Counting charges on membrane-bound peptides

Quantifying the number of charges on peptides bound to interfaces requires reliable estimates of (i) surface coverage and (ii) surface charge, both of which are notoriously difficult parameters to obtain, especially at solid/water interfaces. Here, we report the thermodynamics and electrostatics governing the interactions of l-lysine and l-arginine octamers (Lys8 and Arg8) with supported lipid bilayers prepared.


S2
photobleaching has shown that this method of vesicle preparation produces well-formed bilayers. 40,46 All experiments were conducted in at least triplicate.
C. Experimental Procedure. When acquiring our SHG adsorption isotherms, the lowest oligomer concentration was introduced at a flow rate of 2 mL×min -1 in 0.1 M NaCl and allowed to interact for at least 15 min or until a steady SHG signal was achieved and followed by sequentially higher concentrations. Reversibility studies were also carried out, and in these studies the baseline at 0.1 M NaCl was acquired for at least 45 min. The supported lipid bilayer was then exposed to Lys 8 or

D. Combined Gouy-Chapman/Hill Model.
As discussed in our previous work, 1 using a combination of surface complexation models like the Gouy-Chapman model 2,3 and Hill isotherms (vide infra) (Eq. S1) we are able to provide the lower estimates for charge densities and adsorption free energies arising from the interactions between the polypeptides and supported lipid bilayers. + @A@B S1 Here, 0 is the charge density of the 9:1 DMPC/DMPG bilayer (-0.1 C·m -2 ), 1,4 123 is the charge density of the adsorbed polypeptide at monolayer coverage, K ads is the apparent equilibrium, n is the Hill coefficient describing cooperativity of the adsorption process, M is the bulk peptide concentration, and C elec is the background electrolyte concentration (0.1 M NaCl plus 0.008 M contribution from Tris) (T = ~20.5 °C). In addition to the reversibility studies at 50 µM discussed in the main text, we also completed SHG reversibility studies at 25 µM to match the concentrations used in the QCM-D and LSPR experiments discussed in the main text, and below ( Figure S1A).

Spectroscopy
As described in the main text, due to the expense of the synthesized oligomers of Lys and Arg and the volume that would we needed to achieve concentrations higher than ~10 -3 M, we opted to use an artificial data point to estimate the lower bound for our reported charge density. This data point (shown as the open circle in Figure 3 in the main text) was determined by taking the average of the three data points at the highest Lys 8  We have previously explored the adsorption of higher molecular weight polymers of L -lysine and L -arginine. In those studies, we found that the free energy of adsorption for both PLL and PLR was approximately -50 kJ ·moL -1 . Comparatively, we estimate free energies of adsorption for Lys 8 and Arg 8 of about -40 kJ ·moL -1 . If, however, we compare PLL/PLR to Lys 8 / Arg 8 on the basis of charge concentration instead of polymer concentration, we find that the difference in free energy between PLL/PLR and Lys 8 / Arg 8 is actually much smaller (Table S2) solution was flowed over the LSPR sensor. Then, the sensor was removed and replaced with a gold QCM-D sensor, and 10 mL of Hellmanex, Cobas, and ultrapure water were flowed sequentially through the window cell. All components were dried with N 2 .

V. Bulk Refractive Index Sensitivities of the LSPR Sensors
To calculate optical mass from Δλ max , sensitivities of the sensor were measured in the absence and presence of a supported lipid bilayer (S and S′, respectively). These values were used to calculate the distance L over which the LSPR signal decays to 1/e of the induced evanescent field from the nanoplasmonic gold discs on the sensor. Increasing concentrations of glycerol (0-35 mass% in increments of 5 mass%) were measured in triplicate at 632.8 nm (Rudolph Research J157 Automatic Refractometer). These glycerol solutions were flowed over the LSPR sensor, and changes in frequency, dissipation, and Δλ max were recorded with both QCM-D and LSPR. These measurements were recorded for glycerol solutions before and after the presence of a bilayer. The Δλ max values were plotted against the measured refractive indices, and the slopes of the graphs S6 were linearly fitted to obtain S and S′. The effective refractive index within the LSPR sensing volume, n eff , is then calculated for each replicate, where: Δλ max = S(n eff -n solution ) S2 and n buffer is the refractive index increment of the solution measured in triplicate at 632.8 nm and determined to be 1.334 ± 0.00002 RIU.

VI. Calculation of Optical Mass from LSPR Data
The characteristic decay length L within the LSPR field was calculated from the bulk refractive index sensitivity values in Eq. S2, and determined to be 20 ± 3.3 nm via:

VII. Analysis of Interfacial Electrostatics
The spatial charge distribution is averaged over the x,y plane and binned (with a width of d = 0.2 Å) according to the value of z coordinate, in which L is the area of the simulation cell in the x,y dimension, and the bracket indicates ensemble average (2,500 frames from the MD trajectories are used for each system); the bilayer center is set to be at z = 0. Plots of ( ) for the systems analyzed are shown in Figure S4. The integrated charge density from the bilayer center up to a given z value is denoted as ( ): The electrostatic potential is calculated by noting from Gauss's law that, where 0 is the vacuum permittivity; when applying Gauss's law, the system is assumed to be symmetrical with respect to the bilayer center (thus the electric field at z is given by = ( )/ 0 , which is integrated from z to ¥ to obtain the electrostatic potential relative to the bulk).
For a symmetrical system, this expression is equivalent to the double integration expression commonly used in the literature, 13, 14 To apply the Gouy-Chapman model in the context of interpreting the SHG experiment, it is assumed here that the measurement senses the electrostatic potential due to all charges from the bilayer center up to a virtual interface located at z. Thus the electrostatic potential at this interface predicted by the Gouy-Chapman model and the integrated charge density are related through the Grahame's equation, 15 where c is the salt concentration in M, N A is Avogadro's number, } is the relative permittivity of the solvent, n is valence of salt ions (for the present case, n=1), e is the elementary charge, k B is Boltzmann's constant, and T is temperature.
To evaluate the applicability of the Gouy-Chapman model to the lipid/water interface, electrostatic potential and integrated charge density computed from the microscopic MD simulations are best fitted to the Grahame's equation by adjusting the relative permittivity, } , S9 which is expected to be different from the value for bulk solution. 16 Since the precise location of the interface is not straightforward to determine, the fitting was done for a series of z values close to the location of the lipid phosphate groups (see Figure 6 in the main text). Such analysis is not straightforward for the Arg 8 /Lys 8 systems due to the significant heterogeneity in the computed electrostatic potential in the x,y plane (see Figure S5); therefore, the fitting to the Gouy-Chapman model was done only for the 9:1 DMPC/DMPG system.    Figure S4. Charge density (total and from different components), ( ), and integrated charge density (total and from different components), ( ), as a function of z from MD simulations (computed based on Eqs. 11-12) for Arg 8 -9:1 DMPC/DMPG, Lys 8 -9:1 DMPC/DMPG and 9:1 DMPC/DMPG systems. The charge distributions are averaged over 2500 frames in 50 ns production run. S16 Figure S5. Electrostatic potential (in Volt) in the plane of z = 30 Å computed using 5000 snapshots from MD trajectories. The top panel is for the Arg 8 -9:1 DMPC/DMPG system, and the bottom is for the Lys 8 -9:1 DMPC/DMPG system. There is significant level of heterogeneity in the electrostatic potential due to the heterogeneous adsorption of the peptides on the membrane surface. S17 Figure S6: Radial distribution functions (RDFs) and integrated RDFs for representative atoms in the amino acid side chains (left: Arg NH1/NH2; right: Lys NZ) with respect to DMPC/DMPG phosphorus atoms from atomistic simulations of 10 × 10 × 18 nm 3 systems. Each RDF is averaged over 1000 frames (~50 ns). The results highlight that the cationic residues preferentially interact with anionic lipids (DMPG).