Large amplitude conformational change in proteins explored with a plastic network model: adenylate kinase

Genome-Wide Identification and Expression Analysis of ADK Gene Family Members in Cotton under Abiotic Stress

Adenosine kinase (ADK) is a key enzyme widely distributed in plants, playing an important role in maintaining cellular energy homeostasis and regulating plant growth, development, and responses to environmental stresses. However, research on ADK genes in cotton (Gossypium hirsutum), an economically significant crop, has been limited. This study identified 92 ADK genes from four cotton species (G. arboreum, G. raimondii, G. hirsutum, and G. barbadense) using HMMER and Local BLASTP methods and classified them into six groups. Chromosomal localization revealed a random distribution of ADK genes in G. hirsutum, with 13 genes located on the At subgenome and 14 genes on the Dt subgenome. Gene structure analysis showed consistency in exon-intron organization within subgroups, while conserved motif analysis identified subgroup-specific motifs, indicating functional diversity. Synteny and collinearity mapping analysis revealed that the primary expansion mechanisms of the ADK gene family in cotton are polyploidy and segmental duplication. Cis-regulatory elements in GhADK promoters were classified into light response, hormone response, developmental regulation, and stress response. We also analyzed the expression patterns of GhADK genes under a low temperature (4 °C) and drought conditions. Most GhADK genes responded to cold stress with different expression patterns, indicating their roles in rapid response and long-term cold adaptation. Under drought stress, expression patterns varied, with some genes showing sustained high expression levels. The qRT-PCR validation of transcriptomic data confirmed the stress-induced expression patterns of selected GhADK genes. Functional analysis through the VIGS silencing of GhADK25 demonstrated its importance in cold and drought stress responses, with silencing resulting in poor growth under stress, highlighting its significance in stress tolerance. This study provides a basis for further understanding the evolutionary relationships and functions of the cotton ADK gene family.

NMR and Single-Molecule FRET Insights into Fast Protein Motions and Their Relation to Function

Proteins often undergo large-scale conformational transitions, in which secondary and tertiary structure elements (loops, helices, and domains) change their structures or their positions with respect to each other. Simple considerations suggest that such dynamics should be relatively fast, but the functional cycles of many proteins are often relatively slow. Sophisticated experimental methods are starting to tackle this dichotomy and shed light on the contribution of large-scale conformational dynamics to protein function. In this review, we focus on the contribution of single-molecule Förster resonance energy transfer and nuclear magnetic resonance (NMR) spectroscopies to the study of conformational dynamics. We briefly describe the state of the art in each of these techniques and then point out their similarities and differences, as well as the relative strengths and weaknesses of each. Several case studies, in which the connection between fast conformational dynamics and slower function has been demonstrated, are then introduced and discussed. These examples include both enzymes and large protein machines, some of which have been studied by both NMR and fluorescence spectroscopies.

Membrane lateral organization from potential energy disconnectivity graph

Understanding the thermodynamic and kinetic properties of biomolecules requires elucidation of their complex energy landscape. A disconnectivity graph analysis of the energy landscape provides a framework for mapping the multi-dimensional landscape onto a two-dimensional representation while preserving the key features of the energy landscape. Several studies show that the structure or shape of the disconnectity graph is directly associated with the function of protein and nucleic acid molecules. In this review, we discuss how disconnectivity analysis of the potential energy surface can be extended to lipid molecules to glean important information about membrane organization. The shape of the disconnectivity graphs can be used to predict the lateral organization of multi-component lipid bilayer. We hope that this review encourages the use of disconnectivity graphs routinely by membrane biophysicists to predict the lateral organization of lipids.

The ATPase asymmetry: Novel computational insight into coupling diverse FO motors with tripartite F1

ATP synthase, a crucial enzyme for cellular bioenergetics, operates via the coordinated coupling of an FO motor, which presents variable symmetry, and a tripartite F1 motor. Despite extensive research, the understanding of their coupling dynamics, especially with non-10-fold symmetrical FO motors, remains incomplete. This study investigates the coupling patterns between eightfold and ninefold FO motors and the constant threefold F1 motor using coarse-grained molecular dynamics simulations. We unveil that in the case of a ninefold FO motor, a 3-3-3 motion is most likely to occur, whereas a 3-3-2 motion predominates with an eightfold FO motor. Furthermore, our findings propose a revised model for the coupling method, elucidating that the pathways' energy usage is primarily influenced by F1 rotation and conformational changes hindered by the b-subunits. Our results present a crucial step toward comprehending the energy landscape and mechanisms governing ATP synthase operation.

Study on the allosteric activation mechanism of SHP2 via elastic network models and neural relational inference molecular dynamics simulation

As a ubiquitous protein tyrosine phosphatase, SHP2 is involved in PD-1/PD-L1 mediated tumor immune escape and undergoes substantial conformational changes. Therefore, it is considered an ideal target for tumor intervention. However, the allosteric mechanisms of SHP2 binding PD-1 intracellular ITIM/ITSM phosphopeptides remain unclear, which greatly hinders the development of novel structure-based anticancer allosteric inhibitors. In this work, the open and closed structural models of SHP2 are first constructed based on this knowledge; next their motion modes are investigated via elastic network models such as the Gaussian network model (GNM), anisotropic network model (ANM) and adaptive anisotropic network model (aANM); and finally, a possible allosteric signaling pathway is proposed using a neural relational inference molecular dynamics (NRI-MD) simulation embedded with an artificial intelligence (AI) strategy. In GNM and ANM, the N-SH2, C-SH2 and PTP domains all exhibit distinct dynamics partitions, and the N-SH2/C-SH2 regions show a rigid rotation relative to PTP. According to a series of intermediate snapshots given by aANM, N-SH2 is first identified with pY223 specifically, inducing a D'E-loop to change from β-sheets to random coils, and then, C-SH2 serves as a fulcrum to drive N-SH2 to rotate 110° completely away from the original active sites of PTP. Finally, a possible allosteric signaling-transfer path for SHP2, namely R220-R138-T108-R32, is proposed based on NRI-MD sampling. This work provides a possible allosteric mechanism of SHP2, which is helpful for the following design of novel allosteric inhibitors and is expected to be used in clinical synergies with PD-1 monoclonal antibody.

FO-F1 coupling and symmetry mismatch in ATP synthase resolved in every FO rotation step

FOF1 ATP synthase, a ubiquitous enzyme that synthesizes most ATP in living cells, is composed of two rotary motors: a membrane-embedded proton-driven FO motor and a catalytic F1 motor. These motors share both central and peripheral stalks. Although both FO and F1 have pseudo-symmetric structures, their symmetries do not match. How symmetry mismatch is solved remains elusive because of the missing intermediate structures of the rotational steps. Here, for the case of Bacillus PS3 ATP synthases with three- and 10-fold symmetries in F1 and FO, respectively, we uncovered the mechanical couplings between FO and F1 at every 36° rotation step via molecular dynamics simulations and comparative studies of cryoelectron microscopy (cryo-EM) structures from three species. We found that the mismatch could be solved using several elements: 1) the F1 head partially rotates relative to the FO a subunit via elastic distortion of the b subunits, 2) the rotor is twisted, and 3) comparisons of cryo-EM structures further suggest that the c ring rotary angles can deviate from the symmetric ones. In addition, the F1 motor may have non-canonical structures, relieving stronger frustration. Thus, we provide new insights for solving the symmetry mismatch problem.

Allosteric communication between ligand binding domains modulates substrate inhibition in adenylate kinase

Enzymes play a vital role in life processes; they control chemical reactions and allow functional cycles to be synchronized. Many enzymes harness large-scale motions of their domains to achieve tremendous catalytic prowess and high selectivity for specific substrates. One outstanding example is provided by the three-domain enzyme adenylate kinase (AK), which catalyzes phosphotransfer between ATP to AMP. Here we study the phenomenon of substrate inhibition by AMP and its correlation with domain motions. Using single-molecule FRET spectroscopy, we show that AMP does not block access to the ATP binding site, neither by competitive binding to the ATP cognate site nor by directly closing the LID domain. Instead, inhibitory concentrations of AMP lead to a faster and more cooperative domain closure by ATP, leading in turn to an increased population of the closed state. The effect of AMP binding can be modulated through mutations throughout the structure of the enzyme, as shown by the screening of an extensive AK mutant library. The mutation of multiple conserved residues reduces substrate inhibition, suggesting that substrate inhibition is an evolutionary well conserved feature in AK. Combining these insights, we developed a model that explains the complex activity of AK, particularly substrate inhibition, based on the experimentally observed opening and closing rates. Notably, the model indicates that the catalytic power is affected by the microsecond balance between the open and closed states of the enzyme. Our findings highlight the crucial role of protein motions in enzymatic activity.

Role of Repeated Conformational Transitions in Substrate Binding of Adenylate Kinase

The catalytic cycle of the enzyme adenylate kinase involves large conformational motions between open and closed states. A previous single-molecule experiment showed that substrate binding tends to accelerate both the opening and the closing rates and that a single turnover event often involves multiple rounds of conformational switching. In this work, we showed that the repeated conformational transitions of adenylate kinase are essential for the relaxation of incorrectly bound substrates into the catalytically competent conformation by combining all-atom and coarse-grained molecular simulations. In addition, free energy calculations based on all-atom and coarse-grained models demonstrated that the enzyme with incorrectly bound substrates has much a lower free energy barrier for domain opening compared to that with the correct substrate conformation, which may explain the the acceleration of the domain opening rate by substrate binding. The results of this work provide mechanistic understanding to previous experimental observations and shed light onto the interplay between conformational dynamics and enzyme catalysis.

Integration of Adenylate Kinase 1 with Its Peptide Conformational Imprint

In the present study, molecularly imprinted polymers (MIPs) were used as a tool to grasp a targeted α-helix or β-sheet of protein. During the fabrication of the hinge-mediated MIPs, elegant cavities took shape in a special solvent on quartz crystal microbalance (QCM) chips. The cavities, which were complementary to the protein secondary structure, acted as a peptide conformational imprint (PCI) for adenylate kinase 1 (AK1). We established a promising strategy to examine the binding affinities of human AK1 in conformational dynamics using the peptide-imprinting method. Moreover, when bound to AK1, PCIs are able to gain stability and tend to maintain higher catalytic activities than free AK1. Such designed fixations not only act on hinges as accelerators; some are also inhibitors. One example of PCI inhibition of AK1 catalytic activity takes place when PCI integrates with an AK1_9-23 β-sheet. In addition, conformation ties, a general MIP method derived from random-coil AK1_133-144 in buffer/acetonitrile, are also inhibitors. The inhibition may be due to the need for this peptide to execute conformational transition during catalysis.

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.

Protein Fluctuations in Response to Random External Forces

Elastic network models (ENMs) have been widely used in the last decades to investigate protein motions and dynamics. There the intrinsic fluctuations based on the isolated structures are obtained from the normal modes of these elastic networks, and they generally show good agreement with the B-factors extracted from X-ray crystallographic experiments, which are commonly considered to be indicators of protein flexibility. In this paper, we propose a new approach to analyze protein fluctuations and flexibility, which has a more appropriate physical basis. It is based on the application of random forces to the protein ENM to simulate the effects of collisions of solvent on a protein structure. For this purpose, we consider both the Cα-atom coarse-grained anisotropic network model (ANM) and an elastic network augmented with points included for the crystallized waters. We apply random forces to these protein networks everywhere, as well as only on the protein surface alone. Despite the randomness of the directions of the applied perturbations, the computed average displacements of the protein network show a remarkably good agreement with the experimental B-factors. In particular, for our set of 919 protein structures, we find that the highest correlation with the B-factors is obtained when applying forces to the external surface of the water-augmented ANM (an overall gain of 3% in the Pearson’s coefficient for the entire dataset, with improvements up to 30% for individual proteins), rather than when evaluating the fluctuations obtained from the normal modes of a standard Cα-atom coarse-grained ANM. It follows that protein fluctuations should be considered not just as the intrinsic fluctuations of the internal dynamics, but also equally well as responses to external solvent forces, or as a combination of both.

Cooperative multivalent receptor binding promotes exposure of the SARS-CoV-2 fusion machinery core

The molecular events that permit the spike glycoprotein of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) to bind and enter cells are important to understand for both fundamental and therapeutic reasons. Spike proteins consist of S1 and S2 domains, which recognize angiotensin-converting enzyme 2 (ACE2) receptors and contain the viral fusion machinery, respectively. Ostensibly, the binding of spike trimers to ACE2 receptors promotes dissociation of the S1 domains and exposure of the fusion machinery, although the molecular details of this process have yet to be observed. We report the development of bottom-up coarse-grained (CG) models consistent with cryo-electron tomography data, and the use of CG molecular dynamics simulations to investigate viral binding and S2 core exposure. We show that spike trimers cooperatively bind to multiple ACE2 dimers at virion-cell interfaces in a manner distinct from binding between soluble proteins, which processively induces S1 dissociation. We also simulate possible variant behavior using perturbed CG models, and find that ACE2-induced S1 dissociation is primarily sensitive to conformational state populations and the extent of S1/S2 cleavage, rather than ACE2 binding affinity. These simulations reveal an important concerted interaction between spike trimers and ACE2 dimers that primes the virus for membrane fusion and entry.

Physics of biomolecular recognition and conformational dynamics

Biomolecular recognition usually leads to the formation of binding complexes, often accompanied by large-scale conformational changes. This process is fundamental to biological functions at the molecular and cellular levels. Uncovering the physical mechanisms of biomolecular recognition and quantifying the key biomolecular interactions are vital to understand these functions. The recently developed energy landscape theory has been successful in quantifying recognition processes and revealing the underlying mechanisms. Recent studies have shown that in addition to affinity, specificity is also crucial for biomolecular recognition. The proposed physical concept of intrinsic specificity based on the underlying energy landscape theory provides a practical way to quantify the specificity. Optimization of affinity and specificity can be adopted as a principle to guide the evolution and design of molecular recognition. This approach can also be used in practice for drug discovery using multidimensional screening to identify lead compounds. The energy landscape topography of molecular recognition is important for revealing the underlying flexible binding or binding-folding mechanisms. In this review, we first introduce the energy landscape theory for molecular recognition and then address four critical issues related to biomolecular recognition and conformational dynamics: (1) specificity quantification of molecular recognition; (2) evolution and design in molecular recognition; (3) flexible molecular recognition; (4) chromosome structural dynamics. The results described here and the discussions of the insights gained from the energy landscape topography can provide valuable guidance for further computational and experimental investigations of biomolecular recognition and conformational dynamics.

Normal-mode driven exploration of protein domain motions

Domain motions involved in the function of proteins can often be well described as a combination of motions along a handfull of low-frequency modes, that is, with the values of a few normal coordinates. This means that, when the functional motion of a protein is unknown, it should prove possible to predict it, since it amounts to guess a few values. However, without the help of additional experimental data, using normal coordinates for generating accurate conformers far away from the initial one is not so straightforward. To do so, a new approach is proposed: instead of building conformers directly with the values of a subset of normal coordinates, they are built in two steps, the conformer built with normal coordinates being just used for defining a set of distance constraints, the final conformer being built so as to match them. Note that this approach amounts to transform the problem of generating accurate protein conformers using normal coordinates into a better known one: the distance-geometry problem, which is herein solved with the help of the ROSETTA software. In the present study, this approach allowed to rebuild accurately six large amplitude conformational changes, using at most six low-frequency normal coordinates. As a consequence of the low-dimensionality of the corresponding subspace, random exploration also proved enough for generating low-energy conformers close to the known end-point of the conformational change of the LAO binding protein, lysozyme T4 and adenylate kinase.

Allosteric and transport modulation of human concentrative nucleoside transporter 3 at the atomic scale

Nucleosides are important precursors of nucleotide synthesis in cells, and nucleoside transporters play an important role in many physiological processes by mediating transmembrane transport and absorption. During nucleoside transport, such proteins undergo a significant conformational transition between the outward- and inward-facing states, which leads to alternating access of the substrate-binding site to either side of the membrane. In this work, a variety of molecular simulation methods have been applied to comparatively investigate the motion modes of human concentrative nucleoside transporter 3 (hCNT3) in three states, as well as global and local cavity conformational changes; and finally, a possible elevator-like transport mechanism consistent with experimental data was proposed. The results of the Gaussian network model (GNM) and anisotropic network model (ANM) show that hCNT3 as a whole tends to contract inwards and shift towards a membrane inside, exhibiting an allosteric process that is more energetically favorable than the rigid conversion. To reveal the complete allosteric process of hCNT3 in detail, a series of intermediate conformations were obtained by an adaptive anisotropic network model (aANM). One of the simulated intermediate states is similar to that of a crystal structure, which indicates that the allosteric process is reliable; the state with lower energy is slightly inclined to the inward-facing structure rather than the expected intermediate crystal structure. The final HOLE analysis showed that except for the outward-facing state, the transport channels were gradually enlarged, which was conductive to the directional transport of nucleosides. Our work provides a theoretical basis for the multistep elevator-like transportation mechanism of nucleosides, which helps to further understand the dynamic recognition between nucleoside substrates and hCNT3 as well as the design of nucleoside anticancer drugs.

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.

A generic force field for simulating native protein structures using dissipative particle dynamics

A coarse-grained force field for molecular dynamics simulations of the native structures of proteins in a dissipative particle dynamics (DPD) framework is developed. The parameters for bonded interactions are derived by mapping the bonds and angles for 20 amino acids onto target distributions obtained from fully atomistic simulations in explicit solvent. A dual-basin potential is introduced for stabilizing backbone angles, to cover a wide spectrum of protein secondary structures. The backbone dihedral potential enables folding of the protein from an unfolded initial state to the folded native structure. The proposed force field is validated by evaluating the structural properties of several model peptides and proteins including the SARS-CoV-2 fusion peptide, consisting of α-helices, β-sheets, loops and turns. Detailed comparisons with fully atomistic simulations are carried out to assess the ability of the proposed force field to stabilize the different secondary structures present in proteins. The compact conformations of the native states were evident from the radius of gyration and the high intensity peaks of the root mean square deviation histograms, which were found to be within 0.4 nm. The Ramachandran-like energy landscape on the phase space of backbone angles (θ) and dihedrals (ϕ) effectively captured the conformational phase space of α-helices at ∼(ϕ = 50°,θ = 90°) and β-strands at ∼(ϕ = ±180°,θ = 90-120°). Furthermore, the residue-residue native contacts were also well reproduced by the proposed DPD model. The applicability of the model to multidomain complexes was assessed using lysozyme and a large α-helical bacterial pore-forming toxin, cytolysin A. Our study illustrates that the proposed force field is generic, and can potentially be extended for efficient in silico investigations of membrane bound polypeptides and proteins using DPD simulations.

Multiscale Enhanced Sampling Using Machine Learning

Multiscale enhanced sampling (MSES) allows for an enhanced sampling of all-atom protein structures by coupling with the accelerated dynamics of the associated coarse-grained (CG) model. In this paper, we propose an MSES extension to replace the CG model with the dynamics on the reduced subspace generated by a machine learning approach, the variational autoencoder (VAE). The molecular dynamic (MD) trajectories of the ribose-binding protein (RBP) in both the closed and open forms were used as the input by extracting the inter-residue distances as the structural features in order to train the VAE model, allowing the encoded latent layer to characterize the difference in the structural dynamics of the closed and open forms. The interpolated data characterizing the RBP structural change in between the closed and open forms were thus efficiently generated in the low-dimensional latent space of the VAE, which was then decoded into the time-series data of the inter-residue distances and was useful for driving the structural sampling at an atomistic resolution via the MSES scheme. The free energy surfaces on the latent space demonstrated the refinement of the generated data that had a single basin into the simulated data containing two closed and open basins, thus illustrating the usefulness of the MD simulation together with the molecular mechanics force field in recovering the correct structural ensemble.

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.

Understanding enzyme behavior in a crowded scenario through modulation in activity, conformation and dynamics

Macromolecular crowding, inside the physiological interior, modulates the energy landscape of biological macromolecules in multiple ways. Amongst these, enzymes occupy a special place and hence understanding the function of the same in the crowded interior is of utmost importance. In this study, we have investigated the manner in which the multidomain enzyme, AK3L1 (PDB ID: 1ZD8), an isoform of adenylate kinase, has its features affected in presence of commonly used crowders (PEG 8, Dextran 40, Dextran 70, and Ficoll 70). Michaelis Menten plots reveal that the crowders in general enhance the activity of the enzyme, with the K_m and V_max values showing significant variations. Ficoll 70, induced the maximum activity for AK3L1 at 100 g/L, beyond which the activity reduced. Ensemble FRET studies were performed to provide insights into the relative domain (LID and CORE) displacements in presence of the crowders. Solvation studies reveal that the protein matrix surrounding the probe CPM (7-diethylamino-3-(4-maleimido-phenyl)-4-methylcoumarin) gets restricted in presence of the crowders, with Ficoll 70 providing the maximum rigidity, the same being linked to the decrease in the activity of the enzyme. Through our multipronged approach, we have observed a distinct correlation between domain displacement, enzyme activity and associated dynamics. Thus, keeping in mind the complex nature of enzyme activity and the surrounding bath of dense soup that the biological entity remains immersed in, indeed more such approaches need to be undertaken to have a better grasp of the "enzymes in the crowd".

Genome-Wide Identification and Expression Analysis of Tomato ADK Gene Family during Development and Stress

Adenylate kinase (ADK) is widely distributed in organisms and plays an important role in cellular energy homeostasis. In plants, ADK has important functions in plant growth and development regulation as well as in adaptation to the environment. However, little information is available about the ADK genes in tomato (Solanum lycopersicum), an important economic crop. To investigate the characteristics and functions of ADK genes in tomato, a total of 11 ADK genes were identified and named according to their chromosomal locations. The ADK family in Arabidopsis, tomato, potato, and rice was divided into six groups, and motif analysis revealed that each SlADK protein contained five to eight conserved motifs. A total of 4 to 19 exons were identified in tomato ADK gene family members, and interestingly, most members possessed 4 exons. Several stress response elements were identified in the promoter regions of SlADKs. The 11 SlADKs were randomly distributed on 9 of the 12 tomato chromosomes. Three duplication events were observed between tomato chromosomes, and a high degree of conservation of synteny was demonstrated between tomato and potato. The online TomExpress platform prediction revealed that SlADKs were expressed in various tissues and organs, basically consistent with the data obtained from real-time quantitative PCR (qPCR). The qPCR verification was also performed to determine the expression level of SlADKs and demonstrated that the genes responded to multiple abiotic stresses, such as drought, salt, and cold. Besides, the qPCR results showed that SlADK transcription was responsive to most of the applied hormone treatment. For correlation network analysis under 44 global conditions, the results showed that the number of 17, 3, 4, and 6 coexpressed genes matched with SlADK5, 8, 9, and 11, respectively. For specific gene function analysis, expression of SlADK10 was inhibited using virus-induced gene silencing (VIGS). Compared to wild-type plants, plants with silenced SlADK10 gene had poor drought resistance, indicating SlADK10 regulated drought tolerance of tomato positively. In summary, the information provided in the present study will be helpful to understand the evolutionary relationship and their roles of tomato ADK gene family in further research.

Cooperative multivalent receptor binding promotes exposure of the SARS-CoV-2 fusion machinery core

The molecular events that permit the spike glycoprotein of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) to bind, fuse, and enter cells are important to understand for both fundamental and therapeutic reasons. Spike proteins consist of S1 and S2 domains, which recognize angiotensin-converting enzyme 2 (ACE2) receptors and contain the viral fusion machinery, respectively. Ostensibly, the binding of spike trimers to ACE2 receptors promotes the preparation of the fusion machinery by dissociation of the S1 domains. We report the development of bottom-up coarse-grained (CG) models validated with cryo-electron tomography (cryo-ET) data, and the use of CG molecular dynamics simulations to investigate the dynamical mechanisms involved in viral binding and exposure of the S2 trimeric core. We show that spike trimers cooperatively bind to multiple ACE2 dimers at virion-cell interfaces. The multivalent interaction cyclically and processively induces S1 dissociation, thereby exposing the S2 core containing the fusion machinery. Our simulations thus reveal an important concerted interaction between spike trimers and ACE2 dimers that primes the virus for membrane fusion and entry.

Coarse-Grained Modeling of Multiple Pathways in Conformational Transitions of Multi-Domain Proteins

Large-scale conformational transitions in multi-domain proteins are often essential for their functions. To investigate the transitions, it is necessary to explore multiple potential pathways, which involve different intermediate structures. Here, we present a multi-basin (MB) coarse-grained (CG) structure-based Go̅ model for describing transitions in proteins with more than two moving domains. This model is an extension of our dual-basin Go̅ model in which system-dependent parameters are determined systematically using the multistate Bennett acceptance ratio method. In the MB Go̅ model for multi-domain proteins, we assume that intermediate structures may have partial inter-domain native contacts. This approach allows us to search multiple transition pathways that involve distinct intermediate structures using the CG molecular dynamics (MD) simulations. We apply this scheme to an enzyme, adenylate kinase (AdK), which has three major domains and can move along two different pathways. Using the optimized mixing parameters for each pathway, AdK shows frequent transitions between the Open, Closed, and the intermediate basins and samples a wide variety of conformations within each basin. The explored multiple transition pathways could be compared with experimental data and examined in more detail by atomistic MD simulations.

A multiscale coarse-grained model of the SARS-CoV-2 virion

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is the causative agent of the COVID-19 pandemic. Computer simulations of complete viral particles can provide theoretical insights into large-scale viral processes including assembly, budding, egress, entry, and fusion. Detailed atomistic simulations are constrained to shorter timescales and require billion-atom simulations for these processes. Here, we report the current status and ongoing development of a largely "bottom-up" coarse-grained (CG) model of the SARS-CoV-2 virion. Data from a combination of cryo-electron microscopy (cryo-EM), x-ray crystallography, and computational predictions were used to build molecular models of structural SARS-CoV-2 proteins, which were then assembled into a complete virion model. We describe how CG molecular interactions can be derived from all-atom simulations, how viral behavior difficult to capture in atomistic simulations can be incorporated into the CG models, and how the CG models can be iteratively improved as new data become publicly available. Our initial CG model and the detailed methods presented are intended to serve as a resource for researchers working on COVID-19 who are interested in performing multiscale simulations of the SARS-CoV-2 virion.

A Multiscale Coarse-grained Model of the SARS-CoV-2 Virion

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is the causative agent of the COVID-19 pandemic. Computer simulations of complete viral particles can provide theoretical insights into large-scale viral processes including assembly, budding, egress, entry, and fusion. Detailed atomistic simulations, however, are constrained to shorter timescales and require billion-atom simulations for these processes. Here, we report the current status and on-going development of a largely "bottom-up" coarse-grained (CG) model of the SARS-CoV-2 virion. Structural data from a combination of cryo-electron microscopy (cryo-EM), x-ray crystallography, and computational predictions were used to build molecular models of structural SARS-CoV-2 proteins, which were then assembled into a complete virion model. We describe how CG molecular interactions can be derived from all-atom simulations, how viral behavior difficult to capture in atomistic simulations can be incorporated into the CG models, and how the CG models can be iteratively improved as new data becomes publicly available. Our initial CG model and the detailed methods presented are intended to serve as a resource for researchers working on COVID-19 who are interested in performing multiscale simulations of the SARS-CoV-2 virion.

Significance Statement

This study reports the construction of a molecular model for the SARS-CoV-2 virion and details our multiscale approach towards model refinement. The resulting model and methods can be applied to and enable the simulation of SARS-CoV-2 virions.

Double-Well Ultra-Coarse-Grained Model to Describe Protein Conformational Transitions

The double-well model is usually used to describe the conformational transition between two states of a protein. Since conformational changes usually occur within a relatively large time scale, coarse-grained models are often used to accelerate the dynamic process due to their inexpensive computational cost. In this work, we develop a double-well ultra-coarse-grained (DW-UCG) model to describe the conformational transitions of the adenylate kinase, glutamine-binding protein, and lactoferrin. The coarse-grained simulation results show that the DW-UCG model of adenylate kinase captures the crucial intermediate states in the LID-closing and NMP-closing pathways, reflecting the key secondary structural changes in the conformational transition. A comparison of the different DW-UCG models of adenylate kinase indicates that an appropriate choice of bead resolution could generate the free energy landscape that is comparable to that from the residue-based model. The coarse-grained simulations for the glutamine-binding protein and lactoferrin also demonstrate that the DW-UCG model is valid in reproducing the correct two-state behavior for their functional study, which indicates the potential application of the DW-UCG model in investigating the mechanism of conformational changes of large proteins.

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.

Role of substrate-product frustration on enzyme functional dynamics

Natural enzymes often have enormous catalytic power developed by evolution. Revealing the underlying physical strategy used by enzymes to achieve high catalysis efficiency is one of the central focuses in the field of biological physics. Our recent work demonstrated that multisubstrate enzymes can utilize steric frustration encountered in the substrate-product cobound complex to overcome the bottleneck of the enzymatic cycle [W. Li et al., Phys. Rev. Lett. 122, 238102 (2019)10.1103/PhysRevLett.122.238102]. However, the key atomic-level interactions by which the steric frustration contributes to the enzymatic cycle remain elusive. In this work we study the microscopic mechanism for the role of the substrate-product frustration on the key physical steps in the enzymatic cycle of adenylate kinase (AdK), a multisubstrate enzyme catalyzing the reversible phosphoryl transfer reaction ATP+AMP⇋ADP+ADP. By using atomistic molecular dynamics simulations with enhanced sampling, we showed that the competitive interactions from the phosphate groups of the substrate ATP and product ADP in the ATP-ADP cobound complex of the AdK lead to local frustration in the binding pockets. Such local frustration disrupts the hydrogen bond network around the binding pockets, which causes lowered barrier height for the opening of the enzyme conformations and expedited release of the bottleneck product ADP. Our results directly demonstrated from the atomistic level that the local frustration in the active sites of the enzyme can be utilized to facilitate the key physical steps of the enzymatic cycle, providing numerical evidence to the predictions of the previous theoretical work.

A Two-Ended Data-Driven Accelerated Sampling Method for Exploring the Transition Pathways between Two Known States of Protein

Conformational transitions of protein between different states are often associated with their biological functions. These dynamic processes, however, are usually not easy to be well characterized by experimental measurements, mainly because of inadequate temporal and spatial resolution. Meantime, sampling of configuration space with molecular dynamics (MD) simulations is still a challenge. Here we proposed a robust two-ended data-driven accelerated (teDA2) conformational sampling method, which drives the structural change in an adaptively updated feature space without introducing a bias potential. teDA2 was applied to explore adenylate kinase (ADK), a model with well characterized "open" and "closed" states. A single conformational transition event of ADK could be achieved within only a few or tens of nanoseconds sampled with teDA2. By analyzing hundreds of transition events, we reproduced different mechanisms and the associated pathways for domain motion of ADK reported in the literature. The multiroute characteristic of ADK was confirmed by the fact that some metastable states identified with teDA2 resemble available crystal structures determined at different conditions. This feature was further validated with Markov state modeling with independent MD simulations. Therefore, our work provides strong evidence for the conformational plasticity of protein, which is mainly due to the inherent degree of flexibility. As a reliable and efficient enhanced sampling protocol, teDA2 could be used to study the dynamics between functional states of various biomolecular machines.

Allosteric communication in molecular machines via information exchange: what can be learned from dynamical modeling

Allosteric regulation is crucial for the operation of protein machines and molecular motors. A major challenge is to characterize and quantify the information exchange underlying allosteric communication between remote functional sites in a protein, and to identify the involved relevant pathways. We review applications of two topical approaches of dynamical protein modeling, a kinetic-based single-molecule stochastic model, which employs information thermodynamics to quantify allosteric interactions, and structure-based coarse-grained modeling to characterize intra-molecular couplings in terms of conformational motions and propagating mechanical strain. Both descriptions resolve the directionality of allosteric responses within a protein, emphasizing the concept of causality as the principal hallmark of protein allostery. We discuss the application of techniques from information thermodynamics to dynamic protein elastic networks and evolutionary designed model structures, and the ramifications for protein allostery.

Building a macro-mixing dual-basin Gō model using the Multistate Bennett Acceptance Ratio

The dual-basin Gō-model is a structural-based coarsegrained model for simulating a conformational transition between two known structures of a protein. Two parameters are required to produce a dual-basin potential mixed using two single-basin potentials, although the determination of mixing parameters is usually not straightforward. Here, we have developed an efficient scheme to determine the mixing parameters using the Multistate Bennett Acceptance Ratio (MBAR) method after short simulations with a set of parameters. In the scheme, MBAR allows us to predict observables at various unsimulated conditions, which are useful to improve the mixing parameters in the next round of iterative simulations. The number of iterations that are necessary for obtaining the converged mixing parameters are significantly reduced in the scheme. We applied the scheme to two proteins, the glutamine binding protein and the ribose binding protein, for showing the effectiveness in the parameter determination. After obtaining the converged parameters, both proteins show frequent conformational transitions between open and closed states, providing the theoretical basis to investigate structure-dynamics-function relationships of the proteins.

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.

GPathFinder: Identification of Ligand-Binding Pathways by a Multi-Objective Genetic Algorithm

Protein-ligand docking is a widely used method to generate solutions for the binding of a small molecule with its target in a short amount of time. However, these methods provide identification of physically sound protein-ligand complexes without a complete view of the binding process dynamics, which has been recognized to be a major discriminant in binding affinity and ligand selectivity. In this paper, a novel piece of open-source software to approach this problem is presented, called GPathFinder. It is built as an extension of the modular GaudiMM platform and is able to simulate ligand diffusion pathways at atomistic level. The method has been benchmarked on a set of 20 systems whose ligand-binding routes were studied by other computational tools or suggested from experimental "snapshots". In all of this set, GPathFinder identifies those channels that were already reported in the literature. Interestingly, the low-energy pathways in some cases indicate novel possible binding routes. To show the usefulness of GPathFinder, the analysis of three case systems is reported. We believe that GPathFinder is a software solution with a good balance between accuracy and computational cost, and represents a step forward in extending protein-ligand docking capacities, with implications in several fields such as drug or enzyme design.

Overcoming the Bottleneck of the Enzymatic Cycle by Steric Frustration

The enormous catalytic power of natural enzymes relies on the ability to overcome the bottleneck event in the enzymatic cycle, yet the underlying physical mechanisms are not fully understood. Here, by performing molecular simulations of the whole enzymatic cycle for a model multisubstrate enzyme with a dynamic energy landscape model, we show that multisubstrate enzymes can utilize steric frustration to facilitate the rate-limiting product-release step. During the enzymatic cycles, the bottleneck product is actively squeezed out by the binding of a new substrate at the neighboring site through the population of a substrate-product cobound complex, in which the binding pockets are frustrated due to steric incompatibility. Such steric frustration thereby enables an active mechanism of product release driven by substrate-binding energy, facilitating the enzymatic cycle.

Multiconfigurational Coarse-Grained Molecular Dynamics

Standard low resolution coarse-grained modeling techniques have difficulty capturing multiple configurations of protein systems. Here, we present a method for creating accurate coarse-grained (CG) models with multiple configurations using a linear combination of functions or “states”. Individual CG models are created to capture the individual states, and the approximate coupling between the two states is determined from an all-atom potential of mean force. We show that the resulting multiconfiguration coarse-graining (MCCG) method accurately captures the transition state as well as the free energy between the two states. We have tested this method on the folding of dodecaalanine, as well as the amphipathic helix of endophilin.

Electrostatic interactions determine entrance/release order of substrates in the catalytic cycle of adenylate kinase

Adenylate kinase is a monomeric phosphotransferase with important biological function in regulating concentration of adenosine triphosphate (ATP) in cells, by transferring the terminal phosphate group from ATP to adenosine monophosphate (AMP) and forming two adenosine diphosphate (ADP) molecules. During this reaction, the kinase may undergo a large conformational transition, forming different states with its substrates. Although many structures of the protein are available, atomic details of the whole process remain unclear. In this article, we use both conventional molecular dynamics (MD) simulation and an enhanced sampling technique called parallel cascade selection MD simulation to explore different conformational states of the Escherichia coli adenylate kinase. Based on the simulation results, we propose a possible entrance/release order of substrates during the catalytic cycle. The substrate-free protein prefers an open conformation, but changes to a closed state once ATP·Mg enters into its binding pocket first and then AMP does. After the reaction of ATP transferring the terminal phosphate group to AMP, ADP·Mg and ADP are released sequentially, and finally the whole catalyze cycle is completed. Detailed contact and distance analysis reveals that the entrance/release order of substrates may be largely controlled by electrostatic interactions between the protein and the substrates.

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.

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.

Atomic clusters with addressable complexity

A general formulation for constructing addressable atomic clusters is introduced, based on one or more reference structures. By modifying the well depths in a given interatomic potential in favour of nearest-neighbour interactions that are defined in the reference(s), the potential energy landscape can be biased to make a particular permutational isomer the global minimum. The magnitude of the bias changes the resulting potential energy landscape systematically, providing a framework to produce clusters that should self-organise efficiently into the target structure. These features are illustrated for small systems, where all the relevant local minima and transition states can be identified, and for the low-energy regions of the landscape for larger clusters. For a 55-particle cluster, it is possible to design a target structure from a transition state of the original potential and to retain this structure in a doubly addressable landscape. Disconnectivity graphs based on local minima that have no direct connections to a lower minimum provide a helpful way to visualise the larger databases. These minima correspond to the termini of monotonic sequences, which always proceed downhill in terms of potential energy, and we identify them as a class of biminimum. Multiple copies of the target cluster are treated by adding a repulsive term between particles with the same address to maintain distinguishable targets upon aggregation. By tuning the magnitude of this term, it is possible to create assemblies of the target cluster corresponding to a variety of structures, including rings and chains.

Interaction between adenylate kinase 3 and glyceraldehyde-3-phosphate dehydrogenase from Chlamydomonas reinhardtii

The critical and ubiquitous enzyme adenylate kinase (ADK) catalyzes the nucleotide phosphoryl exchange reaction: 2ADP ↔ ATP + AMP. The ADK3 in the chloroplasts of the green alga Chlamydomonas reinhardtii, bears an unusual C-terminal extension that is similar to the C-terminal end of the intrinsically disordered protein CP12. In this study, we report that this enzyme, when oxidized but not when reduced, is able to interact with the chloroplast glyceraldehyde-3-phosphate dehydrogenase (GAPDH) forming a stable complex as shown by native electrophoresis and mass spectrometry. In this bienzyme complex, the activity of ADK3 is unchanged while the NADPH-dependent activity of GAPDH is significantly inhibited. Moreover ADK3, like CP12, can protect GAPDH against thermal inactivation and aggregation. The ADK3-GAPDH bienzyme complex is unable to recruit phosphoribulokinase (PRK), in contrast with the ternary complex formed between GAPDH-CP12 and PRK. The interaction between ADK3 and GAPDH might be a mechanism to regulate the crucial ATP: NADPH ratio within chloroplasts to optimize the Calvin-Benson cycle during rapid fluctuation in environmental resources.

ENZYMES

Adenylate kinase (EC 2.7.4.3), glyceraldehyde-3-phosphate dehydrogenase (GAPDH, EC 1.2.1.13), phosphoribulokinase (PRK, EC 2.7.1.19).

Dissipation at the angstrom scale: Probing the surface and interior of an enzyme

Pursuing a materials science approach to understanding the deformability of enzymes, we introduce measurements of the phase of the mechanical response function within the nanorheology paradigm. Driven conformational motion of the enzyme is dissipative as characterized by the phase measurements. The dissipation originates both from the surface hydration layer and the interior of the molecule, probed by examining the effect of point mutations on the mechanics. We also document changes in the mechanics of the enzyme examined, guanylate kinase, upon binding its four substrates. GMP binding stiffens the molecule, ATP and ADP binding softens it, while there is no clear mechanical signature of GDP binding. A hyperactive two-Gly mutant is found to possibly trade specificity for speed. Global deformations of enzymes are shown to be dependent on both hydration layer and polypeptide chain dynamics.

Morphing and docking visualisation of biomolecular structures using Multi-Dimensional Scaling

Protein structures are often solved at atomic resolution in two states defining a functional movement but intervening conformations are usually unknown. Morphing methods generate intervening conformations between two known structures. When viewed as an animation using molecular graphics, a smooth, direct morph enables the eye to track changes in structure that might be otherwise missed. We present a morphing method that aims to linearly interpolate interatomic distances and which uses SMACOF (Scaling by MAjorisation of COmplicated Function) and multigrid techniques with a cut-off distance based weighting that optimizes the MolProbity score of intervening structures. The all-atom morphs are smooth, move directly between the two structures, and are shown, in general, to pass closer to a set of known intermediates than those generated using other methods. The techniques are also used for docking by putting the unbound structures in a "near-approach pose" and then morphing to the bound complex. The resulting GPU-accelerated tools are available on a webserver, Morphit_Pro, at http://morphit-pro.cmp.uea.ac.uk/ and more than 5000 domains movements available at the DynDom website can now be viewed as morphs http://morphit-pro.cmp.uea.ac.uk/dyndom/.