Combined Mass and Structural Kinetic Analysis of Multistate

Here, M1 and M2 represent the mass of bound peptide in each state. .... section) combining mass and birefringence (lower is better, 0 is a perfect fit...
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Combined Mass and Structural Kinetic Analysis of Multistate Antimicrobial Peptide−Membrane Interactions Daniel J. Hirst,† Tzong-Hsien Lee,† Marcus J. Swann,‡ and Marie-Isabel Aguilar*,† †

Department of Biochemistry and Molecular Biology, Monash University, Clayton, Victoria 3800, Australia Farfield Group, Biolin Scientific AB, Klarabergsviadukten 70, House D, Floor 8, SE-111 64 Stockholm, Sweden

‡

S Supporting Information *

ABSTRACT: Kinetic analysis of peptide−membrane interactions generally involves a curve fitting process with no information about what the different curves may physically correspond to. Given the multistep process of peptide−membrane interactions, a computational method that utilizes physical parameters that relate to both peptide binding and membrane structure would provide new insight into this complex process. In this study, kinetic models accounting for two-state and three-state mechanisms were fitted to our previously reported simultaneous real-time measurements of mass and birefringence during the binding and dissociation of the peptide HPA3 (Hirst, D.; Lee, T.-H.; Swann, M.; Unabia, S.; Park, Y.; Hahm, K.-S.; Aguilar, M. Eur. Biophys. J. 2011, 40, 503−514); significantly, the mass and birefringence are constrained by the same set of kinetic constants, allowing the unification of peptide binding patterns with membrane structure changes. For the saturated phospholipid dimyristoyl-phosphatidylcholine (DMPC) the two-state model was sufficient to account for the observed changes in mass and birefringence, whereas for the unsaturated phospholipid 1-palmitoyl-2oleoyl-sn-glycero-3-phosphocholine (POPC) the two-state model was found to be inadequate and a three-state model gave a significantly better fit. The third state of interaction for POPC was found to disrupt the bilayer much more than the previous two states. We propose a hypothesis for the mechanism of membrane permeabilization based on the results featuring a loosely bound first state, a tightly bound second state, and a highly membrane-disrupting third state. The results demonstrate the importance of the difference in membrane fluidity between the gel phase DMPC and the liquid crystal phase POPC for peptide−membrane interactions and establish the combination of DPI and kinetic modeling as a powerful tool for revealing features of peptide− membrane interaction mechanisms, including intermediate states between initial binding and full membrane disruption.

T

surface creating defects that allow passage of solutes, the sinking-raft model,17 and others. However, these models typically best describe the end state of the permeabilization process, with the process from initial membrane binding to the final disrupted state remaining unclear. Moreover, these models are likely to be a simplification, and in reality the activity of AMPs may combine aspects of multiple mechanisms. To determine the details of such mechanisms, the kinetic properties of the destabilization process must first be investigated. Kinetic models of peptide−membrane interactions simulate a pathway from initial peptide binding to the final state of membrane permeabilization, giving insights into potential intermediate states and rates of reaction. This knowledge is vital for understanding antimicrobial peptide efficacy since the rate of the overall process is limited by its slowest steps; the creation of improved antimicrobial peptides should be guided by understanding of the most important intermediate states in the interaction process. Recent studies have shown that while

he rapid increase in antibiotic resistance among bacterial pathogens is a major problem for health care services2 with hundreds of thousands of hospitalizations and tens of thousands of deaths per year.3 Despite the urgent need for new antimicrobial agents, there has been a substantial decline in new therapeutics brought to the market in recent years.4 Antimicrobial peptides (AMPs) offer several advantages compared with conventional small-molecule drugs; they are much less susceptible to antibiotic resistance and have a broad spectrum of activity.5 However, low efficacy and bioavailability, high cost, and toxicity has hampered use of AMPs as therapeutic drugs.6 AMPs are widely believed to act principally by disrupting and permeabilizing the cell membrane.7,8 However, a lack of clear understanding of the precise processes by which this occurs has hindered the rational design of improved AMPs.6 A number of conceptual models have been proposed for the mechanisms by which antimicrobial peptides cause membrane permeabilization.6 These include the barrel−stave pore model,9−11 in which peptides insert into the bilayer forming a hydrophobic channel, the toroidal pore model,12,13 in which peptides form pores by inducing local curvature in the bilayer, the carpet model,11,14−16 in which peptides perturb the membrane © 2013 American Chemical Society

Received: July 4, 2013 Accepted: September 3, 2013 Published: September 3, 2013 9296

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membrane. Our initial findings indicated that a simple two-state model is insufficient to describe the features of peptide binding once birefringence is taken into account in the analysis, and the introduction of a third state is necessary to provide a wellfitted model. We believe the ability to discern a link between individual peptide states and bilayer membrane disruption is unprecedented in the literature.

initial binding typically takes place on time scales of seconds, or even milliseconds,18 further processes may occur over time scales of minutes or hours.19,20 The study of biological interaction kinetics has been greatly aided by the development of optical biosensor techniques, particularly surface plasmon resonance (SPR). Data from these instruments suggested that simple bimolecular interactions (for surface interactions, known as Langmuir binding) were inadequate in some cases to explain the obtained sensorgrams for protein−protein interactions.21 This led to the development of two-state kinetic models, first theoretically22 and then fitted to experimental data.23 This concept was later applied to peptide− membrane interactions for the antimicrobial peptides magainin and melittin, as well as other peptides.24−27 These studies gave good fits when modeling the mass of peptide bound to the membrane over time. However, other techniques for measuring membrane structure suggest a more complicated picture,1,28 indicating that between initial binding and the final, active state there may be one or more intermediate steps. Recent studies have suggested models for peptide−membrane interactions involving three bound states using linear dichroism19 and fluorescence spectroscopy.20 While these approaches provide insights into the role of the peptide in the interaction process, the state of the membrane remains poorly studied. Since AMPs operate by directly disrupting membranes, determining the role of the membrane in the process is crucial to understanding their activity. The effect of membrane properties such as charge, polarity, fluidity, internal structure, and curvature may all affect interactions between peptides, and dynamic changes in membrane structure are likely to be a feature of the mechanism of membrane permeabilization. However, the real-time effects of these features remain poorly studied. Dual polarization interferometry (DPI) allows the simultaneous measurement in real time of the mass bound to and the birefringence (i.e., membrane ordering) of a lipid bilayer,29 providing information on the kinetics of membrane deformation and disintegration associated with various stages of peptide binding. This data therefore has the potential to be used to elucidate features of the mechanism of action for AMPs. In this study, we used the output of DPI from our previous research1 to fit kinetic models designed to approximate possible interaction processes. The aims of this study were twofold: first, to develop multiple-state kinetic modeling techniques for characterizing peptide−membrane interactions, by combining mass and birefringence data obtained using the DPI, and second, to use these techniques to investigate differences between the binding of an antimicrobial peptide (HPA3) to saturated gel phase [dimyristoyl-phosphatidylcholine (DMPC)] and unsaturated fluid phase (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC)] lipid bilayers, and the characterization of individual states involved in those processes. These two lipids have been chosen on the basis of the otherwise comparable properties such as identical headgroup chemical structure and bilayer thickness. The models assume a sequential pathway for each peptide that includes either two or three states in the binding mechanism (a one-state model was easily rejected and was not studied in detail). Previous models have only taken into account the amount of peptide bound to the membrane. Using the birefringence data obtained from the DPI, we fit both mass and birefringence simultaneously, allowing the more detailed investigation of intermediate stages of binding and the study of the impact of individual peptide states on the structure of the

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METHODS Dual Polarization Interferometry. The methods used to generate the experimental data used in the development of the kinetic models were described previously.1 Briefly, the buffer (10 mM MOPS, 150 mM NaCl, pH 7) and unmodified silicon oxynitride chip were calibrated as previously described.1 The transition temperature for DMPC bilayers is 23 °C30 and that for POPC is −2 °C,31 allowing the influence of bilayer fluidity to be investigated as the data used in this study was obtained at 20 °C. The unilamellar DMPC and POPC bilayers were prepared by depositing the 100 nm liposome solution on the chip in the presence of 1 mM CaCl2.1 The resulting bilayer properties were highly consistent and reproducible as shown in Supporting Information Table S1. Following bilayer formation on the chip, a solution of 10 μM HPA3 was injected at 40 μL/min for 240 s followed by washing with buffer to remove loosely bound peptide. This procedure results in a binding phase lasting about 200 s (once the delay in starting the injection is taken into account), during which the lipid bilayer is exposed to the peptide solution, followed by a buffer wash (dissociation phase) lasting for a duration of at least 15 min. The DPI gives raw output in the form of phase shifts for transverse magnetic (TM) and transverse electric (TE) polarization modes. Analysis of this raw experimental data using Analight Explorer gives simultaneous measurements of mass per unit area and birefringence as previously described in detail in several reports.28,29,32−35 Two-State Model. The basic two-state model24 describes the following process, where P and L are the unbound peptide and lipid, respectively, P1 and P2 are the first and second membrane-bound peptide states, and L1 and L2 are the corresponding membrane states: ka2 ka1 P + LHoooIP1L1HoooIP2L 2 kd1 kd2

(1)

with differential equations dM1 = ka1C P(mp* − M1 − M 2) − kd1M1 − ka2M1 + kd2M 2 dt (2a)

dM 2 = ka2M1 − kd2M 2 dt

(2b)

Here, M1 and M2 represent the mass of bound peptide in each state. CP is the effective molar concentration of the peptide in solution, m*p is the (constant) maximum amount of bound peptide (without taking into account any loss of peptide binding sites from bilayer expansion; see below), and ka1, kd1, ka2, and kd2 are the rate constants of the reactions in eq 1. To take into account the possibility of bilayer expansion resulting in a loss of mass per unit area, the equations were modified to 9297

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a Bold numbers are the values of the parameters for the best fit. Numbers in brackets are an estimate of the range of each parameter that permits an error no more than 25% greater than the best fit (see the Supporting Information for details of the calculation of these ranges). bm*p : maximum mass of peptide on membrane assuming full coverage. cka1, ka2, ka3: first, second, and third binding association constants. dkd1, kd2, kd3: first, second, and third binding dissociation constants. en1, n2, n3: membrane disordering parameter for state 1, state 2, and state 3, respectively. feL: bilayer expansion coefficient (dimensionless). Lipid mass loss per unit of peptide in the final state (usually positive values indicate mass loss). gFit: combined least-squares error (see the Methods section) combining mass and birefringence (lower is better, 0 is a perfect fit, no upper limit).

1.20 (0.86−1.65) −6.90 −4.53 −10.1 (−7.80to−6.08) (−5.65to−3.31) (−16.6 to −7.7) 9.2 (6.0−14.4) 18.5 (11.8−30.8)

0 (0−9.4)

0.53 (0.37−0.86

2.1 (1.8−2.7)

0 (0−5.7)

3.74 (2.11−7.35) 3.50 (2.44−5.27)

0.498

0.81 (0.59−11.66) 1.372 −5.47 −8.65 (−6.04to−4.95) (−12.0 to −6.2)

7.02 (4.8−11.5)

0.070 3.21 (1.22−23.2) −5.43 −4.46 1.1 (−7.1 to 7.1) (−5.60to−5.28) (−4.53to−4.39)

0.182

3217 (2639−4101)

RESULTS Modeling Rationale. Using previously reported experimental data,1 a basic two-state model, as used in Mozsolits et al.,24 was first attempted, with birefringence modified linearly

0.587 (0.568−0.606)

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1.5 (0.7−2.2)

A detailed discussion and derivation of equations is provided in the Supporting Information. Numerical Modeling. Details of the numerical methods used are provided in the Supporting Information. Parameters for the best fit for each bilayer are listed in Table 1. The quality of fit was determined by a weighted least-squares method taking into account both modeled mass and birefringence, and estimates of the variation in each parameter are also listed in Table 1. An additional term was also added to the model to account for the shape of the concentration transition at the beginning and end of the injection due to the fluidic system of the DPI (see the Supporting Information and Table S2); these adjustments do not significantly affect the main conclusions of this study.

3528 (2923−4489)

(7b)

0.488 (0.462−0.518)

B(t ) = n1M1(t ) + n2M 2(t ) + n3M3(t )

12.6 (10.8−15.4)

(7a)

49.6 (41.3−62.4)

M(t ) = M1(t ) + M 2(t ) + M3(t )(1 + eL)

9731 (8934−10825)

and total mass and birefringence calculated by

0.808 (0.798−0.820)

(6c)

6.9 (3.5−10.8)

dM3 = ka3M 2 − kd3M3 dt

10.2 (8.3−13.1)

(6b)

36.8 (27.9−51.5)

dM 2 = ka2M1 − kd2M 2 − ka3M 2 + kd3M3 dt

9475 (8416−11368)

(6a)

0.812 (0.785−0.848)

− kd1M1 − ka2M1 + kd2M 2

Table 1. Model Parameters Giving the Best Fit for Each Peptide−Membrane Systema

⎛ ⎛ ⎞ eM ⎞ dM1 = ka1C P⎜⎜mp*⎜1 − L 3 ⎟ − M1 − M 2 − M3⎟⎟ dt mL ⎠ ⎝ ⎝ ⎠

DMPC twostate DMPC threestate POPC twostate POPC threestate

with differential equations

5.1 (3.0−6.6)

n2 (× 10−3) mm2 ng−1e kd3 (× 10−3) s−1d

(5)

ka3 (× 10−3) s−1c

ka3 ka2 ka1 P + LHoooIP1L1HoooIP2L 2HoooIP3L3 kd1 kd2 kd3

n1 (× 10−3) mm2 ng−1e

where M(t) and B(t) represent the total (peptide and lipid layer) mass and birefringence change relative to an unperturbed bilayer at time t. Three-State Model. The three-state model is an extension of the two-state model represented by the following schematic:

kd2 (× 10−4) s−1d

(4b)

ka2 (× 10−3) s−1c

B(t ) = n1M1(t ) + n2M 2(t )

kd1 (× 10−3) s−1d

(4a)

ka1 M−1 s−1c

M(t ) = M1(t ) + M 2(t )(1 + eL)

n3 (× 10−3) mm2 ng−1e

where mL is the total lipid mass prior to injection and eL is a parameter of the model for the proportionality between peptide in state 2 and lipid mass loss. The peptide states are related to the time-series mass and birefringence data by

0.15 (0.10−0.17)

eLf

(3b)

m*p ng/mm2b

dM 2 = ka2M1 − kd2M 2 dt

(3a)

lipid

− ka2M1 + kd2M 2

errorg

⎛ ⎛ ⎞ eM ⎞ dM1 = ka1C P⎜⎜mp*⎜1 − L 2 ⎟ − M1 − M 2⎟⎟ − kd1M1 dt mL ⎠ ⎝ ⎝ ⎠

−5.05 −4.32 (−5.30to−4.80) (−4.45to−4.18)

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the DMPC membrane increased to about 0.65 ng/mm2. There is an initial period of rapid binding, after which the rate of binding decreases rapidly, flattening the binding curve (Figure 1A, blue curve). At the same time, the birefringence drops in a similar manner, first rapidly, and then flattening out (Figure 1B, blue curve). During the dissociation phase, the mass of peptide decreases and the birefringence increases, as would be expected for peptide dissociation from the membrane. However, both changes remain significantly different from the preinjection levels, even after 30 min, indicating that a significant amount of peptide has not dissociated. Using the birefringence−mass curve (Figure 1C, blue curve) to directly compare peptide binding to membrane changes, it can be seen that the birefringence− mass relationship is essentially linear, indicating a proportional relationship between the two variables. Analysis of Binding to DMPC Using a Two-State Model. One-state modeling was found to be inadequate for modeling the binding curve; one-state models always show the mass of peptide bound quickly returning to zero in the dissociation phase, whereas we see a rapid initial drop, but retention of a substantial portion (>50%) of the mass. A twostate model (Figure 1, parts A and B, red line) was found to give a very good fit to both the mass and birefringence, with a combined least-squares error of 0.182. Viewing the deconvolution of these states (Figure 1, parts A and B), we see that the peptide binds rapidly to the membrane in state 1, then gradually converts into state 2 over the course of the binding phase. In the dissociation phase, the amount of state 1 peptide drops away rapidly to almost zero, while the amount of peptide in state 2 remains relatively stable, dropping only very slowly. The membrane disordering parameter of both states is quite similar (Table 1, n1 vs n2) (−5.05 × 10−3 for state 1 vs −4.32 × 10−3 for state 2), suggesting that the difference between the two states has only a minor impact on membrane structure. The two states appear to represent a switch from a more labile state (state 1, which dissociates rapidly) and a stably bound state (state 2, which dissociates only very slowly). Indeed, this difference can be seen in the difference between the kd1 and kd2 values, where kd1 is >50-fold higher than kd2, indicating a much slower dissociation for the second state compared to the first. The modeling also indicates a small amount of membrane expansion, of about 0.1 ng/mm2 or 2% of the total lipid mass. Analysis of Binding to DMPC Using a Three-State Model. While the two-state model already gives a very good fit to the data for binding to DMPC, we also applied the threestate model to investigate whether it would further improve the fit, and the results are shown in Supporting Information Figure S1. The combined least-squares error for the three-state fit was 0.070, indicating a significant improvement over the two-state model, although the original two-state fit was already quite good, matching the general features of the mass and birefringence curves. Considering the deconvolution for this model, the first two states are very similar in their shape to the twostate model for both mass and birefringence (comparing parts A and B of Figure 1 with parts A and B of Supporting Information Figure S1). The main difference is the third state, which accounts for only a small proportion of the peptide mass and has virtually zero (and indeed slightly positive) contribution to birefringence (Supporting Information Figure S1B), but results in a relatively significant reduction in lipid bilayer mass of about 0.13 ng/mm2 (Supporting Information Figure S1B, yellow line). We consider the presence of a state with a zero contribution to birefringence to be physically unlikely

in proportion to each peptide state (as in eq 4b above). The membrane disordering coefficient quantifies the proportionality between the mass of peptide in one state and the disordering effect that the peptides in that state have on the membrane. A negative value of this parameter indicates a disordering effect (relative to unbound membrane), while a positive value (which is infrequently observed) would indicate an ordering effect. For negative values, the magnitude of the number indicates the degree of disruption of the membrane structure. As discussed below, while such a model gave a good fit with the binding to DMPC, it gave a very poor fit with the binding to POPC; in particular, such a model was incapable of replicating the decrease in birefringence during the dissociation phase. Introducing a three-state model improved the fit for POPC somewhat, but had little effect on the fit for DMPC. However, for POPC in particular, the decline in mass in the final stages of the injection (Supporting Information Figure S6A, blue line) was still poorly replicated, with the model showing a steady increase in mass toward the end of the injection. We considered two main hypotheses to explain this discrepancy; either the peptide concentration declines significantly during the injection due to imperfect fluidics (a decline of about 30% is required to match the data) or the lipid bilayer itself loses mass per unit area (whether by general expansion, lipid molecule displacement by insertion of the peptide, or the removal of lipid from the surface). We chose to model the latter hypothesis in detail since there was a distinct difference in the magnitude of the effect between DMPC and POPC bilayers across multiple experimental runs, suggesting that it is related to the bilayer properties rather than peptide concentration (which was constant across all experiments). Also, only 160 μL of the 200 μL loop was injected to prevent such a drop in peptide concentration. Bilayer expansion was modeled by assuming a linear decrease in bilayer mass proportional to the mass of peptide in the final state (i.e., the second state for the two-state model and the third state for the three-state model). Indeed, accounting for lipid bilayer expansion, using eqs 3 and 4 for the twostate model and 6 and 7 for the three-state model, resulted in improvements in the fit in all cases, although the effect was much more pronounced for the three-state model, reducing the error by more than half for both bilayer types and satisfactorily matching the main qualitative features of binding and dissociation for the three-state model (but not the two-state model) on POPC. These findings are supported by recent atomic force microscopy (AFM) observations of laterally expanding pores induced in lipid bilayers by antimicrobial and neurodegenerative peptides.36,37 For ease of comparison, only the model results using bilayer expansion are shown in full below in Table 1. See the Supporting Information for the table of parameters (Table S3) and figures (Figures S3−S6) for the model results without bilayer expansion. An important feature of this modeling is the ability to link membrane structure changes to peptide states. This is quantified by the membrane disordering parameter for each state, which describes the amount each given peptide in the state contributes to disordering the membrane. Large (more negative) values indicate a highly disruptive effect, while smaller values (closer to zero) indicate states with a less disruptive effect on the membrane. Binding of HPA3 to DMPC. Figure 1A−C shows the binding of 10 μM HPA3 to DMPC fitted with a two-state model. During the binding phase, the mass of HPA3 bound to 9299

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Figure 1. Binding of 10 μM HPA3 to DMPC fitted with a two-state model (left column) and to POPC fitted with a three-state model (right column): (A) comparison and deconvolution of mass change vs time for binding to DMPC fitted with a two-state model; (B) comparison and deconvolution of birefringence change vs time for binding to DMPC fitted with a two-state model; (C) comparison of birefringence change vs mass change for binding to DMPC fitted with a two-state model; (D) comparison and deconvolution of mass change vs time for binding to POPC fitted with a three-state model; (E) comparison and deconvolution of birefringence change vs time for binding to POPC fitted with a three-state model; (F) comparison of birefringence change vs mass change for binding to POPC fitted with a three-state model. Blue lines: experimental data. Red lines: models fitted to the data using a two-state model (for panels A−C) or a three-state model (for panels D−F). Gray lines: models fitted to the data using a two-state model for purposes of comparison (POPC only). Green lines: deconvolution of model state 1. Magenta lines: deconvolution of model state 2. Cyan lines: deconvolution of model state 3 (POPC only). Yellow lines: effect of supported bilayer expansion (mass vs time plots only).

(although possible), and this improved fit may be a result of spurious overfitting rather than a reflection of actual physical events. It should also be noted that the improvement in fit between the two-state and three-state models is almost entirely due to the model’s simulation of bilayer expansion; comparing two-state and three-state models without bilayer expansion gives combined least-squares errors of 0.210 and 0.203, respectively (Supporting Information Table S3). Binding of HPA3 to POPC. The binding of HPA3 to POPC appears superficially similar to DMPC, with a rapid binding and partial dissociation (Figure 1D, blue line).

However, there is a significant difference in the birefringence curve during the dissociation phase (Figure 1E, blue line), where after an initial small increase, the birefringence continues to decline to the point where it fell below even the minimum observed in the binding phase. This observation suggests that the bound peptide continues to further disrupt the membrane despite a significant proportion of the peptide dissociating. Analysis of Binding to POPC Using a Two-State Model. Supporting Information Figure S2 shows the binding of 10 μM HPA3 to POPC fitted with a two-state model. While the two-state model can give quite a good fit for the binding 9300

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curve of mass alone, it gave a poor fit once birefringence is included. Comparing the best fit-model with the data (Supporting Information Figure S2, parts A and B) it can be easily seen that the model cannot fit the data, with important features missing such as the rapid drop in mass at the onset of the dissociation phase and the gradual decrease in birefringence during the rest of the dissociation phase. Such a divergence shows that the two-state model is incapable of adequately representing this interaction once membrane structure dynamics are taken into account. The combined least-squares error of this model for binding to POPC is 1.372, more than 7 times higher than the two-state model for binding to DMPC, again indicating a much poorer fit. Analysis of Binding to POPC Using a Three-State Model. Figure 1D−F shows the binding of 10 μM HPA3 to POPC fitted with a three-state model. Use of a three-state model resulted in a significantly improved fit, with the combined least-squares error at 0.498, more than a 3-fold improvement over the two-state model (shown in gray for comparison), although not as close as the fits to the DMPC binding curve. Nonetheless, the three-state model clearly shows a much closer match to the actual data than the two-state model (two-state fit from Supporting Information Figure S2 is shown in Figure 1D−F as a gray line for comparison), both quantitatively and qualitatively. In particular, the gradual decrease in birefringence in the dissociation phase is fully accounted for. There is still some discrepancy in the binding phase, in which the reduction in birefringence after the initial rapid decrease is slower in the experimental data than the model suggests. The fit for the mass, on the other hand, is very good, with only minor discrepancies. An additional consideration here in favor of the three-state model is its robustness: the three-state model continues to track the experimental data to the end of the time period (Figure 1, parts D and E), so it is likely that small changes in the end point would have a negligible effect on the model statistics. However, the two-state model diverges significantly in both mass and birefringence (Supporting Information Figure S2, parts A and C) such that a small change in time period might significantly affect the model statistics. Deconvolution of the three states (Figure 1, parts D and E) reveals that the first two states show a similar pattern to the two states seen when binding to DMPC: the initial rise in the binding is almost entirely by peptide binding in state 1, which then gradually converts to state 2 during the rest of the binding phase. During the dissociation phase, the amount of peptide in state 1 rapidly falls to near zero, while the peptide in state 2 falls away much more slowly. However, in contrast to the models for binding to DMPC, here we see a substantial conversion of state 2 to a new state 3. The mass of the peptide in this state remains only a fraction of the total, but its effect on birefringence (Figure 1E) is very significant: at the end of the model run this state accounts for about 75% of the effect on birefringence, despite only accounting for about 50% of peptide mass. This is due to the membrane disordering parameter for state 3 being significantly larger (n3 = −10.1 × 10−3) than for the previous states (n1 = −6.90 × 10−3, n2 = −4.53 × 10−3) (Table 1). Furthermore, the amount of peptide in this state continues to increase during the dissociation phase; it is the continued conversion of state 2 into state 3 that allows the birefringence to continue to decrease further. The significant improvement to the fit, from both a quantitative and qualitative perspective, together with the larger contribution from the added third process demonstrates that the closer fit is likely to

be due to a genuinely closer approximation of the actual process, and not merely the automatic improvement to a fit from adding additional parameters (even if not justified) as may be the case for the binding to DMPC. This is also consistent with our previous study1 in which we reported very different circular dichroism (CD) spectra for HPA3 in DMPC and POPC in their equilibrium bound states.

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DISCUSSION Proposed Mechanism, Including the Roles of Each State. Previous evidence has pointed toward at least a twostate model for the activities of membrane-active peptides such as the antimicrobial peptides,24−27 usually involving an initial binding state and a conformational change into an active state. However, further examination of intermediate states between these two events has, until recently, been hampered by the lack of analytical techniques capable of clearly distinguishing such states. Our previous study1 showed clear qualitative differences in binding mechanism between DMPC and POPC, with a more complex mechanism for POPC, but at the time these differences could not be quantified. The evidence provided here strongly suggests that, while a two-state model may be effective in modeling the binding of HPA3 to DMPC, it is inadequate for modeling binding to POPC, since the fit to the two-state model was poor and did not match the features of the binding data. On the other hand, the three-state model, while not ideal, clearly showed a much better fit. The feature allowing this distinction is the ability of the DPI technology to simultaneously measure mass and birefringence; without the birefringence data, the POPC mass data alone can be fitted adequately using a two-state model. With the birefringence, however, the two-state model cannot fit both the mass and birefringence simultaneously, while a more complex three-state model allows for the fitting of this more complex process. By examining the parameters for the models, not only can the number of states be determined, but useful information about these states and the conversions between them can be obtained from the model parameters providing the best fit. While some caution should be used regarding the absolute values of the parameters, since a good fit can be obtained with a range of values, substantial differences are useful for guiding potential physical explanations. On the basis of the data shown, we propose a three-state model for binding of HPA3 to the bilayer (for which the third state may not be present when binding to DMPC), as represented in eq 5 (in the Methods section) and depicted in Figure 2.

Figure 2. Schematic depicting the interconversion of states 1 (P1L1), 2 (P2L2), and 3 (P3L3) in the binding of HPA3 to a fluid phase phospholipid bilayer fitted with a three-state model.

Some recent studies have also reported three-state models for peptide−membrane interactions. Ennaceur et al. reported a rapid process followed by two slow processes for a model cyclic peptide binding to an egg phosphatidylcholine membrane.19 9301

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A significant observation is the improved fits obtained with the inclusion of a lipid removal or expansion coefficient eL. Lipid removal through dissolution or solubilization of the lipid is not considered a likely scenario, as this process would be expected to eventually remove the entire bilayer from the chip surface, something that has not been observed here. The observation of bilayer expansion at the same time as peptide insertion or pore formation can be expected to be a fundamental requirement of a system where a dynamic surfacebound bilayer accommodates inserted peptides and pores, with the peptide or pore taking the place (per unit area) of some of the lipid in the structure, as has been observed for these peptides with scanning electron microscopy38,40 and other peptides by atomic force microscopy.36,37 In addition, the degree of membrane disruption by HPA3 has been shown to increase with increasing unsaturation of the lipid acyl chains.41 Macroscopically for the measurement on a planar bilayer this implies at least a transient increase in lipid pressure and a significant lateral displacement of lipid, something that is usually ignored in planar bilayer measurements in general. The observation of such expansion is reasonable since the flow cell configuration allows the bilayer to expand outside of the detection window. One valid question is whether the mobility of the lipid is sufficient for such an effect to take place. The diffusion coefficient of a lipid molecule in POPC is 1.9 × 10−11 m2 s−1,42 meaning that by diffusion alone, a lipid molecule can travel >6 μm s−1. This means that over the time scale of the sample injection a lipid molecule could travel several times the half-width of the 1 mm fluidic channel in which the measurement is made. So the bilayer has more than sufficient mobility for peptide accommodation via macroscopic bilayer expansion to occur. Another interesting point to note is that the value obtained for the expansion coefficient, close to unity for POPC, is within the expected range for such a displacement process due to peptide insertion. Furthermore, it can be anticipated that the size of this coefficient will vary with the size of the membrane defect, or the footprint of the peptide within the bilayer. Given the above model, it appears from our results that the transitions between the second and third state are most critical for peptide activity, as this has both a low ka value (indicating slow transition to the third state) and a high kd value (indicating more rapid return to the second state). Hence in order to improve peptide efficacy, the most effective strategy would involve increasing the ka3 or decreasing the kd3, or both. Alternative Models. While the above results clearly show that the sequential two-state model is insufficient for explaining the binding dynamics observed for binding to POPC, it is less clear what the alternative model should be. Here we have shown a sequential three-state model, which shows a clear improvement in fit and is conceptually a simple extension of the two-state model. However, alternatives are possible, and our preliminary testing suggests that a model simulating a two-state with a separate simple one-state pathway (which may arise, for example, if the peptide exists as a dimer in solution which then binds to the bilayer differently to the monomer) also provides a significant improvement in fit. Other considerations may include extending the model further to a four-state model (whether sequential or some form of parallel reactions), accounting for cooperativity in the conversions between states, adding a time lag between mass and birefringence changes for each state, and using a nonlinear relation between mass and birefringence. For such investigations, however, it is important to keep the following in mind: (1) complex models including

Ningsih et al. also found, for a modified melittin peptide, that a three-state process was needed to represent fluorescence lifetime measurements, suggesting rapid initial binding, a slower second process (or combined processes) to form intermediates, and a third process resulting in pore formation.20 In our model, the peptide binds initially in the state P1L1, and then gradually converts from P1L1 to P2L2, and also from P2L2 to P3L3. At first, most bound peptide will be in state P1L1, then there will be a mix of P1L1 and P2L2, and finally a mix of all three states P1L1, P2L2, and P3L3. The first state, which we may call a “loose” or “labile” state, is formed by the peptide binding rapidly to the surface from solution and dissociating at a fairly rapid rate. This state accounts for the rapid binding of the peptide at the start of the binding phase and for the initial drop in mass at the beginning of the dissociation phase. This description is supported by the model parameters: the ka1 values are in the thousands, showing that significant binding may occur, and rapidly, even at micromolar concentrations; the kd1 values are at about 0.02, indicating reasonably quick dissociation (equivalent to about 70% of the peptide dissociating per minute). The second state is a “tightly bound” state; it is formed by a conformational change from the first “loose” state by a rearrangement of the peptide to adjust to the flexible membrane structure. This state forms at a reasonable rate from the peptide in the forward reaction from the first “loose” state, but the reverse reaction is very slow: peptide bound in this state tends to stay bound; only about 6% (on POPC, and even less on DMPC) converts back to the first state per minute, according to the kd2 value of 0.001. This state accounts for the fact that a significant mass of peptide remains bound to the membrane even after a long period of time is allowed for the peptide to dissociate. Looking at the membrane disordering parameter for these first two states we can see they are quite similar for both DMPC and POPC, although the second state is somewhat smaller for both lipids. This suggests that the transformation between these two states is related more to the peptide, although there may be some easing of membrane disruption, and is consistent with our previous study1 in which we reported different CD spectra for HPA3 in DMPC and POPC. The decrease in the magnitude of membrane disordering in the present study was somewhat surprising as it was not immediately visible from the plots in our original study;1 indeed, one might expect subsequent states to have successively larger impacts on the birefringence as the disruption process progresses, but the current analysis suggests that this may not always occur. The third state is the “disruptive” state (only clearly identifiable when binding to POPC), in which the peptide dramatically disrupts the bilayer to which it is bound. This state appears quite slowly, since its formation first requires the peptide to undergo the first two reaction steps. Once this state is formed, however, it results in significant disordering of the membrane, with the membrane disordering parameter at least an order of magnitude higher than that for the previous two states. We believe this state is responsible for the formation of defects in the membrane that allow the leakage of molecules through the membrane.38,39 The parameters for the conversion from the second state to the third indicate that, given enough time, the two states exist in equilibrium, although the total amount of peptide will be gradually reduced by the slow conversion of peptide in state 2 to state 1, which then dissociates. 9302

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many parameters may take a very long time to “locate” the best fit; often even the three-state model shown above ends up trapped in a local minimum, despite better fits being possible; (2) the addition of parameters to models can only be justified when the fit is significantly improved. Kinetic modeling is often performed by fitting a range of concentrations using the same parameters. However, we found that the parameters that resulted in a good fit for one concentration did not necessarily fit well for other concentrations. We believe that this is due to the complexity of peptide− membrane interactions and the changes in membrane structure at different peptide loadings; in reality rather than two or three distinct states there is likely a continuum of different states, of which the three identified here are the most prominent and long-lasting at this concentration. So, for example, if state 2 represents a reordered peptide−lipid complex on the bilayer surface, the size of this complex may be concentrationdependent, and if state 3 represents the formation of a porelike structure, this may also vary in size with peptide concentration. Given the complexity of the system it is therefore unlikely to find parameters that are consistent across a wide range of concentrations, without adopting a much more complex model. However, we do find that the same general patterns apply; for example, for HPA3 binding to POPC, n3 < n1 < n2 (where n1, n2, and n3 are the membrane disordering coefficients for the three states) applies regardless of concentration, even though the values themselves may differ somewhat. Differences in mechanism due to concentration have been reported for the human antimicrobial peptide LL-37, where up to three different types of interactions were reported for differing concentrations.43 Contrast between Binding to DMPC and POPC. When constructing a model biophysical membrane for the analysis of peptide−membrane interactions, the main criterion for the composition of the model membrane has been the headgroup and, in particular, its charge. Charge plays an important role in peptide−membrane interactions due to electrostatic interactions between charged amino acid residues in the peptide and the charged headgroups of lipid molecules. Charge is also biologically significant, since prokaryotes typically have zwitterionic lipid headgroups while eukaryotes have anionic headgroups. The results here show, on the other hand, that hydrophobic acyl chains on the interior of the membrane also play an important role in determining the mechanism of peptide binding, in this case causing a switch from what appears to be primarily two-state binding to a more complicated mechanism, likely with three states, and certainly inconsistent with a two-state mechanism, confirming the difference we1 and others41 have observed in previous studies. We believe this is a result of the increased fluidity of the POPC membrane; at the experimental temperature of 20 °C, DMPC is in the gel phase, a fairly rigid and well-ordered structure that restricts the movement of the peptide and restricts insertion, while POPC is in the fluid phase, a more flexible structure that allows penetration by the peptide into the bilayer. These results further underscore the significance of the lipid properties in biophysical peptide−membrane studies.

greatly enhanced. In particular, crucial information about the response of the lipid bilayer to peptide binding can be quantitatively analyzed, allowing the description of the peptide−membrane system in terms of distinct intermediate states with different levels of membrane disruption. Using this data, we have proposed a hypothesis about the binding of HPA3 to fluid state membranes: first, peptides bind rapidly to the membrane to form the first state, which is only loosely attached to the membrane and has a high dissociation rate, but still some membrane disruption; peptides progress more slowly to the second state, which is a reorganization of peptides into a more tightly bound position with some membrane rearrangement; finally, a third state which causes significant membrane disruption, accompanied by membrane spreading, which is much more significant with POPC. The results also reveal a quantitative difference between binding to DMPC and POPC and highlight the importance of the appropriate selection of model membranes for biophysical studies.

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ASSOCIATED CONTENT

S Supporting Information *

Figures of mass and birefringence vs time and mass vs birefringence for models assuming no supported lipid bilayer expansion. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +61-3-9905-3723. Fax: +61-3-9902-9500. Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The financial support of the Faculty of Medicine, Nursing & Health Sciences, Monash University, ATA Scientific, the Australian Research Council, the Potter Foundation, the National Heart Foundation and the European Union Framework Project 7 ASMENA is gratefully acknowledged.

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REFERENCES

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CONCLUSIONS While kinetic modeling is already a powerful tool for analyzing sensorgrams for mass changes, here we have shown that by extending the methods to cover a measure of membrane structure, that is, birefringence, the knowledge gained can be 9303

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