Energy landscape along an enzymatic reaction trajectory: hinges or cracks?

Surveying biomolecular frustration at atomic resolution

To function, biomolecules require sufficient specificity of interaction as well as stability to live in the cell while still being able to move. Thermodynamic stability of only a limited number of specific structures is important so as to prevent promiscuous interactions. The individual interactions in proteins, therefore, have evolved collectively to give funneled minimally frustrated landscapes but some strategic parts of biomolecular sequences located at specific sites in the structure have been selected to be frustrated in order to allow both motion and interaction with partners. We describe a framework efficiently to quantify and localize biomolecular frustration at atomic resolution by examining the statistics of the energy changes that occur when the local environment of a site is changed. The location of patches of highly frustrated interactions correlates with key biological locations needed for physiological function. At atomic resolution, it becomes possible to extend frustration analysis to protein-ligand complexes. At this resolution one sees that drug specificity is correlated with there being a minimally frustrated binding pocket leading to a funneled binding landscape. Atomistic frustration analysis provides a route for screening for more specific compounds for drug discovery.

The analysis of biomolecular frustration yielded insights into several aspects of protein behavior. Here the authors describe a framework to efficiently quantify and localize biomolecular frustration within proteins at atomic resolution, and observe that drug specificity is correlated with a minimally frustrated binding pocket leading to a funneled binding landscape.

Simulations of Phage T7 Capsid Expansion Reveal the Role of Molecular Sterics on Dynamics

Molecular dynamics techniques provide numerous strategies for investigating biomolecular energetics, though quantitative analysis is often only accessible for relatively small (frequently monomeric) systems. To address this limit, we use simulations in combination with a simplified energetic model to study complex rearrangements in a large assembly. We use cryo-EM reconstructions to simulate the DNA packaging-associated 3 nm expansion of the protein shell of an initially assembled phage T7 capsid (called procapsid or capsid I). This is accompanied by a disorder-order transition and expansion-associated externalization displacement of the 420 N-terminal tails of the shell proteins. For the simulations, we use an all-atom structure-based model (1.07 million atoms), which is specifically designed to probe the influence of molecular sterics on dynamics. We find that the rate at which the N-terminal tails undergo translocation depends heavily on their position within hexons and pentons. Specifically, trans-shell displacements of the hexon E subunits are the most frequent and hexon A subunits are the least frequent. The simulations also implicate numerous tail translocation intermediates during tail translocation that involve topological traps, as well as sterically induced barriers. The presented study establishes a foundation for understanding the precise relationship between molecular structure and phage maturation.

Nanosecond-Timescale Dynamics and Conformational Heterogeneity in Human GCK Regulation and Disease

Human glucokinase (GCK) is the prototypic example of an emerging class of proteins with allosteric-like behavior that originates from intrinsic polypeptide dynamics. High-resolution NMR investigations of GCK have elucidated millisecond-timescale dynamics underlying allostery. In contrast, faster motions have remained underexplored, hindering the development of a comprehensive model of cooperativity. Here, we map nanosecond-timescale dynamics and structural heterogeneity in GCK using a combination of unnatural amino acid incorporation, time-resolved fluorescence, and ¹⁹F nuclear magnetic resonance spectroscopy. We find that a probe inserted within the enzyme's intrinsically disordered loop samples multiple conformations in the unliganded state. Glucose binding and disease-associated mutations that suppress cooperativity alter the number and/or relative population of these states. Together, the nanosecond kinetics characterized here and the millisecond motions known to be essential for cooperativity provide a dynamical framework with which we address the origins of cooperativity and the mechanism of activated, hyperinsulinemia-associated, noncooperative variants.

Forging tools for refining predicted protein structures

Refining predicted protein structures with all-atom molecular dynamics simulations is one route to producing, entirely by computational means, structural models of proteins that rival in quality those that are determined by X-ray diffraction experiments. Slow rearrangements within the compact folded state, however, make routine refinement of predicted structures by unrestrained simulations infeasible. In this work, we draw inspiration from the fields of metallurgy and blacksmithing, where practitioners have worked out practical means of controlling equilibration by mechanically deforming their samples. We describe a two-step refinement procedure that involves identifying collective variables for mechanical deformations using a coarse-grained model and then sampling along these deformation modes in all-atom simulations. Identifying those low-frequency collective modes that change the contact map the most proves to be an effective strategy for choosing which deformations to use for sampling. The method is tested on 20 refinement targets from the CASP12 competition and is found to induce large structural rearrangements that drive the structures closer to the experimentally determined structures during relatively short all-atom simulations of 50 ns. By examining the accuracy of side-chain rotamer states in subensembles of structures that have varying degrees of similarity to the experimental structure, we identified the reorientation of aromatic side chains as a step that remains slow even when encouraging global mechanical deformations in the all-atom simulations. Reducing the side-chain rotamer isomerization barriers in the all-atom force field is found to further speed up refinement.

Oscillating Piconewton Force Manipulation on Single-Molecule Enzymatic Conformational and Reaction Dynamics

Oscillation force has been demonstrated in theoretical studies as a critical role in unraveling the comprehensive enzymatic dynamics and addressing its regulation on enzyme activity. Utilizing the imposed external mechanical oscillation force by our newly developed magnetic tweezers coupled with a single-molecule photon-stamping imaging spectroscopic microscope, we experimentally studied a millisecond-scale oscillation force manipulation on single horseradish peroxidase enzymatic conformational and reaction dynamics. We have studied the enzymatic reaction dynamics and found that the enzyme activity changes under the real-time oscillatory force manipulation. Moreover, the oscillation force shows the capability of manipulating the enzyme active-site conformational state as well as the nascent-formed product's interaction with the active site of the enzyme, which impacts on the product release pathways. Specifically, we have identified that there are two product releasing pathways, the solvation-mediated diffusion releasing pathway and the spilling-out releasing pathway. We have observed that the spilling-out pathway can be significantly perturbed by the oscillatory force manipulation. Our correlated interpretation of enzymatic conformational and reaction dynamics provides a new insight into the comprehensive understanding of the complex conformational dynamics evolved in an enzymatic reaction. Technically, we have also demonstrated a novel approach capable of unfolding an enzyme under an enzymatic reaction condition in real time and, furthermore, by using an oscillatory mechanical weak piconewton force to manipulate enzyme conformations, and the enzyme thermal fluctuation is fully maintained. The real-time in situ fluorescence probe at the enzymatic active site reports the active-site conformational dynamics through each enzymatic reaction turnovers.

Evolved Minimal Frustration in Multifunctional Biomolecules

Protein folding is often viewed in terms of a funneled potential or free energy landscape. A variety of experiments now indicate the existence of multifunnel landscapes, associated with multifunctional biomolecules. Here, we present evidence that these systems have evolved to exhibit the minimal number of funnels required to fulfill their cellular functions, suggesting an extension to the principle of minimum frustration. We find that minimal disruptive mutations result in additional funnels, and the associated structural ensembles become more diverse. The same trends are observed in an atomic cluster. These observations suggest guidelines for rational design of engineered multifunctional biomolecules.

Why Ubiquitin Has Not Evolved

Ubiquitin, discovered less than 50 years ago, tags thousands of diseased proteins for destruction. It is small (only 76 amino acids), and is found unchanged in mammals, birds, fish, and even worms, indicating that ubiquitin is perfect. Key features of its functionality are identified here using critical point thermodynamic scaling theory. These include synchronized pivots and hinges, a stabilizing central pivot, and Fano interference between first- and second-order elements of correlated long-range (allosteric) globular surface shape transitions. Comparison with its closest relative, 76 amino acid Nedd8, shows that the latter lacks all these features. A cracked elastic network model is proposed for the common target shared by many diseased proteins.

Protein dynamics and function from solution state NMR spectroscopy

It is well-established that dynamics are central to protein function; their importance is implicitly acknowledged in the principles of the Monod, Wyman and Changeux model of binding cooperativity, which was originally proposed in 1965. Nowadays the concept of protein dynamics is formulated in terms of the energy landscape theory, which can be used to understand protein folding and conformational changes in proteins. Because protein dynamics are so important, a key to understanding protein function at the molecular level is to design experiments that allow their quantitative analysis. Nuclear magnetic resonance (NMR) spectroscopy is uniquely suited for this purpose because major advances in theory, hardware, and experimental methods have made it possible to characterize protein dynamics at an unprecedented level of detail. Unique features of NMR include the ability to quantify dynamics (i) under equilibrium conditions without external perturbations, (ii) using many probes simultaneously, and (iii) over large time intervals. Here we review NMR techniques for quantifying protein dynamics on fast (ps-ns), slow (μs-ms), and very slow (s-min) time scales. These techniques are discussed with reference to some major discoveries in protein science that have been made possible by NMR spectroscopy.

Strain Mediated Adaptation Is Key for Myosin Mechanochemistry: Discovering General Rules for Motor Activity

A structure-based model of myosin motor is built in the same spirit of our early work for kinesin-1 and Ncd towards physical understanding of its mechanochemical cycle. We find a structural adaptation of the motor head domain in post-powerstroke state that signals faster ADP release from it compared to the same from the motor head in the pre-powerstroke state. For dimeric myosin, an additional forward strain on the trailing head, originating from the postponed powerstroke state of the leading head in the waiting state of myosin, further increases the rate of ADP release. This coordination between the two heads is the essence of the processivity of the cycle. Our model provides a structural description of the powerstroke step of the cycle as an allosteric transition of the converter domain in response to the P_i release. Additionally, the variation in structural elements peripheral to catalytic motor domain is the deciding factor behind diverse directionalities of myosin motors (myosin V & VI). Finally, we observe that there are general rules for functional molecular motors across the different families. Allosteric structural adaptation of the catalytic motor head in different nucleotide states is crucial for mechanochemistry. Strain-mediated coordination between motor heads is essential for processivity and the variation of peripheral structural elements is essential for their diverse functionalities.

Molecular motors are perhaps the most important proteins present in the cell. The importance specifically lies with the fact that these proteins use the chemical energy source (such as ATP) of the cell to generate mechanical work and perform a wide range of functionalities. In this article, we generalize the idea of using structure-based models to explore the mechanochemistry of myosin molecular motors in structural terms. We find that a structural adaptation of the motor head domain in post-powerstroke state signals faster ADP release from the trailing head to maintain its processivity while directionality arises from a careful design of peripheral structural elements. These results along with our earlier results on other motors provide a general rule for motor activity.

Resolution and Characterization of Chemical Steps in Enzyme Catalytic Sequences by Using Low-Temperature and Time-Resolved, Full-Spectrum EPR Spectroscopy in Fluid Cryosolvent and Frozen Solution Systems

Approaches to the resolution and characterization of individual chemical steps in enzyme catalytic sequences, by using temperatures in the cryogenic range of 190-250 K, and kinetics measured by time-resolved, full-spectrum electron paramagnetic resonance spectroscopy in fluid cryosolvent and frozen solution systems, are described. The preparation and performance of the adenosylcobalamin-dependent ethanolamine ammonia-lyase enzyme from Salmonella typhimurium in the two systems exemplifies the biochemical and spectroscopic methods. General advantages of low-temperature studies are (1) slowing of reaction steps, so that measurements can be made by using straightforward T-step kinetic methods and commercial instrumentation, (2) resolution of individual reaction steps, so that first-order kinetic analysis can be applied, and (3) accumulation of intermediates that are not detectable at room temperatures. The broad temperature range from room temperature to 190 K encompasses three regimes: (1) temperature-independent mean free energy surface (corresponding to native behavior); (2) the narrow temperature region of a glass-like transition in the protein, over which the free energy surface changes, revealing dependence of the native reaction on collective protein/solvent motions; and (3) the temperature range below the glass transition region, for which persistent reaction corresponds to nonnative, alternative reaction pathways, in the vicinity of the native configurational envelope. Representative outcomes of low-temperature kinetics studies are portrayed on Eyring and free energy surface (landscape) plots, and guidelines for interpretations are presented.

Probing protein multidimensional conformational fluctuations by single-molecule multiparameter photon stamping spectroscopy

Conformational motions of proteins are highly dynamic and intrinsically complex. To capture the temporal and spatial complexity of conformational motions and further to understand their roles in protein functions, an attempt is made to probe multidimensional conformational dynamics of proteins besides the typical one-dimensional FRET coordinate or the projected conformational motions on the one-dimensional FRET coordinate. T4 lysozyme hinge-bending motions between two domains along α-helix have been probed by single-molecule FRET. Nevertheless, the domain motions of T4 lysozyme are rather complex involving multiple coupled nuclear coordinates and most likely contain motions besides hinge-bending. It is highly likely that the multiple dimensional protein conformational motions beyond the typical enzymatic hinged-bending motions have profound impact on overall enzymatic functions. In this report, we have developed a single-molecule multiparameter photon stamping spectroscopy integrating fluorescence anisotropy, FRET, and fluorescence lifetime. This spectroscopic approach enables simultaneous observations of both FRET-related site-to-site conformational dynamics and molecular rotational (or orientational) motions of individual Cy3-Cy5 labeled T4 lysozyme molecules. We have further observed wide-distributed rotational flexibility along orientation coordinates by recording fluorescence anisotropy and simultaneously identified multiple intermediate conformational states along FRET coordinate by monitoring time-dependent donor lifetime, presenting a whole picture of multidimensional conformational dynamics in the process of T4 lysozyme open-close hinge-bending enzymatic turnover motions under enzymatic reaction conditions. By analyzing the autocorrelation functions of both lifetime and anisotropy trajectories, we have also observed the dynamic and static inhomogeneity of T4 lysozyme multidimensional conformational fluctuation dynamics, providing a fundamental understanding of the enzymatic reaction turnover dynamics associated with overall enzyme as well as the specific active-site conformational fluctuations that are not identifiable and resolvable in the conventional ensemble-averaged experiment.

Comparing the intrinsic dynamics of multiple protein structures using elastic network models

BACKGROUND

Elastic network models (ENMs) are based on the simple idea that a protein can be described as a set of particles connected by springs, which can then be used to describe its intrinsic flexibility using, for example, normal mode analysis. Since the introduction of the first ENM by Monique Tirion in 1996, several variants using coarser protein models have been proposed and their reliability for the description of protein intrinsic dynamics has been widely demonstrated. Lately an increasing number of studies have focused on the meaning of slow dynamics for protein function and its potential conservation through evolution. This leads naturally to comparisons of the intrinsic dynamics of multiple protein structures with varying levels of similarity.

SCOPE OF REVIEW

We describe computational strategies for calculating and comparing intrinsic dynamics of multiple proteins using elastic network models, as well as a selection of examples from the recent literature.

MAJOR CONCLUSIONS

The increasing interest for comparing dynamics across protein structures with various levels of similarity, has led to the establishment and validation of reliable computational strategies using ENMs. Comparing dynamics has been shown to be a viable way for gaining greater understanding for the mechanisms employed by proteins for their function. Choices of ENM parameters, structure alignment or similarity measures will likely influence the interpretation of the comparative analysis of protein motion.

GENERAL SIGNIFICANCE

Understanding the relation between protein function and dynamics is relevant to the fundamental understanding of protein structure-dynamics-function relationship. This article is part of a Special Issue entitled Recent developments of molecular dynamics.

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.

Single-molecule enzymatic conformational dynamics: spilling out the product molecules

Product releasing is an essential step of an enzymatic reaction, and a mechanistic understanding primarily depends on the active-site conformational changes and molecular interactions that are involved in this step of the enzymatic reaction. Here we report our work on the enzymatic product releasing dynamics and mechanism of an enzyme, horseradish peroxidase (HRP), using combined single-molecule time-resolved fluorescence intensity, anisotropy, and lifetime measurements. Our results have shown a wide distribution of the multiple conformational states involved in active-site interacting with the product molecules during the product releasing. We have identified that there is a significant pathway in which the product molecules are spilled out from the enzymatic active site, driven by a squeezing effect from a tight active-site conformational state, although the conventional pathway of releasing a product molecule from an open active-site conformational state is still a primary pathway. Our study provides new insight into the enzymatic reaction dynamics and mechanism, and the information is uniquely obtainable from our combined time-resolved single-molecule spectroscopic measurements and analyses.

Nonlinear excitations match correlated motions unveiled by NMR in proteins: a new perspective on allosteric cross-talk

In this paper we propose a novel theoretical framework for interpreting long-range dynamical correlations unveiled in proteins through NMR measurements. The theoretical rationale relies on the hypothesis that correlated motions in proteins may be reconstructed as large-scale, collective modes sustained by long-lived nonlinear vibrations known as discrete breathers (DB) localized at key, hot-spot sites. DBs are spatially localized modes, whose nonlinear nature hinders resonant coupling with the normal modes, thus conferring them long lifetimes as compared to normal modes. DBs have been predicted to exist in proteins, localized at few hot-spot residues typically within the stiffest portions of the structure. We compute DB modes analytically in the framework of the nonlinear network model, showing that the displacement patterns of many DBs localized at key sites match to a remarkable extent the experimentally uncovered correlation blueprint. The computed dispersion relations prove that it is physically possible for some of these DBs to be excited out of thermal fluctuations at room temperature. Based on our calculations, we speculate that transient energy redistribution among the vibrational modes in a protein might favor the emergence of DB-like bursts of long-lived energy at hot-spot sites with lifetimes in the ns range, able to sustain critical, function-encoding correlated motions. More generally, our calculations provide a novel quantitative tool to predict fold-spanning dynamical pathways of correlated residues that may be central to allosteric cross-talk in proteins.

Manipulating and probing enzymatic conformational fluctuations and enzyme–substrate interactions by single-molecule FRET-magnetic tweezers microscopy

To investigate the critical role of the enzyme–substrate interactions in enzymatic reactions, the enzymatic conformation and enzyme–substrate interaction at a single-molecule level are manipulated by magnetic tweezers, and the impact of the manipulation on enzyme–substrate interactions are simultaneously probed by single-molecule FRET spectroscopy.

STEREODYNAMICS, MASS EFFECT AND DOCKING FROM O(3P) + HD → OH + D AT Ecol = 0.4–1.0eV AND O(3P) + HD → OD + H AT Ecol = 0.5–1.0eV

Quasiclassical Trajectory (QCT) calculation for O(3P) + HD → OH + D and O(3P) + HD → OD + H at E col = 0.4–1.0 eV and 0.5–1.0 eV, respectively, on the lowest PES 1 3A″ of Kuppermann et al. has been done. Distribution p(ϑr) of azimuthal angles between the relative velocity k of the reactants and rotational angular momentum vector j′ of either OH or OD , p(φr) of polar as well as dihedral angles correlating k - k′ -j′, p(ϑr, φr), and PDDCS dependent upon the scattering angle ϑt of either OH , or OD between k and k′ of the reactants and products, respectively, are presented and discussed. The stereodynamics and isotopic mass effects at the smallest possible collision energies 0.4 eV and 0.5 eV for OH and OD , respectively, are significantly different. The significant mass effect with quotient 1/2 of H/D, at the corresponding collision threshold may be applied for the investigation of docking mechanism, drug modification and delivery.

Backtracking due to residual structure in the unfolded state changes the folding of the third fibronectin type III domain from tenascin-C

Residual structure in the unfolded state of a protein may play a crucial role in folding and stability. In the present study, using an all (heavy)-atom structure based model and replica exchange molecular dynamics simulations, we explored the folding landscape of the third fibronectin type III domain from tenascin-C (TNfn3). Specifically, both the wild type (WT) and a variant with two additional amino acids, Gly-Leu (GL), at the C-terminus (WT(+GL)) were studied. We found that, although both domains of TNfn3 are topologically frustrated, the early formation of the native contacts from the C-terminal end of WT(+GL) causes more "backtracking" than in the WT. As a result, the WT exhibits a two-state folding behavior with a broad transition-state ensemble, whereas the WT(+GL) folds through a metastable intermediate state. Furthermore, our study confirmed that the core of both proteins is conformationally heterogeneous and noncompact, and folds late mainly due to backtracking of the part of the core. Finally, in agreement with the previous experimental studies, our results clearly demonstrated distinct thermodynamic behavior of the two proteins with WT(+GL) being more stable.

Allosteric activation transitions in enzymes and biomolecular motors: insights from atomistic and coarse-grained simulations

The chemical step in enzymes is usually preceded by a kinetically distinct activation step that involves large-scale conformational transitions. In "simple" enzymes this step corresponds to the closure of the active site; in more complex enzymes, such as biomolecular motors, the activation step is more complex and may involve interactions with other biomolecules. These activation transitions are essential to the function of enzymes and perturbations in the scale and/or rate of these transitions are implicated in various serious human diseases; incorporating key flexibilities into engineered enzymes is also considered a major remaining challenge in rational enzyme design. Therefore it is important to understand the underlying mechanism of these transitions. This is a significant challenge to both experimental and computational studies because of the allosteric and multi-scale nature of such transitions. Using our recent studies of two enzyme systems, myosin and adenylate kinase (AK), we discuss how atomistic and coarse-grained simulations can be used to provide insights into the mechanism of activation transitions in realistic systems. Collectively, the results suggest that although many allosteric transitions can be viewed as domain displacements mediated by flexible hinges, there are additional complexities and various deviations. For example, although our studies do not find any evidence for "cracking" in AK, our results do underline the contribution of intra-domain properties (e.g., dihedral flexibility) to the rate of the transition. The study of mechanochemical coupling in myosin highlights that local changes important to chemistry require stabilization from more extensive structural changes; in this sense, more global structural transitions are needed to activate the chemistry in the active site. These discussions further emphasize the importance of better understanding factors that control the degree of co-operativity for allosteric transitions, again hinting at the intimate connection between protein stability and functional flexibility. Finally, a number of topics of considerable future interest are briefly discussed.

The origin of minus-end directionality and mechanochemistry of Ncd motors

Adaptation of molecular structure to the ligand chemistry and interaction with the cytoskeletal filament are key to understanding the mechanochemistry of molecular motors. Despite the striking structural similarity with kinesin-1, which moves towards plus-end, Ncd motors exhibit minus-end directionality on microtubules (MTs). Here, by employing a structure-based model of protein folding, we show that a simple repositioning of the neck-helix makes the dynamics of Ncd non-processive and minus-end directed as opposed to kinesin-1. Our computational model shows that Ncd in solution can have both symmetric and asymmetric conformations with disparate ADP binding affinity, also revealing that there is a strong correlation between distortion of motor head and decrease in ADP binding affinity in the asymmetric state. The nucleotide (NT) free-ADP (φ-ADP) state bound to MTs favors the symmetric conformation whose coiled-coil stalk points to the plus-end. Upon ATP binding, an enhanced flexibility near the head-neck junction region, which we have identified as the important structural element for directional motility, leads to reorienting the coiled-coil stalk towards the minus-end by stabilizing the asymmetric conformation. The minus-end directionality of the Ncd motor is a remarkable example that demonstrates how motor proteins in the kinesin superfamily diversify their functions by simply rearranging the structural elements peripheral to the catalytic motor head domain.

Proteins belonging to the kinesin superfamily are responsible for vesicle or organelle transport, spindle morphogenesis, and chromosome sorting during cell division. Interestingly, while most proteins in kinesin superfamily that share the common catalytic motor head domain have plus-end directionality along microtubules, kinesin-14 (Ncd) exhibits minus-end directionality. Despite the several circumstantial evidences on the determining factors for the motor directionality in the last decade, a comprehensive understanding of the mechanism governing the Ncd minus-end directionality is still missing. Our studies provide a clear explanation for this minus-end directionality and the associated mechanochemical cycle. Here, we modeled an Ncd motor by employing structural details available in the literature to simulate its conformational dynamics. Simulations using our structure-based model of Ncd assert that the dynamics due to a simple rearrangement of structural elements, peripheral to the catalytic motor domain, is the key player in determining both the directionality and mechanochemistry unique to Ncd motors. Although Ncd has a different directionality, it uses a similar strategy to kinesin-1 of structural adaptation of the catalytic motor domain. Therefore using the same physical principle of protein folding and very similar structural elements, motors in the kinesin superfamily are able to achieve a variety of biological function.

Dimethyl sulfoxide induced structural transformations and non-monotonic concentration dependence of conformational fluctuation around active site of lysozyme

Experimental studies have observed significant changes in both structure and function of lysozyme (and other proteins) on addition of a small amount of dimethyl sulfoxide (DMSO) in aqueous solution. Our atomistic molecular dynamic simulations of lysozyme in water-DMSO reveal the following sequence of changes on increasing DMSO concentration. (i) At the initial stage (around 5% DMSO concentration) protein's conformational flexibility gets markedly suppressed. From study of radial distribution functions, we attribute this to the preferential solvation of exposed protein hydrophobic residues by the methyl groups of DMSO. (ii) In the next stage (10-15% DMSO concentration range), lysozome partially unfolds accompanied by an increase both in fluctuation and in exposed protein surface area. (iii) Between 15-20% concentration ranges, both conformational fluctuation and solvent accessible protein surface area suddenly decrease again indicating the formation of an intermediate collapse state. These results are in good agreement with near-UV circular dichroism (CD) and fluorescence studies. We explain this apparently surprising behavior in terms of a structural transformation which involves clustering among the methyl groups of DMSO. (iv) Beyond 20% concentration of DMSO, the protein starts its final sojourn towards the unfolding state with further increase in conformational fluctuation and loss in native contacts. Most importantly, analysis of contact map and fluctuation near the active site reveal that both partial unfolding and conformational fluctuations are centered mostly on the hydrophobic core of active site of lysozyme. Our results could offer a general explanation and universal picture of the anomalous behavior of protein structure-function observed in the presence of cosolvents (DMSO, ethanol, tertiary butyl alcohol, dioxane) at their low concentrations.

Biomolecular dynamics: order-disorder transitions and energy landscapes

While the energy landscape theory of protein folding is now a widely accepted view for understanding how relatively weak molecular interactions lead to rapid and cooperative protein folding, such a framework must be extended to describe the large-scale functional motions observed in molecular machines. In this review, we discuss (1) the development of the energy landscape theory of biomolecular folding, (2) recent advances toward establishing a consistent understanding of folding and function and (3) emerging themes in the functional motions of enzymes, biomolecular motors and other biomolecular machines. Recent theoretical, computational and experimental lines of investigation have provided a very dynamic picture of biomolecular motion. In contrast to earlier ideas, where molecular machines were thought to function similarly to macroscopic machines, with rigid components that move along a few degrees of freedom in a deterministic fashion, biomolecular complexes are only marginally stable. Since the stabilizing contribution of each atomic interaction is on the order of the thermal fluctuations in solution, the rigid body description of molecular function must be revisited. An emerging theme is that functional motions encompass order-disorder transitions and structural flexibility provides significant contributions to the free energy. In this review, we describe the biological importance of order-disorder transitions and discuss the statistical-mechanical foundation of theoretical approaches that can characterize such transitions.

Why is F19Ap53 unable to bind MDM2? Simulations suggest crack propagation modulates binding

Why doesn't the F19A mutant of p53 bind to MDM2? Binding thermodynamics have suggested that the loss of packing interactions upon mutating Phe into Ala sidechain results in destabilizing the binding free energy between p53 and MDM2. Does this mutation also modulate the initial recognition between p53 and MDM2? We look at atomistic computer simulations of the process of the initial encounter between wild type p53 peptide and its F19A mutant with the N-terminal domain of MDM2. These simulations show that binding is characterized by a complex multistep process. It starts with the capture of F19 of wild type p53 by certain residues in the MDM2 binding pocket. This initial step anchors the peptide onto the surface of MDM2, and with the consequent reduction in the search space of the peptide, the peptide docks into the partially occluded surface of MDM2. This is similar to a crack forming in an otherwise occluded hydrophobic cavity in MDM2, and the peptide, docked through F19, modulates the propagation of this crack, which subsequently results in the stepwise docking of the rest of the peptide through insertions of W23 and L26. The lack of the bulky sidechain of F in the F19A mutant results in the absence of the initial "grasp" complex, and hence the mutant peptide diffuses randomly on the surface of MDM2 without binding. This is the first such demonstration of the possibility that a "kinetic" effect may partly underlie the destabilized thermodynamics of binding of F19A and is a feature that appears to be conserved in evolution. The observations by Wallace et al. (Mol Cell 2006; 23:251-63) that despite the inability of F19A to bind at the N-terminal domain of MDM2, it gets ubiquitinated, can now be partly understood based on a mechanism whereby the occupation of the binding pocket by ligands/peptides induces, via crack propagation and the dynamics of gatekeeper Y100, the ubiquitination signal for interactions between the acidic domain of MDM2 and the DNA binding domain of p53.

Protein frustratometer: a tool to localize energetic frustration in protein molecules

The frustratometer is an energy landscape theory-inspired algorithm that aims at quantifying the location of frustration manifested in protein molecules. Frustration is a useful concept for gaining insight to the proteins biological behavior by analyzing how the energy is distributed in protein structures and how mutations or conformational changes shift the energetics. Sites of high local frustration often indicate biologically important regions involved in binding or allostery. In contrast, minimally frustrated linkages comprise a stable folding core of the molecule that is conserved in conformational changes. Here, we describe the implementation of these ideas in a webserver freely available at the National EMBNet node-Argentina, at URL: http://lfp.qb.fcen.uba.ar/embnet/.

Allosteric modulation balances thermodynamic stability and restores function of ΔF508 CFTR

Most cystic fibrosis is caused by a deletion of a single residue (F508) in CFTR (cystic fibrosis transmembrane conductance regulator) that disrupts the folding and biosynthetic maturation of the ion channel protein. Progress towards understanding the underlying mechanisms and overcoming the defect remains incomplete. Here, we show that the thermal instability of human ΔF508 CFTR channel activity evident in both cell-attached membrane patches and planar phospholipid bilayers is not observed in corresponding mutant CFTRs of several non-mammalian species. These more stable orthologs are distinguished from their mammalian counterparts by the substitution of proline residues at several key dynamic locations in first N-terminal nucleotide-binding domain (NBD1), including the structurally diverse region, the γ-phosphate switch loop, and the regulatory insertion. Molecular dynamics analyses revealed that addition of the prolines could reduce flexibility at these locations and increase the temperatures of unfolding transitions of ΔF508 NBD1 to that of the wild type. Introduction of these prolines experimentally into full-length human ΔF508 CFTR together with the already recognized I539T suppressor mutation, also in the structurally diverse region, restored channel function and thermodynamic stability as well as its trafficking to and lifetime at the cell surface. Thus, while cellular manipulations that circumvent its culling by quality control systems leave ΔF508 CFTR dysfunctional at physiological temperature, restoration of the delicate balance between the dynamic protein's inherent stability and channel activity returns a near-normal state.

Strand swapping regulates the iron-sulfur cluster in the diabetes drug target mitoNEET

MitoNEET is a recently identified diabetes drug target that coordinates a transferable 2Fe-2S cluster, and additionally contains an unusual strand swap. In this manuscript, we use a dual basin structure-based model to predict and characterize the folding and functionality of strand swapping in mitoNEET. We demonstrate that a strand unswapped conformation is kinetically accessible and that multiple levels of control are employed to regulate the conformational dynamics of the system. Environmental factors such as temperature can shift route preference toward the unswapped pathway. Additionally we see that a region recently identified as contributing to frustration in folding acts as a regulatory hinge loop that modulates conformational balance. Interestingly, strand unswapping transfers strain specifically to cluster-coordinating residues, opening the cluster-coordinating pocket. Strengthening contacts within the cluster-coordinating pocket opens a new pathway between the swapped and unswapped conformation that utilizes cracking to bypass the unfolded basin. These results suggest that local control within distinct regions affect motions important in regulating mitoNEET's 2Fe-2S clusters.

Conformational flexibility and the mechanisms of allosteric transitions in topologically similar proteins

Conformational flexibility plays a central role in allosteric transition of proteins. In this paper, we extend the analysis of our previous study [S. Tripathi and J. J. Portman, Proc. Natl. Acad. Sci. U.S.A. 106, 2104 (2009)] to investigate how relatively minor structural changes of the meta-stable states can significantly influence the conformational flexibility and allosteric transition mechanism. We use the allosteric transitions of the domains of calmodulin as an example system to highlight the relationship between the transition mechanism and the inter-residue contacts present in the meta-stable states. In particular, we focus on the origin of transient local unfolding (cracking), a mechanism that can lower free energy barriers of allosteric transitions, in terms of the inter-residue contacts of the meta-stable states and the pattern of local strain that develops during the transition. We find that the magnitude of the local strain in the protein is not the sole factor determining whether a region will ultimately crack during the transition. These results emphasize that the residue interactions found exclusively in one of the two meta-stable states is the key in understanding the mechanism of allosteric conformational change.

Trimming down a protein structure to its bare foldons: spatial organization of the cooperative unit

Folding of the ribosomal protein S6 is a malleable process controlled by two competing, and partly overlapping, folding nuclei. Together, these nuclei extend over most of the S6 structure, except the edge strand β2, which is consistently missing in the folding transition states; despite being part of the S6 four-stranded sheet, β2 seems not to be part of the cooperative unit of the protein. The question is then whether β2 can be removed from the S6 structure without compromising folding cooperativity or native state integrity. To investigate this, we constructed a truncated variant of S6 lacking β2, reducing the size of the protein from 96 to 76 residues (S6(Δβ2)). The new S6 variant expresses well in Escherichia coli and has a well dispersed heteronuclear single quantum correlation spectrum and a perfectly wild-type-like crystal structure, but with a smaller three-stranded β-sheet. Moreover, S6(Δβ2) displays an archetypical v-shaped chevron plot with decreased slope of the unfolding limb, as expected from a protein with maintained folding cooperativity and reduced size. The results support the notion that foldons, as defined by the structural distribution of the folding nuclei, represent a property-based level of hierarchy in the build-up of larger protein structures and suggest that the role of β2 in S6 is mainly in intermolecular binding, consistent with the position of this strand in the ribosomal assembly.

The energy landscape analysis of cancer mutations in protein kinases

The growing interest in quantifying the molecular basis of protein kinase activation and allosteric regulation by cancer mutations has fueled computational studies of allosteric signaling in protein kinases. In the present study, we combined computer simulations and the energy landscape analysis of protein kinases to characterize the interplay between oncogenic mutations and locally frustrated sites as important catalysts of allostetric kinase activation. While structurally rigid kinase core constitutes a minimally frustrated hub of the catalytic domain, locally frustrated residue clusters, whose interaction networks are not energetically optimized, are prone to dynamic modulation and could enable allosteric conformational transitions. The results of this study have shown that the energy landscape effect of oncogenic mutations may be allosteric eliciting global changes in the spatial distribution of highly frustrated residues. We have found that mutation-induced allosteric signaling may involve a dynamic coupling between structurally rigid (minimally frustrated) and plastic (locally frustrated) clusters of residues. The presented study has demonstrated that activation cancer mutations may affect the thermodynamic equilibrium between kinase states by allosterically altering the distribution of locally frustrated sites and increasing the local frustration in the inactive form, while eliminating locally frustrated sites and restoring structural rigidity of the active form. The energy landsape analysis of protein kinases and the proposed role of locally frustrated sites in activation mechanisms may have useful implications for bioinformatics-based screening and detection of functional sites critical for allosteric regulation in complex biomolecular systems.

Probing single-molecule enzyme active-site conformational state intermittent coherence

The relationship between protein conformational dynamics and enzymatic reactions has been a fundamental focus in modern enzymology. Using single-molecule fluorescence resonance energy transfer (FRET) with a combined statistical data analysis approach, we have identified the intermittently appearing coherence of the enzymatic conformational state from the recorded single-molecule intensity-time trajectories of enzyme 6-hydroxymethyl-7,8-dihydropterin pyrophosphokinase (HPPK) in catalytic reaction. The coherent conformational state dynamics suggests that the enzymatic catalysis involves a multistep conformational motion along the coordinates of substrate-enzyme complex formation and product releasing, presenting as an extreme dynamic behavior intrinsically related to the time bunching effect that we have reported previously. The coherence frequency, identified by statistical results of the correlation function analysis from single-molecule FRET trajectories, increases with the increasing substrate concentrations. The intermittent coherence in conformational state changes at the enzymatic reaction active site is likely to be common and exist in other conformation regulated enzymatic reactions. Our results of HPPK interaction with substrate support a multiple-conformational state model, being consistent with a complementary conformation selection and induced-fit enzymatic loop-gated conformational change mechanism in substrate-enzyme active complex formation.

Statistical mechanics of protein allostery: roles of backbone and side-chain structural fluctuations

A statistical mechanical model of allosteric transition of proteins is developed by extending the structure-based model of protein folding to cases that a protein has two different native conformations. Partition function is calculated exactly within the model and free-energy surfaces associated with allostery are derived. In this paper, the model of allosteric transition proposed in a previous paper [Proc. Natl. Acad. Sci. U.S.A 134, 7775 (2010)] is reformulated to describe both fluctuation in side-chain configurations and that in backbone structures in a balanced way. The model is applied to example proteins, Ras, calmodulin, and CheY: Ras undergoes the allosteric transition between guanosine diphosphate (GDP)-bound and guanosine triphosphate (GTP)-bound forms, and the model results show that the GDP-bound form is stabilized enough to prevent unnecessary signal transmission, but the conformation in the GTP-bound state bears large fluctuation in side-chain configurations, which may help to bind multiple target proteins for multiple pathways of signaling. The calculated results of calmodulin show the scenario of sequential ordering in Ca(2+) binding and the associated allosteric conformational change, which are realized though the sequential appearing of pre-existing structural fluctuations, i.e., fluctuations to show structures suitable to bind Ca(2+) before its binding. Here, the pre-existing fluctuations to accept the second and third Ca(2+) ions are dominated by the side-chain fluctuation. In CheY, the calculated side-chain fluctuation of Tyr106 is coordinated with the backbone structural change in the β4-α4 loop, which explains the pre-existing Y-T coupling process in this protein. Ability of the model to explain allosteric transitions of example proteins supports the view that the large entropic effects lower the free-energy barrier of allosteric transition.

Dynamic allostery: linkers are not merely flexible

Most proteins consist of multiple domains. How do linkers efficiently transfer information between sites that are on different domains to activate the protein? Mere flexibility only implies that the conformations would be sampled. For fast timescales between triggering events and cellular response, which often involves large conformational change, flexibility on its own may not constitute a good solution. We posit that successive conformational states along major allosteric propagation pathways are pre-encoded in linker sequences where each state is encoded by the previous one. The barriers between these states that are hierarchically populated are lower, achieving faster timescales even for large conformational changes. We further propose that evolution has optimized the linker sequences and lengths for efficiency, which explains why mutations in linkers may affect protein function and review the literature in this light.

Frustration, specific sequence dependence, and nonlinearity in large-amplitude fluctuations of allosteric proteins

Proteins have often evolved sequences so as to acquire the ability for regulation via allosteric conformational change. Here we investigate how allosteric dynamics is designed through sequences with nonlinear interaction features. First, for 71 allosteric proteins of which two, open and closed, structures are available, a statistical survey of interactions using an all-atom model with effective solvation shows that those residue contact interactions specific to one of the two states are significantly weaker than are the contact interactions shared by the two states. This interaction feature indicates there is underlying sequence design to facilitate conformational change. Second, based on the energy landscape theory, we implement these interaction features into a new atomic-interaction-based coarse-grained model via a multiscale simulation protocol (AICG). The AICG model outperforms standard coarse-grained models for predictions of the native-state mean fluctuations and of the conformational change direction. Third, using the new model for adenylate kinase, we show that intrinsic fluctuations in one state contain rare and large-amplitude motions nearly reaching the other state. Such large-amplitude motions are realized partly by sequence specificity and partly by the nonlinear nature of contact interactions, leading to cracking. Both features enhance conformational transition rates.

Allostery in the ferredoxin protein motif does not involve a conformational switch

Regulation of protein function via cracking, or local unfolding and refolding of substructures, is becoming a widely recognized mechanism of functional control. Oftentimes, cracking events are localized to secondary and tertiary structure interactions between domains that control the optimal position for catalysis and/or the formation of protein complexes. Small changes in free energy associated with ligand binding, phosphorylation, etc., can tip the balance and provide a regulatory functional switch. However, understanding the factors controlling function in single-domain proteins is still a significant challenge to structural biologists. We investigated the functional landscape of a single-domain plant-type ferredoxin protein and the effect of a distal loop on the electron-transfer center. We find the global stability and structure are minimally perturbed with mutation, whereas the functional properties are altered. Specifically, truncating the L1,2 loop does not lead to large-scale changes in the structure, determined via X-ray crystallography. Further, the overall thermal stability of the protein is only marginally perturbed by the mutation. However, even though the mutation is distal to the iron-sulfur cluster (∼20 Å), it leads to a significant change in the redox potential of the iron-sulfur cluster (57 mV). Structure-based all-atom simulations indicate correlated dynamical changes between the surface-exposed loop and the iron-sulfur cluster-binding region. Our results suggest intrinsic communication channels within the ferredoxin fold, composed of many short-range interactions, lead to the propagation of long-range signals. Accordingly, protein interface interactions that involve L1,2 could potentially signal functional changes in distal regions, similar to what is observed in other allosteric systems.

On the role of frustration in the energy landscapes of allosteric proteins

Natural protein domains must be sufficiently stable to fold but often need to be locally unstable to function. Overall, strong energetic conflicts are minimized in native states satisfying the principle of minimal frustration. Local violations of this principle open up possibilities to form the complex multifunnel energy landscapes needed for large-scale conformational changes. We survey the local frustration patterns of allosteric domains and show that the regions that reconfigure are often enriched in patches of highly frustrated interactions, consistent both with the idea that these locally frustrated regions may act as specific hinges or that proteins may "crack" in these locations. On the other hand, the symmetry of multimeric protein assemblies allows near degeneracy by reconfiguring while maintaining minimally frustrated interactions. We also anecdotally examine some specific examples of complex conformational changes and speculate on the role of frustration in the kinetics of allosteric change.

Mining electron density for functionally relevant protein polysterism in crystal structures

This review focuses on conceptual and methodological advances in our understanding and characterization of the conformational heterogeneity of proteins. Focusing on X-ray crystallography, we describe how polysterism, the interconversion of pre-existing conformational substates, has traditionally been analyzed by comparing independent crystal structures or multiple chains within a single crystal asymmetric unit. In contrast, recent studies have focused on mining electron density maps to reveal previously ‘hidden’ minor conformational substates. Functional tests of the importance of minor states suggest that evolutionary selection shapes the entire conformational landscape, including uniquely configured conformational substates, the relative distribution of these substates, and the speed at which the protein can interconvert between them. An increased focus on polysterism may shape the way protein structure and function is studied in the coming years.

Allostery and population shift in drug discovery

Proteins can exist in a large number of conformations around their native states that can be characterized by an energy landscape. The landscape illustrates individual valleys, which are the conformational substates. From the functional standpoint, there are two key points: first, all functionally relevant substates pre-exist; and second, the landscape is dynamic and the relative populations of the substates will change following allosteric events. Allosteric events perturb the structure, and the energetic strain propagates and shifts the population. This can lead to changes in the shapes and properties of target binding sites. Here we present an overview of dynamic conformational ensembles focusing on allosteric events in signaling. We propose that combining equilibrium fluctuation concepts with genomic screens could help drug discovery.

Protein folding pathways and state transitions described by classical equations of motion of an elastic network model

Protein topology defined by the matrix of residue contacts has proved to be a fruitful basis for the study of protein dynamics. The widely implemented coarse-grained elastic network model of backbone fluctuations has been used to describe crystallographic temperature factors, allosteric couplings, and some aspects of the folding pathway. In the present study, we develop a model of protein dynamics based on the classical equations of motion of a damped network model (DNM) that describes the folding path from a completely unfolded state to the native conformation through a single-well potential derived purely from the native conformation. The kinetic energy gained through the collapse of the protein chain is dissipated through a friction term in the equations of motion that models the water bath. This approach is completely general and sufficiently fast that it can be applied to large proteins. Folding pathways for various proteins of different classes are described and shown to correlate with experimental observations and molecular dynamics and Monte Carlo simulations. Allosteric transitions between alternative protein structures are also modeled within the DNM through an asymmetric double-well potential.

Protein functional landscapes, dynamics, allostery: a tortuous path towards a universal theoretical framework

Energy landscape theories have provided a common ground for understanding the protein folding problem, which once seemed to be overwhelmingly complicated. At the same time, the native state was found to be an ensemble of interconverting states with frustration playing a more important role compared to the folding problem. The landscape of the folded protein – the native landscape – is glassier than the folding landscape; hence, a general description analogous to the folding theories is difficult to achieve. On the other hand, the native basin phase volume is much smaller, allowing a protein to fully sample its native energy landscape on the biological timescales. Current computational resources may also be used to perform this sampling for smaller proteins, to build a ‘topographical map’ of the native landscape that can be used for subsequent analysis. Several major approaches to representing this topographical map are highlighted in this review, including the construction of kinetic networks, hierarchical trees and free energy surfaces with subsequent structural and kinetic analyses. In this review, we extensively discuss the important question of choosing proper collective coordinates characterizing functional motions. In many cases, the substates on the native energy landscape, which represent different functional states, can be used to obtain variables that are well suited for building free energy surfaces and analyzing the protein's functional dynamics. Normal mode analysis can provide such variables in cases where functional motions are dictated by the molecule's architecture. Principal component analysis is a more expensive way of inferring the essential variables from the protein's motions, one that requires a long molecular dynamics simulation. Finally, the two popular models for the allosteric switching mechanism, ‘preexisting equilibrium’ and ‘induced fit’, are interpreted within the energy landscape paradigm as extreme points of a continuum of transition mechanisms. Some experimental evidence illustrating each of these two models, as well as intermediate mechanisms, is presented and discussed.

Computational delineation of the catalytic step of a high-fidelity DNA polymerase

The Bacillus fragment, belonging to a class of high-fidelity polymerases, demonstrates high processivity (adding approximately 115 bases per DNA binding event) and exceptional accuracy (1 error in 10(6) nucleotide incorporations) during DNA replication. We present analysis of structural rearrangements and energetics just before and during the chemical step (phosphodiester bond formation) using a combination of classical molecular dynamics, mixed quantum mechanics molecular mechanics simulations, and free energy computations. We find that the reaction is associative, proceeding via the two-metal-ion mechanism, and requiring the proton on the terminal primer O3' to transfer to the pyrophosphate tail of the incoming nucleotide before the formation of the pentacovalent transition state. Different protonation states for key active site residues direct the system to alternative pathways of catalysis and we estimate a free energy barrier of approximately 12 kcal/mol for the chemical step. We propose that the protonation of a highly conserved catalytic aspartic acid residue is essential for the high processivity demonstrated by the enzyme and suggest that global motions could be part of the reaction free energy landscape.