Nonlinear elasticity, proteinquakes, and the energy landscapes of functional transitions in proteins

The importance of individual protein molecule dynamics in developing and assessing solid state protein preparations

Processing protein solutions into the solid state is a common approach for generating stable amorphous protein mixtures that are suitable for long-term storage. Great care is typically given to protecting the protein native structure during the various drying steps that render it into the amorphous solid state. However, many studies illustrate that chemical and physical degradations still occur in spite of this amorphous material having good glassy properties and it being stored at temperatures below its glass transition temperature (Tg). Because of these persistent issues and recent biophysical studies that have refined the debate ascribing meaning to the molecular dynamical transition temperature and Tg of protein molecules, we provide an updated discussion on the impact of assessing and managing localized, individual protein molecule nondiffusive motions in the context of proteins being prepared into bulk amorphous mixtures. Our aim is to bridge the pharmaceutical studies addressing bulk amorphous preparations and their glassy behavior, with the biophysical studies historically focused on the nondiffusive internal protein dynamics and a protein's activity, along with their combined efforts in assessing the impact of solvent hydrogen-bonding networks on local stability. We also provide recommendations for future research efforts in solid-state formulation approaches.

Global transitions of proteins explored by a multiscale hybrid methodology: application to adenylate kinase

Efficient and accurate mapping of transition pathways is a challenging problem in allosteric proteins. We propose here a to our knowledge new methodology called collective molecular dynamics (coMD). coMD takes advantage of the collective modes of motions encoded by the fold, simultaneously evaluating the interactions and energetics via a full-atomic MD simulation protocol. The basic approach is to deform the structure collectively along the modes predicted by the anisotropic network model, upon selecting them via a Monte Carlo/Metropolis algorithm from among the complete pool of all accessible modes. Application to adenylate kinase, an allosteric enzyme composed of three domains, CORE, LID, and NMP, shows that both open-to-closed and closed-to-open transitions are readily sampled by coMD, with large-scale motions of the LID dominating. An energy-barrier crossing occurs during the NMP movements. The energy barrier originates from a switch between the salt bridges K136-D118 at the LID-CORE interface and K57-E170 and D33-R156 at the CORE-NMP and LID-NMP interfaces, respectively. Despite its simplicity and computing efficiency, coMD yields ensembles of transition pathways in close accord with detailed full atomic simulations, lending support to its utility as a multiscale hybrid method for efficiently exploring the allosteric transitions of multidomain or multimeric proteins.

Protein dynamics of the HIF-2α PAS-B domain upon heterodimerization and ligand binding

Hypoxia-Inducible Factor (HIF) transcription factors are heterodimeric proteins involved in the regulation of oxygen homeostatis. Their upregulation has been related to several tumors with a remarkably poor clinical outcome. The recent discovery of a druggable cavity in the HIF-2α PAS-B domain has opened an unprecedented opportunity for targeting the HIF-2α transcription factor in view of pharmaceutical strategies. Coincidentally, a novel compound able to selectively disrupt the HIF heterodimerization with a submicromolar activity has been reported. In this work, we investigated the molecular mechanisms responsible for the inhibition by comparing the dynamical features of the HIF-2α PAS-B monomer and the HIF-2α PAS-B/HIF-1β PAS-B complex, in the ligand-bound and -unbound states. Plain and biased Molecular Dynamics were used to characterize the differential conformational changes both structurally and energetically.

Analysis of protein conformational transitions using elastic network model

In this chapter, we demonstrate the usage of a coarse-grained elastic network model to analyze protein conformational transitions in the NS3 helicase (NS3hel) of Hepatitis C virus (HCV). This analysis allows us to identify and visualize collective domain motions involved in the conformational transitions and predict the order of structural events during the transitions. It is highly efficient and applicable to many multi-domain protein structures which undergo large conformational changes to fulfill their functions. This method is made available through a Web server ( http://enm.lobos.nih.gov ).

Exploring the conformational transitions of biomolecular systems using a simple two-state anisotropic network model

Biomolecular conformational transitions are essential to biological functions. Most experimental methods report on the long-lived functional states of biomolecules, but information about the transition pathways between these stable states is generally scarce. Such transitions involve short-lived conformational states that are difficult to detect experimentally. For this reason, computational methods are needed to produce plausible hypothetical transition pathways that can then be probed experimentally. Here we propose a simple and computationally efficient method, called ANMPathway, for constructing a physically reasonable pathway between two endpoints of a conformational transition. We adopt a coarse-grained representation of the protein and construct a two-state potential by combining two elastic network models (ENMs) representative of the experimental structures resolved for the endpoints. The two-state potential has a cusp hypersurface in the configuration space where the energies from both the ENMs are equal. We first search for the minimum energy structure on the cusp hypersurface and then treat it as the transition state. The continuous pathway is subsequently constructed by following the steepest descent energy minimization trajectories starting from the transition state on each side of the cusp hypersurface. Application to several systems of broad biological interest such as adenylate kinase, ATP-driven calcium pump SERCA, leucine transporter and glutamate transporter shows that ANMPathway yields results in good agreement with those from other similar methods and with data obtained from all-atom molecular dynamics simulations, in support of the utility of this simple and efficient approach. Notably the method provides experimentally testable predictions, including the formation of non-native contacts during the transition which we were able to detect in two of the systems we studied. An open-access web server has been created to deliver ANMPathway results.

Many biomolecules are like tiny molecular machines that need to change their shapes and visit many states to perform their biological functions. For a complete molecular understanding of a biological process, one needs to have information on the relevant stable states of the system in question, as well as the pathways by which the system travels from one state to another. We report here an efficient computational method that uses the knowledge of experimental structures of a pair of stable states in order to construct an energetically favoravle pathway between them. We adopt a simple representation of the molecular system by replacing the atoms with beads connected by springs and constructing an energy function with two minima around the end-states. We searched for the structure with highest energy that the system is most likely to visit during the transition and created two paths starting from this structure and proceeding toward the end-states. The combined result of these two paths is the minimum energy pathway between the two stable states. We apply this method to study important structural changes in one enzyme and three large proteins that transport small molecules and ions across the cell membrane.

Perspective: Coarse-grained models for biomolecular systems

By focusing on essential features, while averaging over less important details, coarse-grained (CG) models provide significant computational and conceptual advantages with respect to more detailed models. Consequently, despite dramatic advances in computational methodologies and resources, CG models enjoy surging popularity and are becoming increasingly equal partners to atomically detailed models. This perspective surveys the rapidly developing landscape of CG models for biomolecular systems. In particular, this review seeks to provide a balanced, coherent, and unified presentation of several distinct approaches for developing CG models, including top-down, network-based, native-centric, knowledge-based, and bottom-up modeling strategies. The review summarizes their basic philosophies, theoretical foundations, typical applications, and recent developments. Additionally, the review identifies fundamental inter-relationships among the diverse approaches and discusses outstanding challenges in the field. When carefully applied and assessed, current CG models provide highly efficient means for investigating the biological consequences of basic physicochemical principles. Moreover, rigorous bottom-up approaches hold great promise for further improving the accuracy and scope of CG models for biomolecular systems.

Enhancing the quality of protein conformation ensembles with relative populations

The function and dynamics of many proteins are best understood not from a single structure but from an ensemble. A high quality ensemble is necessary for accurately delineating protein dynamics. However, conformations in an ensemble are generally given equal weights. Few attempts were made to assign relative populations to the conformations, mainly due to the lack of right experimental data. Here we propose a method for assigning relative populations to ensembles using experimental residue dipolar couplings (RDC) as constraints, and show that relative populations can significantly enhance an ensemble's ability in representing the native states and dynamics. The method works by identifying conformation states within an ensemble and assigning appropriate relative populations to them. Each of these conformation states is represented by a sub-ensemble consisting of a subset of the conformations. Application to the ubiquitin X-ray ensemble clearly identifies two key conformation states, with relative populations in excellent agreement with previous work. We then apply the method to a reprotonated ERNST ensemble that is enhanced with a switched conformation, and show that as a result of population reweighting, not only the reproduction of RDCs is significantly improved, but common conformational features (particularly the dihedral angle distributions of ϕ 53 and ψ 52) also emerge for both the X-ray ensemble and the reprotonated ERNST ensemble.

An allosteric signaling pathway of human 3-phosphoglycerate kinase from force distribution analysis

3-Phosphogycerate kinase (PGK) is a two domain enzyme, which transfers a phosphate group between its two substrates, 1,3-bisphosphoglycerate bound to the N-domain and ADP bound to the C-domain. Indispensable for the phosphoryl transfer reaction is a large conformational change from an inactive open to an active closed conformation via a hinge motion that should bring substrates into close proximity. The allosteric pathway resulting in the active closed conformation has only been partially uncovered. Using Molecular Dynamics simulations combined with Force Distribution Analysis (FDA), we describe an allosteric pathway, which connects the substrate binding sites to the interdomain hinge region. Glu192 of alpha-helix 7 and Gly394 of loop L14 act as hinge points, at which these two secondary structure elements straighten, thereby moving the substrate-binding domains towards each other. The long-range allosteric pathway regulating hPGK catalytic activity, which is partially validated and can be further tested by mutagenesis, highlights the virtue of monitoring internal forces to reveal signal propagation, even if only minor conformational distortions, such as helix bending, initiate the large functional rearrangement of the macromolecule.

3-Phosphoglycerate kinase (PGK) is an essential enzyme for living organisms. It catalyzes the phospho-transfer reaction between two catabolites during carbohydrate metabolism. In addition to this physiological role, human PGK has been shown to phosphorylate L-nucleoside analogues, potential drugs against viral infection and cancer. PGK is a two domain enzyme, with the two substrates bound to the two separate domains. In order to perform its function the enzyme has to undergo a large conformational change involving a hinge bending to bring the substrates into close proximity. The allosteric pathway from the open non-reactive state of PGK to the closed reactive state as triggered by substrate binding has only been partially uncovered by experimental studies. Here we describe a complete allosteric pathway, which connects the substrate binding sites to the interdomain hinge region using Molecular Dynamics simulations combined with Force Distribution Analysis (FDA). While previously identified key residues involved in PGK domain closure are part of this pathway, we here fill the numerous gaps in the pathway by identifying newly uncovered residues and interesting candidates for future mutational studies.

HDX-MS takes centre stage at unravelling kinase dynamics

In recent years, HDX-MS (hydrogen–deuterium exchange coupled to MS) on biomolecules has evolved from a niche technique to a powerful method in the investigation of protein dynamics. Protein kinases, in particular, represent an area of active study using this technique owing to their well-characterized protein structures and their relevance to diseases such as cancer, immune disorders and neurodegenerative defects. In the present review, we describe how HDX-MS has revealed important dynamic properties of protein kinases and provided insight into the mechanisms of drug binding.

Long-range electron transfer with myoglobin immobilized at Au/mixed-SAM junctions: mechanistic impact of the strong protein confinement

Horse muscle myoglobin (Mb) was tightly immobilized at Au-deposited ~15-Å-thick mixed-type (1:1) alkanethiol SAMs, HS-(CH₂)₁₁-COOH/HS-(CH₂)₁₁-OH, and placed in contact with buffered H₂O or D₂O solutions. Fast-scan cyclic voltammetry (CV) and a Marcus-equation-based analysis were applied to determine unimolecular standard rate constants and reorganization free energies for electron transfer (ET), under variable-temperature (15-55 °C) and -pressure (0.01-150 MPa) conditions. The CV signal was surprisingly stable and reproducible even after multiple temperature and pressure cycles. The data analysis revealed the following values: standard rate constant, 33 s⁻¹ (25 °C, 0.01 MPa, H₂O); reorganization free energy, 0.5 ± 0.1 eV (throughout); activation enthalpy, 12 ± 3 kJ mol⁻¹; activation volume, -3.1 ± 0.2 cm³ mol⁻¹; and pH-dependent solvent kinetic isotope effect (k(H)⁰/k(D)⁰), 0.7-1.4. Furthermore, the values for the rate constant and reorganization free energy are very similar to those previously found for cytochrome c electrostatically immobilized at the monocomponent Au/HS-(CH₂)₁₁-COOH junction. In vivo, Mb apparently forms a natural electrostatic complex with cytochrome b₅ (cyt-b₅) through the "dynamic" (loose) docking pattern, allowing for a slow ET that is intrinsically coupled to the water's removal from the "defective" heme iron (altogether shaping the biological repair mechanism for Mb's "met" form). In contrary, our experiments rather mimic the case of a "simple" (tight) docking of the redesigned (mutant) Mb with cyt-b₅ (Nocek et al. J. Am. Chem. Soc. 2010, 132, 6165-6175). According to our analysis, in this configuration, Mb's distal pocket (linked to the "ligand channel") seems to be arrested within the restricted configuration, allowing the rate-determining reversible ET process to be coupled only to the inner-sphere reorganization (minimal elongation/shortening of an Fe-OH₂ bond) rather than the pronounced detachment (rebinding) of water and, hence, to be much faster.

Strain hardening and highly resilient hydrogels crosslinked by chain-extended reactive pseudo-polyrotaxane

Hydrogels with obvious strain hardening and high resilience properties in both stretching and compressing processes are constructed by simple free-radical copolymerization of acrylamide and reactive pseudo-polyrotaxane.

Seeing the invisible by paramagnetic and diamagnetic NMR

Sparsely populated transient states of proteins and their complexes play an important role in many biological processes including protein-protein and protein-DNA recognition, allostery, conformational selection, induced fit and self-assembly. These states are difficult to study as their low population and transient nature makes them effectively invisible to conventional structural and biophysical techniques. In the present article, I summarize recent NMR developments in our laboratory, including the use of paramagnetic relaxation enhancement, lifetime line broadening and dark-state exchange saturation transfer spectroscopy, that have permitted such sparsely populated states to be detected, characterized and, in some instances, visualized. I illustrate the application of these methods to the elucidation of mechanisms whereby transcription factors locate their specific target sites within an overwhelming sea of non-specific DNA, to the characterization of encounter complexes in protein-protein recognition, to large-scale interdomain motions involved in ligand binding, and to the interaction of monomeric amyloid β-peptide with the surface of amyloid protofibrils and the internal cavity surface of the chaperonin GroEL.

Funneling and frustration in the energy landscapes of some designed and simplified proteins

We explore the similarities and differences between the energy landscapes of proteins that have been selected by nature and those of some proteins designed by humans. Natural proteins have evolved to function as well as fold, and this is a source of energetic frustration. The sequence of Top7, on the other hand, was designed with architecture alone in mind using only native state stability as the optimization criterion. Its topology had not previously been observed in nature. Experimental studies show that the folding kinetics of Top7 is more complex than the kinetics of folding of otherwise comparable naturally occurring proteins. In this paper, we use structure prediction tools, frustration analysis, and free energy profiles to illustrate the folding landscapes of Top7 and two other proteins designed by Takada. We use both perfectly funneled (structure-based) and predictive (transferable) models to gain insight into the role of topological versus energetic frustration in these systems and show how they differ from those found for natural proteins. We also study how robust the folding of these designs would be to the simplification of the sequences using fewer amino acid types. Simplification using a five amino acid type code results in comparable quality of structure prediction to the full sequence in some cases, while the two-letter simplification scheme dramatically reduces the quality of structure prediction.

Differential modulation of functional dynamics and allosteric interactions in the Hsp90-cochaperone complexes with p23 and Aha1: a computational study

Allosteric interactions of the molecular chaperone Hsp90 with a large cohort of cochaperones and client proteins allow for molecular communication and event coupling in signal transduction networks. The integration of cochaperones into the Hsp90 system is driven by the regulatory mechanisms that modulate the progression of the ATPase cycle and control the recruitment of the Hsp90 clientele. In this work, we report the results of computational modeling of allosteric regulation in the Hsp90 complexes with the cochaperones p23 and Aha1. By integrating protein docking, biophysical simulations, modeling of allosteric communications, protein structure network analysis and the energy landscape theory we have investigated dynamics and stability of the Hsp90-p23 and Hsp90-Aha1 interactions in direct comparison with the extensive body of structural and functional experiments. The results have revealed that functional dynamics and allosteric interactions of Hsp90 can be selectively modulated by these cochaperones via specific targeting of the regulatory hinge regions that could restrict collective motions and stabilize specific chaperone conformations. The protein structure network parameters have quantified the effects of cochaperones on conformational stability of the Hsp90 complexes and identified dynamically stable communities of residues that can contribute to the strengthening of allosteric interactions. According to our results, p23-mediated changes in the Hsp90 interactions may provide "molecular brakes" that could slow down an efficient transmission of the inter-domain allosteric signals, consistent with the functional role of p23 in partially inhibiting the ATPase cycle. Unlike p23, Aha1-mediated acceleration of the Hsp90-ATPase cycle may be achieved via modulation of the equilibrium motions that facilitate allosteric changes favoring a closed dimerized form of Hsp90. The results of our study have shown that Aha1 and p23 can modulate the Hsp90-ATPase activity and direct the chaperone cycle by exerting the precise control over structural stability, global movements and allosteric communications in Hsp90.

Nanoscale protein dynamics: a new frontier for neutron spin echo spectroscopy

Recent studies show that neutron spin echo spectroscopy (NSE) can reveal long-range protein domain motions on nanometer lengthscales and on nanosecond to microsecond timescales. This unique capability of NSE provides new opportunities to understand protein dynamics and functions, such as how binding signals are propagated in a protein to distal sites. Here we review our applications of NSE to the study of nanoscale protein domain motions in a set of cell signaling proteins. We summarize the theoretical framework we have developed, which allows one to interpret the NSE data (Biophys. J. 99, 3473 (2010) and Proc. Natl. Acad. Sci. USA 102, 17646 (2005)). Our theoretical framework uses simple concepts from nonequilibrium statistical mechanics, and does not require elaborate molecular dynamics simulations, complex fits to rotational motion, or elastic network models. It is thus more robust than multiparameter techniques that require untestable assumptions. We also demonstrate our experimental scheme involving deuterium labeling of a protein domain or a subunit in a protein complex. We show that our selective deuteration scheme can highlight and resolve specific domain dynamics from the abundant global translational and rotational motions in a protein. Our approach thus clears significant hurdles to the application of NSE for the study of protein dynamics in solution.

Molecular dynamics studies on the conformational transitions of adenylate kinase: a computational evidence for the conformational selection mechanism

Escherichia coli adenylate kinase (ADK) is a monomeric phosphotransferase enzyme that catalyzes reversible transfer of phosphoryl group from ATP to AMP with a large-scale domain motion. The detailed mechanism for this conformational transition remains unknown. In the current study, we performed long time-scale molecular dynamics simulations on both open and closed states of ADK. Based on the structural analyses of the simulation trajectories, we detected over 20 times conformational transitions between the open and closed states of ADK and identified two novel conformations as intermediate states in the catalytic processes. With these findings, we proposed a possible mechanism for the large-scale domain motion of Escherichia coli ADK and its catalytic process: (1) the substrate free ADK adopted an open conformation; (2) ATP bound with LID domain closure; (3) AMP bound with NMP domain closure; (4) phosphoryl transfer occurred with ATP, and AMP converted into two ADPs, and no conformational transition was detected in the enzyme; (5) LID domain opened with one ADP released; (6) another ADP released with NMP domain open. As both open and closed states sampled a wide range of conformation transitions, our simulation strongly supported the conformational selection mechanism for Escherichia coli ADK.

Entropic mechanism of allosteric communication in conformational transitions of dihydrofolate reductase

The mechanism of allosteric conformational transitions of Escherichia coli dihydrofolate reductase (DHFR) is investigated theoretically by applying a newly developed coarse-grained model. Functional forms of interaction potentials in the model depend on the local structural environments around those interactions to represent the many-residue effects due to atomic packing in each local region, and hence, this model is called "the chameleon model". The chameleon model consistently describes the free-energy landscape of two conformational transitions in the catalytic cycle of DHFR, which we call conformational transition 1 (CT1) and conformational transition 2 (CT2); CT1 is accompanied by the hydride transfer reaction, and CT2 is accompanied by the product ligand release. The transition state of CT1 is entropically stabilized by the disordering of loops at the peripheral regions of the protein, which enhances the positively correlated fluctuations at the center part of the protein, showing that the allosteric communication between distant regions through the central region is intrinsically associated with the entropic stabilization of the transition state. The transition state of CT2 is entropically stabilized through the mechanism that enhances the breathing motion of two domains, showing that the difference in the distribution of interactions brings about the difference in the transition mechanism between CT1 and CT2. The chameleon model opens a way to consistently describe the dynamical energy landscape of enzymatic reactions.

Exploration of conformational transition pathways from coarse-grained simulations

MOTIVATION

A new algorithm to trace conformational transitions in proteins is presented. The method uses discrete molecular dynamics as engine to sample protein conformational space. A multiple minima Go-like potential energy function is used in combination with several enhancing sampling strategies, such as metadynamics, Maxwell Demon molecular dynamics and essential dynamics. The method, which shows an unprecedented computational efficiency, is able to trace a wide range of known experimental transitions. Contrary to simpler methods our strategy does not introduce distortions in the chemical structure of the protein and is able to reproduce well complex non-linear conformational transitions. The method, called GOdMD, can easily introduce additional restraints to the transition (presence of ligand, known intermediate, known maintained contacts, …) and is freely distributed to the community through the Spanish National Bioinformatics Institute (http://mmb.irbbarcelona.org/GOdMD).

AVAILABILITY

Freely available on the web at http://mmb.irbbarcelona.org/GOdMD.

Correlated motions and residual frustration in thrombin

Thrombin is the central protease in the cascade of blood coagulation proteases. The structure of thrombin consists of a double β-barrel core surrounded by connecting loops and helices. Compared to chymotrypsin, thrombin has more extended loops that are thought to have arisen from insertions in the serine protease that evolved to impart greater specificity. Previous experiments showed thermodynamic coupling between ligand binding at the active site and distal exosites. We present a combined approach of molecular dynamics (MD), accelerated molecular dynamics (AMD), and analysis of the residual local frustration of apo-thrombin and active-site-bound (PPACK-thrombin). Community analysis of the MD ensembles identified changes upon active site occupation in groups of residues linked through correlated motions and physical contacts. AMD simulations, calibrated on measured residual dipolar couplings, reveal that upon active site ligation, correlated loop motions are quenched, but new ones connecting the active site with distal sites where allosteric regulators bind emerge. Residual local frustration analysis reveals a striking correlation between frustrated contacts and regions undergoing slow time scale dynamics. The results elucidate a motional network that probably evolved through retention of frustrated contacts to provide facile conversion between ensembles of states.

A mechanistic understanding of allosteric immune escape pathways in the HIV-1 envelope glycoprotein

The HIV-1 envelope (Env) spike, which consists of a compact, heterodimeric trimer of the glycoproteins gp120 and gp41, is the target of neutralizing antibodies. However, the high mutation rate of HIV-1 and plasticity of Env facilitates viral evasion from neutralizing antibodies through various mechanisms. Mutations that are distant from the antibody binding site can lead to escape, probably by changing the conformation or dynamics of Env; however, these changes are difficult to identify and define mechanistically. Here we describe a network analysis-based approach to identify potential allosteric immune evasion mechanisms using three known HIV-1 Env gp120 protein structures from two different clades, B and C. First, correlation and principal component analyses of molecular dynamics (MD) simulations identified a high degree of long-distance coupled motions that exist between functionally distant regions within the intrinsic dynamics of the gp120 core, supporting the presence of long-distance communication in the protein. Then, by integrating MD simulations with network theory, we identified the optimal and suboptimal communication pathways and modules within the gp120 core. The results unveil both strain-dependent and -independent characteristics of the communication pathways in gp120. We show that within the context of three structurally homologous gp120 cores, the optimal pathway for communication is sequence sensitive, i.e. a suboptimal pathway in one strain becomes the optimal pathway in another strain. Yet the identification of conserved elements within these communication pathways, termed inter-modular hotspots, could present a new opportunity for immunogen design, as this could be an additional mechanism that HIV-1 uses to shield vulnerable antibody targets in Env that induce neutralizing antibody breadth.

Transitions to catalytically inactive conformations in EGFR kinase

The epidermal growth factor receptor (EGFR) is a key protein in cellular signaling, and its kinase domain (EGFR kinase) is an intensely pursued target of small-molecule drugs. Although both catalytically active and inactive conformations of EGFR kinase have been resolved crystallographically, experimental characterization of the transitions between these conformations remains difficult. Using unbiased, all-atom molecular dynamics simulations, we observed EGFR kinase spontaneously transition from the active to the so-called "Src-like inactive" conformation by way of two sets of intermediate conformations: One corresponds to a previously identified locally disordered state and the other to previously undescribed "extended" conformations, marked by the opening of the ATP-binding site between the two lobes of the kinase domain. We also simulated the protonation-dependent transition of EGFR kinase to another ["Asp-Phe-Gly-out" ("DFG-out")] inactive conformation and observed similar intermediate conformations. A key element observed in the simulated transitions is local unfolding, or "cracking," which supports a prediction of energy landscape theory. We used hydrogen-deuterium (H/D) exchange measurements to corroborate our simulations and found that the simulated intermediate conformations correlate better with the H/D exchange data than existing active or inactive EGFR kinase crystal structures. The intermediate conformations revealed by our simulations of the transition process differ significantly from the existing crystal structures and may provide unique possibilities for structure-based drug discovery.

Simplicity within the complexity: bilateral impact of DMSO on the functional and unfolding patterns of α-chymotrypsin

New understanding of the fundamental links between protein stability, conformational flexibility and function, can be gained through synergic studies on their catalytic and folding/unfolding properties under the influence of stabilizing/destabilizing additives. We explored an impact of dimethyl sulfoxide (DMSO), the moderate effector of multilateral action, on the kinetic (functional) and thermodynamic (thermal unfolding) patterns of a hydrolytic enzyme, α-chymotrypsin (α-CT), over a wide range of additive concentrations, 0-70% (v/v). Both the calorimetric and kinetic data exhibited rich behavior pointing to the complex interplay of global/local stability (and flexibility) patterns. The complex action of DMSO is explained through the negative and positive preferential solvation motifs that prevail for the extreme opposite, native-like and unfolded states, respectively, implying essential stabilization of compact domains by enhancement of interfacial water networks and destabilization of a flexible active site by direct binding of DMSO to the unoccupied specific positions intended for elongated polypeptide substrates.

Global structural motions from the strain of a single hydrogen bond

The origin and biological role of dynamic motions of folded enzymes is not yet fully understood. In this study, we examine the molecular determinants for the dynamic motions within the β-barrel of superoxide dismutase 1 (SOD1), which previously were implicated in allosteric regulation of protein maturation and also pathological misfolding in the neurodegenerative disease amyotrophic lateral sclerosis. Relaxation-dispersion NMR, hydrogen/deuterium exchange, and crystallographic data show that the dynamic motions are induced by the buried H43 side chain, which connects the backbones of the Cu ligand H120 and T39 by a hydrogen-bond linkage through the hydrophobic core. The functional role of this highly conserved H120-H43-T39 linkage is to strain H120 into the correct geometry for Cu binding. Upon elimination of the strain by mutation H43F, the apo protein relaxes through hydrogen-bond swapping into a more stable structure and the dynamic motions freeze out completely. At the same time, the holo protein becomes energetically penalized because the twisting back of H120 into Cu-bound geometry leads to burial of an unmatched backbone carbonyl group. The question then is whether this coupling between metal binding and global structural motions in the SOD1 molecule is an adverse side effect of evolving viable Cu coordination or plays a key role in allosteric regulation of biological function, or both?

PUMA binding induces partial unfolding within BCL-xL to disrupt p53 binding and promote apoptosis

Following DNA damage, nuclear p53 induces the expression of PUMA, a BH3-only protein that binds and inhibits the anti-apoptotic BCL-2 repertoire, including BCL-xL. PUMA, unique amongst BH3-only proteins, disrupts the interaction between cytosolic p53 and BCL-xL, allowing p53 to promote apoptosis via direct activation of the BCL-2 effector molecules, BAX and BAK. Structural investigations using nuclear magnetic resonance spectroscopy and X-ray crystallography revealed that PUMA binding induced partial unfolding of two α-helices within BCL-xL. Wild-type PUMA or a PUMA mutant incapable of causing binding-induced unfolding of BCL-xL equivalently inhibited the anti-apoptotic BCL-2 repertoire to sensitize for death receptor (DR)-activated apoptosis, but only wild-type PUMA promoted p53-dependent, DNA damage-induced apoptosis. Our data suggest that PUMA-induced partial unfolding of BCL-xL disrupts interactions between cytosolic p53 and BCL-xL, releasing the bound p53 to initiate apoptosis. We propose that regulated unfolding of BCL-xL provides a mechanism to promote PUMA-dependent signaling within the apoptotic pathways.

Connecting protein conformational dynamics with catalytic function as illustrated in dihydrofolate reductase

Combined quantum mechanics/molecular mechanics molecular dynamics simulations reveal that the M20 loop conformational dynamics of dihydrofolate reductase (DHFR) is severely restricted at the transition state of the hydride transfer as a result of the M42W/G121V double mutation. Consequently, the double-mutant enzyme has a reduced entropy of activation, i.e., increased entropic barrier, and altered temperature dependence of kinetic isotope effects in comparison with those of wild-type DHFR. Interestingly, in both wild-type DHFR and the double mutant, the average donor-acceptor distances are essentially the same in the Michaelis complex state (~3.5 Å) and the transition state (2.7 Å). It was found that an additional hydrogen bond is formed to stabilize the M20 loop in the closed conformation in the M42W/G121V double mutant. The computational results reflect a similar aim designed to knock out precisely the dynamic flexibility of the M20 loop in a different double mutant, N23PP/S148A.

Self-assembly of Arg-Phe nanostructures via the solid-vapor phase method

We report for the first time on the self-assembly of nanostructures composed exclusively of alternating positively charged and hydrophobic amino acids. A novel arginine/phenylalanine octapeptide, RF8, was synthesized. Because the low hydrophobicity of this sequence makes its spontaneous ordering through solution-based methods difficult, a recently proposed solid-vapor approach was used to obtain nanometric architectures on ITO/PET substrates. The formation of the nanostructures was investigated under different preparation conditions, specifically, under different gas-phase solvents (aniline, water, and dichloromethane), different peptide concentrations in the precursor solution, and different incubation times. The stability of the assemblies was experimentally studied by electron microscopy and thermogravimetric analysis coupled with mass spectrometry. The secondary structure was assessed by infrared and Raman spectroscopy, and the arrays were found to assume an antiparallel β-sheet conformation. FEG-SEM images clearly reveal the appearance of fibrillar structures that form extensive homogeneously distributed networks. A close relationship between the morphology and preparation parameters was found, and a concentration-triggered mechanism was suggested. Molecular dynamics simulations were performed to address the thermal stability and nature of intermolecular interactions of the putative assembly structure. Results obtained when water is considered as solvent shows that a stable lamellar structure is formed containing a thin layer of water in between the RF8 peptides that is stabilized by H-bonding.

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.

Conformational heterogeneity within the LID domain mediates substrate binding to Escherichia coli adenylate kinase: function follows fluctuations

Proteins exist as dynamic ensembles of molecules, implying that protein amino acid sequences evolved to code for both the ground state structure as well as the entire energy landscape of excited states. Accumulating theoretical and experimental evidence suggests that enzymes use such conformational fluctuations to facilitate allosteric processes important for substrate binding and possibly catalysis. This phenomenon can be clearly demonstrated in Escherichia coli adenylate kinase, where experimentally observed local unfolding of the LID subdomain, as opposed to a more commonly postulated rigid-body opening motion, is related to substrate binding. Because "entropy promoting" glycine mutations designed to increase specifically the local unfolding of the LID domain also affect substrate binding, changes in the excited energy landscape effectively tune the function of this enzyme without changing the ground state structure or the catalytic site. Thus, additional thermodynamic information, above and beyond the single folded structure of an enzyme-substrate complex, is likely required for a full and quantitative understanding of how enzymes work.

Force distribution reveals signal transduction in E. coli Hsp90

Heat-shock protein 90 (Hsp90) is an ubiquitous chaperone that is essential for cell function in that it promotes client-protein folding and stabilization. Its function is tightly controlled by an ATP-dependent large conformational transition between the open and closed states of the Hsp90 dimer. The underlying allosteric pathway has remained largely unknown, but it is revealed here in atomistic detail for the Escherichia coli homolog HtpG. Using force-distribution analysis based on molecular-dynamics simulations (>1 μs in total), we identify an internal signaling pathway that spans from the nucleotide-binding site to an ~2.3-nm-distant region in the HtpG middle domain, that serves as a dynamic hinge region, and to a putative client-protein-binding site in the middle domain. The force transmission is triggered by ATP capturing a magnesium ion and thereby rotating and bending a proximal long α-helix, which represents the major force channel into the middle domain. This allosteric mechanism is, with statistical significance, distinct from the dynamics in the ADP and apo states. Tracking the distribution of forces is likely to be a promising tool for understanding and guiding experiments of complex allosteric proteins in general.

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.

Exploring the Dynamic Functional Landscape of Adenylate Kinase Modulated by Substrates

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

Optimization of Algorithms for Modeling Protein Structural Transitions from Sparse Long-Range Spin-Label Distance Constraints

Function-related structural transitions of proteins are often large-scale conformational changes that are related to essential dynamics of a protein, which in turn proceeds along a small number of slow normal modes. Hence, it should be possible to characterize such transitions by an equally small number of distance constraints. These constraints should contain the information how the backbone coordinates move along the active normal modes. Such an approach based on residue-level elastic network models for the protein backbone is optimized with respect to the fit algorithm, constraint selection, and parametrization of the elastic network model. A stable fitting algorithm can be based on energy equipartitioning among the modes in the active space. This stabilization allows for extending active space dimension beyond the number of available constraints, which improves fit quality for transitions with a normal mode spectrum of only slowly increasing frequencies. In constraint selection, discrimination between the active normal modes appears to be more important than achieving large distance changes between initial and final structure. Parametrization of the network model has only a small influence on fit quality, as long as scaling of force constants with the inverse sixth power of the distance between network nodes is maintained. Elastic network models with a uniform force constant below a cutoff distance perform significantly worse. With 50 distance constraints, the optimized approach covers more than 50% of the structural change for 44% of all test cases, between 25 and 50% for 22% of the cases, and it fails for 33%.

Protein dynamics governed by interfaces of high polarity and low packing density

The folding pathway, three-dimensional structure and intrinsic dynamics of proteins are governed by their amino acid sequences. Internal protein surfaces with physicochemical properties appropriate to modulate conformational fluctuations could play important roles in folding and dynamics. We show here that proteins contain buried interfaces of high polarity and low packing density, coined as LIPs: Light Interfaces of high Polarity, whose physicochemical properties make them unstable. The structures of well-characterized equilibrium and kinetic folding intermediates indicate that the LIPs of the corresponding native proteins fold late and are involved in local unfolding events. Importantly, LIPs can be identified using very fast and uncomplicated computational analysis of protein three-dimensional structures, which provides an easy way to delineate the protein segments involved in dynamics. Since LIPs can be retained while the sequences of the interacting segments diverge significantly, proteins could in principle evolve new functional features reusing pre-existing encoded dynamics. Large-scale identification of LIPS may contribute to understanding evolutionary constraints of proteins and the way protein intrinsic dynamics are encoded.

Comparing proteins by their internal dynamics: exploring structure-function relationships beyond static structural alignments

The growing interest for comparing protein internal dynamics owes much to the realisation that protein function can be accompanied or assisted by structural fluctuations and conformational changes. Analogously to the case of functional structural elements, those aspects of protein flexibility and dynamics that are functionally oriented should be subject to evolutionary conservation. Accordingly, dynamics-based protein comparisons or alignments could be used to detect protein relationships that are more elusive to sequence and structural alignments. Here we provide an account of the progress that has been made in recent years towards developing and applying general methods for comparing proteins in terms of their internal dynamics and advance the understanding of the structure-function relationship.

Complex intramolecular mechanics of G-actin--an elastic network study

Systematic numerical investigations of conformational motions in single actin molecules were performed by employing a simple elastic-network (EN) model of this protein. Similar to previous investigations for myosin, we found that G-actin essentially behaves as a strain sensor, responding by well-defined domain motions to mechanical perturbations. Several sensitive residues within the nucleotide-binding pocket (NBP) could be identified, such that the perturbation of any of them can induce characteristic flattening of actin molecules and closing of the cleft between their two mobile domains. Extending the EN model by introduction of a set of breakable links which become effective only when two domains approach one another, it was observed that G-actin can possess a metastable state corresponding to a closed conformation and that a transition to this state can be induced by appropriate perturbations in the NBP region. The ligands were roughly modeled as a single particle (ADP) or a dimer (ATP), which were placed inside the NBP and connected by elastic links to the neighbors. Our approximate analysis suggests that, when ATP is present, it stabilizes the closed conformation of actin. This may play an important role in the explanation why, in the presence of ATP, the polymerization process is highly accelerated.

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.

Cracking phase diagram for the dynamics of an enzyme

We measure the ensemble averaged deformation of an enzyme for an oscillating applied force. From the low frequency divergence of the mechanical susceptibility for the hinge motion of guanylate kinase we obtain a nonequilibrium phase diagram in the frequency-force plane. A phase line separates linear elasticity dynamics from softer (viscoelastic) dynamics. The hinge motion corresponds to crossing this phase line (not to a soft linear elastic mode). The phase line is dramatically shifted in the closed state compared to the open state of the enzyme.

Event detection and sub-state discovery from biomolecular simulations using higher-order statistics: application to enzyme adenylate kinase

Biomolecular simulations at millisecond and longer time-scales can provide vital insights into functional mechanisms. Because post-simulation analyses of such large trajectory datasets can be a limiting factor in obtaining biological insights, there is an emerging need to identify key dynamical events and relating these events to the biological function online, that is, as simulations are progressing. Recently, we have introduced a novel computational technique, quasi-anharmonic analysis (QAA) (Ramanathan et al., PLoS One 2011;6:e15827), for partitioning the conformational landscape into a hierarchy of functionally relevant sub-states. The unique capabilities of QAA are enabled by exploiting anharmonicity in the form of fourth-order statistics for characterizing atomic fluctuations. In this article, we extend QAA for analyzing long time-scale simulations online. In particular, we present HOST4MD--a higher-order statistical toolbox for molecular dynamics simulations, which (1) identifies key dynamical events as simulations are in progress, (2) explores potential sub-states, and (3) identifies conformational transitions that enable the protein to access those sub-states. We demonstrate HOST4MD on microsecond timescale simulations of the enzyme adenylate kinase in its apo state. HOST4MD identifies several conformational events in these simulations, revealing how the intrinsic coupling between the three subdomains (LID, CORE, and NMP) changes during the simulations. Further, it also identifies an inherent asymmetry in the opening/closing of the two binding sites. We anticipate that HOST4MD will provide a powerful and extensible framework for detecting biophysically relevant conformational coordinates from long time-scale simulations.

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.