Supplementary Materials for Real Time SFG Structural Investigation of a Lipid

Bilayer during its Interaction with Melittin

Xiaoyun Chen, Jie Wang, Cornelius B. Kristalyn, Zhan Chen*

Department of Chemistry, University of Michigan, Ann Arbor, MI 48109

SFG Background

In a typical SFG experiment, two pulsed laser beams, one with a fixed frequency in the visible frequency range, and one with a tunable frequency in the infrared frequency range, are overlapped spatially and temporally over the surface/interface of interest. A third beam, the SFG signal, will be generated at the sum frequency of the two input beams. SFG signal intensity I is related to the effective second-order nonlinear susceptibility of the sample surface and the intensities of the two laser input beams by the following equation:

(S1) Different components of can be measured at different polarization combinations of

the three beams involved. For example is measured using s-polarized SFG output,

s-polarized visible input, and p-polarized IR input combination while is measured when the polarizations for all three beams are set to p-polarization. From the measured

components, we can determine various components, (i, j, k can be x, y, or z), of the second order nonlinear susceptibility tensor of the surface, in the laboratory-fixed coordinate system. is a third-rank tensor and has 27 components. However for most biological samples their surfaces are azimuthally symmetric and hence there is a maximum of 7 independent nonzero . Among them is most often used because it probes the vibrational transitions perpendicular to a surface and it can be conveniently measured using the ssp polarization combination. All spectra shown in this paper are collected in this polarization combination unless otherwise specified.

Different components of are selectively probed using different polarization combinations of the input and SFG beams. When the ssp combination is used, the component is measured through the following equation:

(S2), , are the Fresnel factors for the sum frequency, visible input, and

IR input beams respectively, and is the angle between the surface normal and the IR input beam. Equations relating components detected using other polarization combinations to can be found in previous publications (1,2). In Eq. 2 the Fresnel factors and are determined by the experimental setup including input angles, and refractive indices of contacting media. They can be lumped into a proportional factor together with input beam intensity I1 and I2 and local field correction factors (ignored here (3)), so that we have

(S3)

Here is directly related to the observed spectral intensity. The frequency dependence of is described by

(S4)where Aq, ωq, and Γq are the strength, resonant frequency, and damping coefficient of the vibrational mode q respectively, and is the nonresonant background.

Methyl groups are among the best studied functional groups using SFG (4). As mentioned before, we will only focus on the symmetric stretching mode of methyl groups because of its dominant spectral features in both the C-H stretching and C-D stretching ranges for the bilayer system we study here with the ssp polarization combination. Methyl groups are usually treated as having a C3v symmetry, and thus the symmetric stretching mode has only two independent non-zero hyperpolarizibility tensor elements,

and , in the molecular-fixed corordinate system (4,5). For the methyl symmetric stretching mode, is related to through the following equation:

(S5)with being the ratio between and and the brackets denoting averaging over all orientations (1,3). Since and are constants and determined by the structure of methyl groups, it should be clear that spectral intensity of the symmetric stretching mode is directly related to the orientation of methyl groups on a surface and the number density of methyl groups:

(S6)If we take the acyl chain terminal methyl groups from a lipid monolayer as an example, assuming a δ-distribution for the orientation of these methyl groups, we can calculate and plot the relationship of versus θ, as shown in Fig. S1. is at a maximum at an orientation angle of θ=0°, which corresponds to a surface with all methyl groups

perpendicularly oriented. As θ increases, decreases monotonically till it reaches 0 for θ=90o (parallel to the surface).

As a biological sample is unlikely to be perfectly ordered, the assumption of a δ-distribution for orientation angle θ of all methyl groups is oversimplified. We can alleviate this by assuming a certain distribution function such as a Gaussian function for θ:

.

(S7)

For a more or less ordered bilayer unperturbed in its natural state, σ, or the distribution width, in a Gaussian function should be relatively small, while a bilayer whose structure is severely perturbed has a larger distribution width. As

and , the influence of orientation distribution or disordering on spectral intensity can be evaluated. As shown in Fig. S1B, besides number density and orientation, disordering alone can also lead to diminished signal intensity. For a completely random system, no signal will be observed because for every signal-generating moiety, there will be a corresponding one with the opposite orientation so that the signals from them effectively cancel each other.

Figure S1 (A) SFG signals from bilayers are usually dominated by the acyl chain terminal methyl groups. One lipid molecule is highlighted here. Orientation angle θ is the angle between methyl C 3v axis and the surface normal (represented by Z). With a very ordered structure, the lipid’s acyl chain methylene groups are predominantly in all-trans conformation and contribute little SFG signals (the left tail) while a bend in the methylene chain not only causes orientation angle change, but also breaks the local symmetry (the right tail). (B) Dependence of SFG methyl symmetric stretching signal intensity Issp on orientation angle θ and distribution width σ. See text for details.

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SFG Experimental Geometry

Figure S2 Illustration of experimental setup for bilayer-melittin interaction studies and the generation of SFG signals. A total reflection geometry was used. The bilayer was prepared on the right angle face that was immersed in the reservoir containing ~1.8 mL water. The large trough was only used for depositing the second leaflet and was drained before the injection of melittin stock solution.

ATR-FTIR ResultsAs the SFG signal decrease could result from orientation change, flip-flop, and lipid displacement from the surface, ATR-FTIR experiments (not very sensitive towards the first two factors) were carried out to evaluate the extent of lipid displacement.

The absorbance spectrum of a single DPPG/DPPG lipid bilayer immersed in D2O is displayed as the top spectrum in Fig. S3. Both the C-H stretching and C=O stretching modes can be observed. Appropriate amount of melittin stock solution was injected into the solution contacting the bilayer to achieve the concentrations specified in Fig. S3 and the spectra were then taken (with bilayer in D2O as the background spectrum) after at least one hour for the system to equilibrate. At high solution concentrations of melittin, negative peaks were observed in both the C-H and C=O (~1740 cm-1) stretching ranges, indicating part of the lipid molecules originally within the bilayer were displaced from the surface. Some new features were observed between 2800 cm-1 and 3000 cm-1, partially from the peak shift of the bilayer caused by melittin, partially from the C-H moieties from adsorbed melittin molecules. For lower solution concentrations of melittin, only minimal spectral changes could be observed, indicating that the observed SFG signal changes at such concentrations were not due to the negligible lipid displacement.

The noisy features between 2300 cm-1 to 2600 cm-1 were from D2O stretching modes. These features usually manifest themselves as negative peaks when surface water molecules are displaced and as positive peaks when more surface water molecules are present than the background.

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Figure S3 Representative ATR-FTIR spectra of (A) a single DPPG/DPPG lipid bilayer before interacting with melittin, (B) after a DPPG/DPPG bilayer interacted with melittin at 13 M, and (C) after a DPPG/DPPG bilayer interacted with melittin at 0.78 M. (A) was taken with clean ZnSe crystal in D2O as the background. (B) and (C) were taken with a bilayer coated ZnSe crystal in D2O as the background. At 13 M, negative peaks can be clearly seen in C-H stretching range, while almost no such features can be observed for the 0.78 M concentration. All spectra were taken with s-polarization. The dashed lines are intended as guides for the eyes, the assignments for peak 1 through 5 being amide II, amide I, lipid C=O stretching, CH2 symmetric stretching, and CH2 asymmetric stretching modes.

Further analysis of signal change

As mentioned in the paper, SFG signal changes can result from different causes, such as bilayer structural perturbation, transmembrane mixing of lipids (for asymmetric bilayer system), or even displacement of lipids from the solid support surface. ATR-FTIR results indicate that lipid displacement only occurs to a minimum extent below a solution concentration of 1 M (Figure S3). By combining the SFG results obtained using isotopically symmetric/asymmetric bilayers, we can evaluate the contribution of structural perturbation and transmembrane mixing, since the former leads to signal change for both symmetric and asymmetric bilayers while the latter only leads to signal decrease for asymmetric bilayers.

Here we present one set of equations relating the observed signal intensities to the structure of each leaflet of a bilayer and the amount of lipids induced to flip-flop by melittin. The following equations and quantities are based on results obtained with an experimental system using dDPPG/DPPG as the asymmetric bilayer and dDPPG/dDPPG as the symmetric bilayer. When DPPG/dDPPG is used as the asymmetric bilayer, or when DPPG/DPPG is used as the symmetric bilayer, proper subscript changes are required.

(S8)

(S9)

(S10a)

(S10b)

; ; ; (S11)

There are a total of three observed intensities involved at any point of time during the course of bilayer-melittin interactions – the normalized intensity at 2875 cm-1 ( ), the intensity at 2070 cm-1 ( ) from the asymmetric dDPPG/DPPG bilayer, and the intensity at 2070 cm-1 ( ) from the dDPPG/dDPPG symmetric bilayer. Please note that the subscripts “as” and “sy” refer to asymmetric or symmetric bilayers, not asymmetric or symmetric stretching modes. and are the effective 2nd order susceptibilities of the proximal and distal leaflet respectively, contributed from CH3 or CD3 symmetric stretching modes. Though the values of 2nd order susceptibility and SFG hyperpolarizability of CH3 and CD3 groups are different, we can assume the same and

since we are using the normalized . Methyl groups being the dominant signal generating group in both CH and CD stretching ranges, it is reasonable to assume that

, , and are only related to and (this assumption holds true unless the bilayer experiences extensive perturbation such as those induced by melittin concentrations higher than 1 M). Eq. S8-S10 are derived based on the fact that SFG signal intensity is proportional to the square of the effective 2nd order susceptibility, and that the effective 2nd order susceptibility is the vector sum of and . The various experimental parameters such as laser beam intensities, Fresnel factors, input/out beam angles, contacting media refractive indices, etc. can be lumped into the constant c which should remain the same for Eq. S8-S10. Eq. S11 is simply a result of the conservation of lipid molecules, assuming a negligible lipid displacement, and the same number of lipid molecules in each leaflets (for a certain number of lipids that flip from the distal leaflet to the proximal leaflet, the same number of lipids will flip the opposite way). Eq. S11 is used to simplify Eq. S9 and Eq. S10, assuming that the percentage of flip-flopped lipids is N (N ranges from 0, no flip-flop, to 0.5, fully flip-flopped). Depending on the relative magnitude of effective susceptibility from the methyl stretching mode of the two leaflets, Eq. S10 can have two forms. Eq. S10a is applicable when the methyl symmetric stretching signal from the distal leaflet dominates while Eq. S10b is applicable when the signal from the proximal leaflet dominates. Eq. S9 does not have such a complication since the distal leaflet is almost inevitably more perturbed, and the flip-flopped lipids at the equilibrium should not exceed 50%.

From the above analysis, it can be seen that if N, , and can be determined simultaneously, the contribution of structural perturbation and transmembrane mixing can be distinguished, especially for lower concentration experimental where all the above

assumptions should hold true. Interactions between melittin and a DPPG bilayer can thus be quantitatively investigated in terms of the acyl chain terminal methyl groups of each leaflet and lipid flip-flop. However, despite the fact that we have three unknowns (constant c not regarded as an unknown) and three first-order equations, we are disappointed to find that Eq. S8-S10 are not independent and can be simplified into the following equations:

(S12a)

(S12b)

Figure S4 Predicted signal change at 2070 cm-1 for dDPPG/DPPG bilayers interacting with melittin at four representative melittin concentrations. Predicted signal intensities were calculated based on the data shown in Fig. 7 using Eq. S8-S12. See text for details.

Eq. S12a is obtained based on Eq. S10a, and Eq. S12b on Eq. S10b. It dictates that if we know and (both of them can be measured from the dDPPG/DPPG system), then is also known (without having to measure it experimentally from the dDPPG/dDPPG system). To demonstrate the validity of the above analysis, we calculated how from a dDPPG/dDPPG bilayer should change as a function of time based on experimental results obtained from dDPPG/DPPG bilayers as shown in Fig. 7, using Eq. S12. Fig. S4 depicts the calculation results. An overall qualitative agreement between Fig. 6 and Fig. S4 can be observed, illustrating the correctness of the above analysis. However, such results also indicate that based on the three measurements obtained from the asymmetric/symmetric bilayer study, methyl group orientation of each leaflet and the number of flip-flopped lipid molecules cannot be exactly determined. Nevertheless, we still can extract some quantitative interaction information and learn about many interesting phenomena during melittin-bilayer interactions based on Eq. S8-S12. For example, from Fig. 7, the upper limit of structural change as reflected by and can be determined, since the transmembrane mixing

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can only lead to a signal decrease. A practical rule of thumb characterizing the extent of lipid flip-flop can also be defined as follows.

If , no significant flip-flop has occurred; if , there has been significant flip-flop. The rationale is that the CD3 signal (~2070 cm-1) from the dDPPG/dDPPG bilayer system can only exceed that of the asymmetric dDPPG/DPPG system when sufficient lipids flip-flops occur. In another word, adopts the value (which leads to ) when N is sufficiently small, but adopts the value (which leads to ) when N is sufficiently large. It should be pointed out that does not precludes the existence of insignificant transmembrane lipid flip-flop. A quantitative definition of ‘significant’ here depends on the value of and .

Another subtle but interesting observation from Fig. 7 involves the C-H signal intensity change when the bilayer interacted with 0.78 M melittin. Fig. S5A shows that the 2875 cm-1 intensity decreased to zero and then slowly increased. This change is difficult to discern in Fig. 6 due to the scale used. From the above analysis, the moment where the C-H signal decreased to zero corresponded to the situation when

. This time point is where significant flip-flop occurred. Before this point, C-H signal from the distal leaflet dominated since most of the DPPG molecules were in that leaflet. After this transition point, sufficient flip-flop occurred and C-H signal from the proximal leaflet took over. As predicted, Eq. S10a and Eq. S12a applied before this point while Eq. S10b and Eq. S12b became applicable after it. Predicted only matches the observed when the correct form of Eq. S12 is used (Fig. S5B).

Figure S5 Signal intensity change at 2875 cm-1 monitoring melittin (0.78 M) interacting with dDPPG/DPPG bilayers, with melittin injected at time 0 s. The same results are also depicted in Fig. 7 (0.78 M) but with a different scale. The dashed line represents the transition point in time when the C-H signals from both leaflets completely cancelled out ( ). Further signal increase after this point is because the signal from the flip-flopped DPPG in the proximal leaflet overtakes that from the DPPG remaining in the distal leaflet. (B) Comparison between calculated and observed .

and were calculated based on the data shown in Fig. 7

(0.78M). Only the combined results ( before the transition point and

after the transition point) match well with the experimentally observed results. The

combined and the curves are offset by 20 and 40 for clarity.

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