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

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.

Dynamic correlations: exact and approximate methods for mutual information

MOTIVATION

Proteins are dynamic entities that undergo conformational changes critical for their functions. Understanding the communication pathways and information transfer within proteins is crucial for elucidating allosteric interactions in their mechanisms. This study utilizes mutual information (MI) analysis to probe dynamic allostery. Using two cases, Ubiquitin and PLpro, we have evaluated the accuracy and limitations of different approximations including the exact anisotropic and isotropic models, multivariate Gaussian model, isotropic Gaussian model, and the Gaussian Network Model (GNM) in revealing allosteric interactions.

RESULTS

Our findings emphasize the required trajectory length for capturing accurate mutual information profiles. Long molecular dynamics trajectories, 1 ms for Ubiquitin and 100 µs for PLpro are used as benchmarks, assuming they represent the ground truth. Trajectory lengths of approximately 5 µs for Ubiquitin and 1 µs for PLpro marked the onset of convergence, while the multivariate Gaussian model accurately captured mutual information with trajectories of 5 ns for Ubiquitin and 350 ns for PLpro. However, the isotropic Gaussian model is less successful in representing the anisotropic nature of protein dynamics, particularly in the case of PLpro, highlighting its limitations. The GNM, however, provides reasonable approximations of long-range information exchange as a minimalist network model based on a single crystal structure. Overall, the optimum trajectory lengths for effective Gaussian approximations of long-time dynamic behavior depend on the inherent dynamics within the protein's topology. The GNM, by showcasing dynamics across relatively diverse time scales, can be used either as a standalone method or to gauge the adequacy of MD simulation lengths.

AVAILABILITY AND IMPLEMENTATION

Mutual information codes are available at https://github.com/kemaldemirtas/prc-MI.git.

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.

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.

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.

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.

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.

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.

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.

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.

Multiple Pathways and Time Scales for Conformational Transitions in apo-Adenylate Kinase

The open/close transition in adenylate kinase (AK) is regarded as a representative example for large-scale conformational transition in proteins, yet its mechanism remains unclear despite numerous experimental and computational studies. Using extensive (∼50 μs) explicit solvent atomistic simulations and Markov state analysis, we shed new lights on the mechanism of this transition in the apo form of AK. The closed basin of apo AK features an open NMP domain while the LID domain closes and rotates toward it. Therefore, although the computed structural properties of the closed ensemble are consistent with previously reported FRET and PRE measurements, our simulations suggest that NMP closure is likely to follow AMP binding, in contrast to the previous interpretation of FRET and PRE data that the apo state was able to sample the fully closed conformation for "ligand selection". The closed state ensemble is found to be kinetically heterogeneous; multiple pathways and time scales are associated with the open/close transition, providing new clues to the disparate time scales observed in different experiments. Besides interdomain interactions, a novel mutual information analysis identifies specific intradomain interactions that correlate strongly to transition kinetics, supporting observations from previous chimera experiments. While our results underscore the role of internal domain properties in determining the kinetics of open/close transition in apo AK, no evidence is observed for any significant degree of local unfolding during the transition. These observations about AK have general implications to our view of conformational states, transition pathways, and time scales of conformational changes in proteins. The key features and time scales of observed transition pathways are robust and similar from simulations using two popular fixed charge force fields.

Hybrid All-Atom/Coarse-Grained Simulations of Proteins by Direct Coupling of CHARMM and PRIMO Force Fields

Hybrid all-atom/coarse-grained (AA/CG) simulations of proteins offer a computationally efficient compromise where atomistic details are only applied to biologically relevant regions while benefiting from the speedup of treating the remaining parts of a given system at the CG level. The recently developed CG model, PRIMO, allows a direct coupling with an atomistic force field with no additional modifications or coupling terms and the ability to carry out dynamic simulations without any restraints on secondary or tertiary structures. A hybrid AA/CG scheme based on combining all-atom CHARMM and coarse-grained PRIMO representations was validated via molecular dynamics and replica exchange simulations of soluble and membrane proteins. The AA/CG scheme was also tested in the calculation of the free energy profile for the transition from the closed to the open state of adenylate kinase via umbrella sampling molecular dynamics method. The overall finding is that the AA/CG scheme generates dynamics and energetics that are qualitatively and quantitatively comparable to AA simulations while offering the computational advantages of coarse-graining. This model opens the door to challenging applications where high accuracy is required only in parts of large biomolecular complexes.

Molecular simulations of substrate release and coupled conformational motions in adenylate kinase

Conformational opening coupled substrate release is believed to be related to the rate limiting step in the catalysis cycle of the adenylate kinase. However, it is still unclear how the substrate dissociates from its active site and how the substrate release is coupled to conformational changes of the kinase. In this work, by using metadynamics simulations, we investigated the ADP release process and the coupled protein dynamics. We found that the ADP release involves overcoming a high free energy barrier, and protonation of the [Formula: see text]-phosphate of the ADP molecules can drastically reduce the barrier height, therefore, promote the ADP release. We identified several key residues contributing to the high free energy barrier. We also showed that the ADP attached to LID domain leaves the binding pocket earlier than the one attached to the NMP domain. We further observed that the ADP release is accompanied by almost fully opening of the LID domain and partially opening of the NMP domain. Our results provide insight into the molecular mechanism of the substrate release of adenylate kinase and the coupled conformational motions.

Classification of projection images of proteins with structural polymorphism by manifold: a simulation study for x-ray free-electron laser diffraction imaging

Coherent x-ray diffraction imaging (CXDI) enables us to visualize noncrystalline sample particles with micrometer to submicrometer dimensions. Using x-ray free-electron laser (XFEL) sources, two-dimensional diffraction patterns are collected from fresh samples supplied to the irradiation area in the "diffraction-before-destruction" scheme. A recent significant increase in the intensity of the XFEL pulse is promising and will allow us to visualize the three-dimensional structures of proteins using XFEL-CXDI in the future. For the protocol proposed for molecular structure determination using future XFEL-CXDI [T. Oroguchi and M. Nakasako, Phys. Rev. E 87, 022712 (2013)10.1103/PhysRevE.87.022712], we require an algorithm that can classify the data in accordance with the structural polymorphism of proteins arising from their conformational dynamics. However, most of the algorithms proposed primarily require the numbers of conformational classes, and then the results are biased by the numbers. To improve this point, here we examine whether a method based on the manifold concept can classify simulated XFEL-CXDI data with respect to the structural polymorphism of a protein that predominantly adopts two states. After random sampling of the conformations of the two states and in-between states from the trajectories of molecular dynamics simulations, a diffraction pattern is calculated from each conformation. Classification was performed by using our custom-made program suite named enma, in which the diffusion map (DM) method developed based on the manifold concept was implemented. We successfully classify most of the projection electron density maps phase retrieved from diffraction patterns into each of the two states and in-between conformations without the knowledge of the number of conformational classes. We also examined the classification of the projection electron density maps of each of the three states with respect to the Euler angle. The present results suggest that the DM method is imperative for future applications of XFEL-CXDI experiments for proteins, and clarify issues to be taken care of in the future application.

Energetics and structural characterization of the large-scale functional motion of adenylate kinase

Adenylate Kinase (AK) is a signal transducing protein that regulates cellular energy homeostasis balancing between different conformations. An alteration of its activity can lead to severe pathologies such as heart failure, cancer and neurodegenerative diseases. A comprehensive elucidation of the large-scale conformational motions that rule the functional mechanism of this enzyme is of great value to guide rationally the development of new medications. Here using a metadynamics-based computational protocol we elucidate the thermodynamics and structural properties underlying the AK functional transitions. The free energy estimation of the conformational motions of the enzyme allows characterizing the sequence of events that regulate its action. We reveal the atomistic details of the most relevant enzyme states, identifying residues such as Arg119 and Lys13, which play a key role during the conformational transitions and represent druggable spots to design enzyme inhibitors. Our study offers tools that open new areas of investigation on large-scale motion in proteins.

WEBnm@ v2.0: Web server and services for comparing protein flexibility

BACKGROUND

Normal mode analysis (NMA) using elastic network models is a reliable and cost-effective computational method to characterise protein flexibility and by extension, their dynamics. Further insight into the dynamics-function relationship can be gained by comparing protein motions between protein homologs and functional classifications. This can be achieved by comparing normal modes obtained from sets of evolutionary related proteins.

RESULTS

We have developed an automated tool for comparative NMA of a set of pre-aligned protein structures. The user can submit a sequence alignment in the FASTA format and the corresponding coordinate files in the Protein Data Bank (PDB) format. The computed normalised squared atomic fluctuations and atomic deformation energies of the submitted structures can be easily compared on graphs provided by the web user interface. The web server provides pairwise comparison of the dynamics of all proteins included in the submitted set using two measures: the Root Mean Squared Inner Product and the Bhattacharyya Coefficient. The Comparative Analysis has been implemented on our web server for NMA, WEBnm@, which also provides recently upgraded functionality for NMA of single protein structures. This includes new visualisations of protein motion, visualisation of inter-residue correlations and the analysis of conformational change using the overlap analysis. In addition, programmatic access to WEBnm@ is now available through a SOAP-based web service. Webnm@ is available at http://apps.cbu.uib.no/webnma .

CONCLUSION

WEBnm@ v2.0 is an online tool offering unique capability for comparative NMA on multiple protein structures. Along with a convenient web interface, powerful computing resources, and several methods for mode analyses, WEBnm@ facilitates the assessment of protein flexibility within protein families and superfamilies. These analyses can give a good view of how the structures move and how the flexibility is conserved over the different structures.

New crystal structures of adenylate kinase from Streptococcus pneumoniae D39 in two conformations

Adenylate kinases (AdKs; EC 2.7.3.4) play a critical role in intercellular homeostasis by the interconversion of ATP and AMP to two ADP molecules. Crystal structures of adenylate kinase from Streptococcus pneumoniae D39 (SpAdK) have recently been determined using ligand-free and inhibitor-bound crystals belonging to space groups P21 and P1, respectively. Here, new crystal structures of SpAdK in ligand-free and inhibitor-bound states determined at 1.96 and 1.65 Å resolution, respectively, are reported. The new ligand-free crystal belonged to space group C2, with unit-cell parameters a=73.5, b=54.3, c=62.7 Å, β=118.8°. The new ligand-free structure revealed an open conformation that differed from the previously determined conformation, with an r.m.s.d on Cα atoms of 1.4 Å. The new crystal of the complex with the two-substrate-mimicking inhibitor P1,P5-bis(adenosine-5'-)pentaphosphate (Ap5A) belonged to space group P1, with unit-cell parameters a=53.9, b=62.3, c=63.0 Å, α=101.9, β=112.6, γ=89.9°. Despite belonging to the same space group as the previously reported crystal, the new Ap5A-bound crystal contains four molecules in the asymmetric unit, compared with two in the previous crystal, and shows slightly different lattice contacts. These results demonstrate that SpAdK can crystallize promiscuously in different forms and that the open structure is flexible in conformation.

Deciphering the catalysis-associated conformational changes of human adenylate kinase 1 with single-molecule spectroscopy

Human adenylate kinase isoenzyme 1 (AK1) is the key enzyme in maintaining the cellular energy homeostasis. The catalysis-associated conformational changes of AK1 involve large-amplitude rearrangements. To decipher the conformational changes of AK1 at the single-molecule level, we tagged AK1 with two identical fluorophores, one near the substrate-binding site and the other at the boundary of the core domain. We found that magnesium ion binding to AK1 increases the structural heterogeneity of AK1, whereas ADP binding reduces the structural heterogeneity. We exploited the hidden Markov model to extract the underlying catalysis-associated conformational dynamics and determined thermodynamic parameters of the multiple catalytic pathways. The third-order correlation difference calculated from photon fluctuation traces reveals the irreversible nature of the conformational motions, suggesting that single-molecule AK1 is in a nonequilibrium steady state. This discovery offers a fresh viewpoint to look into the molecular mechanisms of cellular biochemistry.

Molecular dynamics studies on the conformational transitions of adenylate kinase: a computational evidence for the conformational selection mechanism

Escherichia coli adenylate kinase (ADK) is a monomeric phosphotransferase enzyme that catalyzes reversible transfer of phosphoryl group from ATP to AMP with a large-scale domain motion. The detailed mechanism for this conformational transition remains unknown. In the current study, we performed long time-scale molecular dynamics simulations on both open and closed states of ADK. Based on the structural analyses of the simulation trajectories, we detected over 20 times conformational transitions between the open and closed states of ADK and identified two novel conformations as intermediate states in the catalytic processes. With these findings, we proposed a possible mechanism for the large-scale domain motion of Escherichia coli ADK and its catalytic process: (1) the substrate free ADK adopted an open conformation; (2) ATP bound with LID domain closure; (3) AMP bound with NMP domain closure; (4) phosphoryl transfer occurred with ATP, and AMP converted into two ADPs, and no conformational transition was detected in the enzyme; (5) LID domain opened with one ADP released; (6) another ADP released with NMP domain open. As both open and closed states sampled a wide range of conformation transitions, our simulation strongly supported the conformational selection mechanism for Escherichia coli ADK.

Exploring the Dynamic Functional Landscape of Adenylate Kinase Modulated by Substrates

Adenylate kinase (ADK) has been explored widely, through both experimental and theoretical studies. However, still less is known about how the functional dynamics of ADK is modulated explicitly by its natural substrates. Here, we report a quantitative study of the dynamic energy landscape for ADK responding to the substrate binding by integrating both experimental investigations and theoretical modeling. We make theoretical predictions which are in remarkable agreement with the single molecule experiments on the substrate-bound complex. With our combined models of ADK in its apo form, in the presence of AMP or ATP, and in complex with both substrates, we specifically address the following key questions: (1) Are there intermediate state(s) during their catalytic cycle and if so how many? (2) How many pathways are there along the open-to-closed transitions and what are their corresponding weights? (3) How do substrates influence the pathway weights and the stability of the intermediates? (4) Which lid's motion is rate-limiting along the turnover cycle, the NMP or the LID domain? Our models predict two major parallel stepwise pathways and two on-pathway intermediates which are denoted as IN (NMP domain open while LID domain closed) and IL (LID domain open and NMP domain closed), respectively. Further investigation of temperature effects suggests that the IN pathway is dominant at room temperature, but the IL pathway is dominant at the optimal temperature. This leads us to propose that the IL pathway is more dominant by entropy and IN pathway by enthalpy. Remarkably, our results show that even with maximum concentrations of natural substrates, ADK still fluctuates between multiple functional states, reflecting an intrinsic capability of large-scale conformational fluctuations which may be essential to its biological function. The results based on the dual-ligands model provide the theoretical validation of random bisubstrate biproducts (Bi-Bi) mechanism for the enzymatic reaction of ADK. Additionally, the pathway flux analysis strongly suggests that the motion of the NMP domain is the rate-determining step for the conformational cycle (opening and closing).

Conservation of functionally important global motions in an enzyme superfamily across varying quaternary structures

The α-d-phosphohexomutase superfamily comprises enzymes involved in carbohydrate metabolism that are found in all kingdoms of life. Recent biophysical studies have shown for the first time that several of these enzymes exist as dimers in solution, prompting an examination of the oligomeric state of all proteins of known structure in the superfamily (11 different proteins; 31 crystal structures) via computational and experimental analyses. We find that these proteins range in quaternary structure from monomers to tetramers, with 6 of the 11 known structures being likely oligomers. The oligomeric state of these proteins not only is associated in some cases with enzyme subgroup (i.e., substrate specificity) but also appears to depend on domain of life, with the two archaeal proteins existing as higher-order oligomers. Within the oligomers, three distinct interfaces are observed, one of which is found in both archaeal and bacterial proteins. Normal mode analysis shows that the topological arrangement of the oligomers permits domain 4 of each protomer to move independently as required for catalysis. Our analysis suggests that the advantages associated with protein flexibility in this enzyme family are of sufficient importance to be maintained during the evolution of multiple independent oligomers. This study is one of the first showing that global motions may be conserved not only within protein families but also across members of a superfamily with varying oligomeric structures.

Biomolecular dynamics: order-disorder transitions and energy landscapes

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

Quaternary structure, conformational variability and global motions of phosphoglucosamine mutase

Phosphoglucosamine mutase (PNGM) is a bacterial enzyme that participates in the peptidoglycan biosynthetic pathway. Recent crystal structures of PNGM from two bacterial pathogens, Bacillus anthracis and Francisella tularensis, have revealed key structural features of this enzyme for the first time. Here, we follow up on several novel findings from the crystallographic studies, including the observation of a structurally conserved interface between polypeptide chains and conformational variability of the C-terminal domain. Small-angle X-ray scattering of B. anthracis PNGM shows that this protein is a dimer in solution. Comparisons of the four independent polypeptide chains from the two structures reveals conserved residues and structural changes involved in the conformational variability, as well as a significant rotation of the C-terminal domain, of nearly 60°, between the most divergent conformers. Furthermore, the fluctuation dynamics of PNGM are examined via normal mode analyses. The most mobile region of the protein is its C-terminal domain, consistent with observations from the crystal structures. Large regions of correlated, collective motions are identified exclusively for the dimeric state of the protein, comprising both contiguous and noncontiguous structural domains. The motions observed in the lowest frequency normal mode of the dimer result in dynamically coupled opening and closing of the two active sites. The global motions identified in this study support the importance of the conformational change of PNGM in function, and suggest that the dimeric state of this protein may confer advantages consistent with its evolutionary conservation.