Small- and large-scale conformational changes of adenylate kinase: a molecular dynamics study of the subdomain motion and mechanics

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.

Kinematic analysis of kinases and their oncogenic mutations - Kinases and their mutation kinematic analysis

Protein kinases are crucial cellular enzymes that facilitate the transfer of phosphates from adenosine triphosphate (ATP) to their substrates, thereby regulating numerous cellular activities. Dysfunctional kinase activity often leads to oncogenic conditions. Chosen by using structural similarity to 5UG9, we selected 79 crystal structures from the PDB and based on the position of the phenylalanine side chain in the DFG motif, we classified these 79 crystal structures into 5 group clusters. Our approach applies our kinematic flexibility analysis (KFA) to explore the flexibility of kinases in various activity states and examine the impact of the activation loop on kinase structure. KFA enables the rapid decomposition of macromolecules into different flexibility regions, allowing comprehensive analysis of conformational structures. The results reveal that the activation loop of kinases acts as a "lock" that stabilizes the active conformation of kinases by rigidifying the adjacent α-helices. Furthermore, we investigate specific kinase mutations, such as the L858R mutation commonly associated with non-small cell lung cancer, which induces increased flexibility in active-state kinases. In addition, through analyzing the hydrogen bond pattern, we examine the substructure of kinases in different states. Notably, active-state kinases exhibit a higher occurrence of α-helices compared to inactive-state kinases. This study contributes to the understanding of biomolecular conformation at a level relevant to drug development.

Conformational dynamics of adenylate kinase in crystals

Adenylate kinase is a ubiquitous enzyme in living systems and undergoes dramatic conformational changes during its catalytic cycle. For these reasons, it is widely studied by genetic, biochemical, and biophysical methods, both experimental and theoretical. We have determined the basic crystal structures of three differently liganded states of adenylate kinase from Methanotorrus igneus, a hyperthermophilic organism whose adenylate kinase is a homotrimeric oligomer. The multiple copies of each protomer in the asymmetric unit of the crystal provide a unique opportunity to study the variation in the structure and were further analyzed using advanced crystallographic refinement methods and analysis tools to reveal conformational heterogeneity and, thus, implied dynamic behaviors in the catalytic cycle.

Molecular characterization and immunological properties of Echinococcus granulosus sensu stricto (G1) ADK1 and ADK8

Adenylate kinases (ADKs) are one of the important enzymes regulating adenosine triphosphate (ATP) metabolism in Echinococcus granulosus sensu lato. The objective of the present study was to explore the molecular characteristics and immunological properties of E. granulosus sensu stricto (G1) adenylate kinase 1 (EgADK1) and adenylate kinase 8 (EgADK8). EgADK1 and EgADK8 were cloned and expressed, and the molecular characteristics of EgADK1 and EgADK8 were analyzed through different bioinformatics tools. Western blotting was used to examine the reactogenicity of recombinant adenylate kinase 1 (rEgADK1) and recombinant adenylate kinase 8 (rEgADK8) and to evaluate their diagnostic value. The expression profiles of EgADK1 and EgADK8 in 18-day-old strobilated worms and protoscoleces were analyzed by quantitative real-time PCR, and their distribution in 18-day-old strobilated worms, the germinal layer, and protoscoleces was determined by immunofluorescence localization. EgADK1 and EgADK8 were successfully cloned and expressed. Bioinformatics analysis predicted that EgADK1 and EgADK8 have multiple phosphorylation sites and B-cell epitopes. Compared with EgADK8, EgADK1 and other parasite ADKs have higher sequence similarity. In addition, both cystic echinococcosis (CE)-positive sheep sera and Cysticercus tenuicollis-infected goat sera could recognize rEgADK1 and rEgADK8. EgADK1 and EgADK8 were localized in protoscoleces, the germinal layer, and 18-day-old strobilated worms. EgADK1 and EgADK8 showed no significant difference in their transcription level in 18-day-old strobilated worms and protoscoleces, suggesting that EgADK1 and EgADK8 may play an important role in the growth and development of E. granulosus sensu lato. Since EgADK1 and EgADK8 can be recognized by other parasite-positive sera, they are not suitable as candidate antigens for the diagnosis of CE.

Information-theoretical measures identify accurate low-resolution representations of protein configurational space

The steadily growing computational power employed to perform molecular dynamics simulations of biological macromolecules represents at the same time an immense opportunity and a formidable challenge. In fact, large amounts of data are produced, from which useful, synthetic, and intelligible information has to be extracted to make the crucial step from knowing to understanding. Here we tackled the problem of coarsening the conformational space sampled by proteins in the course of molecular dynamics simulations. We applied different schemes to cluster the frames of a dataset of protein simulations; we then employed an information-theoretical framework, based on the notion of resolution and relevance, to gauge how well the various clustering methods accomplish this simplification of the configurational space. Our approach allowed us to identify the level of resolution that optimally balances simplicity and informativeness; furthermore, we found that the most physically accurate clustering procedures are those that induce an ultrametric structure of the low-resolution space, consistently with the hypothesis that the protein conformational landscape has a self-similar organisation. The proposed strategy is general and its applicability extends beyond that of computational biophysics, making it a valuable tool to extract useful information from large datasets.

Iterative Landmark-Based Umbrella Sampling (ILBUS) Protocol for Sampling of Conformational Space of Biomolecules

Computer simulations of biomolecules such as molecular dynamics often suffer from insufficient sampling. Due to limited computational resources, insufficient sampling prevents obtaining proper equilibrium distributions of observed properties. To deal with this problem, we proposed a simulation protocol for efficient resampling of collected off-equilibrium trajectories. These trajectories are utilized for the initial mapping of the conformational space, which is later properly resampled by the introduced Iterative Landmark-Based Umbrella Sampling (ILBUS) method. Reconstruction of static equilibrium properties is achieved by the multistate Bennett acceptance ratio (MBAR) method, which enables efficient use of simulated data. The ILBUS protocol is geometry-based and does not demand any additional collective variable or a dimensional-reduction technique. The only requirement is a set of suitably spaced reference conformations, which serve as landmarks in the mapped conformational space. Additionally, the ILBUS protocol encompasses an iterative process that optimizes the force constant used in the umbrella sampling simulation. Such tuning is an inherent feature of the protocol and does not need to be performed by the user in advance. Furthermore, even the simulations with suboptimal force constants can be used in estimates by MBAR. We demonstrate the feasibility and the performance of this approach in the study of the conformational landscape of the alanine dipeptide, met-enkephalin, and adenylate kinase.

Mutual information analysis of the dynamic correlation between side chains in proteins

Protein dynamics play an essential role in function regulation. In recent years, many experimental and theoretical studies have shown that changes in protein fluctuations in the backbone and side chains fulfill a pivotal role associated with amino acid mutations, chemical modifications, and ligand binding. The dynamic correlations between protein side chains have not been sufficiently studied, and no reliable analysis method has been available so far. Therefore, we developed a method to evaluate the dynamic correlation between protein side chains using mutual information and molecular dynamics simulations. To eliminate the structural superposition errors dealing with conventional analysis methods, and to accurately extract the intrinsic fluctuation properties of the side chains, we employed distance principal component analysis (distPCA). The motion of the side chain was then projected onto the eigenvector space obtained by distPCA, and the mutual information between the projected motions was calculated. The proposed method was then applied to a small protein "eglin c" and the mutants. The results show that even a single mutation significantly changed the dynamic correlations and also suggest that the dynamic change is deeply related to the stability. Those results indicate that our developed method could be useful for analyzing the molecular mechanism of allosteric communication in proteins.

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".

A journey through mapping space: characterising the statistical and metric properties of reduced representations of macromolecules

ABSTRACT

A mapping of a macromolecule is a prescription to construct a simplified representation of the system in which only a subset of its constituent atoms is retained. As the specific choice of the mapping affects the analysis of all-atom simulations as well as the construction of coarse-grained models, the characterisation of the mapping space has recently attracted increasing attention. We here introduce a notion of scalar product and distance between reduced representations, which allows the study of the metric and topological properties of their space in a quantitative manner. Making use of a Wang-Landau enhanced sampling algorithm, we exhaustively explore such space, and examine the qualitative features of mappings in terms of their squared norm. A one-to-one correspondence with an interacting lattice gas on a finite volume leads to the emergence of discontinuous phase transitions in mapping space, which mark the boundaries between qualitatively different reduced representations of the same molecule.

Ligand-protein interactions in lysozyme investigated through a dual-resolution model

A fully atomistic (AT) modeling of biological macromolecules at relevant length- and time-scales is often cumbersome or not even desirable, both in terms of computational effort required and a posteriori analysis. This difficulty can be overcome with the use of multiresolution models, in which different regions of the same system are concurrently described at different levels of detail. In enzymes, computationally expensive AT detail is crucial in the modeling of the active site in order to capture, for example, the chemically subtle process of ligand binding. In contrast, important yet more collective properties of the remainder of the protein can be reproduced with a coarser description. In the present work, we demonstrate the effectiveness of this approach through the calculation of the binding free energy of hen egg white lysozyme with the inhibitor di-N-acetylchitotriose. Particular attention is payed to the impact of the mapping, that is, the selection of AT and coarse-grained residues, on the binding free energy. It is shown that, in spite of small variations of the binding free energy with respect to the active site resolution, the separate contributions coming from different energetic terms (such as electrostatic and van der Waals interactions) manifest a stronger dependence on the mapping, thus pointing to the existence of an optimal level of intermediate resolution.

The crystal structures of Thermus thermophilus CMP kinase complexed with a phosphoryl group acceptor and donor

Nucleoside monophosphate kinases play crucial roles in biosynthesis and regeneration of nucleotides. These are bi-substrate enzymes that catalyze reversible transfers of a phosphoryl group between ATP and nucleoside monophosphate. These enzymes are comprised of the CORE domain, the NMP-binding domain, and the LID domain. Large conformational rearrangement of the three domains occurs during the catalytic cycle. Although many structures of CMP kinase have been determined, only limited structural information has been available on the conformational changes along the reaction pathway. We determined five crystal structures of CMP kinase of Thermus thermophilus HB8 in ligand-free form and the CMP "open", CMP "closed", ADP-CDP-Gd3+-, and CDP-bound forms at resolutions of 1.7, 2.2, 1.5, 1.6, and 1.7 Å, respectively. The ligand-free form was in an open conformation, whereas the structures of the CMP "closed", ADP-CDP-Gd3+-, and CDP-bound forms were in a closed conformation, in which the shift of the NMP-binding domain and LID domain caused closure of the substrate-binding cleft. Interestingly, the CMP "open" form was in an open conformation even with CMP bound, implying intrinsic conformational fluctuation. The structure of the ADP-CDP complex is the first structure of CMP kinase with a phosphoryl group donor and an acceptor. Upon simultaneous binding of ADP and CDP, the side chains of several residues in the LID domain moved toward the nucleotides without global open-closed conformational changes compared to those in the CMP "closed" and CDP complexes. These global and local conformational changes may be crucial for the substrate recognition and catalysis. The terminal phosphate groups of ADP and CDP had similar geometry to those of two ADP in AMP kinase, suggesting common catalytic mechanisms to other nucleoside monophosphate kinases. Our findings are expected to contribute to detailed understanding of the reaction mechanism of CMP kinase.

Perturb-Scan-Pull: A Novel Method Facilitating Conformational Transitions in Proteins

Conformational transitions in proteins facilitate precise physiological functions. Therefore, it is crucial to understand the mechanisms underlying these processes to modulate protein function. Yet, studying structural and dynamical properties of proteins is notoriously challenging due to the complexity of the underlying potential energy surfaces (PES). We have previously developed the perturbation-response scanning (PRS) method to identify key residues that participate in the communication network responsible for specific conformational transitions. PRS is based on a residue-by-residue scan of the protein to determine the subset of residues/forces which provide the closest conformational change leading to a target conformational state, inasmuch as linear response theory applies to these motions. Here, we develop a novel method to further evaluate if conformational transitions may be triggered on the PES. We aim to study functionally relevant conformational transitions in proteins by using results obtained from PRS and feeding them as inputs to steered molecular dynamics simulations. The success and the transferability of the method are evaluated on three protein systems having different complexities of motion on the PES: calmodulin, adenylate kinase, and bacterial ferric binding protein. We find that the method captures the target conformation, while providing key residues and the optimum paths with relatively low free energy profiles.

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

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

Exploring Conformational Change of Adenylate Kinase by Replica Exchange Molecular Dynamic Simulation

Replica exchange molecular dynamics (REMD) simulation is a popular enhanced sampling method that is widely used for exploring the atomic mechanism of protein conformational change. However, the requirement of huge computational resources for REMD, especially with the explicit solvent model, largely limits its application. In this study, the availability and efficiency of a variant of velocity-scaling REMD (vsREMD) was assessed with adenylate kinase as an example. Although vsREMD achieved results consistent with those from conventional REMD and experimental studies, the number of replicas required for vsREMD (30) was much less than that for conventional REMD (80) to achieve a similar acceptance rate (∼0.2), demonstrating high efficiency of vsREMD to characterize the protein conformational change and associated free-energy profile. Thus, vsREMD is a highly efficient approach for studying the large-scale conformational change of protein systems.

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.

Optimal Coarse-Grained Site Selection in Elastic Network Models of Biomolecules

Elastic network models, simple structure-based representations of biomolecules where atoms interact via short-range harmonic potentials, provide great insight into a molecule's internal dynamics and mechanical properties at extremely low computational cost. Their efficiency and effectiveness have made them a pivotal instrument in the computer-aided study of proteins and, since a few years, also of nucleic acids. In general, the coarse-grained sites, i.e. those effective force centers onto which the all-atom structure is mapped, are constructed based on intuitive rules: a typical choice for proteins is to retain only the C _α atoms of each amino acid. However, a mapping strategy relying only on the atom type and not the local properties of its embedding can be suboptimal compared to a more careful selection. Here, we present a strategy in which the subset of atoms, each of which is mapped onto a unique coarse-grained site of the model, is selected in a stochastic search aimed at optimizing a cost function. The latter is taken to be a simple measure of the consistency between the harmonic approximation of an elastic network model and the harmonic model obtained through exact integration of the discarded degrees of freedom. The method is applied to two representatives of structurally very different types of biomolecules: the protein adenylate kinase and the RNA molecule adenine riboswitch. Our analysis quantifies the substantial impact that an algorithm-driven selection of coarse-grained sites can have on a model's properties.

Concurrent coupling of realistic and ideal models of liquids and solids in Hamiltonian adaptive resolution simulations

To understand the properties of a complex system it is often illuminating to perform a comparison with a simpler, even idealised one. A prototypical application of this approach is the calculation of free energies and chemical potentials in liquids, which can be decomposed in the sum of ideal and excess contributions. In the same spirit, in computer simulations it is possible to extract useful information on a given system making use of setups where two models, an accurate one and a simpler one, are concurrently employed and directly coupled. Here, we tackle the issue of coupling atomistic or, more in general, interacting models of a system with the corresponding idealised representations: for a liquid, this is the ideal gas, i.e. a collection of non-interacting particles; for a solid, we employ the ideal Einstein crystal, a construct in which particles are decoupled from one another and restrained by a harmonic, exactly integrable potential. We describe in detail the practical and technical aspects of these simulations, and suggest that the concurrent usage and coupling of realistic and ideal models represents a promising strategy to investigate liquids and solids in silico.

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.

Substrate Binding Specifically Modulates Domain Arrangements in Adenylate Kinase

The enzyme adenylate kinase (ADK) features two substrate binding domains that undergo large-scale motions during catalysis. In the apo state, the enzyme preferentially adopts a globally open state with accessible binding sites. Binding of two substrate molecules (AMP + ATP or ADP + ADP) results in a closed domain conformation, allowing efficient phosphoryl-transfer catalysis. We employed molecular dynamics simulations to systematically investigate how the individual domain motions are modulated by the binding of substrates. Two-dimensional free-energy landscapes were calculated along the opening of the two flexible lid domains for apo and holo ADK as well as for all single natural substrates bound to one of the two binding sites of ADK. The simulations reveal a strong dependence of the conformational ensembles on type and binding position of the bound substrates and a nonsymmetric behavior of the lid domains. Altogether, the ensembles suggest that, upon initial substrate binding to the corresponding lid site, the opposing lid is maintained open and accessible for subsequent substrate binding. In contrast, ATP binding to the AMP-lid induces global domain closing, preventing further substrate binding to the ATP-lid site. This might constitute a mechanism by which the enzyme avoids the formation of a stable but enzymatically unproductive state.

Ligand Docking to Intermediate and Close-To-Bound Conformers Generated by an Elastic Network Model Based Algorithm for Highly Flexible Proteins

Incorporating receptor flexibility in small ligand-protein docking still poses a challenge for proteins undergoing large conformational changes. In the absence of bound structures, sampling conformers that are accessible by apo state may facilitate docking and drug design studies. For this aim, we developed an unbiased conformational search algorithm, by integrating global modes from elastic network model, clustering and energy minimization with implicit solvation. Our dataset consists of five diverse proteins with apo to complex RMSDs 4.7-15 Å. Applying this iterative algorithm on apo structures, conformers close to the bound-state (RMSD 1.4-3.8 Å), as well as the intermediate states were generated. Dockings to a sequence of conformers consisting of a closed structure and its "parents" up to the apo were performed to compare binding poses on different states of the receptor. For two periplasmic binding proteins and biotin carboxylase that exhibit hinge-type closure of two dynamics domains, the best pose was obtained for the conformer closest to the bound structure (ligand RMSDs 1.5-2 Å). In contrast, the best pose for adenylate kinase corresponded to an intermediate state with partially closed LID domain and open NMP domain, in line with recent studies (ligand RMSD 2.9 Å). The docking of a helical peptide to calmodulin was the most challenging case due to the complexity of its 15 Å transition, for which a two-stage procedure was necessary. The technique was first applied on the extended calmodulin to generate intermediate conformers; then peptide docking and a second generation stage on the complex were performed, which in turn yielded a final peptide RMSD of 2.9 Å. Our algorithm is effective in producing conformational states based on the apo state. This study underlines the importance of such intermediate states for ligand docking to proteins undergoing large transitions.

Mapping the Dynamics Landscape of Conformational Transitions in Enzyme: The Adenylate Kinase Case

Conformational transition describes the essential dynamics and mechanism of enzymes in pursuing their various functions. The fundamental and practical challenge to researchers is to quantitatively describe the roles of large-scale dynamic transitions for regulating the catalytic processes. In this study, we tackled this challenge by exploring the pathways and free energy landscape of conformational changes in adenylate kinase (AdK), a key ubiquitous enzyme for cellular energy homeostasis. Using explicit long-timescale (up to microseconds) molecular dynamics and bias-exchange metadynamics simulations, we determined at the atomistic level the intermediate conformational states and mapped the transition pathways of AdK in the presence and absence of ligands. There is clearly chronological operation of the functional domains of AdK. Specifically in the ligand-free AdK, there is no significant energy barrier in the free energy landscape separating the open and closed states. Instead there are multiple intermediate conformational states, which facilitate the rapid transitions of AdK. In the ligand-bound AdK, the closed conformation is energetically most favored with a large energy barrier to open it up, and the conformational population prefers to shift to the closed form coupled with transitions. The results suggest a perspective for a hybrid of conformational selection and induced fit operations of ligand binding to AdK. These observations, depicted in the most comprehensive and quantitative way to date, to our knowledge, emphasize the underlying intrinsic dynamics of AdK and reveal the sophisticated conformational transitions of AdK in fulfilling its enzymatic functions. The developed methodology can also apply to other proteins and biomolecular systems.

SPECTRUS: A Dimensionality Reduction Approach for Identifying Dynamical Domains in Protein Complexes from Limited Structural Datasets

Identifying dynamical, quasi-rigid domains in proteins provides a powerful means for characterizing functionally oriented structural changes via a parsimonious set of degrees of freedom. In fact, the relative displacements of few dynamical domains usually suffice to rationalize the mechanics underpinning biological functionality in proteins and can even be exploited for structure determination or refinement purposes. Here we present SPECTRUS, a general scheme that, by solely using amino acid distance fluctuations, can pinpoint the innate quasi-rigid domains of single proteins or large complexes in a robust way. Consistent domains are usually obtained by using either a pair of representative structures or thousands of conformers. The functional insights offered by the approach are illustrated for biomolecular systems of very different size and complexity such as kinases, ion channels, and viral capsids. The decomposition tool is available as a software package and web server at spectrus.sissa.it.

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.

Conformational preferences underlying reduced activity of a thermophilic ribonuclease H

The conformational basis for reduced activity of the thermophilic ribonuclease HI enzyme from Thermus thermophilus, compared to its mesophilic homolog from Escherichia coli, is elucidated using a combination of NMR spectroscopy and molecular dynamics (MD) simulations. Explicit-solvent all-atom MD simulations of the two wild-type proteins and an E. coli mutant in which a glycine residue is inserted after position 80 to mimic the T. thermophilus protein reproduce the differences in conformational dynamics determined from (15)N spin-relaxation NMR spectroscopy of three loop regions that surround the active site and contain functionally important residues: the glycine-rich region, the handle region, and the β5/αE loop. Examination of the MD trajectories indicates that the thermophilic protein samples conformations productive for substrate binding and activity less frequently than the mesophilic enzyme, although these differences may manifest as either increased or decreased relative flexibility of the different regions. Additional MD simulations indicate that mutations increasing activity of the T. thermophilus enzyme at mesophilic temperatures do so by reconfiguring the local environments of the mutated sites to more closely resemble active conformations. Taken together, the results show that both locally increased and decreased flexibility contribute to an overall reduction in activity of T. thermophilus ribonuclease H compared to its mesophilic E. coli homolog.

Thermal adaptation of conformational dynamics in ribonuclease H

The relationship between inherent internal conformational processes and enzymatic activity or thermodynamic stability of proteins has proven difficult to characterize. The study of homologous proteins with differing thermostabilities offers an especially useful approach for understanding the functional aspects of conformational dynamics. In particular, ribonuclease HI (RNase H), an 18 kD globular protein that hydrolyzes the RNA strand of RNA:DNA hybrid substrates, has been extensively studied by NMR spectroscopy to characterize the differences in dynamics between homologs from the mesophilic organism E. coli and the thermophilic organism T. thermophilus. Herein, molecular dynamics simulations are reported for five homologous RNase H proteins of varying thermostabilities and enzymatic activities from organisms of markedly different preferred growth temperatures. For the E. coli and T. thermophilus proteins, strong agreement is obtained between simulated and experimental values for NMR order parameters and for dynamically averaged chemical shifts, suggesting that these simulations can be a productive platform for predicting the effects of individual amino acid residues on dynamic behavior. Analyses of the simulations reveal that a single residue differentiates between two different and otherwise conserved dynamic processes in a region of the protein known to form part of the substrate-binding interface. Additional key residues within these two categories are identified through the temperature-dependence of these conformational processes.

The relationship between enzymatic activity and protein stability has long been a difficult problem in the study of protein biochemistry. Enzymes may undergo structural changes in order to bind substrates, catalyze chemical reactions, and release products, but flexibility often is inversely correlated with thermodynamic stability. Proteins from organisms that are adapted to high temperature can be both more rigid and less active at ambient temperature than their homologs from organisms that grow at lower temperatures. For this reason, studying homologous pairs of proteins from organisms adapted to different thermal environments is a productive way to identify functionally important motions. In this work we perform comparative analyses of molecular dynamics simulations for five ribonuclease H proteins of varying thermal stabilities, isolated from organisms that grow in varying thermal environments. We identify two different mechanisms of motion in a region of the protein that interacts with substrate molecules, suggesting at least two forms of thermal adaptation in this protein family.

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.

Ultrafast real-time visualization of active site flexibility of flavoenzyme thymidylate synthase ThyX

In many bacteria the flavoenzyme thymidylate synthase ThyX produces the DNA nucleotide deoxythymidine monophosphate from dUMP, using methylenetetrahydrofolate as carbon donor and NADPH as hydride donor. Because all three substrates bind in close proximity to the catalytic flavin adenine dinucleotide group, substantial flexibility of the ThyX active site has been hypothesized. Using femtosecond time-resolved fluorescence spectroscopy, we have studied the conformational heterogeneity and the conformational interconversion dynamics in real time in ThyX from the hyperthermophilic bacterium Thermotoga maritima. The dynamics of electron transfer to excited flavin adenine dinucleotide from a neighboring tyrosine residue are used as a sensitive probe of the functional dynamics of the active site. The fluorescence decay spanned a full three orders of magnitude, demonstrating a very wide range of conformations. In particular, at physiological temperatures, multiple angstrom cofactor-residue displacements occur on the picoseconds timescale. These experimental findings are supported by molecular dynamics simulations. Binding of the dUMP substrate abolishes this flexibility and stabilizes the active site in a configuration where dUMP closely interacts with the flavin cofactor and very efficiently quenches fluorescence itself. Our results indicate a dynamic selected-fit mechanism where binding of the first substrate dUMP at high temperature stabilizes the enzyme in a configuration favorable for interaction with the second substrate NADPH, and more generally have important implications for the role of active site flexibility in enzymes interacting with multiple poly-atom substrates and products. Moreover, our data provide the basis for exploring the effect of inhibitor molecules on the active site dynamics of ThyX and other multisubstrate flavoenzymes.

The underappreciated role of allostery in the cellular network

Allosteric propagation results in communication between distinct sites in the protein structure; it also encodes specific effects on cellular pathways, and in this way it shapes cellular response. One example of long-range effects is binding of morphogens to cell surface receptors, which initiates a cascade of protein interactions that leads to genome activation and specific cellular action. Allosteric propagation results from combinations of multiple factors, takes place through dynamic shifts of conformational ensembles, and affects the equilibria of macromolecular interactions. Here, we (a) emphasize the well-known yet still underappreciated role of allostery in conveying explicit signals across large multimolecular assemblies and distances to specify cellular action; (b) stress the need for quantitation of the allosteric effects; and finally, (c) propose that each specific combination of allosteric effectors along the pathway spells a distinct function. The challenges are colossal; the inspiring reward will be predicting function, misfunction, and outcomes of drug regimes.

Allosteric activation transitions in enzymes and biomolecular motors: insights from atomistic and coarse-grained simulations

The chemical step in enzymes is usually preceded by a kinetically distinct activation step that involves large-scale conformational transitions. In "simple" enzymes this step corresponds to the closure of the active site; in more complex enzymes, such as biomolecular motors, the activation step is more complex and may involve interactions with other biomolecules. These activation transitions are essential to the function of enzymes and perturbations in the scale and/or rate of these transitions are implicated in various serious human diseases; incorporating key flexibilities into engineered enzymes is also considered a major remaining challenge in rational enzyme design. Therefore it is important to understand the underlying mechanism of these transitions. This is a significant challenge to both experimental and computational studies because of the allosteric and multi-scale nature of such transitions. Using our recent studies of two enzyme systems, myosin and adenylate kinase (AK), we discuss how atomistic and coarse-grained simulations can be used to provide insights into the mechanism of activation transitions in realistic systems. Collectively, the results suggest that although many allosteric transitions can be viewed as domain displacements mediated by flexible hinges, there are additional complexities and various deviations. For example, although our studies do not find any evidence for "cracking" in AK, our results do underline the contribution of intra-domain properties (e.g., dihedral flexibility) to the rate of the transition. The study of mechanochemical coupling in myosin highlights that local changes important to chemistry require stabilization from more extensive structural changes; in this sense, more global structural transitions are needed to activate the chemistry in the active site. These discussions further emphasize the importance of better understanding factors that control the degree of co-operativity for allosteric transitions, again hinting at the intimate connection between protein stability and functional flexibility. Finally, a number of topics of considerable future interest are briefly discussed.

Molecular mechanism of allosteric communication in Hsp70 revealed by molecular dynamics simulations

Investigating ligand-regulated allosteric coupling between protein domains is fundamental to understand cell-life regulation. The Hsp70 family of chaperones represents an example of proteins in which ATP binding and hydrolysis at the Nucleotide Binding Domain (NBD) modulate substrate recognition at the Substrate Binding Domain (SBD). Herein, a comparative analysis of an allosteric (Hsp70-DnaK) and a non-allosteric structural homolog (Hsp110-Sse1) of the Hsp70 family is carried out through molecular dynamics simulations, starting from different conformations and ligand-states. Analysis of ligand-dependent modulation of internal fluctuations and local deformation patterns highlights the structural and dynamical changes occurring at residue level upon ATP-ADP exchange, which are connected to the conformational transition between closed and open structures. By identifying the dynamically responsive protein regions and specific cross-domain hydrogen-bonding patterns that differentiate Hsp70 from Hsp110 as a function of the nucleotide, we propose a molecular mechanism for the allosteric signal propagation of the ATP-encoded conformational signal.

Allostery, or the capability of proteins to respond to ligand binding events with a variation in structure or dynamics at a distant site, is a common feature for biomolecular function and regulation in a large number of proteins. Intra-protein connections and inter-residue coordinations underlie allosteric mechanisms and react to binding primarily through a finely tuned modulation of motions and structures at the microscopic scale. Hence, all-atom molecular dynamics simulations are suitable to investigate the molecular basis of allostery. Moreover, understanding intra-protein communication pathways at atomistic resolutions offers unique opportunities in rational drug design. Proteins of the Hsp70 family are allosteric molecular chaperones involved in maintaining cellular protein homeostasis. These proteins are involved in several types of cancer, neurodegenerative diseases, aging and infections and are therefore pharmaceutically relevant targets. In this work we have analyzed, by multiple molecular dynamics simulations, the long-range dynamical and conformational effects of ligands bound to Hsp70, and found relevant differences in comparison to the known non-allosteric structural homolog Hsp110. The resulting model of the mechanism of allosteric propagation offers the opportunity of identifying on-pathway allosteric druggable sites, which we propose could guide rational drug-design efforts targeting Hsp70.

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).

Comparing proteins by their internal dynamics: exploring structure-function relationships beyond static structural alignments

The growing interest for comparing protein internal dynamics owes much to the realisation that protein function can be accompanied or assisted by structural fluctuations and conformational changes. Analogously to the case of functional structural elements, those aspects of protein flexibility and dynamics that are functionally oriented should be subject to evolutionary conservation. Accordingly, dynamics-based protein comparisons or alignments could be used to detect protein relationships that are more elusive to sequence and structural alignments. Here we provide an account of the progress that has been made in recent years towards developing and applying general methods for comparing proteins in terms of their internal dynamics and advance the understanding of the structure-function relationship.

Multiscale Coarse-Graining via Normal Mode Analysis

A multiscale coarse-graining method called the normal-mode analysis based fluctuation matching (NMA-FM) is developed for constructing coarse-grained models of biomolecular systems. In the framework of normal-mode analysis, an arbitrary fine-grained model can be systematically converted to a more coarse-grained model, while the crucial low-frequency motions of the fine-grained system are able to be reproduced in the coarse-grained modeling. The method relies on the technique of fluctuation matching that has been devised earlier for parametrizing heterogeneous elastic network models based on data from atomistic molecular dynamics simulations. The new approach is quite efficient since it avoids expensive atomistic molecular dynamics simulations and can start from already coarse-grained elastic network models. In the practical aspect, the method is suitable for conformational analyses of large biomacromolecules and calculations of mechanical properties of biomaterials, which is demonstrated by the studied systems including an amyloid dimer, lysozyme and adenylate kinase proteins, and the S2 subdomain of myosin.

Elastic network normal modes provide a basis for protein structure refinement

It is well recognized that thermal motions of atoms in the protein native state, the fluctuations about the minimum of the global free energy, are well reproduced by the simple elastic network models (ENMs) such as the anisotropic network model (ANM). Elastic network models represent protein dynamics as vibrations of a network of nodes (usually represented by positions of the heavy atoms or by the C(α) atoms only for coarse-grained representations) in which the spatially close nodes are connected by harmonic springs. These models provide a reliable representation of the fluctuational dynamics of proteins and RNA, and explain various conformational changes in protein structures including those important for ligand binding. In the present paper, we study the problem of protein structure refinement by analyzing thermal motions of proteins in non-native states. We represent the conformational space close to the native state by a set of decoys generated by the I-TASSER protein structure prediction server utilizing template-free modeling. The protein substates are selected by hierarchical structure clustering. The main finding is that thermal motions for some substates, overlap significantly with the deformations necessary to reach the native state. Additionally, more mobile residues yield higher overlaps with the required deformations than do the less mobile ones. These findings suggest that structural refinement of poorly resolved protein models can be significantly enhanced by reduction of the conformational space to the motions imposed by the dominant normal modes.

Modulation of a pre-existing conformational equilibrium tunes adenylate kinase activity

Structural plasticity is often required for distinct microscopic steps during enzymatic reaction cycles. Adenylate kinase from Escherichia coli (AK(eco)) populates two major conformations in solution; the open (inactive) and closed (active) state, and the overall turnover rate is inversely proportional to the lifetime of the active conformation. Therefore, structural plasticity is intimately coupled to enzymatic turnover in AK(eco). Here, we probe the open to closed conformational equilibrium in the absence of bound substrate with NMR spectroscopy and molecular dynamics simulations. The conformational equilibrium in absence of substrate and, in turn, the turnover number can be modulated with mutational- and osmolyte-driven perturbations. Removal of one hydrogen bond between the ATP and AMP binding subdomains results in a population shift toward the open conformation and a resulting increase of k(cat). Addition of the osmolyte TMAO to AK(eco) results in population shift toward the closed conformation and a significant reduction of k(cat). The Michaelis constants (K(M)) scale with the change in k(cat), which follows from the influence of the population of the closed conformation for substrate binding affinity. Hence, k(cat) and K(M) are mutually dependent, and in the case of AK(eco), any perturbation that modulates k(cat) is mirrored with a proportional response in K(M). Thus, our results demonstrate that the equilibrium constant of a pre-existing conformational equilibrium directly affects enzymatic catalysis. From an evolutionary perspective, our findings suggest that, for AK(eco), there exists ample flexibility to obtain a specificity constant (k(cat)/K(M)) that commensurate with the exerted cellular selective pressure.

Event detection and sub-state discovery from biomolecular simulations using higher-order statistics: application to enzyme adenylate kinase

Biomolecular simulations at millisecond and longer time-scales can provide vital insights into functional mechanisms. Because post-simulation analyses of such large trajectory datasets can be a limiting factor in obtaining biological insights, there is an emerging need to identify key dynamical events and relating these events to the biological function online, that is, as simulations are progressing. Recently, we have introduced a novel computational technique, quasi-anharmonic analysis (QAA) (Ramanathan et al., PLoS One 2011;6:e15827), for partitioning the conformational landscape into a hierarchy of functionally relevant sub-states. The unique capabilities of QAA are enabled by exploiting anharmonicity in the form of fourth-order statistics for characterizing atomic fluctuations. In this article, we extend QAA for analyzing long time-scale simulations online. In particular, we present HOST4MD--a higher-order statistical toolbox for molecular dynamics simulations, which (1) identifies key dynamical events as simulations are in progress, (2) explores potential sub-states, and (3) identifies conformational transitions that enable the protein to access those sub-states. We demonstrate HOST4MD on microsecond timescale simulations of the enzyme adenylate kinase in its apo state. HOST4MD identifies several conformational events in these simulations, revealing how the intrinsic coupling between the three subdomains (LID, CORE, and NMP) changes during the simulations. Further, it also identifies an inherent asymmetry in the opening/closing of the two binding sites. We anticipate that HOST4MD will provide a powerful and extensible framework for detecting biophysically relevant conformational coordinates from long time-scale simulations.

Direct and allosteric inhibition of the FGF2/HSPGs/FGFR1 ternary complex formation by an antiangiogenic, thrombospondin-1-mimic small molecule

Fibroblast growth factors (FGFs) are recognized targets for the development of therapies against angiogenesis-driven diseases, including cancer. The formation of a ternary complex with the transmembrane tyrosine kinase receptors (FGFRs), and heparan sulphate proteoglycans (HSPGs) is required for FGF2 pro-angiogenic activity. Here by using a combination of techniques including Nuclear Magnetic Resonance, Molecular Dynamics, Surface Plasmon Resonance and cell-based binding assays we clarify the molecular mechanism of inhibition of an angiostatic small molecule, sm27, mimicking the endogenous inhibitor of angiogenesis, thrombospondin-1. NMR and MD data demonstrate that sm27 engages the heparin-binding site of FGF2 and induces long-range dynamics perturbations along FGF2/FGFR1 interface regions. The functional consequence of the inhibitor binding is an impaired FGF2 interaction with both its receptors, as demonstrated by SPR and cell-based binding assays. We propose that sm27 antiangiogenic activity is based on a twofold-direct and allosteric-mechanism, inhibiting FGF2 binding to both its receptors.