In silico prediction of drug solubility: 4. Will simple potentials suffice?

In view of the extreme importance of reliable computational prediction of aqueous drug solubility, we have established a Monte Carlo simulation procedure which appears, in principle, to yield reliable solubilities even for complex drug molecules. A theory based on judicious application of linear response and mean field approximations has been found to reproduce the computationally demanding free energy determinations by simulation while at the same time offering mechanistic insight. The focus here is on the suitability of the model of both drug and solvent, i.e., the force fields. The optimized potentials for liquid simulations all atom (OPLS-AA) force field, either intact or combined with partial charges determined either by semiempirical AM1/CM1A calculations or taken from the condensed-phase optimized molecular potentials for atomistic simulation studies (COMPASS) force field has been used. The results illustrate the crucial role of the force field in determining drug solubilities. The errors in interaction energies obtained by the simple force fields tested here are still found to be too large for our purpose but if a component of this error is systematic and readily removed by empirical adjustment the results are significantly improved. In fact, consistent use of the OPLS-AA Lennard-Jones force field parameters with partial charges from the COMPASS force field will in this way produce good predictions of amorphous drug solubility within 1 day on a standard desktop PC. This is shown here by the results of extensive new simulations for a total of 47 drug molecules which were also improved by increasing the water box in the hydration simulations from 500 to 2000 water molecules.

In silico prediction of drug solubility. 3. Free energy of solvation in pure amorphous matter.

The solubility of drugs in water is investigated in a series of papers. In this work, we address the process of bringing a drug molecule from the vapor into a pure drug amorphous phase. This step enables us to actually calculate the solubility of amorphous drugs in water. In our general approach, we, on one hand, perform rigorous free energy simulations using a combination of the free energy perturbation and thermodynamic integration methods. On the other hand, we develop an approximate theory containing parameters that are easily accessible from conventional Monte Carlo simulations, thereby reducing the computation time significantly. In the theory for solvation, we assume that DeltaG* = DeltaGcav + ELJ + EC/2, where the free energy of cavity formation, DeltaGcav, in pure drug systems is obtained using a theory for hard-oblate spheroids, and ELJ and EC are the Lennard-Jones and Coulomb interaction energies between the chosen molecule and the others in the fluid. The theoretical predictions for the free energy of solvation in pure amorphous matter are in good agreement with free energy simulation data for 46 different drug molecules. These results together with our previous studies support our theoretical approach. By using our previous data for the free energy of hydration, we compute the total free energy change of bringing a molecule from the amorphous phase into water. We obtain good agreement between the theory and simulations. It should be noted that to obtain accurate results for the total process, high precision data are needed for the individual subprocesses. Finally, for eight different substances, we compare the experimental amorphous and crystalline solubility in water with the results obtained by the proposed theory with reasonable success.

In silico prediction of drug solubility: 1. Free energy of hydration.

As a first step in the computational prediction of drug solubility the free energy of hydration, DeltaG*(vw) in TIP4P water has been computed for a data set of 48 drug molecules using the free energy of perturbation method and the optimized potential for liquid simulations all-atom force field. The simulations were performed in two steps, where first the Coulomb and then the Lennard-Jones interactions between the solute and the water molecules were scaled down from full to zero strength to provide physical understanding and simpler predictive models. The results have been interpreted using a theory assuming DeltaG*(vw) = A(MS)gamma + E(LJ) + E(C)/2 where A(MS) is the molecular surface area, gamma is the water-vapor surface tension, and E(LJ) and E(C) are the solute-water Lennard-Jones and Coulomb interaction energies, respectively. It was found that by a proper definition of the molecular surface area our results as well as several results from the literature were found to be in quantitative agreement using the macroscopic surface tension of TIP4P water. This is in contrast to the surface tension for water around a spherical cavity that previously has been shown to be dependent on the size of the cavity up to a radius of approximately 1 nm. The step of scaling down the electrostatic interaction can be represented by linear response theory.

In silico prediction of drug solubility: 2. Free energy of solvation in pure melts.

The solubility of drugs in water is investigated in a series of papers and in the current work. The free energy of solvation, DeltaG*(vl), of a drug molecule in its pure drug melt at 673.15 K (400 degrees C) has been obtained for 46 drug molecules using the free energy perturbation method. The simulations were performed in two steps where first the Coulomb and then the Lennard-Jones interactions were scaled down from full to no interaction. The results have been interpreted using a theory assuming that DeltaG*(vl) = DeltaG(cav) + E(LJ) + E(C)/2 where the free energy of cavity formation, DeltaG(cav), in these pure drug systems was obtained using hard body theories, and E(LJ) and E(C) are the Lennard-Jones and Coulomb interaction energies, respectively, of one molecule with the other ones. Since the main parameter in hard body theories is the volume fraction, an equation of state approach was used to estimate the molecular volume. Promising results were obtained using a theory for hard oblates, in which the oblate axial ratio was calculated from the molecular surface area and volume obtained from simulations. The Coulomb term, E(C)/2, is half of the Coulomb energy in accord with linear response, which showed good agreement with our simulation results. In comparison with our previous results on free energy of hydration, the Coulomb interactions in pure drug systems are weaker, and the van der Waals interactions play a more important role.

Toward efficient chemical potential calculations by expanded ensemble simulations; to make the free energy pathway fairly level.

A scheme is suggested of how to construct good bias potentials ("balancing factors") to be used in expanded ensemble (EE) calculations of chemical potentials of solutions. A combination of two strategies are used: (i) to use a pathway for particle insertions that avoids large variations in free energy and (ii) to use calculated free energy derivatives to construct a bias potential that makes the pathway fairly level. Only a few very short simulations are needed to accomplish the latter, and then, a full EE simulation is done to obtain the chemical potential. By practical calculations of the chemical potential of benzene, cyclohexane, and benzylamine in water, it is shown that this method is at least equally efficient to the recent adaptive EE (AEE) method by Aberg et al. (J. Chem. Phys. 2004, 120, 3370). Furthermore, the new method provides an alternative strategy that complements existing EE methods.