Coarse-grained model of entropic allostery

Probing conformational dynamics of DNA binding by CO-sensing transcription factor, CooA

The transcription factor CooA is a CRP/FNR (cAMP receptor protein/ fumarate and nitrate reductase) superfamily protein that uses heme to sense carbon monoxide (CO). Allosteric activation of CooA in response to CO binding is currently described as a series of discrete structural changes, without much consideration for the potential role of protein dynamics in the process of DNA binding. This work uses site-directed spin-label electron paramagnetic resonance spectroscopy (SDSL-EPR) to probe slow timescale (μs-ms) conformational dynamics of CooA with a redox-stable nitroxide spin label, and IR spectroscopy to probe the environment at the CO-bound heme. A series of cysteine substitution variants were created to selectively label CooA in key functional regions, the heme-binding domain, the 4/5-loop, the hinge region, and the DNA binding domain. The EPR spectra of labeled CooA variants are compared across three functional states: Fe(III) "locked off", Fe(II)-CO "on", and Fe(II)-CO bound to DNA. We observe changes in the multicomponent EPR spectra at each location; most notably in the hinge region and DNA binding domain, broadening the description of the CooA allosteric mechanism to include the role of protein dynamics in DNA binding. DNA-dependent changes in IR vibrational frequency and band broadening further suggest that there is conformational heterogeneity in the active WT protein and that DNA binding alters the environment of the heme-bound CO.

Mechanisms of DNA-Mediated Allostery

Proteins often regulate their activities via allostery-or action at a distance-in which the binding of a ligand at one binding site influences the affinity for another ligand at a distal site. Although less studied than in proteins, allosteric effects have been observed in experiments with DNA as well. In these experiments two or more proteins bind at distinct DNA sites and interact indirectly with each other, via a mechanism mediated by the linker DNA molecule. We develop a mechanical model of DNA/protein interactions which predicts three distinct mechanisms of allostery. Two of these involve an enthalpy-mediated allostery, while a third mechanism is entropy driven. We analyze experiments of DNA allostery and highlight the distinctive signatures allowing one to identify which of the proposed mechanisms best fits the data.

Transient association between proteins elicits alteration of dynamics at sites far away from interfaces

Proteins are known to undergo structural changes upon binding to partner proteins. However, the prevalence, extent, location, and function of change in protein dynamics due to transient protein-protein interactions is not well documented. Here, we have analyzed a dataset of 58 protein-protein complexes of known three-dimensional structure and structures of their corresponding unbound forms to evaluate dynamics changes induced by binding. Fifty-five percent of cases showed significant dynamics change away from the interfaces. This change is not always accompanied by an observed structural change. Binding of protein partner is found to alter inter-residue communication within the tertiary structure in about 90% of cases. Also, residue motions accessible to proteins in unbound form were not always maintained in the bound form. Further analyses revealed functional roles for the distant site where dynamics change was observed. Overall, the results presented here strongly suggest that alteration of protein dynamics due to binding of a partner protein commonly occurs.

The Role of Conformational Dynamics and Allostery in Modulating Protein Evolution

Advances in sequencing techniques and statistical methods have made it possible not only to predict sequences of ancestral proteins but also to identify thousands of mutations in the human exome, some of which are disease associated. These developments have motivated numerous theories and raised many questions regarding the fundamental principles behind protein evolution, which have been traditionally investigated horizontally using the tip of the phylogenetic tree through comparative studies of extant proteins within a family. In this article, we review a vertical comparison of the modern and resurrected ancestral proteins. We focus mainly on the dynamical properties responsible for a protein's ability to adapt new functions in response to environmental changes. Using the Dynamic Flexibility Index and the Dynamic Coupling Index to quantify the relative flexibility and dynamic coupling at a site-specific, single-amino-acid level, we provide evidence that the migration of hinges, which are often functionally critical rigid sites, is a mechanism through which proteins can rapidly evolve. Additionally, we show that disease-associated mutations in proteins often result in flexibility changes even at positions distal from mutational sites, particularly in the modulation of active site dynamics.

How proteins' negative cooperativity emerges from entropic optimisation of versatile collective fluctuations

The fact that allostery, a nonlocal signaling between distant binding sites, can arise mainly from the entropy balance of collective thermal modes, without conformational changes, is by now well known. However, the propensity to generate negative cooperativity is still unclear. Starting from an elastic-network picture of small protein complexes, in which effector binding is modeled by locally altering interaction strengths in lieu of adding a node-spring pair, we elucidate mechanisms particularly for such negative cooperativity. The approach via a few coupled harmonic oscillators with internal elastic strengths allows us to trace individual eigenmodes, their frequencies, and their statistical weights through successive bindings. We find that the alteration of the oscillators' couplings is paramount to covering both signs of allostery. Binding-modified couplings create a rich set of eigenmodes individually for each binding state, modes inaccessible to an ensemble of noninteracting units. The associated shifts of collective-mode frequencies, nonuniform with respect to modes and binding states, result in an enhanced optimizability, reflected by a subtle phase map of allosteric behaviors.

Allostery in Its Many Disguises: From Theory to Applications

Allosteric regulation plays an important role in many biological processes, such as signal transduction, transcriptional regulation, and metabolism. Allostery is rooted in the fundamental physical properties of macromolecular systems, but its underlying mechanisms are still poorly understood. A collection of contributions to a recent interdisciplinary CECAM (Center Européen de Calcul Atomique et Moléculaire) workshop is used here to provide an overview of the progress and remaining limitations in the understanding of the mechanistic foundations of allostery gained from computational and experimental analyses of real protein systems and model systems. The main conceptual frameworks instrumental in driving the field are discussed. We illustrate the role of these frameworks in illuminating molecular mechanisms and explaining cellular processes, and describe some of their promising practical applications in engineering molecular sensors and informing drug design efforts.

Eigenvector centrality for characterization of protein allosteric pathways

Determining the principal energy-transfer pathways responsible for allosteric communication in biomolecules remains challenging, partially due to the intrinsic complexity of the systems and the lack of effective characterization methods. In this work, we introduce the eigenvector centrality metric based on mutual information to elucidate allosteric mechanisms that regulate enzymatic activity. Moreover, we propose a strategy to characterize the range of correlations that underlie the allosteric processes. We use the V-type allosteric enzyme imidazole glycerol phosphate synthase (IGPS) to test the proposed methodology. The eigenvector centrality method identifies key amino acid residues of IGPS with high susceptibility to effector binding. The findings are validated by solution NMR measurements yielding important biological insights, including direct experimental evidence for interdomain motion, the central role played by helix h[Formula: see text], and the short-range nature of correlations responsible for the allosteric mechanism. Beyond insights on IGPS allosteric pathways and the nature of residues that could be targeted by therapeutic drugs or site-directed mutagenesis, the reported findings demonstrate the eigenvector centrality analysis as a general cost-effective methodology to gain fundamental understanding of allosteric mechanisms at the molecular level.

Ligand-regulated oligomerisation of allosterically interacting proteins

The binding of ligands to distinct sites at proteins or at protein clusters is often cooperative or anti-cooperative due to allosteric signalling between those sites. The allostery is usually attributed to a configurational change of the proteins from a relaxed to a configurationally different tense state. Alternatively, as originally proposed by Cooper and Dryden, a tense state may be achieved by merely restricting the thermal vibrations of the protein around its mean configuration. In this work, we provide theoretical tools to investigate fluctuation allostery using cooling and titration experiments in which ligands regulate dimerisation, or ring or chain formation. We discuss in detail how ligands may regulate the supramolecular (co)polymerisation of liganded and unliganded proteins.

Biosensor libraries harness large classes of binding domains for construction of allosteric transcriptional regulators

The ability of bacteria to sense specific molecules within their environment and trigger metabolic responses in accordance is an invaluable biotechnological resource. While many transcription factors (TFs) mediating such processes have been studied, only a handful have been leveraged for molecular biology applications. To expand the repertoire of biotechnologically relevant sensors we present a strategy for the construction and testing of chimeric TF libraries, based on the fusion of highly soluble periplasmic binding proteins (PBPs) with DNA-binding domains (DBDs). We validate this concept by constructing and functionally testing two unique sense-and-respond regulators for benzoate, an environmentally and industrially relevant metabolite. This work will enable the development of tailored biosensors for novel synthetic regulatory circuits.

Bacterially encoded environmental sensor proteins are potentially a rich source of transcriptional control but only a few have been harnessed for biotechnological applications. Here the authors develop a general strategy for designing custom-made monogenic synthetic sensors and validate the approach by designing two sense-and-respond regulators for benzoate.

The 'allosteron' model for entropic allostery of self-assembly

Using the simple 'allosteron' model, we show that it is possible, in principle, to elicit pathways by which fluctuation allostery affects self-assembly of protein complexes. We treat the cases of (i) protein fibrils and nucleation, (ii) n-mer protein complexes, and (iii) weakly attractive allosteric interactions in protein-like soft nanoscale objects that can be tuned to define exclusive self-associating families.This article is part of a discussion meeting issue 'Allostery and molecular machines'.

Exothermicity Is Not a Necessary Condition for Enhanced Diffusion of Enzymes

Recent experiments have revealed that the diffusivity of exothermic and fast enzymes is enhanced when they are catalytically active, and different physical mechanisms have been explored and quantified to account for this observation. We perform measurements on the endothermic and relatively slow enzyme aldolase, which also shows substrate-induced enhanced diffusion. We propose a new physical paradigm, which reveals that the diffusion coefficient of a model enzyme hydrodynamically coupled to its environment increases significantly when undergoing changes in conformational fluctuations in a substrate concentration dependent manner, and is independent of the overall turnover rate of the underlying enzymatic reaction. Our results show that substrate-induced enhanced diffusion of enzyme molecules can be explained within an equilibrium picture and that the exothermicity of the catalyzed reaction is not a necessary condition for the observation of this phenomenon.

Mechanisms of Differential Allosteric Modulation in Homologous Proteins: Insights from the Analysis of Internal Dynamics and Energetics of PDZ Domains

Allostery is a general phenomenon in proteins whereby a perturbation at one site reverberates into a functional change at another one, through modulation of its conformational dynamics. Herein, we address the problem of how the molecular signal encoded by a ligand is differentially transmitted through the structures of two homologous PDZ proteins: PDZ2, which responds to binding with structural and dynamical changes in regions distal from the ligand site, and PDZ3, which is characterized by less-intense dynamical variations. We use novel methods of analysis of MD simulations in the unbound and bound states to investigate the determinants of the differential allosteric behavior of the two proteins. The analysis of the correlations between the redistribution of stabilization energy and local fluctuation patterns highlights the nucleus of residues responsible for the stabilization of the 3D fold, the stability core, as the substructure that defines the difference in the allosteric response: in PDZ2, it undergoes a consistent dynamic and energetic reorganization, whereas in PDZ3, it remains largely unperturbed. Specifically, we observe for PDZ2 a significant anticorrelation between the motions of distal loops and residues of the stability core and differences in the correlation patterns between the bound and unbound states. Such variation is not observed in PDZ3, indicating that its energetics and internal dynamics are less affected by the presence/absence of the ligand. Finally, we propose a model with a direct link between the modulation of the structural, energetic and dynamic properties of a protein, and its allosteric response to a perturbation.

Dynamic Transmission of Protein Allostery without Structural Change: Spatial Pathways or Global Modes?

We examine the contrast between mechanisms for allosteric signaling that involve structural change, and those that do not, from the perspective of allosteric pathways. In particular we treat in detail the case of fluctuation-allostery by which amplitude modulation of the thermal fluctuations of the elastic normal modes conveys the allosteric signal, and address the question of what an allosteric pathway means in this case. We find that a perturbation theory of thermal elastic solids and nonperturbative approach (by super-coarse-graining elasticity into internal bending modes) have opposite signatures in their structure of correlated pathways. We illustrate the effect from analysis of previous results from GlxR of Corynebacterium glutamicum, an example of the CRP/FNR transcription family of allosteric homodimers. We find that the visibility of both correlated pathways and disconnected sites of correlated motion in this protein suggests that mechanisms of local elastic stretch and bend are recruited for the purpose of creating and controlling allosteric cooperativity.

The Role of Protein-Ligand Contacts in Allosteric Regulation of the Escherichia coli Catabolite Activator Protein

Allostery is a fundamental process by which ligand binding to a protein alters its activity at a distant site. Both experimental and theoretical evidence demonstrate that allostery can be communicated through altered slow relaxation protein dynamics without conformational change. The catabolite activator protein (CAP) of Escherichia coli is an exemplar for the analysis of such entropically driven allostery. Negative allostery in CAP occurs between identical cAMP binding sites. Changes to the cAMP-binding pocket can therefore impact the allosteric properties of CAP. Here we demonstrate, through a combination of coarse-grained modeling, isothermal calorimetry, and structural analysis, that decreasing the affinity of CAP for cAMP enhances negative cooperativity through an entropic penalty for ligand binding. The use of variant cAMP ligands indicates the data are not explained by structural heterogeneity between protein mutants. We observe computationally that altered interaction strength between CAP and cAMP variously modifies the change in allosteric cooperativity due to second site CAP mutations. As the degree of correlated motion between the cAMP-contacting site and a second site on CAP increases, there is a tendency for computed double mutations at these sites to drive CAP toward noncooperativity. Naturally occurring pairs of covarying residues in CAP do not display this tendency, suggesting a selection pressure to fine tune allostery on changes to the CAP ligand-binding pocket without a drive to a noncooperative state. In general, we hypothesize an evolutionary selection pressure to retain slow relaxation dynamics-induced allostery in proteins in which evolution of the ligand-binding site is occurring.

Global low-frequency motions in protein allostery: CAP as a model system

Allostery is a fundamental process by which ligand binding to a protein alters its activity at a distant site. There is considerable evidence that allosteric cooperativity can be communicated by the modulation of protein dynamics without conformational change. The Catabolite Activator Protein (CAP) of Escherichia coli is an important experimental exemplar for entropically driven allostery. Here we discuss recent experimentally supported theoretical analysis that highlights the role of global low-frequency dynamics in allostery in CAP and identify how allostery arises as a natural consequence of changes in global low-frequency protein fluctuations on ligand binding.

A conformational factorisation approach for estimating the binding free energies of macromolecules

We present a conformational factorization approach. The theory is based on a superposition partition function, decomposed as a sum over contributions from local minima. The factorisation greatly reduces the number of minima that need to be considered, by employing the same local configurations for groups that are sufficiently distant from the binding site. The theory formalises the conditions required to analyse how our definition of the binding site region affects the free energy difference between the apo and holo states. We employ basin-hopping parallel tempering to sample minima that contribute significantly to the partition function, and calculate the binding free energies within the harmonic normal mode approximation. A further significant gain in efficiency is achieved using a recently developed local rigid body framework in both the sampling and the normal mode analysis, which reduces the number of degrees of freedom. We benchmark this approach for human aldose reductase (PDB code 2INE). When varying the size of the rigid region, the free energy difference converges for factorisation of groups at a distance of 14 Å from the binding site, which corresponds to 80% of the protein being locally rigidified.

Case study on temperature-accelerated molecular dynamics simulation of ligand dissociation: inducer dissociation from the Lac repressor protein

We studied ligand dissociation from the inducer-binding domain of the Lac repressor protein using temperature-accelerated molecular dynamics (TAMD) simulations. With TAMD, ligand dissociation could be observed within relatively short simulation time. This allowed many dissociation trajectories to be sampled. Under the adiabatic approximation of TAMD, all but one degree of freedom of the system were sampled from usual canonical ensembles at room temperature. Thus, meaningful statistical analyses could be carried out on the trajectories. A systematic approach was proposed to analyze possible correlations between ligand dissociation and fluctuations of various protein conformational coordinates. These analyses employed relative entropies, allowing both linear and nonlinear correlations to be considered. Applying the simulation and analysis methods to the inducer binding domain of the Lac repressor protein, we found that ligand dissociation from this protein correlated mainly with fluctuations of side-chain conformations of a few residues that surround the binding pocket. In addition, the two binding sites of the dimeric protein were dynamically coupled: occupation of one site by an inducer molecule could significantly reduce or slow down conformational dynamics around the other binding pocket.

Quantitative theory of hydrophobic effect as a driving force of protein structure

Various studies suggest that the hydrophobic effect plays a major role in driving the folding of proteins. In the past, however, it has been challenging to translate this understanding into a predictive, quantitative theory of how the full pattern of sequence hydrophobicity in a protein shapes functionally important features of its tertiary structure. Here, we extend and apply such a phenomenological theory of the sequence-structure relationship in globular protein domains, which had previously been applied to the study of allosteric motion. In an effort to optimize parameters for the model, we first analyze the patterns of backbone burial found in single-domain crystal structures, and discover that classic hydrophobicity scales derived from bulk physicochemical properties of amino acids are already nearly optimal for prediction of burial using the model. Subsequently, we apply the model to studying structural fluctuations in proteins and establish a means of identifying ligand-binding and protein-protein interaction sites using this approach.

Epitope fluctuations in the human papillomavirus are under dynamic allosteric control: a computational evaluation of a new vaccine design strategy

The dynamic properties of the capsid of the human papillomavirus (HPV) type 16 were examined using classical molecular dynamics simulations. By systematically comparing the structural fluctuations of the capsid protein, a strong dynamic allosteric connection between the epitope containing loops and the h4 helix located more than 50 Å away is identified, which was not recognized thus far. Computer simulations show that restricting the structural fluctuations of the h4 helix is key to rigidifying the epitopes, which is thought to be required for eliciting a proper immune response. The allostery identified in the components of the HPV is nonclassical because the mean structure of the epitope carrying loops remains unchanged, but as a result of allosteric effect the structural fluctuations are altered significantly, which in turn changes the biochemical reactivity profile of the epitopes. Exploiting this novel insight, a new vaccine design strategy is proposed wherein a relatively small virus capsid fragment is deposited on a silica nanoparticle in such a way that the fluctuations of the h4 helix are suppressed. The structural and dynamic properties of the epitope carrying loops on this hybrid nanoparticle match the characteristics of epitopes found on the full virus-like particle precisely, suggesting that these nanoparticles may serve as potent, cost-effective, and safe alternatives to traditionally developed vaccines. The structural and dynamic properties of the hybrid nanoparticle are examined in detail to establish the general concepts of the proposed new design.

Allostery without conformation change: modelling protein dynamics at multiple scales

The original ideas of Cooper and Dryden, that allosteric signalling can be induced between distant binding sites on proteins without any change in mean structural conformation, has proved to be a remarkably prescient insight into the rich structure of protein dynamics. It represents an alternative to the celebrated Monod-Wyman-Changeux mechanism and proposes that modulation of the amplitude of thermal fluctuations around a mean structure, rather than shifts in the structure itself, give rise to allostery in ligand binding. In a complementary approach to experiments on real proteins, here we take a theoretical route to identify the necessary structural components of this mechanism. By reviewing and extending an approach that moves from very coarse-grained to more detailed models, we show that, a fundamental requirement for a body supporting fluctuation-induced allostery is a strongly inhomogeneous elastic modulus. This requirement is reflected in many real proteins, where a good approximation of the elastic structure maps strongly coherent domains onto rigid blocks connected by more flexible interface regions.

Allostery in protein domains reflects a balance of steric and hydrophobic effects

Allosteric conformational change underlies biological function in many proteins. Allostery refers to a conformational event in which one region of a protein undergoes structural rearrangement in response to a stimulus applied to a different region of the same protein. Here, I show for a variety of proteins that a simple, phenomenological model of the dependence of protein conformation on hydrophobic burial energy allows one to compute low-energy conformational fluctuations for a given sequence by using linear programming to find optimized combinations of sequence-specific hydrophobic burial modes that satisfy steric constraints. From these fluctuations one may calculate allosteric couplings between different sites in a protein domain. Although the physical basis of protein structure is complex and multifactorial, a simplified description of conformational energy in terms of the hydrophobic effect alone is sufficient to give a mechanistic explanation for many biologically important allosteric events.

A new concept to reveal protein dynamics based on energy dissipation

Protein dynamics is essential for its function, especially for intramolecular signal transduction. In this work we propose a new concept, energy dissipation model, to systematically reveal protein dynamics upon effector binding and energy perturbation. The concept is applied to better understand the intramolecular signal transduction during allostery of enzymes. The E. coli allosteric enzyme, aspartokinase III, is used as a model system and special molecular dynamics simulations are designed and carried out. Computational results indicate that the number of residues affected by external energy perturbation (i.e. caused by a ligand binding) during the energy dissipation process shows a sigmoid pattern. Using the two-state Boltzmann equation, we define two parameters, the half response time and the dissipation rate constant, which can be used to well characterize the energy dissipation process. For the allostery of aspartokinase III, the residue response time indicates that besides the ACT2 signal transduction pathway, there is another pathway between the regulatory site and the catalytic site, which is suggested to be the β15-αK loop of ACT1. We further introduce the term “protein dynamical modules” based on the residue response time. Different from the protein structural modules which merely provide information about the structural stability of proteins, protein dynamical modules could reveal protein characteristics from the perspective of dynamics. Finally, the energy dissipation model is applied to investigate E. coli aspartokinase III mutations to better understand the desensitization of product feedback inhibition via allostery. In conclusion, the new concept proposed in this paper gives a novel holistic view of protein dynamics, a key question in biology with high impacts for both biotechnology and biomedicine.

Physics met biology, and the consequence was

We summarise the contributions to the discussion and the links between them. The complex relationship between the physical and biological sciences demonstrates three "axes of tension": the role of simulation, the interplay between levels of explanation, and the generality of "laws". We identify examples of true synergy between approaches that genuinely explore new research territory, and underscore the contemporary value of the type of discussions contained in this volume.

Approximations, idealizations and 'experiments' at the physics-biology interface

This paper, which is based on recent empirical research at the University of Leeds, the University of Edinburgh, and the University of Bristol, presents two difficulties which arise when condensed matter physicists interact with molecular biologists: (1) the former use models which appear to be too coarse-grained, approximate and/or idealized to serve a useful scientific purpose to the latter; and (2) the latter have a rather narrower view of what counts as an experiment, particularly when it comes to computer simulations, than the former. It argues that these findings are related; that computer simulations are considered to be undeserving of experimental status, by molecular biologists, precisely because of the idealizations and approximations that they involve. The complexity of biological systems is a key factor. The paper concludes by critically examining whether the new research programme of 'systems biology' offers a genuine alternative to the modelling strategies used by physicists. It argues that it does not.

Role of fluctuations in ligand binding cooperativity of membrane receptors

Signal transduction upon binding of a ligand to a membrane protein can occur not only via allosteric conformational changes but also through fluctuations. We report a numerical study on the influence of conformational fluctuations on the cooperativity of a binding reaction in a simple model of an integral membrane receptor consisting of transmembrane helices. We find that small fluctuations lateral as well as perpendicular to the membrane can increase the cooperativity, with the former more dominant. Moreover, too much fluctuation induces negative cooperativity. Proteins with fewer than four helices do not show positive cooperativity under any circumstances. This behavior is rather robust, and independent of the receptor topology or ligand size. Fluctuations measured in all-atom molecular dynamics simulations of a G-protein coupled receptor fall within the predicted region of maximum cooperativity.

Activation of nanoscale allosteric protein domain motion revealed by neutron spin echo spectroscopy

NHERF1 is a multidomain scaffolding protein that assembles signaling complexes, and regulates the cell surface expression and endocytic recycling of a variety of membrane proteins. The ability of the two PDZ domains in NHERF1 to assemble protein complexes is allosterically modulated by the membrane-cytoskeleton linker protein ezrin, whose binding site is located as far as 110 Ångstroms away from the PDZ domains. Here, using neutron spin echo (NSE) spectroscopy, selective deuterium labeling, and theoretical analyses, we reveal the activation of interdomain motion in NHERF1 on nanometer length-scales and on submicrosecond timescales upon forming a complex with ezrin. We show that a much-simplified coarse-grained model suffices to describe interdomain motion of a multidomain protein or protein complex. We expect that future NSE experiments will benefit by exploiting our approach of selective deuteration to resolve the specific domain motions of interest from a plethora of global translational and rotational motions. Our results demonstrate that the dynamic propagation of allosteric signals to distal sites involves changes in long-range coupled domain motions on submicrosecond timescales, and that these coupled motions can be distinguished and characterized by NSE.

Proteins move! Protein dynamics and long-range allostery in cell signaling

An emerging point of view in protein chemistry is that proteins are not the static objects that are displayed in textbooks but are instead dynamic actors. Protein dynamics plays a fundamental role in many diseases, and spans a large hierarchy of timescales, from picoseconds to milliseconds or even longer. Nanoscale protein domain motion on length scales comparable to protein dimensions is key to understanding how signals are relayed through multiple protein-protein interactions. A canonical example is how the scaffolding proteins NHERF1 and ezrin work in coordination to assemble crucial membrane complexes. As membrane-cytoskeleton scaffolding proteins, these provide excellent prototypes for understanding how regulatory signals are relayed through protein-protein interactions between the membrane and the cytoskeleton. Here, we review recent progress in understanding the structure and dynamics of the interaction. We describe recent novel applications of neutron spin echo spectroscopy to reveal the dynamic propagation of allosteric signals by nanoscale protein motion, and present a guide to the future study of dynamics and its application to the cure of disease.

Substrate-modulated thermal fluctuations affect long-range allosteric signaling in protein homodimers: exemplified in CAP

The role of conformational dynamics in allosteric signaling of proteins is increasingly recognized as an important and subtle aspect of this ubiquitous phenomenon. Cooperative binding is commonly observed in proteins with twofold symmetry that bind two identical ligands. We construct a coarse-grained model of an allosteric coupled dimer and show how the signal can be propagated between the distant binding sites via change in slow global vibrational modes alone. We demonstrate that modulation on substrate binding of as few as 5-10 slow modes can give rise to cooperativity observed in biological systems and that the type of cooperativity is given by change of interaction between the two monomers upon ligand binding. To illustrate the application of the model, we apply it to a challenging test case: the catabolite activator protein (CAP). CAP displays negative cooperativity upon association with two identical ligands. The conformation of CAP is not affected by the binding, but its vibrational spectrum undergoes a strong modification. Intriguingly, the first binding enhances thermal fluctuations, yet the second quenches them. We show that this counterintuitive behavior is, in fact, necessary for an optimal anticooperative system, and captured within a well-defined region of the model's parameter space. From analyzing the experimental results, we conclude that fast local modes take an active part in the allostery of CAP, coupled to the more-global slow modes. By including them into the model, we elucidate the role of the modes on different timescales. We conclude that such dynamic control of allostery in homodimers may be a general phenomenon and that our model framework can be used for extended interpretation of thermodynamic parameters in other systems.

A schematic model for molecular affinity and binding with Ising variables

After discussing the relevance of statistical physics in molecular recognition processes, we present a schematic model for ligand-receptor association based on an Ising chain. We discuss the possible behaviors of the affinity when the stiffness of the ligand increases. We also consider the case of flexible receptors. A variety of interesting behaviors is obtained, including some affinity modulation upon bond hardening or softening. The affinity of a ligand for its receptor is shown to depend on the details of its rigidity profile, and we question the possibility of encoding information in the rigidities as well as in the shape. An exhaustive study of the selectivity of patterns with length n < 8 is carried out. Connection with other spin models, in particular spin glasses is mentioned in the conclusion.

All-atom normal-mode analysis reveals an RNA-induced allostery in a bacteriophage coat protein

Assembly of the T=3 bacteriophage MS2 is initiated by the binding of a 19 nucleotide RNA stem loop from within the phage genome to a symmetric coat protein dimer. This binding event effects a folding of the FG loop in one of the protein subunits of the dimer and results in the formation of an asymmetric dimer. Since both the symmetric and asymmetric forms of the dimer are needed for the assembly of the protein container, this allosteric switch plays an important role in the life cycle of the phage. We provide here details of an all-atom normal-mode analysis of this allosteric effect. The results suggest that asymmetric contacts between the A -duplex RNA phosphodiester backbone of the stem loop with the EF loop in one coat protein subunit results in an increased dynamic behavior of its FG loop. The four lowest-frequency modes, which encompass motions predominantly on the FG loops, account for over 90% of the increased dynamic behavior due to a localization of the vibrational pattern on a single FG loop. Finally, we show that an analysis of the allosteric effect using an elastic network model fails to predict this localization effect, highlighting the importance of using an all-atom full force field method for this problem.

Quantifying Correlations Between Allosteric Sites in Thermodynamic Ensembles

Allostery describes altered protein function at one site due to a perturbation at another site. One mechanism of allostery involves correlated motions, which can occur even in the absence of substantial conformational change. We present a novel method, "MutInf", to identify statistically significant correlated motions from equilibrium molecular dynamics simulations. Our approach analyzes both backbone and sidechain motions using internal coordinates to account for the gear-like twists that can take place even in the absence of the large conformational changes typical of traditional allosteric proteins. We quantify correlated motions using a mutual information metric, which we extend to incorporate data from multiple short simulations and to filter out correlations that are not statistically significant. Applying our approach to uncover mechanisms of cooperative small molecule binding in human interleukin-2, we identify clusters of correlated residues from 50 ns of molecular dynamics simulations. Interestingly, two of the clusters with the strongest correlations highlight known cooperative small-molecule binding sites and show substantial correlations between these sites. These cooperative binding sites on interleukin-2 are correlated not only through the hydrophobic core of the protein but also through a dynamic polar network of hydrogen bonding and electrostatic interactions. Since this approach identifies correlated conformations in an unbiased, statistically robust manner, it should be a useful tool for finding novel or "orphan" allosteric sites in proteins of biological and therapeutic importance.

Allosteric role of the large-scale domain opening in biological catch-binding

The proposed model demonstrates the allosteric role of the two-domain region of the receptor protein in the increased lifetimes of biological receptor/ligand bonds subjected to an external force. The interaction between the domains is represented by a bounded potential, containing two minima corresponding to the attached and separated conformations of the two protein domains. The dissociative potential with a single minimum describing receptor/ligand binding fluctuates between deep and shallow states, depending on whether the domains are attached or separated. A number of valuable analytic expressions are derived and are used to interpret experimental data for two catch bonds. The P-selectin/P-selectin-glycoprotein-ligand-1 (PSGL-1) bond is controlled by the interface between the epidermal growth factor (EGF) and lectin domains of P-selectin, and the type 1 fimbrial adhesive protein (FimH)/mannose bond is governed by the interface between the lectin and pilin domains of FimH. Catch-binding occurs in these systems when the external force stretches the receptor proteins and increases the interdomain distance. The allosteric effect is supported by independent measurements, in which the domains are kept separated by attachment of another ligand. The proposed model accurately describes the experimentally observed anomalous behavior of the lifetimes of the P-selectin/PSGL-1 and FimH/mannose complexes as a function of applied force and provides valuable insights into the mechanism of catch-binding.

Configurational entropy in protein-peptide binding: computational study of Tsg101 ubiquitin E2 variant domain with an HIV-derived PTAP nonapeptide

Configurational entropy is thought to influence biomolecular processes, but there are still many open questions about this quantity, including its magnitude, its relationship to molecular structure, and the importance of correlation. The mutual information expansion (MIE) provides a novel and systematic approach to extracting configurational entropy changes due to correlated motions from molecular simulations. We present the first application of the MIE method to protein-ligand binding using multiple molecular dynamics simulations to study the association of the ubiquitin E2 variant domain of the protein Tsg101 and an HIV-derived nonapeptide. This investigation utilizes the second-order MIE approximation, which accounts for correlations between all pairs of degrees of freedom. The computed change in configurational entropy is large and has a major contribution from changes in pairwise correlation. The results also reveal intricate structure-entropy relationships. Thus, the present analysis suggests that in order for a model of binding to be accurate, it must include a careful accounting of configurational entropy changes.

Allostery: absence of a change in shape does not imply that allostery is not at play

Allostery is essential for controlled catalysis, signal transmission, receptor trafficking, turning genes on and off, and apoptosis. It governs the organism's response to environmental and metabolic cues, dictating transient partner interactions in the cellular network. Textbooks taught us that allostery is a change of shape at one site on the protein surface brought about by ligand binding to another. For several years, it has been broadly accepted that the change of shape is not induced; rather, it is observed simply because a larger protein population presents it. Current data indicate that while side chains can reorient and rewire, allostery may not even involve a change of (backbone) shape. Assuming that the enthalpy change does not reverse the free-energy change due to the change in entropy, entropy is mainly responsible for binding.

Pathways for conformational change in nitrogen regulatory protein C from discrete path sampling

Pathways corresponding to the conformational change in nitrogen regulatory protein C are calculated using the CHARMM19 force field with an implicit solvation model. Our analysis employs the discrete path sampling approach to grow a database of local minima and transition states from the potential energy surface that contains kinetically relevant pathways. The pathways with the largest contribution to the phenomenological two-state rate constants are found to exhibit a number of structural features that agree with experimental observations. Further details of the calculated pathways for conformational change may therefore provide useful predictions of how this large-scale motion is achieved.

Role of intermolecular forces in defining material properties of protein nanofibrils

Protein molecules have the ability to form a rich variety of natural and artificial structures and materials. We show that amyloid fibrils, ordered supramolecular nanostructures that are self-assembled from a wide range of polypeptide molecules, have rigidities varying over four orders of magnitude, and constitute a class of high-performance biomaterials. We elucidate the molecular origin of fibril material properties and show that the major contribution to their rigidity stems from a generic interbackbone hydrogen-bonding network that is modulated by variable side-chain interactions.

Ligand-induced conformational changes and conformational dynamics in the solution structure of the lactose repressor protein

We present here the results of a series of small-angle X-ray scattering studies aimed at understanding the role of conformational changes and structural flexibility in DNA binding and allosteric signaling in a bacterial transcription regulator, lactose repressor protein (LacI). Experiments were designed to detect possible conformational changes that occur when LacI binds either DNA or the inducer IPTG, or both. Our studies included the native LacI dimer of homodimers and a dimeric variant (R3), enabling us to probe conformational changes within the homodimers and distinguish them from those involving changes in the homodimer-homodimer relationships. The scattering data indicate that removal of operator DNA (oDNA) from R3 results in an unfolding and extension of the hinge helix that connects the LacI regulatory and DNA-binding domains. In contrast, only very subtle conformational changes occur in the R3 dimer-oDNA complex upon IPTG binding, indicative of small adjustments in the orientations of domains and/or subdomains within the structure. The binding of IPTG to native (tetrameric) LacI-oDNA complexes also appears to facilitate a modest change in the average homodimer-homodimer disposition. Notably, the crystal structure of the native LacI-oDNA complex differs significantly from the average solution conformation. The solution scattering data are best fit by an ensemble of structures that includes (1) approximately 60% of the V-shaped dimer of homodimers observed in the crystal structure and (2) approximately 40% of molecules with more "open" forms, such as those generated when the homodimers move with respect to each other about the tetramerization domain. In gene regulation, such a flexible LacI would be beneficial for the interaction of its two DNA-binding domains, positioned at the tips of the V, with the required two of three LacI operators needed for full repression.

Nonequilibrium dynamic mechanism for allosteric effect

Allosteric regulation is often viewed as thermodynamic in nature. However, protein internal motions during an enzymatic reaction cycle can slow the hoping processes over numerous potential barriers. We propose that regulating molecules may function by modifying the nonequilibrium protein dynamics. The theory predicts that an enzyme under the new mechanism has a different temperature dependence, waiting time distribution of the turnover cycle, and dynamic fluctuation patterns with and without an effector. Experimental tests of the theory are proposed.

Mimicking cAMP-dependent allosteric control of protein kinase A through mechanical tension

We report the activation of an enzyme complex by mechanical tension. Protein kinase A, a tetrameric enzyme that, in the cell, is allosterically controlled by cAMP, has been modified by the insertion of a "molecular spring" on the regulatory subunit. The spring is made of DNA, and its stiffness can be varied externally by hybridization to a complementary strand. This allows us to exert a controlled mechanical tension between the two points on the protein's surface where the spring is attached. We show that upon applying the tension, we can activate the enzyme with efficiency comparable to the activation by its natural regulatory molecule, cAMP.

A simple physical description of DNA dynamics: quasi-harmonic analysis as a route to the configurational entropy

It has become increasingly apparent that the dynamic as well as the structural properties of biological macromolecules are important to their function. However, information concerning molecular flexibility can be difficult to obtain experimentally at the atomic level. Computer modelling techniques such as molecular dynamics (MD) have therefore proved invaluable in advancing our understanding of biomolecular flexibility. This paper describes how a combination of atomistic MD simulations and quasi-harmonic analysis can be used to describe the dynamics of duplex DNA, with a particular emphasis on methods for calculating differences in configurational entropies. We demonstrate that DNA possesses remarkably simple mechanical properties relative to globular proteins, making it an ideal system for exploring biomolecular flexibility in general. Our results also highlight the importance of solvent viscosity in determining the dynamic behaviour of DNA in aqueous solution.

Entropy and barrier-controlled fluctuations determine conformational viscoelasticity of single biomolecules

Biological macromolecules have complex and nontrivial energy landscapes, endowing them with a unique conformational adaptability and diversity in function. Hence, understanding the processes of elasticity and dissipation at the nanoscale is important to molecular biology and emerging fields such as nanotechnology. Here we analyze single molecule fluctuations in an atomic force microscope, using a generic model of biopolymer viscoelasticity that includes local "internal" conformational dissipation. Comparing two biopolymers, dextran and cellulose (polysaccharides with and without local bistable transitions), demonstrates that signatures of simple conformational change are minima in both the elastic and internal friction constants around a characteristic force. A novel analysis of dynamics on a bistable energy landscape provides a simple explanation: an elasticity driven by the entropy, and friction by a barrier-controlled hopping time of populations between states, which is surprisingly distinct to the well-known relaxation time. This nonequilibrium microscopic analysis thus provides a means of quantifying new dynamical features of the energy landscape of the glucopyranose ring, revealing an unexpected underlying roughness and information on the shape of the barrier of the chair-boat transition in dextran. The results presented herein provide a basis toward probing the viscoelasticity of macromolecular conformational transitions on more complex energy landscapes, such as during protein folding.

Guanylate kinase, induced fit, and the allosteric spring probe

Since the introduction of the induced-fit theory by D. E. Koshland Jr., it has been established that conformational motion invariably accompanies the execution of protein function. The catalytic activity of kinases, specifically, is associated with large conformational changes ( approximately 1 nm amplitude). In the case of guanylate kinase, upon substrate binding, the LID and nucleotide-monophosphate-binding domains are brought together and toward the CORE with large concerted movements about the alpha3 (helix 3) axis. However, whether the change in conformation mostly affects the catalytic rate or mostly increases binding affinities for one or the other substrate is unclear. We investigate this question using a nanotechnology approach based on mechanical stress. Using an "allosteric spring probe", we bias conformational states in favor of the "open" (substrate-free) conformation of the enzyme; the result is that the binding constant for the substrate guanosine monophosphate (GMP) is reduced by up to a factor of 10, whereas the binding constant for adenosine triphosphate (ATP) and the catalytic rate are essentially unaffected. The results show that the GMP-induced conformational change, which promotes catalysis, does not promote ATP binding, consistent with previous mutagenesis studies. Furthermore, they show that this conformational change is of the induced-fit type with respect to GMP binding (but not ATP binding). We elaborate on this point by proposing a quantitative criterion for the classification of conformational changes with respect to the induced-fit theory. More generally, these results show that the allosteric spring probe can be used to affect enzymatic activity in a continuously controlled manner, and also to affect specific steps of the reaction mechanism while leaving others unaffected. It is presumed that this will enable informative comparisons with the results of future molecular dynamics or statistical mechanics computations.

Dynamic allostery of protein alpha helical coiled-coils

Alpha helical coiled-coils appear in many important allosteric proteins such as the dynein molecular motor and bacteria chemotaxis transmembrane receptors. As a mechanism for transmitting the information of ligand binding to a distant site across an allosteric protein, an alternative to conformational change in the mean static structure is an induced change in the pattern of the internal dynamics of the protein. We explore how ligand binding may change the intramolecular vibrational free energy of a coiled-coil, using parameterized coarse-grained models, treating the case of dynein in detail. The models predict that coupling of slide, bend and twist modes of the coiled-coil transmits an allosteric free energy of approximately 2kBT, consistent with experimental results. A further prediction is a quantitative increase in the effective stiffness of the coiled-coil without any change in inherent flexibility of the individual helices. The model provides a possible and experimentally testable mechanism for transmission of information through the alpha helical coiled-coil of dynein.

Coupling of global and local vibrational modes in dynamic allostery of proteins

It is now recognized that internal global protein dynamics play an important role in the allosteric function of many proteins. Alterations of protein flexibility on effector binding affect the entropic cost of binding at a distant site. We present a coarse-grained model for a potential amplification of such entropic allostery due to coupling of fast, localized modes to the slow, global modes. We show how such coupling can give rise to large compensating entropic and enthalpic terms. The model corresponds to the pattern of calorimetry and NMR data from experiments on the Met repressor.

Allosteric control through mechanical tension

Conformational changes of proteins modulate their function. In allosteric control, the conformational change is induced by the binding of a signaling molecule. Here we insert a "molecular spring" on the enzyme guanylate kinase, to control the conformation of this protein. The stiffness of the spring can be varied externally, which allows one to exert a controlled mechanical tension between the two points on the protein's surface where the spring is attached. We show that by applying and releasing the tension we can reversibly turn the enzyme off and on.