Predicting order of conformational changes during protein conformational transitions using an interpolated elastic network model

Modeling and Simulation of the NMDA Receptor at Coarse-Grained and Atomistic Levels

N-Methyl-D-aspartate (NMDA) receptors are glutamate-gated excitatory channels that play essential roles in brain functions. While high-resolution structures were solved for an allosterically inhibited form of functional NMDA receptor, other key functional states (particularly the active open-channel state) have not yet been resolved at atomic resolutions. To decrypt the molecular mechanism of the NMDA receptor activation, structural modeling and simulation are instrumental in providing detailed information about the dynamics and energetics of the receptor in various functional states. In this chapter, we describe coarse-grained modeling of the NMDA receptor using an elastic network model and related modeling/analysis tools (e.g., normal mode analysis, flexibility and hotspot analysis, cryo-EM flexible fitting, and transition pathway modeling) based on available structures. Additionally, we show how to build an atomistic model of the active-state receptor with targeted molecular dynamics (MD) simulation and explore its energetics and dynamics with conventional MD simulation. Taken together, these modeling and simulation can offer rich structural and dynamic information which will guide experimental studies of the activation of this key receptor.

MDexciteR: Enhanced Sampling Molecular Dynamics by Excited Normal Modes or Principal Components Obtained from Experiments

Molecular dynamics with excited normal modes (MDeNM) is an enhanced sampling method for exploring conformational changes in proteins with minimal biases. The excitation corresponds to injecting kinetic energy along normal modes describing intrinsic collective motions. Herein, we developed a new automated open-source implementation, MDexciteR (https://github.com/mcosta27/MDexciteR), enabling the integration of MDeNM with two commonly used simulation programs with GPU support. Second, we generalized the method to include the excitation of principal components calculated from experimental ensembles. Finally, we evaluated whether the use of coarse-grained normal modes calculated with elastic network representations preserved the performance and accuracy of the method. The advantages and limitations of these new approaches are discussed based on results obtained for three different protein test cases: two globular and a protein/membrane system.

Protein conformational transitions explored by a morphing approach based on normal mode analysis in internal coordinates

Large-scale conformational changes are essential for proteins to function properly. Given that these transition events rarely occur, however, it is challenging to comprehend their underlying mechanisms through experimental and theoretical approaches. In this study, we propose a new computational methodology called internal coordinate normal mode-guided elastic network interpolation (ICONGENI) to predict conformational transition pathways in proteins. Its basic approach is to sample intermediate conformations by interpolating the interatomic distance between two end-point conformations with the degrees of freedom constrained by the low-frequency dynamics afforded by normal mode analysis in internal coordinates. For validation of ICONGENI, it is applied to proteins that undergo open-closed transitions, and the simulation results (i.e., simulated transition pathways) are compared with those of another technique, to demonstrate that ICONGENI can explore highly reliable pathways in terms of thermal and chemical stability. Furthermore, we generate an ensemble of transition pathways through ICONGENI and investigate the possibility of using this method to reveal the transition mechanisms even when there are unknown metastable states on rough energy landscapes.

Molecular mechanisms underlying menthol binding and activation of TRPM8 ion channel

Menthol in mints elicits coolness sensation by selectively activating TRPM8 channel. Although structures of TRPM8 were determined in the apo and liganded states, the menthol-bounded state is unresolved. To understand how menthol activates the channel, we docked menthol to the channel and systematically validated our menthol binding models with thermodynamic mutant cycle analysis. We observed that menthol uses its hydroxyl group as a hand to specifically grab with R842, and its isopropyl group as legs to stand on I846 and L843. By imaging with fluorescent unnatural amino acid, we found that menthol binding induces wide-spread conformational rearrangements within the transmembrane domains. By Φ analysis based on single-channel recordings, we observed a temporal sequence of conformational changes in the S6 bundle crossing and the selectivity filter leading to channel activation. Therefore, our study suggested a 'grab and stand' mechanism of menthol binding and how menthol activates TRPM8 at the atomic level.

Exploring Conformational Space with Thermal Fluctuations Obtained by Normal-Mode Analysis

Proteins in their native states can be represented as ensembles of conformers in dynamical equilibrium. Thermal fluctuations are responsible for transitions between these conformers. Normal-modes analysis (NMA) using elastic network models (ENMs) provides an efficient procedure to explore global dynamics of proteins commonly associated with conformational transitions. In the present work, we present an iterative approach to explore protein conformational spaces by introducing structural distortions according to their equilibrium dynamics at room temperature. The approach can be used either to perform unbiased explorations of conformational space or to explore guided pathways connecting two different conformations, e.g., apo and holo forms. In order to test its performance, four proteins with different magnitudes of structural distortions upon ligand binding have been tested. In all cases, the conformational selection model has been confirmed and the conformational space between apo and holo forms has been encompassed. Different strategies have been tested that impact on the efficiency either to achieve a desired conformational change or to achieve a balanced exploration of the protein conformational multiplicity.

Large-Scale Conformational Changes and Protein Function: Breaking the in silico Barrier

Large-scale conformational changes are essential to link protein structures with their function at the cell and organism scale, but have been elusive both experimentally and computationally. Over the past few years developments in cryo-electron microscopy and crystallography techniques have started to reveal multiple snapshots of increasingly large and flexible systems, deemed impossible only short time ago. As structural information accumulates, theoretical methods become central to understand how different conformers interconvert to mediate biological function. Here we briefly survey current in silico methods to tackle large conformational changes, reviewing recent examples of cross-validation of experiments and computational predictions, which show how the integration of different scale simulations with biological information is already starting to break the barriers between the in silico, in vitro, and in vivo worlds, shedding new light onto complex biological problems inaccessible so far.

Normal Mode Analysis as a Routine Part of a Structural Investigation

Normal mode analysis (NMA) is a technique that can be used to describe the flexible states accessible to a protein about an equilibrium position. These states have been shown repeatedly to have functional significance. NMA is probably the least computationally expensive method for studying the dynamics of macromolecules, and advances in computer technology and algorithms for calculating normal modes over the last 20 years have made it nearly trivial for all but the largest systems. Despite this, it is still uncommon for NMA to be used as a component of the analysis of a structural study. In this review, we will describe NMA, outline its advantages and limitations, explain what can and cannot be learned from it, and address some criticisms and concerns that have been voiced about it. We will then review the most commonly used techniques for reducing the computational cost of this method and identify the web services making use of these methods. We will illustrate several of their possible uses with recent examples from the literature. We conclude by recommending that NMA become one of the standard tools employed in any structural study.

Coarse-Grained Protein Dynamics Studies Using Elastic Network Models

Elastic networks have been used as simple models of proteins to study their slow structural dynamics. They consist of point-like particles connected by linear Hookean springs and hence are convenient for linear normal mode analysis around a given reference structure. Furthermore, dynamic simulations using these models can provide new insights. As the computational cost associated with these models is considerably lower compared to that of all-atom models, they are also convenient for comparative studies between multiple protein structures. In this review, we introduce examples of coarse-grained molecular dynamics studies using elastic network models and their derivatives, focusing on the nonlinear phenomena, and discuss their applicability to large-scale macromolecular assemblies.

Modeling of Protein Structural Flexibility and Large-Scale Dynamics: Coarse-Grained Simulations and Elastic Network Models

Fluctuations of protein three-dimensional structures and large-scale conformational transitions are crucial for the biological function of proteins and their complexes. Experimental studies of such phenomena remain very challenging and therefore molecular modeling can be a good alternative or a valuable supporting tool for the investigation of large molecular systems and long-time events. In this minireview, we present two alternative approaches to the coarse-grained (CG) modeling of dynamic properties of protein systems. We discuss two CG representations of polypeptide chains used for Monte Carlo dynamics simulations of protein local dynamics and conformational transitions, and highly simplified structure-based elastic network models of protein flexibility. In contrast to classical all-atom molecular dynamics, the modeling strategies discussed here allow the quite accurate modeling of much larger systems and longer-time dynamic phenomena. We briefly describe the main features of these models and outline some of their applications, including modeling of near-native structure fluctuations, sampling of large regions of the protein conformational space, or possible support for the structure prediction of large proteins and their complexes.

The conformational wave in capsaicin activation of transient receptor potential vanilloid 1 ion channel

The capsaicin receptor TRPV1 has been intensively studied by cryo-electron microscopy and functional tests. However, though the apo and capsaicin-bound structural models are available, the dynamic process of capsaicin activation remains intangible, largely due to the lack of a capsaicin-induced open structural model and the low occupancy of the transition states. Here we report that reducing temperature toward the freezing point substantially increased channel closure events even in the presence of saturating capsaicin. We further used a combination of fluorescent unnatural amino acid (fUAA) incorporation, computational modeling, and rate-equilibrium linear free-energy relationships analysis (Φ-analysis) to derive the fully open capsaicin-bound state model, and reveal how the channel transits from the apo to the open state. We observed that capsaicin initiates a conformational wave that propagates through the S4–S5 linker towards the S6 bundle and finally reaching the selectivity filter. Our study provides a temporal mechanism for capsaicin activation of TRPV1.

The capsaicin receptor TRPV1 has been structurally characterized, but the capsaicin activation dynamics remain elusive. Here authors use fluorescent unnatural amino acid incorporation, computational modeling and Φ-analysis to derive the capsaicin-bound open state model and reveal the capsaicin induced conformational changes.

Ab initio sampling of transition paths by conditioned Langevin dynamics

We propose a novel stochastic method to generate Brownian paths conditioned to start at an initial point and end at a given final point during a fixed time t_f under a given potential U(x). These paths are sampled with a probability given by the overdamped Langevin dynamics. We show that these paths can be exactly generated by a local stochastic partial differential equation. This equation cannot be solved in general but we present several approximations that are valid either in the low temperature regime or in the presence of barrier crossing. We show that this method warrants the generation of statistically independent transition paths. It is computationally very efficient. We illustrate the method first on two simple potentials, the two-dimensional Mueller potential and the Mexican hat potential, and then on the multi-dimensional problem of conformational transitions in proteins using the "Mixed Elastic Network Model" as a benchmark.

Normal mode-guided transition pathway generation in proteins

The biological function of proteins is closely related to its structural motion. For instance, structurally misfolded proteins do not function properly. Although we are able to experimentally obtain structural information on proteins, it is still challenging to capture their dynamics, such as transition processes. Therefore, we need a simulation method to predict the transition pathways of a protein in order to understand and study large functional deformations. Here, we present a new simulation method called normal mode-guided elastic network interpolation (NGENI) that performs normal modes analysis iteratively to predict transition pathways of proteins. To be more specific, NGENI obtains displacement vectors that determine intermediate structures by interpolating the distance between two end-point conformations, similar to a morphing method called elastic network interpolation. However, the displacement vector is regarded as a linear combination of the normal mode vectors of each intermediate structure, in order to enhance the physical sense of the proposed pathways. As a result, we can generate more reasonable transition pathways geometrically and thermodynamically. By using not only all normal modes, but also in part using only the lowest normal modes, NGENI can still generate reasonable pathways for large deformations in proteins. This study shows that global protein transitions are dominated by collective motion, which means that a few lowest normal modes play an important role in this process. NGENI has considerable merit in terms of computational cost because it is possible to generate transition pathways by partial degrees of freedom, while conventional methods are not capable of this.

Probing the Structural Dynamics of the NMDA Receptor Activation by Coarse-Grained Modeling

N-Methyl-D-aspartate (NMDA) receptors are glutamate-gated excitatory channels that play essential roles in brain functions. High-resolution structures have been solved for an allosterically inhibited and agonist-bound form of a functional NMDA receptor; however, other key functional states (particularly the active open-channel state) were only resolved at moderate resolutions by cryo-electron microscopy (cryo-EM). To decrypt the mechanism of the NMDA receptor activation, structural modeling is essential to provide presently missing information about structural dynamics. We performed systematic coarse-grained modeling using an elastic network model and related modeling/analysis tools (e.g., normal mode analysis, flexibility and hotspot analysis, cryo-EM flexible fitting, and transition pathway modeling) based on an active-state cryo-EM map. We observed extensive conformational changes that allosterically couple the extracellular regulatory and agonist-binding domains to the pore-forming trans-membrane domain (TMD), and validated these, to our knowledge, new observations against known mutational and functional studies. Our results predict two key modes of collective motions featuring shearing/twisting of the extracellular domains relative to the TMD, reveal subunit-specific flexibility profiles, and identify functional hotspot residues at key domain-domain interfaces. Finally, by examining the conformational transition pathway between the allosterically inhibited form and the active form, we predict a discrete sequence of domain motions, which propagate from the extracellular domains to the TMD. In summary, our results offer rich structural and dynamic information, which is consistent with the literature on structure-function relationships in NMDA receptors, and will guide in-depth studies on the activation dynamics of this important neurotransmitter receptor.

Directional Force Originating from ATP Hydrolysis Drives the GroEL Conformational Change

Protein functional mechanisms usually require conformational changes, and often there are known structures for the different conformational states. However, usually neither the origin of the driving force nor the underlying pathways for these conformational transitions is known. Exothermic chemical reactions may be an important source of forces that drive conformational changes. Here we investigate this type of force originating from ATP hydrolysis in the chaperonin GroEL, by applying forces originating from the chemical reaction. Specifically, we apply directed forces to drive the GroEL conformational changes and learn that there is a highly specific direction for applied forces to drive the closed form to the open form. For this purpose, we utilize coarse-grained elastic network models. Principal component analysis on 38 GroEL experimental structures yields the most important motions, and these are used in structural interpolation for the construction of a coarse-grained free energy landscape. In addition, we investigate a more random application of forces with a Monte Carlo method and demonstrate pathways for the closed-open conformational transition in both directions by computing trajectories that are shown upon the free energy landscape. Initial root mean square deviation (RMSD) between the open and closed forms of the subunit is 14.7 Å and final forms from our simulations reach an average RMSD of 3.6 Å from the target forms, closely matching the level of resolution of the coarse-grained model.

Minimum action transition paths connecting minima on an energy surface

Dynamics is essential to the biological functions of many bio-molecules, yet our knowledge of dynamics remains fragmented. Experimental techniques for studying bio-molecules either provide high resolution information on static conformations of the molecule or provide low-resolution, ensemble information that does not shed light on single molecule dynamics. In parallel, bio-molecular dynamics occur at time scale that are not yet attainable through detailed simulation methods. These limitations are especially noticeable when studying transition paths. To address this issue, we report in this paper two methods that derive meaningful trajectories for proteins between two of their conformations. The first method, MinActionPath, uses approximations of the potential energy surface for the molecule to derive an analytical solution of the equations of motion related to the concept of minimum action path. The second method, RelaxPath, follows the same principle of minimum action path but implements a more sophisticated potential, including a mixed elastic potential and a collision term to alleviate steric clashes. Using this new potential, the equations of motion cannot be solved analytically. We have introduced a relaxation method for solving those equations. We describe both the theories behind the two methods and their implementations, focusing on the specific techniques we have used that make those implementations amenable to study large molecular systems. We have illustrated the performance of RelaxPath on simple 2D systems. We have also compared MinActionPath and RelaxPath to other methods for generating transition paths on a well suited test set of large proteins, for which the end points of the trajectories as well as an intermediate conformation between those end points are known. We have shown that RelaxPath outperforms those other methods, including MinActionPath, in its ability to generate trajectories that get close to the known intermediates. We have also shown that the structures along the RelaxPath trajectories remain protein-like. Open source versions of the two programs MinActionPath and RelaxPath are available by request.

Probing the structural dynamics of the CRISPR-Cas9 RNA-guided DNA-cleavage system by coarse-grained modeling

In the adaptive immune systems of many bacteria and archaea, the Cas9 endonuclease forms a complex with specific guide/scaffold RNA to identify and cleave complementary target sequences in foreign DNA. This DNA targeting machinery has been exploited in numerous applications of genome editing and transcription control. However, the molecular mechanism of the Cas9 system is still obscure. Recently, high-resolution structures have been solved for Cas9 in different structural forms (e.g., unbound forms, RNA-bound binary complexes, and RNA-DNA-bound tertiary complexes, corresponding to an inactive state, a pre-target-bound state, and a cleavage-competent or product state), which offered key structural insights to the Cas9 mechanism. To further probe the structural dynamics of Cas9 interacting with RNA and DNA at the amino-acid level of details, we have performed systematic coarse-grained modeling using an elastic network model and related analyses. Our normal mode analysis predicted a few key modes of collective motions that capture the observed conformational changes featuring large domain motions triggered by binding of RNA and DNA. Our flexibility analysis identified specific regions with high or low flexibility that coincide with key functional sites (such as DNA/RNA-binding sites, nuclease cleavage sites, and key hinges). We also identified a small set of hotspot residues that control the energetics of functional motions, which overlap with known functional sites and offer promising targets for future mutagenesis efforts to improve the specificity of Cas9. Finally, we modeled the conformational transitions of Cas9 from the unbound form to the binary complex and then the tertiary complex, and predicted a distinct sequence of domain motions. In sum, our findings have offered rich structural and dynamic details relevant to the Cas9 machinery, and will guide future investigation and engineering of the Cas9 systems. Proteins 2017; 85:342-353. © 2016 Wiley Periodicals, Inc.

Understand spiciness: mechanism of TRPV1 channel activation by capsaicin

Capsaicin in chili peppers bestows the sensation of spiciness. Since the discovery of its receptor, transient receptor potential vanilloid 1 (TRPV1) ion channel, how capsaicin activates this channel has been under extensive investigation using a variety of experimental techniques including mutagenesis, patch-clamp recording, crystallography, cryo-electron microscopy, computational docking and molecular dynamic simulation. A framework of how capsaicin binds and activates TRPV1 has started to merge: capsaicin binds to a pocket formed by the channel’s transmembrane segments, where it takes a “tail-up, head-down” configuration. Binding is mediated by both hydrogen bonds and van der Waals interactions. Upon binding, capsaicin stabilizes the open state of TRPV1 by “pull-and-contact” with the S4-S5 linker. Understanding the ligand-host interaction will greatly facilitate pharmaceutical efforts to develop novel analgesics targeting TRPV1.

Prediction and validation of protein intermediate states from structurally rich ensembles and coarse-grained simulations

Protein conformational changes are at the heart of cell functions, from signalling to ion transport. However, the transient nature of the intermediates along transition pathways hampers their experimental detection, making the underlying mechanisms elusive. Here we retrieve dynamic information on the actual transition routes from principal component analysis (PCA) of structurally-rich ensembles and, in combination with coarse-grained simulations, explore the conformational landscapes of five well-studied proteins. Modelling them as elastic networks in a hybrid elastic-network Brownian dynamics simulation (eBDIMS), we generate trajectories connecting stable end-states that spontaneously sample the crystallographic motions, predicting the structures of known intermediates along the paths. We also show that the explored non-linear routes can delimit the lowest energy passages between end-states sampled by atomistic molecular dynamics. The integrative methodology presented here provides a powerful framework to extract and expand dynamic pathway information from the Protein Data Bank, as well as to validate sampling methods in general.

Protein conformational changes are key to a wide range of cellular functions but remain difficult to access experimentally. Here the authors describe eBDIMS, a novel approach to predict intermediates observed in structural transition pathways from experimental ensembles.

Probing the structural dynamics of the SNARE recycling machine based on coarse-grained modeling

Membrane fusion in eukaryotes is driven by the formation of a four-helix bundle by three SNARE proteins. To recycle the SNARE proteins, they must be disassembled by the ATPase NSF and four SNAP proteins which together form a 20S supercomplex. Recently, the first high-resolution structures of the NSF (in both ATP and ADP state) and 20S (in four distinct states termed I, II, IIIa, and IIIb) were solved by cryo-electron microscopy (cryo-EM), which have paved the way for structure-driven studies of the SNARE recycling mechanism. To probe the structural dynamics of SNARE disassembly at amino-acid level of details, a systematic coarse-grained modeling based on an elastic network model and related analyses were performed. Our normal mode analysis of NSF, SNARE, and 20S predicted key modes of collective motions that partially account for the observed structural changes, and illuminated how the SNARE complex can be effectively destabilized by untwisting and bending motions of the SNARE complex driven by the amino-terminal domains of NSF in state II. Our flexibility analysis identified regions with high/low flexibility that coincide with key functional sites (such as the NSF-SNAPs-SNARE binding sites). A subset of hotspot residues that control the above collective motions, which will make promising targets for future mutagenesis studies were also identified. Finally, the conformational changes in 20S as induced by the transition of NSF from ATP to ADP state were modeled, and a concerted untwisting motion of SNARE/SNAPs and a sideway flip of two amino-terminal domains were observed. In sum, the findings have offered new structural and dynamic details relevant to the SNARE disassembly mechanism, and will guide future functional studies of the SNARE recycling machinery. Proteins 2016; 84:1055-1066. © 2016 Wiley Periodicals, Inc.

A combined coarse-grained and all-atom simulation of TRPV1 channel gating and heat activation

Coarse-grained modeling and all-atom molecular dynamics simulation provide insight into the mechanism for heat activation of TRPV1 gating.

The transient receptor potential (TRP) channels act as key sensors of various chemical and physical stimuli in eukaryotic cells. Despite years of study, the molecular mechanisms of TRP channel activation remain unclear. To elucidate the structural, dynamic, and energetic basis of gating in TRPV1 (a founding member of the TRPV subfamily), we performed coarse-grained modeling and all-atom molecular dynamics (MD) simulation based on the recently solved high resolution structures of the open and closed form of TRPV1. Our coarse-grained normal mode analysis captures two key modes of collective motions involved in the TRPV1 gating transition, featuring a quaternary twist motion of the transmembrane domains (TMDs) relative to the intracellular domains (ICDs). Our transition pathway modeling predicts a sequence of structural movements that propagate from the ICDs to the TMDs via key interface domains (including the membrane proximal domain and the C-terminal domain), leading to sequential opening of the selectivity filter followed by the lower gate in the channel pore (confirmed by modeling conformational changes induced by the activation of ICDs). The above findings of coarse-grained modeling are robust to perturbation by lipids. Finally, our MD simulation of the ICD identifies key residues that contribute differently to the nonpolar energy of the open and closed state, and these residues are predicted to control the temperature sensitivity of TRPV1 gating. These computational predictions offer new insights to the mechanism for heat activation of TRPV1 gating, and will guide our future electrophysiology and mutagenesis studies.

Path Similarity Analysis: A Method for Quantifying Macromolecular Pathways

Diverse classes of proteins function through large-scale conformational changes and various sophisticated computational algorithms have been proposed to enhance sampling of these macromolecular transition paths. Because such paths are curves in a high-dimensional space, it has been difficult to quantitatively compare multiple paths, a necessary prerequisite to, for instance, assess the quality of different algorithms. We introduce a method named Path Similarity Analysis (PSA) that enables us to quantify the similarity between two arbitrary paths and extract the atomic-scale determinants responsible for their differences. PSA utilizes the full information available in 3N-dimensional configuration space trajectories by employing the Hausdorff or Fréchet metrics (adopted from computational geometry) to quantify the degree of similarity between piecewise-linear curves. It thus completely avoids relying on projections into low dimensional spaces, as used in traditional approaches. To elucidate the principles of PSA, we quantified the effect of path roughness induced by thermal fluctuations using a toy model system. Using, as an example, the closed-to-open transitions of the enzyme adenylate kinase (AdK) in its substrate-free form, we compared a range of protein transition path-generating algorithms. Molecular dynamics-based dynamic importance sampling (DIMS) MD and targeted MD (TMD) and the purely geometric FRODA (Framework Rigidity Optimized Dynamics Algorithm) were tested along with seven other methods publicly available on servers, including several based on the popular elastic network model (ENM). PSA with clustering revealed that paths produced by a given method are more similar to each other than to those from another method and, for instance, that the ENM-based methods produced relatively similar paths. PSA was applied to ensembles of DIMS MD and FRODA trajectories of the conformational transition of diphtheria toxin, a particularly challenging example. For the AdK transition, the new concept of a Hausdorff-pair map enabled us to extract the molecular structural determinants responsible for differences in pathways, namely a set of conserved salt bridges whose charge-charge interactions are fully modelled in DIMS MD but not in FRODA. PSA has the potential to enhance our understanding of transition path sampling methods, validate them, and to provide a new approach to analyzing conformational transitions.

Many proteins are nanomachines that perform mechanical or chemical work by changing their three-dimensional shape and cycle between multiple conformational states. Computer simulations of such conformational transitions provide mechanistic insights into protein function but such simulations have been challenging. In particular, it is not clear how to quantitatively compare current simulation methods or to assess their accuracy. To that end, we present a general and flexible computational framework for quantifying transition paths—by measuring mutual geometric similarity—that, compared with existing approaches, requires minimal a-priori assumptions and can take advantage of full atomic detail alongside heuristic information derived from intuition. Using our Path Similarity Analysis (PSA) framework in parallel with several existing quantitative approaches, we examine transitions generated for a toy model of a transition and two biological systems, the enzyme adenylate kinase and diphtheria toxin. Our results show that PSA enables the quantitative comparison of different path sampling methods and aids the identification of potentially important atomistic motions by exploiting geometric information in transition paths. The method has the potential to enhance our understanding of transition path sampling methods, validate them, and to provide a new approach to analyzing macromolecular conformational transitions.

Bridging between NMA and Elastic Network Models: Preserving All-Atom Accuracy in Coarse-Grained Models

Dynamics can provide deep insights into the functional mechanisms of proteins and protein complexes. For large protein complexes such as GroEL/GroES with more than 8,000 residues, obtaining a fine-grained all-atom description of its normal mode motions can be computationally prohibitive and is often unnecessary. For this reason, coarse-grained models have been used successfully. However, most existing coarse-grained models use extremely simple potentials to represent the interactions within the coarse-grained structures and as a result, the dynamics obtained for the coarse-grained structures may not always be fully realistic. There is a gap between the quality of the dynamics of the coarse-grained structures given by all-atom models and that by coarse-grained models. In this work, we resolve an important question in protein dynamics computations—how can we efficiently construct coarse-grained models whose description of the dynamics of the coarse-grained structures remains as accurate as that given by all-atom models? Our method takes advantage of the sparseness of the Hessian matrix and achieves a high efficiency with a novel iterative matrix projection approach. The result is highly significant since it can provide descriptions of normal mode motions at an all-atom level of accuracy even for the largest biomolecular complexes. The application of our method to GroEL/GroES offers new insights into the mechanism of this biologically important chaperonin, such as that the conformational transitions of this protein complex in its functional cycle are even more strongly connected to the first few lowest frequency modes than with other coarse-grained models.

Proteins and other biomolecules are not static but are constantly in motion. Moreover, they possess intrinsic collective motion patterns that are tightly linked to their functions. Thus, an accurate and detailed description of their motions can provide deep insights into their functional mechanisms. For large protein complexes with hundreds of thousands of atoms or more, an atomic level description of the motions can be computationally prohibitive, and so coarse-grained models with fewer structural details are often used instead. However, there can be a big gap between the quality of motions derived from atomic models and those from coarse-grained models. In this work, we solve an important problem in protein dynamics studies: how to preserve the atomic-level accuracy in describing molecular motions while using coarse-grained models? We accomplish this by developing a novel iterative matrix projection method that dramatically speeds up the computations. This method is significant since it promises accurate descriptions of protein motions approaching an all-atom level even for the largest biomolecular complexes. Results shown here for a large molecular chaperonin demonstrate how this can provide new insights into its functional process.

Probing the folded state and mechanical unfolding pathways of T4 lysozyme using all-atom and coarse-grained molecular simulation

The Bacteriophage T4 Lysozyme (T4L) is a prototype modular protein comprised of an N-terminal and a C-domain domain, which was extensively studied to understand the folding/unfolding mechanism of modular proteins. To offer detailed structural and dynamic insights to the folded-state stability and the mechanical unfolding behaviors of T4L, we have performed extensive equilibrium and steered molecular dynamics simulations of both the wild-type (WT) and a circular permutation (CP) variant of T4L using all-atom and coarse-grained force fields. Our all-atom and coarse-grained simulations of the folded state have consistently found greater stability of the C-domain than the N-domain in isolation, which is in agreement with past thermostatic studies of T4L. While the all-atom simulation cannot fully explain the mechanical unfolding behaviors of the WT and the CP variant observed in an optical tweezers study, the coarse-grained simulations based on the Go model or a modified elastic network model (mENM) are in qualitative agreement with the experimental finding of greater unfolding cooperativity in the WT than the CP variant. Interestingly, the two coarse-grained models predict different structural mechanisms for the observed change in cooperativity between the WT and the CP variant--while the Go model predicts minor modification of the unfolding pathways by circular permutation (i.e., preserving the general order that the N-domain unfolds before the C-domain), the mENM predicts a dramatic change in unfolding pathways (e.g., different order of N/C-domain unfolding in the WT and the CP variant). Based on our simulations, we have analyzed the limitations of and the key differences between these models and offered testable predictions for future experiments to resolve the structural mechanism for cooperative folding/unfolding of T4L.

Structure-Encoded Global Motions and Their Role in Mediating Protein-Substrate Interactions

Recent structure-based computational studies suggest that, in contrast to the classical description of equilibrium fluctuations as wigglings and jigglings, proteins have access to well-defined spectra of collective motions, called intrinsic dynamics, encoded by their structure under native state conditions. In particular, the global modes of motions (at the low frequency end of the spectrum) are shown by multiple studies to be highly robust to minor differences in the structure or to detailed interactions at the atomic level. These modes, encoded by the overall fold, usually define the mechanisms of interactions with substrates. They can be estimated by low-resolution models such as the elastic network models (ENMs) exclusively based on interresidue contact topology. The ability of ENMs to efficiently assess the global motions intrinsically favored by the overall fold as well as the relevance of these predictions to the dominant changes in structure experimentally observed for a given protein in the presence of different substrates suggest that the intrinsic dynamics plays a role in mediating protein-substrate interactions. These observations underscore the functional significance of structure-encoded dynamics, or the importance of the predisposition to favor functional global modes in the evolutionary selection of structures.

Structural mechanism underlying capsaicin binding and activation of the TRPV1 ion channel

Capsaicin bestows spiciness by activating TRPV1 channel with exquisite potency and selectivity. Although a capsaicin-bound channel structure was previously resolved by cryo-EM at 4.2- to 4.5-Å resolution, capsaicin was registered as a small electron density, reflecting neither its chemical structure nor specific ligand-channel interactions--important details required for mechanistic understanding. We obtained the missing atomic-level details by iterative computation and confirmed them by systematic site-specific functional tests. We observed that the bound capsaicin takes a 'tail-up, head-down' configuration. The vanillyl and amide groups form specific interactions to anchor its bound position, while the aliphatic tail may sample a range of conformations, making it invisible in cryo-EM images. Capsaicin stabilizes TRPV1's open state by 'pull-and-contact' interactions between the vanillyl group and the S4-S5 linker. Our study provides a structural mechanism for the agonistic function of capsaicin and its analogs, and demonstrates an effective approach to obtain atomic-level information from cryo-EM structures.

A multi-scale-multi-stable model for the rhodopsin photocycle

We report a multi-scale simulation study of the photocycle of the rhodopsins. The quasi-atomistic representation ("united atoms" UA) of retinal is combined with a minimalist coarse grained (CG, one-bead-per amino acid) representation of the protein, in a hybrid UA/CG approach, which is the homolog of QM/MM, but at lower resolution. An accurate multi-stable parameterization of the model allows simulating each state and transition among them, and the combination of different scale representation allows addressing the entire photocycle. We test the model on bacterial rhodopsin, for which more experimental data are available, and then also report results for mammalian rhodopsins. In particular, the analysis of simulations reveals the spontaneous appearance of meta-stable states in quantitative agreement with experimental data.

iMODS: internal coordinates normal mode analysis server

Normal mode analysis (NMA) in internal (dihedral) coordinates naturally reproduces the collective functional motions of biological macromolecules. iMODS facilitates the exploration of such modes and generates feasible transition pathways between two homologous structures, even with large macromolecules. The distinctive internal coordinate formulation improves the efficiency of NMA and extends its applicability while implicitly maintaining stereochemistry. Vibrational analysis, motion animations and morphing trajectories can be easily carried out at different resolution scales almost interactively. The server is versatile; non-specialists can rapidly characterize potential conformational changes, whereas advanced users can customize the model resolution with multiple coarse-grained atomic representations and elastic network potentials. iMODS supports advanced visualization capabilities for illustrating collective motions, including an improved affine-model-based arrow representation of domain dynamics. The generated all-heavy-atoms conformations can be used to introduce flexibility for more advanced modeling or sampling strategies. The server is free and open to all users with no login requirement at http://imods.chaconlab.org.

Exploring the conformational transitions of biomolecular systems using a simple two-state anisotropic network model

Biomolecular conformational transitions are essential to biological functions. Most experimental methods report on the long-lived functional states of biomolecules, but information about the transition pathways between these stable states is generally scarce. Such transitions involve short-lived conformational states that are difficult to detect experimentally. For this reason, computational methods are needed to produce plausible hypothetical transition pathways that can then be probed experimentally. Here we propose a simple and computationally efficient method, called ANMPathway, for constructing a physically reasonable pathway between two endpoints of a conformational transition. We adopt a coarse-grained representation of the protein and construct a two-state potential by combining two elastic network models (ENMs) representative of the experimental structures resolved for the endpoints. The two-state potential has a cusp hypersurface in the configuration space where the energies from both the ENMs are equal. We first search for the minimum energy structure on the cusp hypersurface and then treat it as the transition state. The continuous pathway is subsequently constructed by following the steepest descent energy minimization trajectories starting from the transition state on each side of the cusp hypersurface. Application to several systems of broad biological interest such as adenylate kinase, ATP-driven calcium pump SERCA, leucine transporter and glutamate transporter shows that ANMPathway yields results in good agreement with those from other similar methods and with data obtained from all-atom molecular dynamics simulations, in support of the utility of this simple and efficient approach. Notably the method provides experimentally testable predictions, including the formation of non-native contacts during the transition which we were able to detect in two of the systems we studied. An open-access web server has been created to deliver ANMPathway results.

Many biomolecules are like tiny molecular machines that need to change their shapes and visit many states to perform their biological functions. For a complete molecular understanding of a biological process, one needs to have information on the relevant stable states of the system in question, as well as the pathways by which the system travels from one state to another. We report here an efficient computational method that uses the knowledge of experimental structures of a pair of stable states in order to construct an energetically favoravle pathway between them. We adopt a simple representation of the molecular system by replacing the atoms with beads connected by springs and constructing an energy function with two minima around the end-states. We searched for the structure with highest energy that the system is most likely to visit during the transition and created two paths starting from this structure and proceeding toward the end-states. The combined result of these two paths is the minimum energy pathway between the two stable states. We apply this method to study important structural changes in one enzyme and three large proteins that transport small molecules and ions across the cell membrane.

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.

Elucidating the ensemble of functionally-relevant transitions in protein systems with a robotics-inspired method

Background

Many proteins tune their biological function by transitioning between different functional states, effectively acting as dynamic molecular machines. Detailed structural characterization of transition trajectories is central to understanding the relationship between protein dynamics and function. Computational approaches that build on the Molecular Dynamics framework are in principle able to model transition trajectories at great detail but also at considerable computational cost. Methods that delay consideration of dynamics and focus instead on elucidating energetically-credible conformational paths connecting two functionally-relevant structures provide a complementary approach. Effective sampling-based path planning methods originating in robotics have been recently proposed to produce conformational paths. These methods largely model short peptides or address large proteins by simplifying conformational space.

Methods

We propose a robotics-inspired method that connects two given structures of a protein by sampling conformational paths. The method focuses on small- to medium-size proteins, efficiently modeling structural deformations through the use of the molecular fragment replacement technique. In particular, the method grows a tree in conformational space rooted at the start structure, steering the tree to a goal region defined around the goal structure. We investigate various bias schemes over a progress coordinate for balance between coverage of conformational space and progress towards the goal. A geometric projection layer promotes path diversity. A reactive temperature scheme allows sampling of rare paths that cross energy barriers.

Results and conclusions

Experiments are conducted on small- to medium-size proteins of length up to 214 amino acids and with multiple known functionally-relevant states, some of which are more than 13Å apart of each-other. Analysis reveals that the method effectively obtains conformational paths connecting structural states that are significantly different. A detailed analysis on the depth and breadth of the tree suggests that a soft global bias over the progress coordinate enhances sampling and results in higher path diversity. The explicit geometric projection layer that biases the exploration away from over-sampled regions further increases coverage, often improving proximity to the goal by forcing the exploration to find new paths. The reactive temperature scheme is shown effective in increasing path diversity, particularly in difficult structural transitions with known high-energy barriers.

Structure-based simulations of the translocation mechanism of the hepatitis C virus NS3 helicase along single-stranded nucleic acid

The NS3 helicase of Hepatitis C virus is an ATP-fueled molecular motor that can translocate along single-stranded (ss) nucleic acid, and unwind double-stranded nucleic acids. It makes a promising antiviral target and an important prototype system for helicase research. Despite recent progress, the detailed mechanism of NS3 helicase remains unknown. In this study, we have combined coarse-grained (CG) and atomistic simulations to probe the translocation mechanism of NS3 helicase along ssDNA. At the residue level of detail, our CG simulations have captured functionally important interdomain motions of NS3 helicase and reproduced single-base translocation of NS3 helicase along ssDNA in the 3'-5' direction, which is in good agreement with experimental data and the inchworm model. By combining the CG simulations with residue-specific perturbations to protein-DNA interactions, we have identified a number of key residues important to the translocation machinery that agree with previous structural and mutational studies. Additionally, our atomistic simulations with targeted molecular dynamics have corroborated the findings of CG simulations and further revealed key protein-DNA hydrogen bonds that break/form during the transitions. This study offers, to our knowledge, the most detailed and realistic simulations of translocation mechanism of NS3 helicase. The simulation protocol established in this study will be useful for designing inhibitors that target the translocation machinery of NS3 helicase, and for simulations of a variety of nucleic-acid-based molecular motors.

The mechanism of the converter domain rotation in the recovery stroke of myosin motor protein

Upon ATP binding, myosin motor protein is found in two alternative conformations, prerecovery state M* and postrecovery state M**. The transition from one state to the other, known as the recovery stroke, plays a key role in the myosin functional cycle. Despite much recent research, the microscopic details of this transition remain elusive. A critical step in the recovery stroke is the rotation of the converter domain from "up" position in prerecovery state to "down" position in postrecovery state that leads to the swing of the lever arm attached to it. In this work, we demonstrate that the two rotational states of the converter domain are determined by the interactions within a small structural motif in the force-generating region of the protein that can be accurately modeled on computers using atomic representation and explicit solvent. Our simulations show that the transition between the two states is controlled by a small helix (SH1) located next to the relay helix and relay loop. A small translation in the position of SH1 away from the relay helix is seen to trigger the transition from "up" state to "down" state. The transition is driven by a cluster of hydrophobic residues I687, F487, and F506 that make significant contributions to the stability of both states. The proposed mechanism agrees well with the available structural and mutational studies.

Coarse-grained modeling of the structural states and transition underlying the powerstroke of dynein motor domain

This study aims to model a minimal dynein motor domain capable of motor function, which consists of the linker domain, six AAA+ modules (AAA1-AAA6), coiled coil stalk, and C-terminus domain. To this end, we have used the newly solved X-ray structures of dynein motor domain to perform a coarse-grained modeling of dynein's post- and pre-powerstroke conformation and the conformational transition between them. First, we have used normal mode analysis to identify a single normal mode that captures the coupled motions of AAA1-AAA2 closing and linker domain rotation, which enables the ATP-driven recovery stroke of dynein. Second, based on the post-powerstroke conformation solved crystallographically, we have modeled dynein's pre-powerstroke conformation by computationally inducing AAA1-AAA2 closing and sliding of coiled coil stalk, and the resulting model features a linker domain near the pre-powerstroke position and a slightly tilted stalk. Third, we have modeled the conformational transition from pre- to post-powerstroke conformation, which predicts a clear sequence of structural events that couple microtubule binding, powerstroke and product release, and supports a signaling path from stalk to AAA1 via AAA3 and AAA4. Finally, we have found that a closed AAA3-AAA4 interface (compatible with nucleotide binding) is essential to the mechano-chemical coupling in dynein. Our modeling not only offers unprecedented structural insights to the motor function of dynein as described by past single-molecule, fluorescence resonance energy transfer, and electron microscopy studies, but also provides new predictions for future experiments to test.

Interactions between relay helix and Src homology 1 (SH1) domain helix drive the converter domain rotation during the recovery stroke of myosin II

Myosin motor protein exists in two alternative conformations, prerecovery state M* and postrecovery state M**, on adenosine triphosphate binding. The details of the M*-to-M** transition, known as the recovery stroke to reflect its role as the functional opposite of the force-generating power stroke, remain elusive. The defining feature of the postrecovery state is a kink in the relay helix, a key part of the protein involved in force generation. In this article, we determine the interactions that are responsible for the appearance of the kink. We design a series of computational models that contain three other segments, relay loop, converter domain, and Src homology 1 (SH1) domain helix, with which relay helix interacts and determine their structure in accurate replica exchange molecular dynamics simulations in explicit solvent. By conducting an exhaustive combinatorial search among different models, we find that: (1) the converter domain must be attached to the relay helix during the transition, so it does not interfere with other parts of the protein and (2) the structure of the relay helix is controlled by SH1 helix. The kink is strongly coupled to the position of SH1 helix. It arises as a result of direct interactions between SH1 and the relay helix and leads to a rotation of the C-terminal part of the relay helix, which is subsequently transmitted to the converter domain.

Accurate flexible fitting of high-resolution protein structures to small-angle x-ray scattering data using a coarse-grained model with implicit hydration shell

Small-angle x-ray scattering (SAXS) is a powerful technique widely used to explore conformational states and transitions of biomolecular assemblies in solution. For accurate model reconstruction from SAXS data, one promising approach is to flexibly fit a known high-resolution protein structure to low-resolution SAXS data by computer simulations. This is a highly challenging task due to low information content in SAXS data. To meet this challenge, we have developed what we believe to be a novel method based on a coarse-grained (one-bead-per-residue) protein representation and a modified form of the elastic network model that allows large-scale conformational changes while maintaining pseudobonds and secondary structures. Our method optimizes a pseudoenergy that combines the modified elastic-network model energy with a SAXS-fitting score and a collision energy that penalizes steric collisions. Our method uses what we consider a new implicit hydration shell model that accounts for the contribution of hydration shell to SAXS data accurately without explicitly adding waters to the system. We have rigorously validated our method using five test cases with simulated SAXS data and three test cases with experimental SAXS data. Our method has successfully generated high-quality structural models with root mean-squared deviation of 1 ∼ 3 Å from the target structures.

Accurate flexible fitting of high-resolution protein structures into cryo-electron microscopy maps using coarse-grained pseudo-energy minimization

Cryo-electron microscopy (cryo-EM) has been widely used to explore conformational states of large biomolecular assemblies. The detailed interpretation of cryo-EM data requires the flexible fitting of a known high-resolution protein structure into a low-resolution cryo-EM map. To this end, we have developed what we believe is a new method based on a two-bead-per-residue protein representation, and a modified form of the elastic network model that allows large-scale conformational changes while maintaining pseudobonds and secondary structures. Our method minimizes a pseudo-energy which linearly combines various terms of the modified elastic network model energy with a cryo-EM-fitting score and a collision energy that penalizes steric collisions. Unlike previous flexible fitting efforts using the lowest few normal modes, our method effectively utilizes all normal modes so that both global and local structural changes can be fully modeled. We have validated our method for a diverse set of 10 pairs of protein structures using simulated cryo-EM maps with a range of resolutions and in the absence/presence of random noise. We have shown that our method is both accurate and efficient compared with alternative techniques, and its performance is robust to the addition of random noise. Our method is also shown to be useful for the flexible fitting of three experimental cryo-EM maps.

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.

Phenylketonuria as a model for protein misfolding diseases and for the development of next generation orphan drugs for patients with inborn errors of metabolism

The lecture dedicated to Professor Horst Bickel describes the advances, successes, and opportunities concerning the understanding of the biochemical and molecular basis of phenylketonuria and the innovative treatment strategies introduced for these patients during the last 60 years. These concepts were transferred to other inborn errors of metabolism and led to significant reduction in morbidity and to an improvement in quality of life. Important milestones were the successful development of a low-phenylalanine diet for phenylketonuria patients, the recognition of tetrahydrobiopterin as an option to treat these individuals pharmacologically, and finally market approval of this drug. The work related to the discovery of a pharmacological treatment led metabolic researchers and pediatricians to new insights into the molecular processes linked to mutations in the phenylalanine hydroxylase gene at the cellular and structural level. Again, phenylketonuria became a prototype disorder for a previously underestimated but now rapidly expanding group of diseases: protein misfolding disorders with loss of function. Due to potential general biological mechanisms underlying these disorders, the door may soon open to a systematic development of a new class of pharmaceutical products. These pharmacological chaperones are likely to correct misfolding of proteins involved in numerous genetic and nongenetic diseases.

Protein folding pathways and state transitions described by classical equations of motion of an elastic network model

Protein topology defined by the matrix of residue contacts has proved to be a fruitful basis for the study of protein dynamics. The widely implemented coarse-grained elastic network model of backbone fluctuations has been used to describe crystallographic temperature factors, allosteric couplings, and some aspects of the folding pathway. In the present study, we develop a model of protein dynamics based on the classical equations of motion of a damped network model (DNM) that describes the folding path from a completely unfolded state to the native conformation through a single-well potential derived purely from the native conformation. The kinetic energy gained through the collapse of the protein chain is dissipated through a friction term in the equations of motion that models the water bath. This approach is completely general and sufficiently fast that it can be applied to large proteins. Folding pathways for various proteins of different classes are described and shown to correlate with experimental observations and molecular dynamics and Monte Carlo simulations. Allosteric transitions between alternative protein structures are also modeled within the DNM through an asymmetric double-well potential.