Ilja V. Khavrutskii

Free Energy for the Permeation of Na + and Cl - Ions and Their Ion-Pair through a Zwitterionic Dimyristoyl Phosphatidylcholine Lipid Bilayer by Umbrella Integration with Harmonic Fourier Beads

Understanding the mechanism of ion permeation across lipid bilayers is key to controlling osmotic pressure and developing new ways of delivering charged, drug-like molecules inside cells. Recent reports suggest ion-pairing as the mechanism to lower the free energy barrier for the ion permeation in disagreement with predictions from the simple electrostatic models. In this paper we quantify the effect of ion-pairing or charge quenching on the permeation of Na+ and Cl− ions across DMPC lipid bilayer by computing the corresponding potentials of mean force (PMFs) using fully atomistic molecular dynamics simulations. We find that the free energy barrier to permeation reduces in the order Na+−Cl− ion-pair (27.6 kcal/mol) > Cl− (23.6 kcal/mol) > Na+ (21.9 kcal/mol). Furthermore, with the help of these PMFs we derive the change in the binding free energy between the Na+ and Cl− with respect to that in water as a function of the bilayer permeation depth. Despite the fact that the bilayer boosts the Na+−Cl− ion binding free energy by as high as 17.9 kcal/mol near its center, ion-pairing between such hydrophilic ions as Na+ and Cl− does not assist their permeation. However, based on a simple thermodynamic cycle, we suggest that ion-pairing between ions of opposite charge and solvent philicity could enhance ion permeation. Comparison of the computed permeation barriers for Na+ and Cl− ions with available experimental data supports this notion. This work establishes general computational methodology to address ion-pairing in fluid anisotropic media and details the ion permeation mechanism on atomic level.

Computing accurate potentials of mean force in electrolyte solutions with the generalized gradient-augmented harmonic Fourier beads method

We establish the accuracy of the novel generalized gradient-augmented harmonic Fourier beads (ggaHFB) method in computing free-energy profiles or potentials of mean force (PMFs) through comparison with two independent conventional techniques. In particular, we employ umbrella sampling with one dimensional weighted histogram analysis method (WHAM) and free molecular dynamics simulation of radial distribution functions to compute the PMF for the Na(+)-Cl(-) ion-pair separation to 16 A in 1.0M NaCl solution in water. The corresponding ggaHFB free-energy profile in six dimensional Cartesian space is in excellent agreement with the conventional benchmarks. We then explore changes in the PMF in response to lowering the NaCl concentration to physiological 0.3 and 0.1M, and dilute 0.0M concentrations. Finally, to expand the scope of the ggaHFB method, we formally develop the free-energy gradient approximation in arbitrary nonlinear coordinates. This formal development underscores the importance of the logarithmic Jacobian correction to reconstruct true PMFs from umbrella sampling simulations with either WHAM or ggaHFB techniques when nonlinear coordinate restraints are used with Cartesian propagators. The ability to employ nonlinear coordinates and high accuracy of the computed free-energy profiles further advocate the use of the ggaHFB method in studies of rare events in complex systems.

A transition path ensemble study reveals a linchpin role for Mg(2+) during rate-limiting ADP release from protein kinase A.

Protein kinases are key regulators of diverse signaling networks critical for growth and development. Protein kinase A (PKA) is an important kinase prototype that phosphorylates protein targets at Ser and Thr residues by converting ATP to ADP. Mg2+ ions play a crucial role in regulating phosphoryl transfer and can limit overall enzyme turnover by affecting ADP release. However, the mechanism by which Mg2+ participates in ADP release is poorly understood. Here we use a novel transition path ensemble technique, the harmonic Fourier beads method, to explore the atomic and energetic details of the Mg2+-dependent ADP binding and release. Our studies demonstrate that adenine-driven ADP binding to PKA creates three ion-binding sites at the ADP/PKA interface that are absent otherwise. Two of these sites bind the previously characterized Mg2+ ions, whereas the third site binds a monovalent cation with high affinity. This third site can bind the P-3 residue of substrate proteins and may serve as a reporter of the active site occupation. Binding of Mg2+ ions restricts mobility of the Gly-rich loop that closes over the active site. We find that simultaneous release of ADP with Mg2+ ions from the active site is unfeasible. Thus, we conclude that Mg2+ ions act as a linchpin and that at least one ion must be removed prior to pyrophosphate-driven ADP release. The results of the present study enhance understanding of Mg2+-dependent association of nucleotides with protein kinases.

Harmonic Fourier beads method for studying rare events on rugged energy surfaces.

We present a robust, distributable method for computing minimum free energy paths of large molecular systems with rugged energy landscapes. The method, which we call harmonic Fourier beads (HFB), exploits the Fourier representation of a path in an appropriate coordinate space and proceeds iteratively by evolving a discrete set of harmonically restrained path points-beads-to generate positions for the next path. The HFB method does not require explicit knowledge of the free energy to locate the path. To compute the free energy profile along the final path we employ an umbrella sampling method in two generalized dimensions. The proposed HFB method is anticipated to aid the study of rare events in biomolecular systems. Its utility is demonstrated with an application to conformational isomerization of the alanine dipeptide in gas phase.

Conformational change of the methionine 20 loop of Escherichia coli dihydrofolate reductase modulates pKa of the bound dihydrofolate.

We evaluate the pKa of dihydrofolate (H2F) at the N5 position in three ternary complexes with Escherichia coli dihydrofolate reductase (ecDHFR), namely ecDHFR(NADP+:H2F) in the closed form (1), and the Michaelis complexes ecDHFR(NADPH:H2F) in the closed (2) and occluded (3) forms, by performing free energy perturbation with molecular dynamics simulations (FEP/MD). Our simulations suggest that in the Michaelis complex the pKa is modulated by the Met20 loop fluctuations, providing the largest pKa shift in substates with a “tightly closed” loop conformation; in the “partially closed/open” substates, the pKa is similar to that in the occluded complex. Conducive to the protonation, tightly closing the Met20 loop enhances the interactions of the cofactor and the substrate with the Met20 side chain and aligns the nicotinamide ring of the cofactor coplanar with the pterin ring of the substrate. Overall, the present study favors the hypothesis that N5 is protonated directly from solution and provides further insights into the mechanism of the substrate protonation.

Probing the Donor and Acceptor Substrate Specificity of the γ-Glutamyl Transpeptidase

γ-Glutamyl transpeptidase (GGT) is a two-substrate enzyme that plays a central role in glutathione metabolism and is a potential target for drug design. GGT catalyzes the cleavage of γ-glutamyl donor substrates and the transfer of the γ-glutamyl moiety to an amine of an acceptor substrate or water. Although structures of bacterial GGT have revealed details of the protein-ligand interactions at the donor site, the acceptor substrate site is relatively undefined. The recent identification of a species-specific acceptor site inhibitor, OU749, suggests that these inhibitors may be less toxic than glutamine analogues. Here we investigated the donor and acceptor substrate preferences of Bacillus anthracis GGT (CapD) and applied computational approaches in combination with kinetics to probe the structural basis of the enzymes substrate and inhibitor binding specificities and compare them with human GGT. Site-directed mutagenesis studies showed that the R432A and R520S variants exhibited 6- and 95-fold decreases in hydrolase activity, respectively, and that their activity was not stimulated by the addition of the l-Cys acceptor substrate, suggesting an additional role in acceptor binding and/or catalysis of transpeptidation. Rat GGT (and presumably HuGGT) has strict stereospecificity for L-amino acid acceptor substrates, while CapD can utilize both L- and D-acceptor substrates comparably. Modeling and kinetic analysis suggest that R520 and R432 allow two alternate acceptor substrate binding modes for L- and D-acceptors. R432 is conserved in Francisella tularensis, Yersinia pestis, Burkholderia mallei, Helicobacter pylori and Escherichia coli, but not in human GGT. Docking and MD simulations point toward key residues that contribute to inhibitor and acceptor substrate binding, providing a guide to designing novel and specific GGT inhibitors.

Generalized gradient-augmented harmonic Fourier beads method with multiple atomic and/or center-of-mass positional restraints

We describe a generalization of the gradient-augmented harmonic Fourier beads method for finding minimum free-energy transition path ensembles and similarly minimum potential energy paths to allow positional restraints on the centers of mass of selected atoms. The generalized gradient-augmented harmonic Fourier beads (ggaHFB) method further extends the scope of the HFB methodology to studying molecule transport across various mobile phases such as lipid membranes. Furthermore, the new implementation improves the applicability of the HFB method to studies of ligand binding, protein folding, and enzyme catalysis as well as modeling equilibrium pulling experiments. Like its predecessor, the ggaHFB method provides accurate energy profiles along the specified paths and in certain simple cases avoids the need for path optimization. The utility of the ggaHFB method is demonstrated with an application to the water permeation through a single-wall (5,5) carbon nanotube with a diameter of 6.78 A and length of 16.0 A. We provide a simple rationale as to why water enters the hydrophobic nanotube and why it does so in pulses and in wire assembly.

A line integral reaction path approximation for large systems via nonlinear constrained optimization: Application to alanine dipeptide and the β hairpin of protein G

A variation of the line integral method of Elber with self-avoiding walk has been implemented using a state of the art nonlinear constrained optimization procedure. The new implementation appears to be robust in finding approximate reaction paths for small and large systems. Exact transition states and intermediates for the resulting paths can easily be pinpointed with subsequent application of the conjugate peak refinement method [S. Fischer and M. Karplus, Chem. Phys. Lett. 194, 252 (1992)] and unconstrained minimization, respectively. Unlike previous implementations utilizing a penalty function approach, the present implementation generates an exact solution of the underlying problem. Most importantly, this formulation does not require an initial guess for the path, which makes it particularly useful for studying complex molecular rearrangements. The method has been applied to conformational rearrangements of the alanine dipeptide in the gas phase and in water, and folding of the beta hairpin of protein G in water. In the latter case a procedure was developed to systematically sample the potential energy surface underlying folding and reconstruct folding pathways within the nearest-neighbor hopping approximation.

Dengue virus antibody database: Systematically linking serotype-specificity with epitope mapping in dengue virus

Background A majority infections caused by dengue virus (DENV) are asymptomatic, but a higher incidence of severe illness, such as dengue hemorrhagic fever, is associated with secondary infections, suggesting that pre-existing immunity plays a central role in dengue pathogenesis. Primary infections are typically associated with a largely serotype-specific antibody response, while secondary infections show a shift to a broadly cross-reactive antibody response. Methods/Principal findings We hypothesized that the basis for the shift in serotype-specificity between primary and secondary infections can be found in a change in the antibody fine-specificity. To investigate the link between epitope- and serotype-specificity, we assembled the Dengue Virus Antibody Database, an online repository containing over 400 DENV-specific mAbs, each annotated with information on 1) its origin, including the immunogen, host immune history, and selection methods, 2) binding/neutralization data against all four DENV serotypes, and 3) epitope mapping at the domain or residue level to the DENV E protein. We combined epitope mapping and activity information to determine a residue-level index of epitope propensity and cross-reactivity and generated detailed composite epitope maps of primary and secondary antibody responses. We found differing patterns of epitope-specificity between primary and secondary infections, where secondary responses target a distinct subset of epitopes found in the primary response. We found that secondary infections were marked with an enhanced response to cross-reactive epitopes, such as the fusion-loop and E-dimer region, as well as increased cross-reactivity in what are typically more serotype-specific epitope regions, such as the domain I-II interface and domain III. Conclusions/Significance Our results support the theory that pre-existing cross-reactive memory B cells form the basis for the secondary antibody response, resulting in a broadening of the response in terms of cross-reactivity, and a focusing of the response to a subset of epitopes, including some, such as the fusion-loop region, that are implicated in poor neutralization and antibody-dependent enhancement of infection.

A Reaction Path Study of the Catalysis and Inhibition of the Bacillus anthracis CapD γ-Glutamyl Transpeptidase

The CapD enzyme of Bacillus anthracis is a γ-glutamyl transpeptidase from the N-terminal nucleophile hydrolase superfamily that covalently anchors the poly-γ-D-glutamic acid (pDGA) capsule to the peptidoglycan. The capsule hinders phagocytosis of B. anthracis by host cells and is essential for virulence. The role CapD plays in capsule anchoring and remodeling makes the enzyme a promising target for anthrax medical countermeasures. Although the structure of CapD is known, and a covalent inhibitor, capsidin, has been identified, the mechanisms of CapD catalysis and inhibition are poorly understood. Here, we used a computational approach to map out the reaction steps involved in CapD catalysis and inhibition. We found that the rate-limiting step of either CapD catalysis or inhibition was a concerted asynchronous formation of the tetrahedral intermediate with a barrier of 22-23 kcal/mol. However, the mechanisms of these reactions differed for the two amides. The formation of the tetrahedral intermediate with pDGA was substrate-assisted with two proton transfers. In contrast, capsidin formed the tetrahedral intermediate in a conventional way with one proton transfer. Interestingly, capsidin coupled a conformational change in the catalytic residue of the tetrahedral intermediate to stretching of the scissile amide bond. Furthermore, capsidin took advantage of iminol-amide tautomerism of its diacetamide moiety to convert the tetrahedral intermediate to the acetylated CapD. As evidence of the promiscuous nature of CapD, the enzyme cleaved the amide bond of capsidin by attacking it on the opposite side compared to pDGA.