Folding Speed Research Articles

The folding pathway of an engineered circularly permuted PDZ domain

To understand the role of sequence connectivity in the folding pathway of a multi-state protein, we have analysed the folding kinetics of an engineered circularly permuted PDZ domain. This variant has been designed with the specific aim of posing two of the strands participating in the stabilisation of an early folding nucleus as contiguous elements in the primary structure. Folding of the circularly permuted PDZ2 has been explored by a variety of different experimental approaches including stopped-flow and continuous-flow kinetics, as well as ligand-induced folding experiments. Data reveal that although circular permutation introduces a significant destabilisation of the native state, a folding intermediate is stabilised and accumulated prior folding. Furthermore, quantitative analysis of the observed kinetics indicates an acceleration of the early folding events by more than two orders of magnitude. The results support the importance of sequence connectivity both in the mechanism and the speed of protein folding.

Tertiary Interactions Determine the Accuracy of RNA Folding

RNAs must fold into unique three-dimensional structures to function in the cell, but how each polynucleotide finds its native structure is not understood. To investigate whether the stability of the tertiary structure determines the speed and accuracy of RNA folding, docking of a tetraloop with its receptor in a bacterial group I ribozyme was perturbed by site-directed mutagenesis. Disruption of the tetraloop or its receptor destabilizes tertiary interactions throughout the ribozyme by 2-3 kcal/mol, demonstrating that tertiary interactions form cooperatively in the transition from a native-like intermediate to the native state. Nondenaturing PAGE and RNase T1 digestion showed that base pairs form less homogeneously in the mutant RNAs during the transition from the unfolded state to the intermediate. Thus, tertiary interactions between helices bias the ensemble of secondary structures toward native-like conformations. Time-resolved hydroxyl radical footprinting showed that the wild-type ribozyme folds completely within 5-20 ms. By contrast, only 40-60% of a tetraloop mutant ribozyme folds in 30-40 ms, with the remainder folding in 30-200 s via nonnative intermediates. Therefore, destabilization of tetraloop-receptor docking introduces an alternate folding pathway in the otherwise smooth energy landscape of the wild-type ribozyme. Our results show that stable tertiary structure increases the flux through folding pathways that lead directly and rapidly to the native structure.

Suppressor Mutations in the Transmembrane Segments of P-glycoprotein Promote Maturation of Processing Mutants and Disrupt a Subset of Drug-binding Sites

Defective folding of cystic fibrosis transmembrane conductance regulator protein missing Phe508 (DeltaF508) is the major cause of cystic fibrosis. The folding defect in DeltaF508 cystic fibrosis transmembrane conductance regulator might be correctable because misfolding of a P-glycoprotein (P-gp; ABCB1) mutant lacking the equivalent residue (DeltaY490) could be corrected with drug substrates or by introduction of an arginine residue into transmembrane (TM) segments 5 (I306R) or 6 (F343R). Possible mechanisms of arginine rescue were that they mimicked some of the effects of drug substrate interactions with P-gp or that they affected global folding such that all drug substrate/modulator interactions with P-gp were altered. To distinguish between these mechanisms, we tested whether arginines introduced into other TMs predicted to line the drug-binding pocket (TM1 or TM3) would affect folding. It was found that mutation of L65R(TM1) or T199R(TM3) promoted maturation of processing mutants. We then tested whether arginine suppressor mutations had local or global effects on P-gp interactions with drug substrates and modulators. The L65R(TM1), T199R(TM3), I306R(TM5), or F343R(TM6) mutations were introduced into the P-gp mutant L339C(TM6)/F728C(TM7), and thiol cross-linking was carried out in the presence of various concentrations of vinblastine, cyclosporin A, or rhodamine B. The presence of arginine residues reduced the apparent affinity of P-gp for vinblastine (L65R, T199R, and I306R), cyclosporin (I306R and F343R), or rhodamine B (F343R) by 4-60-fold. These results show that the arginine mutations affect a subset of drug-binding sites and suggest that they rescue processing mutants by mimicking drug substrate interactions with P-gp.

Mutational robustness and geometrical form in protein structures

Theoretical studies of RNA and lattice protein models suggest that mutationally robust or the so-called designable phenotypes tend to have special geometric features such as being more compact and more geometrically regular. Such geometrical forms have been also linked to speed of folding and stability properties that may also assist in promoting mutational robustness. Here we test these theoretical predictions on a non-redundant collection of 2,660 experimentally determined structures from the PDB (Protein Data Bank) and CATH (Class Architecture Topology Homologous superfamily) database. We first developed an index summarizing the geometrical regularity of the structures and then used this index to show that the statistical pattern of empirical data is consistent with the theoretical predictions relating geometry to mutational robustness. Mutationally robust proteins tend to be more symmetric and compact. But, the relationship between compactness and robustness cannot be explained simply by the geometrical packing of individual amino acids in proteins; rather, it is the property of the whole system that is related to the statistical characteristics of the folding landscape. Finally, we hypothesize that a triplet relationship between mutational robustness, stability and form is a general properties of objects that optimize real-valued relationships between sequences and discrete structures.

Protein folding kinetics: barrier effects in chemical and thermal denaturation experiments.

Recent experimental work on fast protein folding brings about an intriguing paradox. Microsecond-folding proteins are supposed to fold near or at the folding speed limit (downhill folding), but yet their folding behavior seems to comply with classical two-state analyses, which imply the crossing of high free energy barriers. However, close inspection of chemical and thermal denaturation kinetic experiments in fast-folding proteins reveals systematic deviations from two-state behavior. Using a simple one-dimensional free energy surface approach we find that such deviations are indeed diagnostic of marginal folding barriers. Furthermore, the quantitative analysis of available fast-kinetic data indicates that many microsecond-folding proteins fold downhill in native conditions. All of these proteins are then promising candidates for an atom-by-atom analysis of protein folding using nuclear magnetic resonance.1 We also find that the diffusion coefficient for protein folding is strongly temperature dependent, corresponding to an activation energy of approximately 1 kJ.mol-1 per protein residue. As a consequence, the folding speed limit at room temperature is about an order of magnitude slower than the approximately 1 micros estimates from high-temperature T-jump experiments. Our analysis is quantitatively consistent with the available thermodynamic and kinetic data on slow two-state folding proteins and provides a straightforward explanation for the apparent fast-folding paradox.

Kinetics of Internal-Loop Formation in Polypeptide Chains: A Simulation Study

The speed of simple diffusional motions, such as the formation of loops in the polypeptide chain, places one physical limit on the speed of protein folding. Many experimental studies have explored the kinetics of formation of end-to-end loops in polypeptide chains; however, protein folding more often requires the formation of contacts between interior points on the chain. One expects that, for loops of fixed contour length, interior loops will form more slowly than end-to-end loops, owing to the additional excluded volume associated with the “tails”. We estimate the magnitude of this effect by generating ensembles of randomly coiled, freely jointed chains, and then using the theory of Szabo, Schulten, and Schulten to calculate the corresponding contact formation rates for these ensembles. Adding just a few residues, to convert an end-to-end loop to an internal loop, sharply decreases the contact rate. Surprisingly, the relative change in rate increases for a longer loop; sufficiently long tails, however, actually reverse the effect and accelerate loop formation slightly. Our results show that excluded volume effects in real, full-length polypeptides may cause the rates of loop formation during folding to depart significantly from the values derived from recent loop-formation experiments on short peptides.

Conformational Equilibration Time of Unfolded Protein Chains and the Folding Speed Limit

The speed with which the conformers of unfolded protein chains interconvert is a fundamental question in the study of protein folding. Kinetic evidence is presented here for the time constant for interconversion of disparate unfolded chain conformations of a small globular protein, cytochrome c, in the presence of guanidine hydrochloride denaturant. The axial binding reactions of histidine and methionine residues with the Fe(II) heme cofactor were monitored with time-resolved magnetic circular dichroism spectroscopy after photodissociation of the CO complexes of unfolded protein obtained from horse and tuna and from several histidine mutants of the horse protein. A kinetic model fitting both the reaction rate constants and spectra of the intermediates was used to obtain a quantitative estimate of the conformational diffusion time. The latter parameter was approximated as a first-order time constant for exchange between conformational subensembles presenting either a methionine or a histidine residue to the heme iron for facile binding. The mean diffusional time constant of the wild type and variants was 3 +/- 2 mus, close to the folding "speed limit". The implications of the relatively rapid conformational equilibration time observed are discussed in terms of the energy landscape and classical pathway time regimes of folding, for which the conformational diffusion time can be considered a pivot point.

Watching hydrogen-bond dynamics in a β-turn by transient two-dimensional infrared spectroscopy

X-ray crystallography and nuclear magnetic resonance measurements provide us with atomically resolved structures of an ever-growing number of biomolecules. These static structural snapshots are important to our understanding of biomolecular function, but real biomolecules are dynamic entities that often exploit conformational changes and transient molecular interactions to perform their tasks. Nuclear magnetic resonance methods can follow such structural changes, but only on millisecond timescales under non-equilibrium conditions. Time-resolved X-ray crystallography has recently been used to monitor the photodissociation of CO from myoglobin on a subnanosecond timescale, yet remains challenging to apply more widely. In contrast, two-dimensional infrared spectroscopy, which maps vibrational coupling between molecular groups and hence their relative positions and orientations, is now routinely used to study equilibrium processes on picosecond timescales. Here we show that the extension of this method into the non-equilibrium regime allows us to observe in real time in a short peptide the weakening of an intramolecular hydrogen bond and concomitant opening of a beta-turn. We find that the rate of this process is two orders of magnitude faster than the 'folding speed limit' established for contact formation between protein side chains.

Correlation between Protein Stability Cores and Protein Folding Kinetics: A Case Study on Pseudomonas aeruginosa Apo-Azurin

This paper reports a combined computational and experimental study of the correlation between protein stability cores and folding kinetics. An empirical potential function was developed, and it was used for analyzing interaction energies among secondary structure elements. Studies on a beta sandwich protein, Pseudomonas aeruginosa azurin, showed that the computationally identified substructure with the strongest interactions in the native state is identical to the "interlocked pair" of beta strands, an invariant motif found in most sandwich-like proteins. Moreover, previous and new in vitro folding results revealed that the identified substructure harbors most residues that form native-like interactions in the folding transition state. These observations demonstrate that the potential function is effective in revealing the relative strength of interactions among various protein parts; they also strengthen the suggestion that the most stable regions in native proteins favor stable interactions early during folding.

Structural Features of the GroEL-GroES Nano-Cage Required for Rapid Folding of Encapsulated Protein

GroEL and GroES form a chaperonin nano-cage for proteins up to approximately 60 kDa to fold in isolation. Here we explored the structural features of the chaperonin cage critical for rapid folding of encapsulated substrates. Modulating the volume of the GroEL central cavity affected folding speed in accordance with confinement theory. Small proteins (approximately 30 kDa) folded more rapidly as the size of the cage was gradually reduced to a point where restriction in space slowed folding dramatically. For larger proteins (approximately 40-50 kDa), either expanding or reducing cage volume decelerated folding. Additionally, interactions with the C-terminal, mildly hydrophobic Gly-Gly-Met repeat sequences of GroEL protruding into the cavity, and repulsion effects from the negatively charged cavity wall were required for rapid folding of some proteins. We suggest that by combining these features, the chaperonin cage provides a physical environment optimized to catalyze the structural annealing of proteins with kinetically complex folding pathways.

Computational design of proteins stereochemically optimized in size, stability, and folding speed

Artificial proteins potentially barrier-free in the folding kinetics are approached computationally under the guidance of protein-folding theories. The smallest and fastest folding globular protein triple-helix-bundle (THB) is so modified as to minimize or eliminate its presumed barriers in folding speed. As the barriers may reside in the ordering of either secondary or tertiary structure, the elements of both secondary and tertiary structure in the protein are targeted for prenucleation with suitable stereochemically constrained amino acid residues. The required elements of topology and sequence for the THB are optimized independently; first the topology is optimized with simulated annealing in polypeptides of highly simplified alphabet; next, the sequence in side chains is optimized using the standard inverse design methods. The resultant three best-adapted THBs, variable in topology and distinctive in sequences, are assessed by comparing them with a few benchmark proteins. The results of mainly molecular dynamics (MD) comparisons, undertaken in explicit water at different temperatures, show that the designed sequences are favorably placed against the chosen benchmarks as THB proteins potentially thermostable in the native folds. Folding simulation experiments with MD establish that the designed sequences are rapid in the folding of individual helices, but not in the evolution of tertiary structure; energetic cum topological frustrations remain but could be the artifacts of the starting conformations that were chosen in the THBs in the folding simulations. Overall, a practical high-throughput approach for de novo protein design has been developed that may have fruitful application for any type of tertiary structure.

Hairpin folding rates reflect mutations within and remote from the turn region

Hairpins play a central role in numerous protein folding and misfolding scenarios. Prior studies of hairpin folding, many conducted with analogs of a sequence from the B1 domain of protein G, suggest that faster folding can be achieved only by optimizing the turn propensity of the reversing loop. Based on studies using dynamic NMR, the native GB1 sequence is a slow folding hairpin (k(F)(278)=1.5 x 10(4)/s). GB1 hairpin analogs spanning a wide range of thermodynamic stabilities (DeltaG(U)(298)=-3.09 to+3.25 kJ/mol) were examined. Fold-stabilizing changes in the reversing loop can act either by accelerating folding or retarding unfolding; we present examples of both types. The introduction of an attractive side-chain/side-chain Coulombic interaction at the chain termini further stabilizes this hairpin. The 1.9-fold increase in folding rate constant observed for this change at the chain termini implies that this Coulombic interaction contributes before or at the transition state. This observation is difficult to rationalize by "zipper" folding pathways that require native turn formation as the sole nucleating event; it also suggests that Coulombic interactions should be considered in the design of systems intended to probe the protein folding speed limit.

Engineering a β-Sheet Protein toward the Folding Speed Limit

Recent experimental studies have shown that alpha-helical proteins can approach the folding "speed limit", where folding switches from an activated to a downhill process in free energy. beta-sheet proteins are generally thought to fold more slowly than helix bundles. However, based on studies of hairpins, folding should still be able to approach the microsecond time scale. Here we demonstrate how the hPin1 WW domain, a triple-stranded beta-sheet protein with a sharp thermodynamic melting transition, can be engineered toward the folding "speed limit" without a significant loss in thermal denaturation cooperativity.

Internal friction in the ultrafast folding of the tryptophan cage

Protein folding is a diffusional process, and the speed of folding is controlled by the frictional forces that act on the polypeptide chain. Several previous studies have suggested that the bulk viscosity of the solvent is the only important source of friction in folding reactions. By contrast, our studies of the folding dynamics of the Tryptophan Cage, a small, ultrafast-folding protein, show clear evidence for additional frictional forces that are independent of the solvent viscosity. The nature of this internal friction appears qualitatively different for the folding vs. unfolding reactions. We expect that this phenomenon could significantly influence the rate of many folding processes that proceed on sufficiently fast (∼μs) time scales. In particular, it may limit folding speeds to values substantially slower than the diffusion limits estimated from simple contact-formation studies in polypeptides.

Diffusional limits to the speed of protein folding: fact or friction?

Proteins fold by diffusional motion, driven by molecular collisions but limited byfrictional drag. We then expect that the timescale of simple diffusional motionsof the polypeptide chain defines the minimum time, or the maximum rate, forfolding phenomena in general. However, such ‘speed limits’ are very rapid. Theyfar exceed the rate of folding that is observed in even the fastest-folding smallproteins. Why do proteins fold much more slowly than the diffusional limits predict?We present experimental evidence that, in addition to solvent friction, internaldissipative forces within a protein can slow the dynamics. These internal frictionforces may ultimately set a much more restrictive limit on the speed of folding.

Fold-Speed Control in Collapsing Mixed Phospholipid Monolayers

Mixed monolayers of dipalmitoylphosphatidylcholine (DPPC) and dipalmitoyl-phosphatidylserine are compressed beyond their collapse pressure. Primary and secondary folds that grow perpendicular to the compression direction are observed using Brewster angle microscopy. The secondary fold velocity is measured with a fast charge-coupled device camera. We observe a reduction in secondary fold speed when increasing the mole fraction of the softer DPPC component in the monolayer. The fracture kinetics follows theoretical predictions for the fold coarsening dynamics of uniaxially stressed three-dimensional systems.

How Do Cofactors Modulate Protein Folding?

Cofactors are essential components of many proteins for biological activity. Characterization of several cofactor-binding proteins has shown that cofactors often have the ability to interact specifically with the unfolded polypeptides. This suggests that cofactor-coordination prior to polypeptide folding may be a relevant path in vivo. By binding before folding, the cofactor may affect both the mechanism and speed of folding. Here, we discuss three different cofactors that modulate protein-folding processes in vitro.

Comprehensive Analysis of Protein Folding Activation Thermodynamics Reveals a Universal Behavior Violated by Kinetically Stable Proteases

Alpha-lytic protease (alpha LP) and Streptomyces griseus protease B (SGPB) are two extracellular serine proteases whose folding is absolutely dependent on the existence of their companion pro regions. Moreover, the native states of these proteins are, at best, marginally stable, with the apparent stability resulting from being kinetically trapped in the native state by large barriers to unfolding. Here, in an effort to understand the physical properties that distinguish kinetically and thermodynamically stable proteins, we study the temperature-dependences of the folding and unfolding kinetics of alpha LP and SGPB without their pro regions, and compare their behavior to a comprehensive set of other proteins. For the folding activation thermodynamics, we find some remarkable universal behaviors in the thermodynamically stable proteins that are violated dramatically by alpha LP. Despite significant variations in deltaC(P,F)++, the maximal folding speed occurs within the narrow biological temperature range for all proteins, except for alpha LP, with its maximal folding speed shifted lower by 200 K. This implies evolutionary pressures on folding speed for typical proteins, but not for alpha LP. In addition, the folding free energy barrier in the biological temperature range for most proteins is predominantly enthalpic, but purely entropic for alpha LP. The unfolding of alpha LP and SGPB is distinguished by three properties: a remarkably large deltaC(P,U)++, a very high deltaG(U)++, and a maximum deltaG(u)++ at the optimal growth temperature for the organism. While other proteins display each of these traits to some approximation, the simultaneous optimization of all three occurs only in the kinetically stable proteins, and appears to be required to maximize their unfolding cooperativity, by suppressing local unfolding events, and slowing the rate of global unfolding. Together, these properties extend the lifetime of these enzymes in the highly proteolytic extracellular environment. Attaining such functional properties seems possible only through the gross perturbation of the folding thermodynamics, which in turn has required the co-evolution of pro regions as folding catalysts.

Protein folding stabilizing time measurement: A direct folding process and three-dimensional random walk simulation

Protein particles undergo Brownian motion and collisions in solution. The diffusive collisions may lead to aggregation. For proteins to fold successfully the process has to occur quickly and before significant collision takes place. The speed of protein folding was deduced by studying the correlation time of a lysozyme refolding process from autocorrelation function analysis of the mean collision time and aggregation/soluble ratio of protein. It is a measure of time before which an aggregate can be formed and also is the time measure for a protein to fold into a stable state. We report on the protein folding stabilizing time of a lysozyme system to be 25.5–27.5 μs (<±4%) between 295 and 279 K via direct folding experimental studies, supported by a three-dimensional random walk simulation of diffusion-limited aggregation model. Aggregation is suppressed when the protein is folded to a stable form. Spontaneous folding and diffusion-limited aggregation are antagonistic in nature. Meanwhile, the resultant aggresome, suggested by Raman and mass spectroscopy, may be formed by cross-linkages of disulfide bonds and hydrophobic interactions.

Internal friction controls the speed of protein folding from a compact configuration.

Several studies have found millisecond protein folding reactions to be controlled by the viscosity of the solvent: Reducing the viscosity allows folding to accelerate. In the limit of very low solvent viscosity, however, one expects a different behavior. Internal interactions, occurring within the solvent-excluded interior of a compact molecule, should impose a solvent-independent upper limit to folding speed once the bulk diffusional motions become sufficiently rapid. Why has this not been observed? We have studied the effect of solvent viscosity on the folding of cytochrome c from a highly compact, late-stage intermediate configuration. Although the folding rate accelerates as the viscosity declines, it tends toward a finite limiting value approximately 10(5) s(-1) as the viscosity tends toward zero. This limiting rate is independent of the cosolutes used to adjust solvent friction. Therefore, interactions within the interior of a compact denatured polypeptide can limit the folding rate, but the limiting time scale is very fast. It is only observable when the solvent-controlled stages of folding are exceedingly rapid or else absent. Interestingly, we find a very strong temperature dependence in these "internal friction"-controlled dynamics, indicating a large energy scale for the interactions that govern reconfiguration within compact, near-native states of a protein.