Metal Ion Capture Mechanism of a Copper Metallochaperone.

A novel cation-π interaction between the bound Cu(+) metal ion and Trp44 in the periplasmic Cu(+)/Ag(+) metallochaperone Escherichia coli CusF protects Cu(+) from the oxidative influence of the periplasm. In a popular model of metal ion transfer, a conformational change in the metal binding loop disrupts the cation-π interaction and moves Trp44 aside to provide access to the occluded metal ion binding site in an "open" conformation. In this study, our molecular dynamics simulations support this putative mechanism of metal ion transfer. We find that the apoprotein undergoes a transition back and forth from the crystallographically observed "closed" state to the hypothesized open conformation over multiple microseconds. In agreement with nuclear magnetic resonance data, our simulations show that similar transitions are prohibited in Cu(+)·CusF, suggesting that the conformational transitions are gated by a metal ion-mediated second-shell hydrogen bond between metal binding residue His36 and Asp37 of the metal binding loop region. Ab initio quantum mechanical calculations indicate that metal ion binding strengthens this interaction significantly, much like what is found in the case of other metalloproteins. The study builds toward a common evolutionary role of metal ion-mediated second-shell hydrogen bonds in metalloprotein structure and function.

Role of substrate dynamics in protein prenylation reactions.

CONSPECTUS: The role dynamics plays in proteins is of intense contemporary interest. Fundamental insights into how dynamics affects reactivity and product distributions will facilitate the design of novel catalysts that can produce high quality compounds that can be employed, for example, as fuels and life saving drugs. We have used molecular dynamics (MD) methods and combined quantum mechanical/molecular mechanical (QM/MM) methods to study a series of proteins either whose substrates are too far away from the catalytic center or whose experimentally resolved substrate binding modes cannot explain the observed product distribution. In particular, we describe studies of farnesyl transferase (FTase) where the farnesyl pyrophosphate (FPP) substrate is ∼8 Šfrom the zinc-bound peptide in the active site of FTase. Using MD and QM/MM studies, we explain how the FPP substrate spans the gulf between it and the active site, and we have elucidated the nature of the transition state (TS) and offered an alternate explanation of experimentally observed kinetic isotope effects (KIEs). Our second story focuses on the nature of substrate dynamics in the aromatic prenyltransferase (APTase) protein NphB and how substrate dynamics affects the observed product distribution. Through the examples chosen we show the power of MD and QM/MM methods to provide unique insights into how protein substrate dynamics affects catalytic efficiency. We also illustrate how complex these reactions are and highlight the challenges faced when attempting to design de novo catalysts. While the methods used in our previous studies provided useful insights, several clear challenges still remain. In particular, we have utilized a semiempirical QM model (self-consistent charge density functional tight binding, SCC-DFTB) in our QM/MM studies since the problems we were addressing required extensive sampling. For the problems illustrated, this approach performed admirably (we estimate for these systems an uncertainty of ∼2 kcal/mol), but it is still a semiempirical model, and studies of this type would benefit greatly from more accurate ab initio or DFT models. However, the challenge with these methods is to reach the level of sampling needed to study systems where large conformational changes happen in the many nanoseconds to microsecond time regimes. Hence, how to couple expensive and accurate QM methods with sophisticated sampling algorithms is an important future challenge especially when large-scale studies of catalyst design become of interest. The use of MD and QM/MM models to elucidate enzyme catalytic pathways and to design novel catalytic agents is in its infancy but shows tremendous promise. While this Account summarizes where we have been, we also discuss briefly future directions that improve our fundamental ability to understand enzyme catalysis.

Models for the Metal Transfer Complex of the N-Terminal Region of CusB and CusF.

The tripartite CusCFBA pump in Escherichia coli is a very effective heavy metal extrusion system specific for Cu(I) and Ag(I). The N-terminal region of the membrane fusion protein CusB (CusB-NT) is highly disordered, and hence, experimentally characterizing its structure is challenging. In a previous study, this disorder was confirmed with molecular dynamics simulations, although some key structural elements were determined. It was experimentally shown that CusB-NT is fully functional in transferring the metal from the metallochaperone CusF. In this study, we docked these two entities together and formed two representative metal coordination modes, which consist of residues from both proteins. In this way, we created two potential CusB-NT/CusF complexes that share coordination of Cu(I) and thereby represent structural models for the metal transfer process. Each model complex was simulated for 4 µs. The previously observed structural disorder in CusB-NT disappeared upon complexation with CusF. The only differences between the two models occurred in the M21-M36 loop region of CusB-NT and the open flap of CusF: we observed the model with two CusB-NT methionine residues and a CusF methionine as the metal coordination site (termed "MMM") to be more stable than the model with a CusB-NT methionine, a CusF methionine, and a CusF histidine ligating the metal (termed "MMH"). The observed stability of the MMM model was probed for an additional 2 µs, yielding a total simulation time of 6 µs. We hypothesize that both MMM and MMH configurations might take part in the metal exchange process in which the MMH configuration would appear first and would be followed by the MMM configuration. Given the experimental finding of comparable binding affinities of CusB-NT and CusF, the increased stability of the MMM configuration might be a determinant for the transfer from CusF to CusB-NT. The metal would be transferred from the more CusF-dominated metal binding environment (MMH model) to a more CusB-dominated one (MMM model) in which the coordination environment is more stable. From the MMM model, the metal ion would ultimately be coordinated by the CusB methionines only, which would complete the Cu(I) transfer process.

A combined cheminformatic and bioinformatic approach to address the proteolytic stability challenge in peptide-based drug discovery.

We have created models to predict cleavage sites for several human proteases including caspase-1, caspase-3, caspase-6, caspase-7, cathepsin B, cathepsin D, cathepsin G, cathepsin K, cathepsin L, elastase-2, granzyme A, granzyme B, matrix metallopeptidase-2 (MMP2), MMP7, MMP9, thrombin, and trypsin-1. Rather than representing the sequence pattern around the potential cleavage site through a series of flags with each flag representing one of the 20 standard amino acids, we first represent each amino acid by its calculated properties. For these calculated properties, we use validated cheminformatic descriptors, such as molecular weight, logP, and polar surface area, of the individual amino acids. Finally, the cleavage site-specific descriptors are calculated through various combinations of the individual amino acid descriptors for the residues surrounding the cleavage site. Some of these combinations do not take into account the location of the residue, as long as it is in a prescribed neighborhood of the potential cleavage site, whereas others are sensitive to the precise order of the residues in the sequence. The key advantage of this approach is that it allows one to perform meaningful calculations with nonstandard amino acids for which little or no data exists. Finally, using both docking and molecular dynamics simulations, we examine the potential for and limitations of protease crystal structures to impact the design of proteolytically stable peptides.

Structure and dynamics of the N-terminal domain of the Cu(I) binding protein CusB.

CusCFBA is one of the metal efflux systems in Escherichia coli that is highly specific for its substrates, Cu(I) and Ag(I). It serves to protect the bacteria in environments that have lethal concentrations of these metals. The membrane fusion protein CusB is the periplasmic piece of CusCFBA, which has not been fully characterized by crystallography because of its extremely disordered N-terminal region. This region has both structural and functional importance because it has been experimentally proven to transfer the metal by itself from the metallochaperone CusF and to induce a structural change in the rest of CusB to increase Cu(I)/Ag(I) resistance. Understanding metal uptake from the periplasm is critical to gain insight into the mechanism of the whole CusCFBA pump, which makes resolving a structure for the N-terminal region necessary because it contains the metal binding site. We ran extensive molecular dynamics simulations to reveal the structural and dynamic properties of both the apo and Cu(I)-bound versions of the CusB N-terminal region. In contrast to its functional companion CusF, Cu(I) binding to the N-terminus of CusB causes only a slight, local stabilization around the metal site. The trajectories were analyzed in detail, revealing extensive structural disorder in both the apo and holo forms of the protein. CusB was further analyzed by breaking the protein up into three subdomains according to the extent of the observed disorder: the N- and C-terminal tails, the central beta strand motif, and the M21-M36 loop connecting the two metal-coordinating methionine residues. Most of the observed disorder was traced back to the tail regions, leading us to hypothesize that the latter two subdomains (residues 13-45) may form a functionally competent metal-binding domain because the tail regions appear to play no role in metal binding.

Energetics of zinc-mediated interactions in the allosteric pathways of metal sensor proteins.

A metal-mediated interprotomer hydrogen bond has been implicated in the allosteric mechanism of DNA operator binding in several metal-sensing proteins. Using computational methods, we investigate the energetics of such zinc-mediated interactions in members of the ArsR/SmtB family of proteins (CzrA, SmtB, CadC, and NmtR) and the MarR family zinc-uptake repressor AdcR, which feature similar interactions, but in sites that differ widely in their allosteric responsiveness. We provide novel structural insight into previously uncharacterized allosteric forms of these proteins using computational methodologies. We find this metal-mediated interaction to be significantly stronger (∼8 kcal/mol) at functional allosteric metal binding sites compared to a nonresponsive site (CadC) and the apo-proteins. Simulations of the apo-proteins further reveal that the high interaction energy works to overcome the considerable disorder at these hydrogen-bonding sites and functions as a "switch" to lock in a weak DNA-binding conformation once metal is bound. These findings suggest a conserved functional role of metal-mediated second coordination shell hydrogen bonds at allosterically responsive sites in zinc-sensing transcription regulators.

Solution NMR refinement of a metal ion bound protein using metal ion inclusive restrained molecular dynamics methods.

Correctly calculating the structure of metal coordination sites in a protein during the process of nuclear magnetic resonance (NMR) structure determination and refinement continues to be a challenging task. In this study, we present an accurate and convenient means by which to include metal ions in the NMR structure determination process using molecular dynamics (MD) simulations constrained by NMR-derived data to obtain a realistic and physically viable description of the metal binding site(s). This method provides the framework to accurately portray the metal ions and its binding residues in a pseudo-bond or dummy-cation like approach, and is validated by quantum mechanical/molecular mechanical (QM/MM) MD calculations constrained by NMR-derived data. To illustrate this approach, we refine the zinc coordination complex structure of the zinc sensing transcriptional repressor protein Staphylococcus aureus CzrA, generating over 130 ns of MD and QM/MM MD NMR-data compliant sampling. In addition to refining the first coordination shell structure of the Zn(II) ion, this protocol benefits from being performed in a periodically replicated solvation environment including long-range electrostatics. We determine that unrestrained (not based on NMR data) MD simulations correlated to the NMR data in a time-averaged ensemble. The accurate solution structure ensemble of the metal-bound protein accurately describes the role of conformational sampling in allosteric regulation of DNA binding by zinc and serves to validate our previous unrestrained MD simulations of CzrA. This methodology has potentially broad applicability in the structure determination of metal ion bound proteins, protein folding and metal template protein-design studies.

Solution structure of Mycobacterium tuberculosis NmtR in the apo state: insights into Ni(II)-mediated allostery.

Mycobacterium tuberculosis is an obligate human respiratory pathogen that encodes approximately 10 arsenic repressor (ArsR) family regulatory proteins that allow the organism to respond to a wide range of changes in its immediate microenvironment. How individual ArsR repressors have evolved to respond to selective stimuli is of intrinsic interest. The Ni(II)/Co(II)-specific repressor NmtR and related actinomycete nickel sensors harbor a conserved N-terminal α-NH(2)-Gly2-His3-Gly4 sequence. Here, we present the solution structure of homodimeric apo-NmtR and show that the core of the molecule adopts a typical winged-helix ArsR repressor (α1-α2-α3-αR-ß1-ß2-α5) "open conformation" that is similar to that of the related zinc sensor Staphylococcus aureus CzrA, but harboring long, flexible N-terminal (residues 2-16) and C-terminal (residues 109-120) extensions. Binding of Ni(II) to the regulatory sites induces strong paramagnetic broadening of the α5 helical region and the extreme N-terminal tail to residue 10. Ratiometric pulse chase amidination mass spectrometry reveals that the rate of amidination of the α-amino group of Gly2 is strongly attenuated in the Ni(II) complex relative to the apo state and noncognate Zn(II) complex. Ni(II) binding also induces dynamic disorder on the microsecond to millisecond time scale of key DNA interacting regions that likely contributes to the negative regulation of DNA binding by Ni(II). Molecular dynamics simulations and quantum chemical calculations reveal that NmtR readily accommodates a distal Ni(II) hexacoordination model involving the α-amine and His3 of the N-terminal region and α5 residues Asp91', His93', His104, and His107, which collectively define a new metal sensing site configuration in ArsR family regulators.

Simulations of allosteric motions in the zinc sensor CzrA.

The zinc sensing transcriptional repressor Staphylococcus aureus CzrA represents an excellent model system to understand how metal sensor proteins maintain cellular metal homeostasis. Zn(II) binding induces a quaternary structural switch from a "closed" conformation to a more "open" conformation, reducing the DNA binding affinity by 4 orders of magnitude. In this study, we use classical molecular dynamics and quantum mechanical/molecular mechanical molecular dynamics simulations to investigate the molecular basis for the large conformational motions and allosteric coupling free energy (~6 kcal/mol) associated with Zn(II) binding. Our simulations successfully capture the closed to open allosteric switching in DNA bound CzrA on Zn(II) binding. They reveal that zinc binding quenches global conformational sampling by CzrA, whereas DNA binding enhances the mobility of residues in the allosteric metal binding sites. These findings are in close agreement with experiments. We also identify networks of residues involved in correlated and anticorrelated motions that connect the metal binding and DNA binding sites. Our analysis of the essential dynamics shows metal ion binding to be the primary driving force for the quaternary structural change in CzrA. We also show that Zn(II) binding limits the conformational space sampled by CzrA and causes the electrostatic surface potential at the DNA binding interface to become less favorable toward DNA binding. Finally, our simulations provide strong support for a proposed hydrogen-bonding pathway that physically connects the metal binding residue, His97, to the DNA binding interface through the αR helix that is present only in the Zn(II)-bound state. Overall, our simulations provide molecular-level insights into the mechanism of allosteric regulation by CzrA and demonstrate the importance of protein motion in its biological activity.

Insight into the cation-π interaction at the metal binding site of the copper metallochaperone CusF.

The periplasmic Cu(+)/Ag(+) chaperone CusF features a novel cation-π interaction between a Cu(+)/Ag(+) ion and Trp44 at the metal binding site. The nature and strength of the Cu(+)/Ag(+)-Trp44 interactions were investigated using computational methodologies. Quantum-mechanical (QM) calculations showed that the Cu(+) and Ag(+) interactions with Trp44 are of similar strength (~14 kcal/mol) and bond order. Quantum-mechanical/molecular-mechanical (QM/MM) calculations showed that Cu(+) binds in a distorted tetrahedral coordination environment in the Trp44Met mutant, which lacks the cation-π interaction. Molecular dynamics (MD) simulations of CusF in the apo and Cu(+)-bound states emphasized the importance of the Cu(+)-Trp44 interaction in protecting Cu(+) from water oxidation. The protein structure does not change over the time scale of hundreds of nanoseconds in the metal-bound state. The metal recognition site exhibits small motions in the apo state but remains largely preorganized toward metal binding. Trp44 remains oriented to form the cation-π interaction in the apo state and faces an energetic penalty to move away from the metal ion. Cu(+) binding quenches the protein's internal motions in regions linked to binding CusB, suggesting that protein motions play an essential role in Cu(+) transfer to CusB.

Finding a needle in the haystack: computational modeling of Mg2+ binding in the active site of protein farnesyltransferase.

Studies aimed at elucidating the unknown Mg2+ binding site in protein farnesyltransferase (FTase) are reported. FTase catalyzes the transfer of a farnesyl group to a conserved cysteine residue (Cys1p) on a target protein, an important step for proteins in the signal transduction pathways (e.g., Ras). Mg2+ ions accelerate the protein farnesylation reaction by up to 700-fold. The exact function of Mg2+ in catalysis and the structural characteristics of its binding remain unresolved to date. Molecular dynamics (MD) simulations addressing the role of magnesium ions in FTase are presented, and relevant octahedral binding motifs for Mg2+ in wild-type (WT) FTase and the Dß352A mutant are explored. Our simulations suggest that the addition of Mg2+ ions causes a conformational change to occur in the FTase active site, breaking interactions known to keep FPP in its inactive conformation. Two relevant Mg2+ ion binding motifs were determined in WT FTase. In the first binding motif, WT1, the Mg2+ ion is coordinated to D352ß, zinc-bound D297ß, two water molecules, and one oxygen atom from the α- and ß-phosphates of farnesyl diphosphate (FPP). The second binding motif, WT2, is identical with the exception of the zinc-bound D297ß being replaced by a water molecule in the Mg2+ coordination complex. In the Dß352A mutant Mg2+ binding motif, D297ß, three water molecules, and one oxygen atom from the α- and ß-phosphates of FPP complete the octahedral coordination sphere of Mg2+. Simulations of WT FTase, in which Mg2+ was replaced by water in the active site, recreated the salt bridges and hydrogen-bonding patterns around FPP, validating these simulations. In all Mg2+ binding motifs, a key hydrogen bond was identified between a magnesium-bound water and Cys1p, bridging the two metallic binding sites and, thereby, reducing the equilibrium distance between the reacting atoms of FPP Cys1p. The free energy profiles calculated for these systems provide a qualitative understanding of experimental results. They demonstrate that the two reactive atoms approach each other more readily in the presence of Mg2+ in WT FTase and mutant. The flexible WT2 model was found to possess the lowest barrier toward the conformational change, suggesting it is the preferred Mg2+ binding motif in WT FTase. In the mutant, the absence of D352ß makes the transition toward a conformational change harder. Our calculations find support for the proposal that D352ß performs a critical role in Mg2+ binding and Mg2+ plays an important role in the conformational transition step.

Impact of mutation on proton transfer reactions in ketosteroid isomerase: insights from molecular dynamics simulations.

The two proton transfer reactions catalyzed by ketosteroid isomerase (KSI) involve a dienolate intermediate stabilized by hydrogen bonds with Tyr14 and Asp99. Molecular dynamics simulations based on an empirical valence bond model are used to examine the impact of mutating these residues on the hydrogen-bonding patterns, conformational changes, and van der Waals and electrostatic interactions during the proton transfer reactions. While the rate constants for the two proton transfer steps are similar for wild-type (WT) KSI, the simulations suggest that the rate constant for the first proton transfer step is smaller in the mutants due to the significantly higher free energy of the dienolate intermediate relative to the reactant. The calculated rate constants for the mutants D99L, Y14F, and Y14F/D99L relative to WT KSI are qualitatively consistent with the kinetic experiments indicating a significant reduction in the catalytic rates along the series of mutants. In the simulations, WT KSI retained two hydrogen-bonding interactions between the substrate and the active site, while the mutants typically retained only one hydrogen-bonding interaction. A new hydrogen-bonding interaction between the substrate and Tyr55 was observed in the double mutant, leading to the prediction that mutation of Tyr55 will have a greater impact on the proton transfer rate constants for the double mutant than for WT KSI. The electrostatic stabilization of the dienolate intermediate relative to the reactant was greater for WT KSI than for the mutants, providing a qualitative explanation for the significantly reduced rates of the mutants. The active site exhibited restricted motion during the proton transfer reactions, but small conformational changes occurred to facilitate the proton transfer reactions by strengthening the hydrogen-bonding interactions and by bringing the proton donor and acceptor closer to each other with the proper orientation for proton transfer. Thus, these calculations suggest that KSI forms a preorganized active site but that the structure of this preorganized active site is altered upon mutation. Moreover, small conformational changes due to stochastic thermal motions are required within this preorganized active site to facilitate the proton transfer reactions.

Hybrid quantum/classical molecular dynamics simulations of the proton transfer reactions catalyzed by ketosteroid isomerase: analysis of hydrogen bonding, conformational motions, and electrostatics.

Hybrid quantum/classical molecular dynamics simulations of the two proton transfer reactions catalyzed by ketosteroid isomerase are presented. The potential energy surfaces for the proton transfer reactions are described with the empirical valence bond method. Nuclear quantum effects of the transferring hydrogen increase the rates by a factor of approximately 8, and dynamical barrier recrossings decrease the rates by a factor of 3-4. For both proton transfer reactions, the donor-acceptor distance decreases substantially at the transition state. The carboxylate group of the Asp38 side chain, which serves as the proton acceptor and donor in the first and second steps, respectively, rotates significantly between the two proton transfer reactions. The hydrogen-bonding interactions within the active site are consistent with the hydrogen bonding of both Asp99 and Tyr14 to the substrate. The simulations suggest that a hydrogen bond between Asp99 and the substrate is present from the beginning of the first proton transfer step, whereas the hydrogen bond between Tyr14 and the substrate is virtually absent in the first part of this step but forms nearly concurrently with the formation of the transition state. Both hydrogen bonds are present throughout the second proton transfer step until partial dissociation of the product. The hydrogen bond between Tyr14 and Tyr55 is present throughout both proton transfer steps. The active site residues are more mobile during the first step than during the second step. The van der Waals interaction energy between the substrate and the enzyme remains virtually constant along the reaction pathway, but the electrostatic interaction energy is significantly stronger for the dienolate intermediate than for the reactant and product. Mobile loop regions distal to the active site exhibit significant structural rearrangements and, in some cases, qualitative changes in the electrostatic potential during the catalytic reaction. These results suggest that relatively small conformational changes of the enzyme active site and substrate strengthen the hydrogen bonds that stabilize the intermediate, thereby facilitating the proton transfer reactions. Moreover, the conformational and electrostatic changes associated with these reactions are not limited to the active site but rather extend throughout the entire enzyme.

Studying allosteric regulation in metal sensor proteins using computational methods.

In this chapter, we describe advances made in understanding the mechanism of allosteric regulation of DNA operator binding in the ArsR/SmtB family of metal-sensing proteins using computational methods. The paradigm, zinc-sensing transcriptional repressor Staphylococcus aureus CzrA represents an excellent model system to understand how metal sensor proteins maintain cellular metal homeostasis. Here, we discuss studies that helped to characterize a metal ion-mediated hydrogen-bonding pathway (HBP) that plays a dominant role in the allosteric mechanism of DNA operator binding in these proteins. The chapter discusses computational methods used to provide a molecular basis for the large conformational motions and allosteric coupling free energy (~6kcal/mol) associated with Zn(II) binding in CzrA. We present an accurate and convenient means by which to include metal ions in the nuclear magnetic resonance (NMR) structure determination process using molecular dynamics (MD) constrained by NMR-derived data. The method provides a realistic and physically viable description of the metal-binding site(s) and has potentially broad applicability in the structure determination of metal ion-bound proteins, protein folding, and metal template protein-design studies. Finally, our simulations provide strong support for a proposed HBP that physically connects the metal-binding residue, His97, to the DNA-binding interface through the αR helix that is present only in the Zn(II)-bound state. We find the interprotomer hydrogen bond interaction to be significantly stronger (~8kcal/mol) at functional allosteric metal-binding sites compared to the apo proteins. This interaction works to overcome the considerable disorder at these hydrogen-bonding sites in apo protein and functions as a "switch" to lock in a weak DNA-binding conformation once metal is bound. This interaction is found to be considerably weaker in nonresponsive metal-binding sites. These findings suggest a conserved functional role of metal-mediated second-shell coordination hydrogen bonds at allosterically responsive sites in zinc-sensing transcription regulators.

Characterizing solution surface loop conformational flexibility of the GM2 activator protein.

GM2AP has a ß-cup topology with numerous X-ray structures showing multiple conformations for some of the surface loops, revealing conformational flexibility that may be related to function, where function is defined as either membrane binding associated with ligand binding and extraction or interaction with other proteins. Here, site-directed spin labeling (SDSL) electron paramagnetic resonance (EPR) spectroscopy and molecular dynamic (MD) simulations are used to characterize the mobility and conformational flexibility of various structural regions of GM2AP. A series of 10 single cysteine amino acid substitutions were generated, and the constructs were chemically modified with the methanethiosulfonate spin label. Continuous wave (CW) EPR line shapes were obtained and subsequently simulated using the microscopic order macroscopic disorder (MOMD) program. Line shapes for sites that have multiple conformations in the X-ray structures required two spectral components, whereas spectra of the remaining sites were adequately fit with single-component parameters. For spin labeled sites L126C and I66C, spectra were acquired as a function of temperature, and simulations provided for the determination of thermodynamic parameters associated with conformational change. Binding to GM2 ligand did not alter the conformational flexibility of the loops, as evaluated by EPR and NMR spectroscopies. These results confirm that the conformational flexibility observed in the surface loops of GM2AP crystals is present in solution and that the exchange is slow on the EPR time scale (>ns). Furthermore, MD simulation results are presented and agree well with the conformational heterogeneity revealed by SDSL.

Rational Design of Particle Mesh Ewald Compatible Lennard-Jones Parameters for +2 Metal Cations in Explicit Solvent.

Metal ions play significant roles in biological systems. Accurate molecular dynamics (MD) simulations on these systems require a validated set of parameters. Although there are more detailed ways to model metal ions, the nonbonded model, which employs a 12-6 Lennard-Jones (LJ) term plus an electrostatic potential is still widely used in MD simulations today due to its simple form. However, LJ parameters have limited transferability due to different combining rules, various water models and diverse simulation methods. Recently, simulations employing a Particle Mesh Ewald (PME) treatment for long-range electrostatics have become more and more popular owing to their speed and accuracy. In the present work we have systematically designed LJ parameters for 24 +2 metal (M(II)) cations to reproduce different experimental properties appropriate for the Lorentz-Berthelot combining rules and PME simulations. We began by testing the transferability of currently available M(II) ion LJ parameters. The results showed that there are differences between simulations employing Ewald summation with other simulation methods and that it was necessary to design new parameters specific for PME based simulations. Employing the thermodynamic integration (TI) method and performing periodic boundary MD simulations employing PME, allowed for the systematic investigation of the LJ parameter space. Hydration free energies (HFEs), the ion-oxygen distance in the first solvation shell (IOD) and coordination numbers (CNs) were obtained for various combinations of the parameters of the LJ potential for four widely used water models (TIP3P, SPC/E, TIP4P and TIP4PEW). Results showed that the three simulated properties were highly correlated. Meanwhile, M(II) ions with the same parameters in different water models produce remarkably different HFEs but similar structural properties. It is difficult to reproduce various experimental values simultaneously because the nonbonded model underestimates the interaction between the metal ions and water molecules at short range. Moreover, the extent of underestimation increases successively for the TIP3P, SPC/E, TIP4PEW and TIP4P water models. Nonetheless, we fitted a curve to describe the relationship between ε (the well depth) and radius (Rmin/2) from experimental data on noble gases to facilitate the generation of the best possible compromise models. Hence, by targeting different experimental values, we developed three sets of parameters for M(II) cations for three different water models (TIP3P, SPC/E and TIP4PEW). These parameters we feel represent the best possible compromise that can be achieved using the nonbonded model for the ions in combination with simple water models. From a computational uncertainty analysis we estimate that the uncertainty in our computed HFEs is on the order of ±1kcal/mol. Further improvements will require more advanced non-bonded models likely with inclusion of polarization.

Implementation of umbrella integration within the framework of the empirical valence bond approach.

The umbrella integration method for calculating the potential of mean force (PMF) for a chemical reaction is implemented within the empirical valence bond (EVB) framework. In this implementation, the PMF is generated along the energy gap reaction coordinate, and the biasing potential is the difference between the mapping potential, which is defined to be a linear combination of the valence bond state energies, and the EVB ground state energy. The umbrella integration method is based on the derivative of the PMF with respect to the reaction coordinate. An analytical expression for this derivative applicable to certain types of EVB potentials is presented. The advantages of the umbrella integration method are illustrated by the application of both umbrella integration and the weighted histogram analysis method to the hydride transfer reaction catalyzed by the enzyme dihydrofolate reductase. This application demonstrates that the umbrella integration method reduces the statistical errors, converges efficiently, and does not require significantly overlapping windows. A modified version of the weighted histogram analysis method that shares these advantages is also proposed and implemented.