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

Identifying Allosteric Hotspots with Dynamics: Application to Inter- and Intra-species Conservation

The rapidly growing volume of data being produced by next-generation sequencing initiatives is enabling more in-depth analyses of conservation than previously possible. Deep sequencing is uncovering disease loci and regions under selective constraint, despite the fact that intuitive biophysical reasons for such constraint are sometimes absent. Allostery may often provide the missing explanatory link. We use models of protein conformational change to identify allosteric residues by finding essential surface pockets and information-flow bottlenecks, and we develop a software tool that enables users to perform this analysis on their own proteins of interest. Though fundamentally 3D-structural in nature, our analysis is computationally fast, thereby allowing us to run it across the PDB and to evaluate general properties of predicted allosteric residues. We find that these tend to be conserved over diverse evolutionary time scales. Finally, we highlight examples of allosteric residues that help explain poorly understood disease-associated variants.

Bespoke Bias for Obtaining Free Energy Differences within Variationally Enhanced Sampling

Obtaining efficient sampling of multiple metastable states through molecular dynamics and hence determining free energy differences is central for understanding many important phenomena. Here we present a new biasing strategy, which employs the recent variationally enhanced sampling approach (Valsson and Parrinello Phys. Rev. Lett. 2014, 113, 090601). The bias is constructed from an intuitive model of the local free energy surface describing fluctuations around metastable minima and depends on only a few parameters which are determined variationally such that efficient sampling between states is obtained. The bias constructed in this manner largely reduces the need of finding a set of collective variables that completely spans the conformational space of interest, as they only need to be a locally valid descriptor of the system about its local minimum. We introduce the method and demonstrate its power on two representative examples.

Evolution of the concept of conformational dynamics of enzyme functions over half of a century: A personal view

To most physicists, it was always evident that conformational fluctuation is an inherent property of all molecules. Its existence in proteins was mentioned first by Linderström-Lang and Schellman in 1959 based on their hydrogen-deuterium exchange experiments. The "induced fit" mechanism to explain ligand-induced conformational changes was suggested by Koshland in 1958. Straub combined these two concepts in his "fluctuation fit" theory in 1964. The era of protein X-ray crystallography imposed a static view of protein structures. With proteins becoming accessible to NMR analysis, conformational dynamics could be mapped, and a new wave of dynamic interpretation of enzymatic catalysis and molecular recognition appeared. Energy landscapes, energy funnels, conformational selection, conformational distribution shifts are now frequent terms in interpreting biomolecular recognition and enzymatic catalysis. All these interpretations are based on the concept that evolution uses the conformational fluctuations of enzymes to develop efficient and dynamic catalytic machines. In a resurrection of the original "fluctuation fit" concept, it is generally recognized now that spatial and temporal events of catalysis are equally important to describe its mechanism. This special issue, dedicated to the memory of Henryk Eisenberg, prompted us to look back at the last 50 years of development of a concept that-like other important concepts-appeared, evolved and became accepted during the period covered by the scientific lifespan of Henryk.

Water-Mediated Energy Dynamics in a Homodimeric Hemoglobin

We examine energy dynamics in the unliganded and liganded states of the homodimeric hemoglobin from Scapharca inaequivalvis (HbI), which exhibits cooperativity mediated by the cluster of water molecules at the interface upon ligand binding and dissociation. We construct and analyze a dynamic network in which nodes representing the residues, hemes, and water cluster are connected by edges that represent energy transport times, as well as a nonbonded network (NBN) indicating regions that respond rapidly to local strain within the protein via nonbonded interactions. One of the two largest NBNs includes the Lys30-Asp89 salt bridge critical for stabilizing the dimer. The other includes the hemes and surrounding residues, as well as, in the unliganded state, the cluster of water molecules between the globules. Energy transport in the protein appears to be controlled by the Lys30-Asp89 salt bridge critical for stabilizing the dimer, as well as the interface water cluster in the unliganded state. Possible connections between energy transport dynamics in response to local strain identified here and allosteric transitions in HbI are discussed.

Conformational Selection and Induced Fit Mechanisms in the Binding of an Anticancer Drug to the c-Src Kinase

Understanding the conformational changes associated with the binding of small ligands to their biological targets is a fascinating and meaningful question in chemistry, biology and drug discovery. One of the most studied and important is the so-called "DFG-flip" of tyrosine kinases. The conserved three amino-acid DFG motif undergoes an "in to out" movement resulting in a particular inactive conformation to which "type II" kinase inhibitors, such as the anti-cancer drug Imatinib, bind. Despite many studies, the details of this prototypical conformational change are still debated. Here we combine various NMR experiments and surface plasmon resonance with enhanced sampling molecular dynamics simulations to shed light into the conformational dynamics associated with the binding of Imatinib to the proto-oncogene c-Src. We find that both conformational selection and induced fit play a role in the binding mechanism, reconciling opposing views held in the literature. Moreover, an external binding pose and local unfolding (cracking) of the aG helix are observed.

Principles and Overview of Sampling Methods for Modeling Macromolecular Structure and Dynamics

Investigation of macromolecular structure and dynamics is fundamental to understanding how macromolecules carry out their functions in the cell. Significant advances have been made toward this end in silico, with a growing number of computational methods proposed yearly to study and simulate various aspects of macromolecular structure and dynamics. This review aims to provide an overview of recent advances, focusing primarily on methods proposed for exploring the structure space of macromolecules in isolation and in assemblies for the purpose of characterizing equilibrium structure and dynamics. In addition to surveying recent applications that showcase current capabilities of computational methods, this review highlights state-of-the-art algorithmic techniques proposed to overcome challenges posed in silico by the disparate spatial and time scales accessed by dynamic macromolecules. This review is not meant to be exhaustive, as such an endeavor is impossible, but rather aims to balance breadth and depth of strategies for modeling macromolecular structure and dynamics for a broad audience of novices and experts.

Molecular simulations of substrate release and coupled conformational motions in adenylate kinase

Conformational opening coupled substrate release is believed to be related to the rate limiting step in the catalysis cycle of the adenylate kinase. However, it is still unclear how the substrate dissociates from its active site and how the substrate release is coupled to conformational changes of the kinase. In this work, by using metadynamics simulations, we investigated the ADP release process and the coupled protein dynamics. We found that the ADP release involves overcoming a high free energy barrier, and protonation of the [Formula: see text]-phosphate of the ADP molecules can drastically reduce the barrier height, therefore, promote the ADP release. We identified several key residues contributing to the high free energy barrier. We also showed that the ADP attached to LID domain leaves the binding pocket earlier than the one attached to the NMP domain. We further observed that the ADP release is accompanied by almost fully opening of the LID domain and partially opening of the NMP domain. Our results provide insight into the molecular mechanism of the substrate release of adenylate kinase and the coupled conformational motions.

Steric interactions lead to collective tilting motion in the ribosome during mRNA-tRNA translocation

Translocation of mRNA and tRNA through the ribosome is associated with large-scale rearrangements of the head domain in the 30S ribosomal subunit. To elucidate the relationship between 30S head dynamics and mRNA–tRNA displacement, we apply molecular dynamics simulations using an all-atom structure-based model. Here we provide a statistical analysis of 250 spontaneous transitions between the A/P–P/E and P/P–E/E ensembles. Consistent with structural studies, the ribosome samples a chimeric ap/P–pe/E intermediate, where the 30S head is rotated ∼18°. It then transiently populates a previously unreported intermediate ensemble, which is characterized by a ∼10° tilt of the head. To identify the origins of head tilting, we analyse 781 additional simulations in which specific steric features are perturbed. These calculations show that head tilting may be attributed to specific steric interactions between tRNA and the 30S subunit (PE loop and protein S13). Taken together, this study demonstrates how molecular structure can give rise to large-scale collective rearrangements.

During protein elongation, the translocation of mRNA and tRNA molecules across the 30S ribosomal subunit is associated with large-scale motions of the 30S head domain. Here the authors carry out MD simulations to probe the associated steric interactions and identify novel tilting motions during the late stages of translocation.

Exploring the mechanochemical cycle of dynein motor proteins: structural evidence of crucial intermediates

Exploration of the biologically relevant pathways of dynein's mechanochemical cycle using structure based models.

New generation of elastic network models

The intrinsic flexibility of proteins and nucleic acids can be grasped from remarkably simple mechanical models of particles connected by springs. In recent decades, Elastic Network Models (ENMs) combined with Normal Model Analysis widely confirmed their ability to predict biologically relevant motions of biomolecules and soon became a popular methodology to reveal large-scale dynamics in multiple structural biology scenarios. The simplicity, robustness, low computational cost, and relatively high accuracy are the reasons behind the success of ENMs. This review focuses on recent advances in the development and application of ENMs, paying particular attention to combinations with experimental data. Successful application scenarios include large macromolecular machines, structural refinement, docking, and evolutionary conservation.

A stochastic roadmap method to model protein structural transitions

Evidence is emerging that the role of protein structure in disease needs to be rethought. Sequence mutations in proteins are often found to affect the rate at which a protein switches between structures. Modeling structural transitions in wildtype and variant proteins is central to understanding the molecular basis of disease. This paper investigates an efficient algorithmic realization of the stochastic roadmap simulation framework to model structural transitions in wildtype and variants of proteins implicated in human disorders. Our results indicate that the algorithm is able to extract useful information on the impact of mutations on protein structure and function.

Normal-Mode Analysis of Circular DNA at the Base-Pair Level. 2. Large-Scale Configurational Transformation of a Naturally Curved Molecule

Fine structural and energetic details embedded in the DNA base sequence, such as intrinsic curvature, are important to the packaging and processing of the genetic material. Here we investigate the internal dynamics of a 200 bp closed circular molecule with natural curvature using a newly developed normal-mode treatment of DNA in terms of neighboring base-pair "step" parameters. The intrinsic curvature of the DNA is described by a 10 bp repeating pattern of bending distortions at successive base-pair steps. We vary the degree of intrinsic curvature and the superhelical stress on the molecule and consider the normal-mode fluctuations of both the circle and the stable figure-8 configuration under conditions where the energies of the two states are similar. To extract the properties due solely to curvature, we ignore other important features of the double helix, such as the extensibility of the chain, the anisotropy of local bending, and the coupling of step parameters. We compare the computed normal modes of the curved DNA model with the corresponding dynamical features of a covalently closed duplex of the same chain length constructed from naturally straight DNA and with the theoretically predicted dynamical properties of a naturally circular, inextensible elastic rod, i.e., an O-ring. The cyclic molecules with intrinsic curvature are found to be more deformable under superhelical stress than rings formed from naturally straight DNA. As superhelical stress is accumulated in the DNA, the frequency, i.e., energy, of the dominant bending mode decreases in value, and if the imposed stress is sufficiently large, a global configurational rearrangement of the circle to the figure-8 form takes place. We combine energy minimization with normal-mode calculations of the two states to decipher the configurational pathway between the two states. We also describe and make use of a general analytical treatment of the thermal fluctuations of an elastic rod to characterize the motions of the minicircle as a whole from knowledge of the full set of normal modes. The remarkable agreement between computed and theoretically predicted values of the average deviation and dispersion of the writhe of the circular configuration adds to the reliability in the computational approach. Application of the new formalism to the computed modes of the figure-8 provides insights into macromolecular motions which are beyond the scope of current theoretical treatments.

Computing the Amino Acid Specificity of Fluctuations in Biomolecular Systems

We developed a new amino acid specific method for the computation of spatial fluctuations of proteins around their native structures. We show the consistency with experimental values and the increased performance in comparison to an established model, based on statistical estimates for a set of test proteins. We apply the new method to HIV-1 protease in its wild-type form and to a V82F-I84V mutant that shows resistance to protease inhibitors. We further show how the method can be successfully used to explain the molecular biophysics of drug resistance of the mutant.

Towards a Molecular Understanding of the Link between Imatinib Resistance and Kinase Conformational Dynamics

Due to its inhibition of the Abl kinase domain in the BCR-ABL fusion protein, imatinib is strikingly effective in the initial stage of chronic myeloid leukemia with more than 90% of the patients showing complete remission. However, as in the case of most targeted anti-cancer therapies, the emergence of drug resistance is a serious concern. Several drug-resistant mutations affecting the catalytic domain of Abl and other tyrosine kinases are now known. But, despite their importance and the adverse effect that they have on the prognosis of the cancer patients harboring them, the molecular mechanism of these mutations is still debated. Here by using long molecular dynamics simulations and large-scale free energy calculations complemented by in vitro mutagenesis and microcalorimetry experiments, we model the effect of several widespread drug-resistant mutations of Abl. By comparing the conformational free energy landscape of the mutants with those of the wild-type tyrosine kinases we clarify their mode of action. It involves significant and complex changes in the inactive-to-active dynamics and entropy/enthalpy balance of two functional elements: the activation-loop and the conserved DFG motif. What is more the T315I gatekeeper mutant has a significant impact on the binding mechanism itself and on the binding kinetics.

Single-molecule spectroscopy reveals how calmodulin activates NO synthase by controlling its conformational fluctuation dynamics

Mechanisms that regulate the nitric oxide synthase enzymes (NOS) are of interest in biology and medicine. Although NOS catalysis relies on domain motions, and is activated by calmodulin binding, the relationships are unclear. We used single-molecule fluorescence resonance energy transfer (FRET) spectroscopy to elucidate the conformational states distribution and associated conformational fluctuation dynamics of the two electron transfer domains in a FRET dye-labeled neuronal NOS reductase domain, and to understand how calmodulin affects the dynamics to regulate catalysis. We found that calmodulin alters NOS conformational behaviors in several ways: It changes the distance distribution between the NOS domains, shortens the lifetimes of the individual conformational states, and instills conformational discipline by greatly narrowing the distributions of the conformational states and fluctuation rates. This information was specifically obtainable only by single-molecule spectroscopic measurements, and reveals how calmodulin promotes catalysis by shaping the physical and temporal conformational behaviors of NOS.

Enhanced Diffusion of Enzymes that Catalyze Exothermic Reactions

Enzymes have been recently found to exhibit enhanced diffusion due to their catalytic activities. A recent experiment [C. Riedel et al., Nature (London) 517, 227 (2015)] has found evidence that suggests this phenomenon might be controlled by the degree of exothermicity of the catalytic reaction involved. Four mechanisms that can lead to this effect, namely, self-thermophoresis, boost in kinetic energy, stochastic swimming, and collective heating are critically discussed, and it is shown that only the last two can be strong enough to account for the observations. The resulting quantitative description is used to examine the biological significance of the effect.

Protein viscoelastic dynamics: a model system

A model system inspired by recent experiments on the dynamics of a folded protein under the influence of a sinusoidal force is investigated and found to replicate many of the response characteristics of such a system. The essence of the model is a strongly overdamped oscillator described by a harmonic restoring force for small displacements that reversibly yields to stress under sufficiently large displacement. This simple dynamical system also reveals unexpectedly rich behavior-exhibiting a series of dynamical transitions and analogies with equilibrium thermodynamic phase transitions. The effects of noise and of inertia are briefly considered and described.

Thermal-induced force release in oxyhemoglobin

Oxygen is released to living tissues via conformational changes of hemoglobin from R-state (oxyhemoglobin) to T-state (desoxyhemoglobin). The detailed mechanism of this process is not yet fully understood. We have carried out micromechanical experiments on oxyhemoglobin crystals to determine the behavior of the Young’s modulus and the internal friction for temperatures between 20 °C and 70 °C. We have found that around 49 °C oxyhemoglobin crystal samples undergo a sudden and strong increase of their Young’s modulus, accompanied by a sudden decrease of the internal friction. This sudden mechanical change (and the ensuing force release) takes place in a partially unfolded state and precedes the full denaturation transition at higher temperatures. After this transformation, the hemoglobin crystals have the same mechanical properties as their initial state at room temperatures. We conjecture that it can be relevant for explaining the oxygen-releasing function of native oxyhemoglobin when the temperature is increased, e.g. due to active sport. The effect is specific for the quaternary structure of hemoglobin, and is absent for myoglobin with only one peptide sequence.

Structural and dynamic insights into the energetics of activation loop rearrangement in FGFR1 kinase

Protein tyrosine kinases differ widely in their propensity to undergo rearrangements of the N-terminal Asp–Phe–Gly (DFG) motif of the activation loop, with some, including FGFR1 kinase, appearing refractory to this so-called ‘DFG flip'. Recent inhibitor-bound structures have unexpectedly revealed FGFR1 for the first time in a ‘DFG-out' state. Here we use conformationally selective inhibitors as chemical probes for interrogation of the structural and dynamic features that appear to govern the DFG flip in FGFR1. Our detailed structural and biophysical insights identify contributions from altered dynamics in distal elements, including the αH helix, towards the outstanding stability of the DFG-out complex with the inhibitor ponatinib. We conclude that the αC-β4 loop and ‘molecular brake' regions together impose a high energy barrier for this conformational rearrangement, and that this may have significance for maintaining autoinhibition in the non-phosphorylated basal state of FGFR1.

Receptor tyrosine kinases are key mediators of cell proliferation that have been implicated in several disease states for which they represent promising drug targets. Here the authors determine the thermodynamic basis for the low propensity of FGFR1 to access the DFG-Phe-out conformation required to bind type-II inhibitors.

The Atomistic Mechanism of Conformational Transition of Adenylate Kinase Investigated by Lorentzian Structure-Based Potential

We present a new all-atom structure-based method to study protein conformational transitions using Lorentzian attractive interactions based on native structures. The variability of each native contact is estimated based on evolutionary information using a machine learning method. To test the validity of this approach, we have investigated the conformational transition of adenylate kinase (ADK). The intrinsic boundedness of the Lorentzian attractive interactions facilitated frequent conformational transitions, and consequently we were able to observe more than 1000 structural interconversions between the open and closed states of ADK out of a total of 6 μs MD simulations. ADK has three domains: the nucleoside monophosphate (NMP) binding domain, the LID-domain, and the CORE domain, which catalyze the interconversion between ATP and ADP. We identified two transition states: a more frequent LID-closed-NMP-open (TS1) state and a less frequent LID-open-NMP-closed (TS2) state. The transition was found to be symmetric in both directions via TS1. We also obtained an off-pathway metastable state that was previously observed with physics-based all-atom simulations but not with coarse-grained models. In the metastable state, the LID domain was slightly twisted and formed contacts with the NMP domain. Our model correctly identified a total of 14 out of the top 16 residues with highest fluctuation by NMR experiment, thus showing excellent agreement with experimental NMR relaxation data and overwhelmingly better results than existing models.

Exploring the balance between folding and functional dynamics in proteins and RNA

As our understanding of biological dynamics continues to be refined, it is becoming clear that biomolecules can undergo transitions between ordered and disordered states as they execute functional processes. From a computational perspective, studying disorder events poses a challenge, as they typically occur on long timescales, and the associated molecules are often large (i.e., hundreds of residues). These size and time requirements make it advantageous to use computationally inexpensive models to characterize large-scale dynamics, where more highly detailed models can provide information about individual sub-steps associated with function. To reduce computational demand, one often uses a coarse-grained representation of the molecule or a simplified description of the energetics. In order to use simpler models to identify transient disorder in RNA and proteins, it is imperative that these models can accurately capture structural fluctuations about folded configurations, as well as the overall stability of each molecule. Here, we explore a class of simplified model for which all non-hydrogen atoms are explicitly represented. We find that this model can provide a consistent description of protein folding and native-basin dynamics for several representative biomolecules. We additionally show that the native-basin fluctuations of tRNA and the ribosome are robust to variations in the model. Finally, the extended variable loop in tRNAIle is predicted to be very dynamic, which may facilitate biologically-relevant rearrangements. Together, this study provides a foundation that will aid in the application of simplified models to study disorder during function in ribonucleoprotein (RNP) assemblies.

Intramolecular vibrations in low-frequency normal modes of amino acids: L-alanine in the neat solid state

This paper presents a theoretical analysis of the low-frequency phonons of L-alanine by using the solid-state density functional theory at the Γ point. We are particularly interested in the intramolecular vibrations accessing low-frequency phonons via harmonic coupling with intermolecular vibrations. A new mode-analysis method is introduced to quantify the vibrational characteristics of such intramolecular vibrations. We find that the torsional motions of COO(-) are involved in low-frequency phonons, although COO(-) is conventionally assumed to undergo localized torsion. We also find the broad distributions of intramolecular vibrations relevant to important functional groups of amino acids, e.g., the COO(-) and NH3(+) torsions, in the low-frequency phonons. The latter finding is illustrated by the concept of frequency distribution of vibrations. These findings may lead to immediate implications in other amino acid systems.

Atomic torsional modal analysis for high-resolution proteins

We introduce a formulation for normal mode analyses of globular proteins that significantly improves on an earlier one-parameter formulation [M. M. Tirion, Phys. Rev. Lett. 77, 1905 (1996)] that characterized the slow modes associated with protein data bank structures. Here we develop that empirical potential function that is minimized at the outset to include two features essential to reproduce the eigenspectra and associated density of states in the 0 to 300cm-1 frequency range, not merely the slow modes. First, introduction of preferred dihedral-angle configurations via use of torsional stiffness constants eliminates anomalous dispersion characteristics due to insufficiently bound surface side chains and helps fix the spectrum thin tail frequencies (100-300cm-1). Second, we take into account the atomic identities and the distance of separation of all pairwise interactions, improving the spectrum distribution in the 20 to 300cm-1 range. With these modifications, not only does the spectrum reproduce that of full atomic potentials, but we obtain stable reliable eigenmodes for the slow modes and over a wide range of frequencies.

Identification of tail binding effect of kinesin-1 using an elastic network model

Kinesin is a motor protein that delivers cargo inside a cell. Kinesin has many different families, but they perform basically same function and have same motions. The walking motion of kinesin enables the cargo delivery inside the cell. Autoinhibition of kinesin is important because it explains how function of kinesin inside a cell is stopped. Former researches showed that tail binding is related to autoinhibition of kinesin. In this work, we performed normal mode analysis with elastic network model using different conformation of kinesin to determine the effect of tail binding by considering four models such as functional form, autoinhibited form, autoinhibited form without tail, and autoinhibited form with carbon structure. Our calculation of the thermal fluctuation and cross-correlation shows the change of tail-binding region in structural motion. Also strain energy of kinesin showed that elimination of tail binding effect leads the structure to have energetically similar behavior with the functional form.

Energetics and structural characterization of the large-scale functional motion of adenylate kinase

Adenylate Kinase (AK) is a signal transducing protein that regulates cellular energy homeostasis balancing between different conformations. An alteration of its activity can lead to severe pathologies such as heart failure, cancer and neurodegenerative diseases. A comprehensive elucidation of the large-scale conformational motions that rule the functional mechanism of this enzyme is of great value to guide rationally the development of new medications. Here using a metadynamics-based computational protocol we elucidate the thermodynamics and structural properties underlying the AK functional transitions. The free energy estimation of the conformational motions of the enzyme allows characterizing the sequence of events that regulate its action. We reveal the atomistic details of the most relevant enzyme states, identifying residues such as Arg119 and Lys13, which play a key role during the conformational transitions and represent druggable spots to design enzyme inhibitors. Our study offers tools that open new areas of investigation on large-scale motion in proteins.

Mapping allostery through computational glycine scanning and correlation analysis of residue-residue contacts

Understanding allosteric mechanisms is essential for the physical control of molecular switches and downstream cellular responses. However, it is difficult to decode essential allosteric motions in a high-throughput scheme. A general two-pronged approach to performing automatic data reduction of simulation trajectories is presented here. The first step involves coarse-graining and identifying the most dynamic residue-residue contacts. The second step is performing principal component analysis of these contacts and extracting the large-scale collective motions expressed via these residue-residue contacts. We demonstrated the method using a protein complex of nuclear receptors. Using atomistic modeling and simulation, we examined the protein complex and a set of 18 glycine point mutations of residues that constitute the binding pocket of the ligand effector. The important motions that are responsible for the allostery are reported. In contrast to conventional induced-fit and lock-and-key binding mechanisms, a novel "frustrated-fit" binding mechanism of RXR for allosteric control was revealed.

Opportunities and challenges for time-resolved studies of protein structural dynamics at X-ray free-electron lasers

X-ray free-electron lasers (XFELs) are revolutionary X-ray sources. Their time structure, providing X-ray pulses of a few tens of femtoseconds in duration; and their extreme peak brilliance, delivering approximately 10¹² X-ray photons per pulse and facilitating sub-micrometre focusing, distinguish XFEL sources from synchrotron radiation. In this opinion piece, I argue that these properties of XFEL radiation will facilitate new discoveries in life science. I reason that time-resolved serial femtosecond crystallography and time-resolved wide angle X-ray scattering are promising areas of scientific investigation that will be advanced by XFEL capabilities, allowing new scientific questions to be addressed that are not accessible using established methods at storage ring facilities. These questions include visualizing ultrafast protein structural dynamics on the femtosecond to picosecond time-scale, as well as time-resolved diffraction studies of non-cyclic reactions. I argue that these emerging opportunities will stimulate a renaissance of interest in time-resolved structural biochemistry.

Visualizing transient dark states by NMR spectroscopy

Myriad biological processes proceed through states that defy characterization by conventional atomic-resolution structural biological methods. The invisibility of these 'dark' states can arise from their transient nature, low equilibrium population, large molecular weight, and/or heterogeneity. Although they are invisible, these dark states underlie a range of processes, acting as encounter complexes between proteins and as intermediates in protein folding and aggregation. New methods have made these states accessible to high-resolution analysis by nuclear magnetic resonance (NMR) spectroscopy, as long as the dark state is in dynamic equilibrium with an NMR-visible species. These methods - paramagnetic NMR, relaxation dispersion, saturation transfer, lifetime line broadening, and hydrogen exchange - allow the exploration of otherwise invisible states in exchange with a visible species over a range of timescales, each taking advantage of some unique property of the dark state to amplify its effect on a particular NMR observable. In this review, we introduce these methods and explore two specific techniques - paramagnetic relaxation enhancement and dark state exchange saturation transfer - in greater detail.

On the relationship between low-frequency normal modes and the large-scale conformational changes of proteins

Normal mode analysis is a computational technique that allows to study the dynamics of biological macromolecules. It was first applied to small protein cases, more than thirty years ago. The interest in this technique then raised when it was realized that it can provide insights about the large-scale conformational changes a protein can experience, for instance upon ligand binding. As it was also realized that studying highly simplified protein models can provide similar insights, meaning that this kind of analysis can be both quick and simple to handle, several applications were proposed, in the context of various structural biology techniques. This review focuses on these applications, as well as on how the functional relevance of the lowest-frequency modes of proteins was established.

What protein folding teaches us about biological function and molecular machines

Protein folding was the first area of molecular biology for which a systematic statistical-mechanical analysis of dynamics was developed. As a result, folding is described as a process by which a disordered protein chain diffuses across a high-dimensional energy landscape and finally reaches the folded ensemble. Folding studies have produced countless theoretical concepts that are generalizable to other biomolecular processes, such as the functional dynamics of molecular assemblies. Common themes in folding and function include the dominant role of excluded volume, that a balance between energetic roughness and geometrical effects guides dynamics, and that folding/functional landscapes are relatively smooth. Here, we discuss how insights into protein folding have been applied to investigate the functional dynamics of biomolecular assemblies.

WEBnm@ v2.0: Web server and services for comparing protein flexibility

BACKGROUND

Normal mode analysis (NMA) using elastic network models is a reliable and cost-effective computational method to characterise protein flexibility and by extension, their dynamics. Further insight into the dynamics-function relationship can be gained by comparing protein motions between protein homologs and functional classifications. This can be achieved by comparing normal modes obtained from sets of evolutionary related proteins.

RESULTS

We have developed an automated tool for comparative NMA of a set of pre-aligned protein structures. The user can submit a sequence alignment in the FASTA format and the corresponding coordinate files in the Protein Data Bank (PDB) format. The computed normalised squared atomic fluctuations and atomic deformation energies of the submitted structures can be easily compared on graphs provided by the web user interface. The web server provides pairwise comparison of the dynamics of all proteins included in the submitted set using two measures: the Root Mean Squared Inner Product and the Bhattacharyya Coefficient. The Comparative Analysis has been implemented on our web server for NMA, WEBnm@, which also provides recently upgraded functionality for NMA of single protein structures. This includes new visualisations of protein motion, visualisation of inter-residue correlations and the analysis of conformational change using the overlap analysis. In addition, programmatic access to WEBnm@ is now available through a SOAP-based web service. Webnm@ is available at http://apps.cbu.uib.no/webnma .

CONCLUSION

WEBnm@ v2.0 is an online tool offering unique capability for comparative NMA on multiple protein structures. Along with a convenient web interface, powerful computing resources, and several methods for mode analyses, WEBnm@ facilitates the assessment of protein flexibility within protein families and superfamilies. These analyses can give a good view of how the structures move and how the flexibility is conserved over the different structures.

Evolution, energy landscapes and the paradoxes of protein folding

Protein folding has been viewed as a difficult problem of molecular self-organization. The search problem involved in folding however has been simplified through the evolution of folding energy landscapes that are funneled. The funnel hypothesis can be quantified using energy landscape theory based on the minimal frustration principle. Strong quantitative predictions that follow from energy landscape theory have been widely confirmed both through laboratory folding experiments and from detailed simulations. Energy landscape ideas also have allowed successful protein structure prediction algorithms to be developed. The selection constraint of having funneled folding landscapes has left its imprint on the sequences of existing protein structural families. Quantitative analysis of co-evolution patterns allows us to infer the statistical characteristics of the folding landscape. These turn out to be consistent with what has been obtained from laboratory physicochemical folding experiments signaling a beautiful confluence of genomics and chemical physics.

Local packing modulates diversity of iron pathways and cooperative behavior in eukaryotic and prokaryotic ferritins

Ferritin-like molecules show a remarkable combination of the evolutionary conserved activity of iron uptake and release that engage different pores in the conserved ferritin shell. It was hypothesized that pore selection and iron traffic depend on dynamic allostery with no conformational changes in the backbone. In this study, we detect the allosteric networks in Pseudomonas aeruginosa bacterioferritin (BfrB), bacterial ferritin (FtnA), and bullfrog M and L ferritins (Ftns) by a network-weaving algorithm (NWA) that passes threads of an allosteric network through highly correlated residues using hierarchical clustering. The residue-residue correlations are calculated in the packing-on elastic network model that introduces atom packing into the common packing-off model. Applying NWA revealed that each of the molecules has an extended allosteric network mostly buried inside the ferritin shell. The structure of the networks is consistent with experimental observations of iron transport: The allosteric networks in BfrB and FtnA connect the ferroxidase center with the 4-fold pores and B-pores, leaving the 3-fold pores unengaged. In contrast, the allosteric network directly links the 3-fold pores with the 4-fold pores in M and L Ftns. The majority of the network residues are either on the inner surface or buried inside the subunit fold or at the subunit interfaces. We hypothesize that the ferritin structures evolved in a way to limit the influence of functionally unrelated events in the cytoplasm on the allosteric network to maintain stability of the translocation mechanisms. We showed that the residue-residue correlations and the resultant long-range cooperativity depend on the ferritin shell packing, which, in turn, depends on protein sequence composition. Switching from the packing-on to the packing-off model reduces correlations by 35%-38% so that no allosteric network can be found. The influence of the side-chain packing on the allosteric networks explains the diversity in mechanisms of iron traffic suggested by experimental approaches.

Dissipative dynamics of enzymes

We explore enzyme conformational dynamics at sub-Å resolution, specifically, temperature effects. The ensemble-averaged mechanical response of the folded enzyme is viscoelastic in the whole temperature range between the warm and cold denaturation transitions. The dissipation parameter γ of the viscoelastic description decreases by a factor of 2 as the temperature is raised from 10 to 45 °C; the elastic parameter K shows a similar decrease. Thus, when probed dynamically, the enzyme softens for increasing temperature. Equilibrium mechanical experiments with the DNA spring (and a different enzyme) also show, qualitatively, a small softening for increasing temperature.

Thermodynamic analysis of F1-ATPase rotary catalysis using high-speed imaging

F1-ATPase (F1) is a rotary motor protein fueled by ATP hydrolysis. Although the mechanism for coupling rotation and catalysis has been well studied, the molecular details of individual reaction steps remain elusive. In this study, we performed high-speed imaging of F1 rotation at various temperatures using the total internal reflection dark-field (TIRDF) illumination system, which allows resolution of the F1 catalytic reaction into elementary reaction steps with a high temporal resolution of 72 µs. At a high concentration of ATP, F1 rotation comprised distinct 80° and 40° substeps. The 80° substep, which exhibited significant temperature dependence, is triggered by the temperature-sensitive reaction, whereas the 40° substep is triggered by ATP hydrolysis and the release of inorganic phosphate (Pi). Then, we conducted Arrhenius analysis of the reaction rates to obtain the thermodynamic parameters for individual reaction steps, that is, ATP binding, ATP hydrolysis, Pi release, and TS reaction. Although all reaction steps exhibited similar activation free energy values, ΔG(‡) = 53-56 kJ mol(-1), the contributions of the enthalpy (ΔH(‡)), and entropy (ΔS(‡)) terms were significantly different; the reaction steps that induce tight subunit packing, for example, ATP binding and TS reaction, showed high positive values of both ΔH(‡) and ΔS(‡). The results may reflect modulation of the excluded volume as a function of subunit packing tightness at individual reaction steps, leading to a gain or loss in water entropy.

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.

The structural basis for cancer treatment decisions

Cancer treatment decisions rely on genetics, large data screens and clinical pharmacology. Here we point out that genetic analysis and treatment decisions may overlook critical elements in cancer development, progression and drug resistance. Two critical structural elements are missing in genetics-based decision-making: the mechanisms of oncogenic mutations and the cellular network which is rewired in cancer. These lay the foundation for the structural basis for cancer treatment decisions, which is rooted in the physical principles of the molecular conformational behavior of single molecules and their interactions. Improved tumor mutational analysis platforms and knowledge of the redundant pathways which can take over in cancer, may not only supplement known actionable findings, but forecast possible cancer progression and resistance. Such forward-looking can be powerful, endowing the oncologist with mechanistic insight and cancer prognosis, and consequently more informed treatment options. Examples include redundant pathways taking over after inhibition of EGFR constitutive activation, mutations in PIK3CA p110α and p85, and the non-hotspot AKT1 mutants conferring constitutive membrane localization.

Specificity and affinity quantification of flexible recognition from underlying energy landscape topography

Flexibility in biomolecular recognition is essential and critical for many cellular activities. Flexible recognition often leads to moderate affinity but high specificity, in contradiction with the conventional wisdom that high affinity and high specificity are coupled. Furthermore, quantitative understanding of the role of flexibility in biomolecular recognition is still challenging. Here, we meet the challenge by quantifying the intrinsic biomolecular recognition energy landscapes with and without flexibility through the underlying density of states. We quantified the thermodynamic intrinsic specificity by the topography of the intrinsic binding energy landscape and the kinetic specificity by association rate. We found that the thermodynamic and kinetic specificity are strongly correlated. Furthermore, we found that flexibility decreases binding affinity on one hand, but increases binding specificity on the other hand, and the decreasing or increasing proportion of affinity and specificity are strongly correlated with the degree of flexibility. This shows more (less) flexibility leads to weaker (stronger) coupling between affinity and specificity. Our work provides a theoretical foundation and quantitative explanation of the previous qualitative studies on the relationship among flexibility, affinity and specificity. In addition, we found that the folding energy landscapes are more funneled with binding, indicating that binding helps folding during the recognition. Finally, we demonstrated that the whole binding-folding energy landscapes can be integrated by the rigid binding and isolated folding energy landscapes under weak flexibility. Our results provide a novel way to quantify the affinity and specificity in flexible biomolecular recognition.

Flexibility in biomolecular recognition is crucial for the function. Flexibility often leads to moderate binding affinity but high binding specificity, challenging the conventional wisdom that high specificity is guaranteed by high affinity. Currently, understanding of the relationship between affinity and specificity in flexible biomolecular recognition is still obscure, even in a qualitative way. By exploring the intrinsic biomolecular recognition energy landscapes, we provided a novel way to quantify the thermodynamic intrinsic specificity by energy landscape topography and kinetic specificity by association rate. We show quantitatively that flexibility decreases binding affinity while increases binding specificity, and the relative changes in affinity and specificity are strongly correlated with the degree of flexibility. Our results show that more (less) flexibility leads to weaker (stronger) coupling between affinity and specificity. Importantly, we demonstrated that flexibility modulates affinity and specificity through the underlying energy landscape. Our study establishes the quantitative relationship among flexibility, affinity and specificity, bridging the gap between theory and experiments.

Visualizing a protein quake with time-resolved X-ray scattering at a free-electron laser

We describe a method to measure ultrafast protein structural changes using time-resolved wide-angle X-ray scattering at an X-ray free-electron laser. We demonstrated this approach using multiphoton excitation of the Blastochloris viridis photosynthetic reaction center, observing an ultrafast global conformational change that arises within picoseconds and precedes the propagation of heat through the protein. This provides direct structural evidence for a 'protein quake': the hypothesis that proteins rapidly dissipate energy through quake-like structural motions.

Allostery within a transcription coactivator is predominantly mediated through dissociation rate constants

The kinase-inducible domain interacting (KIX) domain of CREB binding protein binds to multiple intrinsically disordered transcription factors in vivo at two distinct sites on its surface. Several reports have been made of allosteric communication between these two sites in this well-characterized model system. In this work, we have performed fluorescence stopped-flow measurements to investigate the kinetics of binding of five KIX binding proteins. We find that they all have similar association and dissociation rate constants for complex formation, despite their wide range of intrinsic helical propensities. Furthermore, by careful arrangement of pseudofirst-order conditions, we have been able to show that both association and dissociation rate constants are decreased when a partner is bound at the alternative site. These decreases suggest that positive allosteric effects are not mediated by structural changes in binding sites but rather, through a more general mechanism, largely mediated through dissociation, which we propose is largely related to changes in the flexibility of the KIX domain itself.

Order and disorder control the functional rearrangement of influenza hemagglutinin

Influenza hemagglutinin (HA), a homotrimeric glycoprotein crucial for membrane fusion, undergoes a large-scale structural rearrangement during viral invasion. X-ray crystallography has shown that the pre- and postfusion configurations of HA2, the membrane-fusion subunit of HA, have disparate secondary, tertiary, and quaternary structures, where some regions are displaced by more than 100 Å. To explore structural dynamics during the conformational transition, we studied simulations of a minimally frustrated model based on energy landscape theory. The model combines structural information from both the pre- and postfusion crystallographic configurations of HA2. Rather than a downhill drive toward formation of the central coiled-coil, we discovered an order-disorder transition early in the conformational change as the mechanism for the release of the fusion peptides from their burial sites in the prefusion crystal structure. This disorder quickly leads to a metastable intermediate with a broken threefold symmetry. Finally, kinetic competition between the formation of the extended coiled-coil and C-terminal melting results in two routes from this intermediate to the postfusion structure. Our study reiterates the roles that cracking and disorder can play in functional molecular motions, in contrast to the downhill mechanical interpretations of the "spring-loaded" model proposed for the HA2 conformational transition.

Conformational Transition Pathways of Epidermal Growth Factor Receptor Kinase Domain from Multiple Molecular Dynamics Simulations and Bayesian Clustering

The epidermal growth factor receptor (EGFR) is aberrantly activated in various cancer cells and an important target for cancer treatment. Deep understanding of EGFR conformational changes between the active and inactive states is of pharmaceutical interest. Here we present a strategy combining multiply targeted molecular dynamics simulations, unbiased molecular dynamics simulations, and Bayesian clustering to investigate transition pathways during the activation/inactivation process of EGFR kinase domain. Two distinct pathways between the active and inactive forms are designed, explored, and compared. Based on Bayesian clustering and rough two-dimensional free energy surfaces, the energy-favorable pathway is recognized, though DFG-flip happens in both pathways. In addition, another pathway with different intermediate states appears in our simulations. Comparison of distinct pathways also indicates that disruption of the Lys745-Glu762 interaction is critically important in DFG-flip while movement of the A-loop significantly facilitates the conformational change. Our simulations yield new insights into EGFR conformational transitions. Moreover, our results verify that this approach is valid and efficient in sampling of protein conformational changes and comparison of distinct pathways.

Structure-based simulations reveal concerted dynamics of GPCR activation

G protein-coupled receptors (GPCRs) are a vital class of proteins that transduce biological signals across the cell membrane. However, their allosteric activation mechanism is not fully understood; crystal structures of active and inactive receptors have been reported, but the functional pathway between these two states remains elusive. Here, we use structure-based (Gō-like) models to simulate activation of two GPCRs, rhodopsin and the β₂ adrenergic receptor (β₂AR). We used data-derived reaction coordinates that capture the activation mechanism for both proteins, showing that activation proceeds through quantitatively different paths in the two systems. Both reaction coordinates are determined from the dominant concerted motions in the simulations so the technique is broadly applicable. There were two surprising results. First, the main structural changes in the simulations were distributed throughout the transmembrane bundle, and not localized to the obvious areas of interest, such as the intracellular portion of Helix 6. Second, the activation (and deactivation) paths were distinctly nonmonotonic, populating states that were not simply interpolations between the inactive and active structures. These transitions also suggest a functional explanation for β₂AR's basal activity: it can proceed through a more broadly defined path during the observed transitions.