Solubility of paracetamol in ethanol by molecular dynamics using the extended Einstein crystal method and experiments

A streamlined molecular-dynamics workflow for computing solubilities of molecular and ionic crystals

Computing the solubility of crystals in a solvent using atomistic simulations is notoriously challenging due to the complexities and convergence issues associated with free-energy methods, as well as the slow equilibration in direct-coexistence simulations. This paper introduces a molecular-dynamics workflow that simplifies and robustly computes the solubility of molecular or ionic crystals. This method is considerably more straightforward than the state-of-the-art, as we have streamlined and optimised each step of the process. Specifically, we calculate the chemical potential of the crystal using the gas-phase molecule as a reference state, and employ the S0 method to determine the concentration dependence of the chemical potential of the solute. We use this workflow to predict the solubilities of sodium chloride in water, urea polymorphs in water, and paracetamol polymorphs in both water and ethanol. Our findings indicate that the predicted solubility is sensitive to the chosen potential energy surface. Furthermore, we note that the harmonic approximation often fails for both molecular crystals and gas molecules at or above room temperature, and that the assumption of an ideal solution becomes less valid for highly soluble substances.

Comparative Drug Solubility Studies Using Shake-Flask Versus a Laser-Based Robotic Method

Drug solubility is of central importance to the pharmaceutical sciences, but reported values often show discrepancies. Various factors have been discussed in the literature to account for such differences, but the influence of manual testing in comparison to a robotic system has not been studied adequately before. In this study, four expert researchers were asked to measure the solubility of four drugs with various solubility behaviors (i.e., paracetamol, mesalazine, lamotrigine, and ketoconazole) in the same laboratory with the same instruments, method, and material sources and repeated their measurements after a time interval. In addition, the same solubility data were determined using an automated laser-based setup. The results suggest that manual testing leads to a handling influence on measured solubility values, and the results were discussed in more detail as compared to the automated laser-based system. Within the framework of unavoidable uncertainties of solubility testing, it is a possibility to combine minimal experimental testing that is preferably automated with mathematical modeling. That is a practical suggestion to support future pharmaceutical development in a more efficient way.

A unified approach for calculating free energies of liquid and defective crystals based on thermodynamic integration

The free energy calculation is fundamentally important in the research of physics, chemistry and materials. Thermodynamic integration is the most common way to estimate free energies. In the research, we proposed a unified approach using atomic simulations to calculate the free energies of liquid and defective crystals. The new approach is based on thermodynamic integration (TI) using two alchemical pathways. Softcore potentials are developed for three-body interatomic potentials to realize the alchemical pathways. Employing the new approach, the free energy of the liquid can be calculated without requiring another reference system. The free energy of the defective crystal can be calculated directly at high temperature. It avoids the singularity at the integration endpoint caused by the defect diffusion which is a serious problem in the widely used Einstein crystal method. In addition, the new approach can capture the whole free energy of the defective crystal including the contribution of anharmonic and configurational entropy which are particularly important at high temperature. The new method is simple yet effective and can be extended to different materials and more complex liquid and defective crystal systems.

Predicting the Solubility of Nonelectrolyte Solids Using a Combination of Molecular Simulation with the Solubility Parameter Method MOSCED: Application to the Wastewater Contaminants Monuron, Diuron, Atrazine and Atenolol

Methods to predict the equilibrium solubility of nonelectrolyte solids are indispensable for early-stage process development, design, and feasibility studies. Conventional analytic methods typically require reference data to regress parameters, which may not be available or limited for novel systems. Molecular simulation is a promising alternative, but is computationally intensive. Here, we demonstrate the ability to use a small number of molecular simulation free energy calculations to generate reference data to regress model parameters for the analytical MOSCED (modified separation of cohesive energy density) model. The result is an efficient analytical method to predict the equilibrium solubility of nonelectrolyte solids. The method is demonstrated for the wastewater contaminants monuron, diuron, atrazine and atenolol. Predictions for monuron, diuron and atrazine are in reasonable agreement with MOSCED parameters regressed using experimental solubility data. Predictions for atenolol are inferior, suggesting a potential limitation in the adopted molecular models, or the solvents selected to generate the necessary reference data.

Calculation Methods of Solution Chemical Potential and Application in Emulsion Microencapsulation

Several new biased sampling methods were summarized for solution chemical potential calculation methods in the field of emulsion microencapsulation. The principles, features, and calculation efficiencies of various biased Widom insertion sampling methods were introduced, including volume detection bias, simulation ensemble bias, and particle insertion bias. The proper matches between various types of solution in emulsion and biased Widom methods were suggested, following detailed analyses on the biased insertion techniques. The volume detection bias methods effectively improved the accuracy of the data and the calculation efficiency by inserting detection particles and were suggested to be used for the calculation of solvent chemical potential for the homogeneous aqueous phase of the emulsion. The chemical potential of water, argon, and fluorobenzene (a typical solvent of the oil phase in double emulsion) was calculated by a new, optimized volume detection bias proposed by this work. The recently developed Well-Tempered(WT)-Metadynamics method skillfully constructed low-density regions for particle insertion and dynamically adjusted the system configuration according to the potential energy around the detection point, and hence, could be used for the oil-polymer mixtures of microencapsulation emulsion. For the macromolecule solutes in the oil or aqueous phase of the emulsion, the particle insertion bias could be applied to greatly increase the success rate of Widom insertions. Readers were expected to choose appropriate biased Widom methods to carry out their calculations on chemical potential, fugacity, and solubility of solutions based on the system molecular properties, inspired by this paper.

Free energies of crystals computed using Einstein crystal with fixed center of mass and differing spring constants

Free energies of crystals computed using a center of mass constraint require a finite-size correction, as shown in previous work by Polson et al. [J. Chem. Phys. 112, 5339-5342 (2000)]. Their reference system is an Einstein crystal with equal spring constants. In this paper, we extend the work of Polson et al. [J. Chem. Phys. 112, 5339-5342 (2000)] to the case of differing spring constants. The generalization is convenient for constraining the center of mass in crystals with atoms of differing masses, and it helps to optimize the free energy calculations. To test the theory, we compare the free energies of LiI and NaCl crystals from calculations with differing spring constants to those computed using equal spring constants. Using these center of mass finite size corrections, we compute the true free energies of these crystals for different system sizes to eliminate the intrinsic finite-size effects. These calculations help demonstrate the size of these finite-size corrections relative to other contributions to the absolute free energy of the crystals.

Novel Physics-Based Ensemble Modeling Approach That Utilizes 3D Molecular Conformation and Packing to Access Aqueous Thermodynamic Solubility: A Case Study of Orally Available Bromodomain and Extraterminal Domain Inhibitor Lead Optimization Series

Drug design with patient centricity for ease of administration and pill burden requires robust understanding of the impact of chemical modifications on relevant physicochemical properties early in lead optimization. To this end, we have developed a physics-based ensemble approach to predict aqueous thermodynamic crystalline solubility, with a 2D chemical structure as the input. Predictions for the bromodomain and extraterminal domain (BET) inhibitor series show very close match (0.5 log unit) with measured thermodynamic solubility for cases with low crystal anisotropy and good match (1 log unit) for high anisotropy structures. The importance of thermodynamic solubility is clearly demonstrated by up to a 4 log unit drop in solubility compared to kinetic (amorphous) solubility in some cases and implications thereof, for instance on human dose. We have also demonstrated that incorporating predicted crystal structures in thermodynamic solubility prediction is necessary to differentiate (up to 4 log unit) between solubility of molecules within the series. Finally, our physics-based ensemble approach provides valuable structural insights into the origins of 3-D conformational landscapes, crystal polymorphism, and anisotropy that can be leveraged for both drug design and development.

From adaptive resolution to molecular dynamics of open systems

ABSTRACT

We provide an overview of the Adaptive Resolution Simulation method (AdResS) based on discussing its basic principles and presenting its current numerical and theoretical developments. Examples of applications to systems of interest to soft matter, chemical physics, and condensed matter illustrate the method's advantages and limitations in its practical use and thus settle the challenge for further future numerical and theoretical developments.

Absolute chemical potentials for complex molecules in fluid phases: A centroid reference for predicting phase equilibria

Solid-fluid phase equilibria are difficult to predict in simulations because bound degrees of freedom in the crystal phase must be converted to free translations and rotations in the fluid phase. Here, we avoid the solid-to-fluid transformation step by starting with chemical potentials for two reference systems, one for the fluid phase and one for the solid phase. For the solid, we start from the Einstein crystal and transform to the fully interacting molecular crystal. For the fluid phase, we introduce a new reference system, the "centroid," and then transform to gas phase molecules. We illustrate the new calculations by predicting the sublimation vapor pressure of succinic acid in the temperature range of 300 K-350 K.

Performing solvation free energy calculations in LAMMPS using the decoupling approach

The decoupling approach to solvation free energy calculations requires scaling the interactions between the solute and the solution with all intramolecular interactions preserved. This paper reports a new procedure that makes it possible to these calculations in LAMMPS. The procedure is tested against built-in GROMACS capabilities. The model compounds chosen to test our methodology are ethanol and biphenyl. The LAMMPS and GROMACS results obtained are in good agreement with each other. This work should help perform solvation free energy calculations in LAMMPS and/or other molecular dynamics software having no built-in functions to implement the decoupling approach.

Solubility prediction for a soluble organic molecule via chemical potentials from density of states

While the solubility of a substance is a fundamental property of widespread significance, its prediction from first principles (starting from only the knowledge of the molecular structure of the solute and solvent) remains a challenge. Recently, we proposed a robust and efficient method to predict the solubility from the density of states of a solute-solvent system using classical molecular simulation. The efficiency, and indeed the generality, of the method has now been enhanced by extending it to calculate solution chemical potentials (rather than probability distributions as done previously), from which solubility may be accessed. The method has been employed to predict the chemical potential of Form 1 of urea in both water and methanol for a range of concentrations at ambient conditions and for two charge models. The chemical potential calculations were validated by thermodynamic integration with the two sets of values being in excellent agreement. The solubility determined from the chemical potentials for urea in water ranged from 0.46 to 0.50 mol kg^-1, while that for urea in methanol ranged from 0.62 to 0.85 mol kg^-1, over the temperature range 298-328 K. In common with other recent studies of solubility prediction from molecular simulation, the predicted solubilities differ markedly from experimental values, reflecting limitations of current forcefields.

Steering a solute between coexisting solvation states: Revisiting nonequilibrium work relations and the calculation of free energy differences

By analogy with single-molecule pulling experiments, we present a computational framework to obtain free energy differences between complex solvation states. To illustrate our approach, we focus on the calculation of solvation free energies (SFEs). However, the method can be readily extended to cases involving more complex solutes and solvation conditions as well as to the calculation of binding free energies. The main idea is to drag the solute across the simulation box where atomistic and ideal gas representations of the solvent coexist at constant temperature and chemical potential. At finite pulling speeds, the resulting work allows one to extract SFEs via nonequilibrium relations, whereas at infinitely slow pulling speeds, this process becomes equivalent to the thermodynamic integration method. Results for small molecules well agree with literature data and pave the way to systematic studies of arbitrarily large and complex molecules.

On computing the solubility of molecular systems subject to constraints using the extended Einstein crystal method

A method to compute solubilities for molecular systems using atomistic simulations, based on an extension of the Einstein crystal method, has recently been presented [Li et al., J. Chem. Phys. 146, 214110 (2017)]. This methodology is particularly appealing to compute solubilities in cases of practical importance including, but not limited to, solutions where the solute is sparingly soluble and molecules of importance for the pharmaceutical industry, which are often characterized by strong polar interactions and slow relaxation time scales. The mathematical derivation of this methodology hinges on a factorization of the partition function which is not necessarily applicable in the case of a system subject to holonomic molecular constraints. We show here that, although the mathematical procedure to derive it is slightly different, essentially the same mathematical relation for calculating the solubility can be safely applied for computing the solubility of systems subject to constraints, which are the majority of the systems used for practical molecular simulations.