Single-molecule fluorescence spectroscopy maps the folding landscape of a large protein

Outcome of the First wwPDB Hybrid/Integrative Methods Task Force Workshop

Structures of biomolecular systems are increasingly computed by integrative modeling that relies on varied types of experimental data and theoretical information. We describe here the proceedings and conclusions from the first wwPDB Hybrid/Integrative Methods Task Force Workshop held at the European Bioinformatics Institute in Hinxton, UK, on October 6 and 7, 2014. At the workshop, experts in various experimental fields of structural biology, experts in integrative modeling and visualization, and experts in data archiving addressed a series of questions central to the future of structural biology. How should integrative models be represented? How should the data and integrative models be validated? What data should be archived? How should the data and models be archived? What information should accompany the publication of integrative models?

Single-molecule chemo-mechanical unfolding reveals multiple transition state barriers in a small single-domain protein

A fundamental question in protein folding is whether proteins fold through one or multiple trajectories. While most experiments indicate a single pathway, simulations suggest proteins can fold through many parallel pathways. Here, we use a combination of chemical denaturant, mechanical force and site-directed mutations to demonstrate the presence of multiple unfolding pathways in a simple, two-state folding protein. We show that these multiple pathways have structurally different transition states, and that seemingly small changes in protein sequence and environment can strongly modulate the flux between the pathways. These results suggest that in vivo, the crowded cellular environment could strongly influence the mechanisms of protein folding and unfolding. Our study resolves the apparent dichotomy between experimental and theoretical studies, and highlights the advantage of using a multipronged approach to reveal the complexities of a protein's free-energy landscape.

Although most protein folding experiments can be explained by a single pathway, theoretical evidence suggests the presence of multiple pathways. Here, the authors resolve this using a combination of force, chemical denaturation and mutagenesis to modulate the flux between parallel pathways.

Error-based extraction of states and energy landscapes from experimental single-molecule time-series

Characterization of states, the essential components of the underlying energy landscapes, is one of the most intriguing subjects in single-molecule (SM) experiments due to the existence of noise inherent to the measurements. Here we present a method to extract the underlying state sequences from experimental SM time-series. Taking into account empirical error and the finite sampling of the time-series, the method extracts a steady-state network which provides an approximation of the underlying effective free energy landscape. The core of the method is the application of rate-distortion theory from information theory, allowing the individual data points to be assigned to multiple states simultaneously. We demonstrate the method's proficiency in its application to simulated trajectories as well as to experimental SM fluorescence resonance energy transfer (FRET) trajectories obtained from isolated agonist binding domains of the AMPA receptor, an ionotropic glutamate receptor that is prevalent in the central nervous system.

Protein unfolding from free-energy calculations: integration of the Gaussian network model with bond binding energies

Motivated by single molecule experiments, we study thermal unfolding pathways of four proteins, chymotrypsin inhibitor, barnase, ubiquitin, and adenylate kinase, using bond network models that combine bond energies and elasticity. The protein elasticity is described by the Gaussian network model (GNM), to which we add prescribed bond binding energies that are assigned to all (nonbackbone) connecting bonds in the GNM of native state and assumed identical for simplicity. Using exact calculation of the Helmholtz free energy for this model, we consider bond rupture single events. The bond designated for rupture is chosen by minimizing the free-energy difference for the process, over all (nonbackbone) bonds in the network. Plotting the free-energy profile along this pathway at different temperatures, we observe a few major partial unfolding, metastable or stable, states, that are separated by free-energy barriers and change role as the temperature is raised. In particular, for adenylate kinase we find three major partial unfolding states, which is consistent with single molecule FRET experiments [Pirchi et al., Nat. Commun. 2, 493 (2011)] for which hidden Markov analysis reveals between three and five such states. Such states can play a major role in enzymatic activity.

Shedding light on protein folding, structural and functional dynamics by single molecule studies

The advent of advanced single molecule measurements unveiled a great wealth of dynamic information revolutionizing our understanding of protein dynamics and behavior in ways unattainable by conventional bulk assays. Equipped with the ability to record distribution of behaviors rather than the mean property of a population, single molecule measurements offer observation and quantification of the abundance, lifetime and function of multiple protein states. They also permit the direct observation of the transient and rarely populated intermediates in the energy landscape that are typically averaged out in non-synchronized ensemble measurements. Single molecule studies have thus provided novel insights about how the dynamic sampling of the free energy landscape dictates all aspects of protein behavior; from its folding to function. Here we will survey some of the state of the art contributions in deciphering mechanisms that underlie protein folding, structural and functional dynamics by single molecule fluorescence microscopy techniques. We will discuss a few selected examples highlighting the power of the emerging techniques and finally discuss the future improvements and directions.

In the multi-domain protein adenylate kinase, domain insertion facilitates cooperative folding while accommodating function at domain interfaces

Having multiple domains in proteins can lead to partial folding and increased aggregation. Folding cooperativity, the all or nothing folding of a protein, can reduce this aggregation propensity. In agreement with bulk experiments, a coarse-grained structure-based model of the three-domain protein, E. coli Adenylate kinase (AKE), folds cooperatively. Domain interfaces have previously been implicated in the cooperative folding of multi-domain proteins. To understand their role in AKE folding, we computationally create mutants with deleted inter-domain interfaces and simulate their folding. We find that inter-domain interfaces play a minor role in the folding cooperativity of AKE. On further analysis, we find that unlike other multi-domain proteins whose folding has been studied, the domains of AKE are not singly-linked. Two of its domains have two linkers to the third one, i.e., they are inserted into the third one. We use circular permutation to modify AKE chain-connectivity and convert inserted-domains into singly-linked domains. We find that domain insertion in AKE achieves the following: (1) It facilitates folding cooperativity even when domains have different stabilities. Insertion constrains the N- and C-termini of inserted domains and stabilizes their folded states. Therefore, domains that perform conformational transitions can be smaller with fewer stabilizing interactions. (2) Inter-domain interactions are not needed to promote folding cooperativity and can be tuned for function. In AKE, these interactions help promote conformational dynamics limited catalysis. Finally, using structural bioinformatics, we suggest that domain insertion may also facilitate the cooperative folding of other multi-domain proteins.

Most individual protein domains fold in an all or nothing fashion. This cooperative folding is important because it reduces the existence of partially folded proteins which can stick to each other and create disease causing aggregates. However, numerous proteins have multiple domains, independent units of folding, stability and/or function. Several such proteins also fold cooperatively. It is thought that strong interactions between individual domains allow the folding to propagate from a nucleating domain to neighbouring ones and this enables cooperative folding in multi-domain proteins. Here, we computationally study the folding of the three-domain protein AKE and find instead that the topology of the protein, wherein the two less stable domains are inserted into the more stable one, promotes folding cooperativity. When the more stable domain is folded, the ends of the inserted domains are constrained and this allows them to fold easily. In such a protein topology, strong inter-domain interactions are not needed to promote folding cooperativity. Interface amino acids which would have been involved in ensuring that the domains fit together correctly can now be tuned for binding or catalysis or conformational transitions. Thus, inserted domains may be present in multi-domain proteins to promote both function and folding.

Molecular dynamics simulation of configurational ensembles compatible with experimental FRET efficiency data through a restraint on instantaneous FRET efficiencies

Förster resonance energy transfer (FRET) measurements are widely used to investigate (bio)molecular interactions or/and association. FRET efficiencies, the primary data obtained from this method, give, in combination with the common assumption of isotropic chromophore orientation, detailed insight into the lengthscale of molecular phenomena. This study illustrates the application of a FRET efficiency restraint during classical atomistic molecular dynamics simulations of a mutant mastoparan X peptide in either water or 7 M aqueous urea. The restraint forces acting on the donor and acceptor chromophores ensure that the sampled peptide configurational ensemble satisfies the experimental primary data by modifying interchromophore separation and chromophore transition dipole moment orientations. By means of a conformational cluster analysis, it is seen that indeed different configurational ensembles may be sampled without and with application of the restraint. In particular, while the FRET efficiency and interchromophore distances monitored in an unrestrained simulation may differ from the experimentally-determined values, they can be brought in agreement with experimental data through usage of the FRET efficiency restraining potential. Furthermore, the present results suggest that the assumption of isotropic chromophore orientation is not always justified. The FRET efficiency restraint allows the generation of configurational ensembles that may not be accessible with unrestrained simulations, and thereby supports a meaningful interpretation of experimental FRET results in terms of the underlying molecular degrees of freedom. Thus, it offers an additional tool to connect the realms of computer and wet-lab experimentation.

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.

Shedding light on protein folding landscapes by single-molecule fluorescence

Single-molecule (SM) fluorescence methods have been increasingly instrumental in our current understanding of a number of key aspects of protein folding and aggregation landscapes over the past decade. With the advantage of a model free approach and the power of probing multiple subpopulations and stochastic dynamics directly in a heterogeneous structural ensemble, SM methods have emerged as a principle technique for studying complex systems such as intrinsically disordered proteins (IDPs), globular proteins in the unfolded basin and during folding, and early steps of protein aggregation in amyloidogenesis. This review highlights the application of these methods in investigating the free energy landscapes, folding properties and dynamics of individual protein molecules and their complexes, with an emphasis on inherently flexible systems such as IDPs.

Chaperones rescue luciferase folding by separating its domains

Over the last 50 years, significant progress has been made toward understanding how small single-domain proteins fold. However, very little is known about folding mechanisms of medium and large multidomain proteins that predominate the proteomes of all forms of life. Large proteins frequently fold cotranslationally and/or require chaperones. Firefly (Photinus pyralis) luciferase (Luciferase, 550 residues) has been a model of a cotranslationally folding protein whose extremely slow refolding (approximately days) is catalyzed by chaperones. However, the mechanism by which Luciferase misfolds and how chaperones assist Luciferase refolding remains unknown. Here we combine single-molecule force spectroscopy (atomic force microscopy (AFM)/single-molecule force spectroscopy) with steered molecular dynamic computer simulations to unravel the mechanism of chaperone-assisted Luciferase refolding. Our AFM and steered molecular dynamic results show that partially unfolded Luciferase, with the N-terminal domain remaining folded, can refold robustly without chaperones. Complete unfolding causes Luciferase to get trapped in very stable non-native configurations involving interactions between N- and C-terminal residues. However, chaperones allow the completely unfolded Luciferase to refold quickly in AFM experiments, strongly suggesting that chaperones are able to sequester non-natively contacting residues. More generally, we suggest that many chaperones, rather than actively promoting the folding, mimic the ribosomal exit tunnel and physically separate protein domains, allowing them to fold in a cotranslational-like sequential process.

Energy landscape views for interplays among folding, binding, and allostery of calmodulin domains

Ligand binding modulates the energy landscape of proteins, thus altering their folding and allosteric conformational dynamics. To investigate such interplay, calmodulin has been a model protein. Despite much attention, fully resolved mechanisms of calmodulin folding/binding have not been elucidated. Here, by constructing a computational model that can integrate folding, binding, and allosteric motions, we studied in-depth folding of isolated calmodulin domains coupled with binding of two calcium ions and associated allosteric conformational changes. First, mechanically pulled simulations revealed coexistence of three distinct conformational states: the unfolded, the closed, and the open states, which is in accord with and augments structural understanding of recent single-molecule experiments. Second, near the denaturation temperature, we found the same three conformational states as well as three distinct binding states: zero, one, and two calcium ion bound states, leading to as many as nine states. Third, in terms of the nine-state representation, we found multiroute folding/binding pathways and shifts in their probabilities with the calcium concentration. At a lower calcium concentration, "combined spontaneous folding and induced fit" occurs, whereas at a higher concentration, "binding-induced folding" dominates. Even without calcium binding, we observed that the folding pathway of calmodulin domains can be modulated by the presence of metastable states. Finally, full-length calmodulin also exhibited an intriguing coupling between two domains when applying tension.

High-throughput single-molecule studies of protein-DNA interactions

Fluorescence and force-based single-molecule studies of protein-nucleic acid interactions continue to shed critical insights into many aspects of DNA and RNA processing. As single-molecule assays are inherently low-throughput, obtaining statistically relevant datasets remains a major challenge. Additionally, most fluorescence-based single-molecule particle-tracking assays are limited to observing fluorescent proteins that are in the low-nanomolar range, as spurious background signals predominate at higher fluorophore concentrations. These technical limitations have traditionally limited the types of questions that could be addressed via single-molecule methods. In this review, we describe new approaches for high-throughput and high-concentration single-molecule biochemical studies. We conclude with a discussion of outstanding challenges for the single-molecule biologist and how these challenges can be tackled to further approach the biochemical complexity of the cell.

Markov state models of biomolecular conformational dynamics

It has recently become practical to construct Markov state models (MSMs) that reproduce the long-time statistical conformational dynamics of biomolecules using data from molecular dynamics simulations. MSMs can predict both stationary and kinetic quantities on long timescales (e.g. milliseconds) using a set of atomistic molecular dynamics simulations that are individually much shorter, thus addressing the well-known sampling problem in molecular dynamics simulation. In addition to providing predictive quantitative models, MSMs greatly facilitate both the extraction of insight into biomolecular mechanism (such as folding and functional dynamics) and quantitative comparison with single-molecule and ensemble kinetics experiments. A variety of methodological advances and software packages now bring the construction of these models closer to routine practice. Here, we review recent progress in this field, considering theoretical and methodological advances, new software tools, and recent applications of these approaches in several domains of biochemistry and biophysics, commenting on remaining challenges.

Collapse of a long axis: single-molecule Förster resonance energy transfer and serpin equilibrium unfolding

The energy required for mechanical inhibition of target proteases is stored in the native structure of inhibitory serpins and accessed by serpin structural remodeling. The overall serpin fold is ellipsoidal with one long and two short axes. Most of the structural remodeling required for function occurs along the long axis, while expansion of the short axes is associated with misfolded, inactive forms. This suggests that ellipticity, as typified by the long axis, may be important for both function and folding. Placement of donor and acceptor fluorophores approximately along the long axis or one of the short axes allows single-pair Förster resonance energy transfer (spFRET) to report on both unfolding transitions and the time-averaged shape of different conformations. Equilibrium unfolding and refolding studies of the well-characterized inhibitory serpin α1-antitrypsin reveal that the long axis collapses in the folding intermediates while the monitored short axis expands. These energetically distinct intermediates are thus more spherical than the native state. Our spFRET studies agree with other equilibrium unfolding studies that found that the region around one of the β strands, s5A, which helps define the long axis and must move for functionally required loop insertion, unfolds at low denaturant concentrations. This supports a connection between functionally important structural lability and unfolding in the inhibitory serpins.

Complex RNA folding kinetics revealed by single-molecule FRET and hidden Markov models

We have developed a hidden Markov model and optimization procedure for photon-based single-molecule FRET data, which takes into account the trace-dependent background intensities. This analysis technique reveals an unprecedented amount of detail in the folding kinetics of the Diels–Alderase ribozyme. We find a multitude of extended (low-FRET) and compact (high-FRET) states. Five states were consistently and independently identified in two FRET constructs and at three Mg²⁺ concentrations. Structures generally tend to become more compact upon addition of Mg²⁺. Some compact structures are observed to significantly depend on Mg²⁺ concentration, suggesting a tertiary fold stabilized by Mg²⁺ ions. One compact structure was observed to be Mg²⁺-independent, consistent with stabilization by tertiary Watson–Crick base pairing found in the folded Diels–Alderase structure. A hierarchy of time scales was discovered, including dynamics of 10 ms or faster, likely due to tertiary structure fluctuations, and slow dynamics on the seconds time scale, presumably associated with significant changes in secondary structure. The folding pathways proceed through a series of intermediate secondary structures. There exist both compact pathways and more complex ones, which display tertiary unfolding, then secondary refolding, and, subsequently, again tertiary refolding.

Spectral Rate Theory for Two-State Kinetics

Classical rate theories often fail in cases where the observable(s) or order parameter(s) used is a poor reaction coordinate or the observed signal is deteriorated by noise, such that no clear separation between reactants and products is possible. Here, we present a general spectral two-state rate theory for ergodic dynamical systems in thermal equilibrium that explicitly takes into account how the system is observed. The theory allows the systematic estimation errors made by standard rate theories to be understood and quantified. We also elucidate the connection of spectral rate theory with the popular Markov state modeling approach for molecular simulation studies. An optimal rate estimator is formulated that gives robust and unbiased results even for poor reaction coordinates and can be applied to both computer simulations and single-molecule experiments. No definition of a dividing surface is required. Another result of the theory is a model-free definition of the reaction coordinate quality. The reaction coordinate quality can be bounded from below by the directly computable observation quality, thus providing a measure allowing the reaction coordinate quality to be optimized by tuning the experimental setup. Additionally, the respective partial probability distributions can be obtained for the reactant and product states along the observed order parameter, even when these strongly overlap. The effects of both filtering (averaging) and uncorrelated noise are also examined. The approach is demonstrated on numerical examples and experimental single-molecule force-probe data of the p5ab RNA hairpin and the apo-myoglobin protein at low pH, focusing here on the case of two-state kinetics.

Comparing protein folding in vitro and in vivo: foldability meets the fitness challenge

In this review, we compare and contrast current knowledge about in vitro and in vivo protein folding. Major advances in understanding fundamental principles underlying protein folding in optimized in vitro conditions have yielded detailed physicochemical principles of folding landscapes for small, single domain proteins. In addition, there has been increased research focusing on the key features of protein folding in the cell that differentiate it from in vitro folding, such as co-translational folding, chaperone-facilitated folding, and folding in crowded conditions with many weak interactions. Yet these two research areas have not been bridged effectively in research carried out to date. This review points to gaps between the two that are ripe for future research. Moreover, we emphasize the biological selection pressures that impact protein folding in vivo and how fitness drives the evolution of protein sequences in ways that may place foldability in tension with other requirements on a given protein. We suggest that viewing the physicochemical process of protein folding through the lens of evolution will unveil new insights and pose novel challenges about in-cell folding landscapes.

Single-molecule FRET of protein structure and dynamics - a primer

Single-molecule spectroscopy has developed into a widely used method for probing the structure, dynamics, and mechanisms of biomolecular systems, especially in combination with Förster resonance energy transfer (FRET). In this introductory tutorial, essential concepts and methods will be outlined, from the FRET process and the basic considerations for sample preparation and instrumentation to some key elements of data analysis and photon statistics. Different approaches for obtaining dynamic information over a wide range of timescales will be explained and illustrated with examples, including the quantitative analysis of FRET efficiency histograms, correlation spectroscopy, fluorescence trajectories, and microfluidic mixing.

Deciphering the catalysis-associated conformational changes of human adenylate kinase 1 with single-molecule spectroscopy

Human adenylate kinase isoenzyme 1 (AK1) is the key enzyme in maintaining the cellular energy homeostasis. The catalysis-associated conformational changes of AK1 involve large-amplitude rearrangements. To decipher the conformational changes of AK1 at the single-molecule level, we tagged AK1 with two identical fluorophores, one near the substrate-binding site and the other at the boundary of the core domain. We found that magnesium ion binding to AK1 increases the structural heterogeneity of AK1, whereas ADP binding reduces the structural heterogeneity. We exploited the hidden Markov model to extract the underlying catalysis-associated conformational dynamics and determined thermodynamic parameters of the multiple catalytic pathways. The third-order correlation difference calculated from photon fluctuation traces reveals the irreversible nature of the conformational motions, suggesting that single-molecule AK1 is in a nonequilibrium steady state. This discovery offers a fresh viewpoint to look into the molecular mechanisms of cellular biochemistry.

Single vesicle biochips for ultra-miniaturized nanoscale fluidics and single molecule bioscience

One of the major bottlenecks in the development of biochips is maintaining the structure and function of biomolecules when interfacing them with hard matter (glass, plastics, metals, etc.), a challenge that is exacerbated during miniaturization that inevitably increases the interface to volume ratio of these devices. Biochips based on immobilized vesicles circumvent this problem by encapsulating biomolecules in the protective environment of a lipid bilayer, thus minimizing interactions with hard surfaces. Here we review the development of biochips based on arrays of single nanoscale vesicles, their fabrication via controlled self-assembly, and their characterization using fluorescence microscopy. We also highlight their applications in selected fields such as nanofluidics and single molecule bioscience. Despite their great potential for improved biocompatibility, extreme miniaturization and high throughput, single vesicle biochips are still a niche technology that has yet to establish its commercial relevance.

Single-Molecule Analysis of Cytochrome c Folding by Monitoring the Lifetime of an Attached Fluorescent Probe

Conformational dynamics of proteins are important for function. However, obtaining information about specific conformations is difficult for samples displaying heterogeneity. Here, time-resolved fluorescence resonance energy transfer is used to characterize the folding of single cytochrome c molecules. In particular, measurements of the fluorescence lifetimes of individual cytochrome c molecules labeled with a single dye that is quenched by energy transfer to the heme were used to monitor conformational transitions of the protein under partially denaturing conditions. These studies indicate significantly more conformational heterogeneity than has been described previously. Importantly, the use of a purified singly-labeled sample made a direct comparison to ensemble data possible. The distribution of lifetimes of single-proteins was compared to the distribution of lifetimes determined from analysis of ensemble lifetime fluorescence data. The results show broad agreement between single-molecule and ensemble data, with a similar range of lifetimes. However, the single-molecule data reveal greater conformational heterogeneity.

Microfluidic mixer designed for performing single-molecule kinetics with confocal detection on timescales from milliseconds to minutes

Microfluidic mixing in combination with single-molecule spectroscopy allows the investigation of complex biomolecular processes under non-equilibrium conditions. Here we present a protocol for building, installing and operating microfluidic mixing devices optimized for this purpose. The mixer is fabricated by replica molding with polydimethylsiloxane (PDMS), which allows the production of large numbers of devices at a low cost using a single microfabricated silicon mold. The design is based on hydrodynamic focusing combined with diffusive mixing and allows single-molecule kinetics to be recorded over five orders of magnitude in time, from 1 ms to ∼100 s. Owing to microfabricated particle filters incorporated in the inlet channels, the devices provide stable flow for many hours to days without channel blockage, which allows reliable collection of high-quality data. Modular design enables rapid exchange of samples and mixing devices, which are mounted in a specifically designed holder for use with a confocal microscopy detection system. Integrated Peltier elements provide temperature control from 4 to 37 °C. The protocol includes the fabrication of a silicon master, production of the microfluidic devices, instrumentation setup and data acquisition. Once a silicon master is available, devices can be produced and experiments started within ∼1 d of preparation. We demonstrate the performance of the system with single-molecule Förster resonance energy transfer (FRET) measurements of kinetics of protein folding and conformational changes. The dead time of 1 ms, as predicted from finite element calculations, was confirmed by the measurements.

Extracting conformational memory from single-molecule kinetic data

Single-molecule data often come in the form of stochastic time trajectories. A key question is how to extract an underlying kinetic model from the data. A traditional approach is to assume some discrete state model, that is, a model topology, and to assume that transitions between states are Markovian. The transition rates are then selected according to which ones best fit the data. However, in experiments, each apparent state can be a broad ensemble of states or can be hiding multiple interconverting states. Here, we describe a more general approach called the non-Markov memory kernel (NMMK) method. The idea is to begin with a very broad class of non-Markov models and to let the data directly select for the best possible model. To do so, we adapt an image reconstruction approach that is grounded in maximum entropy. The NMMK method is not limited to discrete state models for the data; it yields a unique model given the data, it gives error bars for the model, and it does not assume Markov dynamics. Furthermore, NMMK is less wasteful of data by letting the entire data set determine the model. When the data warrants, the NMMK gives a memory kernel that is Markovian. We highlight, by numerical example, how conformational memory extracted using this method can be translated into useful mechanistic insight.

Exploring the Dynamic Functional Landscape of Adenylate Kinase Modulated by Substrates

Adenylate kinase (ADK) has been explored widely, through both experimental and theoretical studies. However, still less is known about how the functional dynamics of ADK is modulated explicitly by its natural substrates. Here, we report a quantitative study of the dynamic energy landscape for ADK responding to the substrate binding by integrating both experimental investigations and theoretical modeling. We make theoretical predictions which are in remarkable agreement with the single molecule experiments on the substrate-bound complex. With our combined models of ADK in its apo form, in the presence of AMP or ATP, and in complex with both substrates, we specifically address the following key questions: (1) Are there intermediate state(s) during their catalytic cycle and if so how many? (2) How many pathways are there along the open-to-closed transitions and what are their corresponding weights? (3) How do substrates influence the pathway weights and the stability of the intermediates? (4) Which lid's motion is rate-limiting along the turnover cycle, the NMP or the LID domain? Our models predict two major parallel stepwise pathways and two on-pathway intermediates which are denoted as IN (NMP domain open while LID domain closed) and IL (LID domain open and NMP domain closed), respectively. Further investigation of temperature effects suggests that the IN pathway is dominant at room temperature, but the IL pathway is dominant at the optimal temperature. This leads us to propose that the IL pathway is more dominant by entropy and IN pathway by enthalpy. Remarkably, our results show that even with maximum concentrations of natural substrates, ADK still fluctuates between multiple functional states, reflecting an intrinsic capability of large-scale conformational fluctuations which may be essential to its biological function. The results based on the dual-ligands model provide the theoretical validation of random bisubstrate biproducts (Bi-Bi) mechanism for the enzymatic reaction of ADK. Additionally, the pathway flux analysis strongly suggests that the motion of the NMP domain is the rate-determining step for the conformational cycle (opening and closing).

Multidomain protein solves the folding problem by multifunnel combined landscape: theoretical investigation of a Y-family DNA polymerase

Approximately three-fourths of eukaryotic proteins are composed of multiple independently folded domains. However, much of our understanding is based on single domain proteins or isolated domains whose studies directly lead to well-known energy landscape theory in which proteins fold by navigating through a funneled energy landscape toward native structure ensembles. The degrees of freedom for proteins with multiple domains are many orders of magnitude larger than that for single domain proteins. Now, the question arises: How do the multidomain proteins solve the "protein folding problem"? Here, we specifically address this issue by exploring the structure folding relationship of Sulfolobus solfataricus DNA polymerase IV (DPO4), a prototype Y-family DNA polymerase which contains a polymerase core consisting of a palm (P domain), a finger (F domain), and a thumb domain (T domain) in addition to a little finger domain (LF domain). The theoretical results are in good agreement with the experimental data and lead to several theoretical predictions. Finally, we propose that for rapid folding into well-defined conformations which carry out the biological functions, four-domain DPO4 employs a divide-and-conquer strategy, that is, combining multiple individual folding funnels into a single funnel (domains fold independently and then coalesce). In this way, the degrees of freedom for multidomain proteins are polynomial rather than exponential, and the conformational search process can be reduced effectively from a large to a smaller time scale.

Slow unfolded-state structuring in Acyl-CoA binding protein folding revealed by simulation and experiment

Protein folding is a fundamental process in biology, key to understanding many human diseases. Experimentally, proteins often appear to fold via simple two- or three-state mechanisms involving mainly native-state interactions, yet recent network models built from atomistic simulations of small proteins suggest the existence of many possible metastable states and folding pathways. We reconcile these two pictures in a combined experimental and simulation study of acyl-coenzyme A binding protein (ACBP), a two-state folder (folding time ~10 ms) exhibiting residual unfolded-state structure, and a putative early folding intermediate. Using single-molecule FRET in conjunction with side-chain mutagenesis, we first demonstrate that the denatured state of ACBP at near-zero denaturant is unusually compact and enriched in long-range structure that can be perturbed by discrete hydrophobic core mutations. We then employ ultrafast laminar-flow mixing experiments to study the folding kinetics of ACBP on the microsecond time scale. These studies, along with Trp-Cys quenching measurements of unfolded-state dynamics, suggest that unfolded-state structure forms on a surprisingly slow (~100 μs) time scale, and that sequence mutations strikingly perturb both time-resolved and equilibrium smFRET measurements in a similar way. A Markov state model (MSM) of the ACBP folding reaction, constructed from over 30 ms of molecular dynamics trajectory data, predicts a complex network of metastable stables, residual unfolded-state structure, and kinetics consistent with experiment but no well-defined intermediate preceding the main folding barrier. Taken together, these experimental and simulation results suggest that the previously characterized fast kinetic phase is not due to formation of a barrier-limited intermediate but rather to a more heterogeneous and slow acquisition of unfolded-state structure.

Energy landscape and multiroute folding of topologically complex proteins adenylate kinase and 2ouf-knot

While fast folding of small proteins has been relatively well characterized by experiments and theories, much less is known for slow folding of larger proteins, for which recent experiments suggested quite complex and rich folding behaviors. Here, we address how the energy landscape theory can be applied to these slow folding reactions. Combining the perfect-funnel approximation with a multiscale method, we first extended our previous atomic-interaction based coarse grained (AICG) model to take into account local flexibility of protein molecules. Using this model, we then investigated the energy landscapes and folding routes of two proteins with complex topologies: a multidomain protein adenylate kinase (AKE) and a knotted protein 2ouf-knot. In the AKE folding, consistent with experimental results, the kinetic free energy surface showed several substates between the fully unfolded and native states. We characterized the structural features of these substates and transitions among them, finding temperature-dependent multiroute folding. For protein 2ouf-knot, we found that the improved atomic-interaction based coarse-grained model can spontaneously tie a knot and fold the protein with a probability up to 96%. The computed folding rate of the knotted protein was much slower than that of its unknotted counterpart, in agreement with experimental findings. Similar to the AKE case, the 2ouf-knot folding exhibited several substates and transitions among them. Interestingly, we found a dead-end substate that lacks the knot, thus suggesting backtracking mechanisms.

A simple model predicts experimental folding rates and a hub-like topology

A simple model is presented that describes general features of protein folding, in good agreement with experimental results and detailed all-atom simulations. Starting from microscopic physics, and with no free parameters, this model predicts that protein folding occurs remarkably quickly because native-like states are kinetic hubs. A hub-like network arises naturally out of microscopic physical concerns, specifically the kinetic longevity of native contacts during a search of globular conformations. The model predicts folding times scaling as τ(f) ~ e(ξN) in the number of residues, but because the model shows ξ is small, the folding times are much faster than Levinthal's approximation. Importantly, the folding time scale is found to be small due to the topology and structure of the network. We show explicitly how our model agrees with generic experimental features of the folding process, including the scaling of τ(f) with N, two-state thermodynamics, a sharp peak in C(V), and native-state fluctuations.