Downhill Folding Research Articles

Bridging Experiments and Native-Centric Simulations of a Downhill Folding Protein.

Experiments and atomistic simulations have independently contributed to the mechanistic understanding of protein folding. However, a coherent detailed picture explicitly combining both is currently lacking, a problem that seriously limits the amount of information that can be extracted. An alternative to atomistic models with physics-based potentials is the native-centric (i.e., Go̅ type) coarse-grained models, which for many years have been successfully employed to qualitatively understand features of protein folding energy landscapes. Again, quantitative validation of Go̅ models against experimental equilibrium unfolding curves is often not attempted. Here we use an atomistic topology-based model to study the folding mechanism of PDD, a protein that folds over a marginal thermodynamic barrier of ∼0.5 kBT at midpoint conditions. We find that the simulations are in exquisite agreement with several equilibrium experimental measurements including differential scanning calorimetry (DSC), an observable that is possibly the most challenging to reproduce from explicit-chain models. The dynamics, inferred using a detailed Markov state model, display a classical Chevron-like trend with a continuum of relaxation times under both folding and unfolding conditions, a signature feature of downhill folding. The number of populated microstates and the connectivity between them are shown to be temperature dependent with a maximum near the thermal denaturation midpoint, thus linking the macroscopic observation of a peak in the DSC profile of downhill folding proteins and the underlying microstate dynamics. The mechanistic picture derived from our analysis thus sheds light on the intricate and tunable nature of the downhill protein folding ensembles. In parallel, our work highlights the power of coarse-grained models to reproduce experiments at a quantitative level while also pointing at specific directions for their improvement.

A Method for Extracting the Free Energy Surface and Conformational Dynamics of Fast-Folding Proteins from Single Molecule Photon Trajectories.

Single molecule fluorescence spectroscopy holds the promise of providing direct measurements of protein folding free energy landscapes and conformational motions. However, fulfilling this promise has been prevented by technical limitations, most notably, the difficulty in analyzing the small packets of photons per millisecond that are typically recorded from individual biomolecules. Such limitation impairs the ability to accurately determine conformational distributions and resolve sub-millisecond processes. Here we develop an analytical procedure for extracting the conformational distribution and dynamics of fast-folding proteins directly from time-stamped photon arrival trajectories produced by single molecule FRET experiments. Our procedure combines the maximum likelihood analysis originally developed by Gopich and Szabo with a statistical mechanical model that describes protein folding as diffusion on a one-dimensional free energy surface. Using stochastic kinetic simulations, we thoroughly tested the performance of the method in identifying diverse fast-folding scenarios, ranging from two-state to one-state downhill folding, as a function of relevant experimental variables such as photon count rate, amount of input data, and background noise. The tests demonstrate that the analysis can accurately retrieve the original one-dimensional free energy surface and microsecond folding dynamics in spite of the sub-megahertz photon count rates and significant background noise levels of current single molecule fluorescence experiments. Therefore, our approach provides a powerful tool for the quantitative analysis of single molecule FRET experiments of fast protein folding that is also potentially extensible to the analysis of any other biomolecular process governed by sub-millisecond conformational dynamics.

Constrained versus unconstrained folding free-energy landscapes

Protein folding can be described as a downhill process that brings the configuration of a chain of amino acids down to the bottom of a smooth free-energy funnel. Here, we use a recently developed coarse-grained protein model to assess the importance of frustration in the folding free-energy landscape. We compare the landscapes of natural proteins, computationally designed sequences, and structure-based potentials that force the contacts between the amino acids to adopt the native structure. Our results show that the structure-based potentials give a poor representation of the folding free-energy landscape, and that frustration is not just a perturbation over an otherwise perfect downhill folding.

Systematically constructing kinetic transition network in polypeptide from top to down: trajectory mapping.

Molecular dynamics (MD) simulation is an important tool for understanding bio-molecules in microscopic temporal/spatial scales. Besides the demand in improving simulation techniques to approach experimental scales, it becomes more and more crucial to develop robust methodology for precisely and objectively interpreting massive MD simulation data. In our previous work [J Phys Chem B 114, 10266 (2010)], the trajectory mapping (TM) method was presented to analyze simulation trajectories then to construct a kinetic transition network of metastable states. In this work, we further present a top-down implementation of TM to systematically detect complicate features of conformational space. We first look at longer MD trajectory pieces to get a coarse picture of transition network at larger time scale, and then we gradually cut the trajectory pieces in shorter for more details. A robust clustering algorithm is designed to more effectively identify the metastable states and transition events. We applied this TM method to detect the hierarchical structure in the conformational space of alanine-dodeca-peptide from microsecond to nanosecond time scales. The results show a downhill folding process of the peptide through multiple pathways. Even in this simple system, we found that single common-used order parameter is not sufficient either in distinguishing the metastable states or predicting the transition kinetics among these states.

Dynamic heterogeneity in the folding/unfolding transitions of FiP35.

Molecular dynamics simulations have become an important tool in studying protein dynamics over the last few decades. Atomistic simulations on the order of micro- to milliseconds are becoming feasible and are used to study the state-of-the-art experiments in atomistic detail. Yet, analyzing the high-dimensional-long-temporal trajectory data is still a challenging task and sometimes leads to contradictory results depending on the analyses. To reveal the dynamic aspect of the trajectory, here we propose a simple approach which uses a time correlation function matrix and apply to the folding/unfolding trajectory of FiP35 WW domain [Shaw et al., Science 330, 341 (2010)]. The approach successfully characterizes the slowest mode corresponding to the folding/unfolding transitions and determines the free energy barrier indicating that FiP35 is not an incipient downhill folder. The transition dynamics analysis further reveals that the folding/unfolding transition is highly heterogeneous, e.g., the transition path time varies by ∼100 fold. We identify two misfolded states and show that the dynamic heterogeneity in the folding/unfolding transitions originates from the trajectory being trapped in the misfolded and half-folded intermediate states rather than the diffusion driven by a thermal noise. The current results help reconcile the conflicting interpretations of the folding mechanism and highlight the complexity in the folding dynamics. This further motivates the need to understand the transition dynamics beyond a simple free energy picture using simulations and single-molecule experiments.

Probing the Downhill Folding Kinetics of Lambda{6-85} Mutants with Optical Tweezers

Protein folding is a process of molecular self-assembly during which a disordered polypeptide chain collapses to form a compact and well-defined three-dimensional structure. The process of folding is described as a path on a multi-dimensional energy landscape. If at each folding step along the path a decrease of entropy is nearly compensated by a decrease of enthalpy, these proteins are termed downhill folders and display ultrafast kinetics. Studying downhill folders allows understanding of fundamental principles of folding by resolving intramolecular dynamics in a step-by-step manner. However, there is still lack of knowledge about details of downhill energy landscapes, as the direct time-resolving experimental studies of ultrafast processes has been limited to a few ensemble methods.Here, we present a comparative study of single-molecule protein folding using optical tweezers that provide the possibility to measure structural dynamics with sub-millisecond and nanometer resolution. We characterize the folding dynamics of three different lambda repressor variants: a two-state folder LambdaWT∗ (Y22W) and two downhill folding variants, LambdaYA (Y22W/Q33Y/G46,48A) and LambdaHA (Y22W/Q33H/G46,48A). We show that force perturbation of their energy landscape slowed down the ultrafast kinetics of downhill folders, making it accessible to single-molecule studies. Interestingly, the downhill variants of lambda repressor appeared as two-state folders under load with significantly different folding kinetics and force dependence. A comparison between these variants allowed us to extract fine details of their underlying energy landscape.

Barrierless Transition Identified during Folding of Barstar by using Time-Resolved FRET from 5-Flurotryptophan

Despite a large volume of theoretical support for barrierless (downhill) folding of proteins, the extent of experimental observation is rather limited. This limitation is even more striking when we address the kinetic process of folding rather than equilibrium titrations of folding-unfolding transition. In this work we use the fluorescence of a single 5-Fluorotryptophan (F-Trp) in barstar as the energy donor and study the evolution of intramolecular distances and distance distributions during the kinetics of folding. Enhanced homogeneity of fluorescence decay kinetics of F-Trp when compared to that of Trp enables unequivocal interpretation of distribution of fluorescence lifetimes obtained from the Maximum Entropy Method (MEM) as arising from folded and unfolded conformations of the protein. Of the two intramolecular distances monitored during the folding process, W53-C82 distance showed continuous decrease while W53-C40 distance behaved in a two-state manner. Implication of these observations to the folding process is discussed.

Thermodynamics of downhill folding: multi-probe analysis of PDD, a protein that folds over a marginal free energy barrier.

Downhill folding proteins fold in microseconds by crossing a very low or no free energy barrier (<3 RT), and exhibit a complex unfolding behavior in equilibrium. Such unfolding complexity is due to the weak thermodynamic coupling that exists between the various structural segments of these proteins, and it is manifested in unfolding curves that differ depending on the structural probe employed to monitor the process. Probe-dependent unfolding has important practical implications because it permits one to investigate the folding energy landscape in detail using multiprobe thermodynamic experiments. This type of thermodynamic behavior has been investigated in depth on the protein BBL, an example of extreme (one-state) downhill folding in which there is no free energy barrier at any condition, including the denaturation midpoint. However, an open question is, to what extent is such thermodynamic behavior observed on less extreme downhill folders? Here we perform a multiprobe spectroscopic characterization of the microsecond folder PDD, a structural and functional homologue of BBL that folds within the downhill regime, but is not an example of one-state downhill folding; rather at the denaturation midpoint PDD folds by crossing an incipient free energy barrier. Model-free analysis of the unfolding curves from four different spectroscopic probes together with differential scanning calorimetry reveals a dispersion of ∼9 K in the apparent melting temperature and also marked differences in unfolding broadness (from ∼50 to ∼130 kJ mol(-1) when analyzed with a two-state model), confirming that such properties are also observed on less extreme downhill folders. We subsequently perform a global quantitative analysis of the unfolding data of PDD using the same ME statistical mechanical model that was used before for the BBL domain. The analysis shows that this simple model captures all of the features observed on the unfolding of PDD (i.e., the intensity and temperature dependence of the different spectroscopic signals). From the model we estimate a free energy landscape for PDD in which the maximal thermodynamic barrier (i.e., at the denaturation midpoint) is only ∼0.5 RT, consistent with previous independent estimates. Our results highlight that multiprobe unfolding experiments in equilibrium combined with statistical mechanical modeling provide important insights into the structural events that take place during the unfolding process of downhill proteins, and thus effectively probe the free energy landscape of these proteins.

Fast protein folding kinetics

Fast-folding proteins have been a major focus of computational and experimental study because they are accessible to both techniques: they are small and fast enough to be reasonably simulated with current computational power, but have dynamics slow enough to be observed with specially developed experimental techniques. This coupled study of fast-folding proteins has provided insight into the mechanisms, which allow some proteins to find their native conformation well <1 ms and has uncovered examples of theoretically predicted phenomena such as downhill folding. The study of fast folders also informs our understanding of even 'slow' folding processes: fast folders are small; relatively simple protein domains and the principles that govern their folding also govern the folding of more complex systems. This review summarizes the major theoretical and experimental techniques used to study fast-folding proteins and provides an overview of the major findings of fast-folding research. Finally, we examine the themes that have emerged from studying fast folders and briefly summarize their application to protein folding in general, as well as some work that is left to do.

Exact Partition Function Zeros of the Wako-Saitô-Muñoz-Eaton Protein Model

Protein is an intrinsically finite size system with heterogeneous components, which is in contrast to infinite-size homogeneous systems studied in traditional statistical physics, and it is of interest to see to what extent methodologies of statistical physics can be used for studying protein folding. Partition function zeros(PFZs) method is a tool used in statistical physics for studying phase transition, where instead of computing quantities in real temperature, the zeros of the partition function in the complex temperature plane are examined. In this work, I show that the PFZs method can be used for distinguishing two-state and barrierless downhill folding transitions, by computing exact partition function zeros of the Wako-Saito-Munoz-Eaton protein model. I compute the PFZs for various secondary structural elements, and for two proteins 1BBL and 1I6C, which exhibit features that clearly distinguish distinct types of folding transitions. The result is expected to form basis for further application of the method to finite heterogeneous systems.Physical Review Letters 110 (2013) 248101.

Slow proton transfer coupled to unfolding explains the puzzling results of single-molecule experiments on BBL, a paradigmatic downhill folding protein.

A battery of thermodynamic, kinetic, and structural approaches has indicated that the small α-helical protein BBL folds-unfolds via the one-state downhill scenario. Yet, single-molecule fluorescence spectroscopy offers a more conflicting view. Single-molecule experiments at pH 6 show a unique half-unfolded conformational ensemble at mid denaturation, whereas other experiments performed at higher pH show a bimodal distribution, as expected for two-state folding. Here we use thermodynamic and laser T-jump kinetic experiments combined with theoretical modeling to investigate the pH dependence of BBL stability, folding kinetics and mechanism within the pH 6–11 range. We find that BBL unfolding is tightly coupled to the protonation of one of its residues with an apparent pKa of ∼7. Therefore, in chemical denaturation experiments around neutral pH BBL unfolds gradually, and also converts in binary fashion to the protonated species. Moreover, under the single-molecule experimental conditions (denaturant midpoint and 279 K), we observe that proton transfer is much slower than the ∼15 microseconds folding-unfolding kinetics of BBL. The relaxation kinetics is distinctly biphasic, and the overall relaxation time (i.e. 0.2–0.5 ms) becomes controlled by the proton transfer step. We then show that a simple theoretical model of protein folding coupled to proton transfer explains quantitatively all these results as well as the two sets of single-molecule experiments, including their more puzzling features. Interestingly, this analysis suggests that BBL unfolds following a one-state downhill folding mechanism at all conditions. Accordingly, the source of the bimodal distributions observed during denaturation at pH 7–8 is the splitting of the unique conformational ensemble of BBL onto two slowly inter-converting protonation species. Both, the unprotonated and protonated species unfold gradually (one-state downhill), but they exhibit different degree of unfolding at any given condition because the native structure is less stable for the protonated form.

Engineering Folding Dynamics from Two-State to Downhill: Application to λ-Repressor

One strategy for reaching the downhill folding regime, primarily exploited for the λ6–85 protein fragment, consists of cumulatively introducing mutations that speed up folding. This is an experimentally demanding process where chemical intuition usually serves as a guide for the choice of amino acid residues to mutate. Such an approach can be aided by computational methods that screen for protein engineering hot spots. Here we present one such method that involves sampling the energy landscape of the pseudo-wild-type protein and investigating the effect of point mutations on this landscape. Using a novel metric for the cooperativity, we identify those residues leading to the least cooperative folding. The folding dynamics of the selected mutants are then directly characterized and the differences in the kinetics are analyzed within a Markov-state model framework. Although the method is general, here we present results for a coarse-grained topology-based simulation model of λ-repressor, whose barrier is reduced from an initial value of ∼4kBT at the midpoint to ∼1kBT, thereby reaching the downhill folding regime.

Multiscaled exploration of coupled folding and binding of an intrinsically disordered molecular recognition element in measles virus nucleoprotein

Numerous relatively short regions within intrinsically disordered proteins (IDPs) serve as molecular recognition elements (MoREs). They fold into ordered structures upon binding to their partner molecules. Currently, there is still a lack of in-depth understanding of how coupled binding and folding occurs in MoREs. Here, we quantified the unbound ensembles of the α-MoRE within the intrinsically disordered C-terminal domain of the measles virus nucleoprotein. We developed a multiscaled approach by combining a physics-based and an atomic hybrid model to decipher the mechanism by which the α-MoRE interacts with the X domain of the measles virus phosphoprotein. Our multiscaled approach led to remarkable qualitative and quantitative agreements between the theoretical predictions and experimental results (e.g., chemical shifts). We found that the free α-MoRE rapidly interconverts between multiple discrete partially helical conformations and the unfolded state, in accordance with the experimental observations. We quantified the underlying global folding-binding landscape. This leads to a synergistic mechanism in which the recognition event proceeds via (minor) conformational selection, followed by (major) induced folding. We also provided evidence that the α-MoRE is a compact molten globule-like IDP and behaves as a downhill folder in the induced folding process. We further provided a theoretical explanation for the inherent connections between "downhill folding," "molten globule," and "intrinsic disorder" in IDP-related systems. Particularly, we proposed that binding and unbinding of IDPs proceed in a stepwise way through a "kinetic divide-and-conquer" strategy that confers them high specificity without high affinity.

Gradual Disordering of the Native State on a Slow Two-State Folding Protein Monitored by Single-Molecule Fluorescence Spectroscopy and NMR

Theory predicts that folding free energy landscapes are intrinsically malleable and as such are expected to respond to perturbations in topographically complex ways. Structural changes upon perturbation have been observed experimentally for unfolded ensembles, folding transition states, and fast downhill folding proteins. However, the native state of proteins that fold in a two-state fashion is conventionally assumed to be structurally invariant during unfolding. Here we investigate how the native and unfolded states of the chicken α-spectrin SH3 domain (a well characterized slow two-state folder) change in response to chemical denaturants and/or temperature. We can resolve the individual properties of the two end-states across the chemical unfolding transition employing single-molecule fluorescence spectroscopy (SM-FRET) and across the thermal unfolding transition by NMR because SH3 folds-unfolds in the slow chemical exchange regime. Our results demonstrate that α-spectrin SH3 unfolds in a canonical way in the sense that it converts between the native state and an unfolded ensemble that expands in response to chemical denaturants. However, as conditions become increasingly destabilizing, the native state also expands gradually, and a large fraction of its native intramolecular hydrogen bonds break up. This gradual disordering of the native state takes place in times shorter than the 100 μs resolution of our SM-FRET experiments. α-Spectrin SH3 thus showcases the extreme plasticity of folding landscapes, which extends to the native state of slow two-state proteins. Our results point to the idea that folding mechanisms under physiological conditions might be quite different from those obtained by linear extrapolation from denaturing conditions. Furthermore, they highlight a pressing need for re-evaluating the conventional procedures for analyzing and interpreting folding experiments, which may be based on too-simplistic assumptions.

Exact partition function zeros of the Wako-Saitô-Muñoz-Eaton protein model.

I compute exact partition function zeros of the Wako-Saitô-Muñoz-Eaton model for various secondary structural elements and for two proteins, 1BBL and 1I6C, by using both analytic and numerical methods. Two-state and barrierless downhill folding transitions can be distinguished by a gap in the distribution of zeros at the positive real axis.

Using VIPT-jump to distinguish between different folding mechanisms: application to BBL and a Trpzip.

Protein folding involves a large number of sequential molecular steps or conformational substates. Thus, experimental characterization of the underlying folding energy landscape for any given protein is difficult. Herein, we present a new method that can be used to determine the major characteristics of the folding energy landscape in question, e.g., to distinguish between activated and barrierless downhill folding scenarios. This method is based on the idea that the conformational relaxation kinetics of different folding mechanisms at a given final condition will show different dependences on the initial condition. We show, using both simulation and experiment, that it is possible to differentiate between disparate kinetic folding models by comparing temperature jump (T-jump) relaxation traces obtained with a fixed final temperature and varied initial temperatures, which effectively varies the initial potential (VIP) of the system of interest. We apply this method (hereafter refer to as VIPT-jump) to two model systems, tryptophan zipper (Trpzip)-2c and BBL, and our results show that BBL exhibits characteristics of barrierless downhill folding, whereas Trpzip-2c folding encounters a free energy barrier. In addition, using the T-jump data of BBL we are able to provide, via Langevin dynamics simulations, a realistic estimate of its conformational diffusion coefficient.

Microsecond folding experiments and simulations: a match is made

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

Eigenvalues of the homogeneous finite linear one step master equation: Applications to downhill folding

Motivated by the observed time scales in protein systems said to fold "downhill," we have studied the finite, linear master equation, with uniform rates forward and backward as a model of the downhill process. By solving for the system eigenvalues, we prove the claim that in situations where there is no free energy barrier a transition between single- and multi-exponential kinetics occurs at sufficient bias (towards the native state). Consequences for protein folding, especially the downhill folding scenario, are briefly discussed.

Downhill Protein Folding Modules as Scaffolds for Broad-Range Ultrafast Biosensors

Conformational switches are macromolecules that toggle between two states (active/inactive or folded/unfolded) upon specific binding to a target molecule. These molecular devices provide an excellent scaffold for developing real-time biosensors. Here we take this concept one step beyond to build high-performance conformational rheostat sensors. The rationale is to develop sensors with expanded dynamic range and faster response time by coupling a given signal to the continuous (rather than binary) unfolding process of one-state downhill folding protein modules. As proof of concept we investigate the pH and ionic-strength sensing capabilities of the small α-helical protein BBL. Our results reveal that such a pH/ionic-strength sensor exhibits a linear response over 4 orders of magnitude in analyte concentration, compared to the 2 orders of magnitude for switches, and nearly concentration-independent microsecond response times.

Configuration-Dependent Diffusion Dynamics of Downhill and Two-State Protein Folding

Configuration-dependent diffusion (CDD) is important for protein folding kinetics with small thermodynamic barriers. CDD can be even more crucial in downhill folding without thermodynamic barriers. We explored the CDD of a downhill protein (BBL), and a two-state protein (CI2). The hidden kinetic barriers due to CDD were revealed. The increased ~1 k(B)T kinetic barrier is in line with experimental value based on other fast folding proteins. Compared to that of CI2, the effective free-energy profile of BBL is found to be significantly influenced by CDD, and the kinetics are totally determined by diffusion. These findings are consistent with both earlier bulk and single-molecule fluorescence measurements. In addition, we found the temperature dependence of CDD. We also found that the ratio of folding transition temperature against optimal kinetic folding temperature can provide both a quantitative measure for the underlying landscape topography and an indicator for the possible appearance of downhill folding. Our study can help for a better understanding of the role of diffusion in protein folding dynamics.