Discrete breathers in protein structures

Discrete breathers in a triangular β-Fermi-Pasta-Ulam-Tsingou lattice

A practical approach to the search for (quasi-) discrete breathers (DBs) in a triangular β-FPUT lattice (after Fermi, Pasta, Ulam, and Tsingou) is proposed. DBs are obtained by superimposing localizing functions on delocalized nonlinear vibrational modes (DNVMs) having frequencies above the phonon spectrum of the lattice. Zero-dimensional and one-dimensional DBs are obtained. The former ones are localized in both spatial dimensions, and the latter ones are only in one dimension. Among the one-dimensional DBs, two families are considered: the first is based on the DNVMs of a triangular lattice, and the second is based on the DNVMs of a chain. We speculate that our systematic approach on the triangular β-FPUT lattice reveals all possible types of spatially localized oscillations with frequencies bifurcating from the upper edge of the phonon band as all DNVMs with frequencies above the phonon band are analyzed.

Visualizing correlated motion with HDBSCAN clustering

Correlated motion analysis provides a method for understanding communication between and dynamic similarities of biopolymer residues and domains. The typical equal-time correlation matrices-frequently visualized with pseudo-colorings or heat maps-quickly convey large regions of highly correlated motion but hide more subtle similarities of motion. Here we propose a complementary method for visualizing correlations within proteins (or general biopolymers) that quickly conveys intuition about which residues have a similar dynamic behavior. For grouping residues, we use the recently developed non-parametric clustering algorithm HDBSCAN. Although the method we propose here can be used to group residues using correlation as a similarity matrix-the most straightforward and intuitive method-it can also be used to more generally determine groups of residues which have similar dynamic properties. We term these latter groups "Dynamic Domains", as they are based not on spatial closeness but rather closeness in the column space of a correlation matrix. We provide examples of this method across three human proteins of varying size and function-the Nf-Kappa-Beta essential modulator, the clotting promoter Thrombin and the mismatch repair protein (dimer) complex MutS-alpha. Although the examples presented here are from all-atom molecular dynamics simulations, this visualization technique can also be used on correlations matrices built from any ensembles of conformations from experiment or computation.

Nonlinear network model analysis of vibrational energy transfer and localisation in the Fenna-Matthews-Olson complex

Collective protein modes are expected to be important for facilitating energy transfer in the Fenna-Matthews-Olson (FMO) complex of photosynthetic green sulphur bacteria, however to date little work has focussed on the microscopic details of these vibrations. The nonlinear network model (NNM) provides a computationally inexpensive approach to studying vibrational modes at the microscopic level in large protein structures, whilst incorporating anharmonicity in the inter-residue interactions which can influence protein dynamics. We apply the NNM to the entire trimeric FMO complex and find evidence for the existence of nonlinear discrete breather modes. These modes tend to transfer energy to the highly connected core pigments, potentially opening up alternative excitation energy transfer routes through their influence on pigment properties. Incorporating localised modes based on these discrete breathers in the optical spectra calculations for FMO using ab initio site energies and excitonic couplings can substantially improve their agreement with experimental results.

Protein Ensembles: How Does Nature Harness Thermodynamic Fluctuations for Life? The Diverse Functional Roles of Conformational Ensembles in the Cell

All soluble proteins populate conformational ensembles that together constitute the native state. Their fluctuations in water are intrinsic thermodynamic phenomena, and the distributions of the states on the energy landscape are determined by statistical thermodynamics; however, they are optimized to perform their biological functions. In this review we briefly describe advances in free energy landscape studies of protein conformational ensembles. Experimental (nuclear magnetic resonance, small-angle X-ray scattering, single-molecule spectroscopy, and cryo-electron microscopy) and computational (replica-exchange molecular dynamics, metadynamics, and Markov state models) approaches have made great progress in recent years. These address the challenging characterization of the highly flexible and heterogeneous protein ensembles. We focus on structural aspects of protein conformational distributions, from collective motions of single- and multi-domain proteins, intrinsically disordered proteins, to multiprotein complexes. Importantly, we highlight recent studies that illustrate functional adjustment of protein conformational ensembles in the crowded cellular environment. We center on the role of the ensemble in recognition of small- and macro-molecules (protein and RNA/DNA) and emphasize emerging concepts of protein dynamics in enzyme catalysis. Overall, protein ensembles link fundamental physicochemical principles and protein behavior and the cellular network and its regulation.

Similarity in Shape Dictates Signature Intrinsic Dynamics Despite No Functional Conservation in TIM Barrel Enzymes

The conservation of the intrinsic dynamics of proteins emerges as we attempt to understand the relationship between sequence, structure and functional conservation. We characterise the conservation of such dynamics in a case where the structure is conserved but function differs greatly. The triosephosphate isomerase barrel fold (TBF), renowned for its 8 β-strand-α-helix repeats that close to form a barrel, is one of the most diverse and abundant folds found in known protein structures. Proteins with this fold have diverse enzymatic functions spanning five of six Enzyme Commission classes, and we have picked five different superfamily candidates for our analysis using elastic network models. We find that the overall shape is a large determinant in the similarity of the intrinsic dynamics, regardless of function. In particular, the β-barrel core is highly rigid, while the α-helices that flank the β-strands have greater relative mobility, allowing for the many possibilities for placement of catalytic residues. We find that these elements correlate with each other via the loops that link them, as opposed to being directly correlated. We are also able to analyse the types of motions encoded by the normal mode vectors of the α-helices. We suggest that the global conservation of the intrinsic dynamics in the TBF contributes greatly to its success as an enzymatic scaffold both through evolution and enzyme design.

Function changing mutations in glucocorticoid receptor evolution correlate with their relevance to mode coupling

Nonlinear effects in protein dynamics are expected to play role in function, particularly of allosteric nature, by facilitating energy transfer between vibrational modes. A recently proposed method focusing on the non-Gaussian shape of the configurational population near equilibrium projects this information onto real space in order to identify the aminoacids relevant to function. We here apply this method to three ancestral proteins in glucocorticoid receptor (GR) family and show that the mutations that restrict functional activity during GR evolution correlate significantly with locations that are highlighted by the nonlinear contribution to the near-native configurational distribution. Our findings demonstrate that the analysis of nonlinear effects in protein dynamics can be harnessed into a predictive tool for functional site determination.

Cutoff lensing: predicting catalytic sites in enzymes

Predicting function-related amino acids in proteins with unknown function or unknown allosteric binding sites in drug-targeted proteins is a task of paramount importance in molecular biomedicine. In this paper we introduce a simple, light and computationally inexpensive structure-based method to identify catalytic sites in enzymes. Our method, termed cutoff lensing, is a general procedure consisting in letting the cutoff used to build an elastic network model increase to large values. A validation of our method against a large database of annotated enzymes shows that optimal values of the cutoff exist such that three different structure-based indicators allow one to recover a maximum of the known catalytic sites. Interestingly, we find that the larger the structures the greater the predictive power afforded by our method. Possible ways to combine the three indicators into a single figure of merit and into a specific sequential analysis are suggested and discussed with reference to the classic case of HIV-protease. Our method could be used as a complement to other sequence- and/or structure-based methods to narrow the results of large-scale screenings.

Energy transfer in molecular devices

Protein machines often exhibit long-range interplay between different sites in order to achieve their biological tasks. We investigate and characterize the nonlinear energy localization and the basic mechanisms of energy transfer in protein devices. By studying two different model protein machines, with different biological functions, we show that genuinely nonlinear phenomena are responsible for energy transport between the different machine sites involved in the biological functions. The energy transfer turns out to be extremely efficient from an energetic point of view: by changing the energy initially provided to the model device, we identify a well defined range of energies where the time for the energy transport to occur is minimal and the amount of transferred energy is a maximum. Furthermore, by introducing an implicit solvent, we show that the energy is localized on the internal residues of the protein structure, thus minimizing the dissipation.

Hotspot mutations in KIT receptor differentially modulate its allosterically coupled conformational dynamics: impact on activation and drug sensitivity

Receptor tyrosine kinase KIT controls many signal transduction pathways and represents a typical allosterically regulated protein. The mutation-induced deregulation of KIT activity impairs cellular physiological functions and causes serious human diseases. The impact of hotspots mutations (D816H/Y/N/V and V560G/D) localized in crucial regulatory segments, the juxtamembrane region (JMR) and the activation (A-) loop, on KIT internal dynamics was systematically studied by molecular dynamics simulations. The mutational outcomes predicted in silico were correlated with in vitro and in vivo activation rates and drug sensitivities of KIT mutants. The allosteric regulation of KIT in the native and mutated forms is described in terms of communication between the two remote segments, JMR and A-loop. A strong correlation between the communication profile and the structural and dynamical features of KIT in the native and mutated forms was established. Our results provide new insight on the determinants of receptor KIT constitutive activation by mutations and resistance of KIT mutants to inhibitors. Depiction of an intra-molecular component of the communication network constitutes a first step towards an integrated description of vast communication pathways established by KIT in physiopathological contexts.

Receptor tyrosine kinase KIT plays a crucial role in the regulation of cell signaling. This allosterically controlled activity may be affected by gain-of-function mutations that promote the development of several cancers. Identification of the molecular basis of KIT constitutive activation and allosteric regulation has inspired computational study of KIT hotspot mutations. In the present contribution, we investigated the mutation-induced effects on KIT conformational dynamics and intra-protein communication conditionally on the mutation location and the nature of the substituting amino acid. Our data elucidate that all studied mutations stabilize an inactive non-autoinhibited state of KIT over the inactive auto-inhibited state prevalent for the native protein. This shift in the protein conformational landscape promotes KIT constitutive activation. Our in silico analysis established correlations between the structural and dynamical effects induced by oncogenic mutations and the mutants auto-activation rates and drug sensitivities measured in vitro and in vivo. Particularly, the A-loop mutations stabilize the drug-resistant forms, while the JMR mutations may facilitate inhibitors binding to the active site. Cross-correlations established between local and long-range structural and dynamical effects demonstrate the allosteric character of the gain-of-function mutations mode of action.

Correlated motions are a fundamental property of β-sheets

Correlated motions in proteins can mediate fundamental biochemical processes such as signal transduction and allostery. The mechanisms that underlie these processes remain largely unknown due mainly to limitations in their direct detection. Here, based on a detailed analysis of protein structures deposited in the protein data bank, as well as on state-of-the art molecular simulations, we provide general evidence for the transfer of structural information by correlated backbone motions, mediated by hydrogen bonds, across β-sheets. We also show that the observed local and long-range correlated motions are mediated by the collective motions of β-sheets and investigate their role in large-scale conformational changes. Correlated motions represent a fundamental property of β-sheets that contributes to protein function.

Allosteric pathway identification through network analysis: from molecular dynamics simulations to interactive 2D and 3D graphs

Allostery is a universal phenomenon that couples the information induced by a local perturbation (effector) in a protein to spatially distant regulated sites. Such an event can be described in terms of a large scale transmission of information (communication) through a dynamic coupling between structurally rigid (minimally frustrated) and plastic (locally frustrated) clusters of residues. To elaborate a rational description of allosteric coupling, we propose an original approach - MOdular NETwork Analysis (MONETA) - based on the analysis of inter-residue dynamical correlations to localize the propagation of both structural and dynamical effects of a perturbation throughout a protein structure. MONETA uses inter-residue cross-correlations and commute times computed from molecular dynamics simulations and a topological description of a protein to build a modular network representation composed of clusters of residues (dynamic segments) linked together by chains of residues (communication pathways). MONETA provides a brand new direct and simple visualization of protein allosteric communication. A GEPHI module implemented in the MONETA package allows the generation of 2D graphs of the communication network. An interactive PyMOL plugin permits drawing of the communication pathways between chosen protein fragments or residues on a 3D representation. MONETA is a powerful tool for on-the-fly display of communication networks in proteins. We applied MONETA for the analysis of communication pathways (i) between the main regulatory fragments of receptors tyrosine kinases (RTKs), KIT and CSF-1R, in the native and mutated states and (ii) in proteins STAT5 (STAT5a and STAT5b) in the phosphorylated and the unphosphorylated forms. The description of the physical support for allosteric coupling by MONETA allowed a comparison of the mechanisms of (a) constitutive activation induced by equivalent mutations in two RTKs and (b) allosteric regulation in the activated and non-activated STAT5 proteins. Our theoretical prediction based on results obtained with MONETA was validated for KIT by in vitro experiments. MONETA is a versatile analytical and visualization tool entirely devoted to the understanding of the functioning/malfunctioning of allosteric regulation in proteins - a crucial basis to guide the discovery of next-generation allosteric drugs.

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

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

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.

Exploring signal transduction in heteromultimeric protein based on energy dissipation model

Dynamic intersubunit interactions are key elements in the regulation of many biological systems. A better understanding of how subunits interact with each other and how their interactions are related to dynamic protein structure is a fundamental task in biology. In this paper, a heteromultimeric allosteric protein, Corynebacterium glutamicum aspartokinase, is used as a model system to explore the signal transduction involved in intersubunit interactions and allosteric communication with an emphasis on the intersubunit signaling process. For this purpose, energy dissipation simulation and network construction are conducted for each subunit and the whole protein. Comparison with experimental results shows that the new approach is able to predict all the mutation sites that have been experimentally proved to desensitize allosteric regulation of the enzyme. Additionally, analysis revealed that the function of the effector threonine is to facilitate the binding of the two subunits without contributing to the allosteric communication. During the allosteric regulation upon the binding of the effector lysine, signals can be transferred from the β-subunit to the catalytic site of the α-subunit through both a direct way of intersubunit signal transduction, and an indirect way: first, to the regulatory region of the α-subunit by intersubunit signal transduction and then to the catalytic region by intramolecular signal transduction. Therefore, the new approach is able to illustrate the diversity of the underlying mechanisms when the strength of feedback inhibition by the effector(s) is modulated, providing useful information that has potential applications in engineering heteromultimeric allosteric regulation.

Perturbation centrality and turbine: a novel centrality measure obtained using a versatile network dynamics tool

Analysis of network dynamics became a focal point to understand and predict changes of complex systems. Here we introduce Turbine, a generic framework enabling fast simulation of any algorithmically definable dynamics on very large networks. Using a perturbation transmission model inspired by communicating vessels, we define a novel centrality measure: perturbation centrality. Hubs and inter-modular nodes proved to be highly efficient in perturbation propagation. High perturbation centrality nodes of the Met-tRNA synthetase protein structure network were identified as amino acids involved in intra-protein communication by earlier studies. Changes in perturbation centralities of yeast interactome nodes upon various stresses well recapitulated the functional changes of stressed yeast cells. The novelty and usefulness of perturbation centrality was validated in several other model, biological and social networks. The Turbine software and the perturbation centrality measure may provide a large variety of novel options to assess signaling, drug action, environmental and social interventions.

Revealing the properties of plant defensins through dynamics

Defensins are potent, ancient natural antibiotics that are present in organisms ranging from lower organisms to humans. Although the structures of several defensins have been well characterized, the dynamics of only a few have been studied. This review discusses the diverse dynamics of two plant defensins for which the structure and dynamics have been characterized, both in the free state and in the presence of target membranes. Multiple motions are observed in loops and in secondary structure elements and may be related to twisting or breathing of the α-helix and β-sheet. This complex behavior is altered in the presence of an interface and is responsive to the presence of the putative target. The stages of membrane recognition and disruption can be mapped over a large time scale range, demonstrating that defensins in solution exist as an ensemble of different conformations, a subset of which is selected upon membrane binding. Therefore, studies on the dynamics have revealed that defensins interact with membranes through a mechanism of conformational selection.

Hot spots in a network of functional sites

It is of significant interest to understand how proteins interact, which holds the key phenomenon in biological functions. Using dynamic fluctuations in high frequency modes, we show that the Gaussian Network Model (GNM) predicts hot spot residues with success rates ranging between S 8–58%, C 84–95%, P 5–19% and A 81–92% on unbound structures and S 8–51%, C 97–99%, P 14–50%, A 94–97% on complex structures for sensitivity, specificity, precision and accuracy, respectively. High specificity and accuracy rates with a single property on unbound protein structures suggest that hot spots are predefined in the dynamics of unbound structures and forming the binding core of interfaces, whereas the prediction of other functional residues with similar dynamic behavior explains the lower precision values. The latter is demonstrated with the case studies; ubiquitin, hen egg-white lysozyme and M2 proton channel. The dynamic fluctuations suggest a pseudo network of residues with high frequency fluctuations, which could be plausible for the mechanism of biological interactions and allosteric regulation.

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

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

Structure and dynamics of molecular networks: a novel paradigm of drug discovery: a comprehensive review

Despite considerable progress in genome- and proteome-based high-throughput screening methods and in rational drug design, the increase in approved drugs in the past decade did not match the increase of drug development costs. Network description and analysis not only give a systems-level understanding of drug action and disease complexity, but can also help to improve the efficiency of drug design. We give a comprehensive assessment of the analytical tools of network topology and dynamics. The state-of-the-art use of chemical similarity, protein structure, protein-protein interaction, signaling, genetic interaction and metabolic networks in the discovery of drug targets is summarized. We propose that network targeting follows two basic strategies. The "central hit strategy" selectively targets central nodes/edges of the flexible networks of infectious agents or cancer cells to kill them. The "network influence strategy" works against other diseases, where an efficient reconfiguration of rigid networks needs to be achieved by targeting the neighbors of central nodes/edges. It is shown how network techniques can help in the identification of single-target, edgetic, multi-target and allo-network drug target candidates. We review the recent boom in network methods helping hit identification, lead selection optimizing drug efficacy, as well as minimizing side-effects and drug toxicity. Successful network-based drug development strategies are shown through the examples of infections, cancer, metabolic diseases, neurodegenerative diseases and aging. Summarizing >1200 references we suggest an optimized protocol of network-aided drug development, and provide a list of systems-level hallmarks of drug quality. Finally, we highlight network-related drug development trends helping to achieve these hallmarks by a cohesive, global approach.

Probing molecular mechanisms of the Hsp90 chaperone: biophysical modeling identifies key regulators of functional dynamics

Deciphering functional mechanisms of the Hsp90 chaperone machinery is an important objective in cancer biology aiming to facilitate discovery of targeted anti-cancer therapies. Despite significant advances in understanding structure and function of molecular chaperones, organizing molecular principles that control the relationship between conformational diversity and functional mechanisms of the Hsp90 activity lack a sufficient quantitative characterization. We combined molecular dynamics simulations, principal component analysis, the energy landscape model and structure-functional analysis of Hsp90 regulatory interactions to systematically investigate functional dynamics of the molecular chaperone. This approach has identified a network of conserved regions common to the Hsp90 chaperones that could play a universal role in coordinating functional dynamics, principal collective motions and allosteric signaling of Hsp90. We have found that these functional motifs may be utilized by the molecular chaperone machinery to act collectively as central regulators of Hsp90 dynamics and activity, including the inter-domain communications, control of ATP hydrolysis, and protein client binding. These findings have provided support to a long-standing assertion that allosteric regulation and catalysis may have emerged via common evolutionary routes. The interaction networks regulating functional motions of Hsp90 may be determined by the inherent structural architecture of the molecular chaperone. At the same time, the thermodynamics-based "conformational selection" of functional states is likely to be activated based on the nature of the binding partner. This mechanistic model of Hsp90 dynamics and function is consistent with the notion that allosteric networks orchestrating cooperative protein motions can be formed by evolutionary conserved and sparsely connected residue clusters. Hence, allosteric signaling through a small network of distantly connected residue clusters may be a rather general functional requirement encoded across molecular chaperones. The obtained insights may be useful in guiding discovery of allosteric Hsp90 inhibitors targeting protein interfaces with co-chaperones and protein binding clients.

Discovery of intramolecular signal transduction network based on a new protein dynamics model of energy dissipation

A novel approach to reveal intramolecular signal transduction network is proposed in this work. To this end, a new algorithm of network construction is developed, which is based on a new protein dynamics model of energy dissipation. A key feature of this approach is that direction information is specified after inferring protein residue-residue interaction network involved in the process of signal transduction. This enables fundamental analysis of the regulation hierarchy and identification of regulation hubs of the signaling network. A well-studied allosteric enzyme, E. coli aspartokinase III, is used as a model system to demonstrate the new method. Comparison with experimental results shows that the new approach is able to predict all the sites that have been experimentally proved to desensitize allosteric regulation of the enzyme. In addition, the signal transduction network shows a clear preference for specific structural regions, secondary structural types and residue conservation. Occurrence of super-hubs in the network indicates that allosteric regulation tends to gather residues with high connection ability to collectively facilitate the signaling process. Furthermore, a new parameter of propagation coefficient is defined to determine the propagation capability of residues within a signal transduction network. In conclusion, the new approach is useful for fundamental understanding of the process of intramolecular signal transduction and thus has significant impact on rational design of novel allosteric proteins.

Modeling of relay helix functional dynamics and feasibility of experimental verification by neutron scattering

Cellular long-range transport involves motor proteins (MPs) (especially, kinesin and myosin) which contain a so-called relay helix. Its motion is of crucial importance to the conversion of chemical energy released in ATP hydrolysis into the coordinated mechanical movement of the entire motor protein. In this paper, we propose two combined nonlinear mechanisms for this particular functional activity and suggest the application of neutron scattering assays to experimentally determine the incoherent dynamic structure factor S(q,ω). We argue that this type of experiment is not only feasible but it could offer significant insights into the mechanism of MP function at a molecular level.

Dynamic allostery: linkers are not merely flexible

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

Discrete breathers in a realistic coarse-grained model of proteins

We report the results of molecular dynamics simulations of an off-lattice protein model featuring a physical force-field and amino-acid sequence. We show that localized modes of nonlinear origin, discrete breathers (DBs), emerge naturally as continuations of a subset of high-frequency normal modes residing at specific sites dictated by the native fold. DBs are time-periodic, space-localized vibrational modes that exist generically in nonlinear discrete systems and are known for their resilience and ability to concentrate energy for long times. In the case of the small β-barrel structure that we consider, DB-mediated localization occurs on the turns connecting the strands. At high energies, DBs stabilize the structure by concentrating energy on a few sites, while their collapse marks the onset of large-amplitude fluctuations of the protein. Furthermore, we show how breathers develop as energy-accumulating centres following perturbations even at distant locations, thus mediating efficient and irreversible energy transfers. Remarkably, due to the presence of angular potentials, the breather induces a local static distortion of the native fold. Altogether, the combination of these two nonlinear effects may provide a ready means for remotely controlling local conformational changes in proteins.

Induced fit, conformational selection and independent dynamic segments: an extended view of binding events

Single molecule and NMR measurements of protein dynamics increasingly uncover the complexity of binding scenarios. Here, we describe an extended conformational selection model that embraces a repertoire of selection and adjustment processes. Induced fit can be viewed as a subset of this repertoire, whose contribution is affected by the bond types stabilizing the interaction and the differences between the interacting partners. We argue that protein segments whose dynamics are distinct from the rest of the protein ('discrete breathers') can govern conformational transitions and allosteric propagation that accompany binding processes and, as such, might be more sensitive to mutational events. Additionally, we highlight the dynamic complexity of binding scenarios as they relate to events such as aggregation and signalling, and the crowded cellular environment.

Predicting important residues and interaction pathways in proteins using Gaussian Network Model: binding and stability of HLA proteins

A statistical thermodynamics approach is proposed to determine structurally and functionally important residues in native proteins that are involved in energy exchange with a ligand and other residues along an interaction pathway. The structure-function relationships, ligand binding and allosteric activities of ten structures of HLA Class I proteins of the immune system are studied by the Gaussian Network Model. Five of these models are associated with inflammatory rheumatic disease and the remaining five are properly functioning. In the Gaussian Network Model, the protein structures are modeled as an elastic network where the inter-residue interactions are harmonic. Important residues and the interaction pathways in the proteins are identified by focusing on the largest eigenvalue of the residue interaction matrix. Predicted important residues match those known from previous experimental and clinical work. Graph perturbation is used to determine the response of the important residues along the interaction pathway. Differences in response patterns of the two sets of proteins are identified and their relations to disease are discussed.

We propose a statistical thermodynamics model for determining structurally and functionally important residues in ligand-protein interactions. Our method identifies the path that the protein uses in transferring information from one point to the other. We show that a few energetically active residues are most efficient in energy exchange with the surroundings acting as ‘energy gates’. The remaining important residues that we identify are situated along the interaction path. These are the hub residues. Strong correlations exist between energy gates and hub residues along the interaction path, thus relating to allostery and cooperative binding. We studied the structure-function, ligand binding and allosteric activities of ten models of HLA Class I proteins of the immune system. Five of these models belong to the HLA-B*2705 allele and are strongly associated with a chronic inflammatory rheumatic disease. The remaining five from the HLA-B*2709 allele of the same protein are the corresponding properly functioning ones. We show that differences in the contact maps of the two types lead to significant and consistent changes in the fluctuation profile, making the HLA-B*2705 alleles respond too strongly to perturbation.

Targeted activation in deterministic and stochastic systems

Metastable escape is ubiquitous in many physical systems and is becoming a concern in engineering design as these designs (e.g., swarms of vehicles, coupled building energetics, nanoengineering, etc.) become more inspired by dynamics of biological, molecular and other natural systems. In light of this, we study a chain of coupled bistable oscillators which has two global conformations and we investigate how specialized or targeted disturbance is funneled in an inverse energy cascade and ultimately influences the transition process between the conformations. We derive a multiphase averaged approximation to these dynamics which illustrates the influence of actions in modal coordinates on the coarse behavior of this process. An activation condition that predicts how the disturbance influences the rate of transition is then derived. The prediction tools are derived for deterministic dynamics and we also present analogous behavior in the stochastic setting and show a divergence from Kramers activation behavior under targeted activation conditions.

Long-range energy transfer in proteins

Proteins are large and complex molecular machines. In order to perform their function, most of them need energy, e.g. either in the form of a photon, as in the case of the visual pigment rhodopsin, or through the breaking of a chemical bond, as in the presence of adenosine triphosphate (ATP). Such energy, in turn, has to be transmitted to specific locations, often several tens of A away from where it is initially released. Here we show, within the framework of a coarse-grained nonlinear network model, that energy in a protein can jump from site to site with high yields, covering in many instances remarkably large distances. Following single-site excitations, few specific sites are targeted, systematically within the stiffest regions. Such energy transfers mark the spontaneous formation of a localized mode of nonlinear origin at the destination site, which acts as an efficient energy-accumulating center. Interestingly, yields are found to be optimum for excitation energies in the range of biologically relevant ones.

Statistical thermodynamics of residue fluctuations in native proteins

Statistical thermodynamics of residue fluctuations of native proteins in a temperature, pressure, and force reservoir is formulated. The general theory is discussed in terms of harmonic and anharmonic fluctuations of residues. The two elastic network models based on the harmonic approximation, the anisotropic network and the Gaussian network models are discussed as the limiting cases of the general theory. The heat capacity and the correlations between the energy fluctuations and residue fluctuations are obtained for the harmonic approximation. The formulation is extended to large fluctuations of residues in order to account for effects of anharmonicity. The fluctuation probability function is constructed for this purpose as a tensorial Hermite series expansion with higher order moments of fluctuations as coefficients. Evaluation of the higher order moments using the proposed statistical thermodynamics model is explained. The formulation is applied to a hexapeptide and the fluctuations of residues obtained by molecular dynamics simulations are characterized in the framework of the model developed. In particular, coupling of two different modes in the nonlinear model is discussed in detail.