Microsecond folding experiments and simulations: a match is made

From covalent transition states in chemistry to noncovalent in biology: from β- to Φ-value analysis of protein folding

Solving the mechanism of a chemical reaction requires determining the structures of all the ground states on the pathway and the elusive transition states linking them. 2024 is the centenary of Brønsted's landmark paper that introduced the β-value and structure-activity studies as the only experimental means to infer the structures of transition states. It involves making systematic small changes in the covalent structure of the reactants and analysing changes in activation and equilibrium-free energies. Protein engineering was introduced for an analogous procedure, Φ-value analysis, to analyse the noncovalent interactions in proteins central to biological chemistry. The methodology was developed first by analysing noncovalent interactions in transition states in enzyme catalysis. The mature procedure was then applied to study transition states in the pathway of protein folding - 'part (b) of the protein folding problem'. This review describes the development of Φ-value analysis of transition states and compares and contrasts the interpretation of β- and Φ-values and their limitations. Φ-analysis afforded the first description of transition states in protein folding at the level of individual residues. It revealed the nucleation-condensation folding mechanism of protein domains with the transition state as an expanded, distorted native structure, containing little fully formed secondary structure but many weak tertiary interactions. A spectrum of transition states with various degrees of structural polarisation was then uncovered that spanned from nucleation-condensation to the framework mechanism of fully formed secondary structure. Φ-analysis revealed how movement of the expanded transition state on an energy landscape accommodates the transition from framework to nucleation-condensation mechanisms with a malleability of structure as a unifying feature of folding mechanisms. Such movement follows the rubric of analysis of classical covalent chemical mechanisms that began with Brønsted. Φ-values are used to benchmark computer simulation, and Φ and simulation combine to describe folding pathways at atomic resolution.

Insights on Aggregation of Hen Egg-White Lysozyme from Raman Spectroscopy and MD Simulations

Protein misfolding and aggregation play a significant role in several neurodegenerative diseases. In the present work, the spontaneous aggregation of hen egg-white lysozyme (HEWL) in an alkaline pH 12.2 at an ambient temperature was studied to obtain molecular insights. The time-dependent changes in spectral peaks indicated the formation of β sheets and their effects on the backbone and amino acids during the aggregation process. Introducing iodoacetamide revealed the crucial role of intermolecular disulphide bonds amidst monomers in the aggregation process. These findings were corroborated by Molecular Dynamics (MD) simulations and protein-docking studies. MD simulations helped establish and visualize the unfolding of the proteins when exposed to an alkaline pH. Protein docking revealed a preferential dimer formation between the HEWL monomers at pH 12.2 compared with the neutral pH. The combination of Raman spectroscopy and MD simulations is a powerful tool to study protein aggregation mechanisms.

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.

Mechanism of Thermal Protein Aggregation: Experiments and Molecular Dynamics Simulations on the High-Temperature Behavior of Myoglobin

Proteins that encounter unfavorable solvent conditions are prone to aggregation, a phenomenon that remains poorly understood. This work focuses on myoglobin (Mb) as a model protein. Upon heating, Mb produces amorphous aggregates. Thermal unfolding experiments at low concentration (where aggregation is negligible), along with centrifugation assays, imply that Mb aggregation proceeds via globally unfolded conformers. This contrasts studies on other proteins that emphasized the role of partially folded structures as aggregate precursors. Molecular dynamics (MD) simulations were performed to gain insights into the mechanism by which heat-unfolded Mb molecules associate with one another. A prerequisite for these simulations was the development of a method for generating monomeric starting structures. Periodic boundary condition artifacts necessitated the implementation of a partially immobilized water layer lining the walls of the simulation box. Aggregation simulations were performed at 370 K to track the assembly of monomeric Mb into pentameric species. Binding events were preceded by multiple unsuccessful encounters. Even after association, protein-protein contacts remained in flux. Binding was mediated by hydrophobic contacts, along with salt bridges that involved hydrophobically embedded Lys residues. Overall, this work illustrates that atomistic MD simulations are well suited for garnering insights into protein aggregation mechanisms.

Protein Folding Dynamics as Diffusion on a Free Energy Surface: Rate Equation Terms, Transition Paths, and Analysis of Single-Molecule Photon Trajectories

The rates of protein (un)folding are often described as diffusion on the projection of a hyperdimensional energy landscape onto a few (ideally one) order parameters. Testing such an approximation by experiment requires resolving the reactive transition paths of individual molecules, which is now becoming feasible with advanced single-molecule spectroscopic techniques. This has also sparked the interest of theorists in better understanding reactive transition paths. Here we focus on these issues aiming to establish (i) practical guidelines for the mechanistic interpretation of transition path times (TPT) and (ii) methods to extract the free energy surface and protein dynamics from the maximum likelihood analysis of photon trajectories (MLA-PT). We represent the (un)folding rates as diffusion on a 1D free energy surface with the FRET efficiency as a reaction coordinate proxy. We then perform diffusive kinetic simulations on surfaces with two minima and a barrier, but with different shapes (curvatures, barrier height, and symmetry), coupled to stochastic simulations of photon emissions that reproduce current SM-FRET experiments. From the analysis of transition paths, we find that the TPT is inversely proportional to the barrier height (difference in free energy between minimum and barrier top) for any given surface shape, and that dividing the TPT into climb and descent segments provides key information about the barrier's symmetry. We also find that the original MLA-PT procedure used to determine the TPT from experiments underestimates its value, particularly for the cases with smaller barriers (e.g., fast folders), and we suggest a simple strategy to correct for this bias. Importantly, we also demonstrate that photon trajectories contain enough information to extract the 1D free energy surface's shape and dynamics (if TPT is >4-5-fold longer than the interphoton time) using the MLA-PT directly implemented with a diffusive free energy surface model. When dealing with real (unknown) experimental data, the comparison between the likelihoods of the free energy surface and discrete kinetic three-state models can be used to evaluate the statistical significance of the estimated free energy surface.

Fast pressure-jump all-atom simulations and experiments reveal site-specific protein dehydration-folding dynamics

As theory and experiment have shown, protein dehydration is a major contributor to protein folding. Dehydration upon folding can be characterized directly by all-atom simulations of fast pressure drops, which create desolvated pockets inside the nascent hydrophobic core. Here, we study pressure-drop refolding of three λ-repressor fragment (λ_6-85) mutants computationally and experimentally. The three mutants report on tertiary structure formation via different fluorescent helix-helix contact pairs. All-atom simulations of pressure drops capture refolding and unfolding of all three mutants by a similar mechanism, thus validating the nonperturbative nature of the fluorescent contact probes. Analysis of simulated interprobe distances shows that the α-helix 1-3 pair distance displays a slower characteristic time scale than the 1-2 or 3-2 pair distance. To see whether slow packing of α-helices 1 and 3 is reflected in the rate-limiting folding step, fast pressure-drop relaxation experiments captured refolding on a millisecond time scale. These experiments reveal that refolding monitored by 1-3 contact formation indeed is much slower than when monitored by 1-2 or 3-2 contact formation. Unlike the case of the two-state folder [three-α-helix bundle (α₃D)], whose drying and core formation proceed in concert, λ_6-85 repeatedly dries and rewets different local tertiary contacts before finally forming a solvent-excluded core, explaining the non-two-state behavior observed during refolding in molecular dynamics simulations. This work demonstrates that proteins can explore desolvated pockets and dry globular states numerous times before reaching the native conformation.

A molecular dynamics approach towards evaluating osmotic and thermal stress in the extracellular environment

OBJECTIVE

A molecular dynamics approach to understanding fundamental mechanisms of combined thermal and osmotic stress induced by thermochemical ablation (TCA) is presented.

METHODS

Structural models of fibronectin and fibronectin bound to its integrin receptor provide idealized models for the effects of thermal and osmotic stress in the extracellular matrix. Fibronectin binding to integrin is known to facilitate cell survival. The extracellular environment produced by TCA at the lesion boundary was modelled at 37 °C and 43 °C with added sodium chloride (NaCl) concentrations (0, 40, 80, 160, and 320 mM). Atomistic simulations of solvated proteins were performed using the GROMOS96 force field and TIP3P water model. Computational results were compared with the results of viability studies of human hepatocellular carcinoma (HCC) cell lines HepG2 and Hep3B under matching thermal and osmotic experimental conditions.

RESULTS

Cell viability was inversely correlated with hyperthermal and hyperosmotic stresses. Added NaCl concentrations were correlated with a root mean square fluctuation increase of the fibronectin arginylglycylaspartic acid (RGD) binding domain. Computed interaction coefficients demonstrate preferential hydration of the protein model and are correlated with salt-induced strengthening of hydrophobic interactions. Under the combined hyperthermal and hyperosmotic stress conditions (43 °C and 320 mM added NaCl), the free energy change required for fibronectin binding to integrin was less favorable than that for binding under control conditions (37 °C and 0 mM added NaCl).

CONCLUSION

Results quantify multiple measures of structural changes as a function of temperature increase and addition of NaCl to the solution. Correlations between cell viability and stability measures suggest that protein aggregates, non-functional proteins, and less favorable cell attachment conditions have a role in TCA-induced cell stress.

A quantitative connection of experimental and simulated folding landscapes by vibrational spectroscopy

We break the barrier between simulation and experiment by comparing identical computed and experimental infrared observables.

For small molecule reaction kinetics, computed reaction coordinates often mimic experimentally measured observables quite accurately. Although nowadays simulated and measured biomolecule kinetics can be compared on the same time scale, a gap between computed and experimental observables remains. Here we directly compared temperature-jump experiments and molecular dynamics simulations of protein folding dynamics using the same observable: the time-dependent infrared spectrum. We first measured the stability and folding kinetics of the fastest-folding β-protein, the GTT35 WW domain, using its structurally specific infrared spectrum. The relaxation dynamics of the peptide backbone, β-sheets, turn, and random coil were measured independently by probing the amide I′ region at different frequencies. Next, the amide I′ spectra along folding/unfolding molecular dynamics trajectories were simulated by accurate mixed quantum/classical calculations. The simulated time dependence and spectral amplitudes at the exact experimental probe frequencies provided relaxation and folding rates in agreement with experimental observations. The calculations validated by experiment yield direct structural evidence for a rate-limiting reaction step where an intermediate state with either the first or second hairpin is formed. We show how folding switches from a more homogeneous (apparent two-state) process at high temperature to a more heterogeneous process at low temperature, where different parts of the WW domain fold at different rates.

A new paradigm for atomically detailed simulations of kinetics in biophysical systems

The kinetics of biochemical and biophysical events determined the course of life processes and attracted considerable interest and research. For example, modeling of biological networks and cellular responses relies on the availability of information on rate coefficients. Atomically detailed simulations hold the promise of supplementing experimental data to obtain a more complete kinetic picture. However, simulations at biological time scales are challenging. Typical computer resources are insufficient to provide the ensemble of trajectories at the correct length that is required for straightforward calculations of time scales. In the last years, new technologies emerged that make atomically detailed simulations of rate coefficients possible. Instead of computing complete trajectories from reactants to products, these approaches launch a large number of short trajectories at different positions. Since the trajectories are short, they are computed trivially in parallel on modern computer architecture. The starting and termination positions of the short trajectories are chosen, following statistical mechanics theory, to enhance efficiency. These trajectories are analyzed. The analysis produces accurate estimates of time scales as long as hours. The theory of Milestoning that exploits the use of short trajectories is discussed, and several applications are described.

pH-Dependent cooperativity and existence of a dry molten globule in the folding of a miniprotein BBL

Solution pH plays an important role in protein dynamics, stability, and folding; however, detailed mechanisms remain poorly understood. Here we use continuous constant pH molecular dynamics in explicit solvent with pH replica exchange to describe the pH profile of the folding cooperativity of a miniprotein BBL, which has drawn intense debate in the past. Our data reconciled the two opposing hypotheses (downhill vs. two-state) and uncovered a sparsely populated unfolding intermediate. As pH is lowered from 7 to 5, the folding barrier vanishes. As pH continues to decrease, the unfolding barrier lowers and denaturation is triggered by the protonation of Asp162, consistent with experimental evidence. Interestingly, unfolding proceeded via an intermediate, with intact secondary structure and a compact, unlocked hydrophobic core shielded from solvent, lending support to the recent hypothesis of a universal dry molten globule in protein folding. Our work demonstrates that constant pH molecular dynamics is a unique tool for testing this and other hypotheses to advance the knowledge in protein dynamics, stability, and folding.

Estimating the mean first passage time of protein misfolding

Most theoretical and experimental studies confirm that proteins fold in the time scale of microseconds to milliseconds, but the kinetics of the protein misfolding remains largely unexplored. The kinetics of unfolding-folding-misfolding equilibrium in proteins is formulated in the analytical framework of the Master equation. The folded, unfolded and the misfolded state are characterized in terms of their respective contacts. The Mean First Passage Time (MFPT) to acquire the misfolded conformation from the native or folded state is derived from this equation with different boundary conditions. The MFPT is found to be practically independent of the length of the protein, the number of native contacts and the rate constant for the misfolded to the folded state. The results obtained from the survival probability are directly correlated to the age of onset and appearance of misfolding diseases in humans.

A component analysis of the free energies of folding of 35 proteins: A consensus view on the thermodynamics of folding at the molecular level

What factors favor protein folding? This is a textbook question. Parsing the experimental free energies of folding/unfolding into diverse enthalpic and entropic components of solute and solvent favoring or disfavoring folding is not an easy task. In this study, we present a computational protocol for estimating the free energy contributors to protein folding semi-quantitatively using ensembles of unfolded and native states generated via molecular dynamics simulations. We tested the methodology on 35 proteins with diverse structural motifs and sizes and found that the calculated free energies correlate well with experiment (correlation coefficient ∼ 0.85), enabling us to develop a consensus view of the energetics of folding. As a more sensitive test of the methodology, we also investigated the free energies of folding of an additional 33 single point mutants and obtained a correlation coefficient of 0.8. A notable observation is that the folding free energy components appear to carry signatures of the fold (SCOP classification) of the protein. © 2017 Wiley Periodicals, Inc.

Validation of Molecular Dynamics Simulations for Prediction of Three-Dimensional Structures of Small Proteins

Although various higher-order protein structure prediction methods have been developed, almost all of them were developed based on the three-dimensional (3D) structure information of known proteins. Here we predicted the short protein structures by molecular dynamics (MD) simulations in which only Newton’s equations of motion were used and 3D structural information of known proteins was not required. To evaluate the ability of MD simulationto predict protein structures, we calculated seven short test protein (10–46 residues) in the denatured state and compared their predicted and experimental structures. The predicted structure for Trp-cage (20 residues) was close to the experimental structure by 200-ns MD simulation. For proteins shorter or longer than Trp-cage, root-mean square deviation values were larger than those for Trp-cage. However, secondary structures could be reproduced by MD simulations for proteins with 10–34 residues. Simulations by replica exchange MD were performed, but the results were similar to those from normal MD simulations. These results suggest that normal MD simulations can roughly predict short protein structures and 200-ns simulations are frequently sufficient for estimating the secondary structures of protein (approximately 20 residues). Structural prediction method using only fundamental physical laws are useful for investigating non-natural proteins, such as primitive proteins and artificial proteins for peptide-based drug delivery systems.

Globular Protein Folding In Vitro and In Vivo

In vitro, computational, and theoretical studies of protein folding have converged to paint a rich and complex energy landscape. This landscape is sensitively modulated by environmental conditions and subject to evolutionary pressure on protein function. Of these environments, none is more complex than the cell itself, where proteins function in the cytosol, in membranes, and in different compartments. A wide variety of kinetic and thermodynamics experiments, ranging from single-molecule studies to jump kinetics and from nuclear magnetic resonance to imaging on the microscope, have elucidated how protein energy landscapes facilitate folding and how they are subject to evolutionary constraints and environmental perturbation. Here we review some recent developments in the field and refer the reader to some original work and additional reviews that cover this broad topic in protein science.

Scrutiny of electrostatic-driven conformational ordering of polypeptide chains in DMSO: a study with a model oligopeptide

The molecular mechanism of DMSO-induced stabilisation of β-sheets is attributed to the combination of polar electrostatic interactions among side chains, and backbone desolvation through bulky side chains which promotes backbone hydrogen bonding.

Perspective: Computer simulations of long time dynamics

Atomically detailed computer simulations of complex molecular events attracted the imagination of many researchers in the field as providing comprehensive information on chemical, biological, and physical processes. However, one of the greatest limitations of these simulations is of time scales. The physical time scales accessible to straightforward simulations are too short to address many interesting and important molecular events. In the last decade significant advances were made in different directions (theory, software, and hardware) that significantly expand the capabilities and accuracies of these techniques. This perspective describes and critically examines some of these advances.

Can Local Probes Go Global? A Joint Experiment-Simulation Analysis of λ(6-85) Folding

The process of protein folding is known to involve global motions in a cooperative affair; the structure of most of the protein sequences is gained or lost over a narrow range of temperature, denaturant, or pressure perturbations. At the same time, recent simulations and experiments reveal a complex structural landscape with a rich set of local motions and conformational changes. We couple experimental kinetic and thermodynamic measurements with specifically tailored analysis of simulation data to isolate local versus global folding probes. We find that local probes exhibit lower melting temperatures, smaller surface area changes, and faster kinetics compared to global ones. We also see that certain local probes of folding match the global behavior more closely than others. Our work highlights the importance of using multiple probes to fully characterize protein folding dynamics by theory and experiment.

Conformational Changes of Trialanine in Water Induced by Vibrational Relaxation of the Amide I Mode

Most of the protein-based diseases are caused by anomalies in the functionality and stability of these molecules. Experimental and theoretical studies of the conformational dynamics of proteins are becoming in this respect essential to understand the origin of these anomalies. However, a description of the conformational dynamics of proteins based on mechano-energetic principles still remains elusive because of the intrinsic high flexibility of the peptide chains, the participation of weak noncovalent interactions, and the role of the ubiquitous water solvent. In this work, the conformational dynamics of trialanine dissolved in water (D2O) is investigated through Molecular Dynamics (MD) simulations combined with instantaneous normal modes (INMs) analysis both at equilibrium and after the vibrational excitation of the C-terminal amide I mode. The conformational equilibrium between α and pPII conformers is found to be altered by the intramolecular relaxation of the amide I mode as a consequence of the different relaxation pathways of each conformer which modify the amount of vibrational energy stored in the torsional motions of the tripeptide, so the α → pPII and pPII → α conversion rates are increased differently. The selectivity of the process comes from the shifts of the vibrational frequencies with the conformational changes that modify the resonance conditions driving the intramolecular energy flows.

Advances in free-energy-based simulations of protein folding and ligand binding

Free-energy-based simulations are increasingly providing the narratives about the structures, dynamics and biological mechanisms that constitute the fabric of protein science. Here, we review two recent successes. It is becoming practical: first, to fold small proteins with free-energy methods without knowing substructures and second, to compute ligand-protein binding affinities, not just their binding poses. Over the past 40 years, the timescales that can be simulated by atomistic MD are doubling every 1.3 years--which is faster than Moore's law. Thus, these advances are not simply due to the availability of faster computers. Force fields, solvation models and simulation methodology have kept pace with computing advancements, and are now quite good. At the tip of the spear recently are GPU-based computing, improved fast-solvation methods, continued advances in force fields, and conformational sampling methods that harness external information.

Probing the role of electrostatics of polypeptide main-chain in protein folding by perturbing N-terminal residue stereochemistry: DFT study with oligoalanine models

Energetics of folding (ΔH_E→F, in kcal mol⁻¹) from the extended (E) structure to the folded (F) structure for Ia and Ib critically depend on the geometrical relationship between the backbone peptide units of the polypeptide structure.

Intrinsic coordination for revealing local structural changes in protein folding–unfolding

The local dislocations may be tracked relatively easily with respect to the internal rigid rod.

Fast-folding proteins under stress

Proteins are subject to a variety of stresses in biological organisms, including pressure and temperature, which are the easiest stresses to simulate by molecular dynamics. We discuss the effect of pressure and thermal stress on very-fast-folding model proteins, whose in vitro folding can be fully simulated on computers and compared with experiments. We then discuss experiments that can be used to subject proteins to low- and high-temperature unfolding, as well as low- and high-pressure unfolding. Pressure and temperature are prototypical perturbations that illustrate how close many proteins are to instability, a property that cells can exploit to control protein function. We conclude by reviewing some recent in-cell experiments, and progress being made in simulating and measuring protein stability and function inside live cells.

Microsecond protein dynamics observed at the single-molecule level

How polypeptide chains acquire specific conformations to realize unique biological functions is a central problem of protein science. Single-molecule spectroscopy, combined with fluorescence resonance energy transfer, is utilized to study the conformational heterogeneity and the state-to-state transition dynamics of proteins on the submillisecond to second timescales. However, observation of the dynamics on the microsecond timescale is still very challenging. This timescale is important because the elementary processes of protein dynamics take place and direct comparison between experiment and simulation is possible. Here we report a new single-molecule technique to reveal the microsecond structural dynamics of proteins through correlation of the fluorescence lifetime. This method, two-dimensional fluorescence lifetime correlation spectroscopy, is applied to clarify the conformational dynamics of cytochrome c. Three conformational ensembles and the microsecond transitions in each ensemble are indicated from the correlation signal, demonstrating the importance of quantifying microsecond dynamics of proteins on the folding free energy landscape.

Single molecule spectroscopy can visualise dynamic changes in protein conformation on the submillisecond timescale. Here, Otosu et al. apply two-dimensional fluorescence lifetime correlation spectroscopy to visualise dynamics between seven conformers of cytochrome c on the microsecond timescale.

Mapping fast protein folding with multiple-site fluorescent probes

Fast protein folding involves complex dynamics in many degrees of freedom, yet microsecond folding experiments provide only low-resolution structural information. We enhance the structural resolution of the five-helix bundle protein λ6-85 by engineering into it three fluorescent tryptophan-tyrosine contact probes. The probes report on distances between three different helix pairs: 1-2, 1-3, and 3-2. Temperature jump relaxation experiments on these three mutants reveal two different kinetic timescales: a slower timescale for 1-3 and a faster one for the two contacts involving helix 2. We hypothesize that these differences arise from a single folding mechanism that forms contacts on different timescales, and not from changes of mechanism due to adding the probes. To test this hypothesis, we analyzed the corresponding three distances in one published single-trajectory all-atom molecular-dynamics simulation of a similar mutant. Autocorrelation analysis of the trajectory reveals the same "slow" and "fast" distance change as does experiment, but on a faster timescale; smoothing the trajectory in time shows that this ordering is robust and persists into the microsecond folding timescale. Structural investigation of the all-atom computational data suggests that helix 2 misfolds to produce a short-lived off-pathway trap, in agreement with the experimental finding that the 1-2 and 3-2 distances involving helix 2 contacts form a kinetic grouping distinct from 1 to 3. Our work demonstrates that comparison between experiment and simulation can be extended to several order parameters, providing a stronger mechanistic test.

Comparing Fast Pressure Jump and Temperature Jump Protein Folding Experiments and Simulations

The unimolecular folding reaction of small proteins is now amenable to a very direct mechanistic comparison between experiment and simulation. We present such a comparison of microsecond pressure and temperature jump refolding kinetics of the engineered WW domain FiP35, a model system for β-sheet folding. Both perturbations produce experimentally a faster and a slower kinetic phase, and the "slow" microsecond phase is activated. The fast phase shows differences between perturbation methods and is closer to the downhill limit by temperature jump, but closer to the transiently populated intermediate limit by pressure jump. These observations make more demands on simulations of the folding process than just a rough comparison of time scales. To complement experiments, we carried out several pressure jump and temperature jump all-atom molecular dynamics trajectories in explicit solvent, where FiP35 folded in five of the six simulations. We analyzed our pressure jump simulations by kinetic modeling and found that the pressure jump experiments and MD simulations are most consistent with a 4-state kinetic mechanism. Together, our experimental and computational data highlight FiP35's position at the boundary where activated intermediates and downhill folding meet, and we show that this model protein is an excellent candidate for further pressure jump molecular dynamics studies to compare experiment and modeling at the folding mechanism level.

Interaction Networks in Protein Folding via Atomic-Resolution Experiments and Long-Time-Scale Molecular Dynamics Simulations

The integration of atomic-resolution experimental and computational methods offers the potential for elucidating key aspects of protein folding that are not revealed by either approach alone. Here, we combine equilibrium NMR measurements of thermal unfolding and long molecular dynamics simulations to investigate the folding of gpW, a protein with two-state-like, fast folding dynamics and cooperative equilibrium unfolding behavior. Experiments and simulations expose a remarkably complex pattern of structural changes that occur at the atomic level and from which the detailed network of residue-residue couplings associated with cooperative folding emerges. Such thermodynamic residue-residue couplings appear to be linked to the order of mechanistically significant events that take place during the folding process. Our results on gpW indicate that the methods employed in this study are likely to prove broadly applicable to the fine analysis of folding mechanisms in fast folding proteins.

The roughness of the protein energy landscape results in anomalous diffusion of the polypeptide backbone

Recombination of photolysed protein disulfide bonds confirms subdiffusional backbone motion and measures the roughness of the protein's energy landscape.

A molecular interpretation of 2D IR protein folding experiments with Markov state models

The folding mechanism of the N-terminal domain of ribosomal protein L9 (NTL91-39) is studied using temperature-jump (T-jump) amide I' two-dimensional infrared (2D IR) spectroscopy in combination with spectral simulations based on a Markov state model (MSM) built from millisecond-long molecular dynamics trajectories. The results provide evidence for a compact well-structured folded state and a heterogeneous fast-exchanging denatured state ensemble exhibiting residual secondary structure. The folding rate of 26.4 μs(-1) (at 80°C), extracted from the T-jump response of NTL91-39, compares favorably with the 18 μs(-1) obtained from the MSM. Structural decomposition of the MSM and analysis along the folding coordinate indicates that helix-formation nucleates the global folding. Simulated difference spectra, corresponding to the global folding transition of the MSM, are in qualitative agreement with measured T-jump 2D IR spectra. The experiments demonstrate the use of T-jump 2D IR spectroscopy as a valuable tool for studying protein folding, with direct connections to simulations. The results suggest that in addition to predicting the correct native structure and folding time constant, molecular dynamics simulations carried out with modern force fields provide an accurate description of folding mechanisms in small proteins.

Fast single-molecule FRET spectroscopy: theory and experiment

Single-molecule spectroscopy is widely used to study macromolecular dynamics. Although this technique provides unique information that cannot be obtained at the ensemble level, the possibility of studying fast molecular dynamics is limited by the number of photons detected per unit time (photon count rate), which is proportional to the illumination intensity. However, simply increasing the illumination intensity often does not help because of various photophysical and photochemical problems. In this Perspective, we show how to improve the dynamic range of single-molecule fluorescence spectroscopy at a given photon count rate by considering each and every photon and using a maximum likelihood method. For a photon trajectory with recorded photon colors and inter-photon times, the parameters of a model describing molecular dynamics are obtained by maximizing the appropriate likelihood function. We discuss various likelihood functions, their applicability, and the accuracy of the extracted parameters. The maximum likelihood method has been applied to analyze the experiments on fast two-state protein folding and to measure transition path times. Utilizing other information such as fluorescence lifetimes is discussed in the framework of two-dimensional FRET efficiency-lifetime histograms.

Stability of amyloid oligomers

Molecular simulations are now commonly used to complement experimental techniques in investigating amyloids and their role in human diseases. In this chapter, we will summarize techniques and approaches often used in amyloid simulations and will present recent success stories. Our examples will be focused on lessons learned from molecular dynamics simulations in aqueous environments that start from preformed aggregates. These studies explore the limitations that arise from the choice of force field, the role of mutations in the growth of amyloid aggregates, segmental polymorphism, and the importance of cross-seeding. Furthermore, they give evidence for potential toxicity mechanisms. We finally discuss the role of molecular simulations in the search for aggregation inhibitors.

Statistical mechanics of the denatured state of a protein using replica-averaged metadynamics

The characterization of denatured states of proteins is challenging because the lack of permanent structure in these states makes it difficult to apply to them standard methods of structural biology. In this work we use all-atom replica-averaged metadynamics (RAM) simulations with NMR chemical shift restraints to determine an ensemble of structures representing an acid-denatured state of the 86-residue protein ACBP. This approach has enabled us to reach convergence in the free energy landscape calculations, obtaining an ensemble of structures in relatively accurate agreement with independent experimental data used for validation. By observing at atomistic resolution the transient formation of native and non-native structures in this acid-denatured state of ACBP, we rationalize the effects of single-point mutations on the folding rate, stability, and transition-state structures of this protein, thus characterizing the role of the unfolded state in determining the folding process.

Probing the origins of two-state folding

Many protein systems fold in a two-state manner. Random models, however, rarely display two-state kinetics and thus such behavior should not be accepted as a default. While theories for the prevalence of two-state kinetics have been presented, none sufficiently explain the breadth of experimental observations. A model, making minimal assumptions, is introduced that suggests two-state behavior is likely for any system with an overwhelmingly populated native state. We show two-state folding is a natural consequence of such two-state thermodynamics, and is strengthened by increasing the population of the native state. Further, the model exhibits hub-like behavior, with slow interconversions between unfolded states. Despite this, the unfolded state equilibrates quickly relative to the folding time. This apparent paradox is readily understood through this model. Finally, our results compare favorable with measurements of folding rates as a function of chain length and Keq, providing new insight into these relations.

Achieving Rigorous Accelerated Conformational Sampling in Explicit Solvent

Molecular dynamics simulations can provide valuable atomistic insights into biomolecular function. However, the accuracy of molecular simulations on general-purpose computers depends on the time scale of the events of interest. Advanced simulation methods, such as accelerated molecular dynamics, have shown tremendous promise in sampling the conformational dynamics of biomolecules, where standard molecular dynamics simulations are nonergodic. Here we present a sampling method based on accelerated molecular dynamics in which rotatable dihedral angles and nonbonded interactions are boosted separately. This method (RaMD-db) is a different implementation of the dual-boost accelerated molecular dynamics, introduced earlier. The advantage is that this method speeds up sampling of the conformational space of biomolecules in explicit solvent, as the degrees of freedom most relevant for conformational transitions are accelerated. We tested RaMD-db on one of the most difficult sampling problems - protein folding. Starting from fully extended polypeptide chains, two fast folding α-helical proteins (Trpcage and the double mutant of C-terminal fragment of Villin headpiece) and a designed β-hairpin (Chignolin) were completely folded to their native structures in very short simulation time. Multiple folding/unfolding transitions could be observed in a single trajectory. Our results show that RaMD-db is a promisingly fast and efficient sampling method for conformational transitions in explicit solvent. RaMD-db thus opens new avenues for understanding biomolecular self-assembly and functional dynamics occurring on long time and length scales.

Observation of complete pressure-jump protein refolding in molecular dynamics simulation and experiment

Density is an easily adjusted variable in molecular dynamics (MD) simulations. Thus, pressure-jump (P-jump)-induced protein refolding, if it could be made fast enough, would be ideally suited for comparison with MD. Although pressure denaturation perturbs secondary structure less than temperature denaturation, protein refolding after a fast P-jump is not necessarily faster than that after a temperature jump. Recent P-jump refolding experiments on the helix bundle λ-repressor have shown evidence of a <3 μs burst phase, but also of a ~1.5 ms "slow" phase of refolding, attributed to non-native helical structure frustrating microsecond refolding. Here we show that a λ-repressor mutant is nonetheless capable of refolding in a single explicit solvent MD trajectory in about 19 μs, indicating that the burst phase observed in experiments on the same mutant could produce native protein. The simulation reveals that after about 18.5 μs of conformational sampling, the productive structural rearrangement to the native state does not occur in a single swift step but is spread out over a brief series of helix and loop rearrangements that take about 0.9 μs. Our results support the molecular time scale inferred for λ-repressor from near-downhill folding experiments, where transition-state population can be seen experimentally, and also agrees with the transition-state transit time observed in slower folding proteins by single-molecule spectroscopy.

Ultrafast hydrogen exchange reveals specific structural events during the initial stages of folding of cytochrome c

Many proteins undergo a sharp decrease in chain dimensions during early stages of folding, prior to the rate-limiting step in folding. However, it remains unclear whether compact states are the result of specific folding events or a general hydrophobic collapse of the poly peptide chain driven by the change in solvent conditions. To address this fundamental question, we extended the temporal resolution of NMR-detected H/D exchange labeling experiments into the microsecond regime by adopting a microfluidics approach. By observing the competition between H/D exchange and folding as a function of labeling pH, coupled with direct measurement of exchange rates in the unfolded state, we were able to monitor hydrogen-bond formation for over 50 individual backbone NH groups within the initial 140 microseconds of folding of horse cytochrome c. Clusters of solvent-shielded amide protons were observed in two α-helical segments in the C-terminal half of the protein, while the N-terminal helix remained largely unstructured, suggesting that proximity in the primary structure is a major factor in promoting helix formation and association at early stages of folding, while the entropically more costly long-range contacts between the N- and C-terminal helices are established only during later stages. Our findings clearly indicate that the initial chain condensation in cytochrome c is driven by specific interactions among a subset of α-helical segments rather than a general hydrophobic collapse.

Replica exchange molecular dynamics simulations of an α/β-type small acid soluble protein (SASP)

Small acid soluble proteins (SASPs) of α/β-type play a major role in the resistance of spore DNAs to external assaults. It has been found that α/β-type SASP exhibits intrinsic disorder on isolation, but it acquires a defined native state upon binding to DNA. This disorder to order transition is not yet understood. Other questions related to the role of the thermodynamics and structure of the individual protein in the complex formation remain elusive. Characterization of the unbound state of α/β-type SASP in experiments could be a challenging problem because of the heterogeneous nature of the ensemble. Here, computer simulations can help gain more insights into the unbound state of α/β-type SASP. In the present work, by using replica exchange molecular dynamics (REMD), we simulated an α/β-type SASP on isolation with an implicit solvent. We found that α/β-type SASP undergoes a continuous phase transition with a small free energy barrier, a common feature of intrinsically disordered proteins (IDPs). Additionally, we detected the presence of residual α-helical structures at local level and a high degree of plasticity in the chain which can contribute to the fast disorder to order transition by reducing the fly-casting mechanism.

Single-molecule assays for investigating protein misfolding and aggregation

Protein misfolding and aggregation are relevant to many fields. Recently, their investigation has experienced a revival as a central topic in the research of numerous human diseases, including Parkinson's and Alzheimer's. Much has been learned from ensemble biochemical approaches, but the inherently heterogeneous nature of the underlying processes has obscured many important details. Single-molecule techniques offer unique capabilities to study heterogeneous systems, while providing high temporal and structural resolution to characterize them. In this Perspective, we give an overview of the single-molecule assays that have been applied to protein misfolding and aggregation, which are mainly based on fluorescence and force spectroscopy. We describe some of the technical challenges involved in studying aggregation at the single-molecule level and discuss what has been learned about aggregation mechanisms from the different approaches.