Machine learning can be used to distinguish protein families and generate new proteins belonging to those families.

Proteins are classified into families based on evolutionary relationships and common structure-function characteristics. Availability of large data sets of gene-derived protein sequences drives this classification. Sequence space is exponentially large, making it difficult to characterize family differences. In this work, we show that Machine Learning (ML) methods can be trained to distinguish between protein families. A number of supervised ML algorithms are explored to this end. The most accurate is a Long Short Term Memory (LSTM) classification method that accounts for the sequence context of the amino acids. Sequences for a number of protein families where there are sufficient data to be used in ML are studied. By splitting the data into training and testing sets, we find that this LSTM classifier can be trained to successfully classify the test sequences for all pairs of the families. Also investigated is whether the addition of structural information increases the accuracy of the binary comparisons. It does, but because there is much less available structural than sequence information, the quality of the training degrades. Another variety of LSTM, LSTM_wordGen, a context-dependent word generation algorithm, is used to generate new protein sequences based on seed sequences for the families considered here. Using the original sequences as training data and the generated sequences as test data, the LSTM classification method classifies the generated sequences almost as accurately as the true family members do. Thus, in principle, we have generated new members of these protein families.

Generating intrinsically disordered protein conformational ensembles from a Markov chain.

Intrinsically disordered proteins (IDPs) sample a diverse conformational space. They are important to signaling and regulatory pathways in cells. An entropy penalty must be payed when an IDP becomes ordered upon interaction with another protein or a ligand. Thus, the degree of conformational disorder of an IDP is of interest. We create a dichotomic Markov model that can explore entropic features of an IDP. The Markov condition introduces local (neighbor residues in a protein sequence) rotamer dependences that arise from van der Waals and other chemical constraints. A protein sequence of length N is characterized by its (information) entropy and mutual information, MIMC, the latter providing a measure of the dependence among the random variables describing the rotamer probabilities of the residues that comprise the sequence. For a Markov chain, the MIMC is proportional to the pair mutual information MI which depends on the singlet and pair probabilities of neighbor residue rotamer sampling. All 2N sequence states are generated, along with their probabilities, and contrasted with the probabilities under the assumption of independent residues. An efficient method to generate realizations of the chain is also provided. The chain entropy, MIMC, and state probabilities provide the ingredients to distinguish different scenarios using the terminologies: MoRF (molecular recognition feature), not-MoRF, and not-IDP. A MoRF corresponds to large entropy and large MIMC (strong dependence among the residues' rotamer sampling), a not-MoRF corresponds to large entropy but small MIMC, and not-IDP corresponds to low entropy irrespective of the MIMC. We show that MorFs are most appropriate as descriptors of IDPs. They provide a reasonable number of high-population states that reflect the dependences between neighbor residues, thus classifying them as IDPs, yet without very large entropy that might lead to a too high entropy penalty.

Reweighting ensemble probabilities with experimental histogram data constraints using a maximum entropy principle.

Entropy maximization methods that update a probability distribution P 0(x) to a new distribution P(x) with the use of externally known, averaged constraints find use in diverse areas. Jaynes developed a Maximum Entropy Procedure (MEP) that is an objective approach to incorporate external data to update P 0(x) to P(x). In this work, we consider the MEP in the context of external data known from a probability distribution versus that from a mean and a few higher moments. An immediate problem is that the conventional iterative Lagrange multiplier method, which relies on inverting a certain covariance matrix, is not applicable here because the covariance matrix is not invertible. We introduce an indicator function method that does not suffer from this problem. It leads to an analytic solution to this version of a MEP. As an example, a previously generated ensemble of peptide conformations used to characterize an intrinsically disordered protein is analyzed. The external constraint is on the radius of gyration probability distribution, p(RG), of this peptide. Ensemble observables such as geometric, shape characteristics, the residue end-to-end distance distribution, the all atom-pair distribution function related to the scattering intensity, the polyproline II content, and NMR 3JHNHα three bond couplings are evaluated with the initial and updated ensembles. Some observables are found to be insensitive and others sensitive to the external information. An example of a 24-residue peptide, histatin 5, where an experimentally derived p(RG) is available, is also analyzed.

Five checkpoints maintaining the fidelity of transcription by RNA polymerases in structural and energetic details.

Transcriptional fidelity, which prevents the misincorporation of incorrect nucleoside monophosphates in RNA, is essential for life. Results from molecular dynamics (MD) simulations of eukaryotic RNA polymerase (RNAP) II and bacterial RNAP with experimental data suggest that fidelity may involve as many as five checkpoints. Using MD simulations, the effects of different active site NTPs in both open and closed trigger loop (TL) structures of RNAPs are compared. Unfavorable initial binding of mismatched substrates in the active site with an open TL is proposed to be the first fidelity checkpoint. The leaving of an incorrect substrate is much easier than a correct one energetically from the umbrella sampling simulations. Then, the closing motion of the TL, required for catalysis, is hindered by the presence of mismatched NTPs. Mismatched NTPs also lead to conformational changes in the active site, which perturb the coordination of magnesium ions and likely affect the ability to proceed with catalysis. This step appears to be the most important checkpoint for deoxy-NTP discrimination. Finally, structural perturbations in the template DNA and the nascent RNA in the presence of mismatches likely hinder nucleotide addition and provide the structural foundation for backtracking followed by removing erroneously incorporated nucleotides during proofreading.

The RNA polymerase bridge helix YFI motif in catalysis, fidelity and translocation.

The bridge α-helix in the ß' subunit of RNA polymerase (RNAP) borders the active site and may have roles in catalysis and translocation. In Escherichia coli RNAP, a bulky hydrophobic segment near the N-terminal end of the bridge helix is identified (ß' 772-YFI-774; the YFI motif). YFI is located at a distance from the active center and adjacent to a glycine hinge (ß' 778-GARKG-782) involved in dynamic bending of the bridge helix. Remarkably, amino acid substitutions in YFI significantly alter intrinsic termination, pausing, fidelity and translocation of RNAP. F773V RNAP largely ignores the λ tR2 terminator at 200µM NTPs and is strongly reduced in λ tR2 recognition at 1µM NTPs. F773V alters RNAP pausing and backtracking and favors misincorporation. By contrast, the adjacent Y772A substitution increases fidelity and exhibits other transcriptional defects generally opposite to those of F773V. All atom molecular dynamics simulation revealed two separate functional connections emanating from YFI explaining the distinct effects of substitutions: Y772 communicates with the active site through the link domain in the ß subunit, whereas F773 communicates through the fork domain in the ß subunit. I774 interacts with the F-loop, which also contacts the glycine hinge of the bridge helix. These results identified negative and positive circuits coupled at YFI and employed for regulation of catalysis, elongation, termination and translocation.

Excess dielectron in an ionic liquid as a dynamic bipolaron.

We report an ab initio molecular dynamics simulation study on the accommodation of a dielectron in a pyridinium ionic liquid in both the singlet and triplet state. In contrast to water and liquid ammonia, a dielectron does not prefer to reside in cavity-shaped structures in the ionic liquid. Instead, it prefers to be distributed over more cations, with long-lived diffuse and short-lived localized distributions, and with a triplet ground state and a low-lying, open-shell singlet excited state. The two electrons evolve nonsynchronously in both states via a diffuse-versus-localized interconversion mechanism that features a dynamic bipolaron with a modest mobility, slightly lower than a hydrated electron. This work presents the first detailed study on the structures and dynamics of a dielectron in ionic liquids.

Solvation and evolution dynamics of an excess electron in supercritical CO2.

We present an ab initio molecular dynamics simulation of the dynamics of an excess electron solvated in supercritical CO2. The excess electron can exist in three types of states: CO2-core localized, dual-core localized, and diffuse states. All these states undergo continuous state conversions via a combination of long lasting breathing oscillations and core switching, as also characterized by highly cooperative oscillations of the excess electron volume and vertical detachment energy. All of these oscillations exhibit a strong correlation with the electron-impacted bending vibration of the core CO2, and the core-switching is controlled by thermal fluctuations.

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.

A hamiltonian replica exchange method for building protein-protein interfaces applied to a leucine zipper.

Leucine zippers consist of alpha helical monomers dimerized (or oligomerized) into alpha superhelical structures known as coiled coils. Forming the correct interface of a dimer from its monomers requires an exploration of configuration space focused on the side chains of one monomer that must interdigitate with sites on the other monomer. The aim of this work is to generate good interfaces in short simulations starting from separated monomers. Methods are developed to accomplish this goal based on an extension of a previously introduced [Su and Cukier, J. Phys. Chem. B 113, 9595, (2009)] hamiltonian temperature replica exchange method (HTREM), which scales the hamiltonian in both potential and kinetic energies that was used for the simulation of dimer melting curves. The new method, HTREM_MS (MS designates mean square), focused on interface formation, adds restraints to the hamiltonians for all but the physical system, which is characterized by the normal molecular dynamics force field at the desired temperature. The restraints in the nonphysical systems serve to prevent the monomers from separating too far, and have the dual aims of enhancing the sampling of close in configurations and breaking unwanted correlations in the restrained systems. The method is applied to a 31-residue truncation of the 33-residue leucine zipper (GCN4-p1) of the yeast transcriptional activator GCN4. The monomers are initially separated by a distance that is beyond their capture length. HTREM simulations show that the monomers oscillate between dimerlike and monomerlike configurations, but do not form a stable interface. HTREM_MS simulations result in the dimer interface being faithfully reconstructed on a 2 ns time scale. A small number of systems (one physical and two restrained with modified potentials and higher effective temperatures) are sufficient. An in silico mutant that should not dimerize because it lacks charged residues that provide electrostatic stabilization of the dimer does not with HTREM_MS, giving confidence in the method. The interface formation time scale is sufficiently short that using HTREM_MS as a screening tool to validate leucine zipper design methods may be feasible.

Ferreting out correlations from trajectory data.

Thermally driven materials characterized by complex energy landscapes, such as proteins, exhibit motions on a broad range of space and time scales. Principal component analysis (PCA) is often used to extract modes of motion from protein trajectory data that correspond to coherent, functional motions. In this work, two other methods, maximum covariance analysis (MCA) and canonical correlation analysis (CCA) are formulated in a way appropriate to analyze protein trajectory data. Both methods partition the coordinates used to describe the system into two sets (two measurement domains) and inquire as to the correlations that may exist between them. MCA and CCA provide rotations of the original coordinate system that successively maximize the covariance (MCA) or correlation (CCA) between modes of each measurement domain under suitable constraint conditions. We provide a common framework based on the singular value decomposition of appropriate matrices to derive MCA and CCA. The differences between and strengths and weaknesses of MCA and CCA are discussed and illustrated. The application presented here examines the correlation between the backbone and side chain of the peptide met-enkephalin as it fluctuates between open conformations, found in solution, to closed conformations appropriate to when it is bound to its receptor. Difficulties with PCA carried out in Cartesian coordinates are found and motivate a formulation in terms of dihedral angles for the backbone atoms and selected atom distances for the side chains. These internal coordinates are a more reliable basis for all the methods explored here. MCA uncovers a correlation between combinations of several backbone dihedral angles and selected side chain atom distances of met-enkephalin. It could be used to suggest residues and dihedral angles to focus on to favor specific side chain conformers. These methods could be applied to proteins with domains that, when they rearrange upon ligand binding, may have correlated functional motions or, for multi-subunit proteins, may exhibit correlated subunit motions.

States and migration of an excess electron in a pyridinium-based, room-temperature ionic liquid: an ab initio molecular dynamics simulation exploration.

The structural and electronic properties of an excess electron (EE) in the ionic liquid (IL) 1-methylpyridinium chloride were explored using ab initio molecular dynamics simulations and quantum chemical calculations to give an overall understanding of the solvation and transport behavior of an EE in this IL. The results show that the EE resides in cation pi*-type orbitals and that the electronic states can be characterized by the alternating appearance of localized and delocalized states during the time evolution. The characters of the EE electronic states are determined by the number of cations contributing to the LUMO of the IL. In a localized state one or two cations contribute to the LUMO of the bulk ionic liquid, while in the delocalized state the IL LUMO is composed of pi*-type orbitals spanning nearly all the cations in the cell. The arrangement and fluctuation-induced changes of the orbital components in the empty band produce an alternation of different states and leads to the migration of the excess electron. These findings can be attributed to the special features of the electronic structures and geometries of the IL, and they can be used to explain similarities and differences between pyridinium-based and imidazolium-based ILs in mediating electron migration.

How many atoms are required to characterize accurately trajectory fluctuations of a protein?

Large molecules, whose thermal fluctuations sample a complex energy landscape, exhibit motions on an extended range of space and time scales. Principal component analysis (PCA) is often used to extract dominant motions that in proteins are typically domain motions. These motions are captured in the large eigenvalue (leading) principal components. There is also information in the small eigenvalues, arising from approximate linear dependencies among the coordinates. These linear dependencies suggest that instead of using all the atom coordinates to represent a trajectory, it should be possible to use a reduced set of coordinates with little loss in the information captured by the large eigenvalue principal components. In this work, methods that can monitor the correlation (overlap) between a reduced set of atoms and any number of retained principal components are introduced. For application to trajectory data generated by simulations, where the overall translational and rotational motion needs to be eliminated before PCA is carried out, some difficulties with the overlap measures arise and methods are developed to overcome them. The overlap measures are evaluated for a trajectory generated by molecular dynamics for the protein adenylate kinase, which consists of a stable, core domain, and two more mobile domains, referred to as the LID domain and the AMP-binding domain. The use of reduced sets corresponding, for the smallest set, to one-eighth of the alpha carbon (CA) atoms relative to using all the CA atoms is shown to predict the dominant motions of adenylate kinase. The overlap between using all the CA atoms and all the backbone atoms is essentially unity for a sum over PCA modes that effectively capture the exact trajectory. A reduction to a few atoms (three in the LID and three in the AMP-binding domain) shows that at least the first principal component, characterizing a large part of the LID-binding and AMP-binding motion, is well described. Based on these results, the overlap criterion should be applicable as a guide to postulating and validating coarse-grained descriptions of generic biomolecular assemblies.

Effect of metal ions on radical type and proton-coupled electron transfer channel: sigma-radical vs pi-radical and sigma-channel vs pi-channel in the imide units.

The mechanism of proton transfer (PT)/electron transfer (ET) in imide units, and its regulation by hydrated metal ions, was explored theoretically using density functional theory in a representative model (a nearly planar and cisoid complex between uracil and its N(3)-dehydrogenated radical, UU). In UU (sigma-radical), PT/ET normally occurs via a seven-center, cyclic proton-coupled sigma-electron sigma-channel transfer (PC(sigma)E(sigma)T) mechanism (3.8 kcal/mol barrier height) with a N(3)-->N(3') PT and an O(4)-->O(4') ET. Binding of hydrated metal ions to the dioxygen sites (O(2)/O(2') or/and O(4)/O(4')) of UU may significantly affect its PT/ET cooperative reactivity by changing the radical type (sigma-radical <--> pi-radical) and ET channel (sigma-channel <--> pi-channel), leading to different mechanisms, ranging from PC(sigma)E(sigma)T, to proton-coupled pi-electron sigma-channel transfer (PC(pi)E(sigma)T) to proton-coupled pi-electron pi-channel transfer (PC(pi)E(pi)T). This change originates from an alteration of the ordering of the UU moiety SOMO/HDMO (the singly occupied molecular orbital and the highest doubly occupied molecular orbital), induced by binding of the hydrated metal ions. It is a consequence of three associated factors: the asymmetric reactant structure, electron cloud redistribution, and fixing role of metal ions to structural backbone. The findings regarding the modulation of the PT/ET pathway via hydrated metal ions may provide valuable information for a greater understanding of PT/ET cooperative mechanisms, and an alternative way for designing imide-based molecular devices, such as molecular switches and molecular wires.

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

Adenylate kinase undergoes large-scale motions of its LID and AMP-binding (AMPbd) domains when its apo, open form closes over its substrates, AMP and Mg2+-ATP. It may be an example of an enzyme that provides an ensemble of conformations in its apo state from which its substrates can select and bind to produce catalytically competent conformations. In this work, the fluctuations of the enzyme apo Escherichia coli adenylate kinase (AKE) are obtained with molecular dynamics. The resulting trajectory is analyzed with principal component analysis (PCA) that decomposes the atom motions into orthogonal modes ordered by their decreasing contributions to the total protein fluctuation. In apo AKE, a small set of the PCA modes describes the bulk of the fluctuations. Identification of the atom motions that are important contributors to these modes is improved with the use of a varimax rotation method that rotates the PCA modes to a new mode set that concentrates the atom contributions to a smaller set of atoms in these new modes. In this way, the nature of the important motions of the LID and AMPbd domains are clarified. The dominant PCA modes are used to investigate if apo AKE can fluctuate to conformations that are holo-like, even though the apo trajectory is mainly confined to a region around the initial apo structure. This is accomplished by expressing the difference between the protein coordinates, obtained from the holo and apo crystal structures, using as a basis the PCA modes from the apo AKE trajectory. The coherent motion described by a small set of the apo PCA modes is shown to be able to produce protein conformations that are quite similar to the holo conformation of the protein. In this sense, apo AKE does encode in its fluctuations information about holo-like conformations.

Hamiltonian replica exchange method studies of a leucine zipper dimer.

A melting curve (stability versus temperature) of a leucine zipper dimer was obtained with the use of explicit solvent molecular dynamics (MD). Leucine zippers form stable dimers in solution at physiological temperatures by formation of coiled coil alpha helical structures, using a characteristic heptadic repeating unit. We simulated a 31-residue truncation of the 33 residue parallel two-stranded leucine zipper (GCN4-p1) of the yeast transcriptional activator GCN4 that has four such repeats. The dimer remains bound using conventional MD sampling at the lowest temperature used, while mainly breaking apart at the highest temperature used. However, to obtain a melting curve, the sampling efficiency must be improved, especially at the lower temperatures. Configurational sampling was enhanced with the introduction of a Hamiltonian replica exchange method (HREM), which will be referred to as HTREM, which scales the Hamiltonian in both potential and kinetic energies. The potential scaling is carried out only for the protein-protein and protein-solvent interactions and the kinetic scaling only for the protein degrees of freedom. By limiting the number of scaled degrees of freedom, a smaller number of systems can be used relative to temperature REM where all degrees of freedom are scaled. The HTREM does enhance the sampling especially at the lower temperatures and a melting curve is constructed. A mutant leucine zipper is also simulated where five glutamates are protonated and five lysines are deprotonated in order to investigate the role that electrostatic interactions and salt bridges play in dimer stability. The mutant is considerably less stable than the wild type based on the melting curves. The connection between dimer stability, monomer alpha helix unwinding, and salt bridge presence is investigated. Among the possible salt bridges of GCN4-p1, those found in experiments are also found in the simulation at the lowest simulation temperature, and the corresponding salt bridge fractions at higher temperature are much lower. A difference between the N terminal and C terminal halves of the monomers regarding their alpha helix stability is found, with the N terminal less stable than the C terminal parts, in accord with biophysical analyses of two monomeric 16-residue peptides derived from GCN4-p1.

Hetero-ring-expansion design for adenine-based DNA motifs: evidence from DFT calculations and molecular dynamics simulations.

The design of new DNA motifs is at present a very interesting topic. Recent progress indicates that the hetero-ring-expanded guanine (G) analogues possess enhanced properties compared with natural guanine. In this work, a series of hetero-ring-expanded adenine (A) analogues are designed, and their structures and electronic properties are investigated by means of density functional calculations and molecular dynamics simulations. The results indicate that the designed A-analogues can form stable base pairs with natural counterpart, and the pairing energetics for the Watson-Crick hydrogen-bonded dimers between the expanded A-analogues and natural T exhibit similarity to natural AT. Their tautomeric preferences are close to natural A, too. Furthermore, compared with natural ones, most size-expanded adenines and corresponding base pairs have smaller ionization potentials. In particular, several designed A analogues have ionization potentials even lower than natural G. The electron affinities of these modified A are comparable with that of natural A. The HOMO-LUMO gaps also behave with sensible trends. Most of A-analogues and their interrelated base pairs possess smaller gaps than the corresponding natural base and base pairs. Further, molecular dynamics simulations show the sufficient stabilities of the DNA analogues (dnA.dT)(12) (where nA represents the size-expanded A-analogues designed here) when forming duplexes as the natural one does. Clearly, these observations imply their promising applications as molecular wires and new DNA motifs.

Absorption and fluorescence emission spectroscopic characters of size-expanded yDNA bases and effect of deoxyribose and base pairing.

We present an ab initio study of the optical absorption and emission spectra of size-expanded nucleic acid base analogues (yA, yT, yT-m, yG, yG-t2, and yC) obtained by benzo homologation (see Krueger, A. T.; Lu, H.; Lee, A. H. F.; Kool, E. T. Acc. Chem. Res. 2007, 40, 141 and references therein). Also examined were the effects of linking to deoxyribose and hydrogen bonding to their natural complementary bases (T, A, C, and G, respectively). The calculated excitation and emission energies are in good agreement with the measured data where experimental results are available. The geometries corresponding to the first excited singlet state of yA and yT are found to be quasi-planar, while those for yG and yC are nonplanar. In general, binding to deoxyribose will red shift the absorbance and fluorescence emission maxima of the y-bases. The ground-state geometries of the Watson-Crick analog base pairs (yAT, yTA, yGC, and yCG) are found to be planar, and the calculated interaction energies are very close to those of natural base pairs, indicating that the y-bases can pair with their natural complementary partners to generate stable base pairs. The base pairing has no significant effects on the fluorescence emission of yA, yC, and yT, but blue shifts the fluorescence emission of yG by 22 nm.

Excess electron solvation in an imidazolium-based room-temperature ionic liquid revealed by ab initio molecular dynamics simulations.

We present the first approach to the excess electron solvation in a novel medium, room-temperature ionic liquid, using ab initio molecular dynamics simulation techniques in this work. Results indicate that an excess electron can be solvated in the [dmim](+)Cl(-) IL as long-lived delocalized states and two short-lifetime localized states, one a single-cation-residence parasitical type and the other a double-cation-based solvated type state. The presence of a low-lying pi*-LUMO as the site of excess electron residence in the cation moiety disables the C-H unit as a H-bond donor, while the aromaticity requirement of the rings and the effect of the counterion Cl(-)'s make the resulting ion pairs a weak stabilizer for an excess electron. Although no large solvent reorganization in IL was found at the picosecond scale, the IL fluctuations sufficiently modify the relative energy levels of the excess electron states to permit facile state-to-state conversion and adiabatic migration. The binding energy of the excess electron is only approximately 0.2 eV, further indicating that it is in a quasi-free state, with a large drift mobility, suggesting that ILs are unreactive and promising mediators for transport of excess electrons, in agreement with the experimental findings. The present study provides insight into the novel electron solvation character in a new class of promising media for physical and chemical processes, which are fundamental for understanding of electron migration mechanisms in IL-based applications.

An enhanced molecular dynamics study of HPPK-ATP conformation space exploration and ATP binding to 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 an important target for potential antimicrobial agents. In this work, the mechanism by which HPPK traps and binds ATP is studied by molecular dynamics (MD)-based methods. Based on the ternary crystal structure of HPPK with an ATP mimic and HP, a complex of ATPMg(2) and HPPK is simulated and found to undergo small conformational changes with conventional MD, as does also conventional MD when started from the apo crystal structure. The introduction of restraints in the MD that serve to move HPPK-ATP from its ternary complex (closed) to apo-like (open) forms shows that throughout the restraint path ATP remains bound to HPPK. That ATP remains bound suggests that there is an ensemble of conformations with ATP bound to HPPK that span the apo to more ligand-bound-like conformations, consistent with the pre-existing equilibrium hypothesis of ligand binding, whereby a ligand can select from and bind to a broad range of protein conformations. In the apo-like conformations, ATPMg(2) remains bound to HPPK through a number of mainly salt-bridge-like interactions between several negatively charged residues and the two magnesium cations. The introduction of a reweight method that enhances the sampling of MD by targeting explicit terms in the force field helps define the interactions that bind ATP to HPPK. Using the reweight method, conformational and center of mass motions of ATP, driven by the breaking and making of hydrogen bonds and salt bridges, are identified that lead to ATP separating from HPPK. An elastic normal mode (ENM) approach to opening the ternary complex and closing the apo crystal structures was carried out. The ENM analysis of the apo structure analysis shows one mode that does have a closing motion of HPPK loops, but the direction does not correlate strongly with the loop motions that are required for forming the ternary complex.