Parameter Validation in a Size Independent Manner

Methyl sulfate, which has an analogous functional group to the head group of SDS, serves as a model compound for SDS, and using truncated head groups as a model compound for parameter development has been reported previously.250 To date, there has been no explicit effort to parameterize sulfate groups against experimental osmotic pressure or KBI. However, in the CHARMM36 force field, the ionic oxygens on sulfate groups share the same atom type as the ionic oxygens on phosphate groups, for which Pastor, Roux and co-workers have recently implemented NBFIX parameters for interactions between the phosphate ionic oxygens and Na+

ions.249 Thus, we used these NBFIX parameters for sodium methyl sulfate, and compared our computed osmotic pressure to experimental data.251

Figure 6.1.3.1: Concentration dependent osmotic pressure of sodium methyl sulfate using (a) 1st_-

generation and (b) adapted 2nd-generation ion parameters. All parameters with the exception of GROMOS45A3 demonstrated reasonable agreement with experiments. (c) Concentration- dependent osmotic pressure of potassium methyl sulfate.

As shown in Figure 6.1.3.1a-b, the default parameters from CHARMM36 are capable of reproducing experimental osmotic pressure reasonably well up to ~2M. This perhaps explains

why the CHARMM36 SDS micelle simulations by Tang et. al. yielded reasonable agreement with experimental observation.233 _{With the inclusion of the NBFIX parameters, it improved the}

agreement up to the simulated concentration of ~4M, reinforcing our earlier observations in NaCl simulations that NBFIX corrections are necessary to ensure accurate reproduction of osmotic pressure at higher concentration. For the GROMOS force field series, it was previously demonstrated that micelle structure was most significantly influenced by intermolecular parameters (van der Waals and partial charge parameters).233 _{Therefore, for this study we created}

a modified GROMOS53A6 parameter set that uses the intermolecular parameters from GROMOS53A6 but retains the intramolecular parameters of GROMOS45A3. The results, as shown in Figure 6.1.3.1a, indicate that GROMOS45A3 significantly underpredicts the osmotic pressure of sodium methyl sulfate at concentrations above ~1M. In contrast, the osmotic pressure calculated from GROMOS53A6 is in much better agreement with experimental values. To determine if the existing SDS parameters in the GROMOS force field series can be improved, we combined the methyl sulfate parameters for both GROMOS45A3 and GROMOS53A6 with the ion parameters of the GROMOSKBFF force field, which we denote as GROMOS45A3KBFF and GROMOS53A6KBFF respectively. As shown in Figure 6.1.3.1b, the inclusion of KBFF modifications without any further adjustments significantly improved the agreement with experimental osmotic pressure, to the extent that our results suggest that a KBFF correction to the “inaccurate” GROMOS45A3 force field should yield similar performance to the force fields that produced the correct SDS morphology.

In order to attain a better understanding of the underlying reasons for the ability (or inability) of the various force fields to reproduce experimental osmotic pressure, we analyzed various RDFs that describe the solvent structure around sodium methyl sulfate (MESU). In the

Na+-MESU(O) RDF, a strong first peak was observed in GROMOS45A3, which is indicative of excessive ion pairing, and this property is conspicuously absent in all other force fields tested. This observation correlates with the artifacts observed by Tang et. al., where only the GROMOS45A3 simulations formed crystalline lattice patches of SDS head groups and Na+ ions.233 When we examined the Na+-SPC/E and MESU(O)-SPC/E RDFs, we observed that the strength of the hydration shell is unusually low for GROMOS45A3, and the 2nd-gen ion parameters had the strongest hydration shell behavior. This trend is similar to the analysis reported by Tang et. al. who tested various combinations of ion and water models and concluded that the models with a stronger first solvation shell would produce correct SDS micelle morphology.233 However, unlike the prior work where the choice of ion and water models was systematically explored to find the best combination, our approach suggests that a model which produces good agreement with experimental osmotic pressure is likely to produce accurate SDS micelle structures, thus providing a physical principle and proper justification for the development and selection of parameters for simulating charged surfactant systems.

While we have demonstrated that 2nd-gen ion parameters are capable of reproducing the experimental properties of sodium methyl sulfate, it is also desirable to have a model that can accurately distinguish interactions between different cations. One example is the Hofmeister series, which is a classification of an ion’s ability to affect the solubility of proteins, presumably through their interactions with the side chain functional groups of the protein. Recent developments in KBFF-based force field reported by van der Vegt and co-workers has demonstrated that 2nd-gen ion parameters are able reproduce the Hofmeister series in the context of cation specific binding with protein surface charges.246 _{In the context of our work, we}

inverse behavior compared to sodium methyl sulfate, where potassium methyl sulfate has a higher tendency to form ion-pairs than sodium methyl sulfate, and consequently has a lower osmotic pressure than the ideal value at higher concentrations.251 This is reflected by the fact that the experimental osmotic pressure of potassium methyl sulfate is lower than its ideal value at higher concentration, whereas that of sodium methyl sulfate is higher than its ideal osmotic pressure. Figure 6.1.3.1c illustrates the ability of various GROMOS force fields to reproduce the experimental osmotic pressure of potassium methyl sulfate. As before, the inclusion of the KBFF corrections improve the results, and reasonably good agreement with experimental osmotic pressure is achieved up to a concentration of ~3M. Our results on methyl sulfate suggest that the use of 2nd-gen ion parameters is not only accurate enough to model SDS surfactants in the presence of counter ions, it may also be sufficiently accurate to distinguish interactions based on the identity of the interacting monovalent ion.

Figure 6.1.3.2: Representative snapshots of a SDS micelle with an aggregation number of 100 for (a) CHARMM36, (b) CHARMM36 with NBFIX, (c) GROMOS45A3, (d) GROMOS45A3KBFF, (e) GROMOS53A6 and (f) GROMOS53A6KBFF force field. With KBFF corrections applied to GROMOS45A3, the anomalous crystalline lattice patch formation

Figure 6.1.3.3: RDF of (a) Na+ to SDS(O) and (b) Na+ to Cl- indicates that 1st gen ion models have a much higher propensity to form ion pairs than 2nd-gen ion models. RDF of (c) Na+ to SPC/E, (d) SDS(O) to SPC/E and (e) Cl- to SPC/E indicates a more subtle change in the solvation patterns

Having demonstrated that most of the force fields we tested, with the exception of GROMOS45A3, are able to reproduce the experimental osmotic pressure of sodium methyl sulfate reasonably well up to moderate concentrations of ~2M, we now focus our analysis on SDS micelles to determine the transferability of results between the model compound and the actual SDS surfactant. We simulated a preassembled SDS micelle with an aggregation number of

100 in 0.8 NaCl, which are conditions where Tang et. al. first observed artifacts.233 As illustrated in Figure 6.1.3.2, crystalline patches were only observed in GROMOS45A3, and the corrected GROMOS45A3KBFF produced no discernable patches. Further RDF analysis demonstrates many similarities between the solvent structure of sodium methyl sulfate and SDS micelles. Specifically, the strong peak in the Na+-SDS(O) RDF (Figure 6.1.3.3a) was again observed only for the GROMOS45A3 force field, which corresponds to previous observations in the Na+- MESU(O) RDF. Similarly, there is a minor reduction in the first solvation shell across all ionic species (Figure 6.1.3.3c-e), although the effect is not as pronounced as in sodium methyl sulfate. Interestingly, the Na+-Cl- RDF peak (Figure 6.1.3.3b) for both GROMOS45A3 and GROMOS53A6 is high, indicative of excessive ion pairing between Na+ and Cl-, but this property had no discernable effect on the SDS micelle. We suggest that this may be because the SDS micelles were simulated with a low concentration of 0.8M NaCl.

The simulation of SDS in a salt environment also provides an opportunity to examine the 3-way interactions between SDS, Na+ and Cl-, in terms of comparing the different implementations of 2nd-gen ion models. In the KBFF algorithm, interactions between cations and water are scaled, and only the Na+-SPC/E scaling term was applied in our SDS simulations.244,245 It is interesting that with only the Na+_{-SPC/E scaling term, the interaction between Na}+_-SDS(O)

(see Figure 3.2.3.4 for details) was indirectly modified as well, indicating that scaling the Na+ to water interaction has some second order effect on the interactions between Na+ and other anionic species. In contrast, the NBFIX algorithm provides additional interaction terms between specific ion pairs that scales them accordingly,247,249 and in the context of our SDS simulations NBFIX terms for Na+_-Cl- _{and Na}+_{-SDS(O) interactions were applied. In the context of osmotic pressure}

preference for ions to interact with each other (i.e. contact ion pair) as opposed to interacting with solvent (i.e. solvent-mediated ion pair). Modulating such an effect can be achieved by either scaling attractive forces between ions which indirectly modulates the solvation shell around ions (NBFIX) or adjusting the strength of water-cation interactions, which indirectly changes the strength of other ion-ion interactions. In that sense, modifying one interaction should always have a secondary effect on the other ion pair interactions. Based on our analysis, it appears that changes in the water-cation affinity has magnified consequences compared to changes in the ion- ion affinity.

Figure 6.1.3.4: RDF of (a) Na+ to Cl- and (b) Na+ to SDS(O) indicates that NBFIX scaling parameters do not have second order effects on the interactions of other ion pairs.

Lastly, to determine the effect of the force field on larger SDS constructs representative of industrially-relevant concentrations, we simulated SDS micelles with aggregation number of 400 in 0.26M NaCl. Here, we limit our analysis to GROMOS45A3 which has been previously reported to produce an incorrect morphology,233 and GROMOS45A3KBFF, which according to the Na+-SDS(O) and Na+-Cl- RDF (see Figure 6.1.3.3a, b) obtained from the 100 SDS aggregate simulation, has an equivalent behavior to the other force fields that has produced reasonable geometries.233 As shown in Figure 6.1.3.5, regardless of the initial configuration, the GROMOS45A3 simulation formed a bicelle within 10 ns, with significant Na+ condensation

Figure 6.1.3.5: (a) Time evolution of the geometry of a SDS micelle of aggregation number 400 starting from (a) cylinder and (b) bilayer configuration. The GROMOS45A3 simulations produced incorrect bicelle structures within 10 ns, and the GROMOS45A3KBFF simulations produced correct rod-like micelles.

around the SDS head group. This structure is inconsistent with experimental data that suggests that rod-like micelles are the dominant structure in the regime between the first and second

micelle or a toroidal micelle (a rod-like micelle looped back onto itself) within 10 ns. Thus, our results indicate that using osmotic pressure data of model compounds provide a robust method for parameter development, as it is transferrable to the simulation results of the corresponding surfactant at high aggregation number.