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

MinActionPath2: path generation between different conformations of large macromolecular assemblies by action minimization

Recent progress in solving macromolecular structures and assemblies by cryogenic electron microscopy techniques enables sampling of their conformations in different states that are relevant to their biological function. Knowing the transition path between these conformations would provide new avenues for drug discovery. While the experimental study of transition paths is intrinsically difficult, in-silico methods can be used to generate an initial guess for those paths. The Elastic Network Model (ENM), along with a coarse-grained representation (CG) of the structures are among the most popular models to explore such possible paths. Here we propose an update to our software platform MinActionPath that generates non-linear transition paths based on ENM and CG models, using action minimization to solve the equations of motion. The new website enables the study of large structures such as ribosomes or entire virus envelopes. It provides direct visualization of the trajectories along with quantitative analyses of their behaviors at http://dynstr.pasteur.fr/servers/minactionpath/minactionpath2_submission.

Evaluation of Essential Dynamics and Fixed-Length Coarse Graining for Multidomain Proteins

For multiscale modeling of biomolecules, reliable coarse-grained (CG) models can offer great potential to simulate larger temporal and spatial scales than traditional all-atom (AA) models. In this study, we explore the essential dynamics coarse graining (EDCG) and fixed-length coarse graining (FLCG) approaches for constructing highly coarse-grained models for multidomain proteins (MDPs), with 1 to 10 amino acid residues per CG site. In the studies of 13 MDPs, our data indicate that both EDCG and FLCG can preserve the protein dynamics of MDPs. FLCG, which restricts an equal number of residues in each CG site, represents an excellent approximation to EDCG and a straightforward approach for coarse-graining MDPs. Furthermore, FLCG is tested with a class B G-protein-coupled receptor protein, and the agreement with prior experiments suggests its general application to various MDPs in different environments or conditions. Finally, we demonstrate another application of FLCG through progressive backmapping, showcasing the ability to recover from lower-resolution CG models (6 residues/CG site) to higher-resolution ones (1 residue/CG site). These promising outcomes underscore the broad applicability of FLCG to construct highly or ultra-coarse-grained models of complex biomolecules for multiscale simulations.

Normal mode analysis and comparative study of intrinsic dynamics of alcohol oxidase enzymes from GMC protein family

Glucose-Methanol-Choline (GMC) family enzymes are very important in catalyzing the oxidation of a wide range of structurally diverse substrates. Enzymes that constitute the GMC family, share a common tertiary fold but < 25% sequence identity. Cofactor FAD, FAD binding signature motif, and similar structural scaffold of the active site are common features of oxidoreductase enzymes of the GMC family. Protein functionality mainly depends on protein three-dimensional structures and dynamics. In this study, we used the normal mode analysis method to search the intrinsic dynamics of GMC family enzymes. We have explored the dynamical behavior of enzymes with unique substrate catabolism and active site characteristics from different classes of the GMC family. Analysis of individual enzymes and comparative ensemble analysis of enzymes from different classes has shown conserved dynamic motion at FAD binding sites. The present study revealed that GMC enzymes share a strong dynamic similarity (Bhattacharyya coefficient >90% and root mean squared inner product >52%) despite low sequence identity across the GMC family enzymes. The study predicts that local deformation energy between atoms of the enzyme may be responsible for the catalysis of different substrates. This study may help that intrinsic dynamics can be used to make meaningful classifications of proteins or enzymes from different organisms.Communicated by Ramaswamy H. Sarma.

Sigmoid Accelerated Molecular Dynamics: An Efficient Enhanced Sampling Method for Biosystems

Gaussian accelerated molecular dynamics (GaMD) is recognized as a popular enhanced sampling method for tackling long-standing challenges in biomolecular simulations. Inspired by GaMD, Sigmoid accelerated molecular dynamics (SaMD) is proposed in this work by adding a Sigmoid boost potential to improve the balance between the highest acceleration and accurate reweighting. Compared with GaMD, SaMD extends the accessible time scale and improves the computational efficiency as tested in three tasks. In the alanine dipeptide task, SaMD can produce the free energy landscape with better accuracy and efficiency. In the chignolin folding task, the estimated Gibbs free energy difference can converge to the experimental value ∼30% faster. In the protein-ligand binding task, the bound conformations are closer to the crystal structure with a minimal ligand root-mean-square deviation of 1.7 Å. The binding of the ligand XK263 to the HIV protease is reproduced by SaMD in ∼60% less simulation time.

Investigation of protein-ligand binding motions through protein conformational morphing and clustering of cytochrome bc1-aa3 super complex

Cytochrome b (QcrB) is considered an essential subunit in the electron transport chain that coordinates the action of the entire cytochrome bc1 oxidase. It has been identified as an attractive drug target for a new promising clinical candidate Q203 that depletes the intracellular ATP levels in the bacterium, Mycobacterium tuberculosis. However, single point polymorphism (T313A/I) near the quinol oxidation site of QcrB developed resistance to Q203. In the present study, we analyze the structural changes and drug-resistance mechanism of QcrB due to the point mutation in detail through conformational morphing and molecular docking studies. By morphing, we generated conformers between the open and closed state of the electron transporting cytochrome bc1-aa3 super complex. We clustered them to identify four intermediate structures and relevant intra- and intermolecular motions that may be of functional relevance, especially the binding of Q203 in wild and mutant QcrB intermediate structures and their alteration in developing drug resistance. The difference in the binding score and hydrogen bond interactions between Q203 and the wild-type and mutant intermediate structures of QcrB from molecular docking studies showed that the point mutation T313A severely affected the binding affinity of the candidate drug. Together, the findings provide an in-depth understanding of QcrB inhibition in different conformations, including closed, intermediate, and open states of cytochrome bc1-aa3 super complex in Mycobacterium tuberculosis at the atomic level. We also obtain insights for designing QcrB and cytochrome bc1-aa3 inhibitors as potential therapeutics that may combat drug resistance in tuberculosis.

Structural basis of the conformational and functional regulation of human SERCA2b, the ubiquitous endoplasmic reticulum calcium pump

Sarco/endoplasmic reticulum Ca²⁺ ATPase 2b (SERCA2b), a member of the SERCA family, is expressed ubiquitously and transports Ca²⁺ into the sarco/endoplasmic reticulum using the energy provided by ATP binding and hydrolysis. The crystal structure of SERCA2b in its Ca²⁺ - and ATP-bound (E1∙2Ca²⁺ -ATP) state and cryo-electron microscopy (cryo-EM) structures of the protein in its E1∙2Ca²⁺ -ATP and Ca²⁺ -unbound phosphorylated (E2P) states have provided essential insights into how the overall conformation and ATPase activity of SERCA2b is regulated by the transmembrane helix 11 and the subsequent luminal extension loop, both of which are specific to this isoform. More recently, our cryo-EM analysis has revealed that SERCA2b likely adopts open and closed conformations of the cytosolic domains in the Ca²⁺ -bound but ATP-free (E1∙2Ca²⁺ ) state, and that the closed conformation represents a state immediately prior to ATP binding. This review article summarizes the unique mechanisms underlying the conformational and functional regulation of SERCA2b.

Molecular Modeling is an Enabling Approach to Complement and Enhance Channelopathy Research

Hundreds of human membrane proteins form channels that transport necessary ions and compounds, including drugs and metabolites, yet details of their normal function or how function is altered by genetic variants to cause diseases are often unknown. Without this knowledge, researchers are less equipped to develop approaches to diagnose and treat channelopathies. High-resolution computational approaches such as molecular modeling enable researchers to investigate channelopathy protein function, facilitate detailed hypothesis generation, and produce data that is difficult to gather experimentally. Molecular modeling can be tailored to each physiologic context that a protein may act within, some of which may currently be difficult or impossible to assay experimentally. Because many genomic variants are observed in channelopathy proteins from high-throughput sequencing studies, methods with mechanistic value are needed to interpret their effects. The eminent field of structural bioinformatics integrates techniques from multiple disciplines including molecular modeling, computational chemistry, biophysics, and biochemistry, to develop mechanistic hypotheses and enhance the information available for understanding function. Molecular modeling and simulation access 3D and time-dependent information, not currently predictable from sequence. Thus, molecular modeling is valuable for increasing the resolution with which the natural function of protein channels can be investigated, and for interpreting how genomic variants alter them to produce physiologic changes that manifest as channelopathies. © 2022 American Physiological Society. Compr Physiol 12:3141-3166, 2022.

Study of Allosteric Transitions of Human P-Glycoprotein by Using the Two-State Anisotropic Network Model

Human P-glycoprotein (P-gp) is a kind of ATP-binding cassette (ABC) transporters. Once human P-gp is overexpressed in tumor cells, which can lead to tumor multidrug resistance (MDR). However, the present experimental methods are difficult to obtain the large-scale conformational transition process of human P-gp. In this work, we explored the allosteric pathway of human P-gp from the inward-facing (IF) to the outward-facing (OF) state in the substrate transport process with the two-state anisotropic network model (tANM). These results suggest that the allosteric transitions proceed in a coupled way. The conformational changes of nucleotide-binding domains (NBDs) finally make the transmembrane domains (TMDs) to the OF state via the role of the allosteric propagation of the intracellular helices IH1 and IH2. Additionally, this allosteric pathway is advantageous in energy compared with other methods. This study reveals the conformational transition of P-gp, which contributes to an understanding of the allosteric mechanism of ABC exporters.

Cryo-EM analysis provides new mechanistic insight into ATP binding to Ca2+ -ATPase SERCA2b

Sarco/endoplasmic reticulum Ca²⁺ -ATPase (SERCA) 2b is a ubiquitous SERCA family member that conducts Ca²⁺ uptake from the cytosol to the ER. Herein, we present a 3.3 Å resolution cryo-electron microscopy (cryo-EM) structure of human SERCA2b in the E1·2Ca²⁺ state, revealing a new conformation for Ca²⁺ -bound SERCA2b with a much closer arrangement of cytosolic domains than in the previously reported crystal structure of Ca²⁺ -bound SERCA1a. Multiple conformations generated by 3D classification of cryo-EM maps reflect the intrinsically dynamic nature of the cytosolic domains in this state. Notably, ATP binding residues of SERCA2b in the E1·2Ca²⁺ state are located at similar positions to those in the E1·2Ca²⁺ -ATP state; hence, the cryo-EM structure likely represents a preformed state immediately prior to ATP binding. Consistently, a SERCA2b mutant with an interdomain disulfide bridge that locks the closed cytosolic domain arrangement displayed significant autophosphorylation activity in the presence of Ca²⁺ . We propose a novel mechanism of ATP binding to SERCA2b.

Low-Frequency Harmonic Perturbations Drive Protein Conformational Changes

Protein dynamics has been investigated since almost half a century, as it is believed to constitute the fundamental connection between structure and function. Elastic network models (ENMs) have been widely used to predict protein dynamics, flexibility and the biological mechanism, from which remarkable results have been found regarding the prediction of protein conformational changes. Starting from the knowledge of the reference structure only, these conformational changes have been usually predicted either by looking at the individual mode shapes of vibrations (i.e., by considering the free vibrations of the ENM) or by applying static perturbations to the protein network (i.e., by considering a linear response theory). In this paper, we put together the two previous approaches and evaluate the complete protein response under the application of dynamic perturbations. Harmonic forces with random directions are applied to the protein ENM, which are meant to simulate the single frequency-dependent components of the collisions of the surrounding particles, and the protein response is computed by solving the dynamic equations in the underdamped regime, where mass, viscous damping and elastic stiffness contributions are explicitly taken into account. The obtained motion is investigated both in the coordinate space and in the sub-space of principal components (PCs). The results show that the application of perturbations in the low-frequency range is able to drive the protein conformational change, leading to remarkably high values of direction similarity. Eventually, this suggests that protein conformational change might be triggered by external collisions and favored by the inherent low-frequency dynamics of the protein structure.

The interplay between mitochondria and store-operated Ca2+ entry: Emerging insights into cardiac diseases

Store‐operated Ca²⁺ entry (SOCE) machinery, including Orai channels, TRPCs, and STIM1, is key to cellular calcium homeostasis. The following characteristics of mitochondria are involved in the physiological and pathological regulation of cells: mitochondria mediate calcium uptake through calcium uniporters; mitochondria are regulated by mitochondrial dynamic related proteins (OPA1, MFN1/2, and DRP1) and form mitochondrial networks through continuous fission and fusion; mitochondria supply NADH to the electron transport chain through the Krebs cycle to produce ATP; under stress, mitochondria will produce excessive reactive oxygen species to regulate mitochondria‐endoplasmic reticulum interactions and the related signalling pathways. Both SOCE and mitochondria play critical roles in mediating cardiac hypertrophy, diabetic cardiomyopathy, and cardiac ischaemia‐reperfusion injury. All the mitochondrial characteristics mentioned above are determinants of SOCE activity, and vice versa. Ca²⁺ signalling dictates the reciprocal regulation between mitochondria and SOCE under the specific pathological conditions of cardiomyocytes. The coupling of mitochondria and SOCE is essential for various pathophysiological processes in the heart. Herein, we review the research focussing on the reciprocal regulation between mitochondria and SOCE and provide potential interplay patterns in cardiac diseases.

HOPMA: Boosting Protein Functional Dynamics with Colored Contact Maps

In light of the recent very rapid progress in protein structure prediction, accessing the multitude of functional protein states is becoming more central than ever before. Indeed, proteins are flexible macromolecules, and they often perform their function by switching between different conformations. However, high-resolution experimental techniques such as X-ray crystallography and cryogenic electron microscopy can catch relatively few protein functional states. Many others are only accessible under physiological conditions in solution. Therefore, there is a pressing need to fill this gap with computational approaches. We present HOPMA, a novel method to predict protein functional states and transitions by using a modified elastic network model. The method exploits patterns in a protein contact map, taking its 3D structure as input, and excludes some disconnected patches from the elastic network. Combined with nonlinear normal mode analysis, this strategy boosts the protein conformational space exploration, especially when the input structure is highly constrained, as we demonstrate on a set of more than 400 transitions. Our results let us envision the discovery of new functional conformations, which were unreachable previously, starting from the experimentally known protein structures. The method is computationally efficient and available at https://github.com/elolaine/HOPMA and https://team.inria.fr/nano-d/software/nolb-normal-modes.

Inferring functional units in ion channel pores via relative entropy

Coarse-grained protein models approximate the first-principle physical potentials. Among those modeling approaches, the relative entropy framework yields promising and physically sound results, in which a mapping from the target protein structure and dynamics to a model is defined and subsequently adjusted by an entropy minimization of the model parameters. Minimization of the relative entropy is equivalent to maximization of the likelihood of reproduction of (configurational ensemble) observations by the model. In this study, we extend the relative entropy minimization procedure beyond parameter fitting by a second optimization level, which identifies the optimal mapping to a (dimension-reduced) topology. We consider anisotropic network models of a diverse set of ion channels and assess our findings by comparison to experimental results.

Unravelling the molecular effect of ocellatin-1, F1, K1 and S1, the frog-skin antimicrobial peptides to enhance its therapeutics-quantum and molecular mechanical approaches

Ocellatin AMPs (antimicrobial peptides) are considered to be promising alternative therapeutics to conventional antibiotics. Three-dimensional (3D) structures of ocellatin-F1 with 25 residues have been reported to be potent in terms of bacterial membrane permeability. To investigate the influence of similar ocellatin peptides with 25 residues pertaining to antimicrobial effect, ocellatin-1, K1 and S1 peptides were modelled with ocellatin-F1 as template. Comparative analyses between these peptides were carried out, using computational approaches. From the results of in silico toxicity profile, all peptides were found to be non-toxic with no haemolytic activity. Further sequence analysis, net charge, hydrophobicity and hydrophobic moment revealed the membrane permeable efficacy of ocellatin-1 peptide. Besides, the investigation of peptide electronic structures through density functional theory and quantum chemical (HOMO and LUMO) calculations predicted ocellatin-1 to be a suitable peptide, which can be used as a scaffold for therapeutics. Furthermore, the determination of structural contours such as RMSD, RMSF and Rg through trajectory analysis revealed that ocellatin-1 exhibited strong structural stability. In addition, the trajectory analysis of elements of secondary structure illustrated the alpha helical conformations to be retained in all peptides, except ocellatin-1. On the aforementioned grounds, ocellatin-1 was found to possess the important role of peptide penetration of the bacterial membrane. This study becomes significant, since it is the first time where the structural importance of ocellatin peptides were explored in detail and the therapeutic potential of ocellatin-1 as a peptide-based antimicrobial drug have been theoretically revealed.

Molecular Dynamics Simulation Techniques as Tools in Drug Discovery and Pharmacology: A Focus on Allosteric Drugs

Allosteric drugs are ligands that when bound to an allosteric site modify the conformational state of the pharmacological target, leading then to a modification of functional response upon binding of the endogenous ligand. Pharmacological targets are defined as biological entities, to which a ligand/drug binds and leads to a functional effect. Pharmacological targets can be proteins or nucleic acids. Computational approaches such as molecular dynamics (MD) sped up discovery and identification of allosteric binding sites and allosteric ligands. Classical all-atom and hybrid classical/quantum MD simulations can be generalized as simulation techniques aimed at analysis of atoms and molecular motion. Main limitations of MD simulations are related to high computational costs, that in turn limit the conformational sampling of biological systems. Indeed, other techniques have been developed to overcome limitations of MD, such as enhanced sampling MD simulations. In this chapter, classical MD and enhanced sampling MD simulations will be described, along with their application to drug discovery, with a focus on allosteric drugs.

Data-guided Multi-Map variables for ensemble refinement of molecular movies

Driving molecular dynamics simulations with data-guided collective variables offer a promising strategy to recover thermodynamic information from structure-centric experiments. Here, the three-dimensional electron density of a protein, as it would be determined by cryo-EM or x-ray crystallography, is used to achieve simultaneously free-energy costs of conformational transitions and refined atomic structures. Unlike previous density-driven molecular dynamics methodologies that determine only the best map-model fits, our work employs the recently developed Multi-Map methodology to monitor concerted movements within equilibrium, non-equilibrium, and enhanced sampling simulations. Construction of all-atom ensembles along the chosen values of the Multi-Map variable enables simultaneous estimation of average properties, as well as real-space refinement of the structures contributing to such averages. Using three proteins of increasing size, we demonstrate that biased simulation along the reaction coordinates derived from electron densities can capture conformational transitions between known intermediates. The simulated pathways appear reversible with minimal hysteresis and require only low-resolution density information to guide the transition. The induced transitions also produce estimates for free energy differences that can be directly compared to experimental observables and population distributions. The refined model quality is superior compared to those found in the Protein Data Bank. We find that the best quantitative agreement with experimental free-energy differences is obtained using medium resolution density information coupled to comparatively large structural transitions. Practical considerations for probing the transitions between multiple intermediate density states are also discussed.

Dynamics-Driven Allostery Underlies Ca2+-Mediated Release of SERCA Inhibition by Phospholamban

Sarcoplasmic reticulum (SR) Ca2+-ATPase (SERCA) and phospholamban (PLB) are essential for intracellular Ca2+ transport in myocytes. Ca2+-dependent activation of SERCA-PLB provides a control function that regulates cytosolic and SR Ca2+ levels. Although experimental and computational studies alone have led to a greater insight into SERCA-PLB regulation, the structural mechanisms for Ca2+ binding reversing inhibition of the complex remain poorly understood. Therefore, we have performed atomistic simulations totaling 32.7 μs and cell-based intramolecular fluorescence resonance energy transfer (FRET) experiments to determine structural changes of PLB-bound SERCA in response to binding of a single Ca2+ ion. Complementary MD simulations and FRET experiments showed that open-to-closed transitions in the structure of the headpiece underlie PLB inhibition of SERCA, and binding of a single Ca2+ ion is sufficient to shift the protein population toward a structurally closed structure of the complex. Closure is accompanied by functional interactions between the N-domain β5-β6 loop and the A-domain and the displacement of the catalytic phosphorylation domain toward a competent structure. We propose that reversal of SERCA-PLB inhibition is achieved by stringing together its controlling modules (A-domain and loop Nβ5-β6) with catalytic elements (P-domain) to regulate function during intracellular Ca2+ signaling. We conclude that binding of a single Ca2+ is a critical mediator of allosteric signaling that dictates structural changes and motions that relieve SERCA inhibition by PLB. Understanding allosteric regulation is of paramount importance to guide therapeutic modulation of SERCA and other evolutionarily related ion-motive ATPases.

Atomistic Structure and Dynamics of the Ca2+-ATPase Bound to Phosphorylated Phospholamban

Sarcoplasmic reticulum Ca²⁺-ATPase (SERCA) and phospholamban (PLB) are essential components of the cardiac Ca²⁺ transport machinery. PLB phosphorylation at residue Ser16 (pSer16) enhances SERCA activity in the heart via an unknown structural mechanism. Here, we report a fully atomistic model of SERCA bound to phosphorylated PLB and study its structural dynamics on the microsecond time scale using all-atom molecular dynamics simulations in an explicit lipid bilayer and water environment. The unstructured N-terminal phosphorylation domain of PLB samples different orientations and covers a broad area of the cytosolic domain of SERCA but forms a stable complex mediated by pSer16 interactions with a binding site formed by SERCA residues Arg324/Lys328. PLB phosphorylation does not affect the interaction between the transmembrane regions of the two proteins; however, pSer16 stabilizes a disordered structure of the N-terminal phosphorylation domain that releases key inhibitory contacts between SERCA and PLB. We found that PLB phosphorylation is sufficient to guide the structural transitions of the cytosolic headpiece that are required to produce a competent structure of SERCA. We conclude that PLB phosphorylation serves as an allosteric molecular switch that releases inhibitory contacts and strings together the catalytic elements required for SERCA activation. This atomistic model represents a vivid atomic-resolution visualization of SERCA bound to phosphorylated PLB and provides previously inaccessible insights into the structural mechanism by which PLB phosphorylation releases SERCA inhibition in the heart.

Driving Protein Conformational Cycles in Physiology and Disease: "Frustrated" Amino Acid Interaction Networks Define Dynamic Energy Landscapes: Amino Acid Interaction Networks Change Progressively Along Alpha Tryptophan Synthase's Catalytic Cycle

A general framework by which dynamic interactions within a protein will promote the necessary series of structural changes, or "conformational cycle," required for function is proposed. It is suggested that the free-energy landscape of a protein is biased toward this conformational cycle. Fluctuations into higher energy, although thermally accessible, conformations drive the conformational cycle forward. The amino acid interaction network is defined as those intraprotein interactions that contribute most to the free-energy landscape. Some network connections are consistent in every structural state, while others periodically change their interaction strength according to the conformational cycle. It is reviewed here that structural transitions change these periodic network connections, which then predisposes the protein toward the next set of network changes, and hence the next structural change. These concepts are illustrated by recent work on tryptophan synthase. Disruption of these dynamic connections may lead to aberrant protein function and disease states.

Development and validation of a clinicopathological-based nomogram to predict seeding risk after percutaneous thermal ablation of primary liver carcinoma

Objectives

To develop a clinicopathological‐based nomogram to improve the prediction of the seeding risk of after percutaneous thermal ablation (PTA) in primary liver carcinoma (PLC).

Methods

A total of 2030 patients with PLC who underwent PTA were included between April 2009 and December 2018. The patients were grouped into a training dataset (n = 1024) and an external validation dataset (n = 1006). Baseline characteristics were collected to identify the risk factors of seeding after PTA. The multivariate Cox proportional hazards model based on the risk factors was used to develop the nomogram, which was used for assessment for its predictive accuracy using mainly the Harrell's C‐index and receiver operating characteristic curve (AUC).

Results

The median follow‐up time was 30.3 months (range, 3.2‐115.7 months). The seeding risk was 0.89% per tumor and 1.5% per patient in the training set. The nomogram was developed based on tumor size, subcapsular, α‐fetoprotein (AFP), and international normalized ratio (INR). The 1‐, 2‐, and 3‐year cumulative seeding rates were 0.1%, 0.7% and 1.2% in the low‐risk group, and 1.7%, 6.3% and 6.3% in the high‐risk group, respectively, showing significant statistical difference (P < .001). The nomogram had good calibration and discriminatory abilities in the training set, with C‐indexes of 0.722 (95% confidence interval [CI]: 0.661, 0.883) and AUC of 0.850 (95% CI: 0.767, 0.934). External validation with 1000 bootstrapped sample sets showed a good C‐index of 0.706 (95% CI: 0.546, 0.866) and AUC of 0.736 (95% CI: 0. 646, 0.827).

Conclusions

The clinicopathological‐based nomogram could be used to quantify the probability of seeding risk after PTA in PLC.

Towards gaining sight of multiscale events: utilizing network models and normal modes in hybrid methods

With the explosion of normal mode analyses (NMAs) based on elastic network models (ENMs) in the last decade, and the proven precision of MD simulations for visualizing interactions at atomic scale, many hybrid methods have been proposed in recent years. These aim at exploiting the best of both worlds: the atomic precision of MD that often fall short of exploring time and length scales of biological interest, and the capability of ENM-NMA to predict the cooperative and often functional rearrangements of large structures and assemblies, albeit at low resolution. We present an overview of recent progress in the field with examples of successful applications highlighting the utility of such hybrid methods and pointing to emerging future directions guided by advances in experimental characterization of biomolecular systems structure and dynamics.

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.

Higher Accuracy Achieved for Protein-Ligand Binding Pose Prediction by Elastic Network Model-Based Ensemble Docking

Molecular docking plays an indispensable role in predicting the receptor-ligand interactions in which the protein receptor is usually kept rigid, whereas the ligand is treated as being flexible. Because of the inherent flexibility of proteins, the binding pocket of apo receptors might undergo significant conformational rearrangement upon ligand binding, which limits the prediction accuracy of docking. Here, we present an iterative anisotropic network model (iterANM)-based ensemble docking approach, which generates multiple holo-like receptor structures starting from the apo receptor and incorporates protein flexibility into docking. In a validation data set consisting of 233 chemically diverse cyclin-dependent kinase 2 (CDK2) inhibitors, the iterANM-based ensemble docking achieves higher capacity to reproduce native-like binding poses compared with those using single apo receptor conformation or conformational ensemble from molecular dynamics simulations. The prediction success rate within the top5-ranked binding poses produced by the iterANM can further be improved through reranking with the molecular mechanics-Poisson-Boltzmann surface area method. In a smaller data set with 58 CDK2 inhibitors, the iterANM-based ensemble shows a higher success rate compared with the flexible receptor-based docking procedure AutoDockFR and other receptor conformation generation approaches. Further, an additional docking test consisting of 10 diverse receptor-ligand combinations shows that the iterANM is robustly applicable for different receptor structures. These results suggest the iterANM-based ensemble docking as an accurate, efficient, and practical framework to predict the binding mode of a ligand for receptors with flexibility.

Defining the mobility range of a hinge-type connection using molecular dynamics and metadynamics

A designed disulfide-rich β-hairpin peptide that dimerizes spontaneously served as a hinge-type connection between proteins. Here, we analyze the range of dynamics of this hinge dimer with the aim of proposing new applications for the DNA-encodable peptide and establishing guidelines for the computational analysis of other disulfide hinges. A recent structural analysis based on nuclear magnetic resonance spectroscopy and ion mobility spectrometry revealed an averaged conformation in the hinge region which motivated us to investigate the dynamic behavior using a combination of molecular dynamics simulation, metadynamics and free energy surface analysis to characterize the conformational space available to the hinge. Principal component analysis uncovered two slow modes of the peptide, namely, the opening and closing motion and twisting of the two β-hairpins assembling the hinge. Applying a collective variable (CV) that mimics the first dominating mode, led to a major expansion of the conformational space. The description of the dynamics could be achieved by analysis of the opening angle and the twisting of the β-hairpins and, thus, offers a methodology that can also be transferred to other derivatives. It has been demonstrated that the hinge peptide’s lowest energy conformation consists of a large opening angle and strong twist but is separated by small energy barriers and can, thus, adopt a closed and untwisted structure. With the aim of proposing further applications for the hinge peptide, we simulated its behavior in the sterically congested environment of a four-helix bundle. Preliminary investigations show that one helix is pushed out and a three-helix bundle forms. The insights gained into the dynamics of the tetra-disulfide peptide and analytical guidelines developed in this study may contribute to the understanding of the structure and function of more complex hinge-type proteins, such as the IgG antibody family.

Structural dynamics of P-type ATPase ion pumps

P-type ATPases transport ions across biological membranes against concentration gradients and are essential for all cells. They use the energy from ATP hydrolysis to propel large intramolecular movements, which drive vectorial transport of ions. Tight coordination of the motions of the pump is required to couple the two spatially distant processes of ion binding and ATP hydrolysis. Here, we review our current understanding of the structural dynamics of P-type ATPases, focusing primarily on Ca2+ pumps. We integrate different types of information that report on structural dynamics, primarily time-resolved fluorescence experiments including single-molecule Förster resonance energy transfer and molecular dynamics simulations, and interpret them in the framework provided by the numerous crystal structures of sarco/endoplasmic reticulum Ca2+-ATPase. We discuss the challenges in characterizing the dynamics of membrane pumps, and the likely impact of new technologies on the field.

Large-Scale Biomolecular Conformational Transitions Explored by a Combined Elastic Network Model and Enhanced Sampling Molecular Dynamics

Biomolecules often undergo large-scale conformational transitions when carrying out their functions. However, it is still challenging for conventional molecular dynamics simulations to provide adequate structural dynamics information to interpret associated mechanisms. Here, we present a combined elastic network model and enhanced sampling-based strategy (iterANM-IaMD) by adopting iterANM to construct initial conformation space and enhanced sampling IaMD to explore the free energy landscape along specific large-scale conformational transitions. We applied this strategy to three functionally and structurally distinct proteins (adenylate kinase, calmodulin, and p38α kinase), which undergo striking conformational change upon ligand binding. The simulation results for both free and ligand-bound proteins show qualitative and quantitative agreement with existing studies, suggesting iterANM-IaMD as an accurate and efficient tool to investigate structural dynamics involved in complicated biological processes. Our work also provides insights into the relationship between the dynamics and functionality of biomolecules.

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.

Structure functional insights into calcium binding during the activation of coagulation factor XIII A

The dimeric FXIII-A₂, a pro-transglutaminase is the catalytic part of the heterotetrameric coagulation FXIII-A₂B₂ complex that upon activation by calcium binding/thrombin cleavage covalently cross-links preformed fibrin clots protecting them from premature fibrinolysis. Our study characterizes the recently disclosed three calcium binding sites of FXIII-A concerning evolution, mutual crosstalk, thermodynamic activation profile, substrate binding, and interaction with other similarly charged ions. We demonstrate unique structural aspects within FXIII-A calcium binding sites that give rise to functional differences making FXIII unique from other transglutaminases. The first calcium binding site showed an antagonistic relationship towards the other two. The thermodynamic profile of calcium/thrombin-induced FXIII-A activation explains the role of bulk solvent in transitioning its zymogenic dimeric form to an activated monomeric form. We also explain the indirect effect of solvent ion concentration on FXIII-A activation. Our study suggests FXIII-A calcium binding sites could be putative pharmacologically targetable regions.

Attenuating dependence on structural data in computing protein energy landscapes

Background

Nearly all cellular processes involve proteins structurally rearranging to accommodate molecular partners. The energy landscape underscores the inherent nature of proteins as dynamic molecules interconverting between structures with varying energies. In principle, reconstructing a protein’s energy landscape holds the key to characterizing the structural dynamics and its regulation of protein function. In practice, the disparate spatio-temporal scales spanned by the slow dynamics challenge both wet and dry laboratories. However, the growing number of deposited structures for proteins central to human biology presents an opportunity to infer the relevant dynamics via exploitation of the information encoded in such structures about equilibrium dynamics.

Results

Recent computational efforts using extrinsic modes of motion as variables have successfully reconstructed detailed energy landscapes of several medium-size proteins. Here we investigate the extent to which one can reconstruct the energy landscape of a protein in the absence of sufficient, wet-laboratory structural data. We do so by integrating intrinsic modes of motion extracted off a single structure in a stochastic optimization framework that supports the plug-and-play of different variable selection strategies. We demonstrate that, while knowledge of more wet-laboratory structures yields better-reconstructed landscapes, precious information can be obtained even when only one structural model is available.

Conclusions

The presented work shows that it is possible to reconstruct the energy landscape of a protein with reasonable detail and accuracy even when the structural information about the protein is limited to one structure. By attenuating the dependence on structural data of methods designed to compute protein energy landscapes, the work opens up interesting venues of research on structure-based inference of dynamics. Of particular interest are directions of research that will extend such inference to proteins with no experimentally-characterized structures.

Generalization of the elastic network model for the study of large conformational changes in biomolecules

The elastic network (EN) is a prime model that describes the long-time dynamics of biomolecules. However, the use of harmonic potentials renders this model insufficient for studying large conformational changes of proteins (e.g. stretching of proteins, folding and thermal unfolding). Here, we extend the capabilities of the EN model by using a harmonic approximation described by Lennard-Jones (LJ) interactions for far contacts and native contacts obtained from the standard overlap criterion as in the case of Gō-like models. While our model is validated against the EN model by reproducing the equilibrium properties for a number of proteins, we also show that the model is suitable for the study of large conformation changes by providing various examples. In particular, this is illustrated on the basis of pulling simulations that predict with high accuracy the experimental data on the rupture force of the studied proteins. Furthermore, in the case of DDFLN4 protein, our pulling simulations highlight the advantages of our model with respect to Gō-like approaches, where the latter fail to reproduce previous results obtained by all-atom simulations that predict an additional characteristic peak for this protein. In addition, folding simulations of small peptides yield different folding times for α-helix and β-hairpin, in agreement with experiment, in this way providing further opportunities for the application of our model in studying large conformational changes of proteins. In contrast to the EN model, our model is suitable for both normal mode analysis and molecular dynamics simulation. We anticipate that the proposed model will find applications in a broad range of problems in biology, including, among others, protein folding and thermal unfolding.

Advances in coarse-grained modeling of macromolecular complexes

Recent progress in coarse-grained (CG) molecular modeling and simulation has facilitated an influx of computational studies on biological macromolecules and their complexes. Given the large separation of length-scales and time-scales that dictate macromolecular biophysics, CG modeling and simulation are well-suited to bridge the microscopic and mesoscopic or macroscopic details observed from all-atom molecular simulations and experiments, respectively. In this review, we first summarize recent innovations in the development of CG models, which broadly include structure-based, knowledge-based, and dynamics-based approaches. We then discuss recent applications of different classes of CG models to explore various macromolecular complexes. Finally, we conclude with an outlook for the future in this ever-growing field of biomolecular modeling.

Structure-Guided Protein Transition Modeling with a Probabilistic Roadmap Algorithm

Proteins are macromolecules in perpetual motion, switching between structural states to modulate their function. A detailed characterization of the precise yet complex relationship between protein structure, dynamics, and function requires elucidating transitions between functionally-relevant states. Doing so challenges both wet and dry laboratories, as protein dynamics involves disparate temporal scales. In this paper, we present a novel, sampling-based algorithm to compute transition paths. The algorithm exploits two main ideas. First, it leverages known structures to initialize its search and define a reduced conformation space for rapid sampling. This is key to address the insufficient sampling issue suffered by sampling-based algorithms. Second, the algorithm embeds samples in a nearest-neighbor graph where transition paths can be efficiently computed via queries. The algorithm adapts the probabilistic roadmap framework that is popular in robot motion planning. In addition to efficiently computing lowest-cost paths between any given structures, the algorithm allows investigating hypotheses regarding the order of experimentally-known structures in a transition event. This novel contribution is likely to open up new venues of research. Detailed analysis is presented on multiple-basin proteins of relevance to human disease. Multiscaling and the AMBER ff14SB force field are used to obtain energetically-credible paths at atomistic detail.

Proton Countertransport and Coupled Gating in the Sarcoplasmic Reticulum Calcium Pump

The calcium pump of the sarcoplasmic reticulum (SERCA) is an ATP-driven active transporter of Ca²⁺ ions that functions via an "alternating-access" cycle mechanism. In each cycle, SERCA transports two Ca²⁺ ions toward the lumen of the sarcoplasmic reticulum and two to three protons to the cytoplasm. How the latter conformational transition is coupled to cytoplasmic release of protons remains poorly understood. The present computational study shows how the mechanism of proton countertransport is coupled to the alternating access gating process in SERCA. Molecular dynamics simulation trajectories are generated starting from a series of configurations taken along the E2 to E1 transition pathway determined by the string method with swarms-of-trajectories. Simulations of different protonation configurations at the binding sites reveal how deprotonation events affect the opening of the cytoplasmic gate. The results show that there is a strong coupling between the chronological order of deprotonation, the entry of water molecules into the TM region, and the opening of the cytoplasmic gate. Deprotonation of E309 and E771 is sequential with E309 being the first to lose the proton. The deprotonation promotes the opening of the cytoplasmic gate but leads to a productive gating transition only if it occurs after the transmembrane domain has reached an intermediate conformation. Deprotonation of E309 and E771 is unproductive when it occurs too early because it causes the re-opening of the luminal gate.

Generating conformational transition paths with low potential-energy barriers for proteins

The knowledge of conformational transition paths in proteins can be useful for understanding protein mechanisms. Recently, we have introduced the As-Rigid-As-Possible (ARAP) interpolation method, for generating interpolation paths between two protein conformations. The method was shown to preserve well the rigidity of the initial conformation along the path. However, because the method is totally geometry-based, the generated paths may be inconsistent because the atom interactions are ignored. Therefore, in this article, we would like to introduce a new method to generate conformational transition paths with low potential-energy barriers for proteins. The method is composed of three processing stages. First, ARAP interpolation is used for generating an initial path. Then, the path conformations are enhanced by a clash remover. Finally, Nudged Elastic Band, a path-optimization method, is used to produce a low-energy path. Large energy reductions are found in the paths obtained from the method than in those obtained from the ARAP interpolation method alone. The results also show that ARAP interpolation is a good candidate for generating an initial path because it leads to lower potential-energy paths than two other common methods for path interpolation.

Mechanical transduction of cytoplasmic-to-transmembrane-domain movements in a hyperpolarization-activated cyclic nucleotide-gated cation channel

Hyperpolarization-activated cyclic nucleotide–gated cation (HCN) channels play a critical role in the control of pacemaking in the heart and repetitive firing in neurons. In HCN channels, the intracellular cyclic nucleotide–binding domain (CNBD) is connected to the transmembrane portion of the channel (TMPC) through a helical domain, the C-linker. Although this domain is critical for mechanical signal transduction, the conformational dynamics in the C-linker that transmit the nucleotide-binding signal to the HCN channel pore are unknown. Here, we use linear response theory to analyze conformational changes in the C-linker of the human HCN1 protein, which couple cAMP binding in the CNBD with gating in the TMPC. By applying a force to the tip of the so-called “elbow” of the C-linker, the coarse-grained calculations recapitulate the same conformational changes triggered by cAMP binding in experimental studies. Furthermore, in our simulations, a displacement of the C-linker parallel to the membrane plane (i.e. horizontally) induced a rotational movement resulting in a distinct tilting of the transmembrane helices. This movement, in turn, increased the distance between the voltage-sensing S4 domain and the surrounding transmembrane domains and led to a widening of the intracellular channel gate. In conclusion, our computational approach, combined with experimental data, thus provides a more detailed understanding of how cAMP binding is mechanically coupled over long distances to promote voltage-dependent opening of HCN channels.

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.

Elastic network model of learned maintained contacts to predict protein motion

We present a novel elastic network model, lmcENM, to determine protein motion even for localized functional motions that involve substantial changes in the protein's contact topology. Existing elastic network models assume that the contact topology remains unchanged throughout the motion and are thus most appropriate to simulate highly collective function-related movements. lmcENM uses machine learning to differentiate breaking from maintained contacts. We show that lmcENM accurately captures functional transitions unexplained by the classical ENM and three reference ENM variants, while preserving the simplicity of classical ENM. We demonstrate the effectiveness of our approach on a large set of proteins covering different motion types. Our results suggest that accurately predicting a "deformation-invariant" contact topology offers a promising route to increase the general applicability of ENMs. We also find that to correctly predict this contact topology a combination of several features seems to be relevant which may vary slightly depending on the protein. Additionally, we present case studies of two biologically interesting systems, Ferric Citrate membrane transporter FecA and Arachidonate 15-Lipoxygenase.

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.

Augmenting the anisotropic network model with torsional potentials improves PATH performance, enabling detailed comparison with experimental rate data

PATH algorithms for identifying conformational transition states provide computational parameters-time to the transition state, conformational free energy differences, and transition state activation energies-for comparison to experimental data and can be carried out sufficiently rapidly to use in the "high throughput" mode. These advantages are especially useful for interpreting results from combinatorial mutagenesis experiments. This report updates the previously published algorithm with enhancements that improve correlations between PATH convergence parameters derived from virtual variant structures generated by RosettaBackrub and previously published kinetic data for a complete, four-way combinatorial mutagenesis of a conformational switch in Tryptophanyl-tRNA synthetase.

Methodology for the Simulation of Molecular Motors at Different Scales

Millisecond-scale conformational transitions represent a seminal challenge for traditional molecular dynamics simulations, even with the help of high-end supercomputer architectures. Such events are particularly relevant to the study of molecular motors-proteins or abiological constructs that convert chemical energy into mechanical work. Here, we present a hybrid-simulation scheme combining an array of methods including elastic network models, transition path sampling, and advanced free-energy methods, possibly in conjunction with generalized-ensemble schemes to deliver a viable option for capturing the millisecond-scale motor steps of biological motors. The methodology is already implemented in large measure in popular molecular dynamics programs, and it can leverage the massively parallel capabilities of petascale computers. The applicability of the hybrid method is demonstrated with two examples, namely cyclodextrin-based motors and V-type ATPases.

High-Dimensional Mutant and Modular Thermodynamic Cycles, Molecular Switching, and Free Energy Transduction

Understanding how distinct parts of proteins produce coordinated behavior has driven and continues to drive advances in protein science and enzymology. However, despite consensus about the conceptual basis for allostery, the idiosyncratic nature of allosteric mechanisms resists general approaches. Computational methods can identify conformational transition states from structural changes, revealing common switching mechanisms that impose multistate behavior. Thermodynamic cycles use factorial perturbations to measure coupling energies between side chains in molecular switches that mediate shear during domain motion. Such cycles have now been complemented by modular cycles that measure energetic coupling between separable domains. For one model system, energetic coupling between domains has been shown to be quantitatively equivalent to that between dynamic side chains. Linkages between domain motion, switching residues, and catalysis make nucleoside triphosphate hydrolysis conditional on domain movement, confirming an essential yet neglected aspect of free energy transduction and suggesting the potential generality of these studies.