= 36.69 ± 0.03 mW with drift of 0.3 ± 6 μW/s over 2 h, Figure 1) of the Ti:S oscillator output power. QCM-D experiments carried out under the same solution conditions showed a negative shift in frequency of 6.4 ± 0.7 Hz after introducing 50 nM PAH to the DMPC/DMPG bilayer for 1 h (Complete trace shown in SI). Negative frequency shifts are indicative of PAH association with the bilayer. Following our previously published approach,24,36 we estimate the sensed mass, which includes the polymers and any other hydrodynamically coupled species, predominantly water, to be 115 ± 13 ng/cm2. Using a polycation molar mass of 17.5 kDa and attributing 31% of the mass to water as reported for poly-Llysine layers formed on SiO2 at pH 7 and an ionic strength of 0.05 M,37 the QCM-D mass estimate corresponds to 2.7 (±0.3) × 1012 PAH molecules/cm2. Note that the amount of hydrodynamically coupled species is expected to differ somewhat for the 9:1 DMPC:DMPG bilayer under the solution conditions employed in the present study. Given the propensity of polycations to disrupt bilayers and membranes,2,12 we probed for structural changes along the lipid carbon backbone and the methyl groups on the lipid headgroups using vibrational SFG spectroscopy. The absence of significant spectral changes before and after exposure of the bilayers to 50 nM PAH evident in Figure 2 indicates that
Figure 2. Normalized ssp-polarized SFG spectra of bilayers formed from a 9:1 mixture of DMPC and DMPG in the absence (black, top) and presence of 50 nM PAH (blue, bottom) at 0.1 M NaCl and 0.01 M Tris (pH 7.4).
structural rearrangements within the lipid alkyl chains, as probed by SFG in the C−H stretching region, are negligible under these experimental conditions. We conclude that the PAH polycations interact with the supported bilayers nondisruptively under the conditions of our experiments; this conclusion is also supported by coarse-grained simulations reported in the SI, which show only mild membrane bending upon PAH10/PAH160 adsorption without any major structural perturbation (Figures S4 and S5). As discussed next, this finding makes possible the quantification of interfacial charge densities and binding thermodynamics. 3.2. Free Energy of PAH Adsorption to the Lipid Bilayer. Given the reversibility of PAH attachment to the bilayer, we used the interfacial potential-dependent Eisenthal χ(3) method21−24,36 and recorded the adsorption isotherms shown in Figure 3 to determine the free energy of adsorption of the polycation to the bilayer. Briefly, the SHG intensity (ISHG) of a charged interface can be described by the following equation: ISHG ∝ |ESHG|2 ∝ |χ (2) EωEω + χ (3) EωEω Φ0eiΔγ |2
(1)
Here, ESHG is the SHG electric field (E-field), Eω is the incident E-field oscillating at the fundamental frequency ω, χ(2) and χ(3) are the second- and third-order nonlinear susceptibilities of the 5810
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Figure 3. SHG E-field as a function of (A) PAH (●) concentration at 0.1 M NaCl and (B) PAH (■, 0 M NaCl), AH (□, 0 M NaCl), and AH (○, 0.1 M NaCl) concentration. All solutions were buffered to pH 7.4 with 0.01 M Tris. The black lines are the fits to the double layer model.
desorption (y = A + B[1 − exp{−rofft}]) rate model to the data shown in Figure 1B, which yielded an on-rate of 3.8(1) hr−1 and an off-rate of 0.156(4) hr−1. With a free PAH concentration of 50 nM (from Figure 1), a surface site density of 72 Å2/ lipid,48 or 1.4 × 1014 cm−2, and a bound PAH surface site density of 2.7 × 1012 cm−2 estimated from QCM-D (see section 3.1) we use the following expression to obtain the equilibrium adsorption constant:
system, Φ0 is the electrostatic potential at the surface, and Δγ is the relative phase between the second- and third-order terms.23,38,39 Gouy−Chapman theory can adequately describe the Coulombic potential of lipid bilayers.40 The Gouy− Chapman equation represents a common electrical double layer mean field theory and is given by the following:41−44 Φ0 =
2kBT sinh−1[σ 8000kBTNACelecε0εR ] ze
(2)
Keq =
Here, kB is the Boltzmann constant, T is absolute temperature, z is the charge on the screening electrolyte, e is the elemental charge, NA is Avogadro’s number, Celec is the electrolyte concentration, ε0 is the permittivity in a vacuum, and εR is the relative permittivity of water at 25 °C. Following Salafsky and Eisenthal,45 and given the demonstrated reversibility in our PAH-membrane studies, we combine eqs 1 and 2 with the Langmuir adsorption model for expressing the surface coverage of charged species to arrive at the following fit equation for analyzing the adsorption isotherms:
kon r /([PAH][surface sites]) = on = 9.3(3) × 106M−1 koff roff /[bound PAH]
(4)
This result is within a factor of 3 of the equilibrium constant determined from the adsorption isotherms, which, within the limits of our assumptions, can be considered satisfactory. Reassuringly, the free energies of adsorption determined from the kinetic (50.1(1) kJ/mol) vs the thermodynamic (52.8(7) kJ/mol) analysis are within one kJ/mol of one another. Computations at the coarse-grained level (Figure 4, also see Figure S4) lead to −22 kJ/mol for PAH10 and −45 kJ/mol for
⎛⎛ ⎛ K ads[M] ⎞⎞⎛ 8.44M1/2m2C −1 ⎞⎞ ⎟⎟ ISHG = A + Bsinh−1⎜⎜⎜⎜σ0 + σPAH⎜ ⎟⎟⎟⎜ ⎝ 1 + K ads[M] ⎠⎠⎜⎝ (M + Celec) ⎟⎠⎟⎠ ⎝⎝
(3)
Here, A and B contain the second- and third-order susceptibilities of the system from eq 1, σ0 is the charge density in units of Coulombs per square meter at the zero plane, determined by the number of protonated and deprotonated surface sites and any specifically adsorbed species,46 σPAH is the charge density of the PAH attached at surface at saturation, Kads is the equilibrium constant of PAH adsorption to the bilayer in units of liter per mole, M is the PAH concentration in moles per liter, and Celec is the electrolyte concentration in units of moles per liter. Note that eq 3 is corrected for cgs to SI conversion by a factor of 3.58 when compared to our prior work,24 yielding a charge density for the bilayer in the absence of PAH of −0.11 ± 0.06 C/m2. Fitting eq 3 to the data shown in Figure 3A yields an apparent binding constant of 2.7 (±0.7) × 107 M−1, which, when referenced to the molarity of water (55.5 M) as a standard state for adsorption from solution,47 corresponds to an apparent adsorption free energy, ΔGapp, of −52.7 ± 0.6 kJ/ mol. This value indicates favorable adsorption of PAH to the SLB surface under the conditions of our experiments. We also compared the thermodynamic result with results from fitting a standard first-order adsorption (y = A + B exp{−ront}) and
Figure 4. Calculated binding potentials of mean force (PMFs) for AH and PAH oligomers from CG simulations. The horizontal axis (Δz) is the distance from the center-of-mass of the AH or a PAH oligomer to the center of the lipid bilayer that include lipids within 15 Å from the expected binding site. The error bars indicated statistical error estimated from block average. See SI for discussion of comparison between CG and atomistic simulations.
PAH20; at the atomistic level, the value is about −22 kJ/mol for PAH10 from previous atomistic simulations.49 Therefore, independent simulations at different scales have recapitulated the experimental finding that PAH oligomers bind to a membrane bilayer with considerable affinity. 5811
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Figure 5. Titration behavior of PAH oligomers at different surface binding densities using a simple surface-packing model and MCCE calculations. (A, B) A snapshot of the surface-packing model for PAH10 at a monomer density of 7 × 1014 per cm2 from the top and side view, respectively. (C) Computed titration curves for different surface binding densities. The error bars are computed by choosing different random sets of configurations from the conformational library (see Sect. 3.4) for the PAH10 molecules for each density.
PAH (ca. −50 kJ/mol from the inflection point of the PAH isotherm shown in Figure 3B vs −14.6 kJ/mol for the AH isotherm, both recorded under salt-free conditions), the average free binding energy per ammonium group in PAH is far below that of the allylamine monomer: even if we assume that only 50% of the 190 ammonium groups in PAH are charged (vide infra), a simple additive model would predict the binding free energy of PAH to be 85 times greater (190 × 50% × 14.6 kJ/ mol = 1.4 MJ/mol) when compared to that of the AH monomer. By contrast, the experimentally measured binding free energy difference is a mere factor of 3 to 4. From computational studies, the binding free energy of PAH does not follow a simple additive model either: the computed binding affinity of PAH20 (−42 kJ/mol) is about a factor of 3 of that for the AH monomer (−14 kJ/mol). Such dramatic discrepancy implies either that significant anticooperativity exists in the binding of amine groups in PAH, reminiscent of previous work studying positively charged short peptide sequences,50−52 or that only a small number of groups come into contact with the lipid membrane, possibly due to the formation of loops of PAH sections that are entropically driven.53 The latter scenario is qualitatively consistent with the observation that using configurations collected from atomistic MD simulations of PAH10, packing PAH10 oligomers at the experimentally measured monomer density, leads to significant steric clashes unless these oligomers orient perpendicular to the surface (i.e., only one AH monomer in PAH10 is in direct contact with the surface; see Figure 5a/b for a top/side view); such “vertical packing” is also favored entropically compared to the “sideway packing” in which a large number of amines are bound to the bilayer. Nonetheless, simulating the binding conformation of a long PAH polymer at the lipid bilayer surface at a high packing density remains challenging. Under dilute condition, PAH160 appears to favor an extended conformation, as expected for a polyelectrolyte at a modest salt concentration (see Figure S5); even at the dilute condition, the number of contacts formed between PAH and the bilayer is substantially smaller than the total number of monomers. Moreover, as shown in Table S1, the amount of Na+ released upon PAH160 binding is modest (∼50 for two copies of PAH160), as compared to the expected amount of Na+ release if all monomers were to bind to the
3.3. Average Free Binding Energy per Ammonium Group in PAH Far Below that of Allylamine Monomer. Before discussing the interfacial electrostatics of the system under investigation that can be deduced by fitting eq 3 to the adsorption isotherms, we compare the free energy of PAH adsorption to the bilayer to that of allylamine hydrochloride (AH), the monomer used to synthesize PAH. As shown in Figure 3B, changes in the SHG signal intensity were minor when adding up to 0.2 M AH in 0.1 M NaCl (recall, signal intensities dropped by more than 25% in the PAH experiments shown in Figure 3A). In contrast, substantial signal loss was observed in absence of NaCl, albeit at 6 orders of magnitude larger concentration than the concentration at which we observe PAH attachment in the absence of NaCl. Similar adsorption behavior was observed by SHG using the saturated AH analog, propylamine hydrochloride (PA), which lacks the CC double bond (see Figure S3). This result indicates that the role of the CC double bond in AH adsorption is at most minor under the conditions of our experiments. QCM-D showed a negative shift in frequency of 6.0 ± 1.0 Hz upon exposure of the bilayer to 50 mM AH for 1 h in the absence of NaCl (Complete trace is shown in the SI). The sensed mass, which, again, includes the monomers, hydrodynamically coupled solvent, and other species, was estimated to be 110 ± 20 ng/cm2, corresponding to an upper limit of 1.2 (±0.1) × 1015 monomers/cm2. We note that the amount of coupled water may differ between the cases of AH and PAH adsorption to the bilayer. The monomer density was calculated using a molecular weight of 57.09 g/mol for the monomer, excluding the chloride counterion that dissolves in solution. Fitting eq 3 to the AH adsorption isotherm recorded in the absence of NaCl (Figure 3B) yielded an apparent equilibrium binding constant of 6.2 ± 0.9 M−1 and a ΔGapp value of −14.6 ± 0.4 kJ/mol, again using the 55.5 molarity of water as the standard reference state for adsorption from aqueous solution. This measured binding affinity for AH is close to the computations at both coarse-grained and atomistic values, which are approximately −13 kJ/mol and −10 kJ/mol, respectively, with 0.1 M monovalent salt (see Figure 4 and SI). While our experiments reveal a much less favorable free binding energy of the AH monomer to the bilayer relative to 5812
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Figure 6. Results from atomistic simulation of a large number (320) of AH monomers interacting with a 9:1 DMPC:DMPG lipid bilayer. (A) Distribution of AH molecules (molecular surface shown in blue) near the top leaflet of the bilayer, whose molecular surface is shown in gray; the phosphate groups are also shown in the molecular surface representation (in red) to highlight the significant undulation of the bilayer due to AH binding. (B) Same representation as (A) after a 90° rotation about the z-axis; phosphate groups and half of the lipid bilayer are removed for clarity. (C) An atomistic view of the same snapshot as (A); hydrogen atoms in the lipids are removed for clarity. Note that some AH molecules penetrate deeply into the bilayer due to favorable hydrophobic interactions with the lipid tails; this leads to significant undulation of the bilayer, as indicated by the positions of the phosphate groups. (D) A close-up (top) and zoomed-in (bottom) views of hydrogen bond interactions (green dotted lines) between an AH molecule with the phosphate and glycerol groups in nearby lipids.
Table 2. Summary of Experimental Data
PAHb AHc
binding constant Kads (M−1)
adsorption free energy ΔGads (kJ/mol)
surface charge density σ (C/m2)
mass attached mads (ng/cm2)
number density Nadsa (cm−2)
2.7 ± 0.7 × 107 6.2 ± 0.9
−52.7 ± 0.6 −14.6 ± 0.4
+0.59 ± 0.12 +1.0 ± 0.1
115 ± 13 110 ± 20
2.7 ± 0.3 × 1012 1.2 ± 0.1 × 1015
a Estimate of upper limit. bData for 0.1 M salt concentration in the presence of 0.01 M Tris (pH 7.4). cData for 0.01 M Tris (pH 7.4) and zero added salt.
with just the attached PAH.24 From the fit we find a PAH charge density, σPAH, of +0.59 ± 0.12 C/m2. Combining this estimated surface charge density with the polymer density estimate provided by the QCM-D experiments, 2.7 (±0.3) × 1012 PAH molecules/cm2, we find that only 71 ± 14% of the approximately 190 ammonium groups in the PAH polymer we studied carries an elementary charge. In contrast, the surface charge density of the bilayer with the AH monomer present, σAH, was determined from the fit to be +1.0 ± 0.1 C/m2, which, when combined with QCM-D experiments, would imply that 88 ± 9% of the AH monomers attached to the bilayer are positively charged (Figure 6). Table 2 summarizes these results. 3.5. Mechanistic Considerations. Our finding of apparent partial charge neutralization under the conditions of dense PAH surface coverage (Figure 7) implied by the QCM-D
membrane. Additional experimental and computational studies are needed to resolve the binding mode of PAH polymers at high coverage. A closely related issue concerns the number of monomers in PAH that remains charged upon binding to the membrane surface, as the magnitude of apparent charge may also provide hints regarding the mode of interaction between PAH and the membrane. We show next that interfacial electrostatics can be estimated by combining the SHG χ(3) technique with QCM-D. 3.4. Attached PAH is 30% Charge-Neutralized, while Attached Allyl Amine Monomer Remains Mostly Charged. As mentioned in section 3.2, fitting eq 3 to SHG χ(3) adsorption isotherms yields not only free energies of adsorption, but also surface charge densities. Pairing these data with QCM-D mass estimates provides the charge associated 5813
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clearly suggests that shifts of pKa values at high binding density are an important factor that influences the apparent charge of PAH upon adsorption to the lipid bilayer. A remaining mystery, however, is that while AH monomers have a similar binding density as PAH (when converted to monomer density), the amount of apparent charge for the bound AH monomers is substantially higher than that for bound PAH (Table 2). We speculate that the difference in charge reflects the different modes of interaction between AH/ PAH and the membrane. For the AH monomer, the binding is likely due to direct interaction between the protonated amine and the lipid headgroup (see Figure 6); the strong salt-bridge interaction along with counterions alleviates the electrostatic repulsion between neighboring amine groups. Given the 72 Å2 footprint of the lipid headgroup,48 the estimated lower limits of the average surface area (Table 2) per AH monomer (as well as the PAH polycation) indicate that more than one AH monomer may bind to each lipid headgroup. Yet, we caution that these estimates depend on mass estimates from QCM-D measurements that may include more hydrodynamically coupled water than we have accounted for. For the PAH polycation, the bound conformation likely features loops due to the effects of configurational entropy;53 residues in those loops are less compensated by ionic interactions and therefore subject to more significant electrostatic repulsion, as reflected by the significant pKa shifts discussed above. For more quantitative understanding, simulations with enhanced sampling techniques are needed to establish the binding conformation and protonation states of PAH at high surface coverage.
Figure 7. Cartoon representation of AH (left) and PAH (right) attached to the lipid membrane. Zwitterionic lipid head groups are shown in green, positively charged ammonium groups are shown in blue, anionic lipid head groups are shown in red, and chloride anions are shown in yellow.
measurements points toward a possible interaction mechanism that lowers the Coulombic repulsion among closely interacting amine groups along and/or between the PAH chains. This process is reminiscent of DNA,54−56 where counterions from solution condense onto the charged polymer to form shared ion clouds, or of dense arrays of surface-immobilized amphoteric species, which may pull in sufficient numbers of protons from solution to shift acid−base equilibrium toward charge neutralization.57−59 To estimate the contribution of counterion association to the apparent charge of PAH, we monitor the distribution of counterions (Cl−) around PAH oligomers of different length (PAH10, PAH30 and PAH160) at both atomistic and CG levels. If we define the number of counterions associated with the PAH as those within the first peak of the Cl−···NPAH radial distribution function (see Figures S6), then the amount of remaining apparent charge varies between 60% to 72% regardless of the resolution of the simulation model (see Table 1). Similarly, on the basis of CG simulations of PAH10 and PAH160 binding to a 9:1 DMPC:DMPG membrane, the fraction of estimated remaining charge after neutralization by Cl− is more than 80% (Table 1). Although these estimates are made based on dilute PAH simulations, the qualitative trend does not change significantly when a large number of PAH10 molecules are packed at high density (see Table S2). Therefore, we conclude that while counterion association contributes to the apparent charge reduction of PAH, other factors are likely to contribute as well. Using the surface-packed PAH10 models discussed above (see Figure 5a-b) and MCCE calculations, titration curves computed for different binding densities, including for an isolated PAH10, show (Figure 5c) significant shifts at high binding densities. At the experimentally estimated binding density, the fraction of protonated amines at neutral pH (7) is predicted to be about 20%; with half of the measured packing density (since measured binding density by QCM-D is an upper bound), the fraction of protonated amines at pH 7 is about 50%. Although this is a qualitative analysis, the model
4. CONCLUSIONS We have demonstrated the utility of combining surface-specific nonlinear optical spectroscopy, specifically SHG, with mass measurements by QCM-D for estimating thermodynamic and electrostatic parameters governing the interaction of the common polycation PAH with supported lipid bilayers under low and high salt concentrations. Vibrational SFG spectroscopy showed that PAH does not disrupt the structure of the SLB under the conditions of our experiments. When attached to a bilayer, PAH was shown to be associated with only about 70% of the positive charges it holds in solution at pH 7. Molecular dynamics simulations suggest that PAH pulls in condensed counterions from solution to avoid charge-repulsion along its backbone and with other PAH molecules to attach to, and completely cover, the bilayer surface. In addition, MCCE pKa computations indicate that the amine groups shift their pKa values due to the confined environment upon adsorption to the surface. We also investigated the adsorption of the monomer, allylamine hydrochloride, to supported lipid bilayers. Monomer adsorption to the bilayer was not observed in the presence of NaCl. In the absence of NaCl, the monomer was shown to attach to the bilayer only in the millimolar concentration range, 6 orders of magnitude higher than the concentration at with the polymer attaches to the bilayer. The fit to the monomer adsorption data yielded a ΔGapp value of −14.6 ± 0.4 kJ/mol, indicating a much less favorable attachment of the monomer to the bilayer relative to PAH (−52.7 ± 0.6 kJ/mol), but a higher percent (88 ± 9%) of the amine groups associated with the monomer were found to be positively charged when compared to the polycation. We hypothesize that PAH adsorption is considerably more favorable because of the entropic gains from 5814
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water molecules and counterions released into the bulk during the adsorption process, yet, less favorable than would be expected from a simple additive model in which the free binding energy of the monomer is multiplied by the number of repeat units in the polycation. The binding site itself was shown by simulations to involve the formation of contact ion groups in which three lipid phosphate moieties coordinate to the adsorbate ammonium cation. Our combination of nonlinear optical spectroscopies, QCMD, and computer simulations open a path for the quantification of the charge density associated with other polycations, possibly with different lengths, spaces between positively charged groups, or amount of shielding of the positively charged groups. Connecting these structural characteristics with the quantification of the interaction of polycations with model cell membranes is important for understanding and controlling polycation-membrane interactions. By systematically analyzing how surface charge changes with variations in polymer structure, work using our approach will provide guidance to the design of polymer materials that have the proper amount of charge for given target applications. Our results also provide experimental constraints for theoretical calculations, which yield atomistic views of the structures that are formed when polycations interact with lipid membranes that will be important for predicting polycation-membrane interactions.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/jacs.6b12887. Details regarding the experiments, fitting procedures, and sample preparation and characterization, and negative controls (PDF)
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AUTHOR INFORMATION
Corresponding Author
*[email protected] ORCID
Joel A. Pedersen: 0000-0002-3918-1860 Qiang Cui: 0000-0001-6214-5211 Franz M. Geiger: 0000-0001-8569-4045 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the NSF under the Center for Sustainable Nanotechnology, CHE-1503408. JMT and ACM gratefully acknowledge support through Graduate Research Fellowships from the U.S. National Science Foundation.
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REFERENCES
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DOI: 10.1021/jacs.6b12887 J. Am. Chem. Soc. 2017, 139, 5808−5816
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DOI: 10.1021/jacs.6b12887 J. Am. Chem. Soc. 2017, 139, 5808−5816
