Apo adenylate kinase encodes its holo form: a principal component and varimax analysis

Molecular Docking: Challenges, Advances and its Use in Drug Discovery Perspective

Molecular docking is a process through which small molecules are docked into the macromolecular structures for scoring its complementary values at the binding sites. It is a vibrant research area with dynamic utility in structure-based drug-designing, lead optimization, biochemical pathway and for drug designing being the most attractive tools. Two pillars for a successful docking experiment are correct pose and affinity prediction. Each program has its own advantages and drawbacks with respect to their docking accuracy, ranking accuracy and time consumption so a general conclusion cannot be drawn. Moreover, users don't always consider sufficient diversity in their test sets which results in certain programs to outperform others. In this review, the prime focus has been laid on the challenges of docking and troubleshooters in existing programs, underlying algorithmic background of docking, preferences regarding the use of docking programs for best results illustrated with examples, comparison of performance for existing tools and algorithms, state of art in docking, recent trends of diseases and current drug industries, evidence from clinical trials and post-marketing surveillance are discussed. These aspects of the molecular drug designing paradigm are quite controversial and challenging and this review would be an asset to the bioinformatics and drug designing communities.

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.

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.

¹H, ¹³C, ¹⁵N backbone and side-chain resonance assignments of the human adenylate kinase 1 in apo form

AK1 (Adenylate Kinase 1) plays crucial roles in processes such as cellular phosphotransfer networks, neuronal maturation and regeneration, gating of ABC transporter CFTR, tumor cell metabolism and myocardial energetic homeostasis. Here we report (1)H, (15)N and (13)C backbone and side-chain resonance assignments of the human AK1 protein in apo form. This work lays the essential basis for the further structure determination of hAK1.

Conformational dynamics of a ligand-free adenylate kinase

Adenylate kinase (AdK) is a phosphoryl-transfer enzyme with important physiological functions. Based on a ligand-free open structure and a ligand-bound closed structure solved by crystallography, here we use molecular dynamics simulations to examine the stability and dynamics of AdK conformations in the absence of ligands. We first perform multiple simulations starting from the open or the closed structure, and observe their free evolutions during a simulation time of 100 or 200 nanoseconds. In all seven simulations starting from the open structure, AdK remained stable near the initial conformation. The eight simulations initiated from the closed structure, in contrast, exhibited large variation in the subsequent evolutions, with most (seven) undergoing large-scale spontaneous conformational changes and approaching or reaching the open state. To characterize the thermodynamics of the transition, we propose and apply a new sampling method that employs a series of restrained simulations to calculate a one-dimensional free energy along a curved pathway in the high-dimensional conformational space. Our calculated free energy profile features a single minimum at the open conformation, and indicates that the closed state, with a high (∼13 kcal/mol) free energy, is not metastable, consistent with the observed behaviors of the unrestrained simulations. Collectively, our simulations suggest that it is energetically unfavorable for the ligand-free AdK to access the closed conformation, and imply that ligand binding may precede the closure of the enzyme.

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.

Conformational heterogeneity within the LID domain mediates substrate binding to Escherichia coli adenylate kinase: function follows fluctuations

Proteins exist as dynamic ensembles of molecules, implying that protein amino acid sequences evolved to code for both the ground state structure as well as the entire energy landscape of excited states. Accumulating theoretical and experimental evidence suggests that enzymes use such conformational fluctuations to facilitate allosteric processes important for substrate binding and possibly catalysis. This phenomenon can be clearly demonstrated in Escherichia coli adenylate kinase, where experimentally observed local unfolding of the LID subdomain, as opposed to a more commonly postulated rigid-body opening motion, is related to substrate binding. Because "entropy promoting" glycine mutations designed to increase specifically the local unfolding of the LID domain also affect substrate binding, changes in the excited energy landscape effectively tune the function of this enzyme without changing the ground state structure or the catalytic site. Thus, additional thermodynamic information, above and beyond the single folded structure of an enzyme-substrate complex, is likely required for a full and quantitative understanding of how enzymes work.

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.

Minimum free energy path of ligand-induced transition in adenylate kinase

Large-scale conformational changes in proteins involve barrier-crossing transitions on the complex free energy surfaces of high-dimensional space. Such rare events cannot be efficiently captured by conventional molecular dynamics simulations. Here we show that, by combining the on-the-fly string method and the multi-state Bennett acceptance ratio (MBAR) method, the free energy profile of a conformational transition pathway in Escherichia coli adenylate kinase can be characterized in a high-dimensional space. The minimum free energy paths of the conformational transitions in adenylate kinase were explored by the on-the-fly string method in 20-dimensional space spanned by the 20 largest-amplitude principal modes, and the free energy and various kinds of average physical quantities along the pathways were successfully evaluated by the MBAR method. The influence of ligand binding on the pathways was characterized in terms of rigid-body motions of the lid-shaped ATP-binding domain (LID) and the AMP-binding (AMPbd) domains. It was found that the LID domain was able to partially close without the ligand, while the closure of the AMPbd domain required the ligand binding. The transition state ensemble of the ligand bound form was identified as those structures characterized by highly specific binding of the ligand to the AMPbd domain, and was validated by unrestrained MD simulations. It was also found that complete closure of the LID domain required the dehydration of solvents around the P-loop. These findings suggest that the interplay of the two different types of domain motion is an essential feature in the conformational transition of the enzyme.

Predicting flexible loop regions that interact with ligands: the challenge of accurate scoring

Flexible loop regions play a critical role in the biological function of many proteins and have been shown to be involved in ligand binding. In the context of structure-based drug design, using or predicting an incorrect loop configuration can be detrimental to the study if the loop is capable of interacting with the ligand. Three protein systems, each with at least one flexible loop region in close proximity to the known binding site, were selected for loop prediction using the CorLps program; a six residue loop region from phosphoribosylglycinamide formyltransferase (GART), two nine residue loop regions from cytochrome P450 (CYP) 119, and an 11 residue loop region from enolase were selected for loop prediction. The results of this study indicate that the statistically based DFIRE scoring function implemented in the CorLps program did not accurately rank native-like predicted loop configurations in any protein system. In an attempt to improve the ranking of the native-like predicted loop configurations, the MM/GBSA and the optimized MM/GBSA-dsr scoring functions were used to re-rank the predicted loops with and without bound ligand. In general, single snapshot MM/GBSA scoring provided the best ranking of native-like loop configurations. Based on the scoring function analyses presented, the optimal ranking of native-like loop configurations is still a difficult challenge and the choice of the "best" scoring function appears to be system dependent.

Enzyme closure and nucleotide binding structurally lock guanylate kinase

We investigate the conformational dynamics and mechanical properties of guanylate kinase (GK) using a multiscale approach combining high-resolution atomistic molecular dynamics and low-resolution Brownian dynamics simulations. The GK enzyme is subject to large conformational changes, leading from an open to a closed form, which are further influenced by the presence of nucleotides. As suggested by recent work on simple coarse-grained models of apo-GK, we primarily focus on GK's closure mechanism with the aim to establish a detailed picture of the hierarchy and chronology of structural events essential for the enzymatic reaction. We have investigated open-versus-closed, apo-versus-holo, and substrate-versus-product-loaded forms of the GK enzyme. Bound ligands significantly modulate the mechanical and dynamical properties of GK and rigidity profiles of open and closed states hint at functionally important differences. Our data emphasizes the role of magnesium, highlights a water channel permitting active site hydration, and reveals a structural lock that stabilizes the closed form of the enzyme.

Efficient incorporation of protein flexibility and dynamics into molecular docking simulations

Flexibility and dynamics are protein characteristics that are essential for the process of molecular recognition. Conformational changes in the protein that are coupled to ligand binding are described by the biophysical models of induced fit and conformational selection. Different concepts that incorporate protein flexibility into protein-ligand docking within the context of these two models are reviewed. Several computational studies that discuss the validity and possible limitations of such approaches will be presented. Finally, different approaches that incorporate protein dynamics, e.g., configurational entropy, and solvation effects into docking will be highlighted.

Protein functional landscapes, dynamics, allostery: a tortuous path towards a universal theoretical framework

Energy landscape theories have provided a common ground for understanding the protein folding problem, which once seemed to be overwhelmingly complicated. At the same time, the native state was found to be an ensemble of interconverting states with frustration playing a more important role compared to the folding problem. The landscape of the folded protein – the native landscape – is glassier than the folding landscape; hence, a general description analogous to the folding theories is difficult to achieve. On the other hand, the native basin phase volume is much smaller, allowing a protein to fully sample its native energy landscape on the biological timescales. Current computational resources may also be used to perform this sampling for smaller proteins, to build a ‘topographical map’ of the native landscape that can be used for subsequent analysis. Several major approaches to representing this topographical map are highlighted in this review, including the construction of kinetic networks, hierarchical trees and free energy surfaces with subsequent structural and kinetic analyses. In this review, we extensively discuss the important question of choosing proper collective coordinates characterizing functional motions. In many cases, the substates on the native energy landscape, which represent different functional states, can be used to obtain variables that are well suited for building free energy surfaces and analyzing the protein's functional dynamics. Normal mode analysis can provide such variables in cases where functional motions are dictated by the molecule's architecture. Principal component analysis is a more expensive way of inferring the essential variables from the protein's motions, one that requires a long molecular dynamics simulation. Finally, the two popular models for the allosteric switching mechanism, ‘preexisting equilibrium’ and ‘induced fit’, are interpreted within the energy landscape paradigm as extreme points of a continuum of transition mechanisms. Some experimental evidence illustrating each of these two models, as well as intermediate mechanisms, is presented and discussed.

Conformational coupling, bridge helix dynamics and active site dehydration in catalysis by RNA polymerase

Molecular dynamics simulation of Thermus thermophilus (Tt) RNA polymerase (RNAP) in a catalytic conformation demonstrates that the active site dNMP-NTP base pair must be substantially dehydrated to support full active site closing and optimum conditions for phosphodiester bond synthesis. In silico mutant beta R428A RNAP, which was designed based on substitutions at the homologous position (Rpb2 R512) of Saccharomyces cerevisiae (Sc) RNAP II, was used as a reference structure to compare to Tt RNAP in simulations. Long range conformational coupling linking a dynamic segment of the bridge alpha-helix, the extended fork loop, the active site, and the trigger loop-trigger helix is apparent and adversely affected in beta R428A RNAP. Furthermore, bridge helix bending is detected in the catalytic structure, indicating that bridge helix dynamics may regulate phosphodiester bond synthesis as well as translocation. An active site "latch" assembly that includes a key trigger helix residue Tt beta' H1242 and highly conserved active site residues beta E445 and R557 appears to help regulate active site hydration/dehydration. The potential relevance of these observations in understanding RNAP and DNAP induced fit and fidelity is discussed.

Many local motions cooperate to produce the adenylate kinase conformational transition

Conformational transitions are functionally important in many proteins. In the enzyme adenylate kinase (AK), two small domains (LID and NMP) close over the larger CORE domain; the reverse (opening) motion limits the rate of catalytic turnover. Here, using double-well Gō simulations of Escherichia coli AK, we elaborate on previous investigations of the AK transition mechanism by characterizing the contributions of rigid-body (Cartesian), backbone dihedral, and contact motions to transition-state (TS) properties. In addition, we compare an apo simulation to a pseudo-ligand-bound simulation to reveal insights into allostery. In Cartesian space, LID closure precedes NMP closure in the bound simulation, consistent with prior coarse-grained models of the AK transition. However, NMP-first closure is preferred in the apo simulation. In backbone dihedral space, we find that, as expected, backbone fluctuations are reduced in the O/C transition in parts of all three domains. Among these "quenching" residues, most in the CORE, especially residues 11-13, are rigidified in the TS of the bound simulation, while residues 42-44 in the NMP are flexible in the TS. In contact space, in both apo and bound simulations, one nucleus of closed-state contacts includes parts of the NMP and CORE; CORE-LID contacts are absent in the TS of the apo simulation but formed in the TS of the bound simulation. From these results, we predict mutations that will perturb the opening and/or closing transition rates by changing the entropy of dihedrals and/or the enthalpy of contacts. Furthermore, regarding allostery, the fully closed structure is populated in the apo simulation, but our contact results imply that ligand binding shifts the preferred O/C transition pathway, thus precluding a simple conformational selection mechanism. Finally, the analytical approach and the insights derived from this work may inform the rational design of flexibility and allostery in proteins.

Hamiltonian replica exchange method study of Escherichia coli and Yersinia pestis HPPK

HPPK (6-hydroxymethyl-7,8-dihydropterin pyrophosphokinase) catalyzes the transfer of pyrophosphate from ATP to HP (6-hydroxymethyl-7,8-dihydropterin). This first reaction in the folate biosynthetic pathway is a potential target for antimicrobial agents. A Hamiltonian replica exchange method (HREM) molecular dynamics (MD) approach is used, with the goal of improving conformational sampling, whereby multiple copies of the system are run without requiring a large number of system copies. For HPPK, the aim is to improve conformational sampling around the HP binding pocket and thereby find near-closed conformations (similar but not identical to the binding pocket of HP, as defined by the ternary crystal structure). Near-closed conformations may be better targets for the design of species-selective inhibitors. Well-populated, near-closed conformations of Escherichia coli HPPK (EcHPPK) and Yersinia pestis HPPK (YpHPPK) were found with HREM by focusing on the interactions involving loops 2 and 3 that are known to be the more flexible regions of HPPK. A small number of systems were found to be sufficient to enlarge the sample space substantially, on the basis of root-mean-square fluctuation measures, relative to the results of a conventional MD simulation. By clustering snapshots on the basis of some of the key residues that form the HP binding pocket, distinct HREM-generated conformations are found. Residue displacements mainly from loop 2 are responsible for the distinct conformers found, relative to the crystal structure, for both EcHPPK and YpHPPK. In contrast, the conventional MD simulations of EcHPPK and YpHPPK each lead essentially to one cluster, with use of the same clustering criterion as for the HREM. The shapes of the HREM near-closed binding pockets are qualitatively investigated and found to be different. Some of these conformations are distinguishable between EcHPPK and YpHPPK, indicating that there may be differing species-selective, near-closed conformations suited to HP binding.