Entropic mechanism of large fluctuation in allosteric transition

Accurate prediction of protein folding mechanisms by simple structure-based statistical mechanical models

Recent breakthroughs in highly accurate protein structure prediction using deep neural networks have made considerable progress in solving the structure prediction component of the 'protein folding problem'. However, predicting detailed mechanisms of how proteins fold into specific native structures remains challenging, especially for multidomain proteins constituting most of the proteomes. Here, we develop a simple structure-based statistical mechanical model that introduces nonlocal interactions driving the folding of multidomain proteins. Our model successfully predicts protein folding processes consistent with experiments, without the limitations of protein size and shape. Furthermore, slight modifications of the model allow prediction of disulfide-oxidative and disulfide-intact protein folding. These predictions depict details of the folding processes beyond reproducing experimental results and provide a rationale for the folding mechanisms. Thus, our physics-based models enable accurate prediction of protein folding mechanisms with low computational complexity, paving the way for solving the folding process component of the 'protein folding problem'.

The Wako-Saitô-Muñoz-Eaton Model for Predicting Protein Folding and Dynamics

Despite the recent advances in the prediction of protein structures by deep neutral networks, the elucidation of protein-folding mechanisms remains challenging. A promising theory for describing protein folding is a coarse-grained statistical mechanical model called the Wako-Saitô-Muñoz-Eaton (WSME) model. The model can calculate the free-energy landscapes of proteins based on a three-dimensional structure with low computational complexity, thereby providing a comprehensive understanding of the folding pathways and the structure and stability of the intermediates and transition states involved in the folding reaction. In this review, we summarize previous and recent studies on protein folding and dynamics performed using the WSME model and discuss future challenges and prospects. The WSME model successfully predicted the folding mechanisms of small single-domain proteins and the effects of amino-acid substitutions on protein stability and folding in a manner that was consistent with experimental results. Furthermore, extended versions of the WSME model were applied to predict the folding mechanisms of multi-domain proteins and the conformational changes associated with protein function. Thus, the WSME model may contribute significantly to solving the protein-folding problem and is expected to be useful for predicting protein folding, stability, and dynamics in basic research and in industrial and medical applications.

Weakening of interaction networks with aging in tip-link protein induces hearing loss

Age-related hearing loss (ARHL) is a common condition in humans marking the gradual decrease in hearing with age. Perturbations in the tip-link protein cadherin-23 that absorbs the mechanical tension from sound and maintains the integrity of hearing is associated with ARHL. Here, in search of molecular origins for ARHL, we dissect the conformational behavior of cadherin-23 along with the mutant S47P that progresses the hearing loss drastically. Using an array of experimental and computational approaches, we highlight a lower thermodynamic stability, significant weakening in the hydrogen-bond network and inter-residue correlations among β-strands, due to the S47P mutation. The loss in correlated motions translates to not only a remarkable two orders of magnitude slower folding in the mutant but also to a proportionately complex unfolding mechanism. We thus propose that loss in correlated motions within cadherin-23 with aging may trigger ARHL, a molecular feature that likely holds true for other disease-mutations in β-strand-rich proteins.

The nicotinic acetylcholine receptor: a typical 'allosteric machine'

The concept of allosteric interaction was initially proposed to account for the inhibitory feedback mechanism mediated by bacterial regulatory enzymes. In contrast with the classical mechanism of competitive, steric, interaction between ligands for a common site, allosteric interactions take place between topographically distinct sites and are mediated by a discrete and reversible conformational change of the protein. The concept was soon extended to membrane receptors for neurotransmitters and shown to apply to the signal transduction process which, in the case of the acetylcholine nicotinic receptor (nAChR), links the ACh binding site to the ion channel. Pharmacological effectors, referred to as allosteric modulators, such as Ca²⁺ ions and ivermectin, were discovered that enhance the transduction process when they bind to sites distinct from the orthosteric ACh site and the ion channel. The recent X-ray and electron microscopy structures, at atomic resolution, of the resting and active conformations of several homologues of the nAChR, in combination with atomistic molecular dynamics simulations reveal a stepwise quaternary transition in the transduction process with tertiary changes modifying the boundaries between subunits. These interfaces host orthosteric and allosteric modulatory sites which structural organization changes in the course of the transition. The nAChR appears as a typical allosteric machine. The model emerging from these studies has led to the conception and development of several new pharmacological agents.This article is part of a discussion meeting issue 'Allostery and molecular machines'.

Unified understanding of folding and binding mechanisms of globular and intrinsically disordered proteins

Extensive experimental and theoretical studies have advanced our understanding of the mechanisms of folding and binding of globular proteins, and coupled folding and binding of intrinsically disordered proteins (IDPs). The forces responsible for conformational changes and binding are common in both proteins; however, these mechanisms have been separately discussed. Here, we attempt to integrate the mechanisms of coupled folding and binding of IDPs, folding of small and multi-subdomain proteins, folding of multimeric proteins, and ligand binding of globular proteins in terms of conformational selection and induced-fit mechanisms as well as the nucleation–condensation mechanism that is intermediate between them. Accumulating evidence has shown that both the rate of conformational change and apparent rate of binding between interacting elements can determine reaction mechanisms. Coupled folding and binding of IDPs occurs mainly by induced-fit because of the slow folding in the free form, while ligand binding of globular proteins occurs mainly by conformational selection because of rapid conformational change. Protein folding can be regarded as the binding of intramolecular segments accompanied by secondary structure formation. Multi-subdomain proteins fold mainly by the induced-fit (hydrophobic collapse) mechanism, as the connection of interacting segments enhances the binding (compaction) rate. Fewer hydrophobic residues in small proteins reduce the intramolecular binding rate, resulting in the nucleation–condensation mechanism. Thus, the folding and binding of globular proteins and IDPs obey the same general principle, suggesting that the coarse-grained, statistical mechanical model of protein folding is promising for a unified theoretical description of all mechanisms.

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.

Comparing allosteric transitions in the domains of calmodulin through coarse-grained simulations

Calmodulin (CaM) is a ubiquitous Ca(2+)-binding protein consisting of two structurally similar domains with distinct stabilities, binding affinities, and flexibilities. We present coarse grained simulations that suggest that the mechanism for the domain's allosteric transitions between the open and closed conformations depends on subtle differences in the folded state topology of the two domains. Throughout a wide temperature range, the simulated transition mechanism of the N-terminal domain (nCaM) follows a two-state transition mechanism while domain opening in the C-terminal domain (cCaM) involves unfolding and refolding of the tertiary structure. The appearance of the unfolded intermediate occurs at a higher temperature in nCaM than it does in cCaM consistent with nCaM's higher thermal stability. Under approximate physiological conditions, the simulated unfolded state population of cCaM accounts for 10% of the population with nearly all of the sampled transitions (approximately 95%) unfolding and refolding during the conformational change. Transient unfolding significantly slows the domain opening and closing rates of cCaM, which can potentially influence its Ca(2+)-binding mechanism.

Cooperativity and modularity in protein folding

A simple statistical mechanical model proposed by Wako and Saitô has explained the aspects of protein folding surprisingly well. This model was systematically applied to multiple proteins by Muñoz and Eaton and has since been referred to as the Wako-Saitô-Muñoz-Eaton (WSME) model. The success of the WSME model in explaining the folding of many proteins has verified the hypothesis that the folding is dominated by native interactions, which makes the energy landscape globally biased toward native conformation. Using the WSME and other related models, Saitô emphasized the importance of the hierarchical pathway in protein folding; folding starts with the creation of contiguous segments having a native-like configuration and proceeds as growth and coalescence of these segments. The Φ-values calculated for barnase with the WSME model suggested that segments contributing to the folding nucleus are similar to the structural modules defined by the pattern of native atomic contacts. The WSME model was extended to explain folding of multi-domain proteins having a complex topology, which opened the way to comprehensively understanding the folding process of multi-domain proteins. The WSME model was also extended to describe allosteric transitions, indicating that the allosteric structural movement does not occur as a deterministic sequential change between two conformations but as a stochastic diffusive motion over the dynamically changing energy landscape. Statistical mechanical viewpoint on folding, as highlighted by the WSME model, has been renovated in the context of modern methods and ideas, and will continue to provide insights on equilibrium and dynamical features of proteins.

Characterization of protein folding by a Φ-value calculation with a statistical-mechanical model

The Φ-value analysis approach provides information about transition-state structures along the folding pathway of a protein by measuring the effects of an amino acid mutation on folding kinetics. Here we compared the theoretically calculated Φ values of 27 proteins with their experimentally observed Φ values; the theoretical values were calculated using a simple statistical-mechanical model of protein folding. The theoretically calculated Φ values reflected the corresponding experimentally observed Φ values with reasonable accuracy for many of the proteins, but not for all. The correlation between the theoretically calculated and experimentally observed Φ values strongly depends on whether the protein-folding mechanism assumed in the model holds true in real proteins. In other words, the correlation coefficient can be expected to illuminate the folding mechanisms of proteins, providing the answer to the question of which model more accurately describes protein folding: the framework model or the nucleation-condensation model. In addition, we tried to characterize protein folding with respect to various properties of each protein apart from the size and fold class, such as the free-energy profile, contact-order profile, and sensitivity to the parameters used in the Φ-value calculation. The results showed that any one of these properties alone was not enough to explain protein folding, although each one played a significant role in it. We have confirmed the importance of characterizing protein folding from various perspectives. Our findings have also highlighted that protein folding is highly variable and unique across different proteins, and this should be considered while pursuing a unified theory of protein folding.

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.

Small Molecule Targeting of Protein-Protein Interactions through Allosteric Modulation of Dynamics

The protein–protein interaction (PPI) target class is particularly challenging, but offers potential for “first in class” therapies. Most known PPI small molecules are orthosteric inhibitors but many PPI sites may be fundamentally intractable to this approach. One potential alternative is to consider more attractive, remote small molecule pockets; however, on the whole, allostery is poorly understood and difficult to discover and develop. Here we review the literature in order to understand the basis for allostery, especially as it can apply to PPIs. We suggest that the upfront generation of sophisticated and experimentally validated dynamic models of target proteins can aid in target choice and strategy for allosteric intervention to produce the required functional effect.

Allosteric Regulation of E-Cadherin Adhesion

Cadherins are transmembrane adhesion proteins that maintain intercellular cohesion in all tissues, and their rapid regulation is essential for organized tissue remodeling. Despite some evidence that cadherin adhesion might be allosterically regulated, testing of this has been hindered by the difficulty of quantifying altered E-cadherin binding affinity caused by perturbations outside the ectodomain binding site. Here, measured kinetics of cadherin-mediated intercellular adhesion demonstrated quantitatively that treatment with activating, anti-E-cadherin antibodies or the dephosphorylation of a cytoplasmic binding partner, p120(ctn), increased the homophilic binding affinity of E-cadherin. Results obtained with Colo 205 cells, which express inactive E-cadherin and do not aggregate, demonstrated that four treatments, which induced Colo 205 aggregation and p120(ctn) dephosphorylation, triggered quantitatively similar increases in E-cadherin affinity. Several processes can alter cell aggregation, but these results directly demonstrated the allosteric regulation of cell surface E-cadherin by p120(ctn) dephosphorylation.

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

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

Free energy landscape of activation in a signalling protein at atomic resolution

The interconversion between inactive and active protein states, traditionally described by two static structures, is at the heart of signaling. However, how folded states interconvert is largely unknown due to the inability to experimentally observe transition pathways. Here we explore the free energy landscape of the bacterial response regulator NtrC by combining computation and NMR, and discover unexpected features underlying efficient signaling. We find that functional states are defined purely in kinetic and not structural terms. The need of a well-defined conformer, crucial to the active state, is absent in the inactive state, which comprises a heterogeneous collection of conformers. The transition between active and inactive states occurs through multiple pathways, facilitated by a number of nonnative transient hydrogen bonds, thus lowering the transition barrier through both entropic and enthalpic contributions. These findings may represent general features for functional conformational transitions within the folded state.

Communication over the network of binary switches regulates the activation of A2A adenosine receptor

Dynamics and functions of G-protein coupled receptors (GPCRs) are accurately regulated by the type of ligands that bind to the orthosteric or allosteric binding sites. To glean the structural and dynamical origin of ligand-dependent modulation of GPCR activity, we performed total ~ 5 μsec molecular dynamics simulations of A_2A adenosine receptor (A_2AAR) in its apo, antagonist-bound, and agonist-bound forms in an explicit water and membrane environment, and examined the corresponding dynamics and correlation between the 10 key structural motifs that serve as the allosteric hotspots in intramolecular signaling network. We dubbed these 10 structural motifs “binary switches” as they display molecular interactions that switch between two distinct states. By projecting the receptor dynamics on these binary switches that yield 2¹⁰ microstates, we show that (i) the receptors in apo, antagonist-bound, and agonist-bound states explore vastly different conformational space; (ii) among the three receptor states the apo state explores the broadest range of microstates; (iii) in the presence of the agonist, the active conformation is maintained through coherent couplings among the binary switches; and (iv) to be most specific, our analysis shows that W246, located deep inside the binding cleft, can serve as both an agonist sensor and actuator of ensuing intramolecular signaling for the receptor activation. Finally, our analysis of multiple trajectories generated by inserting an agonist to the apo state underscores that the transition of the receptor from inactive to active form requires the disruption of ionic-lock in the DRY motif.

As the key signal transmitters of a number of physiological processes, G-protein coupled receptors (GPCRs) are arguably one of the most important therapeutic targets. Orchestration of the intra-molecular signaling across transmembrane domain is key for the function of GPCRs. To investigate the microscopic underpinnings of intramolecular signaling that regulates the activation of GPCRs, we performed molecular dynamics simulations of the receptor in three distinct ligand-bound states using A_2A adenosine receptor as a model system of GPCRs. Statistical analyses on the dynamics of and correlation among the 10 “binary switches” reveal that the three receptor states retain distinct dynamic properties. The antagonist- and agonist-bound forms of the receptors explore vastly different conformational space, and the apo form lies between them, yet located closer to the antagonist-bound form. In regard to the agonist-binding triggered activation mechanism, the correlation map among the 10 binary switches unequivocally shows that direct sensing of agonist ligand by the indole ring of W246 actuates the rest of intramolecular signaling.

Protein dynamics and the allosteric transitions of pentameric receptor channels

The recent application of molecular dynamics (MD) methodology to investigate the allosteric transitions of the acetylcholine receptor and its prokaryotic and eukaryotic pentameric homologs has yielded new insights into the mechanisms of signal transduction by these receptors. Combined with available data on X-ray structures, MD techniques enable description of the dynamics of the conformational change at the atomic level, intra-molecular propagation of this signal transduction mechanism as a concerted stepwise process at physiological timescales and the control of this process by allosteric modulators, thereby offering new perspectives for drug design.

What is biased efficacy? Defining the relationship between intrinsic efficacy and free energy coupling

A G protein-coupled receptor (GPCR) is only biologically active when associated with a transduction protein, but it can also switch function by interacting with different types of transduction proteins. Biased agonism arises when the ligand induces the receptor to engage distinct transduction proteins with different efficacies. We briefly review the concept of ligand efficacy, from the classical empirical idea to the current mechanistic views of allosteric regulation in proteins. A combination of these theoretically distinct ideas and methodologies allows us to distinguish true ligand bias from divergences of signalling caused by the system. We also demonstrate a rigorous mathematical connection between the intrinsic efficacy of classical receptor theory and the energetic effect that makes a ligand capable of stabilizing receptor-transducer association in the ternary complex model. This relationship unifies different definitions of efficacy and provides a rational basis for quantifying biased agonism.

Learning To Fold Proteins Using Energy Landscape Theory

This review is a tutorial for scientists interested in the problem of protein structure prediction, particularly those interested in using coarse-grained molecular dynamics models that are optimized using lessons learned from the energy landscape theory of protein folding. We also present a review of the results of the AMH/AMC/AMW/AWSEM family of coarse-grained molecular dynamics protein folding models to illustrate the points covered in the first part of the article. Accurate coarse-grained structure prediction models can be used to investigate a wide range of conceptual and mechanistic issues outside of protein structure prediction; specifically, the paper concludes by reviewing how AWSEM has in recent years been able to elucidate questions related to the unusual kinetic behavior of artificially designed proteins, multidomain protein misfolding, and the initial stages of protein aggregation.

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.

Coupling of lever arm swing and biased Brownian motion in actomyosin

An important unresolved problem associated with actomyosin motors is the role of Brownian motion in the process of force generation. On the basis of structural observations of myosins and actins, the widely held lever-arm hypothesis has been proposed, in which proteins are assumed to show sequential structural changes among observed and hypothesized structures to exert mechanical force. An alternative hypothesis, the Brownian motion hypothesis, has been supported by single-molecule experiments and emphasizes more on the roles of fluctuating protein movement. In this study, we address the long-standing controversy between the lever-arm hypothesis and the Brownian motion hypothesis through in silico observations of an actomyosin system. We study a system composed of myosin II and actin filament by calculating free-energy landscapes of actin-myosin interactions using the molecular dynamics method and by simulating transitions among dynamically changing free-energy landscapes using the Monte Carlo method. The results obtained by this combined multi-scale calculation show that myosin with inorganic phosphate (P_i) and ADP weakly binds to actin and that after releasing P_i and ADP, myosin moves along the actin filament toward the strong-binding site by exhibiting the biased Brownian motion, a behavior consistent with the observed single-molecular behavior of myosin. Conformational flexibility of loops at the actin-interface of myosin and the N-terminus of actin subunit is necessary for the distinct bias in the Brownian motion. Both the 5.5–11 nm displacement due to the biased Brownian motion and the 3–5 nm displacement due to lever-arm swing contribute to the net displacement of myosin. The calculated results further suggest that the recovery stroke of the lever arm plays an important role in enhancing the displacement of myosin through multiple cycles of ATP hydrolysis, suggesting a unified movement mechanism for various members of the myosin family.

Myosin II is a molecular motor that is fueled by ATP hydrolysis and generates mechanical force by interacting with actin filament. Comparison among various myosin structures obtained by X-ray and electron microscope analyses has led to the hypothesis that structural change of myosin in ATP hydrolysis cycle is the driving mechanism of force generation. However, single-molecule experiments have suggested an alternative mechanism in which myosin moves stochastically in a biased direction along actin filament. Computer simulation serves as a platform for assessing these hypotheses by revealing the prominent features of the dynamically changing landscape of actin-myosin interaction. The calculated results show that myosin binds to actin at different locations of actin filament in the weak- and strong-binding states and that the free energy has a global gradient from the weak-binding site to the strong-binding site. Myosin relaxing into the strong-binding state therefore necessarily shows the biased Brownian motion toward the strong-binding site. Lever-arm swing is induced during this relaxation process; therefore, lever-arm swing and the biased Brownian motion are coupled to contribute to the net displacement of myosin. This coupling should affect the dynamical behaviors of muscle and cardiac systems.

Crystal structures of a pentameric ligand-gated ion channel provide a mechanism for activation

Pentameric ligand-gated ion channels mediate fast chemical transmission of nerve signals. The structure of a bacterial proton-gated homolog has been established in its open and locally closed conformations at acidic pH. Here we report its crystal structure at neutral pH, thereby providing the X-ray structures of the two end-points of the gating mechanism in the same pentameric ligand-gated ion channel. The large structural variability in the neutral pH structure observed in the four copies of the pentamer present in the asymmetric unit has been used to analyze the intrinsic fluctuations in this state, which are found to prefigure the transition to the open state. In the extracellular domain (ECD), a marked quaternary change is observed, involving both a twist and a blooming motion, and the pore in the transmembrane domain (TMD) is closed by an upper bend of helix M2 (as in locally closed form) and a kink of helix M1, both helices no longer interacting across adjacent subunits. On the tertiary level, detachment of inner and outer β sheets in the ECD reshapes two essential cavities at the ECD-ECD and ECD-TMD interfaces. The first one is the ligand-binding cavity; the other is close to a known divalent cation binding site in other pentameric ligand-gated ion channels. In addition, a different crystal form reveals that the locally closed and open conformations coexist as discrete ones at acidic pH. These structural results, together with site-directed mutagenesis, physiological recordings, and coarse-grained modeling, have been integrated to propose a model of the gating transition pathway.

Frustration-induced protein intrinsic disorder

Spontaneous folding into a specific native structure is the most important property of protein to perform their biological functions within organisms. Spontaneous folding is understood on the basis of an energy landscape picture based on the minimum frustration principle. Therefore, frustration seemingly only leads to protein functional disorder. However, frustration has recently been suggested to have a function in allosteric regulation. Functional frustration has the possibility to be a key to our deeper understanding of protein function. To explore another functional frustration, we theoretically examined structural frustration, which is designed to induce intrinsic disorder of a protein and its function through the coupled folding and binding. We extended the Wako-Saitô-Muñoz-Eaton model to take into account a frustration effect. With the model, we analyzed the binding part of neuron-restrictive silencer factor and showed that designed structural frustration in it induces intrinsic disorder. Furthermore, we showed that the folding and the binding are cooperative in interacting with a target protein. The cooperativity enables an intrinsically disordered protein to exhibit a sharp switch-like folding response to binding chemical potential change. Through this switch-like response, the structural frustration may contribute to the regulation function of interprotein interaction of the intrinsically disordered protein.

Exact partition function zeros of the Wako-Saitô-Muñoz-Eaton β hairpin model

I compute exact partition function zeros of β hairpins, using both analytic and numerical methods, extending previous work [J. Lee, Phys. Rev. Lett. 110, 248101 (2013)] where only a restricted class of hairpins was considered. The zeros of β hairpins with an odd number of peptide bonds are computed and the difference of the distribution of zeros from those for an even number of peptide bonds is explained in terms of additional entropy of liberating the extra bond at the turn region. Upon the introduction of a hydrophobic core in the central region of the hairpin, the zeros are distributed uniformly on two concentric circles corresponding to the hydrophobic collapse and the transition to the fully folded conformation. One of the circles dissolves as the core moves toward the turn or the tip region, which is explained in terms of the similarity of the intermediate state with the folded or unfolded states. The exact partition function zeros for a hairpin with a more complex structure of native contacts, the 16 C-terminal residues of streptococcal protein G B1, are numerically computed and their loci are closely approximated by concentric circles.

Exact partition function zeros of the Wako-Saitô-Muñoz-Eaton protein model

I compute exact partition function zeros of the Wako-Saitô-Muñoz-Eaton model for various secondary structural elements and for two proteins, 1BBL and 1I6C, by using both analytic and numerical methods. Two-state and barrierless downhill folding transitions can be distinguished by a gap in the distribution of zeros at the positive real axis.

Entropic mechanism of allosteric communication in conformational transitions of dihydrofolate reductase

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

Allostery in the Hsp70 chaperone proteins

Heat shock 70-kDa (Hsp70) chaperones are essential to in vivo protein folding, protein transport, and protein re-folding. They carry out these activities using repeated cycles of binding and release of client proteins. This process is under allosteric control of nucleotide binding and hydrolysis. X-ray crystallography, NMR spectroscopy, and other biophysical techniques have contributed much to the understanding of the allosteric mechanism linking these activities and the effect of co-chaperones on this mechanism. In this chapter these findings are critically reviewed. Studies on the allosteric mechanisms of Hsp70 have gained enhanced urgency, as recent studies have implicated this chaperone as a potential drug target in diseases such as Alzheimer's and cancer. Recent approaches to combat these diseases through interference with the Hsp70 allosteric mechanism are discussed.

Impact of mutations on the allosteric conformational equilibrium

Allostery in a protein involves effector binding at an allosteric site that changes the structure and/or dynamics at a distant, functional site. In addition to the chemical equilibrium of ligand binding, allostery involves a conformational equilibrium between one protein substate that binds the effector and a second substate that less strongly binds the effector. We run molecular dynamics simulations using simple, smooth energy landscapes to sample specific ligand-induced conformational transitions, as defined by the effector-bound and effector-unbound protein structures. These simulations can be performed using our web server (http://salilab.org/allosmod/). We then develop a set of features to analyze the simulations and capture the relevant thermodynamic properties of the allosteric conformational equilibrium. These features are based on molecular mechanics energy functions, stereochemical effects, and structural/dynamic coupling between sites. Using a machine-learning algorithm on a data set of 10 proteins and 179 mutations, we predict both the magnitude and the sign of the allosteric conformational equilibrium shift by the mutation; the impact of a large identifiable fraction of the mutations can be predicted with an average unsigned error of 1k(B)T. With similar accuracy, we predict the mutation effects for an 11th protein that was omitted from the initial training and testing of the machine-learning algorithm. We also assess which calculated thermodynamic properties contribute most to the accuracy of the prediction.

Analysis and elimination of a bias in targeted molecular dynamics simulations of conformational transitions: application to calmodulin

The popular targeted molecular dynamics (TMD) method for generating transition paths in complex biomolecular systems is revisited. In a typical TMD transition path, the large-scale changes occur early and the small-scale changes tend to occur later. As a result, the order of events in the computed paths depends on the direction in which the simulations are performed. To identify the origin of this bias, and to propose a method in which the bias is absent, variants of TMD in the restraint formulation are introduced and applied to the complex open ↔ closed transition in the protein calmodulin. Due to the global best-fit rotation that is typically part of the TMD method, the simulated system is guided implicitly along the lowest-frequency normal modes, until the large spatial scales associated with these modes are near the target conformation. The remaining portion of the transition is described progressively by higher-frequency modes, which correspond to smaller-scale rearrangements. A straightforward modification of TMD that avoids the global best-fit rotation is the locally restrained TMD (LRTMD) method, in which the biasing potential is constructed from a number of TMD potentials, each acting on a small connected portion of the protein sequence. With a uniform distribution of these elements, transition paths that lack the length-scale bias are obtained. Trajectories generated by steered MD in dihedral angle space (DSMD), a method that avoids best-fit rotations altogether, also lack the length-scale bias. To examine the importance of the paths generated by TMD, LRTMD, and DSMD in the actual transition, we use the finite-temperature string method to compute the free energy profile associated with a transition tube around a path generated by each algorithm. The free energy barriers associated with the paths are comparable, suggesting that transitions can occur along each route with similar probabilities. This result indicates that a broad ensemble of paths needs to be calculated to obtain a full description of conformational changes in biomolecules. The breadth of the contributing ensemble suggests that energetic barriers for conformational transitions in proteins are offset by entropic contributions that arise from a large number of possible paths.

Exploration of multi-state conformational dynamics and underlying global functional landscape of maltose binding protein

An increasing number of biological machines have been revealed to have more than two macroscopic states. Quantifying the underlying multiple-basin functional landscape is essential for understanding their functions. However, the present models seem to be insufficient to describe such multiple-state systems. To meet this challenge, we have developed a coarse grained triple-basin structure-based model with implicit ligand. Based on our model, the constructed functional landscape is sufficiently sampled by the brute-force molecular dynamics simulation. We explored maltose-binding protein (MBP) which undergoes large-scale domain motion between open, apo-closed (partially closed) and holo-closed (fully closed) states responding to ligand binding. We revealed an underlying mechanism whereby major induced fit and minor population shift pathways co-exist by quantitative flux analysis. We found that the hinge regions play an important role in the functional dynamics as well as that increases in its flexibility promote population shifts. This finding provides a theoretical explanation of the mechanistic discrepancies in PBP protein family. We also found a functional “backtracking” behavior that favors conformational change. We further explored the underlying folding landscape in response to ligand binding. Consistent with earlier experimental findings, the presence of ligand increases the cooperativity and stability of MBP. This work provides the first study to explore the folding dynamics and functional dynamics under the same theoretical framework using our triple-basin functional model.

A central goal of biology is to understand the function of the organism and its constituent parts at each of its scales of complexity. Function at the molecular level is often realized by changes in conformation. Unfortunately, experimental explorations of global motions critical for functional conformational changes are still challenging. In the present work, we developed a coarse grained triple-well structure-based model to explore the underlying functional landscape of maltose-binding protein (MBP). By quantitative flux analysis, we uncover the underlying mechanism by which the major induced fit and minor population shift pathways co-exist. Though we have previously lent credence to the assertion that dynamical equilibrium between open and minor closed conformations exist for all the free PBPs, the generality of this rule is still a matter of open debate. We found that the hinge flexibility is favorable to population shift mechanism. This finding provides a theoretical explanation of the mechanism discrepancies in PBP protein family. We also simulated the folding dynamics using this functional multi-basin model which successfully reproduced earlier protein melting experiment. This represents an exciting opportunity to characterize the interplay between folding and function, which is a long-standing question in the community. The theoretical approach employed in this study is general and can be applied to other systems.

Structural distributions from single-molecule measurements as a tool for molecular mechanics

A mechanical view provides an attractive alternative for predicting the behavior of complex systems since it circumvents the resource-intensive requirements of atomistic models; however, it remains extremely challenging to characterize the mechanical responses of a system at the molecular level. Here, the structural distribution is proposed to be an effective means to extracting the molecular mechanical properties. End-to-end distance distributions for a series of short poly-L-proline peptides with the sequence P(n)CG(3)K-biotin (n = 8, 12, 15 and 24) were used to experimentally illustrate this new approach. High-resolution single-molecule Förster-type resonance energy transfer (FRET) experiments were carried out and the conformation-resolving power was characterized and discussed in the context of the conventional constant-time binning procedure for FRET data analysis. It was shown that the commonly adopted theoretical polymer models-including the worm-like chain, the freely jointed chain, and the self-avoiding chain-could not be distinguished by the averaged end-to-end distances, but could be ruled out using the molecular details gained by conformational distribution analysis because similar polymers of different sizes could respond to external forces differently. Specifically, by fitting the molecular conformational distribution to a semi-flexible polymer model, the effective persistence lengths for the series of short poly-L-proline peptides were found to be size-dependent with values of ~190 Å, ~67 Å, ~51 Å, and ~76 Å for n = 8, 12, 15, and 24, respectively. A comprehensive computational modeling was carried out to gain further insights for this surprising discovery. It was found that P(8) exists as the extended all-trans isomaer whereas P(12) and P(15) predominantly contained one proline residue in the cis conformation. P(24) exists as a mixture of one-cis (75%) and two-cis (25%) isomers where each isomer contributes to an experimentally resolvable conformational mode. This work demonstrates the resolving power of the distribution-based approach, and the capacity of integrating high-resolution single-molecule FRET experiments with molecular modeling to reveal detailed structural information about the conformation of molecules on the length scales relevant to the study of biological molecules.

Detection of allosteric signal transmission by information-theoretic analysis of protein dynamics

Allostery offers a highly specific way to modulate protein function. Therefore, understanding this mechanism is of increasing interest for protein science and drug discovery. However, allosteric signal transmission is difficult to detect experimentally and to model because it is often mediated by local structural changes propagating along multiple pathways. To address this, we developed a method to identify communication pathways by an information-theoretical analysis of molecular dynamics simulations. Signal propagation was described as information exchange through a network of correlated local motions, modeled as transitions between canonical states of protein fragments. The method was used to describe allostery in two-component regulatory systems. In particular, the transmission from the allosteric site to the signaling surface of the receiver domain NtrC was shown to be mediated by a layer of hub residues. The location of hubs preferentially connected to the allosteric site was found in close agreement with key residues experimentally identified as involved in the signal transmission. The comparison with the networks of the homologues CheY and FixJ highlighted similarities in their dynamics. In particular, we showed that a preorganized network of fragment connections between the allosteric and functional sites exists already in the inactive state of all three proteins.

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

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

Link between allosteric signal transduction and functional dynamics in a multisubunit enzyme: S-adenosylhomocysteine hydrolase

S-adenosylhomocysteine hydrolase (SAHH), a cellular enzyme that plays a key role in methylation reactions including those required for maturation of viral mRNA, is an important drug target in the discovery of antiviral agents. While targeting the active site is a straightforward strategy of enzyme inhibition, evidence of allosteric modulation of active site in many enzymes underscores the molecular origin of signal transduction. Information of co-evolving sequences in SAHH family and the key residues for functional dynamics that can be identified using native topology of the enzyme provide glimpses into how the allosteric signaling network, dispersed over the molecular structure, coordinates intra- and intersubunit conformational dynamics. To study the link between the allosteric communication and functional dynamics of SAHHs, we performed Brownian dynamics simulations by building a coarse-grained model based on the holo and ligand-bound structures. The simulations of ligand-induced transition revealed that the signal of intrasubunit closure dynamics is transmitted to form intersubunit contacts, which in turn invoke a precise alignment of active site, followed by the dimer-dimer rotation that compacts the whole tetrameric structure. Further analyses of SAHH dynamics associated with ligand binding provided evidence of both induced fit and population shift mechanisms and also showed that the transition-state ensemble is akin to the ligand-bound state. Besides the formation of enzyme-ligand contacts at the active site, the allosteric couplings from the residues distal to the active site are vital to the enzymatic function.

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

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

Dynamic allostery: linkers are not merely flexible

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

Analysis of the equilibrium and kinetics of the ankyrin repeat protein myotrophin

We apply the Wako-Saito-Muñoz-Eaton model to the study of myotrophin, a small ankyrin repeat protein, whose folding equilibrium and kinetics have been recently characterized experimentally. The model, which is a native-centric with binary variables, provides a finer microscopic detail than the Ising model that has been recently applied to some different repeat proteins, while being still amenable for an exact solution. In partial agreement with the experiments, our results reveal a weakly three-state equilibrium and a two-state-like kinetics of the wild-type protein despite the presence of a nontrivial free-energy profile. These features appear to be related to a careful "design" of the free-energy landscape, so that mutations can alter this picture, stabilizing some intermediates and changing the position of the rate-limiting step. Also, the experimental findings of two alternative pathways, an N-terminal and a C-terminal one, are qualitatively confirmed, even if the variations in the rates upon the experimental mutations cannot be quantitatively reproduced. Interestingly, the folding and unfolding pathways appear to be different, even if closely related: a property that is not generally considered in the phenomenological interpretation of the experimental data.

Nonadditivity in conformational entropy upon molecular rigidification reveals a universal mechanism affecting folding cooperativity

Previously, we employed a Maxwell counting distance constraint model (McDCM) to describe α-helix formation in polypeptides. Unlike classical helix-coil transition theories, the folding mechanism derives from nonadditivity in conformational entropy caused by rigidification of molecular structure as intramolecular cross-linking interactions form along the backbone. For example, when a hydrogen bond forms within a flexible region, both energy and conformational entropy decrease. However, no conformational entropy is lost when the region is already rigid because atomic motions are not constrained further. Unlike classical zipper models, the same mechanism also describes a coil-to-β-hairpin transition. Special topological features of the helix and hairpin structures allow the McDCM to be solved exactly. Taking full advantage of the fact that Maxwell constraint counting is a mean field approximation applied to the distribution of cross-linking interactions, we present an exact transfer matrix method that does not require any special topological feature. Upon application of the model to proteins, cooperativity within the folding transition is yet again appropriately described. Notwithstanding other contributing factors such as the hydrophobic effect, this simple model identifies a universal mechanism for cooperativity within polypeptide and protein-folding transitions, and it elucidates scaling laws describing hydrogen-bond patterns observed in secondary structure. In particular, the native state should have roughly twice as many constraints as there are degrees of freedom in the coil state to ensure high fidelity in two-state folding cooperativity, which is empirically observed.

Quantitative prediction of protein folding behaviors from a simple statistical model

The statistical nature of the protein folding process requires the use of equally detailed yet simple models that lend themselves to characterize experiments. One such model is the Wako-Saitô-Muñoz-Eaton model, that we extend here to include solvation effects (WSME-S), introduced via empirical terms. We employ the novel version to analyze the folding of two proteins, gpW and SH3, that have similar size and thermodynamic stability but with the former folding 3 orders of magnitude faster than SH3. A quantitative analysis reveals that gpW presents at most marginal barriers, in contrast to SH3 that folds following a simple two-state approximation. We reproduce the observed experimental differences in melting temperature in gpW as seen by different experimental spectroscopic probes and the shape of the rate-temperature plot. In parallel, we predict the folding complexity expected in gpW from the analysis of both the residue-level thermodynamics and kinetics. SH3 serves as a stringent control with neither folding complexity nor dispersion in melting temperatures being observed. The extended model presented here serves as an ideal tool not only to characterize folding data but also to make experimentally testable predictions.

Oligomerization of a retroviral matrix protein is facilitated by backbone flexibility on nanosecond time scale

The oligomerization capacity of the retroviral matrix protein is an important feature that affects assembly of immature virions and their interaction with cellular membrane. A combination of NMR relaxation measurements and advanced analysis of molecular dynamics simulation trajectory provided an unprecedentedly detailed insight into internal mobility of matrix proteins of the Mason-Pfizer monkey virus. Strong evidence have been obtained that the oligomerization capacity of the wild-type matrix protein is closely related to the enhanced dynamics of several parts of its backbone on a nanosecond time scale. Increased flexibility has been observed for two regions: the loop between α-helices α2 and α3 and the C-terminal half of α-helix α3 which accommodate amino acid residues that form the oligomerization interface. On the other hand, matrix mutant R55F that has changed structure and does not exhibit any specific oligomerization in solution was found considerably more rigid. Our results document that conformational selection mechanism together with induced fit and favorable structural preorganization play an important role in the control of the oligomerization process.

Ensemble-based methods for describing protein dynamics

Molecular dynamics (MD) simulation is a natural approach for studying protein dynamics, and coupled with the ideas of multiscale modeling, MD proves to be the gold standard in computational biology to investigate mechanistic details related to protein function. In principle, if MD trajectories are long enough, the ensemble of protein conformations generated allows thermodynamic and kinetic properties to be predicted. We know from experiments that proteins exhibit a high degree of fidelity in function, and that empirical kinetic models are successful in describing kinetics, suggesting that the ensemble of conformations cluster into well-defined thermodynamic states, which are frequently metastable. The experimental evidence suggest that more efficient computational models that retain only essential properties of the protein can be constructed to faithfully reproduce the relatively few observed thermodynamic states, and perhaps describe transition states if the model is sufficiently detailed. Indeed, there are many so-called ensemble-based methods that attempt to generate more complete ensembles than MD can provide by focusing on the most important driving forces through simplified representations of how elements within the protein interact. Although coarse-graining is employed in MD and other approaches, such as in elastic network models, the key distinguishing factor of ensemble-based methods is that they are meant to efficiently generate a large ensemble of conformations without solving explicit equations of motion. This review highlights three types of ensemble-based methods, illustrated by 'COREX' and the Wako-Saito-Munoz-Eaton (WSME) model, the Framework Rigidity Optimized Dynamic Algorithm (FRODA) and the distance constraint model (DCM).