Supplemental Material: Solute Adsorption at Air-Water Interfaces and Induced. Interface Fluctuations: The Hydrophobic Nature of Ions?

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1 Electronic Supplementary Material (ESI) for Physical Chemistry Chemical Physics. This journal is the Owner Societies Supplemental Material: Solute Adsorption at Air-Water Interfaces and Induced Interface Fluctuations: The Hydrophobic Nature of Ions? Shu-Ching Ou, Di Cui, and Sandeep Patel Department of Chemistry and Biochemistry, University of Delaware, Newark, Delaware 976, USA Corresponding author.

2 I. POTENTIAL OF MEAN FORCE: CONVERGENCE AND UNCERTAINTY Figure S shows the comparison of potentials of mean force between nonpolarizable (with TIPP) and Drude polarizable (with SWM-NDP) force fields. The parameters were retrieved from CHARMM6 all-atom force field for simulations with TIPP ; parameters for simulations using Drude Oscillator Model were from Ref. For the same molecule, deeper minima are found using polarizable force fields; however, the values of G vapor G bulk (hydration free energy) are similar. Potential of Mean Force (kcal/mol) a. ETHA b. PRPA c. BUTA non-pol pol d. IBUT e. PENT f. NEOP - restrained z-position (Å) - FIG. S: Potential of mean force as a function of the z-position of a single alkane along the direction normal to the water surface.

3 The uncertainties in potentials of mean force are determined using the approach of Zhu and Hummer : N var[g(ξ N )] var[k ξ z i ] i= (S) where z i is the mean position of z in the i th window, which can be obtained from block averages. K is the force constant. The corresponding standard deviation σ[g(ξ N )] is then the square root of var[g(ξ N )]. In this case, the alkane in the vapor (z restrained =. Å) is set to be the reference state, therefore the window z restrained = -8. Å is expected to have the largest uncertainty. Figure S shows the PMF along with the uncertainty of each window for single pentane in TIPP. The largest uncertainties for the systems are approximately. kcal/mol. The inset shows the time profile of G vapor. As the collective sampling increases, G vapor converges to the value of -.9 kcal/mol. Potential of Mean Force (kcal/mol) G vapor time (ns) reference state restrained z-position (Å) FIG. S: Potential of mean force for single pentane along the direction normal to the water surface, using TIPP water model. The inset shows the time profile of G vapor.

4 II. SINGLE IODIDE Figure S shows the potential of mean force and the coordination number for single iodide along the direction normal to the water surface, using TIPP-FQ water model. For simulation detail, refer to Reference. From Figure Sa, iodide shows a lower free energy state when it resides at the bulk side. Even when the ion is restrained Å away from GDS, there are still water surrounding the single iodide ion. PMF (kcal/mol) <N coor > bulk side GDS vapor side restrained z (Å) a. b. FIG. S: (a) Potential of mean force for single iodide along the direction normal to the water surface, using TIPP-FQ water model. Inset shows the profile near the PMF minimum. (b) The corresponding average coordination number.

III. FLUCTUATION PROFILES: SINGLE PENTANE Figure S displays the height fluctuations (unnormalized) induced by single n-pentane at simulation windows z = -8., -6., -.,. Å. When z = -8.

5 III. FLUCTUATION PROFILES: SINGLE PENTANE Figure S displays the height fluctuations (unnormalized) induced by single n-pentane at simulation windows z = -8., -6., -.,. Å. When z = -8. Å, the solute is too far from the air-water interface to induce any fluctuation, thus it gives a value that characterize the inherent fluctuation of pure TIPP water (.7 Å ). When z =. Å, i.e., pentane is at the water surface, the fluctuation is suppressed. The geometry of the fluctuation profile δh (x, y) possesses radial symmetry. The convergence of fluctuation is displayed in Figure S. The uncertainty can be estimated via block average ; the decorrelated uncertainty is less than. Å. FIG. S: Fluctuation profiles for single pentane (in TIPP) at simulation windows z = -8., -6., -.,. Å. The unit is Å.

6 6 <δh (x=å,y=å)> Sampling time (ns) FIG. S: Convergence of the characteristic fluctuation δ (x =, y = ) for single pentane at z = -6. Å. 6

7 IV. ESTIMATION OF SURFACE ENTROPY USING SURFACE HEIGHT FUNCTION For a random variable x with continuous density f(x), the entropy can be written as 6 S(f) = ln[f(x)]f(x)dx (S) where x = (x, x,, x N ). The density function of the multivariate normal distribution is given by f(x) = πσ / exp{ (x µ) Σ (x µ)} (S) Σ is the covariance matrix, Σ ij = cov(x i, x j ) = E[(x i µ i )(x j µ j )], where µ i = E(x i ) is the expected value of the i th entry of x. We can therefore rewrite the entropy as S = {N + N ln(π)ln + ln Σ } = {lnen + ln(π) N + ln Σ } = ln{(πe)n Σ } (S) = N ln(πe) + ln Σ where Σ is the determinant of covariance matrix Σ. The surface entropy can therefore be estimated with surface height function δh = h h. The covariance matrix (χ) is then defined as χ ij = δh i δh j. The N ln(πe) term is then constant for different windows with the same resolution of grid points (which, in other words, same N). Consequently, we get the entropy described by the fineness of the resolution of grid points, and can be written as: where k B is the Boltzmann constant. S = constant + k B ln χ (S) In the main text, the resolution we used along x and y-dimensions is. Å. For each snapshot we therefore have surface height values, resulting in a covariance matrix with 6 6 elements. However, from the aspect of estimating surface entropy, the resolution of Å may be too fine and computational resource consuming. In practice, we use a coarser resolution of. Å (in x and y) to construct the covariance matrix ( elements) and estimate the surface entropy. In Figure S6, we present the time profile of calculated surface entropy for single methane (using CHARMM6) at solvent bulk, the window that generates largest fluctuations, and at the interface. For this analysis, the accumulated average of the covariance matrix (χ) is calculated every ps; the estimated entropies converge after 8 ns. The difference of entropies can be calculated as S largest = S(z = ) S(z = 8) = 8.k B, S interface = S(z = ) S(z = 8) =.7k B, while S largest and S interface refer to the increment/reduction of 7

8 entropies when the methane is placed at the position that generates the largest fluctuation or at the interface. For the case of pentane, these values are S largest = 8.k B and S interface = 7.k B, respectively. Estimated S (.k B ) z = - Å z = -8 Å z = Å Time (ns) FIG. S6: Time profile of the estimated entropy. 8

9 [] K. Vanommeslaeghe, E. Hatcher, C. Acharya, S. Kundu, S. Zhong, J. Shim, E. Darian, O. Guvench, P. Lopes, I. Vorobyov, et al., J. Comp. Chem., 67 (). [] I. V. Vorobyov, V. M. Anisimov, and A. D. MacKerell, J. Phys. Chem. B 9, 8988 (). [] F. Zhu and G. Hummer, J. Comp. Chem., (). [] H. Flyvbjerg and H. G. Petersen, J. Chem. Phys. 9, 6 (989). [] S. Ou, Y. Hu, S. Patel, and H. Wan, J. Phys. Chem. B 7, 7 (). [6] N. A. Ahmed and D. V. Gokhale, IEEE Trans. Information Theory, 688 (989). 9

Supporting Information

Supporting Information Constant ph molecular dynamics reveals ph-modulated binding of two small-molecule BACE1 inhibitors Christopher R. Ellis 1,, Cheng-Chieh Tsai 1,, Xinjun Hou 2, and Jana Shen 1, 1