Systematic Parametrization Using Water-Octanol Partition Coefficients

THE JOURNAL OF CHEMICAL PHYSICS 147, 094503 (2017) Dissipative particle dynamics: Systematic parametrization using water-octanol partition coefficients Richard L. Anderson,1,a) David J. Bray,1 Andrea S. Ferrante,2,3 Massimo G. Noro,4 Ian P. Stott,4 and Patrick B. Warren4,b) 1STFC Hartree Centre, Scitech Daresbury, Warrington WA4 4AD, United Kingdom 2Novidec Ltd., 3 Brook Hey, Parkgate, Neston CH64 6TH, United Kingdom 3Ferrante Scientific Ltd., 5 Croft Lane, Bromborough CH62 2BX, United Kingdom 4Unilever R&D Port Sunlight, Quarry Road East, Bebington CH63 3JW, United Kingdom (Received 26 June 2017; accepted 17 August 2017; published online 6 September 2017) We present a systematic, top-down, thermodynamic parametrization scheme for dissipative particle dynamics (DPD) using water-octanol partition coefficients, supplemented by water-octanol phase equilibria and pure liquid phase density data. We demonstrate the feasibility of computing the required partition coefficients in DPD using brute-force simulation, within an adaptive semi-automatic staged optimization scheme. We test the methodology by fitting to experimental partition coefficient data for twenty one small molecules in five classes comprising alcohols and poly-alcohols, amines, ethers and simple aromatics, and alkanes (i.e., hexane). Finally, we illustrate the transferability of a subset of the determined parameters by calculating the critical micelle concentrations and mean aggregation numbers of selected alkyl ethoxylate surfactants, in good agreement with reported experimental values. Published by AIP Publishing. [http://dx.doi.org/10.1063/1.4992111] I. INTRODUCTION II. PARTITION COEFFICIENTS In this work, we describe a systematic, top-down The partition coefficient of an uncharged solute molecule parametrization scheme for dissipative particle dynamics is the ratio of the molar concentrations in a pair of coexisting (DPD) based on matching water-octanol partition coefficients, bulk phases, at equilibrium. The bulk phases themselves are water-octanol phase equilibria, and pure liquid phase density typically made up from a pair of (near) immiscible solvents, data. Apart from water, the DPD “beads” in the model rep- and the corresponding partition coefficient is usually reported resent molecular fragments and as such can be assembled to as a base 10 logarithm, cover a wide range of organic materials such as polymers, sur- [S]A factants, oils, and so on. The resulting DPD parameter set can log PA=B = log10 , (1) be used for an equally wide range of applications, and we give [S]B the example of calculating the critical micelle concentrations where [S]A and [S]B are the molar concentrations of a solute and mean aggregation numbers of seven alkyl ethoxylate sur- molecule in the two phases, A and B. factants. Our approach is extensible in the sense that it is easy By far, the most commonly studied partition coefficient is to broaden the molecular “palette” and flexible in the sense that for the water/octanol system (where octanol means 1-octanol the calculations can be re-run semi-automatically if it is nec- in the present work); hereafter we shall denote this specific essary to make different changes to coarse-graining or include partition coefficient as simply log P. The partition coefficient extra moieties or interactions. The remaining manual aspect is a measure of the propensity of a solute to partition between would be potentially amenable to a machine learning opti- hydrophobic and hydrophilic environments and is widely used mizing approach. Finally, turned around, our approach offers across numerous application areas such as toxicology, pharma- a potential novel way of calculating partition coefficients for ceutical drug delivery (pharmacokinetics), and so on.1,2 For new molecules. example, hydrophobic molecules with 1 . log P . 5 are gen- We organize the paper by first describing the parti- erally considered to be cytotoxic since they are able to cross tion coefficients that we use as the principal parametriza- hydrophobic cell membranes whilst retaining sufficient water tion target. We then explain the coarse-grained (CG) DPD solubility to be active.3 model and parametrization strategy. We finally analyze and Given the diverse range of applications, it is not sur- discuss the results. Technical details of the computational prising that a large amount of experimental log P data approach are given in Appendix A, and Appendix B discusses are available both in the primary literature and in curated compressibility matching in DPD. databases, for a wide variety of solute molecules.2,4,5 More- over, diverse numerical methods with varying degrees of sophistication and accuracy have been developed to calculate a)Electronic mail: [email protected] log P values, to augment the existing experimental data. These b)Electronic mail: [email protected] methods include quantitative structure-property relationships 0021-9606/2017/147(9)/094503/12/$30.00 147, 094503-1 Published by AIP Publishing. 094503-2 Anderson et al. J. Chem. Phys. 147, 094503 (2017) (QSPR),6,7 atom-based methods,8 and quantum chem- III. COARSE GRAINED MODEL DEFINITION istry motivated methods such as COSMOtherm/COSMO- In our approach, the DPD beads represent molecular frag- RS.9–11 ments comprising 1–3 “heavy atoms” (i.e., C, O, and N in this Computer simulations, e.g., molecular dynamics (MD) work), with the exception of water (H O) which is treated or Monte Carlo (MC) methods using atom-based potential 2 super-molecularly. This means that a wide variety of both functions or coarse-grained force-fields such as the MAR- aqueous and non-aqueous systems can be modeled by combin- TINI force field,12 provide an additional route to the prediction 13–29 ing these fragments as a kind of a molecular “Lego” game. It of log P for small- or medium-sized solute molecules. also means that the approach is extensible since the molecular There have also been attempts to use multiscale simula- palette is easily enlarged. tion methods mixing atomistic and coarse-grained poten- 13,30 To establish the basis for the above coarse-graining tials. To our knowledge, all published results to date using scheme, we first follow the work of Groot and Rabone in these methods resort to the thermodynamically equivalent defining a water mapping number, in our case Nm = 2 so definition log P = − log10 e × ∆Gtransfer=RT, where ∆Gtransfer that each water bead corresponds, on average, to two water is the Gibbs free energy to transfer 1 mol of solute from molecules.37 Following well established protocols, we also phase A to phase B, and RT is the product of the gas assert that the density of water in our model (in reduced DPD 3 constant R and the temperature T. The transfer free energy units) corresponds to ρrc = 3, where rc denotes the value of can be formally resolved into the difference between sol- the cutoff length for the DPD soft potential acting between vation free energies for which thermodynamic perturba- pairs of beads.38 We can then use the mapping number tautol- tion and thermodynamic integration methods are typically 3 ogy ρNmvm ≡ 1, where vm ≈ 30 Å is the molecular volume of employed.14–17,19–26,31–34 liquid water, to determine that rc ≈ 5.65 Å. This underpins the It is important to note that a direct application of MC conversion of all lengths and molecular densities in the model. methods such as the Widom insertion is not usually viable for In our model, alkane molecules are constructed from atomistic and coarse grained simulation methods based on hard connected (bonded) beads comprising (i) CH2CH2 groups of core or Lennard-Jones potentials at liquid densities.35,36 Also atoms and (ii) CH3, a terminal methyl group. Similarly alcohol determination of the transfer free energy as the difference in molecules are constructed by bonding together alkane beads solvation free energies may require computing the latter with and a specific bead containing an alcohol functionality, e.g., a high degree of precision and accuracy. This makes these comprising the CH2OH group of atoms. Amine molecules fol- methods very demanding. Finally, computing log P this way is low the same model definition where the amine functionality is blind to compensating errors in computing solvation energies captured in a bead comprising CH2NH2 atoms. Benzene rings in the two solvents [or in an equivalent manner, the ratio of are constructed from a total of three beads, each comprising solubilities in Eq. (1)]. Systematic errors of this kind can be CHCH groups, bonded together in a triangle. We name the cor- controlled to some extent by fitting log P simultaneously to responding DPD beads aCHCH to remind that they are part of a range of molecular architectures, as we do in the present an aromatic ring. Ether beads are designated as being formed study. from CH2OCH2 or CH3OCH2 groups, depending on the loca- In carrying out simulations, one could employ pure sol- tion of the bead (central or terminal). Using two bead types vent boxes (i.e., pure water and pure octanol), but it is known for the ethers is essential for reproducing the correct log P for that the results for “dry” octanol (i.e., pure octanol) may be diglyme, for example. Atom to beaded structures are given in drastically different from “wet” octanol since the solubility of detail in TableI. water in octanol is considerable and wet octanol better repre- Having decided on the level of coarse graining, the next sents the experimental situation.28 More realistically therefore, part of the model definition is to specify the bonded and one should equilibrate the solvent boxes, and to address this non-bonded interactions between beads. For the non-bonded problem, one can turn to Gibbs ensemble methods in which interactions, we take the usual DPD pairwise soft repulsion, MC solvent molecule exchange moves are allowed between 1 2 φ = 2 Aij(1 − r=Rij) for r ≤ Rij and φ = 0 for r > Rij.

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