A funneled energy landscape for cytochrome c directly predicts the sequential folding route inferred from hydrogen exchange experiments

Reassessing the exon-foldon correspondence using frustration analysis

Protein folding and evolution are intimately linked phenomena. Here, we revisit the concept of exons as potential protein folding modules across a set of 38 abundant and conserved protein families. Taking advantage of genomic exon-intron organization and extensive protein sequence data, we explore exon boundary conservation and assess the foldon-like behavior of exons using energy landscape theoretic measurements. We found deviations in the exon size distribution from exponential decay indicating selection in evolution. We show that when taken together there is a pronounced tendency to independent foldability for segments corresponding to the more conserved exons, supporting the idea of exon-foldon correspondence. While 45% of the families follow this general trend when analyzed individually, there are some families for which other stronger functional determinants, such as preserving frustrated active sites, may be acting. We further develop a systematic partitioning of protein domains using exon boundary hotspots, showing that minimal common exons correspond with uninterrupted alpha and/or beta elements for the majority of the families but not for all of them.

On the role of native contact cooperativity in protein folding

The consistency of energy landscape theory predictions with available experimental data, as well as direct evidence from molecular simulations, have shown that protein folding mechanisms are largely determined by the contacts present in the native structure. As expected, native contacts are generally energetically favorable. However, there are usually at least as many energetically favorable nonnative pairs owing to the greater number of possible nonnative interactions. This apparent frustration must therefore be reduced by the greater cooperativity of native interactions. In this work, we analyze the statistics of contacts in the unbiased all-atom folding trajectories obtained by Shaw and coworkers, focusing on the unfolded state. By computing mutual cooperativities between contacts formed in the unfolded state, we show that native contacts form the most cooperative pairs, while cooperativities among nonnative or between native and nonnative contacts are typically much less favorable or even anticooperative. Furthermore, we show that the largest network of cooperative interactions observed in the unfolded state consists mainly of native contacts, suggesting that this set of mutually reinforcing interactions has evolved to stabilize the native state.

Genetically Encoded Fluorescent Probe for Detection of Heme-Induced Conformational Changes in Cytochrome c

Cytochrome c (Cytc) is a key redox protein for energy metabolism and apoptosis in cells. The activation of Cytc is composed of several steps, including its transfer to the mitochondrial membrane, binding to cytochrome c heme lyase (CCHL) and covalent attachment to heme. The spectroscopic methods are often applied to study the structural changes of Cytc. However, they require the isolation of Cytc from cells and have limited availability under physiological conditions. Despite recent studies to elucidate the tightly regulated folding mechanism of Cytc, the role of these events and their association with different conformational states remain elusive. Here, we provide a genetically encoded fluorescence method that allows monitoring of the conformational changes of Cytc upon binding to heme and CCHL. Cerulean and Venus fluorescent proteins attached at the N and C terminals of Cytc can be used to determine its unfolded, intermediate, and native states by measuring FRET amplitude. We found that the noncovalent interaction of heme in the absence of CCHL induced a shift in the FRET signal, indicating the formation of a partially folded state. The higher concentration of heme and coexpression of CCHL gave rise to the recovery of Cytc native structure. We also found that Cytc was weakly associated with CCHL in the absence of heme. As a result, a FRET-based fluorescence approach was demonstrated to elucidate the mechanism of heme-induced Cytc conformational changes with spatiotemporal resolution and can be applied to study its interaction with small molecules and other protein partners in living cells.

Exploring the folding energy landscapes of heme proteins using a hybrid AWSEM-heme model

Heme is an active center in many proteins. Here we explore computationally the role of heme in protein folding and protein structure. We model heme proteins using a hybrid model employing the AWSEM Hamiltonian, a coarse-grained forcefield for the protein chain along with AMBER, an all-atom forcefield for the heme. We carefully designed transferable force fields that model the interactions between the protein and the heme. The types of protein-ligand interactions in the hybrid model include thioester covalent bonds, coordinated covalent bonds, hydrogen bonds, and electrostatics. We explore the influence of different types of hemes (heme b and heme c) on folding and structure prediction. Including both types of heme improves the quality of protein structure predictions. The free energy landscape shows that both types of heme can act as nucleation sites for protein folding and stabilize the protein folded state. In binding the heme, coordinated covalent bonds and thioester covalent bonds for heme c drive the heme toward the native pocket. The electrostatics also facilitates the search for the binding site.

Dramatic Shape Changes Occur as Cytochrome c Folds

Extensive experimental studies on the folding of cytochrome c (Cyt c) make this small protein an ideal target for atomic detailed simulations for the purposes of quantitatively characterizing the structural transitions and the associated time scales for folding to the native state from an ensemble of unfolded states. We use previously generated atomically detailed folding trajectories by the stochastic difference equation in length to calculate the time-dependent changes in the small-angle X-ray scattering (SAXS) profiles. Excellent agreement is obtained between experiments and simulations for the time-dependent SAXS spectra, allowing us to identify the structures of the folding intermediates, which shows that Cyt c reaches the native state by a sequential folding mechanism. Using the ensembles of structures along the folding pathways, we show that compaction and the sphericity of Cyt c change dramatically from the prolate ellipsoid shape in the unfolded state to the spherical native state. Our data, which are in unprecedented quantitative agreement with all aspects of time-resolved SAXS experiments, show that hydrophobic collapse and amide group protection coincide on the 100 microseconds time scale, which is in accordance with ultrafast hydrogen/deuterium exchange studies. Based on these results, we propose that compaction of polypeptide chains, accompanied by dramatic shape changes, is a universal characteristic of globular proteins, regardless of the underlying folding mechanism.

Nature's Shortcut to Protein Folding

This Feature Article presents a view of the protein folding transition based on the hypothesis that Nature has built features within the sequences that enable a Shortcut to efficient folding. Nature's Shortcut is proposed to be the early establishment of a set of nonlocal weak contacts, constituting protein loops that significantly constrain regions of the collapsed disordered protein into a native-like low-resolution fluctuating topology of major sections of the backbone. Nature's establishment of this scaffold of nonlocal contacts is claimed to bypass what would otherwise be a nearly hopeless unaided search for the final three-dimensional structure in proteins longer than ∼100 amino acids. To support this main contention of the Feature Article, the loop hypothesis (LH) description of early folding events is experimentally tested with time-resolved Förster resonance energy transfer techniques for adenylate kinase, and the data are shown to be consistent with theoretical predictions from the sequential collapse model (SCM). The experimentally based LH and the theoretically founded SCM are argued to provide a unified picture of the role of nonlocal contacts as constituting Nature's Shortcut to protein folding. Importantly, the SCM is shown to reliably predict key nonlocal contacts utilizing only primary sequence information. This view on Nature's Shortcut is open to the protein community for further detailed assessment, including its practical consequences, by suitable application of advanced experimental and computational techniques.

The Effect of Electrostatic Interactions on the Folding Kinetics of a 3-α-Helical Bundle Protein Family

The trio of protein segment repeats called spectrins diverges by more than 2 orders of magnitude in their folding and unfolding rates, despite having very similar stabilities and almost coincidental topologies. Experimental studies revealed that the mutation of five particular residues dramatically alters the kinetic rates in the slow folders, making them similar to the rates of the fast folder. This is considered to be an exceptional behavior which seems in principle to challenge the current understanding of the protein folding process. In this work, we analyze this scenario, using a simplified computational model, combined with state-of-the-art kinetic analysis techniques. Our model faithfully separates the kinetics of the fast and slow folders and captures the effect of the five mutations. We show that the inclusion of electrostatics in the model is necessary to explain the experimental findings.

Simulations Reveal Multiple Intermediates in the Unzipping Mechanism of Neuronal SNARE Complex

The assembling of the soluble N-ethylmaleimide-sensitive factor attachment protein receptor protein complex is a fundamental step in neuronal exocytosis, and it has been extensively studied in the last two decades. Yet, many details of this process remain inaccessible with the current experimental space and time resolution. Here, we study the zipping mechanism of the soluble N-ethylmaleimide-sensitive factor attachment protein receptor complex computationally by using a coarse-grained model. We explore the different pathways available and analyze their dependence on the computational model employed. We reveal and characterize multiple intermediate states, in agreement with previous experimental findings. We use our model to analyze the influence of single-residue mutations on the thermodynamics of the folding process.

Molecular origin of the weak susceptibility of kinesin velocity to loads and its relation to the collective behavior of kinesins

Motor proteins are active enzymatic molecules that support important cellular processes by transforming chemical energy into mechanical work. Although the structures and chemomechanical cycles of motor proteins have been extensively investigated, the sensitivity of a motor's velocity in response to a force is not well-understood. For kinesin, velocity is weakly influenced by a small to midrange external force (weak susceptibility) but is steeply reduced by a large force. Here, we utilize a structure-based molecular dynamic simulation to study the molecular origin of the weak susceptibility for a single kinesin. We show that the key step in controlling the velocity of a single kinesin under an external force is the ATP release from the microtubule-bound head. Only under large loading forces can the motor head release ATP at a fast rate, which significantly reduces the velocity of kinesin. It underpins the weak susceptibility that the velocity will not change at small to midrange forces. The molecular origin of this velocity reduction is that the neck linker of a kinesin only detaches from the motor head when pulled by a large force. This prompts the ATP binding site to adopt an open state, favoring ATP release and reducing the velocity. Furthermore, we show that two load-bearing kinesins are incapable of equally sharing the load unless they are very close to each other. As a consequence of the weak susceptibility, the trailing kinesin faces the challenge of catching up to the leading one, which accounts for experimentally observed weak cooperativity of kinesins motors.

The case for defined protein folding pathways

We consider the differences between the many-pathway protein folding model derived from theoretical energy landscape considerations and the defined-pathway model derived from experiment. A basic tenet of the energy landscape model is that proteins fold through many heterogeneous pathways by way of amino acid-level dynamics biased toward selecting native-like interactions. The many pathways imagined in the model are not observed in the structure-formation stage of folding by experiments that would have found them, but they have now been detected and characterized for one protein in the initial prenucleation stage. Analysis presented here shows that these many microscopic trajectories are not distinct in any functionally significant way, and they have neither the structural information nor the biased energetics needed to select native vs. nonnative interactions during folding. The opposed defined-pathway model stems from experimental results that show that proteins are assemblies of small cooperative units called foldons and that a number of proteins fold in a reproducible pathway one foldon unit at a time. Thus, the same foldon interactions that encode the native structure of any given protein also naturally encode its particular foldon-based folding pathway, and they collectively sum to produce the energy bias toward native interactions that is necessary for efficient folding. Available information suggests that quantized native structure and stepwise folding coevolved in ancient repeat proteins and were retained as a functional pair due to their utility for solving the difficult protein folding problem.

Protein Folding-How and Why: By Hydrogen Exchange, Fragment Separation, and Mass Spectrometry

Advanced hydrogen exchange (HX) methodology can now determine the structure of protein folding intermediates and their progression in folding pathways. Key developments over time include the HX pulse labeling method with nuclear magnetic resonance analysis, the fragment separation method, the addition to it of mass spectrometric (MS) analysis, and recent improvements in the HX MS technique and data analysis. Also, the discovery of protein foldons and their role supplies an essential interpretive link. Recent work using HX pulse labeling with MS analysis finds that a number of proteins fold by stepping through a reproducible sequence of native-like intermediates in an ordered pathway. The stepwise nature of the pathway is dictated by the cooperative foldon unit construction of the protein. The pathway order is determined by a sequential stabilization principle; prior native-like structure guides the formation of adjacent native-like structure. This view does not match the funneled energy landscape paradigm of a very large number of folding tracks, which was framed before foldons were known and is more appropriate for the unguided residue-level search to surmount an initial kinetic barrier rather than for the overall unfolded-state to native-state folding pathway.

SMOG 2: A Versatile Software Package for Generating Structure-Based Models

Molecular dynamics simulations with coarse-grained or simplified Hamiltonians have proven to be an effective means of capturing the functionally important long-time and large-length scale motions of proteins and RNAs. Originally developed in the context of protein folding, structure-based models (SBMs) have since been extended to probe a diverse range of biomolecular processes, spanning from protein and RNA folding to functional transitions in molecular machines. The hallmark feature of a structure-based model is that part, or all, of the potential energy function is defined by a known structure. Within this general class of models, there exist many possible variations in resolution and energetic composition. SMOG 2 is a downloadable software package that reads user-designated structural information and user-defined energy definitions, in order to produce the files necessary to use SBMs with high performance molecular dynamics packages: GROMACS and NAMD. SMOG 2 is bundled with XML-formatted template files that define commonly used SBMs, and it can process template files that are altered according to the needs of each user. This computational infrastructure also allows for experimental or bioinformatics-derived restraints or novel structural features to be included, e.g. novel ligands, prosthetic groups and post-translational/transcriptional modifications. The code and user guide can be downloaded at http://smog-server.org/smog2.

Effects of heme binding on myoglobin folding: Coarse grained molecular simulations

Many proteins contain cofactors, such as heme, ATP and metal ions. Binding of cofactors is not only essential for their biological functions, but also can reshape the intrinsic energy landscape of protein molecules and modulate the folding and stability. However, the molecular mechanism of cofactor coupled protein folding is not well understood. In this work, we study the cofactor coupled folding of myoglobin, which is a typical cofactor (heme) containing protein, by performing molecular dynamics simulations with a structure-based protein model developed based on the energy landscape theory. We showed that the heme binding increases the stability of the myoglobin. More importantly, the heme binding tends to increase the protein folding cooperativity, and switch the folding process from a “three-state” mechanism to a “two-state” mechanism. We also showed that the folding pathways of the myoglobin can be modulated by the heme binding. By performing comparative simulations, we revealed that the above effects of heme binding are resulted from the heme induced folding of F-helix, which is otherwise unstructured at apo state, and the heme mediated contacting interactions around the heme binding site. The simulation results are consistent with available experimental data, and provide insights into the molecular mechanism of the effects of cofactor binding on the protein folding and stability.

The nature of protein folding pathways

How do proteins fold, and why do they fold in that way? This Perspective integrates earlier and more recent advances over the 50-y history of the protein folding problem, emphasizing unambiguously clear structural information. Experimental results show that, contrary to prior belief, proteins are multistate rather than two-state objects. They are composed of separately cooperative foldon building blocks that can be seen to repeatedly unfold and refold as units even under native conditions. Similarly, foldons are lost as units when proteins are destabilized to produce partially unfolded equilibrium molten globules. In kinetic folding, the inherently cooperative nature of foldons predisposes the thermally driven amino acid-level search to form an initial foldon and subsequent foldons in later assisted searches. The small size of foldon units, ∼ 20 residues, resolves the Levinthal time-scale search problem. These microscopic-level search processes can be identified with the disordered multitrack search envisioned in the "new view" model for protein folding. Emergent macroscopic foldon-foldon interactions then collectively provide the structural guidance and free energy bias for the ordered addition of foldons in a stepwise pathway that sequentially builds the native protein. These conclusions reconcile the seemingly opposed new view and defined pathway models; the two models account for different stages of the protein folding process. Additionally, these observations answer the "how" and the "why" questions. The protein folding pathway depends on the same foldon units and foldon-foldon interactions that construct the native structure.

Frustration in biomolecules

Biomolecules are the prime information processing elements of living matter. Most of these inanimate systems are polymers that compute their own structures and dynamics using as input seemingly random character strings of their sequence, following which they coalesce and perform integrated cellular functions. In large computational systems with finite interaction-codes, the appearance of conflicting goals is inevitable. Simple conflicting forces can lead to quite complex structures and behaviors, leading to the concept of frustration in condensed matter. We present here some basic ideas about frustration in biomolecules and how the frustration concept leads to a better appreciation of many aspects of the architecture of biomolecules, and especially how biomolecular structure connects to function by means of localized frustration. These ideas are simultaneously both seductively simple and perilously subtle to grasp completely. The energy landscape theory of protein folding provides a framework for quantifying frustration in large systems and has been implemented at many levels of description. We first review the notion of frustration from the areas of abstract logic and its uses in simple condensed matter systems. We discuss then how the frustration concept applies specifically to heteropolymers, testing folding landscape theory in computer simulations of protein models and in experimentally accessible systems. Studying the aspects of frustration averaged over many proteins provides ways to infer energy functions useful for reliable structure prediction. We discuss how frustration affects folding mechanisms. We review here how the biological functions of proteins are related to subtle local physical frustration effects and how frustration influences the appearance of metastable states, the nature of binding processes, catalysis and allosteric transitions. In this review, we also emphasize that frustration, far from being always a bad thing, is an essential feature of biomolecules that allows dynamics to be harnessed for function. In this way, we hope to illustrate how Frustration is a fundamental concept in molecular biology.

Learning To Fold Proteins Using Energy Landscape Theory

This review is a tutorial for scientists interested in the problem of protein structure prediction, particularly those interested in using coarse-grained molecular dynamics models that are optimized using lessons learned from the energy landscape theory of protein folding. We also present a review of the results of the AMH/AMC/AMW/AWSEM family of coarse-grained molecular dynamics protein folding models to illustrate the points covered in the first part of the article. Accurate coarse-grained structure prediction models can be used to investigate a wide range of conceptual and mechanistic issues outside of protein structure prediction; specifically, the paper concludes by reviewing how AWSEM has in recent years been able to elucidate questions related to the unusual kinetic behavior of artificially designed proteins, multidomain protein misfolding, and the initial stages of protein aggregation.

Evidence for the sequential folding mechanism in RNase H from an ensemble-based model

The number of distinct protein folding pathways starting from an unfolded ensemble, and hence, the folding mechanism is an intricate function of protein size, sequence complexity, and stability conditions. This has traditionally been a contentious issue particularly because of the ensemble nature of conventional experiments that can mask the complexity of the underlying folding landscape. Recent hydrogen-exchange experiments combined with mass spectrometry (HX-MS) reveal that the folding of RNase H proceeds in a hierarchical fashion with distinct intermediates and following a single discrete path. In our current work, we provide computational evidence for this unique folding mechanism by employing a structure-based statistical mechanical model. Upon calibrating the energetic terms of the model with equilibrium measurements, we predict multiple intermediate states in the folding of RNase H that closely resemble experimental observations. Remarkably, a simplified landscape representation adequately captures the folding complexity and predicts the possibility of a well-defined sequence of folding events. We supplement the statistical model study with both explicit solvent molecular simulations of the helical units and electrostatic calculations to provide structural and energetic insights into the early and late stages of RNase H folding that hint at the frustrated nature of its folding landscape.

Chemical exchange saturation transfer (CEST): an efficient tool for detecting molecular information on proteins' behaviour

In this communication, we report that protein remodeling processes, such as aggregation, unfolding and interaction with lipid membranes, may be investigated by magnetic resonance imaging (MRI) through the CEST mechanism.

Structural transformations of cytochrome c upon interaction with cardiolipin

Interactions of cytochrome c (cyt c) with cardiolipin (CL) play a critical role in early stages of apoptosis. Upon binding to CL, cyt c undergoes changes in secondary and tertiary structure that lead to a dramatic increase in its peroxidase activity. Insertion of the protein into membranes, insertion of CL acyl chains into the protein interior, and extensive unfolding of cyt c after adsorption to the membrane have been proposed as possible modes for interaction of cyt c with CL. Dissociation of Met80 is accompanied by opening of the heme crevice and binding of another heme ligand. Fluorescence studies have revealed conformational heterogeneity of the lipid-bound protein ensemble with distinct polypeptide conformations that vary in the degree of protein unfolding. We correlate these recent findings to other biophysical observations and rationalize the role of experimental conditions in defining conformational properties and peroxidase activity of the cyt c ensemble. Latest time-resolved studies propose the trigger and the sequence of cardiolipin-induced structural transitions of cyt c.

Mapping polymerization and allostery of hemoglobin S using point mutations

Hemoglobin is a complex system that undergoes conformational changes in response to oxygen, allosteric effectors, mutations, and environmental changes. Here, we study allostery and polymerization of hemoglobin and its variants by application of two previously described methods: (i) AllosMod for simulating allostery dynamics given two allosterically related input structures and (ii) a machine-learning method for dynamics- and structure-based prediction of the mutation impact on allostery (Weinkam et al. J. Mol. Biol. 2013, 425, 647-661), now applicable to systems with multiple coupled binding sites, such as hemoglobin. First, we predict the relative stabilities of substates and microstates of hemoglobin, which are determined primarily by entropy within our model. Next, we predict the impact of 866 annotated mutations on hemoglobin's oxygen binding equilibrium. We then discuss a subset of 30 mutations that occur in the presence of the sickle cell mutation and whose effects on polymerization have been measured. Seven of these HbS mutations occur in three predicted druggable binding pockets that might be exploited to directly inhibit polymerization; one of these binding pockets is not apparent in the crystal structure, but only in structures generated by AllosMod. For the 30 mutations, we predict that mutation-induced conformational changes within a single tetramer tend not to significantly impact polymerization; instead, these mutations more likely impact polymerization by directly perturbing a polymerization interface. Finally, our analysis of allostery allows us to hypothesize why hemoglobin evolved to have multiple subunits and a persistent low frequency sickle cell mutation.

Investigations of the low-frequency spectral density of cytochrome c upon equilibrium unfolding

The equilibrium unfolding process of ferric horse heart cytochrome c (cyt c), induced by guanidinium hydrochloride (GdHCl), was studied using UV-vis absorption spectroscopy, resonance Raman spectroscopy, and vibrational coherence spectroscopy (VCS). The unfolding process was successfully fit using a three-state model which included the fully folded (N) and unfolded (U) states, along with an intermediate (I) assigned to a Lys bound heme. The VCS spectra revealed for the first time several low-frequency heme modes that are sensitive to cyt c unfolding: γ(a) (~50 cm(-1)), γ(b) (~80 cm(-1)), γ(c) (~100 cm(-1)), and ν(s)(His-Fe-His) at 205 cm(-1). These out-of-plane modes have potential functional relevance and are activated by protein-induced heme distortions. The free energies for the N-I and the I-U transitions at pH 7.0 and 20 °C were found to be 4.6 kcal/M and 11.6 kcal/M, respectively. Imidazole was also introduced to replace the methionine ligand so the unfolding can be modeled as a two-state system. The intensity of the mode γ(b)~80 cm(-1) remains nearly constant during the unfolding process, while the amplitudes of the other low frequency modes track with spectral changes observed at higher frequency. This confirms that the heme deformation changes are coupled to the protein tertiary structural changes that take place upon unfolding. These studies also reveal that damping of the coherent oscillations depends sensitively on the coupling between heme and the surrounding water solvent.

Becoming a peroxidase: cardiolipin-induced unfolding of cytochrome c

Interactions of cytochrome c (cyt c) with a unique mitochondrial glycerophospholipid cardiolipin (CL) are relevant for the protein's function in oxidative phosphorylation and apoptosis. Binding to CL-containing membranes promotes cyt c unfolding and dramatically enhances the protein's peroxidase activity, which is critical in early stages of apoptosis. We have employed a collection of seven dansyl variants of horse heart cyt c to probe the sequence of steps in this functional transformation. Kinetic measurements have unraveled four distinct processes during CL-induced cyt c unfolding: rapid protein binding to CL liposomes; rearrangements of protein substructures with small unfolding energies; partial insertion of the protein into the lipid bilayer; and extensive protein restructuring leading to "open" extended structures. While early rearrangements depend on a hierarchy of foldons in the native structure, the later process of large-scale unfolding is influenced by protein interactions with the membrane surface. The opening of the cyt c structure exposes the heme group, which enhances the protein's peroxidase activity and also frees the C-terminal helix to aid in the translocation of the protein through CL membranes.

Stepwise protein folding at near amino acid resolution by hydrogen exchange and mass spectrometry

The kinetic folding of ribonuclease H was studied by hydrogen exchange (HX) pulse labeling with analysis by an advanced fragment separation mass spectrometry technology. The results show that folding proceeds through distinct intermediates in a stepwise pathway that sequentially incorporates cooperative native-like structural elements to build the native protein. Each step is seen as a concerted transition of one or more segments from an HX-unprotected to an HX-protected state. Deconvolution of the data to near amino acid resolution shows that each step corresponds to the folding of a secondary structural element of the native protein, termed a "foldon." Each folded segment is retained through subsequent steps of foldon addition, revealing a stepwise buildup of the native structure via a single dominant pathway. Analysis of the pertinent literature suggests that this model is consistent with experimental results for many proteins and some current theoretical results. Two biophysical principles appear to dictate this behavior. The principle of cooperativity determines the central role of native-like foldon units. An interaction principle termed "sequential stabilization" based on native-like interfoldon interactions orders the pathway.

Polymer uncrossing and knotting in protein folding, and their role in minimal folding pathways

We introduce a method for calculating the extent to which chain non-crossing is important in the most efficient, optimal trajectories or pathways for a protein to fold. This involves recording all unphysical crossing events of a ghost chain, and calculating the minimal uncrossing cost that would have been required to avoid such events. A depth-first tree search algorithm is applied to find minimal transformations to fold [Formula: see text], [Formula: see text], [Formula: see text], and knotted proteins. In all cases, the extra uncrossing/non-crossing distance is a small fraction of the total distance travelled by a ghost chain. Different structural classes may be distinguished by the amount of extra uncrossing distance, and the effectiveness of such discrimination is compared with other order parameters. It was seen that non-crossing distance over chain length provided the best discrimination between structural and kinetic classes. The scaling of non-crossing distance with chain length implies an inevitable crossover to entanglement-dominated folding mechanisms for sufficiently long chains. We further quantify the minimal folding pathways by collecting the sequence of uncrossing moves, which generally involve leg, loop, and elbow-like uncrossing moves, and rendering the collection of these moves over the unfolded ensemble as a multiple-transformation "alignment". The consensus minimal pathway is constructed and shown schematically for representative cases of an [Formula: see text], [Formula: see text], and knotted protein. An overlap parameter is defined between pathways; we find that [Formula: see text] proteins have minimal overlap indicating diverse folding pathways, knotted proteins are highly constrained to follow a dominant pathway, and [Formula: see text] proteins are somewhere in between. Thus we have shown how topological chain constraints can induce dominant pathway mechanisms in protein folding.

Impact of mutations on the allosteric conformational equilibrium

Allostery in a protein involves effector binding at an allosteric site that changes the structure and/or dynamics at a distant, functional site. In addition to the chemical equilibrium of ligand binding, allostery involves a conformational equilibrium between one protein substate that binds the effector and a second substate that less strongly binds the effector. We run molecular dynamics simulations using simple, smooth energy landscapes to sample specific ligand-induced conformational transitions, as defined by the effector-bound and effector-unbound protein structures. These simulations can be performed using our web server (http://salilab.org/allosmod/). We then develop a set of features to analyze the simulations and capture the relevant thermodynamic properties of the allosteric conformational equilibrium. These features are based on molecular mechanics energy functions, stereochemical effects, and structural/dynamic coupling between sites. Using a machine-learning algorithm on a data set of 10 proteins and 179 mutations, we predict both the magnitude and the sign of the allosteric conformational equilibrium shift by the mutation; the impact of a large identifiable fraction of the mutations can be predicted with an average unsigned error of 1k(B)T. With similar accuracy, we predict the mutation effects for an 11th protein that was omitted from the initial training and testing of the machine-learning algorithm. We also assess which calculated thermodynamic properties contribute most to the accuracy of the prediction.

Effects of macromolecular crowding on burst phase kinetics of cytochrome c folding

Excluded volume and viscosity effects of crowding agents that mimic crowded conditions in vivo on "classical" burst phase folding kinetics of cytochrome c are assessed in vitro. Upon electron transfer-triggered folding of reduced cytochrome c, far-UV time-resolved circular dichroism (TRCD) is used to monitor folding under different conditions. Earlier work has shown that folding of reduced cytochrome c from the guanidinium hydrochloride-induced unfolded ensemble in dilute phosphate buffer involves kinetic partitioning: one fraction of molecules folds rapidly, on a time scale identical to that of reduction, while the remaining population folds more slowly. In the presence of 220 mg/mL dextran 70, a synthetic macromolecular crowding agent that occupies space but does not interact with proteins, the population of the fast folding step for cytochrome c is greatly reduced. Increasing the viscosity with sucrose to the same microviscosity exhibited by the dextran solution showed no significant decrease in the amplitude of the fast-folding phase of cytochrome c. Experiments show that the unfolded-state heme ligation remains bis-His in the presence of dextran 70, but coarse-grained simulations suggest that the unfolded-state ensemble becomes more compact in the presence of crowders. We conclude that excluded volume effects alter unfolded cytochrome c such that access to fast-folding conformations is reduced.

Origin of the conformational heterogeneity of cardiolipin-bound cytochrome C

Interactions of cytochrome c (cyt c) with cardiolipin (CL) partially unfold the protein, activating its peroxidase function, a critical event in the execution of apoptosis. However, structural features of the altered protein species in the heterogeneous ensemble are difficult to probe with ensemble averaging. Analyses of the dye-to-heme distance distributions P(r) from time-resolved FRET (TR-FRET) have uncovered two distinct types of CL-bound cyt c conformations, extended and compact. We have combined TR-FRET, fluorescence correlation spectroscopy (FCS), and biolayer interferometry to develop a systematic understanding of the functional partitioning between the two conformations. The two subpopulations are in equilibrium with each other, with a submillisecond rate of conformational exchange reflecting the protein folding into a compact non-native state, as well as protein interactions with the lipid surface. Electrostatic interactions with the negatively charged lipid surface that correlate with physiologically relevant changes in CL concentrations strongly affect the kinetics of cyt c binding and conformational exchange. A predominantly peripheral binding mechanism, rather than deep protein insertion into the membrane, provides a rationale for the general denaturing effect of the CL surface and the large-scale protein unfolding. These findings closely relate to cyt c folding dynamics and suggest a general strategy for extending the time window in monitoring the kinetics of folding.

Protein dynamics viewed by hydrogen exchange

To examine the relationship between protein structural dynamics and measurable hydrogen exchange (HX) data, the detailed exchange behavior of most of the backbone amide hydrogens of Staphylococcal nuclease was compared with that of their neighbors, with their structural environment, and with other information. Results show that H-bonded hydrogens are protected from exchange, with HX rate effectively zero, even when they are directly adjacent to solvent. The transition to exchange competence requires a dynamic structural excursion that removes H-bond protection and allows exposure to solvent HX catalyst. The detailed data often make clear the nature of the dynamic excursion required. These range from whole molecule unfolding, through smaller cooperative unfolding reactions of secondary structural elements, and down to local fluctuations that involve as little as a single peptide group or side chain or water molecule. The particular motion that dominates the exchange of any hydrogen is the one that allows the fastest HX rate. The motion and the rate it produces are determined by surrounding structure and not by nearness to solvent or the strength of the protecting H-bond itself or its acceptor type (main chain, side chain, structurally bound water). Many of these motions occur over time scales that are appropriate for biochemical function.

Carbon-deuterium bonds as probes of protein thermal unfolding

We report a residue-specific characterization of the thermal unfolding mechanism of ferric horse heart cytochrome c using C-D bonds site-specifically incorporated at residues dispersed throughout three different structural elements within the protein. As the temperature increases, Met80 first dissociates from the heme center, and the protein populates a folding intermediate before transitioning to a solvent exposed state. With further increases in temperature, the C-terminal helix frays and then loses structure along with the core of the protein. Interestingly, the data also reveal that the state populated at high temperature retains some structure and possibly represents a molten globule. Elucidation of the detailed unfolding mechanism and the structure of the associated molten globule, both of which represent challenges to conventional techniques, highlights the utility of the C-D technique.

Protein folding mechanisms studied by pulsed oxidative labeling and mass spectrometry

Deciphering the mechanisms of protein folding remains a considerable challenge. In this review we discuss the application of pulsed oxidative labeling for tracking protein structural changes in a time-resolved fashion. Exposure to a microsecond OH pulse at selected time points during folding induces the oxidation of solvent-accessible side chains, whereas buried residues are protected. Oxidative modifications can be detected by mass spectrometry. Folding is associated with dramatic accessibility changes, and therefore this method can provide detailed mechanistic insights. Solvent accessibility patterns are complementary to H/D exchange investigations, which report on the extent of hydrogen bonding. This review highlights the application of pulsed OH labeling to soluble proteins as well as membrane proteins.

Temperature dependent equilibrium native to unfolded protein dynamics and properties observed with IR absorption and 2D IR vibrational echo experiments

Dynamic and structural properties of carbonmonoxy (CO)-coordinated cytochrome c(552) from Hydrogenobacter thermophilus (Ht-M61A) at different temperatures under thermal equilibrium conditions were studied with infrared absorption spectroscopy and ultrafast two-dimensional infrared (2D IR) vibrational echo experiments using the heme-bound CO as the vibrational probe. Depending on the temperature, the stretching mode of CO shows two distinct bands corresponding to the native and unfolded proteins. As the temperature is increased from low temperature, a new absorption band for the unfolded protein grows in and the native band decreases in amplitude. Both the temperature-dependent circular dichroism and the IR absorption area ratio R(A)(T), defined as the ratio of the area under the unfolded band to the sum of the areas of the native and unfolded bands, suggest a two-state transition from the native to the unfolded protein. However, it is found that the absorption spectrum of the unfolded protein increases its inhomogeneous line width and the center frequency shifts as the temperature is increased. The changes in line width and center frequency demonstrate that the unfolding does not follow simple two-state behavior. The temperature-dependent 2D IR vibrational echo experiments show that the fast dynamics of the native protein are virtually temperature independent. In contrast, the fast dynamics of the unfolded protein are slower than those of the native protein, and the unfolded protein fast dynamics and at least a portion of the slower dynamics of the unfolded protein change significantly, becoming faster as the temperature is raised. The temperature dependence of the absorption spectrum and the changes in dynamics measured with the 2D IR experiments confirm that the unfolded ensemble of conformers continuously changes its nature as unfolding proceeds, in contrast to the native state, which displays a temperature-independent distribution of structures.

The contribution of entropy, enthalpy, and hydrophobic desolvation to cooperativity in repeat-protein folding

Cooperativity is a defining feature of protein folding, but its thermodynamic and structural origins are not completely understood. By constructing consensus ankyrin repeat protein arrays that have nearly identical sequences, we quantify cooperativity by resolving stability into intrinsic and interfacial components. Heteronuclear NMR and CD spectroscopy show that these constructs adopt ankyrin repeat structures. Applying a one-dimensional Ising model to a series of constructs chosen to maximize information content in unfolding transitions, we quantify stabilities of the terminal capping repeats, and resolve the effects of denaturant into intrinsic and interfacial components. Reversible thermal denaturation resolves interfacial and intrinsic free energies into enthalpic, entropic, and heat capacity terms. Intrinsic folding is entropically disfavored, whereas interfacial interaction is entropically favored and attends a decrease in heat capacity. These results suggest that helix formation and backbone ordering occurs upon intrinsic folding, whereas hydrophobic desolvation occurs upon interfacial interaction, contributing to cooperativity.

The folding of single domain proteins--have we reached a consensus?

Rather than stressing the most recent advances in the field, this review highlights the fundamental topics where disagreement remains and where adequate experimental data are lacking. These topics include properties of the denatured state and the role of residual structure, the nature of the fundamental steps and barriers, the extent of pathway heterogeneity and non-native interactions, recent comparisons between theory and experiment, and finally, dynamical properties of the folding reaction.

Multiple routes and milestones in the folding of HIV-1 protease monomer

Proteins fold on a time scale incompatible with a mechanism of random search in conformational space thus indicating that somehow they are guided to the native state through a funneled energetic landscape. At the same time the heterogeneous kinetics suggests the existence of several different folding routes. Here we propose a scenario for the folding mechanism of the monomer of HIV–1 protease in which multiple pathways and milestone events coexist. A variety of computational approaches supports this picture. These include very long all-atom molecular dynamics simulations in explicit solvent, an analysis of the network of clusters found in multiple high-temperature unfolding simulations and a complete characterization of free-energy surfaces carried out using a structure-based potential at atomistic resolution and a combination of metadynamics and parallel tempering. Our results confirm that the monomer in solution is stable toward unfolding and show that at least two unfolding pathways exist. In our scenario, the formation of a hydrophobic core is a milestone in the folding process which must occur along all the routes that lead this protein towards its native state. Furthermore, the ensemble of folding pathways proposed here substantiates a rational drug design strategy based on inhibiting the folding of HIV–1 protease.

Vaccinia virus virulence factor N1L is a novel promising target for antiviral therapeutic intervention

The 14 kDa homodimeric N1L protein is a potent vaccinia and variola (smallpox) virulence factor. It is not essential for viral replication, but it causes a strong attenuation of viral production in culture when deleted. The N1L protein is predicted to contain the BH3-like binding domain characteristic of Bcl-2 family proteins, and it is able to bind the BH3 peptides. Its overexpression has been reported to prevent infected cells from committing apoptosis. Therefore, interfering with the N1L apoptotic blockade may be a legitimate therapeutic strategy affecting the viral growth. By using in silico ligand docking and an array of in vitro assays, we have identified submicromolar (600 nM) N1L antagonists belonging to the family of polyphenols. Their affinity is comparable to that of the BH3 peptides (70-1000 nM). We have also identified the natural polyphenol resveratrol as a moderate N1L inhibitor. Finally, we show that our ligands efficiently inhibit growth of vaccinia virus.

The folding energy landscape and free energy excitations of cytochrome c

The covalently bound heme cofactor plays a dominant role in the folding of cytochrome c. Because of the complicated inorganic chemistry of the heme, some might consider the folding of cytochrome c to be a special case, following principles different from those used to describe the folding of proteins without cofactors. Recent investigations, however, demonstrate that common models describing folding for many proteins work well for cytochrome c when heme is explicitly introduced, generally providing results that agree with experimental observations. In this Account, we first discuss results from simple native structure-based models. These models include attractive interactions between nonadjacent residues only if they are present in the crystal structure at pH 7. Because attractive nonnative contacts are not included in native structure-based models, their energy landscapes can be described as "perfectly funneled". In other words, native structure-based models are energetically guided towards the native state and contain no energetic traps that would hinder folding. Energetic traps are denoted sources of "frustration", which cause specific transient intermediates to be populated. Native structure-based models do, however, include repulsion between residues due to excluded volume. Nonenergetic traps can therefore exist if the chain, which cannot cross over itself, must partially unfold so that folding can proceed. The ability of native structure-based models to capture this kind of motion is partly responsible for their successful predictions of folding pathways for many types of proteins. Models without frustration describe the sequence of folding events for cytochrome c well (as inferred from hydrogen-exchange experiments), thereby justifying their use as a starting point. At low pH, the experimentally observed folding sequence of cytochrome c deviates from that at pH 7 and from models with perfectly funneled energy landscapes. Here, alternate folding pathways are a result of "chemical frustration". This frustration arises because some regions of the protein are destabilized more than others due to the heterogeneous distribution of titratable residues that are protonated at low pH. Beginning with native structure-based terms, we construct more complex models by adding chemical frustration. These more complex models only modestly perturb the energy landscape, which remains, overall, well funneled. These perturbed models can accurately describe how alternative folding pathways are used at low pH. At alkaline pH, cytochrome c populates distinctly different structural ensembles. For instance, lysine residues are deprotonated and compete for the heme ligation site. The same models that can describe folding at low pH also predict well the structures and relative stabilities of intermediates populated at alkaline pH. The success of models based on funneled energy landscapes suggest that cytochrome c folding is driven primarily by native contacts. The presence of heme appears to add chemical complexity to the folding process, but it does not require fundamental modification of the general principles used to describe folding. Moreover, its added complexity provides a valuable means of probing the folding energy landscape in greater detail than is possible with simpler systems.

The HD-exchange motions of ribosomal protein S6 are insensitive to reversal of the protein-folding pathway

An increasing number of protein structures are found to encompass multiple folding nuclei, allowing their structures to be formed by several competing pathways. A typical example is the ribosomal protein S6, which comprises two folding nuclei (sigma1 and sigma2) defining two competing pathways in the folding energy landscape: sigma1 --> sigma2 and sigma2 --> sigma1. The balance between the two pathways, and thus the order of folding events, is easily controlled by circular permutation. In this study, we make use of this ability to manipulate the folding pathway to demonstrate that the dynamic motions of the S6 structure are independent of how the protein folds. The HD-exchange protection factors remain the same upon complete reversal of the folding order. The phenomenon arises because the HD-exchange motions and the high-energy excitations controlling the folding pathway occur at separated free-energy levels: the Boltzmann distribution of unproductive unfolding attempts samples all unfolding channels in parallel, even those that end up in excessively high barriers. Accordingly, the findings provide a simple rationale for how to interpret native-state dynamics without the need to invoke fluctuations off the normal unfolding reaction coordinate.

Population-based local search for protein folding simulation in the MJ energy model and cubic lattices

We present experimental results on benchmark problems in 3D cubic lattice structures with the Miyazawa-Jernigan energy function for two local search procedures that utilise the pull-move set: (i) population-based local search (PLS) that traverses the energy landscape with greedy steps towards (potential) local minima followed by upward steps up to a certain level of the objective function; (ii) simulated annealing with a logarithmic cooling schedule (LSA). The parameter settings for PLS are derived from short LSA-runs executed in pre-processing and the procedure utilises tabu lists generated for each member of the population. In terms of the total number of energy function evaluations both methods perform equally well, however, PLS has the potential of being parallelised with an expected speed-up in the region of the population size. Furthermore, both methods require a significant smaller number of function evaluations when compared to Monte Carlo simulations with kink-jump moves.

Chemical frustration in the protein folding landscape: grand canonical ensemble simulations of cytochrome c

A grand canonical formalism is developed to combine discrete simulations for chemically distinct species in equilibrium. Each simulation is based on a perturbed funneled landscape. The formalism is illustrated using the alkaline-induced transitions of cytochrome c as observed by FTIR spectroscopy and with various other experimental approaches. The grand canonical simulation method accounts for the acid/base chemistry of deprotonation, the inorganic chemistry of heme ligation and misligation, and the minimally frustrated folding energy landscape, thus elucidating the physics of protein folding involved with an acid/base titration of a protein. The formalism combines simulations for each of the relevant chemical species, varying by protonation and ligation states. In contrast to models based on perfectly funneled energy landscapes that contain only contacts found in the native structure, this study introduces "chemical frustration" from deprotonation and misligation that gives rise to many intermediates at alkaline pH. While the nature of these intermediates cannot be easily inferred from available experimental data, this study provides specific structural details of these intermediates, thus extending our understanding of how cytochrome c changes with an increase in pH. The results demonstrate the importance of chemical frustration for understanding biomolecular energy landscapes.

Electrostatic effects on funneled landscapes and structural diversity in denatured protein ensembles

The denatured state of proteins is heterogeneous and susceptible to general hydrophobic and electrostatic forces, but to what extent does the funneled nature of protein energy landscapes play a role in the unfolded ensemble? We simulate the denatured ensemble of cytochrome c using a series of models. The models pinpoint the efficacy of incorporating energetic funnels toward the native state in contrast with models having no native structure-seeking tendency. These models also contain varying strengths of electrostatic effects and hydrophobic collapse. The simulations based on these models are compared with experimental distributions for the distances between a fluorescent donor and the heme acceptor that were extracted from time-resolved fluorescence energy transfer experiments on cytochrome c. Comparing simulations to detailed experimental data on several labeling sites allows us to quantify the dominant forces in denatured protein ensembles.

Characterization of alkaline transitions in ferricytochrome c using carbon-deuterium infrared probes

The alkaline-induced structural transitions of ferricytochrome c have been studied intensively as a model for how changes in metal ligation contribute to protein function and folding. Previous studies have demonstrated that multiple non-native species accumulate with increasing pH. Here, we used a combination of experiments and simulations to provide a high-resolution view of the changes associated with increasing alkaline conditions. Alkaline-induced transitions were characterized under equilibrium conditions by following changes in the IR absorptions of carbon-deuterium chromophores incorporated at Leu68, Lys72, Lys73, Lys79, and Met80. The data suggest that at least four intermediates are formed as the pH is increased prior to complete unfolding of the protein. The first alkaline transition observed appears to be driven by a single deprotonation and occurs with a midpoint of pH 8.8, but surprisingly, the intermediate formed does not appear to be one of the well-characterized lysine misligates. At higher pH, second and third deprotonations, with a combined apparent midpoint pH of 10.2, induce transitions to Lys73- or Lys79-misligated species. Interestingly, the lysine misligates appear to undergo iron reduction by the coordinated amine. A transition from the lysine misligates to another intermediate, likely a hydroxide-misligated species, is associated with a fourth deprotonation and a midpoint of pH 10.7. Finally, the protein loses tertiary structure with a fifth deprotonation that occurs with a midpoint of pH 12.7. Native topology-based models with enforced misligation are employed to help understand the structures of the observed intermediates.