Scaffold-Constrained Molecular Generation.

One of the major applications of generative models for drug discovery targets the lead-optimization phase. During the optimization of a lead series, it is common to have scaffold constraints imposed on the structure of the molecules designed. Without enforcing such constraints, the probability of generating molecules with the required scaffold is extremely low and hinders the practicality of generative models for de novo drug design. To tackle this issue, we introduce a new algorithm, named SAMOA (Scaffold Constrained Molecular Generation), to perform scaffold-constrained in silico molecular design. We build on the well-known SMILES-based Recurrent Neural Network (RNN) generative model, with a modified sampling procedure to achieve scaffold-constrained generation. We directly benefit from the associated reinforcement learning methods, allowing to design molecules optimized for different properties while exploring only the relevant chemical space. We showcase the method's ability to perform scaffold-constrained generation on various tasks: designing novel molecules around scaffolds extracted from SureChEMBL chemical series, generating novel active molecules on the Dopamine Receptor D2 (DRD2) target, and finally, designing predicted actives on the MMP-12 series, an industrial lead-optimization project.

Tackling Solvent Effects by Coupling Electronic and Molecular Density Functional Theory.

Solvation effects can have a tremendous influence on chemical reactions. However, precise quantum chemistry calculations are most often done either in vacuum neglecting the role of the solvent or using continuum solvent model ignoring its molecular nature. We propose a new method coupling a quantum description of the solute using electronic density functional theory with a classical grand-canonical treatment of the solvent using molecular density functional theory. Unlike a previous work, both densities are minimized self-consistently, accounting for mutual polarization of the molecular solvent and the solute. The electrostatic interaction is accounted using the full electron density of the solute rather than fitted point charges. The introduced methodology represents a good compromise between the two main strategies to tackle solvation effects in quantum calculation. It is computationally more effective than a direct quantum mechanics/molecular mechanics coupling, requiring the exploration of many solvent configurations. Compared to continuum methods, it retains the full molecular-level description of the solvent. We validate this new framework onto two usual benchmark systems: a water solvated in water and the symmetrical nucleophilic substitution between chloromethane and chloride in water. The prediction for the free energy profiles are not yet fully quantitative compared to experimental data, but the most important features are qualitatively recovered. The method provides a detailed molecular picture of the evolution of the solvent structure along the reaction pathway.

Predicting Hydration Free Energies of the FreeSolv Database of Drug-like Molecules with Molecular Density Functional Theory.

We assess the performance of molecular density functional theory (MDFT) to predict hydration free energies of the small drug-like molecules benchmark, FreeSolv. The MDFT in the hypernetted chain approximation (HNC) coupled with a pressure correction predicts experimental hydration free energies of the FreeSolv database within 1 kcal/mol with an average computation time of 2 cpu·min per molecule. This is the same accuracy as for simulation-based free energy calculations that typically require hundreds of cpu·h or tens of gpu·h per molecule.

Structure Factor of EuCl3 Aqueous Solutions via Coupled Molecular Dynamics Simulations and Integral Equations.

Identifying the structure of an aqueous solution is essential to rationalize various phenomena such as crystallization in solution, chemical reactivity, extraction of rare earth elements, and so forth. Despite this, the efforts to describe the structure of an aqueous solution have been hindered by the difficulty to retrieve structural data both from experiments and simulations. To overcome this, first, undersaturated EuCl3 aqueous solutions of concentrations varying from 0.15 to 1.8 mol/kg were studied using X-ray scattering. Second, for the first time, the theoretical X-ray signal of 1.8 mol/kg EuCl3 aqueous solution was simulated, with precise details for the complete range of scattering vectors using coupled molecular dynamics and hypernetted chain integral equations, and satisfactorily compared with the 1.8 mol/kg experimental X-ray scattering signal. The theoretical calculations demonstrate that the experimental structure factor is dominated by Eu3+-Eu3+ correlations.

Hydration free energies and solvation structures with molecular density functional theory in the hypernetted chain approximation.

The capability of molecular density functional theory in its lowest, second-order approximation, equivalent to the hypernetted chain approximation in integral equations, to predict accurately the hydration free-energies and microscopic structure of molecular solutes is explored for a variety of systems: spherical hydrophobic solutes, ions, water as a solute, and the Mobley's dataset of organic molecules. The successes and the caveats of the approach are carefully pinpointed. Compared to molecular simulations with the same force field and the same fixed solute geometries, the theory describes accurately the solvation of cations, less so that of anions or generally H-bond acceptors. Overall, the electrostatic contribution to solvation free-energies of neutral molecules is correctly reproduced. On the other hand, the cavity contribution is poorly described but can be corrected using scaled-particle theory ideas. Addition of a physically motivated, one-parameter cavity correction accounting for both pressure and surface effects in the nonpolar solvation contribution yields a precision of 0.8 kcal/mol for the overall hydration free energies of the whole Mobley's dataset. Inclusion of another one-parameter cavity correction for the electrostatics brings it to 0.6 kcal/mol, that is, kBT. This is accomplished with a three-orders of magnitude numerical speed-up with respect to molecular simulations.

Pressure correction for solvation theories.

Liquid state theories such as integral equations and classical density functional theory often overestimate the bulk pressure of fluids because they require closure relations or truncations of functionals. Consequently, the cost to create a molecular cavity in the fluid is no longer negligible, and those theories predict incorrect solvation free energies. We show how to correct them simply by computing an optimized Van der Walls volume of the solute and removing the undue free energy to create such volume in the fluid. Given this versatile correction, we demonstrate that state-of-the-art solvation theories can predict, within seconds, hydration free energies of a benchmark of small neutral drug-like molecules with the same accuracy as day-long molecular simulations.

Lattice Boltzmann electrokinetics simulation of nanocapacitors.

We propose a method to model metallic surfaces in Lattice Boltzmann Electrokinetics (LBE) simulations, a lattice-based algorithm rooted in kinetic theory which captures the coupled solvent and ion dynamics in electrolyte solutions. This is achieved by a simple rule to impose electrostatic boundary conditions in a consistent way with the location of the hydrodynamic interface for stick boundary conditions. The proposed method also provides the local charge induced on the electrode by the instantaneous distribution of ions under voltage. We validate it in the low voltage regime by comparison with analytical results in two model nanocapacitors: parallel plates and coaxial electrodes. We examine the steady-state ionic concentrations and electric potential profiles (and corresponding capacitance), the time-dependent response of the charge on the electrodes, and the steady-state electro-osmotic profiles in the presence of an additional, tangential electric field. The LBE method further provides the time-dependence of these quantities, as illustrated on the electro-osmotic response. While we do not consider this case in the present work, which focuses on the validation of the method, the latter readily applies to large voltages between the electrodes, as well as to time-dependent voltages. This work opens the way to the LBE simulation of more complex systems involving electrodes and metallic surfaces, such as sensing devices based on nanofluidic channels and nanotubes, or porous electrodes.

A molecular density functional theory approach to electron transfer reactions.

Beyond the dielectric continuum description initiated by Marcus theory, the standard theoretical approach to study electron transfer (ET) reactions in solution or at interfaces is to use classical force field or ab initio molecular dynamics simulations. We present here an alternative method based on liquid-state theory, namely molecular density functional theory, which is numerically much more efficient than simulations while still retaining the molecular nature of the solvent. We begin by reformulating molecular ET theory in a density functional language and show how to compute the various observables characterizing ET reactions from an ensemble of density functional minimizations. In particular, we define within that formulation the relevant order parameter of the reaction, the so-called vertical energy gap, and determine the Marcus free energy curves of both reactant and product states along that coordinate. Important thermodynamic quantities such as the reaction free energy and the reorganization free energies follow. We assess the validity of the method by studying the model Cl0 → Cl+ and Cl0 → Cl- ET reactions in bulk water for which molecular dynamics results are available. The anionic case is found to violate the standard Marcus theory. Finally, we take advantage of the computational efficiency of the method to study the influence of a solid-solvent interface on the ET, by investigating the evolution of the reorganization free energy of the Cl0 → Cl+ reaction when the atom approaches an atomistically resolved wall.

What Does Second-Harmonic Scattering Measure in Diluted Electrolytes?

We derive a theoretical expression of the second harmonic scattering signal in diluted electrolytes compared with bulk water. We show that the enhancement of the signal with respect to pure water observed recently for electrolytes at very low dilution in the micromolar range is a mere manifestation of the Debye screening that makes the infinite-range dipole-dipole solvent correlations in 1/ r3 disappear as soon as the ionic concentration becomes finite. In q space, this translates into a correlation function having a well known singular behavior around q = 0, which drives the observed ionic effects. We find that the signal is independent of the ion-induced long-range behavior of the function ⟨cos ϕ( r)⟩ that has been recently discussed. We find also that the enhancement depends on the experimental geometry and occurs only for in-plane polarization detection, as observed experimentally. On the contrary, the measured isotope effect between light and heavy water cannot be fully explained.

Screened Coulombic Orientational Correlations in Dilute Aqueous Electrolytes.

The ion-induced long-range orientational order between water molecules recently observed in second harmonic scattering experiments and illustrated with large scale molecular dynamics simulations is quantitatively explained using the Ornstein-Zernike integral equation approach of liquid physics. This general effect, not specific to hydrogen-bonding solvents, is controlled by electroneutrality conditions, dipolar interactions, and dielectric+ionic screening. As expected, all numerical theories recover the well-known analytical expressions established 40 years ago.

Efficient molecular density functional theory using generalized spherical harmonics expansions.

We show that generalized spherical harmonics are well suited for representing the space and orientation molecular density in the resolution of the molecular density functional theory. We consider the common system made of a rigid solute of arbitrary complexity immersed in a molecular solvent, both represented by molecules with interacting atomic sites and classical force fields. The molecular solvent density ρ(r,Ω) around the solute is a function of the position r≡(x,y,z) and of the three Euler angles Ω≡(θ,ϕ,ψ) describing the solvent orientation. The standard density functional, equivalent to the hypernetted-chain closure for the solute-solvent correlations in the liquid theory, is minimized with respect to ρ(r,Ω). The up-to-now very expensive angular convolution products are advantageously replaced by simple products between projections onto generalized spherical harmonics. The dramatic gain in speed of resolution enables to explore in a systematic way molecular solutes of up to nanometric sizes in arbitrary solvents and to calculate their solvation free energy and associated microscopic solvent structure in at most a few minutes. We finally illustrate the formalism by tackling the solvation of molecules of various complexities in water.

Transient hydrodynamic finite-size effects in simulations under periodic boundary conditions.

We use lattice-Boltzmann and analytical calculations to investigate transient hydrodynamic finite-size effects induced by the use of periodic boundary conditions. These effects are inevitable in simulations at the molecular, mesoscopic, or continuum levels of description. We analyze the transient response to a local perturbation in the fluid and obtain the local velocity correlation function via linear response theory. This approach is validated by comparing the finite-size effects on the steady-state velocity with the known results for the diffusion coefficient. We next investigate the full time dependence of the local velocity autocorrelation function. We find at long times a crossover between the expected t^{-3/2} hydrodynamic tail and an oscillatory exponential decay, and study the scaling with the system size of the crossover time, exponential rate and amplitude, and oscillation frequency. We interpret these results from the analytic solution of the compressible Navier-Stokes equation for the slowest modes, which are set by the system size. The present work not only provides a comprehensive analysis of hydrodynamic finite-size effects in bulk fluids, which arise regardless of the level of description and simulation algorithm, but also establishes the lattice-Boltzmann method as a suitable tool to investigate such effects in general.

Molecular density functional theory of water including density-polarization coupling.

We present a three-dimensional molecular density functional theory of water derived from first-principles that relies on the particle's density and multipolar polarization density and includes the density-polarization coupling. This brings two main benefits: (i) scalar density and vectorial multipolar polarization density fields are much more tractable and give more physical insight than the full position and orientation densities, and (ii) it includes the full density-polarization coupling of water, that is known to be non-vanishing but has never been taken into account. Furthermore, the theory requires only the partial charge distribution of a water molecule and three measurable bulk properties, namely the structure factor and the Fourier components of the longitudinal and transverse dielectric susceptibilities.

Solvation free-energy pressure corrections in the three dimensional reference interaction site model.

Solvation free energies are efficiently predicted by molecular density functional theory if one corrects the overpressure introduced by the usual homogeneous reference fluid approximation. Sergiievskyi et al. [J. Phys. Chem. Lett. 5, 1935-1942 (2014)] recently derived the rigorous compensation of this excess of pressure (referred as "pressure correction" or PC) and proposed an empirical "ideal gas" supplementary correction (referred as "advanced pressure correction" or PC+) that further enhances the calculated solvation free energies. In a recent paper [M. Misin, M. V. Fedorov, and D. S. Palmer, J. Chem. Phys. 142, 091105 (2015)], those corrections were applied to solvation free energy calculations using the three-dimensional reference interaction site model (3D-RISM). As for classical DFT, PC and PC+ improve greatly the predictions of 3D-RISM, but PC+ is described as decreasing the accuracy. In this article, we derive rigorously the expression of the pressure in 3D-RISM as well as the associated PC and PC+. This provides a consistent way to correct the solvation free-energies calculated by 3D-RISM method.

Unexpected coupling between flow and adsorption in porous media.

We study the interplay between transport and adsorption in porous systems under a fluid flow, based on a lattice Boltzmann scheme extended to account for adsorption. We performed simulations on well-controlled geometries with slit and grooved pores, investigating the influence of adsorption and flow on dispersion coefficient and adsorbed density. In particular, we present a counterintuitive effect where fluid flow induces heterogeneity in the adsorbate, displacing the adsorption equilibrium towards downstream adsorption sites in grooves. We also present an improvement of the adsorption-extended lattice Boltzmann scheme by introducing the possibility for saturating Langmuir-like adsorption, while earlier work focused on linear adsorption phenomena. We then highlight the impact of this change in situations of high concentration of adsorbate.

Molecular density functional theory for water with liquid-gas coexistence and correct pressure.

The solvation of hydrophobic solutes in water is special because liquid and gas are almost at coexistence. In the common hypernetted chain approximation to integral equations, or equivalently in the homogenous reference fluid of molecular density functional theory, coexistence is not taken into account. Hydration structures and energies of nanometer-scale hydrophobic solutes are thus incorrect. In this article, we propose a bridge functional that corrects this thermodynamic inconsistency by introducing a metastable gas phase for the homogeneous solvent. We show how this can be done by a third order expansion of the functional around the bulk liquid density that imposes the right pressure and the correct second order derivatives. Although this theory is not limited to water, we apply it to study hydrophobic solvation in water at room temperature and pressure and compare the results to all-atom simulations. The solvation free energy of small molecular solutes like n-alkanes and hard sphere solutes whose radii range from angstroms to nanometers is now in quantitative agreement with reference all atom simulations. The macroscopic liquid-gas surface tension predicted by the theory is comparable to experiments. This theory gives an alternative to the empirical hard sphere bridge correction used so far by several authors.

Fast Computation of Solvation Free Energies with Molecular Density Functional Theory: Thermodynamic-Ensemble Partial Molar Volume Corrections.

Molecular density functional theory (MDFT) offers an efficient implicit-solvent method to estimate molecule solvation free-energies, whereas conserving a fully molecular representation of the solvent. Even within a second-order approximation for the free-energy functional, the so-called homogeneous reference fluid approximation, we show that the hydration free-energies computed for a data set of 500 organic compounds are of similar quality as those obtained from molecular dynamics free-energy perturbation simulations, with a computer cost reduced by 2-3 orders of magnitude. This requires to introduce the proper partial volume correction to transform the results from the grand canonical to the isobaric-isotherm ensemble that is pertinent to experiments. We show that this correction can be extended to 3D-RISM calculations, giving a sound theoretical justification to empirical partial molar volume corrections that have been proposed recently.

Molecular density functional theory of water describing hydrophobicity at short and long length scales.

We present an extension of our recently introduced molecular density functional theory of water [G. Jeanmairet et al., J. Phys. Chem. Lett. 4, 619 (2013)] to the solvation of hydrophobic solutes of various sizes, going from angstroms to nanometers. The theory is based on the quadratic expansion of the excess free energy in terms of two classical density fields: the particle density and the multipolar polarization density. Its implementation requires as input a molecular model of water and three measurable bulk properties, namely, the structure factor and the k-dependent longitudinal and transverse dielectric susceptibilities. The fine three-dimensional water structure around small hydrophobic molecules is found to be well reproduced. In contrast, the computed solvation free-energies appear overestimated and do not exhibit the correct qualitative behavior when the hydrophobic solute is grown in size. These shortcomings are corrected, in the spirit of the Lum-Chandler-Weeks theory, by complementing the functional with a truncated hard-sphere functional acting beyond quadratic order in density, and making the resulting functional compatible with the Van-der-Waals theory of liquid-vapor coexistence at long range. Compared to available molecular simulations, the approach yields reasonable solvation structure and free energy of hard or soft spheres of increasing size, with a correct qualitative transition from a volume-driven to a surface-driven regime at the nanometer scale.

Accounting for adsorption and desorption in lattice Boltzmann simulations.

We report a Lattice-Boltzmann scheme that accounts for adsorption and desorption in the calculation of mesoscale dynamical properties of tracers in media of arbitrary complexity. Lattice Boltzmann simulations made it possible to solve numerically the coupled Navier-Stokes equations of fluid dynamics and Nernst-Planck equations of electrokinetics in complex, heterogeneous media. With the moment propagation scheme, it became possible to extract the effective diffusion and dispersion coefficients of tracers, or solutes, of any charge, e.g., in porous media. Nevertheless, the dynamical properties of tracers depend on the tracer-surface affinity, which is not purely electrostatic and also includes a species-specific contribution. In order to capture this important feature, we introduce specific adsorption and desorption processes in a lattice Boltzmann scheme through a modified moment propagation algorithm, in which tracers may adsorb and desorb from surfaces through kinetic reaction rates. The method is validated on exact results for pure diffusion and diffusion-advection in Poiseuille flows in a simple geometry. We finally illustrate the importance of taking such processes into account in the time-dependent diffusion coefficient in a more complex porous medium.

Structure and dynamics in yttrium-based molten rare earth alkali fluorides.

The transport properties of molten LiF-YF3 mixtures have been studied by pulsed field gradient nuclear magnetic resonance spectroscopy, potentiometric experiments, and molecular dynamics simulations. The calculated diffusion coefficients and electric conductivities compare very well with the measurements across a wide composition range. We then extract static (radial distribution functions, coordination numbers distributions) and dynamic (cage correlation functions) quantities from the simulations. Then, we discuss the interplay between the microscopic structure of the molten salts and their dynamic properties. It is often considered that variations in the diffusion coefficient of the anions are mainly driven by the evolution of its coordination with the metallic ion (Y(3+) here). We compare this system with fluorozirconate melts and demonstrate that the coordination number is a poor indicator of the evolution of the diffusion coefficient. Instead, we propose to use the ionic bonds lifetime. We show that the weak Y-F ionic bonds in LiF-YF3 do not induce the expected tendency of the fluoride diffusion coefficient to converge toward one of the yttrium cation when the content in YF3 increases. Implications on the validity of the Nernst-Einstein relation for estimating the electrical conductivity are discussed.