Structure of the complex between adenylate kinase from Escherichia coli and the inhibitor Ap5A refined at 1.9 A resolution. A model for a catalytic transition state

Toward the Prediction of Binding Events in Very Flexible, Allosteric, Multidomain Proteins

Knowledge of the structures formed by proteins and small molecules is key to understand the molecular principles of chemotherapy and for designing new and more effective drugs. During the early stage of a drug discovery program, it is customary to predict ligand-protein complexes in silico, particularly when screening large compound databases. While virtual screening based on molecular docking is widely used for this purpose, it generally fails in mimicking binding events associated with large conformational changes in the protein, particularly when the latter involve multiple domains. In this work, we describe a new methodology to generate bound-like conformations of very flexible and allosteric proteins bearing multiple binding sites by exploiting only information on the unbound structure and the putative binding sites. The protocol is validated on the paradigm enzyme adenylate kinase, for which we generated a significant fraction of bound-like structures. A fraction of these conformations, employed in ensemble-docking calculations, allowed to find native-like poses of substrates and inhibitors (binding to the active form of the enzyme), as well as catalytically incompetent analogs (binding the inactive form). Our protocol provides a general framework for the generation of bound-like conformations of challenging drug targets that are suitable to host different ligands, demonstrating high sensitivity to the fine chemical details that regulate protein's activity. We foresee applications in virtual screening, in the prediction of the impact of amino acid mutations on structure and dynamics, and in protein engineering.

Interplay between conformational dynamics and substrate binding regulates enzymatic activity: a single-molecule FRET study

Proteins often harness extensive motions of domains and subunits to promote their function. Deciphering how these movements impact activity is key for understanding life's molecular machinery. The enzyme adenylate kinase is an intriguing example for this relationship; it ensures efficient catalysis by large-scale domain motions that lead to the enclosure of the bound substrates ATP and AMP. Surprisingly, the enzyme is activated by urea, a compound commonly acting as a denaturant. We utilize this phenomenon to decipher the involvement of conformational dynamics in the mechanism of action of the enzyme. Combining single-molecule FRET spectroscopy and enzymatic activity studies, we find that urea promotes the open conformation of the enzyme, aiding the proper positioning of the substrates. Further, urea decreases AMP affinity, paradoxically facilitating a more efficient progression towards the catalytically active complex. These results allow us to define a complete kinetic scheme that includes the open/close transitions of the enzyme and to unravel the important interplay between conformational dynamics and chemical steps, a general property of enzymes. State-of-the-art tools, such as single-molecule fluorescence spectroscopy, offer new insights into how enzymes balance different conformations to regulate activity.

Structural diversity of axonemes across mammalian motile cilia

Reproduction, development and homeostasis depend on motile cilia, whose rhythmic beating is powered by a microtubule-based molecular machine called the axoneme. Although an atomic model of the axoneme is available for the alga Chlamydomonas reinhardtii1, structures of mammalian axonemes are incomplete1-5. Furthermore, we do not fully understand how molecular structures of axonemes vary across motile-ciliated cell types in the body. Here we use cryoelectron microscopy, cryoelectron tomography and proteomics to resolve the 96-nm modular repeat of axonemal doublet microtubules (DMTs) from both sperm flagella and epithelial cilia of the oviduct, brain ventricles and respiratory tract. We find that sperm DMTs are the most specialized, with epithelial cilia having only minor differences across tissues. We build a model of the mammalian sperm DMT, defining the positions and interactions of 181 proteins including 34 newly identified proteins. We elucidate the composition of radial spoke 3 and uncover binding sites of kinases associated with regeneration of ATP and regulation of ciliary motility. We discover a sperm-specific, axoneme-tethered T-complex protein ring complex (TRiC) chaperone that may contribute to construction or maintenance of the long flagella of mammalian sperm. We resolve axonemal dyneins in their prestroke states, illuminating conformational changes that occur during ciliary movement. Our results illustrate how elements of chemical and mechanical regulation are embedded within the axoneme, providing valuable resources for understanding the aetiology of ciliopathy and infertility, and exemplifying the discovery power of modern structural biology.

Identifying the minimal sets of distance restraints for FRET-assisted protein structural modeling

Proteins naturally occur in crowded cellular environments and interact with other proteins, nucleic acids, and organelles. Since most previous experimental protein structure determination techniques require that proteins occur in idealized, non-physiological environments, the effects of realistic cellular environments on protein structure are largely unexplored. Recently, Förster resonance energy transfer (FRET) has been shown to be an effective experimental method for investigating protein structure in vivo. Inter-residue distances measured in vivo can be incorporated as restraints in molecular dynamics (MD) simulations to model protein structural dynamics in vivo. Since most FRET studies only obtain inter-residue separations for a small number of amino acid pairs, it is important to determine the minimum number of restraints in the MD simulations that are required to achieve a given root-mean-square deviation (RMSD) from the experimental structural ensemble. Further, what is the optimal method for selecting these inter-residue restraints? Here, we implement several methods for selecting the most important FRET pairs and determine the number of pairsN r $$ {N}_r $$ that are needed to induce conformational changes in proteins between two experimentally determined structures. We find that enforcing only a small fraction of restraints,N r / N ≲ 0.08 $$ {N}_r/N\lesssim 0.08 $$ , whereN $$ N $$ is the number of amino acids, can induce the conformational changes. These results establish the efficacy of FRET-assisted MD simulations for atomic scale structural modeling of proteins in vivo.

Allostery can convert binding free energies into concerted domain motions in enzymes

Enzymatic mechanisms are typically inferred from structural data. However, understanding enzymes require unravelling the intricate dynamic interplay between dynamics, conformational substates, and multiple protein structures. Here, we use single-molecule nanopore analysis to investigate the catalytic conformational changes of adenylate kinase (AK), an enzyme that catalyzes the interconversion of various adenosine phosphates (ATP, ADP, and AMP). Kinetic analysis validated by hidden Markov models unravels the details of domain motions during catalysis. Our findings reveal that allosteric interactions between ligands and cofactor enable converting binding energies into directional conformational changes of the two catalytic domains of AK. These coordinated motions emerged to control the exact sequence of ligand binding and the affinity for the three different substrates, thereby guiding the reactants along the reaction coordinates. Interestingly, we find that about 10% of enzymes show altered allosteric regulation and ligand affinities, indicating that a subset of enzymes folds in alternative catalytically active forms. Since molecules or proteins might be able to selectively stabilize one of the folds, this observation suggests an evolutionary path for allostery in enzymes. In AK, this complex catalytic framework has likely emerged to prevent futile ATP/ADP hydrolysis and to regulate the enzyme for different energy needs of the cell.

Predicting binding events in very flexible, allosteric, multi-domain proteins

Knowledge of the structures formed by proteins and small molecules is key to understand the molecular principles of chemotherapy and for designing new and more effective drugs. During the early stage of a drug discovery program, it is customary to predict ligand-protein complexes in silico, particularly when screening large compound databases. While virtual screening based on molecular docking is widely used for this purpose, it generally fails in mimicking binding events associated with large conformational changes in the protein, particularly when the latter involve multiple domains. In this work, we describe a new methodology to generate bound-like conformations of very flexible and allosteric proteins bearing multiple binding sites by exploiting only information on the unbound structure and the putative binding sites. The protocol is validated on the paradigm enzyme adenylate kinase, for which we generated a significant fraction of bound-like structures. A fraction of these conformations, employed in ensemble-docking calculations, allowed to find native-like poses of substrates and inhibitors (binding to the active form of the enzyme), as well as catalytically incompetent analogs (binding the inactive form). Our protocol provides a general framework for the generation of bound-like conformations of challenging drug targets that are suitable to host different ligands, demonstrating high sensitivity to the fine chemical details that regulate protein's activity. We foresee applications in virtual screening, in the prediction of the impact of amino acid mutations on structure and dynamics, and in protein engineering.

Evolutionary-Scale Enzymology Enables Biochemical Constant Prediction Across a Multi-Peaked Catalytic Landscape

Quantitatively mapping enzyme sequence-catalysis landscapes remains a critical challenge in understanding enzyme function, evolution, and design. Here, we expand an emerging microfluidic platform to measure catalytic constants-k cat and K M-for hundreds of diverse naturally occurring sequences and mutants of the model enzyme Adenylate Kinase (ADK). This enables us to dissect the sequence-catalysis landscape's topology, navigability, and mechanistic underpinnings, revealing distinct catalytic peaks organized by structural motifs. These results challenge long-standing hypotheses in enzyme adaptation, demonstrating that thermophilic enzymes are not slower than their mesophilic counterparts. Combining the rich representations of protein sequences provided by deep-learning models with our custom high-throughput kinetic data yields semi-supervised models that significantly outperform existing models at predicting catalytic parameters of naturally occurring ADK sequences. Our work demonstrates a promising strategy for dissecting sequence-catalysis landscapes across enzymatic evolution and building family-specific models capable of accurately predicting catalytic constants, opening new avenues for enzyme engineering and functional prediction.

Modeling Conformational Transitions of Biomolecules from Atomic Force Microscopy Images using Normal Mode Analysis

Observing a single biomolecule performing its function is fundamental in biophysics as it provides important information for elucidating the mechanism. High-speed atomic force microscopy (HS-AFM) is a unique and powerful technique that allows the observation of biomolecular motion in a near-native environment. However, the spatial resolution of HS-AFM is limited by the physical size of the cantilever tip, which restricts the ability to obtain atomic details of molecules. In this study, we propose a novel computational algorithm designed to derive atomistic models of conformational dynamics from AFM images. Our method uses normal-mode analysis to describe the expected motions of the molecule, allowing these motions to be represented with a limited number of coordinates. This approach mitigates the problem of overinterpretation inherent in the analysis of AFM images with limited resolution. We demonstrate the effectiveness of our algorithm, NMFF-AFM, using synthetic data sets for three proteins that undergo significant conformational changes. NMFF-AFM is a fast and user-friendly program that requires minimal setup and has the potential to be a valuable tool for biophysical studies using HS-AFM.

Enzyme activation by urea reveals the interplay between conformational dynamics and substrate binding: a single-molecule FRET study

Proteins often harness extensive motions of domains and subunits to promote their function. Deciphering how these movements impact activity is key for understanding life's molecular machinery. The enzyme adenylate kinase is an intriguing example for this relationship; it ensures efficient catalysis by large-scale domain motions that lead to the enclosure of the bound substrates ATP and AMP. At high concentrations, AMP also operates as an allosteric inhibitor of the protein. Surprisingly, the enzyme is activated by urea, a compound commonly acting as a denaturant. Combining single-molecule FRET spectroscopy and enzymatic activity studies, we find that urea interferes with two key mechanisms that contribute to enzyme efficacy. First, urea promotes the open conformation of the enzyme, aiding the proper positioning of the substrates. Second, urea decreases AMP affinity, paradoxically facilitating a more efficient progression towards the catalytically active complex. These results signify the important interplay between conformational dynamics and chemical steps, including binding, in the activity of enzymes. State-of-the-art tools, such as single-molecule fluorescence spectroscopy, offer new insights into how enzymes balance different conformations to regulate activity.

Magnesium induced structural reorganization in the active site of adenylate kinase

Phosphoryl transfer is a fundamental reaction in cellular signaling and metabolism that requires Mg2+ as an essential cofactor. While the primary function of Mg2+ is electrostatic activation of substrates, such as ATP, the full spectrum of catalytic mechanisms exerted by Mg2+ is not known. In this study, we integrate structural biology methods, molecular dynamic (MD) simulations, phylogeny, and enzymology assays to provide molecular insights into Mg2+-dependent structural reorganization in the active site of the metabolic enzyme adenylate kinase. Our results demonstrate that Mg2+ induces a conformational rearrangement of the substrates (ATP and ADP), resulting in a 30° adjustment of the angle essential for reversible phosphoryl transfer, thereby optimizing it for catalysis. MD simulations revealed transitions between conformational substates that link the fluctuation of the angle to large-scale enzyme dynamics. The findings contribute detailed insight into Mg2+ activation of enzymes and may be relevant for reversible and irreversible phosphoryl transfer reactions.

Bayesian reweighting of biomolecular structural ensembles using heterogeneous cryo-EM maps with the cryoENsemble method

Cryogenic electron microscopy (cryo-EM) has emerged as a powerful method for the determination of structures of complex biological molecules. The accurate characterisation of the dynamics of such systems, however, remains a challenge. To address this problem, we introduce cryoENsemble, a method that applies Bayesian reweighting to conformational ensembles derived from molecular dynamics simulations to improve their agreement with cryo-EM data, thus enabling the extraction of dynamics information. We illustrate the use of cryoENsemble to determine the dynamics of the ribosome-bound state of the co-translational chaperone trigger factor (TF). We also show that cryoENsemble can assist with the interpretation of low-resolution, noisy or unaccounted regions of cryo-EM maps. Notably, we are able to link an unaccounted part of the cryo-EM map to the presence of another protein (methionine aminopeptidase, or MetAP), rather than to the dynamics of TF, and model its TF-bound state. Based on these results, we anticipate that cryoENsemble will find use for challenging heterogeneous cryo-EM maps for biomolecular systems encompassing dynamic components.

MDFF_NM: Improved Molecular Dynamics Flexible Fitting into Cryo-EM Density Maps with a Multireplica Normal Mode-Based Search

Molecular Dynamics Flexible Fitting (MDFF) is a widely used tool to refine high-resolution structures into cryo-EM density maps. Despite many successful applications, MDFF is still limited by its high computational cost, overfitting, accuracy, and performance issues due to entrapment within wrong local minima. Modern ensemble-based MDFF tools have generated promising results in the past decade. In line with these studies, we present MDFF_NM, a stochastic hybrid flexible fitting algorithm combining Normal Mode Analysis (NMA) and simulation-based flexible fitting. Initial tests reveal that, besides accelerating the fitting process, MDFF_NM increases the diversity of fitting routes leading to the target, uncovering ensembles of conformations in closer agreement with experimental data. The potential integration of MDFF_NM with other existing methods and integrative modeling pipelines is also discussed.

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.

Protecting Lyophilized Escherichia coli Adenylate Kinase

Drying protein-based drugs, usually via lyophilization, can facilitate storage at ambient temperature and improve accessibility but many proteins cannot withstand drying and must be formulated with protective additives called excipients. However, mechanisms of protection are poorly understood, precluding rational formulation design. To better understand dry proteins and their protection, we examine Escherichia coli adenylate kinase (AdK) lyophilized alone and with the additives trehalose, maltose, bovine serum albumin, cytosolic abundant heat soluble protein D, histidine, and arginine. We apply liquid-observed vapor exchange NMR to interrogate the residue-level structure in the presence and absence of additives. We pair these observations with differential scanning calorimetry data of lyophilized samples and AdK activity assays with and without heating. We show that the amino acids do not preserve the native structure as well as sugars or proteins and that after heating the most stable additives protect activity best.

Towards the understanding of molecular motors and its relationship with local unfolding

Molecular motors are machines essential for life since they convert chemical energy into mechanical work. However, the precise mechanism by which nucleotide binding, catalysis, or release of products is coupled to the work performed by the molecular motor is still not entirely clear. This is due, in part, to a lack of understanding of the role of force in the mechanical-structural processes involved in enzyme catalysis. From a mechanical perspective, one promising hypothesis is the Haldane-Pauling hypothesis which considers the idea that part of the enzymatic catalysis is strain-induced. It suggests that enzymes cannot be efficient catalysts if they are fully complementary to the substrates. Instead, they must exert strain on the substrate upon binding, using enzyme-substrate energy interaction (binding energy) to accelerate the reaction rate. A novel idea suggests that during catalysis, significant strain energy is built up, which is then released by a local unfolding/refolding event known as 'cracking'. Recent evidence has also shown that in catalytic reactions involving conformational changes, part of the heat released results in a center-of-mass acceleration of the enzyme, raising the possibility that the heat released by the reaction itself could affect the enzyme's integrity. Thus, it has been suggested that this released heat could promote or be linked to the cracking seen in proteins such as adenylate kinase (AK). We propose that the energy released as a consequence of ligand binding/catalysis is associated with the local unfolding/refolding events (cracking), and that this energy is capable of driving the mechanical work.

The Biochemical Impact of Extracting an Embedded Adenylate Kinase Domain Using Circular Permutation

Adenylate kinases (AKs) have evolved AMP-binding and lid domains that are encoded as continuous polypeptides embedded at different locations within the discontinuous polypeptide encoding the core domain. A prior study showed that AK homologues of different stabilities consistently retain cellular activity following circular permutation that splits a region with high energetic frustration within the AMP-binding domain into discontinuous fragments. Herein, we show that mesophilic and thermophilic AKs having this topological restructuring retain activity and substrate-binding characteristics of the parental AK. While permutation decreased the activity of both AK homologues at physiological temperatures, the catalytic activity of the thermophilic AK increased upon permutation when assayed >30 °C below the melting temperature of the native AK. The thermostabilities of the permuted AKs were uniformly lower than those of native AKs, and they exhibited multiphasic unfolding transitions, unlike the native AKs, which presented cooperative thermal unfolding. In addition, proteolytic digestion revealed that permutation destabilized each AK in differing manners, and mass spectrometry suggested that the new termini within the AMP-binding domain were responsible for the increased proteolysis sensitivity. These findings illustrate how changes in contact order can be used to tune enzyme activity and alter folding dynamics in multidomain enzymes.

Proteomics and Metabolomics Analysis Reveal the Regulation Mechanism of Linoleate Isomerase Activity and Function in Propionibacterium acnes

Conjugated linoleic acid (CLA) holds significant application prospects due to its anticancer, anti-atherosclerosis, lipid-lowering, weight-loss, and growth-promoting functions. The key to its efficient production lies in optimizing the biocatalytic performance of linoleic acid isomerase (LAI). Here, we constructed a Propionibacterium acnes mutant library and screened positive mutants with high linoleate isomerase activity. The proteomics and metabolomics were used to explore the mechanism in the regulation of linoleic acid isomerase activity. High-throughput proteomics revealed 104 differentially expressed proteins unique to positive mutant strains of linoleic acid isomerase of which 57 were upregulated and 47 were downregulated. These differentially expressed proteins were primarily involved in galactose metabolism, the phosphotransferase system, starch metabolism, and sucrose metabolism. Differential metabolic pathways were mainly enriched in amino acid biosynthesis, including glutamate metabolism, the Aminoacyl-tRNA biosynthesis pathway, and the ABC transporter pathway. The upregulated metabolites include dl-valine and Acetyl coA, while the downregulated metabolites include Glutamic acid and Phosphoenolpyruvate. Overall, the activity of linoleic acid isomerase in the mutant strain was increased by the regulation of key proteins involved in galactose metabolism, sucrose metabolism, and the phosphotransferase system. This study provides a theoretical basis for the development of high-yield CLA food.

Elucidating Dynamics of Adenylate Kinase from Enzyme Opening to Ligand Release

This study explores ligand-driven conformational changes in adenylate kinase (AK), which is known for its open-to-close conformational transitions upon ligand binding and release. By utilizing string free energy simulations, we determine the free energy profiles for both enzyme opening and ligand release and compare them with profiles from the apoenzyme. Results reveal a three-step ligand release process, which initiates with the opening of the adenosine triphosphate-binding subdomain (ATP lid), followed by ligand release and concomitant opening of the adenosine monophosphate-binding subdomain (AMP lid). The ligands then transition to nonspecific positions before complete dissociation. In these processes, the first step is energetically driven by ATP lid opening, whereas the second step is driven by ATP release. In contrast, the AMP lid opening and its ligand release make minor contributions to the total free energy for enzyme opening. Regarding the ligand binding mechanism, our results suggest that AMP lid closure occurs via an induced-fit mechanism triggered by AMP binding, whereas ATP lid closure follows conformational selection. This difference in the closure mechanisms provides an explanation with implications for the debate on ligand-driven conformational changes of AK. Additionally, we determine an X-ray structure of an AK variant that exhibits significant rearrangements in the stacking of catalytic arginines, explaining its reduced catalytic activity. In the context of apoenzyme opening, the sequence of events is different. Here, the AMP lid opens first while the ATP lid remains closed, and the free energy associated with ATP lid opening varies with orientation, aligning with the reported AK opening and closing rate heterogeneity. Finally, this study, in conjunction with our previous research, provides a comprehensive view of the intricate interplay between various structural elements, ligands, and catalytic residues that collectively contribute to the robust catalytic power of the enzyme.

Conformation state-specific monobodies regulate the functions of flexible proteins through conformation trapping

Synthetic binding proteins have emerged as modulators of protein functions through protein-protein interactions (PPIs). Because PPIs are influenced by the structural dynamics of targeted proteins, investigating whether the synthetic-binders-based strategy is applicable for proteins with large conformational changes is important. This study demonstrates the applicability of monobodies (fibronectin type-III domain-based synthetic binding proteins) in regulating the functions of proteins that undergo tens-of-angstroms-scale conformational changes, using an example of the A55C/C77S/V169C triple mutant (Adktm ; a phosphoryl transfer-catalyzing enzyme with a conformational change between OPEN/CLOSED forms). Phage display successfully developed monobodies that recognize the OPEN form (substrate-unbound form), but not the CLOSED form of Adktm . Two OPEN form-specific clones (OP-2 and OP-4) inhibited Adktm kinase activity. Epitope mapping with a yeast-surface display/flow cytometry indicated that OP-2 binds to the substrate-entry side of Adktm , whereas OP-4 binding occurs at another site. Small angle X-ray scattering  coupled with size-exclusion chromatography (SEC-SAXS) indicated that OP-4 binds to the hinge side opposite to the substrate-binding site of Adktm , retaining the whole OPEN-form structure of Adktm . Titration of the OP-4-Adktm complex with Ap5 A, a transition-state analog of Adktm , showed that the conformational shift to the CLOSED form was suppressed although Adktm retained the OPEN-form (i.e., substrate-binding ready form). These results show that OP-4 captures and stabilizes the OPEN-form state, thereby affecting the hinge motion. These experimental results indicate that monobody-based modulators can regulate the functions of proteins that show tens-of-angstroms-scale conformational changes, by trapping specific conformational states generated during large conformational change process that is essential for function exertion.

Insights into Enzymatic Catalysis from Binding and Hydrolysis of Diadenosine Tetraphosphate by E. coli Adenylate Kinase

Adenylate kinases play a crucial role in cellular energy homeostasis through the interconversion of ATP, AMP, and ADP in all living organisms. Here, we explore how adenylate kinase (AdK) from Escherichia coli interacts with diadenosine tetraphosphate (AP4A), a putative alarmone associated with transcriptional regulation, stress, and DNA damage response. From a combination of EPR and NMR spectroscopy together with X-ray crystallography, we found that AdK interacts with AP4A with two distinct modes that occur on disparate time scales. First, AdK dynamically interconverts between open and closed states with equal weights in the presence of AP4A. On a much slower time scale, AdK hydrolyses AP4A, and we suggest that the dynamically accessed substrate-bound open AdK conformation enables this hydrolytic activity. The partitioning of the enzyme into open and closed states is discussed in relation to a recently proposed linkage between active site dynamics and collective conformational dynamics.

Tackling Hysteresis in Conformational Sampling: How to Be Forgetful with MEMENTO

The structure of proteins has long been recognized to hold the key to understanding and engineering their function, and rapid advances in structural biology and protein structure prediction are now supplying researchers with an ever-increasing wealth of structural information. Most of the time, however, structures can only be determined in free energy minima, one at a time. While conformational flexibility may thus be inferred from static end-state structures, their interconversion mechanisms─a central ambition of structural biology─are often beyond the scope of direct experimentation. Given the dynamical nature of the processes in question, many studies have attempted to explore conformational transitions using molecular dynamics (MD). However, ensuring proper convergence and reversibility in the predicted transitions is extremely challenging. In particular, a commonly used technique to map out a path from a starting to a target conformation called steered MD (SMD) can suffer from starting-state dependence (hysteresis) when combined with techniques such as umbrella sampling (US) to compute the free energy profile of a transition. Here, we study this problem in detail on conformational changes of increasing complexity. We also present a new, history-independent approach that we term "MEMENTO" (Morphing End states by Modelling Ensembles with iNdependent TOpologies) to generate paths that alleviate hysteresis in the construction of conformational free energy profiles. MEMENTO utilizes template-based structure modelling to restore physically reasonable protein conformations based on coordinate interpolation (morphing) as an ensemble of plausible intermediates, from which a smooth path is picked. We compare SMD and MEMENTO on well-characterized test cases (the toy peptide deca-alanine and the enzyme adenylate kinase) before discussing its use in more complicated systems (the kinase P38α and the bacterial leucine transporter LeuT). Our work shows that for all but the simplest systems SMD paths should not in general be used to seed umbrella sampling or related techniques, unless the paths are validated by consistent results from biased runs in opposite directions. MEMENTO, on the other hand, performs well as a flexible tool to generate intermediate structures for umbrella sampling. We also demonstrate that extended end-state sampling combined with MEMENTO can aid the discovery of collective variables on a case-by-case basis.

Perspective: How Fast Dynamics Affect Slow Function in Protein Machines

Internal motions in proteins take place on a broad range of time- and space-scales. The potential roles of these dynamics in the biochemical functions of proteins have intrigued biophysicists for many years, and multiple mechanisms to couple motions to function have been proposed. Some of these mechanisms have relied on equilibrium concepts. For example, the modulation of dynamics was proposed to change the entropy of a protein, hence affecting processes such as binding. This so-called dynamic allostery scenario has been demonstrated in several recent experiments. Perhaps even more intriguing may be models that involve out-of-equilibrium operation, which by necessity require the input of energy. We discuss several recent experimental studies that expose such potential mechanisms for coupling dynamics and function. In Brownian ratchets, for example, directional motion is promoted by switching a protein between two free energy surfaces. An additional example involves the effect of microsecond domain-closure dynamics of an enzyme on its much slower chemical cycle. These observations lead us to propose a novel two-time-scale paradigm for the activity of protein machines: fast equilibrium fluctuations take place on the microsecond-millisecond time scale, while on a slower time scale, free energy is invested in order to push the system out of equilibrium and drive functional transitions. Motions on the two time scales affect each other and are essential for the overall function of these machines.

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.

Contrasting effect of ficoll on apo and holo forms of bacterial chemotaxis protein Y: Selective destabilization of the conformationally altered holo form

Chemotaxis Y (CheY), upon metal binding, displays a drastic alteration in its structure and stability. This premise prompted us to study the effect of crowding on the two conformationally distinct states of the same test protein. A comparative analysis on the structure and thermal stability in the presence and absence of the macromolecular crowder, ficoll, and its monomeric unit, sucrose, revealed a contrasting effect of ficoll on the apo and holo forms. In the presence of ficoll while the thermal stability (T_m) of the apo form is enhanced, the thermal stability of the holo form is reduced. The selective lowering of T_m for the holo form in the combined presence of ficoll and sucrose and not in sucrose alone suggests that the contrasting effect is due to the macromolecular nature of ficoll. Since metal-protein interaction remains unperturbed in the presence of ficoll and Mg²⁺ sequestration is ruled out in a systematic manner the alternative possibility for the exclusive reduction in the thermal stability of the holo form is the ficoll-induced modulation of the relative population of apo and holo forms of CheY.

Mechanistic Basis for a Connection between the Catalytic Step and Slow Opening Dynamics of Adenylate Kinase

Escherichia coli adenylate kinase (AdK) is a small, monomeric enzyme that synchronizes the catalytic step with the enzyme's conformational dynamics to optimize a phosphoryl transfer reaction and the subsequent release of the product. Guided by experimental measurements of low catalytic activity in seven single-point mutation AdK variants (K13Q, R36A, R88A, R123A, R156K, R167A, and D158A), we utilized classical mechanical simulations to probe mutant dynamics linked to product release, and quantum mechanical and molecular mechanical calculations to compute a free energy barrier for the catalytic event. The goal was to establish a mechanistic connection between the two activities. Our calculations of the free energy barriers in AdK variants were in line with those from experiments, and conformational dynamics consistently demonstrated an enhanced tendency toward enzyme opening. This indicates that the catalytic residues in the wild-type AdK serve a dual role in this enzyme's function─one to lower the energy barrier for the phosphoryl transfer reaction and another to delay enzyme opening, maintaining it in a catalytically active, closed conformation for long enough to enable the subsequent chemical step. Our study also discovers that while each catalytic residue individually contributes to facilitating the catalysis, R36, R123, R156, R167, and D158 are organized in a tightly coordinated interaction network and collectively modulate AdK's conformational transitions. Unlike the existing notion of product release being rate-limiting, our results suggest a mechanistic interconnection between the chemical step and the enzyme's conformational dynamics acting as the bottleneck of the catalytic process. Our results also suggest that the enzyme's active site has evolved to optimize the chemical reaction step while slowing down the overall opening dynamics of the enzyme.

Insights into the evolution of enzymatic specificity and catalysis: From Asgard archaea to human adenylate kinases

Enzymatic catalysis is critically dependent on selectivity, active site architecture, and dynamics. To contribute insights into the interplay of these properties, we established an approach with NMR, crystallography, and MD simulations focused on the ubiquitous phosphotransferase adenylate kinase (AK) isolated from Odinarchaeota (OdinAK). Odinarchaeota belongs to the Asgard archaeal phylum that is believed to be the closest known ancestor to eukaryotes. We show that OdinAK is a hyperthermophilic trimer that, contrary to other AK family members, can use all NTPs for its phosphorylation reaction. Crystallographic structures of OdinAK-NTP complexes revealed a universal NTP-binding motif, while 19F NMR experiments uncovered a conserved and rate-limiting dynamic signature. As a consequence of trimerization, the active site of OdinAK was found to be lacking a critical catalytic residue and is therefore considered to be "atypical." On the basis of discovered relationships with human monomeric homologs, our findings are discussed in terms of evolution of enzymatic substrate specificity and cold adaptation.

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.

Frustration and the Kinetic Repartitioning Mechanism of Substrate Inhibition in Enzyme Catalysis

Substrate inhibition, whereby enzymatic activity decreases with excess substrate after reaching a maximum turnover rate, is among the most elusive phenomena in enzymatic catalysis. Here, based on a dynamic energy landscape model, we investigate the underlying mechanism by performing molecular simulations and frustration analysis for a model enzyme adenylate kinase (AdK), which catalyzes the phosphoryl transfer reaction ATP + AMP ⇋ ADP + ADP. Intriguingly, these reveal a kinetic repartitioning mechanism of substrate inhibition, whereby excess substrate AMP suppresses the population of an energetically frustrated, but kinetically activated, catalytic pathway going through a substrate (ATP)-product (ADP) cobound complex with steric incompatibility. Such a frustrated pathway plays a crucial role in facilitating the bottleneck product ADP release, and its suppression by excess substrate AMP leads to a slow down of product release and overall turnover. The simulation results directly demonstrate that substrate inhibition arises from the rate-limiting product-release step, instead of the steps for populating the catalytically competent complex as often suggested in previous works. Furthermore, there is a tight interplay between the enzyme conformational equilibrium and the extent of substrate inhibition. Mutations biasing to more closed conformations tend to enhance substrate inhibition. We also characterized the key features of single-molecule enzyme kinetics with substrate inhibition effect. We propose that the above molecular mechanism of substrate inhibition may be relevant to other multisubstrate enzymes in which product release is the bottleneck step.

SPEACH_AF: Sampling protein ensembles and conformational heterogeneity with Alphafold2

The unprecedented performance of Deepmind's Alphafold2 in predicting protein structure in CASP XIV and the creation of a database of structures for multiple proteomes and protein sequence repositories is reshaping structural biology. However, because this database returns a single structure, it brought into question Alphafold's ability to capture the intrinsic conformational flexibility of proteins. Here we present a general approach to drive Alphafold2 to model alternate protein conformations through simple manipulation of the multiple sequence alignment via in silico mutagenesis. The approach is grounded in the hypothesis that the multiple sequence alignment must also encode for protein structural heterogeneity, thus its rational manipulation will enable Alphafold2 to sample alternate conformations. A systematic modeling pipeline is benchmarked against canonical examples of protein conformational flexibility and applied to interrogate the conformational landscape of membrane proteins. This work broadens the applicability of Alphafold2 by generating multiple protein conformations to be tested biologically, biochemically, biophysically, and for use in structure-based drug design.

Machine learning/molecular dynamic protein structure prediction approach to investigate the protein conformational ensemble

Proteins exist in several different conformations. These structural changes are often associated with fluctuations at the residue level. Recent findings show that co-evolutionary analysis coupled with machine-learning techniques improves the precision by providing quantitative distance predictions between pairs of residues. The predicted statistical distance distribution from Multi Sequence Analysis reveals the presence of different local maxima suggesting the flexibility of key residue pairs. Here we investigate the ability of the residue-residue distance prediction to provide insights into the protein conformational ensemble. We combine deep learning approaches with mechanistic modeling to a set of proteins that experimentally showed conformational changes. The predicted protein models were filtered based on energy scores, RMSD clustering, and the centroids selected as the lowest energy structure per cluster. These models were compared to the experimental-Molecular Dynamics (MD) relaxed structure by analyzing the backbone residue torsional distribution and the sidechain orientations. Our pipeline allows to retrieve the experimental structural dynamics experimentally represented by different X-ray conformations for the same sequence as well the conformational space observed with the MD simulations. We show the potential correlation between the experimental structure dynamics and the predicted model ensemble demonstrating the susceptibility of the current state-of-the-art methods in protein folding and dynamics prediction and pointing out the areas of improvement.

ADP-Induced Conformational Transition of Human Adenylate Kinase 1 Is Triggered by Suppressing Internal Motion of α3α4 and α7α8 Fragments on the ps-ns Timescale

Human adenylate kinase 1 (hAK1) plays a vital role in the energetic and metabolic regulation of cell life, and impaired functions of hAK1 are closely associated with many diseases. In the presence of Mg²⁺ ions, hAK1 in vivo can catalyze two ADP molecules into one ATP and one AMP molecule, activating the downstream AMP signaling. The ADP-binding also initiates AK1 transition from an open conformation to a closed conformation. However, how substrate binding triggers the conformational transition of hAK1 is still unclear, and the underlying molecular mechanisms remain elusive. Herein, we determined the solution structure of apo-hAK1 and its key residues for catalyzing ADP, and characterized backbone dynamics characteristics of apo-hAK1 and hAK1-Mg²⁺-ADP complex (holo-hAK1) using NMR relaxation experiments. We found that ADP was primarily bound to a cavity surrounded by the LID, NMP, and CORE domains of hAK1, and identified several critical residues for hAK1 catalyzing ADP including G16, G18, G20, G22, T39, G40, R44, V67, D93, G94, D140, and D141. Furthermore, we found that apo-hAK1 adopts an open conformation with significant ps-ns internal mobility, and Mg²⁺-ADP binding triggered conformational transition of hAK1 by suppressing the ps-ns internal motions of α₃α₄ in the NMP domain and α₇α₈ in the LID domain. Both α₃α₄ and α₇α₈ fragments became more rigid so as to fix the substrate, while the catalyzing center of hAK1 experiences promoted µs-ms conformational exchange, potentially facilitating catalysis reaction and conformational transition. Our results provide the structural basis of hAK1 catalyzing ADP into ATP and AMP, and disclose the driving force that triggers the conformational transition of hAK1, which will deepen understanding of the molecular mechanisms of hAK1 functions.

Computation of the Protein Conformational Transition Pathway on Ligand Binding by Linear Response-Driven Molecular Dynamics

While extremely important for relating the protein structure to its biological function, determination of the protein conformational transition pathway upon ligand binding is made difficult due to the transient nature of intermediates, a large and rugged conformational space, and coupling between protein dynamics and ligand-protein interactions. Existing methods that rely on prior knowledge of the bound (holo) state structure are restrictive. A second concern relates to the correspondence of intermediates obtained to the metastable states on the apo → holo transition pathway. Here, we have taken the protein apo structure and ligand-binding site as only inputs and combined an elastic network model (ENM) representation of the protein Hamiltonian with linear response theory (LRT) for protein-ligand interactions to identify the set of slow normal modes of protein vibrations that have a high overlap with the direction of the protein conformational change. The structural displacement along the chosen direction was performed using excited normal modes molecular dynamics (MDeNM) simulations rather than by the direct use of LRT. Herein, the MDeNM excitation velocity was optimized on-the-fly on the basis of its coupling to protein dynamics and ligand-protein interactions. Thus, a determined set of structures was validated against crystallographic and simulation data on four protein-ligand systems, namely, adenylate kinase-di(adenosine-5')pentaphosphate, ribose binding protein-β-d-ribopyranose, DNA β-glucosyltransferase-uridine-5'-diphosphate, and G-protein α subunit-guanosine-5'-triphosphate, which present important differences in protein conformational heterogeneity, ligand binding mechanism, viz. induced-fit or conformational selection, extent, and nonlinearity in protein conformational changes upon ligand binding, and presence of allosteric effects. The obtained set of intermediates was used as an input to path metadynamics simulations to obtain the free energy profile for the apo → holo transition.

Correlating the Local and Global Dynamics of an Enzyme in the Crowded Milieu

Enzymes are dynamic biological macromolecules, with their catalytic function(s) being largely influenced by the changes in local fluctuations of amino acid side chains as well as global structural modulations that the enzyme undergoes. Such local and global motions can be highly affected inside the crowded physiological interior of the cell. Here, we have addressed the role of dynamic structural flexibility in affecting the activation energy barrier of a flexible multidomain enzyme adenylate kinase (AK3L1, UniProtKB: Q9UIJ7). Activation energy profiles of both local (at three different sites along the polypeptide backbone) and global dynamics of the enzyme have been monitored using solvation studies on the subnanosecond time scale and tryptophan quenching studies over the temperature range of 278-323 K, respectively, under crowded conditions (Ficoll 70, Dextran 40, Dextran 70, and PEG 8). This study not only provides the site-specific mapping of dynamics but reveals that the activation energies associated with these local motions undergo a significant decrease in the presence of macromolecular crowders, providing new insights into how crowding affects internal protein dynamics. The crowded scenario also aids in enhancing the coupling between the local and global motions of the enzyme. Moreover, select portions/regions of the enzyme when taken together can well mirror the overall dynamics of the biomolecule, showing possible energy hotspots along the polypeptide backbone.

Structural dynamics support electrostatic interactions in the active site of Adenylate Kinase

Electrostatic preorganization as well as structural and dynamic heterogeneity are often used to rationalize the remarkable catalytic efficiency of enzymes. However, they are often presented as incompatible because the generation of permanent electrostatic effects implies that the protein structure remains rigid. Here, we use a metric, electric fields, that can treat electrostatic contributions and dynamics effects on equal footing, for a unique perspective on enzymatic catalysis. We find that the residues that contribute the most to electrostatic interactions with the substrate in the active site of Adenylate Kinase (our working example) are also the most flexible residues. Further, entropy-tuning mutations raise flexibility at the picosecond timescale where more conformations can be visited on short time periods, thereby softening the sharp heterogeneity normally visible at the microsecond timescale.

Investigation of the Importance of Protein 3D Structure for Assessing Conservation of Lysine Acetylation Sites in Protein Homologs

Acetylation is a protein post-translational modification (PTM) that can affect a variety of cellular processes. In bacteria, two PTM Nε-acetylation mechanisms have been identified: non-enzymatic/chemical acetylation via acetyl phosphate or acetyl coenzyme A and enzymatic acetylation via protein acetyltransferases. Prior studies have shown that extensive acetylation of Nε-lysine residues of numerous proteins from a variety of bacteria occurs via non-enzymatic acetylation. In Escherichia coli, new Nε-lysine acetyltransferases (KATs) that enzymatically acetylate other proteins have been identified, thus expanding the repertoire of protein substrates that are potentially regulated by acetylation. Therefore, we designed a study to leverage the wealth of structural data in the Protein Data Bank (PDB) to determine: (1) the 3D location of lysine residues on substrate proteins that are acetylated by E. coli KATs, and (2) investigate whether these residues are conserved on 3D structures of their homologs. Five E. coli KAT substrate proteins that were previously identified as being acetylated by YiaC and had 3D structures in the PDB were selected for further analysis: adenylate kinase (Adk), isocitrate dehydrogenase (Icd), catalase HPII (KatE), methionyl-tRNA formyltransferase (Fmt), and a peroxide stress resistance protein (YaaA). We methodically compared over 350 protein structures of these E. coli enzymes and their homologs; to accurately determine lysine residue conservation requires a strategy that incorporates both flexible structural alignments and visual inspection. Moreover, our results revealed discrepancies in conclusions about lysine residue conservation in homologs when examining linear amino acid sequences compared to 3D structures.

NMMD: Efficient cryo-EM flexible fitting based on simultaneous Normal Mode and Molecular Dynamics atomic displacements

Atomic models of cryo electron microscopy (cryo-EM) maps of biomolecular conformations are often obtained by flexible fitting of the maps with available atomic structures of other conformations (e.g., obtained by X-ray crystallography). This article presents a new flexible fitting method, NMMD, which combines normal mode analysis (NMA) and molecular dynamics simulation (MD). Given an atomic structure and a cryo-EM map to fit, NMMD simultaneously estimates global atomic displacements based on NMA and local displacements based on MD. NMMD was implemented by modifying EMfit, a flexible fitting method using MD only, in GENESIS 1.4. As EMfit, NMMD can be run with replica exchange umbrella sampling procedure. The new method was tested using a variety of EM maps (synthetic and experimental, with different noise levels and resolutions). The results of the tests show that adding normal modes to MD-based fitting makes the fitting faster (40% in average) and, in the majority of cases, more accurate.

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.

Tracking the ATP-binding response in adenylate kinase in real time

The biological function of proteins is critically dependent on dynamics inherent to the native structure. Such structural dynamics obey a predefined order and temporal timing to execute the specific reaction. Determination of the cooperativity of key structural rearrangements requires monitoring protein reactions in real time. In this work, we used time-resolved x-ray solution scattering (TR-XSS) to visualize structural changes in the Escherichia coli adenylate kinase (AdK) enzyme upon laser-induced activation of a protected ATP substrate. A 4.3-ms transient intermediate showed partial closing of both the ATP- and AMP-binding domains, which indicates a cooperative closing mechanism. The ATP-binding domain also showed local unfolding and breaking of an Arg¹³¹-Asp¹⁴⁶ salt bridge. Nuclear magnetic resonance spectroscopy data identified similar unfolding in an Arg¹³¹Ala AdK mutant, which refolded in a closed, substrate-binding conformation. The observed structural dynamics agree with a “cracking mechanism” proposed to underlie global structural transformation, such as allostery, in proteins.

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.

Adenylate Kinase-Catalyzed Reaction of AMP in Pieces: Enzyme Activation for Phosphoryl Transfer to Phosphite Dianion

The binding of adenosine 5'-triphosphate (ATP) and adenosine 5'-monophosphate (AMP) to adenylate kinase (AdK) drives closure of lids over the substrate adenosyl groups. We test the hypothesis that this conformational change activates AdK for catalysis. The rate constants for Homo sapiens adenylate kinase 1 (HsAdK1)-catalyzed phosphoryl group transfer to AMP, k_cat/K_m = 7.0 × 10⁶ M^-1 s^-1, and phosphite dianion, (k_HPi)_obs ≤1 × 10^-4 M^-1 s^-1, show that the binding energy of the adenosyl group effects a ≥7.0 × 10¹⁰-fold rate acceleration of phosphoryl transfer from ATP. The third-order rate constant of k_cat/K_HPiK_EA = 260 M^-2 s^-1 for 1-(β-d-erythrofuranosyl)adenine (EA)-activated phosphoryl transfer to phosphite dianion was determined, and the isohypophosphate reaction product characterized by ³¹P NMR. The results demonstrate the following: (i) a ≥14.7 kcal/mol stabilization of the transition state for phosphoryl transfer by the adenosyl group of AMP and a ≥2.6 × 10⁶-fold rate acceleration from the EA-driven conformational change and (ii) the recovery of ≥8.7 kcal/mol of this transition state stabilization for EA-activated phosphoryl transfer from ATP to phosphite.

Dynamic particle swarm optimization of biomolecular simulation parameters with flexible objective functions

Molecular simulations are a powerful tool to complement and interpret ambiguous experimental data on biomolecules to obtain structural models. Such data-assisted simulations often rely on parameters, the choice of which is highly non-trivial and crucial to performance. The key challenge is weighting experimental information with respect to the underlying physical model. We introduce FLAPS, a self-adapting variant of dynamic particle swarm optimization, to overcome this parameter selection problem. FLAPS is suited for the optimization of composite objective functions that depend on both the optimization parameters and additional, a priori unknown weighting parameters, which substantially influence the search-space topology. These weighting parameters are learned at runtime, yielding a dynamically evolving and iteratively refined search-space topology. As a practical example, we show how FLAPS can be used to find functional parameters for small-angle X-ray scattering-guided protein simulations.

Impacts of mutations on dynamic allostery of adenylate kinase

Escherichia coli adenylate kinase (AK) is composed of CORE domain and two branch domains: LID and AMP-binding domain (AMPbd). AK exhibits considerable allostery in a reversible phosphoryl transfer reaction, which is largely attributed to the relative motion of LID and AMPbd with respect to CORE. Such an allosteric conformational change is also evident in the absence of ligands. Recent studies showed that the mutations in branch domains can adjust dynamic allostery and alter the substrate affinity and enzyme activity. In this work, we use all-atom molecular dynamics simulation to study the impacts of mutations in branch domains on AK's dynamic allostery by comparing two double mutants, i.e., LID mutant (Val135Gly, Val142Gly) and AMPbd mutant (Ala37Gly, Ala55Gly), with wild-type. Two mutants undergo considerable conformational fluctuation and exhibit deviation from the initially extended apo state to more compact structures. The LID domain in the LID mutant adjusts its relative position and firmly adheres to CORE. More strikingly, AMPbd mutations affect the relative positions of both the AMPbd domain and remote LID domain. Both domains undergo considerable movement, especially the inherent hinge swing motion of the flexible LID domain. In both mutants, the mutations can enhance the inter-domain interaction. The results about the conformation change of AK in both mutants are in line with the experiment of AK's affinity and activity. As revealed by our findings, the flexibility of branch domains and their inherent motions, especially LID domain, is highly relevant to dynamic allostery in the AK system.

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".

Dynamic Connection between Enzymatic Catalysis and Collective Protein Motions

Enzymes employ a wide range of protein motions to achieve efficient catalysis of chemical reactions. While the role of collective protein motions in substrate binding, product release, and regulation of enzymatic activity is generally understood, their roles in catalytic steps per se remain uncertain. Here, molecular dynamics simulations, enzyme kinetics, X-ray crystallography, and nuclear magnetic resonance spectroscopy are combined to elucidate the catalytic mechanism of adenylate kinase and to delineate the roles of catalytic residues in catalysis and the conformational change in the enzyme. This study reveals that the motions in the active site, which occur on a time scale of picoseconds to nanoseconds, link the catalytic reaction to the slow conformational dynamics of the enzyme by modulating the free energy landscapes of subdomain motions. In particular, substantial conformational rearrangement occurs in the active site following the catalytic reaction. This rearrangement not only affects the reaction barrier but also promotes a more open conformation of the enzyme after the reaction, which then results in an accelerated opening of the enzyme compared to that of the reactant state. The results illustrate a linkage between enzymatic catalysis and collective protein motions, whereby the disparate time scales between the two processes are bridged by a cascade of intermediate-scale motion of catalytic residues modulating the free energy landscapes of the catalytic and conformational change processes.

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.

Multi-Scale Flexible Fitting of Proteins to Cryo-EM Density Maps at Medium Resolution

Structure determination using cryo-electron microscopy (cryo-EM) medium-resolution density maps is often facilitated by flexible fitting. Avoiding overfitting, adjusting force constants driving the structure to the density map, and emulating complex conformational transitions are major concerns in the fitting. To address them, we develop a new method based on a three-step multi-scale protocol. First, flexible fitting molecular dynamics (MD) simulations with coarse-grained structure-based force field and replica-exchange scheme between different force constants replicas are performed. Second, fitted Cα atom positions guide the all-atom structure in targeted MD. Finally, the all-atom flexible fitting refinement in implicit solvent adjusts the positions of the side chains in the density map. Final models obtained via the multi-scale protocol are significantly better resolved and more reliable in comparison with long all-atom flexible fitting simulations. The protocol is useful for multi-domain systems with intricate structural transitions as it preserves the secondary structure of single domains.

Crystal structure of adenylate kinase from an extremophilic archaeon Aeropyrum pernix with ATP and AMP

The crystal structure of an adenylate kinase from an extremophilic archaeon Aeropyrum pernix was determined in complex with full ligands, ATP-Mg2+ and AMP, at a resolution of 2.0 Å. The protein forms a trimer as found for other adenylate kinases from archaea. Interestingly, the reacting three atoms, two phosphorus and one oxygen atoms, were located almost in line, supporting the SN2 nucleophilic substitution reaction mechanism. Based on the crystal structure obtained, the reaction coordinate was estimated by the quantum mechanics calculations combined with molecular dynamics. It was found that the reaction undergoes two energy barriers; the steps for breaking the bond between the oxygen and γ-phosphorus atoms of ATP to produce a phosphoryl fragment and creating the bond between the phosphoryl fragment and the oxygen atom of the β-phosphate group of ADP. The reaction coordinate analysis also suggested the role of amino-acid residues for the catalysis of adenylate kinase.