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.

Generating Intrinsically Disordered Protein Conformational Ensembles from a Database of Ramachandran Space Pair Residue Probabilities Using a Markov Chain.

Intrinsically disordered proteins (IDPs), involved in regulatory pathways and cell signaling, sample a range of conformations. Constructing structural ensembles of IDPs is a difficult task for both experiment and simulation. In this work, we produce potential IDP ensembles using an existing database of pair residue φ and ψ angle probabilities chosen from turn, coil, and bend parts of sequences from the Protein Data Bank. For all residue pair types, a k-means-based discretization is used to create a set of rotamers and their probabilities in this pair Ramachandran space. For a given sequence, a Markov-based probabilistic algorithm is used to create Ramachandran space database-Markov ensembles that are converted to Cartesian coordinates of the backbone atoms. From these Cartesian coordinates and φ and ψ dihedral angles of a sequence, various observables: the radius of gyration and shape parameters, the distance probability distribution that is related to the small-angle X-ray scattering intensity, atom-atom contact percentages, local structural information, NMR three-bond J couplings, CA chemical shifts, and residual dipolar couplings are evaluated. A benchmark set of ensembles for 16 residue, regular sequences is constructed and used to validate the method and to explore the implications of the database for some of the above-mentioned observables. Then, we examine a set of nonapeptides of the form EGAAXAASS where X denotes residues of different characters. These peptides were studied by NMR, and subsequent molecular dynamics (MD) simulations were carried out using various force fields to find which one best agrees with the NMR data. Our analysis of these peptides shows that the combination of the database and the Markov algorithm yields ensembles that agree very well with the NMR and MD results for the above-listed observables. Thus, this database-Markov method is a promising method to generate IDP conformational ensembles.

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.

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.

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.

Theoretical prediction of the p53 gene mutagenic mechanism induced by trans-4-hydroxy-2-nonenal.

The reaction mechanism of guanine with trans-4-hydroxyl-2-nonenal (4-HNE) and the mutagenic mechanism induced by adducts have been theoretically predicted at a molecular level from the energy point of view. 4-HNE directly reacts with guanine via three steps, yielding eventually four main diastereoisomers: trans-4-HNE-dG adducts. A concerted six-atom-centered transition state is proposed for the first step, while the last two steps are involved in four-membered-ring transition states. The third step is the rate-determining step. The studies of base pairing properties of trans-4-HNE-dG adducts with A, T, C, A*, and T* together with the relationship between the mutation and structure of trans-4-HNE-dG indicate that syn- and anti-conformations of trans-4-HNE-dG around the glycosidic bond are favorable for pairing with A* and T*, respectively, in the parental generation. As a result, the GC --> CG or GC --> TA mutation may be generated from the syn-4-HNE-dGA* during replication. Nevertheless, anti-4-HNE-dGT* creates GC --> TA mutation or nonmutagenesis. Moreover, syn-4-HNE-dGA* has a slightly higher probability to be generated than anti-4-HNE-dGT* in the parental generation; therefore, the GC to TA transversion is predominant among the mutations. In addition, no correlation between the mutations and the stereochemistry of C6 and C8 of trans-4-HNE-dG adducts was found in this work. Our mutational results have interpreted well a part of the discrete experimental observations, but the mutagenic process itself has not previously been characterized, through either computation or experiment.

Molecular dynamics of apo-adenylate kinase: a distance replica exchange method for the free energy of conformational fluctuations.

A large domain motion in adenylate kinase from E. coli (AKE) is studied with molecular dynamics. AKE undergoes a large-scale rearrangement of its lid and AMP-binding domains when the open form closes over its substrates, AMP, and Mg2+-ATP, whereby the AMP-binding and lid domains come closer to the core. The third domain, the core, is relatively stable during this motion. A reaction coordinate that monitors the distance between the AMP-binding and core domains is selected to be able to compare with the results of energy transfer experiments. Sampling along this reaction coordinate is carried out by using a distance replica exchange method (DREM), where systems that differ by a restraint potential enforcing different reaction coordinate values are independently simulated with periodic attempts at exchange of these systems. Several methods are used to study the efficiency and convergence properties of the DREM simulation and compared with an analogous non-DREM simulation. The DREM greatly accelerates the rate and extent of configurational sampling and leads to equilibrium sampling as measured by monitoring collective modes obtained from a principal coordinate analysis. The potential of mean force along the reaction coordinate reveals a rather flat region for distances from the open to a relatively closed AKE conformation. The potential of mean force for smaller distances has a distinct minimum that is quite close to that found in the closed form X-ray structure. In concert with a decrease in the reaction coordinate distance (AMP-binding-to-core distance) the lid-to-core distance of AKE also decreases. Therefore, apo AKE can fluctuate from its open form to conformations that are quite similar to its closed form X-ray structure, even in the absence of its substrates.

A molecular dynamics exploration of the catalytic mechanism of yeast cytosine deaminase.

Yeast cytosine deaminase (yCD), a zinc metalloenzyme of significant biomedical interest, is investigated by a series of molecular dynamics simulations in its free form and complexed with its reactant (cytosine), product (uracil), several reaction intermediates, and an intermediate analogue. Quantum chemical calculations, used to construct a model for the catalytic Zn ion with its ligands (two cysteines, a histidine, and one water) show, by comparison with crystal structure data, that the cysteines are deprotonated and the histidine is monoprotonated. The simulations suggest that Glu64 plays a critical role in the catalysis by yCD. The rotation of the Glu64 side-chain carboxyl group that can be protonated or deprotonated permits it to act as a proton shuttle between the Zn-bound water and cytosine and subsequent reaction intermediates. Free energy methods are used to obtain the barriers for these rotations, and they are sufficiently small to permit rotation on a nanosecond time scale. In the course of the reaction, cytosine reorients to a geometry to favor nucleophilic attack by a Zn-bound hydroxide. A stable position for a reaction product, ammonia, was located in the active site, and the free energy of exchange with a water molecule was evaluated. The simulations also reveal small motions of the C-terminus and the loop that contains Phe114 that may be important for reactant binding and product release.

Associative mechanism for phosphoryl transfer: a molecular dynamics simulation of Escherichia coli adenylate kinase complexed with its substrates.

The ternary complex of Escherichia coli adenylate kinase (ECAK) with its substrates adenosine monophosphate (AMP) and Mg-ATP, which catalyzes the reversible transfer of a phosphoryl group between adenosine triphosphate (ATP) and AMP, was studied using molecular dynamics. The starting structure for the simulation was assembled from the crystal structures of ECAK complexed with the bisubstrate analog diadenosine pentaphosphate (AP(5)A) and of Bacillus stearothermophilus adenylate kinase complexed with AP(5)A, Mg(2+), and 4 coordinated water molecules, and by deleting 1 phosphate group from AP(5)A. The interactions of ECAK residues with the various moieties of ATP and AMP were compared to those inferred from NMR, X-ray crystallography, site-directed mutagenesis, and enzyme kinetic studies. The simulation supports the hypothesis that hydrogen bonds between AMP's adenine and the protein are at the origin of the high nucleoside monophosphate (NMP) specificity of AK. The ATP adenine and ribose moieties are only loosely bound to the protein, while the ATP phosphates are strongly bound to surrounding residues. The coordination sphere of Mg(2+), consisting of 4 waters and oxygens of the ATP beta- and gamma-phosphates, stays approximately octahedral during the simulation. The important role of the conserved Lys13 in the P loop in stabilizing the active site by bridging the ATP and AMP phosphates is evident. The influence of Mg(2+), of its coordination waters, and of surrounding charged residues in maintaining the geometry and distances of the AMP alpha-phosphate and ATP beta- and gamma-phosphates is sufficient to support an associative reaction mechanism for phosphoryl transfer.