Interconversion of functional motions between mesophilic and thermophilic adenylate kinases

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

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

Adenylate kinases of thermophiles Aquifex aeolicus and Geobacillus stearothermophilus: biochemical and kinetic studies

Adenylate kinases (AK) play a pivotal role in the regulation of cellular energy. The aim of our work was to achieve the overproduction and purification of AKs from two groups of bacteria and to determine, for the first time, the comprehensive biochemical and kinetic properties of adenylate kinase from Gram-negative Aquifex aeolicus (AK_aq) and Gram-positive Geobacillus stearothermophilus (AK_st). Therefore we determined K_M and V_max values, and the effects of temperature, pH, metal ions, donors of the phosphate groups and inhibitor Ap₅A for both thermophilic AKs. The kinetic studies indicate that both AKs exhibit significantly higher affinity for substrates with the pyrophosphate group than for adenosine monophosphate. AK activation by Mg²⁺ and Mn²⁺ revealed that both ions are efficient in the synthesis of adenosine diphosphate and adenosine triphosphate; however, Mn²⁺ ions at 0.2-2.0 mmol/L concentration were more efficient in the activation of the ATP synthesis than Mg²⁺ ions. Our research demonstrates that zinc ions inhibit the activity of enzymes in both directions, while Ap₅A at a concentration of 10 µmol/L and 50 µmol/L inhibited both enzymes with a different efficiency. Sigmoid-like kinetics were detected at high ATP concentrations not balanced by Mg²⁺, suggesting the allosteric effect of ATP for both bacterial AKs.

Biomolecular QM/MM Simulations: What Are Some of the "Burning Issues"?

QM/MM simulations have become an indispensable tool in many chemical and biochemical investigations. Considering the tremendous degree of success, including recognition by a 2013 Nobel Prize in Chemistry, are there still "burning challenges" in QM/MM methods, especially for biomolecular systems? In this short Perspective, we discuss several issues that we believe greatly impact the robustness and quantitative applicability of QM/MM simulations to many, if not all, biomolecules. We highlight these issues with observations and relevant advances from recent studies in our group and others in the field. Despite such limited scope, we hope the discussions are of general interest and will stimulate additional developments that help push the field forward in meaningful directions.

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.

Exploration of Multistate Conformational Dynamics upon Ligand Binding of a Monomeric Enzyme Involved in Pyrophosphoryl Transfer

HPPK (6-hydroxymethyl-7,8-dihydropterin pyrophosphokinase) is a monomeric protein with 158 residues, which undergoes large-scale conformational changes between apo, open, and holo states responding to ligand binding for its function. It has been explored widely as an excellent target for potential antibacterial drug development. However, little is known about how conformational dynamics between the native states influences the substrate recognition and the functionality of enzymatic catalysis. Here, we report a coarse-grained triple-basin structure-based model upon ligand binding to describe such multiple-state system by the molecular dynamics simulation. With our model, we have made theoretical predictions that are in good agreement with the experimental measurements. Our results revealed the intrinsic conformational fluctuations between apo and open states without ligand binding. We found that HPPK can switch to the activated holo state upon the ordered binding of the two ligands (ATP and HP). We uncovered the underlying mechanism by which major induced fit and minor population shift pathways coexist upon ligand binding by quantitative flux analysis. Additionally, we pointed out the structural origin for the conformational changes and identified the key residues as well as contact interactions. We further explored the temperature effect on the conformational distributions and pathway weights. It gave strong support that higher temperatures promote population shift, while the induced fit pathway is always the predominant activation route of the HPPK system. These findings will provide significant insights of the mechanisms of the multistate conformational dynamics of HPPK upon ligand binding.

Glutamine Hydrolysis by Imidazole Glycerol Phosphate Synthase Displays Temperature Dependent Allosteric Activation

The enzyme imidazole glycerol phosphate synthase (IGPS) is a model for studies of long-range allosteric regulation in enzymes. Binding of the allosteric effector ligand N'-[5'-phosphoribulosyl)formimino]-5-aminoimidazole-4-carboxamide-ribonucleotide (PRFAR) stimulates millisecond (ms) timescale motions in IGPS that enhance its catalytic function. We studied the effect of temperature on these critical conformational motions and the catalytic mechanism of IGPS from the hyperthermophile Thermatoga maritima in an effort to understand temperature-dependent allostery. Enzyme kinetic and NMR dynamics measurements show that apo and PRFAR-activated IGPS respond differently to changes in temperature. Multiple-quantum Carr-Purcell-Meiboom-Gill (CPMG) relaxation dispersion experiments performed at 303, 323, and 343 K (30, 50, and 70°C) reveal that millisecond flexibility is enhanced to a higher degree in apo IGPS than in the PRFAR-bound enzyme as the sample temperature is raised. We find that the flexibility of the apo enzyme is nearly identical to that of its PRFAR activated state at 343 K, whereas conformational motions are considerably different between these two forms of the enzyme at room temperature. Arrhenius analyses of these flexible sites show a varied range of activation energies that loosely correlate to allosteric communities identified by computational methods and reflect local changes in dynamics that may facilitate conformational sampling of the active conformation. In addition, kinetic assays indicate that allosteric activation by PRFAR decreases to 65-fold at 343 K, compared to 4,200-fold at 303 K, which mirrors the decreased effect of PRFAR on ms motions relative to the unactivated enzyme. These studies indicate that at the growth temperature of T. maritima, PFRAR is a weaker allosteric activator than it is at room temperature and illustrate that the allosteric mechanism of IGPS is temperature dependent.

The Atomistic Mechanism of Conformational Transition of Adenylate Kinase Investigated by Lorentzian Structure-Based Potential

We present a new all-atom structure-based method to study protein conformational transitions using Lorentzian attractive interactions based on native structures. The variability of each native contact is estimated based on evolutionary information using a machine learning method. To test the validity of this approach, we have investigated the conformational transition of adenylate kinase (ADK). The intrinsic boundedness of the Lorentzian attractive interactions facilitated frequent conformational transitions, and consequently we were able to observe more than 1000 structural interconversions between the open and closed states of ADK out of a total of 6 μs MD simulations. ADK has three domains: the nucleoside monophosphate (NMP) binding domain, the LID-domain, and the CORE domain, which catalyze the interconversion between ATP and ADP. We identified two transition states: a more frequent LID-closed-NMP-open (TS1) state and a less frequent LID-open-NMP-closed (TS2) state. The transition was found to be symmetric in both directions via TS1. We also obtained an off-pathway metastable state that was previously observed with physics-based all-atom simulations but not with coarse-grained models. In the metastable state, the LID domain was slightly twisted and formed contacts with the NMP domain. Our model correctly identified a total of 14 out of the top 16 residues with highest fluctuation by NMR experiment, thus showing excellent agreement with experimental NMR relaxation data and overwhelmingly better results than existing models.

Discriminating binding mechanisms of an intrinsically disordered protein via a multi-state coarse-grained model

Many proteins undergo a conformational transition upon binding to their cognate binding partner, with intrinsically disordered proteins (IDPs) providing an extreme example in which a folding transition occurs. However, it is often not clear whether this occurs via an "induced fit" or "conformational selection" mechanism, or via some intermediate scenario. In the first case, transient encounters with the binding partner favour transitions to the bound structure before the two proteins dissociate, while in the second the bound structure must be selected from a subset of unbound structures which are in the correct state for binding, because transient encounters of the incorrect conformation with the binding partner are most likely to result in dissociation. A particularly interesting situation involves those intrinsically disordered proteins which can bind to different binding partners in different conformations. We have devised a multi-state coarse-grained simulation model which is able to capture the binding of IDPs in alternate conformations, and by applying it to the binding of nuclear coactivator binding domain (NCBD) to either ACTR or IRF-3 we are able to determine the binding mechanism. By all measures, the binding of NCBD to either binding partner appears to occur via an induced fit mechanism. Nonetheless, we also show how a scenario closer to conformational selection could arise by choosing an alternative non-binding structure for NCBD.

Global transitions of proteins explored by a multiscale hybrid methodology: application to adenylate kinase

Efficient and accurate mapping of transition pathways is a challenging problem in allosteric proteins. We propose here a to our knowledge new methodology called collective molecular dynamics (coMD). coMD takes advantage of the collective modes of motions encoded by the fold, simultaneously evaluating the interactions and energetics via a full-atomic MD simulation protocol. The basic approach is to deform the structure collectively along the modes predicted by the anisotropic network model, upon selecting them via a Monte Carlo/Metropolis algorithm from among the complete pool of all accessible modes. Application to adenylate kinase, an allosteric enzyme composed of three domains, CORE, LID, and NMP, shows that both open-to-closed and closed-to-open transitions are readily sampled by coMD, with large-scale motions of the LID dominating. An energy-barrier crossing occurs during the NMP movements. The energy barrier originates from a switch between the salt bridges K136-D118 at the LID-CORE interface and K57-E170 and D33-R156 at the CORE-NMP and LID-NMP interfaces, respectively. Despite its simplicity and computing efficiency, coMD yields ensembles of transition pathways in close accord with detailed full atomic simulations, lending support to its utility as a multiscale hybrid method for efficiently exploring the allosteric transitions of multidomain or multimeric proteins.

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

Biomolecular conformational transitions are essential to biological functions. Most experimental methods report on the long-lived functional states of biomolecules, but information about the transition pathways between these stable states is generally scarce. Such transitions involve short-lived conformational states that are difficult to detect experimentally. For this reason, computational methods are needed to produce plausible hypothetical transition pathways that can then be probed experimentally. Here we propose a simple and computationally efficient method, called ANMPathway, for constructing a physically reasonable pathway between two endpoints of a conformational transition. We adopt a coarse-grained representation of the protein and construct a two-state potential by combining two elastic network models (ENMs) representative of the experimental structures resolved for the endpoints. The two-state potential has a cusp hypersurface in the configuration space where the energies from both the ENMs are equal. We first search for the minimum energy structure on the cusp hypersurface and then treat it as the transition state. The continuous pathway is subsequently constructed by following the steepest descent energy minimization trajectories starting from the transition state on each side of the cusp hypersurface. Application to several systems of broad biological interest such as adenylate kinase, ATP-driven calcium pump SERCA, leucine transporter and glutamate transporter shows that ANMPathway yields results in good agreement with those from other similar methods and with data obtained from all-atom molecular dynamics simulations, in support of the utility of this simple and efficient approach. Notably the method provides experimentally testable predictions, including the formation of non-native contacts during the transition which we were able to detect in two of the systems we studied. An open-access web server has been created to deliver ANMPathway results.

Many biomolecules are like tiny molecular machines that need to change their shapes and visit many states to perform their biological functions. For a complete molecular understanding of a biological process, one needs to have information on the relevant stable states of the system in question, as well as the pathways by which the system travels from one state to another. We report here an efficient computational method that uses the knowledge of experimental structures of a pair of stable states in order to construct an energetically favoravle pathway between them. We adopt a simple representation of the molecular system by replacing the atoms with beads connected by springs and constructing an energy function with two minima around the end-states. We searched for the structure with highest energy that the system is most likely to visit during the transition and created two paths starting from this structure and proceeding toward the end-states. The combined result of these two paths is the minimum energy pathway between the two stable states. We apply this method to study important structural changes in one enzyme and three large proteins that transport small molecules and ions across the cell membrane.

Balancing bond, nonbond, and gō-like terms in coarse grain simulations of conformational dynamics

Characterization of the protein conformational landscape remains a challenging problem, whether it concerns elucidating folding mechanisms, predicting native structures or modeling functional transitions. Coarse-grained molecular dynamics simulation methods enable exhaustive sampling of the energetic landscape at resolutions of biological interest. The general utility of structure-based models is reviewed along with their differing levels of approximation. Simple Gō models incorporate attractive native interactions and repulsive nonnative contacts, resulting in an ideal smooth landscape. Non-Gō coarse-grained models reduce the parameter set as needed but do not include bias to any desired native structure. While non-Gō models have achieved limited success in protein coarse-graining, they can be combined with native structured-based potentials to create a balanced and powerful force field. Recent applications of such Gō-like models have yielded insight into complex folding mechanisms and conformational transitions in large macromolecules. The accuracy and usefulness of reduced representations are also revealed to be a function of the mathematical treatment of the intrinsic bonded topology.

Experimental evolution of protein-protein interaction networks

The modern synthesis of evolutionary theory and genetics has enabled us to discover underlying molecular mechanisms of organismal evolution. We know that in order to maximize an organism's fitness in a particular environment, individual interactions among components of protein and nucleic acid networks need to be optimized by natural selection, or sometimes through random processes, as the organism responds to changes and/or challenges in the environment. Despite the significant role of molecular networks in determining an organism's adaptation to its environment, we still do not know how such inter- and intra-molecular interactions within networks change over time and contribute to an organism's evolvability while maintaining overall network functions. One way to address this challenge is to identify connections between molecular networks and their host organisms, to manipulate these connections, and then attempt to understand how such perturbations influence molecular dynamics of the network and thus influence evolutionary paths and organismal fitness. In the present review, we discuss how integrating evolutionary history with experimental systems that combine tools drawn from molecular evolution, synthetic biology and biochemistry allow us to identify the underlying mechanisms of organismal evolution, particularly from the perspective of protein interaction networks.

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.

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).

Large-scale motions in the adenylate kinase solution ensemble: coarse-grained simulations and comparison with solution X-ray scattering

While coarse-grained (CG) simulations provide an efficient approach to identify small- and large-scale motions important to protein conformational transitions, coupling with appropriate experimental validation is essential. Here, by comparing small-angle X-ray scattering (SAXS) predictions from CG simulation ensembles of adenylate kinase (AK) with a range of energetic parameters, we demonstrate that AK is flexible in solution in the absence of ligand and that a small population of the closed form exists without ligand. In addition, by analyzing variation of scattering patterns within CG simulation ensembles, we reveal that rigid-body motion of the LID domain corresponds to a dominant scattering feature. Thus, we have developed a novel approach for three-dimensional structural interpretation of SAXS data. Finally, we demonstrate that the agreement between predicted and experimental SAXS can be improved by increasing the simulation temperature or by computationally mutating selected residues to glycine, both of which perturb LID rigid-body flexibility.