Probing the kinetics of single molecule protein folding

We propose an approach to integrate the theory, simulations, and experiments in protein-folding kinetics. This is realized by measuring the mean and high-order moments of the first-passage time and its associated distribution. The full kinetics is revealed in the current theoretical framework through these measurements. In the experiments, information about the statistical properties of first-passage times can be obtained from the kinetic folding trajectories of single molecule experiments (for example, fluorescence). Theoretical/simulation and experimental approaches can be directly related. We study in particular the temperature-varying kinetics to probe the underlying structure of the folding energy landscape. At high temperatures, exponential kinetics is observed; there are multiple parallel kinetic paths leading to the native state. At intermediate temperatures, nonexponential kinetics appears, revealing the nature of the distribution of local traps on the landscape and, as a result, discrete kinetic paths emerge. At very low temperatures, exponential kinetics is again observed; the dynamics on the underlying landscape is dominated by a single barrier. The ratio between first-passage-time moments is proposed to be a good variable to quantitatively probe these kinetic changes. The temperature-dependent kinetics is consistent with the strange kinetics found in folding dynamics experiments. The potential applications of the current results to single-molecule protein folding are discussed.     

Temperature-dependent folding pathways of Pin1 WW domain: an all-atom molecular dynamics simulation of a Gō model

We study the folding thermodynamics and kinetics of the Pin1 WW domain, a three-stranded beta-sheet protein, by using all-atom (except nonpolar hydrogens) discontinuous molecular dynamics simulations at various temperatures with a Gō model. The protein exhibits a two-state folding kinetics near the folding transition temperature. A good agreement between our simulations and the experimental measurements by the Gruebele group has been found, and the simulation sheds new insights into the structure of transition state, which is hard to be straightforwardly captured in experiments. The simulation also reveals that the folding pathways at approximately the transition temperature and at low temperatures are much different, and an intermediate state at a low temperature is predicted. The transition state of this small beta-protein at its folding transition temperature has a well-established hairpin 1 made of beta1 and beta2 strands while its low-temperature kinetic intermediate has a formed hairpin 2 composed of beta2 and beta3 strands. Theoretical results are compared with other simulation results as well as available experimental data. This study confirms that specific side-chain packing in an all-atom Gō model can yield a reasonable prediction of specific folding kinetics for a given protein. Different folding behaviors at different temperatures are interpreted in terms of the interplay of entropy and enthalpy in folding process.     

A Survey of λ Repressor Fragments from Two-State to Downhill Folding

We survey the two-state to downhill folding transition by examining 20 λ_6-85^? mutants that cover a wide range of stabilities and folding rates. We investigated four new λ_6-85^? mutants designed to fold especially rapidly. Two were engineered using the core remodeling of Lim and Sauer, and two were engineered using Ferreiro et al.'s frustratometer. These proteins have probe-dependent melting temperatures as high as 80 °C and exhibit a fast molecular phase with the characteristic temperature dependence of the amplitude expected for downhill folding. The survey reveals a correlation between melting temperature and downhill folding previously observed for the β-sheet protein WW domain. A simple model explains this correlation and predicts the melting temperature at which downhill folding becomes possible. An X-ray crystal structure with a 1.64-Å resolution of a fast-folding mutant fragment shows regions of enhanced rigidity compared to the full wild-type protein.     

The complex kinetics of protein folding in wide temperature ranges

The complex protein folding kinetics in wide temperature ranges is studied through diffusive dynamics on the underlying energy landscape. The well-known kinetic chevron rollover behavior is recovered from the mean first passage time, with the U-shape dependence on temperature. The fastest folding temperature T0 is found to be smaller than the folding transition temperature Tf. We found that the fluctuations of the kinetics through the distribution of first passage time show rather universal behavior, from high-temperature exponential Poissonian kinetics to the relatively low-temperature highly non-exponential kinetics. The transition temperature is at Tk and T0 < Tk < Tf. In certain low-temperature regimes, a power law behavior at long time emerges. At very low temperatures (lower than trapping transition temperature T < T0/(4 approximately 6)), the kinetics is an exponential Poissonian process again.     

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.     

Multiple folding mechanisms of protein ubiquitin

Based on the C(alpha) Go-type model, the folding kinetics and mechanisms of protein ubiquitin with mixed alpha/beta topology are studied by molecular dynamics simulations. The relaxation kinetics shows that there are three phases, namely the major phase, the intermediate phase and the slowest minor phase. The existence of these three phases are relevant to the phenomenon found in experiments. According to our simulations, the folding at high temperatures around the folding transition temperature T(f) is of a two-state process, and the folding nucleus is consisted of contacts between the front end of alpha-helix and the turn(4). The folding at low temperature (approximately T = 0.8) is also studied, where an A-state like structure is found lying on the major folding pathway. The appearance of this structure is related to the stability of the first part (residue 1-51) of protein ubiquitin. As the temperature decreases, the formation of secondary structures, tertiary structures and collapse of the protein are found to be decoupled gradually and the folding mechanism changes from the nucleation-condensation to the diffusion-collision. This feature indicates a unifying common folding mechanism for proteins. The intermediate phase is also studied and is found to represent a folding process via a long-lived intermediate state which is stabilized by strong interactions between the beta(1) and the beta(5) strand. These strong interactions are important for the function of protein ubiquitin as a molecular chaperone. Thus the intermediate phase is assumed as a byproduct of the requirement of protein function. In addition, the validity of the current Go-model is also investigated, and a lower limited temperature for protein ubiquitin T(limit) = 0.8 is proposed. At temperatures higher than this value, the kinetic traps due to glass dynamics cannot be significantly populated and the intermediate states can be reliably identified although there is slight chevron rollover in the folding rates. At temperature lower than T(limit), however, the traps due to glass dynamics become dominant and may be mistaken for real intermediate states. This limitation of valid temperature range prevents us to reveal the burst phase intermediate in the major folding phase since it might only be stabilized at temperatures lower than T(limit), according to experiments. Our works show that caution must be taken when studying low-temperature intermediate states by using the C(alpha) Go-models.     

Probe-dependent and nonexponential relaxation kinetics: unreliable signatures of downhill protein folding

The theoretical suggestion that some proteins may encounter no significant free energy barriers during their folding raises an important question: What experimental signature does this downhill folding produce? Several authors have argued that nonexponential (and especially stretched exponential) or probe‐dependent kinetics represent useful experimental signatures of a downhill free energy surface. Here we examine more closely the connection between unusual kinetics and downhill energy surfaces. Simulation of diffusive relaxation dynamics on a variety of generically downhill, two‐dimensional free energy surfaces shows that these surfaces do not necessarily produce either probe‐dependent or significantly nonexponential kinetics. Conversely, we find that two‐dimensional surfaces with significant (>3k_B T) energy barriers can readily give rise to nonexponential and probe‐dependent kinetics. These results show that downhill folding does not constitute a necessary or sufficient condition for nonexponential and/or probe‐dependent folding kinetics. One cannot easily prove or disprove that a protein folds downhill simply by studying its relaxation kinetics. Proteins 2007. © 2007 Wiley‐Liss, Inc.     

Cooperativity and the origins of rapid, single-exponential kinetics in protein folding

The folding of naturally occurring, single-domain proteins is usually well described as a simple, single-exponential process lacking significant trapped states. Here we further explore the hypothesis that the smooth energy landscape this implies, and the rapid kinetics it engenders, arises due to the extraordinary thermodynamic cooperativity of protein folding. Studying Miyazawa-Jernigan lattice polymers, we find that, even under conditions where the folding energy landscape is relatively optimized (designed sequences folding at their temperature of maximum folding rate), the folding of protein-like heteropolymers is accelerated when their thermodynamic cooperativity is enhanced by enhancing the nonadditivity of their energy potentials. At lower temperatures, where kinetic traps presumably play a more significant role in defining folding rates, we observe still greater cooperativity-induced acceleration. Consistent with these observations, we find that the folding kinetics of our computational models more closely approximates single-exponential behavior as their cooperativity approaches optimal levels. These observations suggest that the rapid folding of naturally occurring proteins is, in part, a consequence of their remarkably cooperative folding.     

Downhill versus Barrier-Limited Folding of BBL 2: Mechanistic Insights from Kinetics of Folding Monitored by Independent Tryptophan Probes

Barrier-free downhill folding has been proposed for the peripheral subunit-binding domain BBL. To date, ultrafast kinetic experiments on BBL, which are crucial for a mechanistic understanding of folding, have been hampered by the lack of good intrinsic spectroscopic probes. Here, we present a detailed kinetic characterization of three single-point tryptophan mutants of BBL that have suitable fluorescence properties for following microsecond and nanosecond folding kinetics using temperature jump fluorescence spectroscopy. Experiments were performed at pH 7, which is optimal for stability and minimizes complications that arise from the presence of an alternative native-state conformation of BBL at lower pH. We examined the dependence of rate and equilibrium constants on concentration of denaturant and found that they follow well-established laws allowing kinetic transients to be related to events in folding and compared with equilibrium data. Logarithms of rate constants versus denaturant concentration yielded plots (chevrons) that are characteristic of barrier-limited folding for all mutants investigated, including a truncated sequence that was previously used in the proposal of downhill folding. The thermodynamic quantities calculated from the rate constants were in excellent agreement with those directly determined from equilibrium denaturation based on empirical two-state equations. We found that sequence truncation of BBL as used in studies proposing downhill folding leads to a large loss in helical content and protein stability, which were exacerbated at the low pH used in those studies. The kinetics and equilibria of folding of BBL fit to conventional barrier-limited kinetics.     

Tuning the heterogeneous early folding dynamics of phosphoglycerate kinase

We recently reported stretched kinetics during the formation of a collapsed, long-lived intermediate state of the large two-domain enzyme phosphoglycerate kinase (PGK). It was postulated that intrinsic roughness of the energy landscape on the way downhill to the intermediate causes the lack of a single time-scale. Here, we investigate several alternative explanations for stretched refolding dynamics in more detail: tyrosine fluorescence, multiple tryptophan probes, and rate differences between independently folding domains. To this end, we systematically simplify PGK in several steps from the full protein with two tryptophan residues and all tyrosine residues probed, to a single domain with only one tryptophan residue and no tyrosine residue probed. The kinetics in the 10 micros to 10 ms range are revealed by laser-induced temperature-jump relaxation experiments. The isolated N-terminal domain forms an intermediate by nearly single-exponential kinetics, but the isolated C-terminal domain shows strongly non-exponential kinetics. Thus, domain interaction and a cis-proline residue between the two domains are ruled out as the sole contributors to heterogeneity during the earliest folding dynamics of the C-terminal domain. We apply two limiting models for the roughness of the energy landscape. A sequential three-state model lumps all the roughness into a single trap. The "strange kinetics" model with logarithmic oscillations developed by Klafter and co-workers distributes the roughness over a larger number of states. Both models explain our data about equally well, but the coincidental values of rate constants in all of our double-exponential fits, and the absence of a spectroscopic signature distinct from the endpoints of the folding process favors more roughness than can be explained by just a single trap.     

Early Aggregated States in the Folding of Interleukin-1β

Kinetic data measured from folding of the protein interleukin-1β fits best to three exponential phases when studied with tryptophan fluorescence but only two exponential phases when measured using other methods. The technique of ANS fluorescence was used to determine whether the additional phase observed in tryptophan fluorescence was also detected with ANS dye binding. Unlike trytophan fluorescence, the ANS fluorescence was highly dependent on the concentration of protein present during the folding experiment. Experimental controls provide evidence that ANS binds to protein aggregates, present at higher concentrations and absent at lower concentrations. Protein concentration-dependent folding studies demonstrate that, at lower interleukin-1β concentrations, tryptophan fluorescence kinetics can be fit adequately with a two exponential fit. This study indicates that (1) measured interleukin-1β folding kinetics fit to a 2 phase model and (2) at higher protein concentrations, transient association of IL-1β may result in a kinetic fit of 3 phases.     

Impact of water activity, temperature, and physical state on the storage stability of Lactobacillus paracasei ssp. paracasei freeze-dried in a lactose matrix

The aim of this study was to determine whether the combined effect of water activity and temperature on inactivation rates of freeze-dried microorganisms in a lactose matrix could be explained in terms of the glass transition theory. The stabilized glass transition temperature, Tg, of the freeze-dried products was determined by differential scanning calorimetry at two different temperatures, T (20 and 37 degrees C), and different water activities (0.07-0.48). This information served as a basis for defining conditions of T and water activity, which led to storage of the bacteria in the glassy (T < Tg) and nonglassy (T > Tg) states. The rates of inactivation of the dry microorganisms subjected to different storage conditions were determined by plate counts and could be described by first-order kinetics. Rates were analyzed as a function of water activity, storage temperature, and the difference between Tg and T. Inactivation below Tg was low; however, Tg could not be regarded as an absolute threshold of bacteria stability during storage. When the cells were stored in the nonglassy state (T > Tg), inactivation proceeded faster, however, not as rapid as suggested by the temperature dependence of the viscosity above the glass transition temperature. Furthermore, the first-order rate constant, k, was dependent on the storage temperature per se rather than on the temperature difference between the glass transition temperature and the storage temperature (T - Tg).     

Conserved and nonconserved features of the folding pathway of hisactophilin, a beta-trefoil protein

Based on previous studies of interleukin-1beta (IL-1beta) and both acidic and basic fibroblast growth factors (FGFs), it has been suggested that the folding of beta-trefoil proteins is intrinsically slow and may occur via the formation of essential intermediates. Using optical and NMR-detected quenched-flow hydrogen/deuterium exchange methods, we have measured the folding kinetics of hisactophilin, another beta-trefoil protein that has < 10% sequence identity and unrelated function to IL-1beta and FGFs. We find that hisactophilin can fold rapidly and with apparently two-state kinetics, except under the most stabilizing conditions investigated where there is evidence for formation of a folding intermediate. The hisactophilin intermediate has significant structural similarities to the IL-1beta intermediate that has been observed experimentally and predicted theoretically using a simple, topology-based folding model; however, it appears to be different from the folding intermediate observed experimentally for acidic FGF. For hisactophilin and acidic FGF, intermediates are much less prominent during folding than for IL-1beta. Considering the structures of the different beta-trefoil proteins, it appears that differences in nonconserved loops and hydrophobic interactions may play an important role in differential stabilization of the intermediates for these proteins.     

Matching simulation and experiment: a new simplified model for simulating protein folding.

Simulations of simplified protein folding models have provided much insight into solving the protein folding problem. We propose here a new off-lattice bead model, capable of simulating several different fold classes of small proteins. We present the sequence for an alpha/beta protein resembling the IgG-binding proteins L and G. The thermodynamics of the folding process for this model are characterized using the multiple multihistogram method combined with constant-temperature Langevin simulations. The folding is shown to be highly cooperative, with chain collapse nearly accompanying folding. Two parallel folding pathways are shown to exist on the folding free energy landscape. One pathway contains an intermediate--similar to experiments on protein G, and one pathway contains no intermediates-similar to experiments on protein L. The folding kinetics are characterized by tabulating mean-first passage times, and we show that the onset of glasslike kinetics occurs at much lower temperatures than the folding temperature. This model is expected to be useful in many future contexts: investigating questions of the role of local versus nonlocal interactions in various fold classes, addressing the effect of sequence mutations affecting secondary structure propensities, and providing a computationally feasible model for studying the role of solvation forces in protein folding.     

Downhill kinetics of biomolecular interface binding: globally connected scenario

We study the kinetics of the biomolecular binding process at the interface using energy landscape theory. The global kinetic connectivity case is considered for a downhill funneled energy landscape. By solving the kinetic master equation, the kinetic time for binding is obtained and shown to have a U-shape curve-dependence on the temperature. The kinetic minimum of the binding time monotonically decreases when the ratio of the underlying energy gap between native state and average non-native states versus the roughness or the fluctuations of the landscape increases. At intermediate temperatures, fluctuations measured by the higher moments of the binding time lead to non-Poissonian, non-exponential kinetics. At both high and very low temperatures, the kinetics is nearly Poissonian and exponential.     

Folding-unfolding thermodynamics of a beta-heptapeptide from equilibrium simulations

The thermodynamics of folding and unfolding of a beta-heptapeptide in methanol solution has been studied at four different temperatures, 298 K, 340 K, 350 K, and 360 K, by molecular dynamics simulation. At each of these temperatures, the 50-ns simulations were sufficient to generate an equilibrium distribution between a relatively small number of conformations (approximately 10(2)), showing that, even above the melting temperature (approximately 340 K), the peptide does not randomly sample conformational space. The free energy of folding and the free energy difference between pairs of conformations have been calculated from their relative populations. The experimentally determined folded conformation at 298 K, a left-handed 3(1)-helix, is at each of the four temperatures the predominant conformation, with its probability and average lifetime decreasing with increasing temperature. The most common intermediates of folding and unfolding are also the same at the four temperatures. Paths and rates of interconversion between different conformations have been determined. It has been found that folding can occur through multiple pathways, not necessarily downhill in free energy, although the final step involves a reduced number of intermediates.     

Exponential decay kinetics in "downhill" protein folding

The observation of single-exponential kinetic phases in early stages of protein folding is often interpreted as evidence that these phases are rate limited by significant energy or entropy barriers. However, although the existence of large barriers reliably implies exponential kinetics, the reverse is not necessarily true. A simple model for the hydrophobic collapse of a chain molecule demonstrates that a barrierless or "downhill" diffusional relaxation can give rise to kinetics that are practically indistinguishable from a pure exponential. Within this model, even a highly nonlinear experimental probe such as resonance energy transfer (F?rster transfer) could exhibit a large amplitude decay (greater than 90% in fluorescence) that deviates from a simple exponential by less than 0.5%. Only a detailed analysis of the dynamics is likely to reveal that a free energy barrier is absent.     

Mapping the transition state of the WW domain beta-sheet

The folding kinetics of a three-stranded antiparallel beta-sheet (WW domain) have been measured by temperature jump relaxation. Folding and activation free energies were determined as a function of temperature for both the wild-type and the mutant domain, W39F, which modifies the beta(2)-beta(3) hydrophobic interface. The folding rate decreases at higher temperatures as a result of the increase in the activation free energy for folding. Phi-Values were obtained for thermal perturbations allowing the primary features of the folding free energy surface to be determined. The results of this analysis indicate a significant shift from an "early" (Phi(T)=0. 4) to a "late" (Phi(T)=0.8) transition state with increasing temperature. The temperature-dependent Phi-value analysis of the wild-type WW domain and of its more stable W39F hydrophobic cluster mutant reveals little participation of residue 39 in the transition state at lower temperature. As the temperature is raised, hydrophobic interactions at the beta(2)-beta(3) interface gain importance in the transition state and the barrier height of the wild-type, which contains the larger tryptophan residue, increases more slowly than the barrier height of the mutant.     

Effects of confinement in chaperonin assisted protein folding: rate enhancement by decreasing the roughness of the folding energy landscape

Chaperonins, such as the GroE complex of the bacteria Escherichia coli, assist the folding of proteins under non-permissive folding conditions by providing a cavity in which the newly translated or translocated protein can be encapsulated. Whether the chaperonin cage plays a passive role in protecting the protein from aggregation, or an active role in accelerating folding rates, remains a matter of debate. Here, we investigate the role of confinement in chaperonin mediated folding through molecular dynamics simulations. We designed a substrate protein with an alpha/beta sandwich fold, a common structural motif found in GroE substrate proteins and confined it to a spherical hydrophilic cage which mimicked the interior of the GroEL/ES cavity. The thermodynamics and kinetics of folding were studied over a wide range of temperature and cage radii. Confinement was seen to significantly raise the collapse temperature, T(c), as a result of the associated entropy loss of the unfolded state. The folding temperature, T(f), on the other hand, remained unaffected by encapsulation, a consequence of the folding mechanism of this protein that involves an initial collapse to a compact misfolded state prior to rearranging to the native state. Folding rates were observed to be either accelerated or retarded compared to bulk folding rates, depending on the temperature of the simulation. Rate enhancements due to confinement were observed only at temperatures above the temperature T(m), which corresponds to the temperature at which the protein folds fastest. For this protein, T(m) lies above the folding temperature, T(f), implying that encapsulation alone will not lead to a rate enhancement under conditions where the native state is stable (T相似文献