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

Biomolecular dynamics: order-disorder transitions and energy landscapes

While the energy landscape theory of protein folding is now a widely accepted view for understanding how relatively weak molecular interactions lead to rapid and cooperative protein folding, such a framework must be extended to describe the large-scale functional motions observed in molecular machines. In this review, we discuss (1) the development of the energy landscape theory of biomolecular folding, (2) recent advances toward establishing a consistent understanding of folding and function and (3) emerging themes in the functional motions of enzymes, biomolecular motors and other biomolecular machines. Recent theoretical, computational and experimental lines of investigation have provided a very dynamic picture of biomolecular motion. In contrast to earlier ideas, where molecular machines were thought to function similarly to macroscopic machines, with rigid components that move along a few degrees of freedom in a deterministic fashion, biomolecular complexes are only marginally stable. Since the stabilizing contribution of each atomic interaction is on the order of the thermal fluctuations in solution, the rigid body description of molecular function must be revisited. An emerging theme is that functional motions encompass order-disorder transitions and structural flexibility provides significant contributions to the free energy. In this review, we describe the biological importance of order-disorder transitions and discuss the statistical-mechanical foundation of theoretical approaches that can characterize such transitions.

Why is F19Ap53 unable to bind MDM2? Simulations suggest crack propagation modulates binding

Why doesn't the F19A mutant of p53 bind to MDM2? Binding thermodynamics have suggested that the loss of packing interactions upon mutating Phe into Ala sidechain results in destabilizing the binding free energy between p53 and MDM2. Does this mutation also modulate the initial recognition between p53 and MDM2? We look at atomistic computer simulations of the process of the initial encounter between wild type p53 peptide and its F19A mutant with the N-terminal domain of MDM2. These simulations show that binding is characterized by a complex multistep process. It starts with the capture of F19 of wild type p53 by certain residues in the MDM2 binding pocket. This initial step anchors the peptide onto the surface of MDM2, and with the consequent reduction in the search space of the peptide, the peptide docks into the partially occluded surface of MDM2. This is similar to a crack forming in an otherwise occluded hydrophobic cavity in MDM2, and the peptide, docked through F19, modulates the propagation of this crack, which subsequently results in the stepwise docking of the rest of the peptide through insertions of W23 and L26. The lack of the bulky sidechain of F in the F19A mutant results in the absence of the initial "grasp" complex, and hence the mutant peptide diffuses randomly on the surface of MDM2 without binding. This is the first such demonstration of the possibility that a "kinetic" effect may partly underlie the destabilized thermodynamics of binding of F19A and is a feature that appears to be conserved in evolution. The observations by Wallace et al. (Mol Cell 2006; 23:251-63) that despite the inability of F19A to bind at the N-terminal domain of MDM2, it gets ubiquitinated, can now be partly understood based on a mechanism whereby the occupation of the binding pocket by ligands/peptides induces, via crack propagation and the dynamics of gatekeeper Y100, the ubiquitination signal for interactions between the acidic domain of MDM2 and the DNA binding domain of p53.

Minimum free energy path of ligand-induced transition in adenylate kinase

Large-scale conformational changes in proteins involve barrier-crossing transitions on the complex free energy surfaces of high-dimensional space. Such rare events cannot be efficiently captured by conventional molecular dynamics simulations. Here we show that, by combining the on-the-fly string method and the multi-state Bennett acceptance ratio (MBAR) method, the free energy profile of a conformational transition pathway in Escherichia coli adenylate kinase can be characterized in a high-dimensional space. The minimum free energy paths of the conformational transitions in adenylate kinase were explored by the on-the-fly string method in 20-dimensional space spanned by the 20 largest-amplitude principal modes, and the free energy and various kinds of average physical quantities along the pathways were successfully evaluated by the MBAR method. The influence of ligand binding on the pathways was characterized in terms of rigid-body motions of the lid-shaped ATP-binding domain (LID) and the AMP-binding (AMPbd) domains. It was found that the LID domain was able to partially close without the ligand, while the closure of the AMPbd domain required the ligand binding. The transition state ensemble of the ligand bound form was identified as those structures characterized by highly specific binding of the ligand to the AMPbd domain, and was validated by unrestrained MD simulations. It was also found that complete closure of the LID domain required the dehydration of solvents around the P-loop. These findings suggest that the interplay of the two different types of domain motion is an essential feature in the conformational transition of the enzyme.

Structural basis of histidine kinase autophosphorylation deduced by integrating genomics, molecular dynamics, and mutagenesis

Signal transduction proteins such as bacterial sensor histidine kinases, designed to transition between multiple conformations, are often ruled by unstable transient interactions making structural characterization of all functional states difficult. This study explored the inactive and signal-activated conformational states of the two catalytic domains of sensor histidine kinases, HisKA and HATPase. Direct coupling analyses, a global statistical inference approach, was applied to >13,000 such domains from protein databases to identify residue contacts between the two domains. These contacts guided structural assembly of the domains using MAGMA, an advanced molecular dynamics docking method. The active conformation structure generated by MAGMA simultaneously accommodated the sequence derived residue contacts and the ATP-catalytic histidine contact. The validity of this structure was confirmed biologically by mutation of contact positions in the Bacillus subtilis sensor histidine kinase KinA and by restoration of activity in an inactive KinA(HisKA):KinD(HATPase) hybrid protein. These data indicate that signals binding to sensor domains activate sensor histidine kinases by causing localized strain and unwinding at the end of the C-terminal helix of the HisKA domain. This destabilizes the contact positions of the inactive conformation of the two domains, identified by previous crystal structure analyses and by the sequence analysis described here, inducing the formation of the active conformation. This study reveals that structures of unstable transient complexes of interacting proteins and of protein domains are accessible by applying this combination of cross-validating technologies.

The shadow map: a general contact definition for capturing the dynamics of biomolecular folding and function

Structure-based models (SBMs) are simplified models of the biomolecular dynamics that arise from funneled energy landscapes. We recently introduced an all-atom SBM that explicitly represents the atomic geometry of a biomolecule. While this initial study showed the robustness of the all-atom SBM Hamiltonian to changes in many of the energetic parameters, an important aspect, which has not been explored previously, is the definition of native interactions. In this study, we propose a general definition for generating atomically grained contact maps called "Shadow". The Shadow algorithm initially considers all atoms within a cutoff distance and then, controlled by a screening parameter, discards the occluded contacts. We show that this choice of contact map is not only well behaved for protein folding, since it produces consistently cooperative folding behavior in SBMs but also desirable for exploring the dynamics of macromolecular assemblies since, it distributes energy similarly between RNAs and proteins despite their disparate internal packing. All-atom structure-based models employing Shadow contact maps provide a general framework for exploring the geometrical features of biomolecules, especially the connections between folding and function.

A structural perspective on the dynamics of kinesin motors

Despite significant fluctuation under thermal noise, biological machines in cells perform their tasks with exquisite precision. Using molecular simulation of a coarse-grained model and theoretical arguments, we envisaged how kinesin, a prototype of biological machines, generates force and regulates its dynamics to sustain persistent motor action. A structure-based model, which can be versatile in adapting its structure to external stresses while maintaining its native fold, was employed to account for several features of kinesin dynamics along the biochemical cycle. This analysis complements our current understandings of kinesin dynamics and connections to experiments. We propose a thermodynamic cycle for kinesin that emphasizes the mechanical and regulatory role of the neck linker and clarify issues related to the motor directionality, and the difference between the external stalling force and the internal tension responsible for the head-head coordination. The comparison between the thermodynamic cycle of kinesin and macroscopic heat engines highlights the importance of structural change as the source of work production in biomolecular machines.

Towards the prediction of order parameters from molecular dynamics simulations in proteins

A molecular understanding of how protein function is related to protein structure requires an ability to understand large conformational changes between multiple states. Unfortunately these states are often separated by high free energy barriers and within a complex energy landscape. This makes it very difficult to reliably connect, for example by all-atom molecular dynamics calculations, the states, their energies, and the pathways between them. A major issue needed to improve sampling on the intermediate states is an order parameter--a reduced descriptor for the major subset of degrees of freedom--that can be used to aid sampling for the large conformational change. We present a method to combine information from molecular dynamics using non-linear time series and dimensionality reduction, in order to quantitatively determine an order parameter connecting two large-scale conformationally distinct protein states. This new method suggests an implementation for molecular dynamics calculations that may be used to enhance sampling of intermediate states.

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.

Density-cluster NMA: A new protein decomposition technique for coarse-grained normal mode analysis

Normal mode analysis has emerged as a useful technique for investigating protein motions on long time scales. This is largely due to the advent of coarse-graining techniques, particularly Hooke's Law-based potentials and the rotational-translational blocking (RTB) method for reducing the size of the force-constant matrix, the Hessian. Here we present a new method for domain decomposition for use in RTB that is based on hierarchical clustering of atomic density gradients, which we call Density-Cluster RTB (DCRTB). The method reduces the number of degrees of freedom by 85-90% compared with the standard blocking approaches. We compared the normal modes from DCRTB against standard RTB using 1-4 residues in sequence in a single block, with good agreement between the two methods. We also show that Density-Cluster RTB and standard RTB perform well in capturing the experimentally determined direction of conformational change. Significantly, we report superior correlation of DCRTB with B-factors compared with 1-4 residue per block RTB. Finally, we show significant reduction in computational cost for Density-Cluster RTB that is nearly 100-fold for many examples.

Structure-based model of allostery predicts coupling between distant sites

Allostery is a phenomenon that couples effector ligand binding at an allosteric site to a structural and/or dynamic change at a distant regulated site. To study an allosteric transition, we vary the size of the allosteric site and its interactions to construct a series of energy landscapes with pronounced minima corresponding to both the effector bound and unbound crystal structures. We use molecular dynamics to sample these landscapes. The degree of perturbation by the effector, modeled by the size of the allosteric site, provides an order parameter for allostery that allows us to determine how microscopic motions give rise to commonly discussed macroscopic mechanisms: (i) induced fit, (ii) population shift, and (iii) entropy driven. These mechanisms involve decreasing structural differences between the effector bound and unbound populations. A metric (ligand-induced cooperativity) can measure how cooperatively a given regulated site responds to effector binding and therefore what kind of allosteric mechanism is involved. We apply the model to three proteins with experimentally characterized transitions: (i) calmodulin-GFP Ca(2+) sensor protein, (ii) maltose binding protein, and (iii) CSL transcription factor. Remarkably, the model is able to reproduce allosteric motion and predict coupling in a manner consistent with experiment.

Coarse-grained molecular simulations of large biomolecules

Recently, we saw a dramatic increase in the number of researches that rely on coarse-grained (CG) simulations for large biomolecules. Here, first, we briefly describe recently developed and used CG models for proteins and nucleic acids. Balance between structure-based and physico-chemical terms is a key issue. We also discuss the multiscale algorithms used to derive CG parameters. Next, we comment on the dynamics used in CG simulations with an emphasis on the importance of hydrodynamic interactions. We then discuss the pros and cons of CG simulations. Finally, we overview recent exciting applications of CG simulations. Publicly available tools and software for CG simulations are also summarized.

Rapid simulation of protein motion: merging flexibility, rigidity and normal mode analyses

Protein function frequently involves conformational changes with large amplitude on timescales which are difficult and computationally expensive to access using molecular dynamics. In this paper, we report on the combination of three computationally inexpensive simulation methods--normal mode analysis using the elastic network model, rigidity analysis using the pebble game algorithm, and geometric simulation of protein motion--to explore conformational change along normal mode eigenvectors. Using a combination of ElNemo and First/Froda software, large-amplitude motions in proteins with hundreds or thousands of residues can be rapidly explored within minutes using desktop computing resources. We apply the method to a representative set of six proteins covering a range of sizes and structural characteristics and show that the method identifies specific types of motion in each case and determines their amplitude limits.

Myosin-V as a mechanical sensor: an elastic network study

According to recent experiments, the molecular-motor myosin behaves like a strain sensor, exhibiting different functional responses when loads in opposite directions are applied to its tail. Within an elastic-network model, we explore the sensitivity of the protein to the forces acting on the tail and find, in agreement with experiments, that such forces invoke conformational changes that should affect filament binding and ADP release. Furthermore, conformational responses of myosin to the application of forces to individual residues in its principal functional regions are systematically investigated and a detailed sensitivity map of myosin-V is thus obtained. The results suggest that the strain-sensor behavior is involved in the intrinsic operation of this molecular motor.

Allostery and binding cooperativity of the catalytic subunit of protein kinase A by NMR spectroscopy and molecular dynamics simulations

The catalytic subunit of cAMP-dependent protein kinase A (PKA-C) is an exquisite example of a single molecule allosteric enzyme, where classical and modern views of allosteric signaling merge. In this chapter, we describe the mapping of PKA-C conformational dynamics and allosteric signaling in the free and bound states using a combination of NMR spectroscopy and molecular dynamics simulations. We show that ligand binding affects the enzyme's conformational dynamics, shaping the free-energy landscape toward the next stage of the catalytic cycle. While nucleotide and substrate binding enhance the enzyme's conformational entropy and define dynamically committed states, inhibitor binding attenuates the internal dynamics in favor of enthalpic interactions and delineates dynamically quenched states. These studies support a central role of conformational dynamics in many aspects of enzymatic turnover and suggest future avenues for controlling enzymatic function.

Using a combination of computational and experimental techniques to understand the molecular basis for protein allostery

Allostery is the process by which remote sites of a system are energetically coupled to elicit a functional response. The early models of allostery such as the Monod-Wyman-Changeux model and the Koshland-Némethy-Filmer model explain the allosteric behavior of multimeric proteins. However, these models do not explain how allostery arises from atomic level in detail. Recent developments in computational methods and experimental techniques have led the beginning of a new age in studying allostery. The combination of computational methods and experiments is a powerful research approach to help answering questions regarding allosteric mechanism at atomic resolution. In this review, three case studies are discussed to illustrate how this combined approach helps to increase our understanding of protein allostery.

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.

Trimming down a protein structure to its bare foldons: spatial organization of the cooperative unit

Folding of the ribosomal protein S6 is a malleable process controlled by two competing, and partly overlapping, folding nuclei. Together, these nuclei extend over most of the S6 structure, except the edge strand β2, which is consistently missing in the folding transition states; despite being part of the S6 four-stranded sheet, β2 seems not to be part of the cooperative unit of the protein. The question is then whether β2 can be removed from the S6 structure without compromising folding cooperativity or native state integrity. To investigate this, we constructed a truncated variant of S6 lacking β2, reducing the size of the protein from 96 to 76 residues (S6(Δβ2)). The new S6 variant expresses well in Escherichia coli and has a well dispersed heteronuclear single quantum correlation spectrum and a perfectly wild-type-like crystal structure, but with a smaller three-stranded β-sheet. Moreover, S6(Δβ2) displays an archetypical v-shaped chevron plot with decreased slope of the unfolding limb, as expected from a protein with maintained folding cooperativity and reduced size. The results support the notion that foldons, as defined by the structural distribution of the folding nuclei, represent a property-based level of hierarchy in the build-up of larger protein structures and suggest that the role of β2 in S6 is mainly in intermolecular binding, consistent with the position of this strand in the ribosomal assembly.

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.

Excited states of ribosome translocation revealed through integrative molecular modeling

The dynamic nature of biomolecules leads to significant challenges when characterizing the structural properties associated with function. While X-ray crystallography and imaging techniques (such as cryo-electron microscopy) can reveal the structural details of stable molecular complexes, strategies must be developed to characterize configurations that exhibit only marginal stability (such as intermediates) or configurations that do not correspond to minima on the energy landscape (such as transition-state ensembles). Here, we present a methodology (MDfit) that utilizes molecular dynamics simulations to generate configurations of excited states that are consistent with available biophysical and biochemical measurements. To demonstrate the approach, we present a sequence of configurations that are suggested to be associated with transfer RNA (tRNA) movement through the ribosome (translocation). The models were constructed by combining information from X-ray crystallography, cryo-electron microscopy, and biochemical data. These models provide a structural framework for translocation that may be further investigated experimentally and theoretically to determine the precise energetic character of each configuration and the transition dynamics between them.

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

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

Single-molecule fluorescence spectroscopy maps the folding landscape of a large protein

Proteins attain their function only after folding into a highly organized three-dimensional structure. Much remains to be learned about the mechanisms of folding of large multidomain proteins, which may populate metastable intermediate states on their energy landscapes. Here we introduce a novel method, based on high-throughput single-molecule fluorescence experiments, which is specifically geared towards tracing the dynamics of folding in the presence of a plethora of intermediates. We employ this method to characterize the folding reaction of a three-domain protein, adenylate kinase. Using thousands of single-molecule trajectories and hidden Markov modelling, we identify six metastable states on adenylate kinase's folding landscape. Remarkably, the connectivity of the intermediates depends on denaturant concentration; at low concentration, multiple intersecting folding pathways co-exist. We anticipate that the methodology introduced here will find broad applicability in the study of folding of large proteins, and will provide a more realistic scenario of their conformational dynamics.

The energy landscape analysis of cancer mutations in protein kinases

The growing interest in quantifying the molecular basis of protein kinase activation and allosteric regulation by cancer mutations has fueled computational studies of allosteric signaling in protein kinases. In the present study, we combined computer simulations and the energy landscape analysis of protein kinases to characterize the interplay between oncogenic mutations and locally frustrated sites as important catalysts of allostetric kinase activation. While structurally rigid kinase core constitutes a minimally frustrated hub of the catalytic domain, locally frustrated residue clusters, whose interaction networks are not energetically optimized, are prone to dynamic modulation and could enable allosteric conformational transitions. The results of this study have shown that the energy landscape effect of oncogenic mutations may be allosteric eliciting global changes in the spatial distribution of highly frustrated residues. We have found that mutation-induced allosteric signaling may involve a dynamic coupling between structurally rigid (minimally frustrated) and plastic (locally frustrated) clusters of residues. The presented study has demonstrated that activation cancer mutations may affect the thermodynamic equilibrium between kinase states by allosterically altering the distribution of locally frustrated sites and increasing the local frustration in the inactive form, while eliminating locally frustrated sites and restoring structural rigidity of the active form. The energy landsape analysis of protein kinases and the proposed role of locally frustrated sites in activation mechanisms may have useful implications for bioinformatics-based screening and detection of functional sites critical for allosteric regulation in complex biomolecular systems.

Pre-existing soft modes of motion uniquely defined by native contact topology facilitate ligand binding to proteins

Modeling protein flexibility constitutes a major challenge in accurate prediction of protein-ligand and protein-protein interactions in docking simulations. The lack of a reliable method for predicting the conformational changes relevant to substrate binding prevents the productive application of computational docking to proteins that undergo large structural rearrangements. Here, we examine how coarse-grained normal mode analysis has been advantageously applied to modeling protein flexibility associated with ligand binding. First, we highlight recent studies that have shown that there is a close agreement between the large-scale collective motions of proteins predicted by elastic network models and the structural changes experimentally observed upon ligand binding. Then, we discuss studies that have exploited the predicted soft modes in docking simulations. Two general strategies are noted: pregeneration of conformational ensembles that are then utilized as input for standard fixed-backbone docking and protein structure deformation along normal modes concurrent to docking. These studies show that the structural changes apparently "induced" upon ligand binding occur selectively along the soft modes accessible to the protein prior to ligand binding. They further suggest that proteins offer suitable means of accommodating/facilitating the recognition and binding of their ligand, presumably acquired by evolutionary selection of the suitable three-dimensional structure.

Enzyme closure and nucleotide binding structurally lock guanylate kinase

We investigate the conformational dynamics and mechanical properties of guanylate kinase (GK) using a multiscale approach combining high-resolution atomistic molecular dynamics and low-resolution Brownian dynamics simulations. The GK enzyme is subject to large conformational changes, leading from an open to a closed form, which are further influenced by the presence of nucleotides. As suggested by recent work on simple coarse-grained models of apo-GK, we primarily focus on GK's closure mechanism with the aim to establish a detailed picture of the hierarchy and chronology of structural events essential for the enzymatic reaction. We have investigated open-versus-closed, apo-versus-holo, and substrate-versus-product-loaded forms of the GK enzyme. Bound ligands significantly modulate the mechanical and dynamical properties of GK and rigidity profiles of open and closed states hint at functionally important differences. Our data emphasizes the role of magnesium, highlights a water channel permitting active site hydration, and reveals a structural lock that stabilizes the closed form of the enzyme.

Binding leverage as a molecular basis for allosteric regulation

Allosteric regulation involves conformational transitions or fluctuations between a few closely related states, caused by the binding of effector molecules. We introduce a quantity called binding leverage that measures the ability of a binding site to couple to the intrinsic motions of a protein. We use Monte Carlo simulations to generate potential binding sites and either normal modes or pairs of crystal structures to describe relevant motions. We analyze single catalytic domains and multimeric allosteric enzymes with complex regulation. For the majority of the analyzed proteins, we find that both catalytic and allosteric sites have high binding leverage. Furthermore, our analysis of the catabolite activator protein, which is allosteric without conformational change, shows that its regulation involves other types of motion than those modulated at sites with high binding leverage. Our results point to the importance of incorporating dynamic information when predicting functional sites. Because it is possible to calculate binding leverage from a single crystal structure it can be used for characterizing proteins of unknown function and predicting latent allosteric sites in any protein, with implications for drug design.

Allosteric protein regulation is the mechanism by which binding of a molecule to one site in a protein affects the activity at another site. Although the two classical phenomenological models, Monod-Wyman-Changeux (MWC) and Koshland-Némethy-Filmer (KNF), span from the case of hemoglobin to membrane receptors, they do not describe the intramolecular interactions involved. The coupling between two allosterically connected sites commonly takes place through coherent collective motion involving the whole protein. We therefore introduce a quantity called binding leverage to measure the strength of the coupling between particular binding sites and such motions. We show that high binding leverage is a characteristic of both allosteric sites and catalytic sites, emphasizing that both enzymatic function and allosteric regulation require a coupling between ligand binding and protein dynamics. We also consider the first known case of purely entropic allostery, where ligand binding only affects the amplitudes of fluctuations. We find that the binding site in this protein does not primarily connect to collective motions – instead the modulation of fluctuations is controlled from a deeply buried and highly connected site. Finally, sites with high binding leverage but no known biological function could be latent allosteric sites, and thus drug targets.

iMod: multipurpose normal mode analysis in internal coordinates

MOTIVATION

Dynamic simulations of systems with biologically relevant sizes and time scales are critical for understanding macromolecular functioning. Coarse-grained representations combined with normal mode analysis (NMA) have been established as an alternative to atomistic simulations. The versatility and efficiency of current approaches normally based on Cartesian coordinates can be greatly enhanced with internal coordinates (IC).

RESULTS

Here, we present a new versatile tool chest to explore conformational flexibility of both protein and nucleic acid structures using NMA in IC. Consideration of dihedral angles as variables reduces the computational cost and non-physical distortions of classical Cartesian NMA methods. Our proposed framework operates at different coarse-grained levels and offers an efficient framework to conduct NMA-based conformational studies, including standard vibrational analysis, Monte-Carlo simulations or pathway exploration. Examples of these approaches are shown to demonstrate its applicability, robustness and efficiency.

CONTACT

pablo@chaconlab.org

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

How does a registry change in dynein's coiled-coil stalk drive binding of dynein to microtubules?

Dynein is a motor protein that transports cellular cargo along the microtubule (MT) by consuming ATP. Dynein's microtubule-binding domain (MTBD) is separated from the ATP-binding core by a ~15 nm stalk that consists of two α-helices forming an antiparallel coiled coil. It was previously suggested that the coiled-coil stalk creates a registry shift to modulate its binding affinity for MT. A crystal structure of the low-affinity form of MTBD was determined, but that of the high-affinity form with the registry shift is not yet available. In this study, we obtained an all-atom model structure for the high-affinity form of MTBD bound to MT by an anisotropic network model, protein-protein docking, and molecular dynamics simulations. We observe that the magnitude of the coiled-coil helix sliding is dramatically reduced near the two prolines that form the stalk-MTBD boundary and subsequently transformed to cyclic movements of MTBD helices, leading to formation of a new salt bridge with MT at the binding interface. The proposed mechanism explains the roles of highly conserved residues such as the two prolines at the stalk-MTBD boundary, the nonpolar tryptophan and proline residues near the binding interface, and the electropositive residues forming salt bridges with MT.

Conformational switching explains the intrinsic multifunctionality of plant light-harvesting complexes

The light-harvesting complexes of photosystem I and II (Lhcas and Lhcbs) of plants display a high structural homology and similar pigment content and organization. Yet, the spectroscopic properties of these complexes, and accordingly their functionality, differ substantially. This difference is primarily due to the charge-transfer (CT) character of a chlorophyll dimer in all Lhcas, which mixes with the excitonic states of these complexes, whereas this CT character is generally absent in Lhcbs. By means of single-molecule spectroscopy near room temperature, we demonstrate that the presence or absence of such a CT state in Lhcas and Lhcbs can occasionally be reversed; i.e., these complexes are able to interconvert conformationally to quasi-stable spectral states that resemble the Lhcs of the other photosystem. The high structural similarity of all the Lhca and Lhcb proteins suggests that the stable conformational states that give rise to the mixed CT-excitonic state are similar for all these proteins, and similarly for the conformations that involve no CT state. This indicates that the specific functions related to Lhca and Lhcb complexes are realized by different stable conformations of a single generic protein structure. We propose that this functionality is modulated and controlled by the protein environment.

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.

Interconversion of functional motions between mesophilic and thermophilic adenylate kinases

Dynamic properties are functionally important in many proteins, including the enzyme adenylate kinase (AK), for which the open/closed transition limits the rate of catalytic turnover. Here, we compare our previously published coarse-grained (double-well Gō) simulation of mesophilic AK from E. coli (AKmeso) to simulations of thermophilic AK from Aquifex aeolicus (AKthermo). In AKthermo, as with AKmeso, the LID domain prefers to close before the NMP domain in the presence of ligand, but LID rigid-body flexibility in the open (O) ensemble decreases significantly. Backbone foldedness in O and/or transition state (TS) ensembles increases significantly relative to AKmeso in some interdomain backbone hinges and within LID. In contact space, the TS of AKthermo has fewer contacts at the CORE-LID interface but a stronger contact network surrounding the CORE-NMP interface than the TS of AKmeso. A “heated” simulation of AKthermo at 375K slightly increases LID rigid-body flexibility in accordance with the “corresponding states” hypothesis. Furthermore, while computational mutation of 7 prolines in AKthermo to their AKmeso counterparts produces similar small perturbations, mutation of these sites, especially positions 8 and 155, to glycine is required to achieve LID rigid-body flexibility and hinge flexibilities comparable to AKmeso. Mutating the 7 sites to proline in AKmeso reduces some hinges' flexibilities, especially hinge 2, but does not reduce LID rigid-body flexibility, suggesting that these two types of motion are decoupled in AKmeso. In conclusion, our results suggest that hinge flexibility and global functional motions alike are correlated with but not exclusively determined by the hinge residues. This mutational framework can inform the rational design of functionally important flexibility and allostery in other proteins toward engineering novel biochemical pathways.

Dynamic properties are functionally important in many proteins, including the enzyme adenylate kinase (AK), which undergoes chemically rate-limiting domain motions coupled to substrate binding. Since mesophiles and thermophiles often differ in functionally important motions, we compare coarse-grained simulations of AKmeso and AKthermo as well as several proline and glycine mutational variants designed to interconvert the dynamics. As might be expected, both domain motions and local unfolding motions are reduced in AKthermo relative to AKmeso. In AKthermo, both of these types of motions can be partially shifted toward more flexible AKmeso by heating or by mutating hinge prolines. However, only mutation to highly flexible glycine produces motions like those of AKmeso. Thus, the rate-limiting global transition likely depends on a combination of hinge flexibility and stability within the LID and NMP domains. Finally, this mutagenic framework can inform the rational design of flexibility and allostery in other proteins toward engineering novel biological control systems.

A normal mode-based geometric simulation approach for exploring biologically relevant conformational transitions in proteins

A three-step approach for multiscale modeling of protein conformational changes is presented that incorporates information about preferred directions of protein motions into a geometric simulation algorithm. The first two steps are based on a rigid cluster normal-mode analysis (RCNMA). Low-frequency normal modes are used in the third step (NMSim) to extend the recently introduced idea of constrained geometric simulations of diffusive motions in proteins by biasing backbone motions of the protein, whereas side-chain motions are biased toward favorable rotamer states. The generated structures are iteratively corrected regarding steric clashes and stereochemical constraint violations. The approach allows performing three simulation types: unbiased exploration of conformational space; pathway generation by a targeted simulation; and radius of gyration-guided simulation. When applied to a data set of proteins with experimentally observed conformational changes, conformational variabilities are reproduced very well for 4 out of 5 proteins that show domain motions, with correlation coefficients r > 0.70 and as high as r = 0.92 in the case of adenylate kinase. In 7 out of 8 cases, NMSim simulations starting from unbound structures are able to sample conformations that are similar (root-mean-square deviation = 1.0-3.1 Å) to ligand bound conformations. An NMSim generated pathway of conformational change of adenylate kinase correctly describes the sequence of domain closing. The NMSim approach is a computationally efficient alternative to molecular dynamics simulations for conformational sampling of proteins. The generated conformations and pathways of conformational transitions can serve as input to docking approaches or as starting points for more sophisticated sampling techniques.

Structural and kinetic mapping of side-chain exposure onto the protein energy landscape

Identification and characterization of structural fluctuations that occur under native conditions is crucial for understanding protein folding and function, but such fluctuations are often rare and transient, making them difficult to study. Native-state hydrogen exchange (NSHX) has been a powerful tool for identifying such rarely populated conformations, but it generally reveals no information about the placement of these species along the folding reaction coordinate or the barriers separating them from the folded state and provides little insight into side-chain packing. To complement such studies, we have performed native-state alkyl-proton exchange, a method analogous to NSHX that monitors cysteine modification rather than backbone amide exchange, to examine the folding landscape of Escherichia coli ribonuclease H, a protein well characterized by hydrogen exchange. We have chosen experimental conditions such that the rate-limiting barrier acts as a kinetic partition: residues that become exposed only upon crossing the unfolding barrier are modified in the EX1 regime (alkylation rates report on the rate of unfolding), while those exposed on the native side of the barrier are modified predominantly in the EX2 regime (alkylation rates report on equilibrium populations). This kinetic partitioning allows for identification and placement of partially unfolded forms along the reaction coordinate. Using this approach we detect previously unidentified, rarely populated conformations residing on the native side of the barrier and identify side chains that are modified only upon crossing the unfolding barrier. Thus, in a single experiment under native conditions, both sides of the rate-limiting barrier are investigated.

Measurement of protein unfolding/refolding kinetics and structural characterization of hidden intermediates by NMR relaxation dispersion

Detailed understanding of protein function and malfunction hinges on the ability to characterize transiently populated states and the transitions between them. Here, we use (15)N, , and (13)CO NMR R(2) relaxation dispersion to investigate spontaneous unfolding and refolding events of native apomyoglobin. Above pH 5.0, dispersion is dominated by processes involving fluctuations of the F-helix region, which is invisible in NMR spectra. Measurements of R(2) dispersion for residues contacted by the F-helix region in the native (N) structure reveal a transient state formed by local unfolding of helix F and undocking from the protein core. A similar state was detected at pH 4.75-4.95 and determined to be an on-pathway intermediate (I1) in a linear three-state unfolding scheme (N&lrarr2;I1&lrarr2;MG) leading to a transiently populated molten globule (MG) state. The slowest steps in unfolding and refolding are N → I1 (36 s(-1)) and MG → I1 (26 s(-1)), respectively. Differences in chemical shift between N and I1 are very small, except in regions adjacent to helix F, showing that their core structures are similar. Chemical shift changes between the N and MG states, obtained from R(2) dispersion, reveal that the transient MG state is structurally similar to the equilibrium MG observed previously at high temperature and low pH. Analysis of MG state chemical shifts shows the location of residual helical structure in the transient intermediate and identifies regions that unfold or rearrange into nonnative structure during the N → MG transition. The experiments also identify regions of energetic frustration that "crack" during unfolding and impede the refolding process.

Dynamic coupling between the LID and NMP domain motions in the catalytic conversion of ATP and AMP to ADP by adenylate kinase

The catalytic conversion of adenosine triphosphate (ATP) and adenosine monophosphate (AMP) to adenosine diphosphate (ADP) by adenylate kinase (ADK) involves large amplitude, ligand induced domain motions, involving the opening and the closing of ATP binding domain (LID) and AMP binding domain (NMP) domains, during the repeated catalytic cycle. We discover and analyze an interesting dynamical coupling between the motion of the two domains during the opening, using large scale atomistic molecular dynamics trajectory analysis, covariance analysis, and multidimensional free energy calculations with explicit water. Initially, the LID domain must open by a certain amount before the NMP domain can begin to open. Dynamical correlation map shows interesting cross-peak between LID and NMP domain which suggests the presence of correlated motion between them. This is also reflected in our calculated two-dimensional free energy surface contour diagram which has an interesting elliptic shape, revealing a strong correlation between the opening of the LID domain and that of the NMP domain. Our free energy surface of the LID domain motion is rugged due to interaction with water and the signature of ruggedness is evident in the observed root mean square deviation variation and its fluctuation time correlation functions. We develop a correlated dynamical disorder-type theoretical model to explain the observed dynamic coupling between the motion of the two domains in ADK. Our model correctly reproduces several features of the cross-correlation observed in simulations.

Dynamically committed, uncommitted, and quenched states encoded in protein kinase A revealed by NMR spectroscopy

Protein kinase A (PKA) is a ubiquitous phosphoryl transferase that mediates hundreds of cell signaling events. During turnover, its catalytic subunit (PKA-C) interconverts between three major conformational states (open, intermediate, and closed) that are dynamically and allosterically activated by nucleotide binding. We show that the structural transitions between these conformational states are minimal and allosteric dynamics encode the motions from one state to the next. NMR and molecular dynamics simulations define the energy landscape of PKA-C, with the substrate allowing the enzyme to adopt a broad distribution of conformations (dynamically committed state) and the inhibitors (high magnesium and pseudosubstrate) locking it into discrete minima (dynamically quenched state), thereby reducing the motions that allow turnover. These results unveil the role of internal dynamics in both kinase function and regulation.

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

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

On the roles of substrate binding and hinge unfolding in conformational changes of adenylate kinase

We characterized the conformational change of adenylate kinase (AK) between open and closed forms by conducting five all-atom molecular-dynamics simulations, each of 100 ns duration. Different initial structures and substrate binding configurations were used to probe the pathways of AK conformational change in explicit solvent, and no bias potential was applied. A complete closed-to-open and a partial open-to-closed transition were observed, demonstrating the direct impact of substrate-mediated interactions on shifting protein conformation. The sampled configurations suggest two possible pathways for connecting the open and closed structures of AK, affirming the prediction made based on available x-ray structures and earlier works of coarse-grained modeling. The trajectories of the all-atom molecular-dynamics simulations revealed the complexity of protein dynamics and the coupling between different domains during conformational change. Calculations of solvent density and density fluctuations surrounding AK did not show prominent variation during the transition between closed and open forms. Finally, we characterized the effects of local unfolding of an important hinge near Pro(177) on the closed-to-open transition of AK and identified a novel mechanism by which hinge unfolding modulates protein conformational change. The local unfolding of Pro(177) hinge induces alternative tertiary contacts that stabilize the closed structure and prevent the opening transition.

Identification of functional motions in the adenylate kinase (ADK) protein family by computational hybrid approaches

Based on integrative computational hybrid approaches that combined statistical coupling analysis (SCA), molecular dynamics (MD), and normal mode analysis (NMA), evolutionarily coupled residues involved in functionally relevant motion in the adenylate kinase protein family were identified. The hybrids identified four top-ranking site pairs that belong to a conserved hydrogen bond network that is involved in the enzyme's flexibility. A second group of top-ranking site pairs was identified in critical regions for functional dynamics, such as those related to enzymatic turnover. The high consistency of the results obtained by SCA with NMA (SCA.NMA) and by SCA.MD hybrid analyses suggests that suitable replacement of the matrix of cross-correlation analysis of atomic fluctuations (derived by using NMA) with those based on MD contributes to the identification of such sites by means of a fast computational calculation. The analysis presented here strongly supports the hypothesis that evolutionary forces, such as coevolution at the sequence level, have promoted functional dynamic properties of the adenylate kinase protein family. Finally, these hybrid approaches can be used to identify, at the residue level, protein motion coordination patterns not previously observed, such as in hinge regions.

Sequence composition and environment effects on residue fluctuations in protein structures

Structure fluctuations in proteins affect a broad range of cell phenomena, including stability of proteins and their fragments, allosteric transitions, and energy transfer. This study presents a statistical-thermodynamic analysis of relationship between the sequence composition and the distribution of residue fluctuations in protein-protein complexes. A one-node-per-residue elastic network model accounting for the nonhomogeneous protein mass distribution and the interatomic interactions through the renormalized inter-residue potential is developed. Two factors, a protein mass distribution and a residue environment, were found to determine the scale of residue fluctuations. Surface residues undergo larger fluctuations than core residues in agreement with experimental observations. Ranking residues over the normalized scale of fluctuations yields a distinct classification of amino acids into three groups: (i) highly fluctuating-Gly, Ala, Ser, Pro, and Asp, (ii) moderately fluctuating-Thr, Asn, Gln, Lys, Glu, Arg, Val, and Cys, and (iii) weakly fluctuating-Ile, Leu, Met, Phe, Tyr, Trp, and His. The structural instability in proteins possibly relates to the high content of the highly fluctuating residues and a deficiency of the weakly fluctuating residues in irregular secondary structure elements (loops), chameleon sequences, and disordered proteins. Strong correlation between residue fluctuations and the sequence composition of protein loops supports this hypothesis. Comparing fluctuations of binding site residues (interface residues) with other surface residues shows that, on average, the interface is more rigid than the rest of the protein surface and Gly, Ala, Ser, Cys, Leu, and Trp have a propensity to form more stable docking patches on the interface. The findings have broad implications for understanding mechanisms of protein association and stability of protein structures.

Large-scale comparison of protein essential dynamics from molecular dynamics simulations and coarse-grained normal mode analyses

A large-scale comparison of essential dynamics (ED) modes from molecular dynamic simulations and normal modes from coarse-grained normal mode methods (CGNM) was performed on a dataset of 335 proteins. As CGNM methods, the elastic network model (ENM) and the rigid cluster normal mode analysis (RCNMA) were used. Low-frequency normal modes from ENM correlate very well with ED modes in terms of directions of motions and relative amplitudes of motions. Notably, a similar performance was found if normal modes from RCNMA were used, despite a higher level of coarse graining. On average, the space spanned by the first quarter of ENM modes describes 84% of the space spanned by the five ED modes. Furthermore, no prominent differences for ED and CGNM modes among different protein structure classes (CATH classification) were found. This demonstrates the general potential of CGNM approaches for describing intrinsic motions of proteins with little computational cost. For selected cases, CGNM modes were found to be more robust among proteins that have the same topology or are of the same homologous superfamily than ED modes. In view of recent evidence regarding evolutionary conservation of vibrational dynamics, this suggests that ED modes, in some cases, might not be representative of the underlying dynamics that are characteristic of a whole family, probably due to insufficient sampling of some of the family members by MD.

Frustration, specific sequence dependence, and nonlinearity in large-amplitude fluctuations of allosteric proteins

Proteins have often evolved sequences so as to acquire the ability for regulation via allosteric conformational change. Here we investigate how allosteric dynamics is designed through sequences with nonlinear interaction features. First, for 71 allosteric proteins of which two, open and closed, structures are available, a statistical survey of interactions using an all-atom model with effective solvation shows that those residue contact interactions specific to one of the two states are significantly weaker than are the contact interactions shared by the two states. This interaction feature indicates there is underlying sequence design to facilitate conformational change. Second, based on the energy landscape theory, we implement these interaction features into a new atomic-interaction-based coarse-grained model via a multiscale simulation protocol (AICG). The AICG model outperforms standard coarse-grained models for predictions of the native-state mean fluctuations and of the conformational change direction. Third, using the new model for adenylate kinase, we show that intrinsic fluctuations in one state contain rare and large-amplitude motions nearly reaching the other state. Such large-amplitude motions are realized partly by sequence specificity and partly by the nonlinear nature of contact interactions, leading to cracking. Both features enhance conformational transition rates.

Allostery in the ferredoxin protein motif does not involve a conformational switch

Regulation of protein function via cracking, or local unfolding and refolding of substructures, is becoming a widely recognized mechanism of functional control. Oftentimes, cracking events are localized to secondary and tertiary structure interactions between domains that control the optimal position for catalysis and/or the formation of protein complexes. Small changes in free energy associated with ligand binding, phosphorylation, etc., can tip the balance and provide a regulatory functional switch. However, understanding the factors controlling function in single-domain proteins is still a significant challenge to structural biologists. We investigated the functional landscape of a single-domain plant-type ferredoxin protein and the effect of a distal loop on the electron-transfer center. We find the global stability and structure are minimally perturbed with mutation, whereas the functional properties are altered. Specifically, truncating the L1,2 loop does not lead to large-scale changes in the structure, determined via X-ray crystallography. Further, the overall thermal stability of the protein is only marginally perturbed by the mutation. However, even though the mutation is distal to the iron-sulfur cluster (∼20 Å), it leads to a significant change in the redox potential of the iron-sulfur cluster (57 mV). Structure-based all-atom simulations indicate correlated dynamical changes between the surface-exposed loop and the iron-sulfur cluster-binding region. Our results suggest intrinsic communication channels within the ferredoxin fold, composed of many short-range interactions, lead to the propagation of long-range signals. Accordingly, protein interface interactions that involve L1,2 could potentially signal functional changes in distal regions, similar to what is observed in other allosteric systems.

On the role of frustration in the energy landscapes of allosteric proteins

Natural protein domains must be sufficiently stable to fold but often need to be locally unstable to function. Overall, strong energetic conflicts are minimized in native states satisfying the principle of minimal frustration. Local violations of this principle open up possibilities to form the complex multifunnel energy landscapes needed for large-scale conformational changes. We survey the local frustration patterns of allosteric domains and show that the regions that reconfigure are often enriched in patches of highly frustrated interactions, consistent both with the idea that these locally frustrated regions may act as specific hinges or that proteins may "crack" in these locations. On the other hand, the symmetry of multimeric protein assemblies allows near degeneracy by reconfiguring while maintaining minimally frustrated interactions. We also anecdotally examine some specific examples of complex conformational changes and speculate on the role of frustration in the kinetics of allosteric change.

Decrypting the sequence of structural events during the gating transition of pentameric ligand-gated ion channels based on an interpolated elastic network model

Despite many experimental and computational studies of the gating transition of pentameric ligand-gated ion channels (pLGICs), the structural basis of how ligand binding couples to channel gating remains unknown. By using a newly developed interpolated elastic network model (iENM), we have attempted to compute a likely transition pathway from the closed- to the open-channel conformation of pLGICs as captured by the crystal structures of two prokaryotic pLGICs. The iENM pathway predicts a sequence of structural events that begins at the ligand-binding loops and is followed by the displacements of two key loops (loop 2 and loop 7) at the interface between the extracellular and transmembrane domain, the tilting/bending of the pore-lining M2 helix, and subsequent movements of M4, M3 and M1 helices in the transmembrane domain. The predicted order of structural events is in broad agreement with the Φ-value analysis of α subunit of nicotinic acetylcholine receptor mutants, which supports a conserved core mechanism for ligand-gated channel opening in pLGICs. Further perturbation analysis has supported the critical role of certain intra-subunit and inter-subunit interactions in dictating the above sequence of events.