ADD Force Field for Sugars and Polyols: Predicting the Additivity of Protein–Osmolyte Interaction

The protein–osmolyte interaction has been shown experimentally to follow an additive construct, where the individual osmolyte–backbone and osmolyte–side-chain interactions contribute to the overall conformational stability of proteins. Here, we computationally reconstruct this additive relation using molecular dynamics simulations, focusing on sugars and polyols, including sucrose and sorbitol, as model osmolytes. A new set of parameters (ADD) is developed for this purpose, using the individual Kirkwood–Buff integrals for sugar–backbone and sugar–side-chain interactions as target experimental data. We show that the ADD parameters can reproduce the additivity of protein–sugar interactions and correctly predict sucrose and sorbitol self-association and their interaction with water. The accurate description of the separate osmolyte–backbone and osmolyte–side-chain contributions also automatically translates into a good prediction of preferential exclusion from the surface of ribonuclease A and α-chymotrypsinogen A. The description of sugar polarity is improved compared to previous force fields, resulting in closer agreement with the experimental data and better compatibility with charged groups, such as the guanidinium moiety. The ADD parameters are developed in combination with the CHARMM36m force field for proteins, but good compatibility is also observed with the AMBER 99SB-ILDN and the OPLS-AA force fields. Overall, exploiting the additivity of protein–osmolyte interactions is a promising approach for the development of new force fields.


Partial Charges of Simulated Carbohydrates
In the KBP 1 force field the partial charges of alcohol O and H are -0.50 and 0.18, respectively.
The magnitude of these charges is increased in the ADD parameterization to -0.65 and 0.33, respectively. The non-alcohol atoms partial charges for the KBP and ADD force fields are the same, and are shown in Figure S1 for the two molecules (sucrose and sorbitol) considered in this work. : Partial charges of sucrose and sorbitol carbon (red) and non-alcohol oxygen (blue) atoms in the KBP and ADD force fields. The partial charge for all alkyl hydrogens is 0.09.

Sidechain Contributions: Comparison between Zwitterionic and Capped Amino Acids
Following the approach described by Auton et al., 2,3 it is assumed that additivity exists also within the single amino acid. The sidechain contribution γ sc can therefore be calculated by subtracting the KB integral γ GLY for glycine (where the sidechain is just a hydrogen atom) S2 to the KB integral of the amino acid i being considered γ i , To verify that the sidechain contribution would not vary depending on the terminal capping conditions, both capped (acetylated and amidated) and zwitterionic amino acids were considered (for both sucrose and sorbitol, sim. 1 and 2 in Table 1 of the main text).
The resulting γ sc values are shown in Figure S2a-c, for the KBP and ADD force fields.
It was observed that the trend was essentially the same for both capped and zwitterionic amino acids. A change in sign was noticed only for the case of serine and the KBP force field, but it should be considered that the γ sc value in this case is close to zero for both the zwitterionic and the capped form, and the absolute difference between the two values is not significant. The simulation results, therefore, seem to confirm the existence of additivity within the individual amino acid (i.e., amino acid KB integral = backbone contribution + side chain contribution). This also means that, in our specific case, both zwitterionic and capped amino acids may be considered to compute the side chain contribution, without dramatically affecting the final results. In the main text, attention was focused on zwitterionic residues, in line with what was done experimentally. 4 The KBP Parameters Lead to Demixing of Sucrose-Guanidinium

Chloride Mixtures
Guanidinium chloride (GdmCl) is a strong denaturant, commonly used in studies of protein folding. For instance, the m value of protecting osmolytes, such as sucrose, is often extracted from its ability to counteract chemical denaturation of proteins induced by GdmCl. The guanidinium group is also encountered in the side chain of arginine, and is responsible for the polar behavior of this amino acid.

S4
Simulations of 1 M sucrose in presence of 4 M GdmCl were performed. Sucrose was described with either the KBP 1 or ADD force field, while a modified version of the Smith force field, 5 derived by Wernersson et al., 6 was used for GdmCl. This GdmCl force field was originally developed using the geometric mean rule for the van der Waals cross-interactions.
We performed the simulations using both the Lorentz-Berthelot (LB) rule (which is the default for CHARMM36) and the geometric mean (G) rule. In the case of the LB combination rule, Lennard-Jones parameters of a cross-interaction are defined as the arithmetic (for σ) or geometric (for ε) mean of the individual atomic values. The geometric combination rule instead prescribes the use of a geometric mean for both σ and ε.
A cubic simulation box with 6 nm side length, containing 130 sucrose molecules, 520 GdmCl ions and 2843 water molecules was built. Water was described using the CHARMM TIP3P water model. 7 The simulations were run for 60 ns at 1 bar and 300 K, and the last 40 ns were used for the analysis of Kirkwood-Buff integrals (KBIs). Gdm + and Cl − were treated as indistinguishable ions during the calculations. All the other simulation details were the same described in the Materials and Methods section of the main text.
The results obtained for these simulations are shown in Table S1, where the following notation was used: i = ions, w = water, s = sucrose. Table S1: Comparison between the ion-ion (G ii ), ion-sucrose (G is ), ion-water (G iw ), sucrose-sucrose (G ss ) and sucrose-water (G sw ) KBIs as obtained experimentally and as predicted by the ADD or KBP force fields, with both the geometric (G) and Lorentz-Berthelot (LB) combination rules.

M GdmCl + 1 M Sucrose
From Table S1 it is clear that both KBP and ADD sucrose are excluded from GdmCl S5 (negative G is ). This agrees with the fact that both force fields predict exclusion of sucrose from charged amino acids (see Figure 2 in the main text). However, in presence of GdmCl, KBP sucrose tends to self-interact (positive G ss ), and the very unfavorable sucrose-ion interaction promotes the ion-ion interactions (positive G ii ). This combination of KBIs may lead to demixing of the solution, and such a phenomen was observed, for instance, during the KBP-G simulation ( Figure S3). This demixing may lead to artefact during simulations, and suggests incompatibility between the KBP and GdmCl force fields. The value of G is is less negative when ADD sucrose is used. This is also in accordance with the lower exclusion of sucrose from the side chain of arginine that was observed using the ADD parameters instead of the KBPs (see Figure 2 in the main text). This translates into less positive (ADD-G) or even negative (ADD-LB) values of G ii . Moreover, the sucrose selfinteraction (G ss ) is always unfavorable when using the ADD force field. The negative values of G ii and G ss for the ADD-LB combination suggest that demixing should be avoided in these conditions. In line with this, no demixing was observed during the ADD-LB simulation.
Overall, the use of the geometric rule instead of the Lorentz-Berthelot rule makes the ion-ion and sucrose-sucrose interactions more favorable, penalizing the sucrose-ion cross-S6 interactions.

ADD and KBP Behavior in the Case of Different Combination Rules
The CHARMM force field uses the Lorentz-Berthelot combination rule for the van der Waals cross-interactions. Simulations 4 in Table 1 Table S2. Table S2: Comparison between the sugar-sugar (G 33 ), and sugar-water (G 13 ) KBIs as obtained experimentally, 8,9 or as predicted by the ADD and KBP force fields with the geometric (G) and Lorentz-Berthelot (LB) rules.

M Sucrose
KBIs KBP-G KBP-LB ADD-G ADD-LB Exp.
where k B is the Boltzmann constant, T is the absolute temperature (300 K in our case), ζ is a constant of 2.837297, η is the viscosity and L is the length of the cubic simulation box.
In particular, η was calculated from the Einstein formula, where η CHARMM TIP3P is the viscosity of CHARMM TIP3P water at 300 K, and φ is the volume fraction of the solute within the box.
The value of η CHARMM TIP3P was here determined from a preliminary simulation. For this purpose, a cubic box, with 8 nm side length, was filled in with CHARMM TIP3P water molecules, energy minimzed with the steepest descent algorithm, and equilibrated for 1 ns S8 at 300 K and 1 bar using Berendsen temperature (1 ps relaxation time) and pressure (1 ps relaxation time) coupling. 13 The system was subsequently simulated for 500 ps at 300 K and 1 bar, controlling temperature and pressure with the Nosé-Hoover thermostat 14 The preferential interaction coefficient Γ(r) (Eq. 12 in the main text) was computed, and is shown in Figure S5 as function of the distance from the protein surface. Considering that the measurement of preferential solvation is characterized by some uncertainty, the results we obtained for the different protein force fields are in the range of the deviation which is generally expected for this type of analysis. This suggests that the ADD parameters behave similarly when CHARMM, AMBER or OPLS are used, showing their compatibility with these widely used force fields. Figure S5: Running value of the preferential interaction coefficient Γ(r), computed for Tr-pzip1 in presence of ADD sucrose, at 1 M concentration. The CHARMM36m, AMBER 99SB-ILDN and OPLS-AA force fields were used for the peptide.