Guillaume Lamoureux

A simple polarizable model of water based on classical Drude oscillators

A simple polarizable water model is developed and optimized for molecular dynamics simulations of the liquid phase under ambient conditions. The permanent charge distribution of the water molecule is represented by three point charges: two hydrogen sites and one additional M site positioned along the HOH bisector. Electronic induction is represented by introducing a classical charged Drude particle attached to the oxygen by a harmonic spring. The oxygen site carries an equal and opposite charge, and is the center of an intermolecular Lennard-Jones interaction. The HOH gas-phase experimental geometry is maintained rigidly and the dipole of the isolated molecule is 1.85 D, in accord with experiment. The model is simulated by considering the dynamics of an extended Lagrangian in which a small mass is attributed to the Drude particles. It is parametrized to reproduce the salient properties of liquid water under ambient conditions. The optimal model, refered to as SWM4-DP for “simple water model with four site...

Modeling induced polarization with classical Drude oscillators: Theory and molecular dynamics simulation algorithm

A simple treatment for incorporating induced polarization in computer simulations is formulated on the basis of the classical Drude oscillator model. In this model, electronic induction is represented by the displacement of a charge-carrying massless particle attached to a polarizable atom under the influence of the local electric field. The traditional self-consistent field (SCF) regime of induced polarization is reproduced if these auxiliary particles are allowed to relax instantaneously to their local energy minima for any given fixed configuration of the atoms in the system. In practice, such treatment is computationally prohibitive for generating molecular dynamics trajectories because the electric field must be recalculated several times iteratively to satisfy the SCF condition, and it is important to seek a more efficient way to simulate the classical Drude oscillator model. It is demonstrated that a close approximation to the SCF regime can be simulated efficiently by considering the dynamics of a...

Determination of Electrostatic Parameters for a Polarizable Force Field Based on the Classical Drude Oscillator

A procedure to determine the electrostatic parameters has been developed for a polarizable empirical force field based on the classical Drude oscillator model. Atomic charges and polarizabilities for a given molecule of interest were derived from restrained fitting to quantum-mechanical electrostatic potentials (ESP) calculated at the B3LYP/ cc-pVDZ or B3LYP/aug-cc-pVDZ levels on grid points located on concentric Connolly surfaces. The determination of the atomic polarizabilities requires a series of perturbed ESP maps, each one representing the electronic response of the molecule in the presence of a background charge placed on Connolly surfaces primarily along chemical bonds and lone pairs. Reference values for the partial atomic charges were taken from the CHARMM27 additive all-atom force field, and those for the polarizabilities were based on adjusted Millers ahp atomic polarizability values. The fitted values of atomic polarizabilities were scaled to reflect the reduced polarization expected for the condensed media and/or to correct for the systematic underestimation of experimental molecular polarizabilities by B3LYP calculations. Following correction of the polarizabilities, the atomic charges were adjusted to reproduce gas-phase dipole moments. The developed scheme has been tested on a set of small molecules representing functional moieties of nucleic acids. The derived electrostatic parameters have been successfully applied in a preliminary polarizable molecular dynamics simulation of a DNA octamer in a box of water with sodium counterions. Thus, this study confirms the feasibility of the use of a polarizable force field based on a classical Drude model for simulations of biomolecules in the condensed phase.

Polarizable empirical force field for nitrogen‐containing heteroaromatic compounds based on the classical Drude oscillator

The polarizable empirical CHARMM force field based on the classical Drude oscillator has been extended to the nitrogen‐containing heteroaromatic compounds pyridine, pyrimidine, pyrrole, imidazole, indole, and purine. Initial parameters for the six‐membered rings were based on benzene with nonbond parameter optimization focused on the nitrogen atoms and adjacent carbons and attached hydrogens. In the case of five‐member rings, parameters were first developed for imidazole and transferred to pyrrole. Optimization of all parameters was performed against an extensive set of quantum mechanical and experimental data. Ab initio data were used for the determination of initial electrostatic parameters, the vibrational analysis, and in the optimization of the relative magnitudes of the Lennard‐Jones (LJ) parameters, through computations of the interactions of dimers of model compounds, model compound‐water interactions, and interactions of rare gases with model compounds. The absolute values of the LJ parameters were determined targeting experimental heats of vaporization, molecular volumes, heats of sublimation, crystal lattice parameters, and free energies of hydration. Final scaling of the polarizabilities from the gas‐phase values by 0.85 was determined by reproduction of the dielectric constants of pyridine and pyrrole. The developed parameter set was extensively validated against additional experimental data such as diffusion constants, heat capacities, and isothermal compressibilities, including data as a function of temperature.

Reorganization free energies and quantum corrections for a model electron self-exchange reaction: comparison of polarizable and non-polarizable solvent models

The solvent contribution to the reorganization free energy for electron self-exchange in aqueous Ru(II)–Ru(III) is computed for two recently developed polarizable water models, AMOEBA [J. Phys. Chem. B 107, 5933 (2003)] and SWM4-NDP [Chem. Phys. Lett. 418, 241 (2005)], and for the earlier POL3 model [J. Phys. Chem. 99, 6208 (1995)], and compared with the reorganization free energy of non-polarizable water models. The ‘solute’, defined as the two ions and their first hydration shells, is treated as non-polarizable. We find that the solvent (‘outer sphere’) reorganization free energy is reduced by 22% for SWM4-NDP and by 11% for POL3 relative to the non-polarizable TIP3P water, but increased by 5% for AMOEBA water. This is less than the ≈38% reduction suggested by standard continuum theory and confirms the view that continuum theory predicts a stronger dependence of solvent reorganization on the optical dielectric constant than what is obtained from atomistic simulation. The varying degree of reduction in reorganization free energy for polarizable water models is the consequence of two opposing effects: (i) reduction in reorganization free energy due to decreased electronic response; and (ii) increase in reorganization free energy due to increased nuclear response. The first effect gives a consistent decrease of about 30%, while the second effect strongly depends on the polarizable water model used and is largest for AMOEBA water. Rate enhancements due to quantum corrections are computed in the harmonic bath approximation and range between 3.8 and 10.9, in good agreement with the estimate obtained from experimental dispersion data of liquid water, 7.7. The rigid non-polarizable water models overestimate the quantum correction in the libration modes, which effectively compensates for the neglect of quantum corrections in the absent stretching modes. About 85% of the solvent reorganization is due to the second and third solvation shell of the ion pair. Size effects caused by the finite number of solvent molecules are minor and much smaller than for oxidation of a single ion.

Peptide Hydrolysis in Thermolysin: Ab Initio QM/MM Investigation of the Glu143-Assisted Water Addition Mechanism

Thermolysin (TLN) is one of the best-studied zinc metalloproteases. Yet the mechanism of action is still under debate. In order to investigate the energetic feasibility of the currently most favored mechanism, we have docked a tripeptide to the active site of TLN and computed the free energy profile at the quantum mechanics/molecular mechanics level of theory. The mechanism consists of three distinct steps:  (i) a Zn-bound water molecule is deprotonated by Glu143 and attacks the carbonyl bond of the substrate; (ii) Glu143 transfers the proton to the amide nitrogen atom; (iii) the nitrogen atom is protonated and the peptide bond is irreversibly broken. The free energy barriers for steps i and iii have almost equal heights, 14.8 and 14.7 kcal/mol, respectively, and are in good agreement with the effective experimental activation barrier obtained for similar substrates, 12.1-13.6 kcal/mol. Transition state stabilization for nucleophilic attack is achieved by formation of a weak coordination bond between the substrate carbonyl oxygen atom and the Zn ion and of three strong hydrogen bonds between the substrate and protonated His231 and two solvent molecules. The transition state for the nucleophilic attack (step i) is more tightly bonded than the enzyme-substrate complex, implying that TLN complies with Paulings hypothesis regarding transition-state stabilization. Glu143, at first unfavorably oriented for protonation of the amide nitrogen atom, displayed large structural fluctuations that facilitated reorganization of the local hydrogen-bond network and transport of the proton to the leaving group on the nanosecond time scale. The present simulations give further evidence that Glu143 is a highly effective proton shuttle which should be assigned a key role in any reaction mechanism proposed for TLN.

Ammonium transporters achieve charge transfer by fragmenting their substrate.

Proteins of the Amt/MEP family facilitate ammonium transport across the membranes of plants, fungi, and bacteria and are essential for growth in nitrogen-poor environments. Some are known to facilitate the diffusion of the neutral NH(3), while others, notably in plants, transport the positively charged NH(4)(+). On the basis of the structural data for AmtB from Escherichia coli , we illustrate the mechanism by which proteins from the Amt family can sustain electrogenic transport. Free energy calculations show that NH(4)(+) is stable in the AmtB pore, reaching a binding site from which it can spontaneously transfer a proton to a pore-lining histidine residue (His168). The substrate diffuses down the pore in the form of NH(3), while the excess proton is cotransported through a highly conserved hydrogen-bonded His168-His318 pair. This constitutes a novel permeation mechanism that confers to the histidine dyad an essential mechanistic role that was so far unknown.

Transport mechanisms in the ammonium transporter family

Ammonium transport is mediated by membrane proteins of the ubiquitous Amt/Rh family. Despite the availability of different X-ray structures that provide many insights on the ammonium permeation process, the molecular details of its mechanism remain controversial. The X-ray structures have revealed that the pore of the Amt and Rh proteins is characterized by a hydrophobic portion about 12A long in which electronic density was observed in crystallographic study of AmtB from Escherichia coli. This electronic density was initially only observed when crystals were grown in presence of ammonium salt and was thus attributed to ammonia (NH(3)) molecules, and lead the authors to suggest that the conduction mechanism in the Amt/Rh proteins involves the single-file diffusion of NH(3) molecules. However, other X-ray crystallography results and molecular mechanics simulations suggest that the pore of AmtB could also be filled with water molecules. The possible presence of water molecules in the pore lumen calls for a reassessment of the growing consensus that Amt/Rh proteins work as plain NH(3) channels. Indeed, functional experiments on plant ammonium transporters and rhesus proteins suggest a variety of permeation mechanisms including the passive diffusion of NH(3), the antiport of NH(4)(+)/H(+), the transport of NH(4)(+), or the cotransport of NH(3)/H(+). We discuss these mechanisms in light of some recent functional and simulation studies on the AmtB transporter and illustrate how they can be reconciled with the available high resolution X-ray data.

Molecular modelling of cation–π interactions

Cation–π interactions have long been considered a challenge for molecular modelling and a shortcoming of most of the commonly used biomolecular force fields. In this article, we provide an overview of current research on molecular modelling of cation–π interactions, with an emphasis on applications to proteins and on our recent polarisable models based on the classical Drude oscillator. We describe the main approaches used to model cation–π interactions in solution and illustrate their relevance to a few case studies: the stability of the villin headpiece subdomain, the blockade of potassium channels by quaternary ammonium ions, and the permeation of ammonium across transporters of the Amt/MEP family.

Mechanism of NH4+ Recruitment and NH3 Transport in Rh Proteins

In human cells, membrane proteins of the rhesus (Rh) family excrete ammonium and play a role in pH regulation. Based on high-resolution structures, Rh proteins are generally understood to act as NH3 channels. Given that cell membranes are permeable to gases like NH3, the role of such proteins remains a paradox. Using molecular and quantum mechanical calculations, we show that a crystallographically identified site in the RhCG pore actually recruits NH4(+), which is found in higher concentration and binds with higher affinity than NH3, increasing the efficiency of the transport mechanism. A proton is transferred from NH4(+) to a signature histidine (the only moiety thermodynamically likely to accept a proton) followed by the diffusion of NH3 down the pore. The excess proton is circulated back to the extracellular vestibule through a hydrogen bond network, which involves a highly conserved and functionally important aspartic acid, resulting in the net transport of NH3.