Supporting Information for. Hydrogen Bonding Structure at Zwitterionic. Lipid/Water Interface

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1 Supporting Information for Hydrogen Bonding Structure at Zwitterionic Lipid/Water Interface Tatsuya Ishiyama,, Daichi Terada, and Akihiro Morita,, Department of Applied Chemistry, Graduate School of Science and Engineering, University of Toyama, Toyama , Japan, Department of Chemistry Graduate School of Science Tohoku University Sendai , Japan, and Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Kyoto , Japan To whom correspondence should be addressed Department of Applied Chemistry, Graduate School of Science and Engineering, University of Toyama, Toyama , Japan Department of Chemistry Graduate School of Science Tohoku University Sendai , Japan Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Kyoto , Japan S1

2 Contents S1. Computational Methodology S2. Modification of Carbonyl Charges S3. Radial Distribution Functions around Polar Sites S2

3 S1. Computational Methodology MD Procedures The molecular models employed in the present MD simulation to generate trajectories were the TIP3P model 1 for water and the CHARMM36 force field (FF) 2 for POPC. The following three steps were taken to carry out the MD simulation; Step 1: Preparation of initial configuration involving water/popc interfaces, Step 2: Equilibration to relax the initial structure, Step 3: Sampling calculation of water/popc monolayer. In Step 1, we employed the PACKMOL package 3 to put the constituent molecules in the simulation cell. The geometry of the molecules were taken from the pdb files available in the MacKerell s website. 4 The number of molecules contained in the simulation cell is 600 for water and 20 for POPC. Initially, the water molecules were randomly placed within a partial region of L x L y L z = 50.0 Å 50.0 Å 33.9 Å in a simulation cell of L x L y L z = 50.0 Å 50.0 Å 80.0 Å dimensions. The water molecules thus form a slab geometry with two surfaces normal to the z direction in the 3-dimensional periodic boundary cell. Then we placed the POPC molecules in the vacant region of the cell with attaching the hydrophilic head groups to the water surface, so that each side of the water slab is covered with 10 POPC molecules. The initial configuration thus prepared has two POPC/water interfaces perpendicular to the z axis. We prepared 128 different initial configurations, which were treated independently in the following steps to augment the statistical sampling. In the equilibration stage of Step 2, first we employed the steepest-descent energy minimization to the initial configuration, which was followed by the equilibration MD run during a total of 20 ns. The equilibration of a system of lipid/water interface typically requires several tens of ns, 5 and we employed the GROMACS package (version 4.6.1) 6 to speed up this process. During the equilibration MD run, the intramolecular stretching vibrations of S3

4 H atoms were constrained with the Lincs algorithm, 7 and the time step was set to 2 fs. The particle-mesh Ewald method 8,9 was employed for long-range electrostatics. The cutoff length of the Lennard-Jones and the real space part of the Ewald sum were taken to be 10 Å. The equilibration MD run (Step 2-1) was conducted at the constant temperature and pressure (NPT) condition of 300 K and 1 atm with the Nose-Hoover thermostat 10,11 and the Parrinello-Rahman barostat 12 during 10 ns. After the relaxation of the system, the system size converges to L x L y L z = Å Å Å on average, in which the lipid bilayer and water slab are formed alternately along the z direction under the periodic boundary condition. The average surface area per a lipid molecule is Å 2. After Step 2-1, the constant volume and temperature (NVT) MD simulation with the Berendsen thermostat 13 was further carried out using a fixed simulation cell of L x L y L z = Å Å Å dimensions during 10 ns (Step 2-2). Accordingly the periodic length along the z axis was elongated to L z = Å, and the configuration was equilibrated by inserting a vacant region between the bilayer of the lipids. Therefore, the water/popc system forms two separated POPC monolayers on both sides of the water slab. In the production run (Step 3) we calculated the structure and the vibrational spectra of water/popc interface using our original code developed for the SFG calculations. At this stage we employed flexible version of TIP3P to allow for the SFG spectroscopic calculations. The intramolecular potential includes the anharmonic term and the bending term: 14,15 u H 2O intra = 6 [k n ( r 1 ) n + k n ( r 2 ) n ] + k θ ( θ) 2, (S1) n=2 where r 1 and r 2 are the displacements of the O-H (O-D) bond lengths from its equilibrium distance, and θ is that of the HOD angle. In most flexible and non-polarizable water models, equilibrium HOH angle decreases while OH bond length increases. 16 Thus in the present flexible TIP3P water model, the equilibrium O-H (O-D) distance is changed from the original value of TIP3P model r eq = Å to r eq = Å and θ HOH,eq = S4

5 to θ HOH,eq = , so that the average molecular geometry of the present model is almost consistent to the original rigid TIP3P model. The potential parameters were parametrized to reproduce IR and SFG spectra of pure water, and we set to k 2 = , k 3 = 0.46, k 4 = 0.65, k 5 = 2.0, k 6 = 5.0 in the atomic units. The parameter of k θ in Eq. (S1) was taken from Ref. 17 We removed the geometry constraint on the H atoms of the lipid molecule in Step 2 to make the POPC model fully flexible. The time step for equation of motion was set to 0.61 fs with NVT ensemble with a fixed simulation cell of L x L y L z = Å Å Å. The MD production run (Step 3) was carried out during 30 ps, after a short equilibration for 10 ps. During the MD run, two stable lipid monolayers were formed in both sides of the water slab. The statistical sampling was taken using parallel computation of 128 independent trajectories starting with different initial configurations, which generates a total of 30 ps ns ensemble average. The statistical data (number density, molecular orientation, and VSFG spectra) shown in the main text were confirmed to be little changed, indicating that the system is well equilibrated. The MD simulation with TIP3P/mCHARMM36 force field was carried out after the end of the Step 3 simulation employing TIP3P/CHARMM36 force field mentioned above. After a short equilibration for 10 ps, the production run (Step 3 ) was carried out during 30 ps to sample the statistics in the parallel computation. VSFG Calculation In the VSFG spectroscopic calculation, we employed the following time correlation function formalism 18 to calculate the resonant part of the second order nonlinear susceptibility χ, χ res pqr = iω Tc IR exp(iω IR t) A pq (t)m r (0) dt, k B T 0 (S2) S5

6 where A pq (t) and M r (t) denote the polarizability tensor and dipole moment vector of the interface system at the time t. The other notations are same as those in Eq. (1) of the main text. A pq (t) and M r (t) are defined as A pq (t) = j α j,pq (t), M r (t) = j µ j,r (t), (S3) where α j,pq (t) and µ j,r (t) are the effective polarizability tensor and dipole moment vector of the j-th molecule at the time t. The effective means that α incorporates the local field correction by definition. 19 The molecular polarizability and dipole moment of water at the instantaneous configuration were calculated with the charge response kernel (CRK) model developed in Ref., 15 while those of POPC molecules were neglected. The effective polarizability and dipole moment in Eq. (S3) were calculated by taking account of the self-consistent polarization interaction, 15 whereas the nonpolarizable models of TIP3P and modified CHARMM36 were used for the trajectory calculations. In the present paper, we discuss the self-part spectrum (Eq. (2) of the main text), χ self pqr = iω Tc IR exp(iω IR t) α i,pq (t)µ i,r (0) dt. k B T 0 i (S4) Here we compare Eqs. (S2) and (S4) (or Eqs. (1) and (2) in the main text). We note that the calculation of Eq. (S2) requires much more statistical sampling than that of Eq. (S4) due to the noise of cross correlation terms α i (t)µ j (0) between distant molecules. We effectively reduced the noise by introducing the damping treatment 20 to neglect the cross correlations of molecules whose O-O distance is over 5.6 Å (the second minimum position of the radial distribution function of O(water)-O(water)). Figure S1 (b) compares the result of Eq. (S2) (black dashed line) and that of Eq. (S4) (black solid line). Although the former is slightly enhanced compared to the latter, the qualitative features of the two spectra well agree with each other. In the decomposition analysis of χ self in Eq. (S4), the upper bound of the time is prac- S6

7 tically set to T c = 1.2 ps. This time scale is sufficiently longer than the O-H stretching vibrational period, while comparable or shorter than that of structural change of water molecules, e.g. lifetime of the hydrogen bonds. In the decomposition analysis, each water molecule is classified at t = 0 of the time correlation function. This classification is effective as the time correlation function decays within T c while the structural change is not substantial. S2. Modification of Carbonyl Charges In the MD simulation of phosphatidylcholine lipid/water interfaces, we found that the partial charges of the lipid carbonyl sites need to be slightly reduced from those of CHARMM36 force field (FF). This modification little alters the structure of the interfaces, though it significantly influences the vibrational spectra. This was motivated by our HD VSFG calculation as argued in the following. The thick black line in Figure S1 (a) shows the Im[χ] spectrum calculated using the TIP3P model for water and the original CHARMM36 FF for the POPC. The calculated spectrum well reproduces the intense positive peak at about 3300 cm 1, though it does not show the high-frequency minor band at about cm 1. This problem has been also observed in other previous classical MD simulations 20,21 (see also Figure 2 of the main text). To clarify the reason of missing high-frequency band, we analyzed the calculated Im[χ] spectrum using the classification scheme of interfacial water in Figure 1 (b) of the main text (e.g. N, P, O, NP, PO,...), where the Im[χ] is decomposed into these classes of water molecules according to the adjacent polar groups. Figure S1 (a) indicates the decomposed results. Note that the sum of the decomposed spectra recover the total spectrum. The result of decomposition clarifies that the main positive band at 3300 cm 1 originates from the NP component (purple dash-dot line). The mechanism of this positive band has been elucidated in details in the main text. One can S7

8 also see in Figure S1 (a) that the second positive component is NPO (gray line) peaked at about 3400 cm 1. This calculated component is located in the lower frequency side than the experimental minor band observed at about cm 1. We argue that the calculated NPO component is excessively red shifted in Figure S1 (a) due to a problem of the FF. The NPO component contains the water molecules adjacent to the carbonyl oxygens (O22 and O32 in Figure 1(a) of the main text) of the lipid. In the CHARMM36 FF 2 the partial charge of the carbonyl oxygen was determined to be 0.63 in reference to methylacetatewater interaction using the Hartree-Fock(HF)/6-31G calculations. The ab initio calculations in the HF/6-31G level is often employed to the modeling of partial charges though it generally overestimates the polarity of molecules. This is because the overestimated polarity is rather consistent to the molecules in water, as the solvation effect arguments the polarity. Thus we calculated the partial charges of methylacetate with the ChelpG method 22 by B3LYP and MP2 with 6-311G(2d,p) basis, and obtained the partial charge of the carbonyl oxygen to be 0.53 by B3LYP and 0.51 by MP2. These values should be more appropriate to the partial charge of the carbonyl oxygen in the gas-phase molecule free from the solvation effect. In the phosphatidylcholine membranes, the carbonyl oxygens are not embedded in water, but are rather located in the hydrophobic chains as is evidenced in the density profile in Figure 4 (a) of the main text. We also estimated the hydration number around the carbonyl oxygens in the POPC/water interface by the MD simulation, and thereby found that the hydration number is 0.87, which is significantly smaller than that of the same site of POPC molecule embedded in water, Considering such a more hydrophobic environment in the lipid, we slightly reduced the polarity of the carbonyl group as in Table 1 of the main text so as to be consistent to those by B3LYP calculation. Hereafter, the FF with this revision is referred to as the modified CHARMM36, mcharmm36, in the present paper. This revision little alters the hydration structure around the carbonyl oxygen, as discussed in Section S3, though it significantly improved the result of vibrational spectrum. S8

9 The Im[χ] spectrum calculated with TIP3P/mCHARMM36 FF is shown in black solid line in Figure S1 (b), which properly reproduces the qualitative features of the experimental VSFG spectrum, including the high-frequency minor band at 3530 cm 1 and the lowfrequency major band at 3300 cm 1. The decomposed Im[χ] spectra with TIP3P/mCHARMM36 FF in Figure S1 (b). Comparing with the results of TIP3P/original CHARMM36 FF (Figure S1 (a)), the NPO component (gray line) shifts toward the higher frequency side to reproduce the minor band of Im[χ]. This shift is due to the reduced local interaction between the carbonyl oxygen and the adjacent water molecules. S3. Radial Distribution Functions around Polar Sites The radial distribution functions (RDFs) of water and the selected sites of POPC molecule discussed in the main text are shown in Figure S2 (a), where the solid lines are the results with TIP3P/CHARMM36 FF and the dashed lines are the ones with TIP3P/mCHARMM36 FF (see Section S2). The difference between both results is small. The hydration structures with clear first peaks are observed for water around polar sites of POPC molecule. For P-O(w) (blue line) and O-O(w) (green line), the second hydration shell is also developed, indicating that water molecules within the second shell are influenced by the polar sites. To examine the orientational structure of water molecules around the polar sites, we define γ as an angle between the water permanent dipole and the radial vector from the polar sites to O(w) (see the inset of Figure S2 (b)). Figure S2 (b) shows cos γ distribution per one water molecules as a function of the radial distance. The positive peak for N-O(w) (red line) and the negative peaks for P-O(w) and O-O(w) (blue and green line) within the first hydration shell manifest a preferential orientation of water molecules around the positive charged choline and the negative charged phosphate and glycerol. In terms of P-O(w) and O- O(w) distributions, clear second negative peak within the second hydration shell is observed, while the distribution for N-O(w) has weak positive and negative peaks within the second S9

10 shell, indicating that the second shell of N-O(w) distribution may be obscure in comparison with that of P-O(w) and O-O(w) distributions. Thus we define water molecules influenced by P and O sites of a POPC molecule as those within the second shell (P-O(w) distance within 6.91 Å, and O-O(w) distance within 5.25 Å), and as those within the first shell for N site (N-O(w) distance within 5.64 Å), in the main text. References (1) Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein, M. L. Comparison of Simple Potential Functions for Simulating Liquid Water. J. Chem. Phys 1983, 79, 926. (2) Klauda, J. B.; Venable, R. M.; Freites, J. A.; amd D. J. Tobias, J. W. O. C.; Mondragon- Ramirez, C.; Vorobyov, I.; MacKerell Jr., A. D.; Pastor, R. W. Update of the CHARMM All-Atom Additive Force Field for Lipids: Validation on Six Lipid Types. J. Phys. Chem. B 2010, 114, (3) Martinez, L.; Andrade, R.; Birgin, E. G.; Martinez, J. M. A Package for Building Initial Configurations for Molecular Dynamics Simulations. J. Comput. Chem. 2009, 30, (4) (5) Moore, P. B.; Lopez, C. F.; Klein, M. L. Dynamical Properties of a Hydrated Lipid Bilayer from a Multinanosecond Molecular Dynamics Simulation. Biophys. J 2001, 81, (6) Hess, B.; Kutzner, C.; van der Spool, D.; Lindahl, E. GROMACS 4: Algorithms for Highly Efficient, Load-Balanced, and Scalable Molecular Simulation. J. Chem. Theory Comput. 2008, 4, 435. (7) Hess, H.; Bekker, B.; Berendsen, H. J.; Fraaije, J. G. E. M. LINCS: A Linear Constraint Solver for Molecular Simulations. J. Comput. Chem. 1997, 18, S10

11 (8) Darden, T.; York, D.; Pedersen, L. Particle Mesh Ewald: An Nlog(N) Method for Ewald Sums in Large Systems. J. Chem. Phys. 1993, 98, (9) Essmann, U.; Perera, L.; Berkowitz, T.; Pedersen, L. A Smooth Particle Mesh Ewald Method. J. Chem. Phys. 1995, 103, (10) Nose, S. A Unified Formulation of the Constant Temperature Molecular Dynamics Methods. J. Chem. Phys. 1984, 81, 511. (11) Hoover, W. G. Canonical Dynamics: Equilibrium Phase-Space Distributions. Phys. Rev. A 1985, 31, (12) Parrinello, M.; Rahman, A. Polymorphic Transitions in Single Crystals: A New Molecular Dynamics Method. J. Appl. Phys. 1981, 52, (13) Berendsen, H. J. C.; Postma, J. P. M.; van Gunsteren, W. F.; DiNola, A.; Haak, J. R. Molecular Dynamics with Coupling to an External Bath. J. Chem. Phys. 1984, 81, (14) Ishiyama, T.; Morita, A. Molecular Dynamics Study of Gas-Liquid Aqueous Sodium Halide Interfaces. I. Flexible and Polarizable Molecular Modeling and Interfacial Properties. J. Phys. Chem. C 2007, 111, 721. (15) Ishiyama, T.; Morita, A. Analysis of Anisotropic Local Field in Sum Frequency Generation Spectroscopy with the Charge Response Kernel Water Model. J. Chem. Phys 2009, 131, (16) Wu, Y.; Tepper, H. L.; Voth, G. A. Flexible Simple Point-Charge Water Model with Improved Liquid-State Properties. J. Chem. Phys. 2006, 124, (17) Gonzalez, M.; Abascal, J. A Flexible Model for Water Based on TIP4P/2005. J. Chem. Phys. 2011, 135, S11

12 (18) Morita, A.; Ishiyama, T. Recent Progress in Theoretical Analysis of Vibrational Sum Frequency Generation Spectroscopy. Phys. Chem. Chem. Phys 2008, 10, (19) Morita, A.; Hynes, J. T. A Theoretical Analysis of the Sum Frequency Generation Spectrum of the Water Surface. II. Time-Dependent Approach. J. Phys. Chem. B 2002, 106, 673. (20) Nagata, Y.; Mukamel, S. Vibrational Sum-Frequency Generation Spectroscopy at the Water/Lipid Interface: Molecular Dynamics Simulation Study. J. Am. Chem. Soc. 2010, 132, (21) Roy, S.; Gruenbaum, S. M.; Skinner, J. L. Theoretical Vibrational Sum-Frequency Generation Spectroscopy of Water near Lipid and Surfactant Monolayer Interfaces. J. Chem. Phys. 2014, 141, 18C502. (22) Breneman, C.; Wiberg, K. Determining Atom-Centered Monopoles from Molecular Electrostatic Potentials. The Need for High Sampling Density in Formamide Conformational Analysis. J. Comput. Chem. 1990, 11, 361. S12

13 Amplitude (arb.unit) Amplitude (arb.unit) (a) (b) Total Frequency (cm 1 ) CHARMM36 N P O NP PO NO NPO Others mcharmm Figure S1: The calculated Im[χ] (thick black lines) and the decomposed spectra for water at the POPC/water interface. (a) the results for the original CHARMM36 FF. (b) the results for the mcharmm36 FF. The decomposition scheme is described in the main text. The black dotted line denotes the result by using Eq. (S2) (Eq. (1) in the main text). S13

14 g N-O(w) P-O(w) O-O(w) (a) r ºA (b) Figure S2: (a) Radial distribution functions of some sites of POPC and water, where O(w) represents the oxygen site of water, N the nitrogen site of POPC, P the phosphate site of POPC, and O the four glycerol oxygen sites of POPC. (b)averaged cos γ distribution. See the inset and the text for the definition of γ. The solid lines are the results with TIP3P/CHARMM36 FF and the dashed lines are the ones with TIP3P/mCHARMM36 FF. S14

Supporting Information

Supporting Information Structure and Dynamics of Uranyl(VI) and Plutonyl(VI) Cations in Ionic Liquid/Water Mixtures via Molecular Dynamics Simulations Katie A. Maerzke, George S. Goff, Wolfgang H. Runde,