Robert E. Duke

Trypsin-ligand binding free energies from explicit and implicit solvent simulations with polarizable potential.

We have calculated the binding free energies of a series of benzamidine‐like inhibitors to trypsin with a polarizable force field using both explicit and implicit solvent approaches. Free energy perturbation has been performed for the ligands in bulk water and in protein complex with molecular dynamics simulations. The binding free energies calculated from explicit solvent simulations are well within the accuracy of experimental measurement and the direction of change is predicted correctly in all cases. We analyzed the molecular dipole moments of the ligands in gas, water and protein environments. Neither binding affinity nor ligand solvation free energy in bulk water shows much dependence on the molecular dipole moments of the ligands. Substitution of the aromatic or the charged group in the ligand results in considerable change in the solvation energy in bulk water and protein whereas the binding affinity varies insignificantly due to cancellation. The effect of chemical modification on ligand charge distribution is mostly local. Replacing benzene with diazine has minimal impact on the atomic multipoles at the amidinium group. We have also utilized an implicit solvent based end‐state approach to evaluate the binding free energies of these inhibitors. In this approach, the polarizable multipole model combined with Poisson‐Boltzmann/surface area (PMPB/SA) provides the electrostatic interaction energy and the polar solvation free energy. Overall the relative binding free energies obtained from the MM‐PMPB/SA model are in good agreement with the experimental data.

Simulations of a Protein Crystal with a High Resolution X-ray Structure: Evaluation of Force Fields and Water Models

We use classical molecular dynamics and 16 combinations of force fields and water models to simulate a protein crystal observed by room-temperature X-ray diffraction. The high resolution of the diffraction data (0.96 Å) and the simplicity of the crystallization solution (nearly pure water) make it possible to attribute any inconsistencies between the crystal structure and our simulations to artifacts of the models rather than inadequate representation of the crystal environment or uncertainty in the experiment. All simulations were extended for 100 ns of production dynamics, permitting some long-time scale artifacts of each model to emerge. The most noticeable effect of these artifacts is a model-dependent drift in the unit cell dimensions, which can become as large as 5% in certain force fields; the underlying cause is the replacement of native crystallographic contacts with non-native ones, which can occur with heterogeneity (loss of crystallographic symmetry) in simulations with some force fields. We find that the AMBER FF99SB force field maintains a lattice structure nearest that seen in the X-ray data, and produces the most realistic atomic fluctuations (by comparison to crystallographic B-factors) of all the models tested. We find that the choice of water model has a minor effect in comparison to the choice of protein model. We also identify a number of artifacts that occur throughout all of the simulations: excessive formation of hydrogen bonds or salt bridges between polar groups and loss of hydrophobic interactions. This study is intended as a foundation for future work that will identify individual parameters in each molecular model that can be modified to improve their representations of protein structure and thermodynamics.

Proposed structural models of human factor Va and prothrombinase

Summary.  Background: The prothrombinase complex consists of factor Xa, FVa, calcium ions, and phospholipid membrane. The prothrombinase complex plays a key role in the blood coagulation process.

An all‐atom solution‐equilibrated model for human extrinsic blood coagulation complex (sTF–VIIa–Xa): a protein–protein docking and molecular dynamics refinement study

Summary.  Tissue factor (TF)‐bound factor (F)VIIa plays a critical role in activating FX, an event that rapidly results in blood coagulation. Despite recent advances in the structural information about soluble TF (sTF)‐bound VIIa and Xa individually, the atomic details of the ternary complex are not known. As part of our long‐term goal to provide a structural understanding of the extrinsic blood coagulation pathway, we built an all atom solution‐equilibrated model of the human sTF–VIIa–Xa ternary complex using protein–protein docking and molecular dynamics (MD) simulations. The starting structural coordinates of sTF–VIIa and Xa were derived from dynamically equilibrated solution structures. Due to the flexible nature of the light‐chain of the Xa molecule, a three‐stage docking approach was employed in which SP (Arg195‐Lys448)/EGF2 (Arg86‐Arg139), EGF1 (Asp46‐Thr85) and GLA (Ala1‐Lys45) domains were docked in a sequential manner. The rigid‐body docking approach of the FTDOCK method in conjunction with filtering based on biochemical knowledge from experimental site‐specific mutagenesis studies provided the strategy. The best complex obtained from the docking experiments was further refined using MD simulations for 3 ns in explicit water. In addition to explaining most of the known experimental site‐specific mutagenesis data pertaining to sTF–VIIa, our model also characterizes likely enzyme‐binding exosites on FVIIa and Xa that may be involved in the ternary complex formation. According to the equilibrated model, the 140s loop of VIIa serves as the key recognition motif for complex formation. Stable interactions occur between the FVIIa 140s loop and the FXa β‐strand B2 region near the sodium‐binding domain, the 160 s loop and the N‐terminal activation loop regions. The helical‐hydrophobic stack region that connects the GLA and EGF1 domains of VIIa and Xa appears to play a potential role in the membrane binding region of the ternary complex. The proposed model may serve as a reasonable structural basis for understanding the exosite‐mediated substrate recognition of sTF–VIIa and to advance understanding of the TFPI‐mediated regulatory pathway of the extrinsic blood coagulation cascade.

A computational modeling and molecular dynamics study of the Michaelis complex of human protein Z-dependent protease inhibitor (ZPI) and factor Xa (FXa)

AbstractProtein Z-dependent protease inhibitor (ZPI) and antithrombin III (AT3) are members of the serpin superfamily of protease inhibitors that inhibit factor Xa (FXa) and other proteases in the coagulation pathway. While experimental structural information is available for the interaction of AT3 with FXa, at present there is no structural data regarding the interaction of ZPI with FXa, and the precise role of this interaction in the blood coagulation pathway is poorly understood. In an effort to gain a structural understanding of this system, we have built a solvent equilibrated three-dimensional structural model of the Michaelis complex of human ZPI/FXa using homology modeling, protein–protein docking and molecular dynamics simulation methods. Preliminary analysis of interactions at the complex interface from our simulations suggests that the interactions of the reactive center loop (RCL) and the exosite surface of ZPI with FXa are similar to those observed from X-ray crystal structure-based simulations of AT3/FXa. However, detailed comparison of our modeled structure of ZPI/FXa with that of AT3/FXa points to differences in interaction specificity at the reactive center and in the stability of the inhibitory complex, due to the presence of a tyrosine residue at the P1 position in ZPI, instead of the P1 arginine residue in AT3. The modeled structure also shows specific structural differences between AT3 and ZPI in the heparin-binding and flexible N-terminal tail regions. Our structural model of ZPI/FXa is also compatible with available experimental information regarding the importance for the inhibitory action of certain basic residues in FXa. FigureSolvent equilibrated models for protein z-dependent protease inhibitor and its initial reactive complex with coagulation factor Xa (show here) are developed.

A finite field method for calculating molecular polarizability tensors for arbitrary multipole rank

A finite field method for calculating spherical tensor molecular polarizability tensors αlm;l′m′ = ∂Δlm/∂ϕl′m′* by numerical derivatives of induced molecular multipole Δlm with respect to gradients of electrostatic potential ϕl′m′* is described for arbitrary multipole ranks l and l′. Interconversion formulae for transforming multipole moments and polarizability tensors between spherical and traceless Cartesian tensor conventions are derived. As an example, molecular polarizability tensors up to the hexadecapole–hexadecapole level are calculated for water using the following ab initio methods: Hartree–Fock (HF), Becke three‐parameter Lee‐Yang‐Parr exchange‐correlation functional (B3LYP), Møller–Plesset perturbation theory up to second order (MP2), and Coupled Cluster theory with single and double excitations (CCSD). In addition, intermolecular electrostatic and polarization energies calculated by molecular multipoles and polarizability tensors are compared with ab initio reference values calculated by the Reduced Variation Space method for several randomly oriented small molecule dimers separated by a large distance. It is discussed how higher order molecular polarizability tensors can be used as a tool for testing and developing new polarization models for future force fields.

Recent Estimates of the Structure of the Factor VIIa (FVIIa)/Tissue Factor (TF) and Factor Xa (FXa) Ternary Complex

The putative structure of the Tissue Factor/Factor VIIa/Factor Xa (TF/FVIIa/FXa) ternary complex is reconsidered. Two independently derived docking models proposed in 2003 (one for our laboratory: CHeA and one from the Scripps laboratory: Ss) are dynamically equilibrated for over 10 ns in an electrically neutral solution using all-atom molecular dynamics. Although the dynamical models (CHeB and Se) differ in atomic detail, there are similarities in that TF is found to interact with the gamma-carboxyglutamic acid (Gla) and Epidermal Growth Factor-like 1 (EGF-1) domains of FXa, and FVIIa is found to interact with the Gla, EGF-2 and serine protease (SP) domains of FXa in both models. FVIIa does not interact with the FXa EGF-1 domain in Se and the EGF domains of FVIIa do not interact with FXa in the CHeB. Both models are consistent with experimentally suggested contacts between the SP domain of FVIIa with the EGF-2 and SP domains of FXa.

A proposed structural model of human protein Z

Analysis of structures and sequence similarities of the vitamin K-dependent (VKD) proteins in the blood coagulation pathway has shown that these proteins have evolved through a series of gene duplications and diversification, acquiring a degree of functional diversity in the process [1–3]. Protein Z (PZ) is a VKD plasma glycoprotein that is highly conserved across different species. It is homologous to the blood coagulation factors VII (FVII), FIX, FX, and protein C (PC). However, PZ differs from other coagulation proteins in that it lacks the critical histidine and serine residues of the catalytic triad, and is therefore not a zymogen of a serine protease (SP) [4,5]. Human PZ was first isolated in 1984 [6], and its gene was characterized in 1998 [7]. PZ is relatively abundant in humans, with a wide plasma concentration range, and circulates as a complex with PZ-dependent protease inhibitor (ZPI) [8–10]. It has been shown to function as a cofactor in the inhibition of activated FX (FXa) by ZPI, causing a thousandfold increase in inhibition in a Ca-dependent manner [11]. The relative abundance in plasma and sequence similarity with other VKD proteins serve to pique our interest in the PZ system. In order to gain a better understanding of the function and evolutionary significance of PZ, it is important to start from structural information at an atomic level. Although PZ was isolated over 20 years ago, its physiologic role in relation to its molecular structure is still not clear. In this study, we propose a solvent-equilibrated structural model of human PZ using homology modeling and molecular dynamics (MD) simulation. The possibility of using this approach is supported by recent findings [12]. Human PZ is a single-chain molecule of 360 residues with four domains: a Gla domain (residues 1–46) with 13 ccarboxyglutamic acid (Gla) residues (residues 7, 8, 11, 15, 17, 20, 21, 26, 27, 30, 33, 35 and 40), two epidermal growth factor (EGF)-like domains – an EGF1 domain (residues 47–83) with a b-hydroxyaspartate (Bha) residue at 64, and an EGF2 domain (residues 85–126) – and an SP-like domain (residues 135–360) with high homology to the catalytic domain of other VKD SPs [4,5]. We have employed an iterative process of homology modeling and structure evaluation followed byMD simulation to construct a solvent-equilibrated structural model of PZ. Two different schemes were adopted to construct the homology model for PZ: one usingmultiple sequence alignment of human FVIIa [13], FIXa [14], FXa [15] and PC [16] sequences, and the other using FVIIa as a single template (see supplementary Fig. S1 for the sequence alignment). A multiple sequence alignment created with CLUSTALW [17] was used as an input to construct 30 homology models using MODELLER 8v2 [18] (see supplementary Fig. S1 for a description of MODELLER parameters). We chose the best model on the basis of the stereochemical values from PROCHECK [19] and objective function values fromMODELLER. This model had nine disulfide bonds (residues 18–23, 51–62, 56–71, 73–82, 89–101, 97–110, 112–125, 163–179 and 287–301). To obtain a refined solvent-equilibrated model and to remove bad contacts in the homology model, we performed an MD simulation using PMEMD9 in the AMBER9 [20] suite with the ff99SB forcefield. The total system was composed of 99 459 atoms, including 12 calcium ions, four sodium counterions for neutralizing the system, and 31 307 TIP3P water molecules. The seven conserved calcium ions in the Gla domain were placed on the basis of FVIIa, and the additional calcium ions were placed with malonate coordination (both carboxylates of Gla involved). Constraints were applied on the backbone during the early stages of minimization and the NPT (fixed number of molecules, pressure and temperature to simulate benchtop conditions) equilibration phase. The final 9-ns unconstrained trajectories (1.5-ps time interval in the NPT ensemble at 1 atm and 300.0 K) were analyzed. For the homologymodel that employed FVIIa as a single template, the refinement protocols above were followed. The backbone root mean square deviation (RMSD) plots of the simulation vs. the starting structures show that the domains are solution equilibrated by 9 ns (Fig. 1A). The overall structure is similar to that of other VKD proteins, especially FVIIa (Fig. 1B). The close contacts in the homology model are removed, and the stereochemical values are also well maintained throughout the simulation. The main findings of the simulation can be summarized as follows: (i) the secondary structural motif of each domain is well maintained and stable during the MD simulation; (ii) the individual domains show relatively smaller RMSDs and fluctuations than the overall structure – the larger RMSD for Correspondence: L. G. Pedersen, Department of Chemistry, UNCCH, Chapel Hill, NC, USA. Tel.: +1 919 962 1578; fax: +1 919 962 2388; e-mail: lee_pedersen@ unc.edu

What causes the enhancement of activity of factor VIIa by tissue factor

inhibition of the tissue factor pathway by tissue factor pathway inhibitor. Proc Natl Acad Sci USA 2006; 103: 3106–11. 14 Martinuzzo M, Iglesias Varela ML, Adamczuk Y, Broze GJ, Forastiero R. Antiphospholipid antibodies and antibodies to tissue factor pathway inhibitor in women with implantation failures or early and late pregnancy losses. J Thromb Haemost 2005; 3: 2587–9. 15 Backos M, Rai R, Baxter N, Chilcott IT, Cohen H, Regan L. Pregnancy complications in women with recurrent miscarriage associated with antiphospholipid antibodies treated with low dose aspirin and heparin. Br J Obstet Gynaecol 1999; 106: 102–7. 16 Rai R, Cohen H, Dave M, Regan L. Randomised controlled trial of aspirin and aspirin plus heparin in pregnant women with recurrent miscarriage associated with phospholipid antibodies (or antiphospholipid antibodies). BMJ 1997; 314: 253–7. 17 Dolitzky M, Inbal A, Segal Y, Weiss A, Brenner B, Carp H. A randomized study of thromboprophylaxis in women with unexplained consecutive recurrent miscarriages. Fertil Steril 2006; 86: 362–6. 18 Brenner B, Hoffman R, Carp H, Dulitsky M, Younis J. Efficacy and safety of two doses of enoxaparin in women with thrombophilia and recurrent pregnancy loss: the LIVE-ENOX study. J Thromb Haemost 2005; 3: 227–9. 19 Aharon A, Lanir N, Drugan A, Brenner B. Placental TFPI is decreased in gestational vascular complications and can be restored by maternal enoxaparin treatment. J Thromb Haemost 2005; 3: 2355–7. 20 van t Veer C, Golden NJ, Kalafatis M, Mann KG. Inhibitory mechanism of the protein C pathway on tissue factor-induced thrombin generation. Synergistic effect in combination with tissue factor pathway inhibitor. J Biol Chem 1997; 272: 7983–94.

Computational study of the putative active form of protein Z (PZa): Sequence design and structural modeling

Although protein Z (PZ) has a domain arrangement similar to the essential coagulation proteins FVII, FIX, FX, and protein C, its serine protease (SP)‐like domain is incomplete and does not exhibit proteolytic activity. We have generated a trial sequence of putative activated protein Z (PZa) by identifying amino acid mutations in the SP‐like domain that might reasonably resurrect the serine protease catalytic activity of PZ. The structure of the activated form was then modeled based on the proposed sequence using homology modeling and solvent‐equilibrated molecular dynamics simulations. In silico docking of inhibitors of FVIIa and FXa to the putative active site of equilibrated PZa, along with structural comparison with its homologous proteins, suggest that the designed PZa can possibly act as a serine protease.