folding transitions observed for small naturally occurring proteins may also reflect the workings of natural selection.     

Protein folding

The problem of protein folding is that how proteins acquire their native unique three‐dimensional structure in the physiological milieu. To solve the problem, the following key questions should be answered: do proteins fold co‐ or post‐translationally, i.e. during or after biosynthesis, what is the mechanism of protein folding, and what is the explanation for fast folding of proteins? The two first questions are discussed in the current review. The general lines are to show that the opinion, that proteins fold after they are synthesized is hardly substantiated and suitable for solving the problem of protein folding and why proteins should fold cotranslationally. A possible tentative model for the mechanism of protein folding is also suggested. To this end, a thorough analysis is made of the biosynthesis, delivery to the folding compartments, and the rates of the biosynthesis, translocation and folding of proteins. A cursory attention is assigned to the role of GroEL/ES‐like chaperonins in protein folding.     

Right‐ and left‐handed three‐helix proteins. I. Experimental and simulation analysis of differences in folding and structure

Despite the large number of publications on three‐helix protein folding, there is no study devoted to the influence of handedness on the rate of three‐helix protein folding. From the experimental studies, we make a conclusion that the left‐handed three‐helix proteins fold faster than the right‐handed ones. What may explain this difference? An important question arising in this paper is whether the modeling of protein folding can catch the difference between the protein folding rates of proteins with similar structures but with different folding mechanisms. To answer this question, the folding of eight three‐helix proteins (four right‐handed and four left‐handed), which are similar in size, was modeled using the Monte Carlo and dynamic programming methods. The studies allowed us to determine the orders of folding of the secondary‐structure elements in these domains and amino acid residues which are important for the folding. The obtained data are in good correlation with each other and with the experimental data. Structural analysis of these proteins demonstrated that the left‐handed domains have a lesser number of contacts per residue and a smaller radius of cross section than the right‐handed domains. This may be one of the explanations of the observed fact. The same tendency is observed for the large dataset consisting of 332 three‐helix proteins (238 right‐ and 94 left‐handed). From our analysis, we found that the left‐handed three‐helix proteins have some less‐dense packing that should result in faster folding for some proteins as compared to the case of right‐handed proteins.Proteins 2013; © 2013 Wiley Periodicals, Inc.     

First principles prediction of protein folding rates

Experimental studies have demonstrated that many small, single-domain proteins fold via simple two-state kinetics. We present a first principles approach for predicting these experimentally determined folding rates. Our approach is based on a nucleation-condensation folding mechanism, where the rate-limiting step is a random, diffusive search for the native tertiary topology. To estimate the rates of folding for various proteins via this mechanism, we first determine the probability of randomly sampling a conformation with the native fold topology. Next, we convert these probabilities into folding rates by estimating the rate that a protein samples different topologies during diffusive folding. This topology-sampling rate is calculated using the Einstein diffusion equation in conjunction with an experimentally determined intra-protein diffusion constant. We have applied our prediction method to the 21 topologically distinct small proteins for which two-state rate data is available. For the 18 beta-sheet and mixed alpha-beta native proteins, we predict folding rates within an average factor of 4, even though the experimental rates vary by a factor of approximately 4 x 10(4). Interestingly, the experimental folding rates for the three four-helix bundle proteins are significantly underestimated by this approach, suggesting that proteins with significant helical content may fold by a faster, alternative mechanism. This method can be applied to any protein for which the structure is known and hence can be used to predict the folding rates of many proteins prior to experiment.     

Optimal region of average side-chain entropy for fast protein folding

Search and study the general principles that govern kinetics and thermodynamics of protein folding generates new insight into the factors that control this process. Here, we demonstrate based on the known experimental data and using theoretical modeling of protein folding that side-chain entropy is one of the general determinants of protein folding. We show for proteins belonging to the same structural family that there exists an optimal relationship between the average side-chain entropy and the average number of contacts per residue for fast folding kinetics. Analysis of side-chain entropy for proteins that fold without additional agents demonstrates that there exists an optimal region of average side-chain entropy for fast folding. Deviation of the average side-chain entropy from the optimal region results in an anomalous protein folding process (prions, alpha-lytic protease, subtilisin, some DNA-binding proteins). Proteins with high or low side-chain entropy would have extended unfolded regions and would require some additional agents for complete folding. Such proteins are common in nature, and their structure properties have biological importance.     

Studies of Pseudomonas aeruginosa azurin mutants: cavities in beta-barrel do not affect refolding speed

Pseudomonas aeruginosa azurin is a blue-copper protein with a Greek-key fold. Removal of copper produces an apoprotein with the same structure as holoazurin. To address the effects on thermodynamic stability and folding dynamics caused by small cavities in a beta-barrel, we have studied the behavior of the apo-forms of wild-type and two mutant (His-46-Gly and His-117-Gly) azurins. The equilibrium- and kinetic-folding and unfolding reactions appear as two-state processes for all three proteins. The thermodynamic stability of the two mutants is significantly decreased as compared with the stability of wild-type azurin, in accord with cavities in or near the hydrophobic interior having an overall destabilizing effect. Large differences are also found in the unfolding rates: the mutants unfold much faster than wild-type azurin. In contrast, the folding-rate constants are almost identical for the three proteins and closely match the rate-constant predicted from the native-state topology of azurin. We conclude that the topology is more important than equilibrium stability in determining the folding speed of azurin.     

Slowing Bacterial Translation Speed Enhances Eukaryotic Protein Folding Efficiency

The mechanisms for de novo protein folding differ significantly between bacteria and eukaryotes, as evidenced by the often observed poor yields of native eukaryotic proteins upon recombinant production in bacterial systems. Polypeptide synthesis rates are faster in bacteria than in eukaryotes, but the effects of general variations in translation rates on protein folding efficiency have remained largely unexplored. By employing Escherichia coli cells with mutant ribosomes whose translation speed can be modulated, we show here that reducing polypeptide elongation rates leads to enhanced folding of diverse proteins of eukaryotic origin. These results suggest that in eukaryotes, protein folding necessitates slow translation rates. In contrast, folding in bacteria appears to be uncoupled from protein synthesis, explaining our findings that a generalized reduction in translation speed does not adversely impact the folding of the endogenous bacterial proteome. Utilization of this strategy has allowed the production of a native eukaryotic multidomain protein that has been previously unattainable in bacterial systems and may constitute a general alternative to the production of aggregation-prone recombinant proteins.     

How long does it take to equilibrate the unfolded state of a protein?

How long does it take to equilibrate the unfolded state of a protein? The answer to this question has important implications for our understanding of why many small proteins fold with two state kinetics. When the equilibration within the unfolded state U is much faster than the folding, the folding kinetics will be two state even if there are many folding pathways with different barriers. Yet the mean first passage times (MFPTs) between different regions of the unfolded state can be much longer than the folding time. This seems to imply that the equilibration within U is much slower than the folding. In this communication we resolve this paradox. We present a formula for estimating the time to equilibrate the unfolded state of a protein. We also present a formula for the MFPT to any state within U, which is proportional to the average lifetime of that state divided by the state population. This relation is valid when the equilibration within U is very fast as compared with folding as it often is for small proteins. To illustrate the concepts, we apply the formulas to estimate the time to equilibrate the unfolded state of Trp-cage and MFPTs within the unfolded state based on a Markov State Model using an ultra-long 208 microsecond trajectory of the miniprotein to parameterize the model. The time to equilibrate the unfolded state of Trp-cage is ∼100 ns while the typical MFPTs within U are tens of microseconds or longer.     

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.     

Influence of medium- and long-range interactions in different folding types of globular proteins

Recognition of protein fold from amino acid sequence is a challenging task. The structure and stability of proteins from different fold are mainly dictated by inter-residue interactions. In our earlier work, we have successfully used the medium- and long-range contacts for predicting the protein folding rates, discriminating globular and membrane proteins and for distinguishing protein structural classes. In this work, we analyze the role of inter-residue interactions in commonly occurring folds of globular proteins in order to understand their folding mechanisms. In the medium-range contacts, the globin fold and four-helical bundle proteins have more contacts than that of DNA-RNA fold although they all belong to all-alpha class. In long-range contacts, only the ribonuclease fold prefers 4-10 range and the other folding types prefer the range 21-30 in alpha/beta class proteins. Further, the preferred residues and residue pairs influenced by these different folds are discussed. The information about the preference of medium- and long-range contacts exhibited by the 20 amino acid residues can be effectively used to predict the folding type of each protein.     

Predicting protein folding rates from geometric contact and amino acid sequence

Protein folding speeds are known to vary over more than eight orders of magnitude. Plaxco, Simons, and Baker (see References) first showed a correlation of folding speed with the topology of the native protein. That and subsequent studies showed, if the native structure of a protein is known, its folding speed can be predicted reasonably well through a correlation with the "localness" of the contacts in the protein. In the present work, we develop a related measure, the geometric contact number, N (alpha), which is the number of nonlocal contacts that are well-packed, by a Voronoi criterion. We find, first, that in 80 proteins, the largest such database of proteins yet studied, N (alpha) is a consistently excellent predictor of folding speeds of both two-state fast folders and more complex multistate folders. Second, we show that folding rates can also be predicted from amino acid sequences directly, without the need to know the native topology or other structural properties.     

Understanding the Folding-Function Tradeoff in Proteins

When an amino-acid sequence cannot be optimized for both folding and function, folding can get compromised in favor of function. To understand this tradeoff better, we devise a novel method for extracting the “function-less” folding-motif of a protein fold from a set of structurally similar but functionally diverse proteins. We then obtain the β-trefoil folding-motif, and study its folding using structure-based models and molecular dynamics simulations. CompariA protein sequence serves two purpson with the folding of wild-type β-trefoil proteins shows that function affects folding in two ways: In the slower folding interleukin-1β, binding sites make the fold more complex, increase contact order and slow folding. In the faster folding hisactophilin, residues which could have been part of the folding-motif are used for function. This reduces the density of native contacts in functional regions and increases folding rate. The folding-motif helps identify subtle structural deviations which perturb folding. These may then be used for functional annotation. Further, the folding-motif could potentially be used as a first step in the sequence design of function-less scaffold proteins. Desired function can then be engineered into these scaffolds.     

Designing a High Throughput Refolding Array Using a Combination of the GroEL Chaperonin and Osmolytes

Although GroE chaperonins and osmolytes had been used separately as protein folding aids, combining these two methods provides a considerable advantage for folding proteins that cannot fold with either osmolytes or chaperonins alone. This technique rapidly identifies superior folding solution conditions for a broad array of proteins that are difficult or impossible to fold by other methods. While testing the broad applicability of this technique, we have discovered that osmolytes greatly simplify the chaperonin reaction by eliminating the requirement for the co-chaperonin GroES which is normally involved in encapsulating folding proteins within the GroEL–GroES cavity. Therefore, combinations of soluble or immobilized GroEL, osmolytes and ATP or even ADP are sufficient to refold the test proteins. The first step in the chaperonin/osmolyte process is to form a stable long-lived chaperonin–substrate protein complex in the absence of nucleotide. In the second step, different osmolyte solutions are added along with nucleotides, thus forming a ‘folding array’ to identify superior folding conditions. The stable chaperonin–substrate protein complex can be concentrated or immobilized prior to osmolyte addition. This procedure prevents-off pathway aggregation during folding/refolding reactions and more importantly allows one to refold proteins at concentrations (~mg/ml) that are substantially higher than the critical aggregation concentration for given protein. This technique can be used for successful refolding of proteins from purified inclusion bodies. Recently, other investigators have used our chaperonin/osmolyte method to demonstrate that a mutant protein that misfolds in human disease can be rescued by GroEL/osmolyte system. Soluble or immobilized GroEL can be easily removed from the released folded protein using simple separation techniques. The method allows for isolation of folded monomeric or oligomeric proteins in quantities sufficient for X-ray crystallography or NMR structural determinations.     

Computer-based redesign of a protein folding pathway.

A fundamental test of our current understanding of protein folding is to rationally redesign protein folding pathways. We use a computer-based design strategy to switch the folding pathway of protein G, which normally involves formation of the second, but not the first, beta-turn at the rate limiting step in folding. Backbone conformations and amino acid sequences that maximize the interaction density in the first beta-hairpin were identified, and two variants containing 11 amino acid replacements were found to be approximately 4 kcal mol-1 more stable than wild type protein G. Kinetic studies show that the redesigned proteins fold approximately 100 x faster than wild type protein and that the first beta-turn is formed and the second disrupted at the rate limiting step in folding.     

Positive selection dictates the choice between kinetic and thermodynamic protein folding and stability in subtilases

Subtilisin E (SbtE) is a member of the ubiquitous superfamily of serine proteases called subtilases and serves as a model for understanding propeptide-mediated protein folding mechanisms. Unlike most proteins that adopt thermodynamically stable conformations, the native state of SbtE is trapped into a kinetically stable conformation. While kinetic stability offers distinct functional advantages to the native state, the constraints that dictate the selection between kinetic and thermodynamic folding and stability remain unknown. Using highly conserved subtilases, we demonstrate that adaptive evolution of sequence dictates selection of folding pathways. Intracellular and extracellular serine proteases (ISPs and ESPs, respectively) constitute two subfamilies within the family of subtilases that have highly conserved sequences, structures, and catalytic activities. Our studies on the folding pathways of subtilisin E (SbtE), an ESP, and its homologue intracellular serine protease 1 (ISP1), an ISP, show that although topology, contact order, and hydrophobicity that drive protein folding reactions are conserved, ISP1 and SbtE fold through significantly different pathways and kinetics. While SbtE absolutely requires the propeptide to fold into a kinetically trapped conformer, ISP1 folds to a thermodynamically stable state more than 1 million times faster and independent of a propeptide. Furthermore, kinetics establish that ISP1 and SbtE fold through different intermediate states. An evolutionary analysis of folding constraints in subtilases suggests that observed differences in folding pathways may be mediated through positive selection of specific residues that map mostly onto the protein surface. Together, our results demonstrate that closely related subtilases can fold through distinct pathways and mechanisms, and suggest that fine sequence details can dictate the choice between kinetic and thermodynamic folding and stability.     

Exploring the complex folding kinetics of RNA hairpins: II. Effect of sequence, length, and misfolded states

The complexity of RNA hairpin folding arises from the interplay between the loop formation, the disruption of the slow-breaking misfolded states, and the formation of the slow-forming native base stacks. We investigate the general physical mechanism for the dependence of the RNA hairpin folding kinetics on the sequence and the length of the hairpin loop and the helix stem. For example, 1), the folding would slow down when a stable GC basepair moves to the middle of the stem; 2), hairpin with GC basepair near the loop would fold/unfold faster than the one with GC near the tail of the stem; 3), within a certain range of the stem length, a longer stem can cause faster folding; and 4), certain misfolded states can assist folding through the formation of scaffold structures to lower the entropic barrier for the folding. All our findings are directly applicable and quantitatively testable in experiments. In addition, our results can be useful for molecular design to achieve desirable fast/slow-folding hairpins, hairpins with/without specific misfolded intermediates, and hairpins that fold along designed pathways.