Role of unfolded state heterogeneity and en-route ruggedness in protein folding kinetics

Hysteretic Pressure Dependence of Ca2+ Binding in LH1 Bacterial Membrane Chromoproteins

Much of the thermodynamic parameter values that support life are set by the properties of proteins. While the denaturing effects of pressure and temperature on proteins are well documented, their precise structural nature is rarely revealed. This work investigates the destabilization of multiple Ca²⁺ binding sites in the cyclic LH1 light-harvesting membrane chromoprotein complexes from two Ca-containing sulfur purple bacteria by hydrostatic high-pressure perturbation spectroscopy. The native (Ca-saturated) and denatured (Ca-depleted) phases of these complexes are well distinguishable by much-shifted bacteriochlorophyll a exciton absorption bands serving as innate optical probes in this study. The pressure-induced denaturation of the complexes related to the failure of the protein Ca-binding pockets and the concomitant breakage of hydrogen bonds between the pigment chromophores and protein environment were found cooperative, involving all or most of the Ca²⁺ binding sites, but irreversible. The strong hysteresis observed in the spectral and kinetic characteristics of phase transitions along the compression and decompression pathways implies asymmetry in the relevant free energy landscapes and activation free energy distributions. A phase transition pressure equal to about 1.9 kbar was evaluated for the complexes from Thiorhodovibrio strain 970 from the pressure dependence of biphasic kinetics observed in the minutes to 100 h time range.

Protein folding in vitro and in the cell: From a solitary journey to a team effort

Correct protein folding is essential for the health and function of living organisms. Yet, it is not well understood how unfolded proteins reach their native state and avoid aggregation, especially within the cellular milieu. Some proteins, especially small, single-domain and apparent two-state folders, successfully attain their native state upon dilution from denaturant. Yet, many more proteins undergo misfolding and aggregation during this process, in a concentration-dependent fashion. Once formed, native and aggregated states are often kinetically trapped relative to each other. Hence, the early stages of protein life are absolutely critical for proper kinetic channeling to the folded state and for long-term solubility and function. This review summarizes current knowledge on protein folding/aggregation mechanisms in buffered solution and within the bacterial cell, highlighting early stages. Remarkably, teamwork between nascent chain, ribosome, trigger factor and Hsp70 molecular chaperones enables all proteins to overcome aggregation propensities and reach a long-lived bioactive state.

Heterogeneity in Protein Folding and Unfolding Reactions

Proteins have dynamic structures that undergo chain motions on time scales spanning from picoseconds to seconds. Resolving the resultant conformational heterogeneity is essential for gaining accurate insight into fundamental mechanistic aspects of the protein folding reaction. The use of high-resolution structural probes, sensitive to population distributions, has begun to enable the resolution of site-specific conformational heterogeneity at different stages of the folding reaction. Different states populated during protein folding, including the unfolded state, collapsed intermediate states, and even the native state, are found to possess significant conformational heterogeneity. Heterogeneity in protein folding and unfolding reactions originates from the reduced cooperativity of various kinds of physicochemical interactions between various structural elements of a protein, and between a protein and solvent. Heterogeneity may arise because of functional or evolutionary constraints. Conformational substates within the unfolded state and the collapsed intermediates that exchange at rates slower than the subsequent folding steps give rise to heterogeneity on the protein folding pathways. Multiple folding pathways are likely to represent distinct sequences of structure formation. Insight into the nature of the energy barriers separating different conformational states populated during (un)folding can also be obtained by resolving heterogeneity.

Mapping Distinct Sequences of Structure Formation Differentiating Multiple Folding Pathways of a Small Protein

To determine experimentally how the multiple folding pathways of a protein differ, in the order in which the structural parts are assembled, has been a long-standing challenge. To resolve whether structure formation during folding can progress in multiple ways, the complex folding landscape of monellin has been characterized, structurally and temporally, using the multisite time-resolved FRET methodology. After an initial heterogeneous polypeptide chain collapse, structure formation proceeds on parallel pathways. Kinetic analysis of the population evolution data across various protein segments provides a clear structural distinction between the parallel pathways. The analysis leads to a phenomenological model that describes how and when discrete segments acquire structure independently of each other in different subensembles of protein molecules. When averaged over all molecules, structure formation is seen to progress as α-helix formation, followed by core consolidation, then β-sheet formation, and last end-to-end distance compaction. Parts of the protein that are closer in the primary sequence acquire structure before parts separated by longer sequence.

Protein folding from heterogeneous unfolded state revealed by time-resolved X-ray solution scattering

One of the most challenging tasks in biological science is to understand how a protein folds. In theoretical studies, the hypothesis adopting a funnel-like free-energy landscape has been recognized as a prominent scheme for explaining protein folding in views of both internal energy and conformational heterogeneity of a protein. Despite numerous experimental efforts, however, comprehensively studying protein folding with respect to its global conformational changes in conjunction with the heterogeneity has been elusive. Here we investigate the redox-coupled folding dynamics of equine heart cytochrome c (cyt-c) induced by external electron injection by using time-resolved X-ray solution scattering. A systematic kinetic analysis unveils a kinetic model for its folding with a stretched exponential behavior during the transition toward the folded state. With the aid of the ensemble optimization method combined with molecular dynamics simulations, we found that during the folding the heterogeneously populated ensemble of the unfolded state is converted to a narrowly populated ensemble of folded conformations. These observations obtained from the kinetic and the structural analyses of X-ray scattering data reveal that the folding dynamics of cyt-c accompanies many parallel pathways associated with the heterogeneously populated ensemble of unfolded conformations, resulting in the stretched exponential kinetics at room temperature. This finding provides direct evidence with a view to microscopic protein conformations that the cyt-c folding initiates from a highly heterogeneous unfolded state, passes through still diverse intermediate structures, and reaches structural homogeneity by arriving at the folded state.

Homodimeric Escherichia coli Toxin CcdB (Controller of Cell Division or Death B Protein) Folds via Parallel Pathways

The existence of parallel pathways in the folding of proteins seems intuitive, yet remains controversial. We explore the folding kinetics of the homodimeric Escherichia coli toxin CcdB (Controller of Cell Division or Death B protein) using multiple optical probes and approaches. Kinetic studies performed as a function of protein and denaturant concentrations demonstrate that the folding of CcdB is a four-state process. The two intermediates populated during folding are present on parallel pathways. Both form by rapid association of the monomers in a diffusion limited manner and appear to be largely unstructured, as they are silent to the optical probes employed in the current study. The existence of parallel pathways is supported by the insensitivity of the amplitudes of the refolding kinetic phases to the different probes used in the study. More importantly, interrupted refolding studies and ligand binding studies clearly demonstrate that the native state forms in a biexponential manner, implying the presence of at least two pathways. Our studies indicate that the CcdA antitoxin binds only to the folded CcdB dimer and not to any earlier folding intermediates. Thus, despite being part of the same operon, the antitoxin does not appear to modulate the folding pathway of the toxin encoded by the downstream cistron. This study highlights the utility of ligand binding in distinguishing between sequential and parallel pathways in protein folding studies, while also providing insights into molecular interactions during folding in Type II toxin-antitoxin systems.

First Passage Times, Lifetimes, and Relaxation Times of Unfolded Proteins

The dynamics of proteins in the unfolded state can be quantified in computer simulations by calculating a spectrum of relaxation times which describes the time scales over which the population fluctuations decay to equilibrium. If the unfolded state space is discretized, we can evaluate the relaxation time of each state. We derive a simple relation that shows the mean first passage time to any state is equal to the relaxation time of that state divided by the equilibrium population. This explains why mean first passage times from state to state within the unfolded ensemble can be very long but the energy landscape can still be smooth (minimally frustrated). In fact, when the folding kinetics is two-state, all of the unfolded state relaxation times within the unfolded free energy basin are faster than the folding time. This result supports the well-established funnel energy landscape picture and resolves an apparent contradiction between this model and the recently proposed kinetic hub model of protein folding. We validate these concepts by analyzing a Markov state model of the kinetics in the unfolded state and folding of the miniprotein NTL9 (where NTL9 is the N-terminal domain of the ribosomal protein L9), constructed from a 2.9 ms simulation provided by D. E. Shaw Research.

Assessment of local friction in protein folding dynamics using a helix cross-linker

Internal friction arising from local steric hindrance and/or the excluded volume effect plays an important role in controlling not only the dynamics of protein folding but also conformational transitions occurring within the native state potential well. However, experimental assessment of such local friction is difficult because it does not manifest itself as an independent experimental observable. Herein, we demonstrate, using the miniprotein trp-cage as a testbed, that it is possible to selectively increase the local mass density in a protein and hence the magnitude of local friction, thus making its effect directly measurable via folding kinetic studies. Specifically, we show that when a helix cross-linker, m-xylene, is placed near the most congested region of the trp-cage it leads to a significant decrease in both the folding rate (by a factor of 3.8) and unfolding rate (by a factor of 2.5 at 35 °C) but has little effect on protein stability. Thus, these results, in conjunction with those obtained with another cross-linked trp-cage and two uncross-linked variants, demonstrate the feasibility of using a nonperturbing cross-linker to help quantify the effect of internal friction. In addition, we estimate that a m-xylene cross-linker could lead to an increase in the roughness of the folding energy landscape by as much as 0.4-1.0k(B)T.

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.

How kinetics within the unfolded state affects protein folding: an analysis based on markov state models and an ultra-long MD trajectory

Understanding how kinetics in the unfolded state affects protein folding is a fundamentally important yet less well-understood issue. Here we employ three different models to analyze the unfolded landscape and folding kinetics of the miniprotein Trp-cage. The first is a 208 μs explicit solvent molecular dynamics (MD) simulation from D. E. Shaw Research containing tens of folding events. The second is a Markov state model (MSM-MD) constructed from the same ultralong MD simulation; MSM-MD can be used to generate thousands of folding events. The third is a Markov state model built from temperature replica exchange MD simulations in implicit solvent (MSM-REMD). All the models exhibit multiple folding pathways, and there is a good correspondence between the folding pathways from direct MD and those computed from the MSMs. The unfolded populations interconvert rapidly between extended and collapsed conformations on time scales ≤40 ns, compared with the folding time of ∼5 μs. The folding rates are independent of where the folding is initiated from within the unfolded ensemble. About 90% of the unfolded states are sampled within the first 40 μs of the ultralong MD trajectory, which on average explores ∼27% of the unfolded state ensemble between consecutive folding events. We clustered the folding pathways according to structural similarity into "tubes", and kinetically partitioned the unfolded state into populations that fold along different tubes. From our analysis of the simulations and a simple kinetic model, we find that, when the mixing within the unfolded state is comparable to or faster than folding, the folding waiting times for all the folding tubes are similar and the folding kinetics is essentially single exponential despite the presence of heterogeneous folding paths with nonuniform barriers. When the mixing is much slower than folding, different unfolded populations fold independently, leading to nonexponential kinetics. A kinetic partition of the Trp-cage unfolded state is constructed which reveals that different unfolded populations have almost the same probability to fold along any of the multiple folding paths. We are investigating whether the results for the kinetics in the unfolded state of the 20-residue Trp-cage is representative of larger single domain proteins.

Using the unfolded state as the reference state improves the performance of statistical potentials

Distance-dependent statistical potentials are an important class of energy functions extensively used in modeling protein structures and energetics. These potentials are obtained by statistically analyzing the proximity of atoms in all combinatorial amino-acid pairs in proteins with known structures. In model evaluation, the statistical potential is usually subtracted by the value of a reference state for better selectivity. An ideal reference state should include the general chemical properties of polypeptide chains so that only the unique factors stabilizing the native structures are retained after calibrating on reference state. However, reference states available as of this writing rarely model specific chemical constraints of peptide bonds and therefore poorly reflect the behavior of polypeptide chains. In this work, we proposed a statistical potential based on unfolded state ensemble (SPOUSE), where the reference state is summarized from the unfolded state ensembles of proteins produced according to the statistical coil model. Due to its better representation of the features of polypeptides, SPOUSE outperforms three of the most widely used distance-dependent potentials not only in native conformation identification, but also in the selection of close-to-native models and correlation coefficients between energy and model error. Furthermore, SPOUSE shows promising possibility of further improvement by integration with the orientation-dependent side-chain potentials.

Protein folding at the exit tunnel

Over five decades of research have yielded a large body of information on how purified proteins attain their native state when refolded in the test tube, starting from a chemically or thermally denatured state. Nevertheless, we still know little about how proteins fold and unfold in their natural biological habitat: the living cell. Indeed, a variety of cellular components, including molecular chaperones, the ribosome, and crowding of the intracellular medium, modulate folding mechanisms in physiologically relevant environments. This review focuses on the current state of knowledge in protein folding in the cell with emphasis on the early stage of a protein's life, as the nascent polypeptide traverses and emerges from the ribosomal tunnel. Given the vectorial nature of ribosome-assisted translation, the transient degree of chain elongation becomes a relevant variable expected to affect nascent protein foldability, aggregation propensity and extent of interaction with chaperones and the ribosome.

Extremely slow intramolecular diffusion in unfolded protein L

A crucial parameter in many theories of protein folding is the rate of diffusion over the energy landscape. Using a microfluidic mixer we have observed the rate of intramolecular diffusion within the unfolded B1 domain of protein L before it folds. The diffusion-limited rate of intramolecular contact is about 20 times slower than the rate in 6 M GdnHCl, and because in these conditions the protein is also more compact, the intramolecular diffusion coefficient decreases 100-500 times. The dramatic slowdown in diffusion occurs within the 250 micros mixing time of the mixer, and there appears to be no further evolution of this rate before reaching the transition state of folding. We show that observed folding rates are well predicted by a Kramers model with a denaturant-dependent diffusion coefficient and speculate that this diffusion coefficient is a significant contribution to the observed rate of folding.

Multiple routes and structural heterogeneity in protein folding

Experimental studies show that many proteins fold along sequential pathways defined by folding intermediates. An intermediate may not always be a single population of molecules but may consist of subpopulations that differ in their average structure. These subpopulations are likely to fold via independent pathways. Parallel folding and unfolding pathways appear to arise because of structural heterogeneity. For some proteins, the folding pathways can effectively switch either because different subpopulations of an intermediate get populated under different folding conditions, or because intermediates on otherwise hidden pathways get stabilized, leading to their utilization becoming discernible, or because mutations stabilize different substructures. Therefore, the same protein may fold via different pathways in different folding conditions. Multiple folding pathways make folding robust, and evolution is likely to have selected for this robustness to ensure that a protein will fold under the varying conditions prevalent in different cellular contexts.

Barrierless evolution of structure during the submillisecond refolding reaction of a small protein

To determine whether a protein folding reaction can occur in the absence of a dominant barrier is crucial for understanding its complexity. Here direct ultrafast kinetic measurements have been used to study the initial submillisecond (sub-ms) folding reaction of the small protein barstar. The cooperativity of the initial folding reaction has been explored by using two probes: fluorescence resonance energy transfer, through which the contraction of two intramolecular distances is measured, and the binding of 8-anilino-1-naphthalene sulfonic acid, through which the formation of hydrophobic clusters is monitored. A fast chain contraction is shown to precede the formation of hydrophobic clusters, indicating that the sub-ms folding reaction is not cooperative. The observed rate constant of the sub-ms folding reaction monitored by 8-anilino-1-naphthalene sulfonic acid fluorescence has been found to be the same in stabilizing conditions (low urea concentrations), in which specific structure is formed, and in marginally stabilizing conditions (higher urea concentrations), where virtually no structure is formed in the product of the sub-ms folding reaction. The observation that the folding rate is independent of the folding conditions suggests that the initial folding reaction occurs in the absence of a dominant free energy barrier. These results provide kinetic evidence that the formation of specific structure need not be slowed down by any significant free energy barrier during the course of a very fast protein folding reaction.

The protein folding problem

The "protein folding problem" consists of three closely related puzzles: (a) What is the folding code? (b) What is the folding mechanism? (c) Can we predict the native structure of a protein from its amino acid sequence? Once regarded as a grand challenge, protein folding has seen great progress in recent years. Now, foldable proteins and nonbiological polymers are being designed routinely and moving toward successful applications. The structures of small proteins are now often well predicted by computer methods. And, there is now a testable explanation for how a protein can fold so quickly: A protein solves its large global optimization problem as a series of smaller local optimization problems, growing and assembling the native structure from peptide fragments, local structures first.

Thermodynamic and kinetic characterization of apoHmpH, a fast-folding bacterial globin

Despite the widespread presence of the globin fold in most living organisms, only eukaryotic globins have been employed as model proteins in folding/stability studies so far. This work introduces the first thermodynamic and kinetic characterization of a prokaryotic globin, that is, the apo form of the heme-binding domain of flavohemoglobin (apoHmpH) from Escherichia coli. This bacterial globin has a widely different sequence but nearly identical structure to its eukaryotic analogues. We show that apoHmpH is a well-folded monomeric protein with moderate stability at room temperature [apparent Delta G degrees (UN(w))=-3.1+/-0.3 kcal mol(-1); m(UN)=-1.7 kcal mol(-1) M(-1)] and predominant alpha-helical structure. Remarkably, apoHmpH is the fastest-folding globin known to date, as it refolds about 4- to 16-fold more rapidly than its eukaryotic analogues (e.g., sperm whale apomyoglobin and soybean apoleghemoglobin), populating a compact kinetic intermediate (beta(I)=0.9+/-0.2) with significant helical content. Additionally, the single Trp120 (located in the native H helix) becomes locked into a fully native-like environment within 6 ms, suggesting that this residue and its closest spatial neighbors complete their folding at ultrafast (submillisecond) speed. In summary, apoHmpH is a bacterial globin that shares the general folding scheme (i.e., a rapid burst phase followed by slower rate-determining phases) of its eukaryotic analogues but displays an overall faster folding and a kinetic intermediate with some fully native-like traits. This study supports the view that the general folding features of bacterial and eukaryotic globins are preserved through evolution while kinetic details differ.

The Ultimate Speed Limit to Protein Folding Is Conformational Searching

More than a dozen proteins are known to be ultrafast folders. In addition to being fast, their kinetics is unusual. Like traditional rate processes, fast folding proteins have activation barriers at low temperatures, but unlike traditional processes, they have negative activation energies at high temperatures. We develop a model of ultrafast folders that joins a macroscopic mass-action model with a microscopic energy landscape description; we call it the Thruway Search Model. We find good agreement with experimental rates and equilibria on 13 ultrafast folders. The observed folding rates are found to be proportional to the number of microscopic folding routes: fast-folding proteins have more parallel microscopic routes on energy landscapes. At high temperatures, where traditional barriers are small, the remaining bottleneck is a search through denatured conformations to find thruway routes to the native state. Negative activation arises because increasing temperature expands the denatured ensemble, broadening the search, slowing the folding to the native state. We find that the upper estimate of the free energy barriers are positive but small, as little as 0.5 kT.

Folding and assembly of co-chaperonin heptamer probed by forster resonance energy transfer

The ring-shaped heptameric co-chaperonin protein 10 (cpn10) is one of few oligomeric beta-sheet proteins that unfold and disassemble reversibly in vitro. Here, we labeled human mitochondrial cpn10 with donor and acceptor dyes to obtain FRET signals. Cpn10 mixed in a 1:1:5 ratio of donor:acceptor:unlabeled monomers form heptamers that are active in an in vitro functional assay. Monomer-monomer affinity, as well as thermal and chemical stability, of the labeled cpn10 is similar to the unlabeled protein, demonstrating that the labels do not perturb the system. Using changes in FRET, we then probed for the first time cpn10 heptamer-monomer assembly/disassembly kinetics. Heptamer dissociation is very slow (1/k(diss) approximately 3h; 20 degrees C, pH 7) corresponding to an activation energy of approximately 50kJ/mol. Ring-ring mixing experiments reveal that cpn10 heptamer dissociation is rate limiting; subsequent associations events are faster. Kinetic inertness explains how cpn10 cycles on and off cpn60 as an intact heptamer in vivo.

Site-specific collapse dynamics guide the formation of the cytochrome c' four-helix bundle

The evolution of tryptophan-to-heme (W/heme) distance distributions extracted from analysis of fluorescence energy transfer kinetics during the refolding of Rhodopseudomonas palustris cytochrome c' reveals dramatic differences between two variants [W32 (Q1A/F32W/W72F) and W72 (Q1A)]. Both W32/heme and W72/heme distance distributions measured at the earliest time point attainable with a continuous-flow mixer (150 mus) confirm that the polypeptide ensemble is not uniformly collapsed and that native structure is not formed. Time-resolved fluorescence spectra indicate that W32 is sequestered from the aqueous solution during the first 700 mus of folding, whereas W72 remains exposed to solvent. The first moment of the W32/heme distance distribution evolves to its native value faster than that of W72, suggesting that the approach of W32 to the heme precedes that of W72.

Kinetic Folding and Assembly Mechanisms Differ for Two Homologous Heptamers

Here we investigate the time-resolved folding and assembly mechanism of the heptameric co-chaperonin protein 10 (cpn10) in vitro. The structure of cpn10 is conserved throughout nature: seven beta-barrel subunits are non-covalently assembled through beta-strand pairings in an overall doughnut-like shape. Kinetic folding/assembly experiments of chemically denatured cpn10 from Homo sapiens (hmcpn10) and Aquifex aeolicus (Aacpn10) were monitored by far-UV circular dichroism and fluorescence. We find the processes to be complex, involving several kinetic steps, and to differ between the mesophilic and hyper-thermophilic proteins. The hmcpn10 molecules partition into two parallel pathways, one involving polypeptide folding before protein-protein assembly and another in which inter-protein interactions take place prior to folding. In contrast, the Aacpn10 molecules follow a single sequential path that includes initial monomer misfolding, relaxation to productive intermediates and, subsequently, final folding and heptamer assembly. An A. aeolicus variant lacking the unique C-terminal extension of Aacpn10 displays the same kinetic mechanism as Aacpn10, signifying that the tail is not responsible for the rapid misfolding step. This study demonstrates that molecular details can overrule similarity of native-state topology in defining apparent protein-biophysical properties.

Specificity of the initial collapse in the folding of the cold shock protein

The two-state folding reaction of the cold shock protein from Bacillus caldolyticus (Bc-Csp) is preceded by a rapid chain collapse. A fast shortening of intra-protein distances was revealed by Förster resonance energy transfer (FRET) measurements with protein variants that carried individual pairs of donor and acceptor chromophores at various positions along the polypeptide chain. Here we investigated the specificity of this rapid compaction. Energy transfer experiments that probed the stretching of strand beta2 and the close approach between the strands beta1 and beta2 revealed that the beta1-beta2 hairpin is barely formed in the collapsed form, although it is native-like in the folding transition state of Bc-Csp. The time course of the collapse could not be resolved by pressure or temperature jump experiments, indicating that the collapsed and extended forms are not separated by an energy barrier. The co-solute (NH4)2SO4 stabilizes both native Bc-Csp and the collapsed form, which suggests that the large hydrated SO4(2-) ions are excluded from the surface of the collapsed form in a similar fashion as they are excluded from folded Bc-Csp. Ethylene glycol increases the stability of proteins because it is excluded preferentially from the backbone, which is accessible in the unfolded state. The collapsed form of Bc-Csp resembles the unfolded form in its interaction with ethylene glycol, suggesting that in the collapsed form the backbone is still accessible to water and small molecules. Our results thus rule out that the collapsed form is a folding intermediate with native-like chain topology. It is better described as a mixture of compact conformations that belong to the unfolded state ensemble. However, some of its structural elements are reminiscent of the native protein.