Colloids and Surfaces B: Biointerfaces 132 (2015) 34–44
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Stability and softening of a lipid monolayer in the presence of a pain-killer drug Uttam Kumar Basak a , Alokmay Datta a , Dhananjay Bhattacharyya b a b
Surface Physics and Material Science Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar City, Kolkata 700064, India Computational Sciences Division, Saha Institute of Nuclear Physics, Kolkata 700064, India
a r t i c l e
i n f o
Article history: Received 23 December 2014 Received in revised form 24 April 2015 Accepted 27 April 2015 Available online 8 May 2015 PACS: 68.18.−g 83.60.Bc 87.14.Cc 83.10.Mj Keywords: Langmuir monolayer Algebraic relaxation Softening DMPC NSAID Chain disordering Molecular dynamics
a b s t r a c t The aim of this study is to investigate the interaction of a drug (Piroxicam, 4-hydroxy-2-methyl-N-(2pyridinyl)-2H-1,2-benzothiazine-3-carboxamide 1,1 dioxide) with a lipid (DMPC) monolayer used as a membrane-mime in terms of drug-induced changes in stability and compressibility with variation in temperature, surface-pressure, drug-dose and ionic states of the monolayers. Drug-induced fluidization is noticed in the − A isotherms through increase in phase-transition pressure at constant temperature. The long-term dynamics of the lipid-monolayer is characterized by algebraic decays in surface-energy E with time t, E ∼ t−p1,2,3 , with an initial decay exponent p1 that changes to p2 after ∼1000 s, and, at high surface pressures and/or drug-dose, to a third exponent p3 after ∼3500 s, suggesting structural reorganizations in the monolayer. With increasing drug–lipid ratio (D/L), p1 shows a decrease ending at an almost constant value after 0.05, p2 shows an almost negligible lowering while p3 shows a monotonic and considerable increase. The reorganization is summarized by proposing two mechanisms: (a) ‘charging–discharging’ where drug-molecules sitting parallel to the interface increase headgroup separations and (b) ‘discharging–charging’ where drug-molecules sitting roughly perpendicular to the interface bring headgroups closer. Drug-induced softening of lipid-monolayers is characterized by the compressibilites of pure and mixed lipid monolayers. Compressibility-change (i.e., compressibility difference between drug/lipid and pure lipid monolayer) with pressure is maximum in the LE–LC transition zone and compressibility-change with drug-dose reveals an optimum dose of drug for maximum increase in compressibility. Molecular dynamics simulation shows that the ordering in the different parts of the lipid chains is changed to different extents in the presence of drugs with maximum change near the headgroups and again points to an optimum dose for maximum disorder. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Non-steroidal anti-inflammatory drugs (NSAIDs), the most common group of drugs used as anti-inflammatory, antipyretic and analgesic agents work by targeting and assembling with the enzyme cyclooxygenase-2 (COX-2) in the cell-membrane, thereby inhibiting the inflammatory function of the latter. This process involves extensive drug–membrane interaction and, since lipids constitute the major structural and active component of the cellmembrane, interactions between NSAIDs and phospholipids has become a focus of research. The complexity of this interaction becomes apparent if we consider the series of ionization states assumed by the drugs and the phospholipid-headgroups at the different pH-values under physiological (pH = 7.4) and pathological
E-mail address: [email protected] (U.K. Basak). http://dx.doi.org/10.1016/j.colsurfb.2015.04.059 0927-7765/© 2015 Elsevier B.V. All rights reserved.
conditions (pH ≈ 5.0), ambient temperatures, interfacial pressures and drug/lipid-headgroup concentration ratios (i.e., drug-dose). The major question from a structural point of view that surely affects bio-functionality is regarding the position and orientation of drug-molecules relative to the lipid-headgroups, how this is affected by the above factors and what effects do the changes in position and orientation have on the mechanical properties of the cell-membrane. It is very important to gain detailed insight into the NSAID-membrane interaction because the therapeutic ability of the drugs is related to this complex event. Langmuir monolayer (LM) has an advantage over other model membranes because of its easy tunability over packing density, lateral pressure, thermal and ionic conditions. Recently there have been few attempts to understand the drug-membrane interaction using LM as a model membrane [1–4]. Marlene et al. have reported NSAID-induced perturbations in the liquid-crystalline phase of DPPC monolayer. Kundu et al. [1] have found an anomalous dependence of NSAID/lipid-monolayer interaction on drug-dose. The
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drug-induced cooperativity of the phase-transition in DPPC monolayer is changed with the ionic states of drugs and lipids [3]. Thus the drug-molecules may change the physical properties of a lipidmonolayer. This modification is, again, decided by the position and orientation of drug-molecules with respect to the lipid-molecules, and in particular, to the phospholipid-headgroups, while its expression is, among others, in the mechanical properties of the lipid assembly. In our specific example of lipid-monolayers in presence of NSAIDs, the major effects of the drug are expected in the mechanical stability of the monolayer over long time scale and in its rigidity. Both these effects have important consequences for biofunctionality of the cell-membrane. The stability of a lipid-monolayer in presence of an NSAID under inflammatory and extreme pH conditions may indicate the long-term stability or otherwise of the membrane under similar conditions in vivo. On the other hand, as mentioned above, NSAID biofunction involves penetration of the cell-membrane and the penetrability of the drug depends on the softening or otherwise of the membrane due to its presence. The effect of NSAIDs on the compressibility of the lipid-monolayer serves as a membrane-mime in this case, too. In this communication, we present the drug-monolayer interaction in terms of drug-induced stability and compressibility-change for varying temperatures, surface densities, drug-doses and ionic states of Piroxicam/DMPC monolayers. At the same time, we try to reveal the microscopic picture of this interaction from molecular ordering using united-atom molecular dynamics (MD) simulations. 2. Experimental details DMPC (dimyristoylphosphatidylcholine), Piroxicam (4-hydroxy-2-methyl-N-(2-pyridinyl)-2H-1,2-benzothiazine-3-carboxamide 1,1-dioxide, C15 H13 N3 O4 S), Chloroform and methanol used are of quoted purity >99%. 115 L of DMPC–Piroxicam solution in chloroform/methanol (9:1, v/v) of four different drug/lipid (D/L, w/w) ratios 0.000 (i.e., pure DMPC), 0.025, 0.050, 0.100 was spread in Langmuir trough on Milli-Q water (resistivity 18.2 M) and compressed with a speed of 5 cm2 /min after solvent evaporation and equilibration. Surface-pressure was measured by a Whilhelmy plate during compression to obtain surface pressure-specific molecular area ( − A) isotherms. Data was collected at 15 ◦ C, 20 ◦ C, 25 ◦ C, 30 ◦ C, 35 ◦ C and 40 ◦ C by maintaining subphase temperature using Julabo Recirculating Cooler (FL300). Data was also collected for different subphase-pH’s, low pH’s (2.5, 3.0, 3.5 and 4.5) using hydrochloric acid (HCl) and high pH’s (6.0, 6.5, 7.0 and 7.5) using sodium bicarbonate (NaHCO3 ). Relaxation (area-fraction vs. time) curves were obtained by recording monolayer area with time at constant surface-pressures of = 20 mN/m to 40 mN/m (at 5 mN/m intervals) and at 43 mN/m and pH = 2.5, 3.5, 4.5 and 5.5 for D/L = 0.000 and 0.025. 3. Experimental results 3.1. LE/LC phase-transition in presence of drug DMPC monolayer undergoes a liquid-expanded (LE) to liquidcondensed (LC) phase transition (t ) as the surface-pressure () is increased [5,6] which corresponds, respectively, to the more fluid ‘gel’ phase and the denser ‘solid’ phase of lipid membranes. Table 1a shows the values of t ’s obtained from surface pressure-specific molecular area ( − A) isotherms of pristine DMPC and Drug/DMPC monolayers at different temperatures. t of pure DMPC monolayers is increased as its temperature is raised. In the LE-phase the hydrocarbon chains of lipids are disordered between the trans and gauche conformations [7] while in the LC-phase they are all-trans in conformation. Thermal movements of lipids prevents the condensation in
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the monolayer resulting in increase in t with temperature. However, what is more interesting is that t is also increased due to the presence of drugs in DMPC monolayer for a constant temperature except at the high temperature of 40 ◦ C. This indicates that the drug-molecules break the ordering in the lipids making the monolayer more fluid. Our studies of stability and softening of DMPC monolayer by Piroxicam are centred around t . 3.2. Stability of monolayers and effects of drug 3.2.1. Reorganization of the monolayers Fig. 2a presents typical − A isotherms of a pure DMPC monolayer at 25 ◦ C (ambient), on water with unadjusted pH (≈5.5) as the reference isotherm; mixture of DMPC with Piroxicam at drug/lipid (D/L) of 0.025 at ambient temperature and unadjusted pH (R = D/L); pure DMPC at 15 ◦ C and unadjusted pH and pure DMPC at 25 ◦ C and pH = 2.5. The area-fraction vs. time (An − t) curves at a particular were obtained by maintaining the monolayer at that -value while recording the monolayer area as a function of time (t) and finally normalizing the area-values with the initial area [8]. The An − t curves were then converted to the surface-energy (E) vs. time (t) curves using the expression E = An , being the surface-pressure corresponding to each An − t curve. Fig. 2b and c shows, again as typical curves, the log E − log t plots for DMPC monolayer at 25 ◦ C and subphase pH = 2.5 for different ’s, in absence and presence of Piroxicam (D/L = 0.025), respectively, while Fig. 1d shows the data of Fig. 1b in a log E − t curve. The effect of drug dosage is shown in Fig. 1e and f where the log E − log t curves for D/L = 0.0, 0.025, 0.05 and 0.1 are shown for 25 ◦ C and subphase pH = 2.5 at = 30 mN/m and 40 mN/m, respectively. From these curves it is clear that, in contrast to DPPC [9] or polymer [10] monolayers, the DMPC monolayer does not show an exponential decay in surface-energy (or surface-area) with time but rather an algebraic decay given by E ∼ t−p where the p-values extracted from Fig. 2b and c, and from Fig. 1e and f are given in Table 1b and c, respectively. This algebraic nature of the decay strongly suggests that it entails neither desorption into the subphase nor nucleation in air [8]. This is confirmed from results of Brewster Angle Microscopy (BAM) carried out on the monolayer using an Imaging Ellipsometer (EP3, Accurion GmbH) and presented for the pristine monolayer at = 40 mN/m after t = 0 s and 2 h in Fig. 2a and b, respectively, while the corresponding BAM images for the mixed-monolayer (D/L = 0.025) are shown in Fig. 2c and d, respectively. The small bright patches on otherwise uniformly dark background show no perceptible change in shape, size or number in any of BAM images. Thus they cannot be taken to signify any observable phase change or clustering. We feel that (a) these are either artefacts or surface structures formed as the lipid monolayer is spread on water surface and (b) both the LE and LC domains have sizes below the in-plane resolution of BAM. The algebraic decay of surface energy with time is consistent with similar decays in two-dimensional systems, especially of complex liquids near the gelation transition [11]. Even in diffusion limited cluster aggregation of droplets in two-dimension the mean field rate equation leading to a sigmoidal growth becomes invalid and the mean cluster size grows algebraically with time [12]. In our system, on the other hand, the surface-area (or surface-energy) of the monolayer decays algebraically. In absence of structural data, we propose that surface-energy change with time corresponds to some structural relaxations whereby the monolayer assumes a closer packing. Stability with surface pressure and drug dosage. It is expected that the ionization states of the lipid-headgroups and the drugs at different subphase-pH’s will affect such structural relaxations. This is borne out from the changes in the p exponents in Table 1b
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Table 1 Results from isotherm studies. (a) Liquid expanded–liquid condensed (LE–LC) phase-transition pressures of drug/lipid (D/L, w/w) monolayers at different temperatures on pure aqueous subphase Temperature (◦ C)
Phase transition pressure t (mN/m)
15 20 25 30 35 40
For D/L = 0.0
For D/L = 0.025
36.5 37.0 41.0 42.0 42.5 45.0
43.3 40.1 43.7 44.1 44.1 42.8
(b) Values of decay exponents at different surface-pressures for D/L = 0.000 and 0.025 for subphase pH = 2.5 Pressure
Decay exponent p1
20 25 30 35 40 43
Decay exponent p2
Decay exponent p3
D/L = 0.000
D/L = 0.025
D/L = 0.000
D/L = 0.025
D/L = 0.000
D/L = 0.025
0.767 0.861 0.797 0.691 0.903 0.891
0.716 0.819 0.912 0.761 0.743 0.691
0.361 0.601 0.423 0.591 0.517 0.578
0.531 0.497 0.431 0.413 0.414 0.322
– – – – 0.312 0.479
– – – – 0.513 0.191
(c) Values of decay exponents at = 30 mN/m and 40 mN/m for D/L = 0.000, 0.025, 0.050 and 0.100 for subphase pH = 2.5 D/L ratio
Decay exponent p1
0.000 0.025 0.050 0.100
Decay exponent p2
Decay exponent p3
= 30 mN/m
= 40 mN/m
= 30 mN/m
= 40 mN/m
= 30 mN/m
= 40 mN/m
0.797 0.912 0.671 0.672
0.903 0.743 0.671 0.679
0.423 0.431 0.449 1.188
0.517 0.414 0.357 0.418
– – 0.789 1.372
– 0.513 1.445 3.239
(d) Values of decay exponents at = 30 mN/m and 40 mN/m for subphase pH = 2.5, 3.5, 4.5 and 5.5 for D/L = 0.025. (w, m, s) z = (weakly, moderately, strongly) zwitterionic, u = undissociated pH
2.5 3.5 4.5 5.5
Ionic state (probable)
Decay exponent p1
Decay exponent p2
Lipid
Drug
= 30 mN/m
= 40 mN/m
= 30 mN/m
= 40 mN/m
= 30 mN/m
= 40 mN/m
u wz wz sz
wz wz mz sz
0.912 0.764 0.731 0.970
0.743 1.000 0.671 0.863
0.431 0.502 0.385 0.699
0.414 0.646 0.637 0.707
– – – 0.273
0.513 0.470 0.419 0.413
and, more emphatically, in Table 1c. The major feature of both these tables and the corresponding curves is the separation of the stabilization dynamics into more than one temporal regime, each with its characteristic p exponent. We also find that the number of such regimes is 2 (with p1 and p2 ) for < 40 mN/m or D/L < 0.05 and 3 (with p1 , p2 and p3 ) for higher values of and D/L, thereby indicating an equivalence of the response of the monolayer to these two quantities on one hand and corresponding with the LE–LC transition, on the other. Table 1c shows that the effect of drug on p1 is a progressive decrease with D/L ending at an almost constant value after 0.05, that on p2 is a smaller lowering (almost negligible) while that on p3 is a monotonic and considerable increase. Stability with pH. The ionization states of the interacting partners depend on the pH of the aqueous subphase. Hence, to understand the effect of these states on the stability of the system, we have presented the p exponents at pH = 2.5, 3.5, 4.5, and 5.5 for the system at D/L = 0.025 and at 25 ◦ C, in Table 1d. Some general comparisons that maybe drawn between the systems at 40 mN/m (purportedly LC phase) with D/L ratio (Table 1c) and pH (Table 1d) are: (1) while p1 decreases with increasing D/L, it oscillates with pH, reaching high values at 3.5 and 5.5, (2) p2 decreases with increasing D/L but increases with pH, and (3) p3 increases with D/L but decreases with increasing pH. The probable ionization states of the
Decay exponent p3
lipid headgroups and the drug, as discussed in a subsection below, are also given in Table 1d. 3.2.2. ‘Charging’ and ‘discharging’ of the monolayers To bring out the drug-induced modifications to the monolayer stability, we have plotted E = EDMPC+Piroxicam − EDMPC vs. time for D/L = 0.025 at pH = 2.5, 3.5, 4.5 and 5.5 and presented them for different ’s in Figs. 4a and 3d, in the respective order. These curves show two classes of behaviour – (a) a swing from increase to decrease in surface-energy as is increased and (b) a reverse swing from decrease to increase with increase in . This variation is almost entirely within the -range of 35 mN/m to 43 mN/m, i.e., the LE–LC transition zone, while basically nothing happens below = 25 mN/m. If we call (a) as ‘charging-discharging’ and (b) as ‘discharging-charging’ then it is interesting to note that there is an alternation in these actions with pH increase – at pH = 2.5 we have a ‘charging-discharging’ between = 40 mN/m and 43 mN/m, at pH = 3.5 this goes to a ‘discharging–charging’ between 35 mN/m and 40 mN/m, at pH = 4.5 continues to be ‘discharging-charging’ between 35 mN/m and 40 mN/m but at pH = 5.5 the ‘chargingdischarging’ reappears between 35 mN/m and 43 mN/m. Structural charges at the headgroup of the lipid-monolayer cause the maximum changes in the monolayer packing and, consequently, the surface-energy and mechanical properties. The
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Fig. 1. (a) Typical − A isotherms of dimyristoyl-phosphatidylcholine (DMPC) under different conditions (see text for details). log(surface-energy, mJ/m2 ) vs. log(time, s) plots for (b) pure DMPC monolayer and (c) DMPC–Piroxicam (D/L, w/w) ratio 0.025, at pH = 2.5 and different surface-pressures and at (e) = 30 mN/m and (f) = 40 mN/m and different drug/lipid ratios, (d) log(surface-energy, mJ/m2 ) vs. time for the same data as in (b).
drug-molecule can change the lipid-headgroup separation and the orientation of drugs and headgroups are decided by their ionization states as controlled by subphase-pH. Our observations suggest that the drug-headgroup morphology undergoes an alternation between two ionization states. In the ‘charging–discharging’ state
drug-molecules probably increase headgroup separations while in the ‘discharging–charging’ state they bring them closer. This scenario is possible if drug-molecules in the former state sit with their rings parallel to the water surface and in the latter with the rings roughly perpendicular to this surface. If we accept this scheme then
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Fig. 2. Brewster angle microscopy (BAM) images of DMPC/Piroxicam monolayers captured at t = 0 s ((a), (c)) and after 2 h ((b), (d)) for D/L = 0.000 and 0.025 respectively at = 40 mN/m.
it is apparent that these two positions of the drug-molecules relative to water surface are decided by the ionization states of the rings through a control of the ring hydrophilicity. The role of drug-dosage is brought out in Fig. 3e and f, where E is plotted against time at 25 ◦ C and subphase pH = 2.5 for D/L = 0.025, 0.05 and 0.1 at = 30 mN/m and 40 mN/m, respectively. At the lower pressure, which corresponds to the LE phase, the drugdosage hugely enhances the ‘charging’ of the monolayer and this ‘charging’ increases with the dose, whereas at the higher pressure, which is near the LE–LC phase boundary, there is a drop in the ‘charging’ at D/L = 0.1, suggesting an overdose. This is consistent with the above model since at higher headgroup concentration (higher ) an increase in drug concentration at the drug–lipid interface above a certain limit may force out-of-plane motion of the rings. 3.3. Drug-induced ‘softening’ of monolayers 3.3.1. Effect of temperature The most relevant physical parameter regarding the drugmembrane interaction which involves penetration of membrane by drug-molecules is the compressibility [13]. We are using the change in compressibility in the lipid-monolayer as a simple model for the situation obtained at the membrane interface. Compressibilities () were calculated using the expression, = − (1/A)(∂A/∂)T . The compressibility-change, (= DMPC+Piroxicam − DMPC ) in DMPC monolayers at pH = 5.5, due to D/L = 0.025, are given as functions of temperature (T ◦ C) and in the contour plot of Fig. 4a. We find that the only significant changes are in the temperature-range of 15–20 ◦ C and the -range of 40–43 mN/m (the LE–LC transition zone) and there is an increase in compressibility going up above 20 m/mN. The corresponding gelation transition temperature for DMPC membrane is 23 ◦ C, hence the compressibility-change
observed for the monolayer transition region due to the drug has strong relevance for membranes, too. The interaction of drugmolecules with lipid-molecules thus seems to prevent rigidity or long-range ordering in lipid-monolayers. In the vicinity of t , the presence of both the gauche and all-trans conformations most probably provides a favourable environment for drug-molecules to enter the cell and express their biofunctionality. 3.3.2. Effect of pH The conformation and the ionic state of DMPC containing an anionic phosphate and a cationic quaternary ammonium groups are very much dependent on the subphase-pH. It has been reported that two ionizable groups, pyridine moiety and enolate group, lead to different pH dependent ionic states in Piroxicam [14,15]. Thus it is important to understand the drug-membrane interaction over the range of extreme pH-values, from ∼2.5 to ∼4.5, inflamed condition (pH ∼ 5.5) and normal physiological condition (pH ∼ 7.5). As seen in the previous section, the drug-membrane interaction is very weak away from t and hence we focus on the pH dependence of drug-membrane interaction around t . Fig. 4b shows through contour plots, the as a function of pH due to the presence of drugs in the DMPC monolayer at 25 ◦ C. The behaviour is very much consistent with the results of mechanical stability with pH. There are essentially two regions of major ‘softening’ at pH ∼ 5.5, while there is a wide region of minor ‘softening’ from 20 mN/m to 35 mN/m, i.e., the LE-phase at pH ∼ 2.5 to 3.5 and two regions of minor ‘softening’ in the LE-phase at pH ∼ 5.5 and 7.5, away from and near t , respectively. The major softening zones are interspersed with a ‘hardening’ zone around pH = 4.5 and spread over = 36 mN/m to 42 mN/m. We can identify the ‘softening’ zones with the ‘charging–discharging’ and the ‘hardening’ zone with the ‘discharging–charging’ zones, respectively and thus are led to conclude that softening of the monolayer increases its stability.
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Fig. 3. E = EDMPC+Piroxicam − EDMPC vs. time at different surface-pressures for D/L = 0.025 and (a) pH = 2.5, (b) pH = 3.5, (c) pH = 4.5 and (d) pH = 5.5, and for different D/L (R) ratios at (e) = 30 and (f) = 40 mN/m.
The repulsion between lipids increases with pH due to deprotonation of the phosphate groups. The anionic form of Piroxicam is dominant for pH > 7. Rozoue et al. observed that the concentration of the zwitterionic Piroxicam increases with pH up to pH ∼ 6.0 while at the same time its lipophilicity increases as a result of the neutralization of the charges due to the dimerization of
zwitterions [14]. Thus the strong drug–lipid interaction at pH = 5.5 may represent a turning point, since at this pH the concentration of zwitterionic nature of headgroups probably reach maximum values whereas at pH > 5.5, the drug-membrane interaction decreases due to the dimerization of zwitterions. At pH = 2.5, there is again a strong affinity of drug-molecules to form ionic associations with
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increased. At ’physiological pH (=7.5) the drug repels the lipidmonolayer and pushes its together resulting in hardening of the monolayer. 3.3.3. Effect of drug-dose The complicated electrostatic interaction between drug and lipid, each containing two ionizable charged groups makes it a complex system. Kundu et al found the anomalous dependence of drug membrane interaction on drug concentration [1]. Similar anomalous behaviour of drug-induced softening with drug-dose is seen in our compressibility studies. The compressibility-change as a function of pressure for three D/L ratios (0.025, 0.050 and 0.100) is shown in Fig. 4c. These results show clearly that while the lipid-monolayer is softened moderately in the LE-phase for all drug-doses, it is softened considerably at the LE–LC transition zone only for D/L = 0.025 and is in fact hardened at this zone for higher drug-dose. This result thus may indicate an optimum dose of drug for cell-membrane penetration and bioefficiency. In extension of our model of the drug dynamics at the interface we suggest that the drug-molecules lie flat on the water surface at low concentration but are aligned with the rings out of the water surface due to mutual repulsion at higher concentrations. This is again effective at high , i.e., high lipid-headgroup concentration at the interface while at low , the drug-headgroup interaction is much reduced and the drugs lead to an average small increase in the headgroup separation. Hence from both the results of pH and drug-dose on druginduced softening of lipid-monolayer, the emerging idea is that of drug-molecule changing its orientation relative to the lipid–water interface with changes in the mean field caused either by pH or by the presence of other drug-molecules. Of these the physiologically more relevant effect is that of drug-dose since that can be externally controlled. However, experimental verification of the orientation of drug-molecules at the lipid–water interface can be aided considerably if the changes in the hydrocarbon chain (tail) ordering due to these changes in molecular orientation are estimated from some other means. To this end, we have carried out molecular dynamics (MD) simulations of the dynamics of a DMPC monolayer in presence of different concentrations of Piroxicam and this is presented in the next section. 4. Simulation details
Fig. 4. Contour plots of compressibility-change ( = DMPC+Piroxicam−DMPC ) as a function of (a) temperature, (b) pH and (c) D/L ratio due to the presence of drug in the DMPC monolayer.
the undissociated, dipolar headgroups of the lipids leading to fluidization of lipid-monolayer. Based on these considerations, we have indicated the probable ionization states of the lipid headgroups and the drug in Table 1d. These considerations and our results reinforce our model of the drug-molecule alternating in the positions of its rings relative to the water surface as pH is
Nine different DMPC/Piroxicam systems with different areal densities and D/L ratios, each containing two monolayers of 120 DMPC molecules around a water block, consistent with the periodic boundary conditions [16], were constructed with Packmol [17,18]. Four reference systems of pure DMPC monolayers with areas per lipid of 49.5, 53.0, 60.5 and 81.5 nm2 /molecule and four DMPC/Piroxicam systems with D/L ratio of 0.025 at the same areal densities and one DMPC/Piroxicam system with D/L ratio of 0.100 and areal density of 60.5 were simulated. The different areal densities were obtained by adjusting the size of the simulation cell in the x- and y-directions. The number of water molecules added to the water block ranged from 1822 to 3998, depending on the size of the simulation cell. Periodic boundary conditions were applied along three spatial dimensions. All the simulation were performed using Groningen Machine for Chemical Simulations (GROMACS-4.5) package [19] with the GROMOS-53a6 parameter set [20,21]. The parameters of the force field for DMPC lipids used for the simulation have been described elsewhere [22,23]. Initial structure and GROMOS-53A6 [24] topology of Piroxicam were obtained using the Automated Topology Builder (ATB) server [25]. All bond lengths were kept constant to
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Fig. 5. Initial and final configurations of lipid ((a), (b)) and drug ((c), (d)) systems show lipid forms monolayer on water whereas drug does not and for drug/lipid system ((e), (f)) drug-molecules come to the interface of the stable monolayers. The drug-molecules are selectively enlarged.
their equilibrium values by LINCS algorithm [26]. The non-bonded Lennard–Jones interaction cut-off was set to a distance of 1.2 nm. A Particle-Mesh Ewald (PME) algorithm with 1.2 nm cut-off and 0.16 Fast-Fourier spacing was used to calculate electrostatic interactions [27]. The equations of motions were integrated using leap-frog integrator with a time step of 2 fs. The system temperature was set to 298 K by Nose–Hoover thermostat [28,29] with a coupling time constant of 0.5 ps and pressure was maintained at 1 bar using the semi-isotropic pressure coupling to a Parinnello–Rahman barostat [30,31] with a time constant of 2.0 ps. Each system was initially energy minimized using the steepest-descent method. After energy minimization, NPT (constant number of particles, pressure and temperature) and NVT (constant number of particles, volume and temperature) equilibration of 20 ns each were conducted prior to the actual MD-run. Although our interest was on the short term equilibrium properties and the MD-run simulations were performed for 400 ns to investigate their long-term stability. We used first 20 ns of MD-run simulations to extract deuterium order parameters. We should point out that since the periodic boundary used has a maximum length of 70 nm, it is expected that only
intra-molecular and intra-domain dynamics can be simulated through this procedure, and in fact inter-domain dynamics could not be visualized. We have also limited our simulations to a situation at ambient pH ( 5.5).
Fig. 6. Snapshots of the lipid-monolayers at (a) A = 81.5 nm2 /molecule and (b) A = 49.5 nm2 /molecule showing gauche to all-trans transformation of lipid alkyl chains with surface density.
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Fig. 7. (a) Deuterium order parameter (Scd) for the two hydrocarbon chains (sn1, blue, sn2, red) along the carbon numbering for the areal densities (A, nm2 /molecule) of 49.5 (square), 60.5 (circle) and 81.5 (up triangle); change in Scd (Scd=ScdDMPC+Piroxicam - ScdDMPC ) with carbon numbering at A = 49.5, D/L = 0.025 (square), A = 53.0, D/L = 0.025 (circle), A = 60.5, D/L = 0.025 (up triangle), A = 81.5, D/L = 0.025 (diamond) and A = 60.5, D/L = 0.100 (down triangle) for (b) sn1 chain and (c) sn2 chain. Orientation of typical Piroxicam molecule (enlarged for better viewing) at water–liquid interface for (d) low and (e) high drug concentration for the same areal density A = 60.5 nm2 /molecule.
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5. Simulation results 5.1. Comparison of experimental and simulation results on the monolayers: consistency check Fig. 5a depicts the snapshot of the initial lipid-monolayer configuration on water before energy minimization. In the initial configuration there is a gap between the water block and lipidheadgroups. The gap has disappeared and lipids have formed a stable monolayer on water after 400 ns of MD-run (Fig. 5b). This is consistent with the experimental studies of DMPC lipids forming a stable monolayer at air/water interface [1,32,33]. Fig. 5c and d shows that the drug-molecules do not form a stable monolayer but aggregate to form clusters inside water. This is again consistent with our experimental results of isotherm studies, where no pressure-rise is noticed during compression and BAM studies where no change in reflectivities is found after spreading drug solution on water. The drug can stay at the interface when both drug and lipid-molecules are spread on water (Fig. 5e and f), again consistent with the experimentally obtained results. Fig. 6a and b depicts the snapshots of the lipid-monolayers respectively at low (A = 81.5 nm2 /molecule) and high 2 (A = 50 nm /molecule) surface densities. At low pressure lipidmolecules are loosely packed and the alkyl chains are in gauche conformations (Fig. 6a). At high pressure, molecules become closely packed and the alkyl chains are in all-trans conformations (Fig. 6b). This is consistent with the experimental studies of Gang et al [34]. They have reported the DPPC lipid chains are conformationally disordered with a significant number of gauche configurations in the LE-phase. The hydrocarbon chains are in an all-trans conformation and are tilted from the surface normal by 25◦ in the LC-phase.
5.2. Drug-induced molecular disorder The intrusion of drugs into lipid-membrane changes molecular ordering in lipid chains. The deuterium order parameter as a function of carbon atom index along the lipid tail (carbon number one is the carbonyl carbon closest to the headgroup) gives the ordering details of the tails in the lipid-membrane [35–37]. The drug-induced softening should be reflected in the change in deuterium order parameter values. The deuterium order parameter (Scd) is defined as S = (1/2)(cos 2 − 1) where is the angle between the molecular vector and the membrane normal and the brackets denote average over time and molecules. g order tool of GROMACS has been used to extract order parameter values of carbon atom Ci by using the molecular vector Ci−1 to Ci+1 of lipid chains from mdrun simulations. No order parameter value is calculated for the first and last carbon atom of the tails. Scd profiles of sn1 and sn2 chains in pure lipid-membranes for different areal densities are shown in Fig. 7a. The order parameter profile of sn1 chain is seen to have a plateau region in the lower and middle part of the chains in which the order parameter remains almost constant, and a drop in order parameter towards 0 at the end of the chain. The order parameter profile for the other chain shows a more ordered region in the middle of the chain only. Both the chains are disordered at low lipid density (A = 81.5 nm2 /molecule). The order parameter value of sn2 chain is increased with lipid density. The order parameter value of sn1 chain for carbon atoms close to the headgroup is increased with lipid density. The ordering of sn1 chains away from the headgroup is maximum at A = 60 nm2 /molecule. This disordering of different parts of the tails are consistent with the experimental observation on the bilayer where the part of the chain near the headgroup region is found to be more ordered [3].
43
Both chains become disordered at very high lipid density (A = 49.5 nm2 /molecule). Although chains are close packed and ordered at A = 49.5 nm2 /molecule the calculated order parameter value is low due to membrane deformation. In general, the monolayers with the larger areal density remained planar throughout the simulations and the monolayers with smaller areal density get deformed sometimes with partial loss of molecules into subphase [16,38]. At A = 49.5 nm2 /molecule lipid membrane buckled and few lipid-molecules were observed to emerge out of the monolayer into the subphase during the molecular dynamics simulation. Fig. 7b and c shows the change in order parameters in the presence of drug in lipid-monolayers. For each case, the alkyl chains become disordered in the presence of drug except at A = 49.5 nm2 /molecule. The unusual behaviour at A = 49.5 nm2 /molecule is due to extreme deformation of lipid membrane and material loss from the interface to water subphase. For sn1 chain Scd is maximum at 11th carbon atom for A = 53.0 nm2 /molecule, at 9th carbon atom for A = 60.5 nm2 /molecule and at 8th for A = 81.5 nm2 /molecule. For sn2 chain Scd is maximum at 10th carbon atom for A = 53.0 nm2 /molecule, at 11th for A = 60.5 nm2 /molecule and at 8th for A = 81.5 nm2 /molecule. Thus the drug-induced disordering effect on the alkyl chains is minimum near the headgroup region. This is consistent with the drug-induced change in cooperativity in a lipid bilayer [3]. Both the chains become ordered as D/L ratio is increased from 0.025 to 0.100. This is consistent with the anomalous behaviour on drug concentration observed in our compressibility studies. Again this is analogous to the order parameter value of both chains increasing with lipid density and shows the equivalence of high surface pressure and high drug-dose, consistent with the experimental data on stability and compressibility. Fig. 7d and e shows the orientation of drug-molecules at the interface for D/L = 0.025 and 0.100, respectively. It is clear that in the former case the molecule has its rings roughly parallel to the interface which in the latter they are roughly perpendicular, bearing out the proposed model to explain the stability and compressibility variations with drug dosage. Hence we can temporarily assign this model for the drug–lipid interaction.
6. Conclusion Isotherms of pure-lipid monolayers show that LE–LC phase transition pressure (t ) is raised as the temperature is increased. The increase in t at constant temperature in the presence of drug indicates drug-induced fluidization in drug/lipid monolayers. This is reflected in the − A isotherm of drug/lipid monolayer with the variation of pressure, temperature, subphase-pH and drug-dose. The long-term dynamics of the lipid-monolayer are studied to investigate monolayer stability. DMPC monolayer is found to be very stable and unlike DPPC or polymer monolayers, follows an algebraic decay in surface-area or surface-energy E with time t, given by E ∼ t−p , where p is the decay exponent. Each decay curve has two distinct temporal regions at low surface pressure and/or drug-dose and three at high values of these quantities. This nature of decay suggests that the decay entails neither desorption into the subphase nor nucleation on the subphase as confirmed by BAM studies. Drug-induced modifications to the monolayer stability are tentatively modelled by introducing two opposite mechanisms: (a) ‘charging–discharging’ where the drug-molecule sitting with its rings parallel to the water surface increases the separation between the headgroups and (b) ‘discharging–charging’ where the rings sitting roughly perpendicular to the water surface bring the headgroups closer. The orientations of drugs relative to water surface in the above two mechanisms are found to be decided by the molecular ionization states. Drug-induced softening of lipid-monolayer is
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characterized by obtaining the compressibilities of pure and mixed monolayers as a function of surface-pressure, temperature, pH and drug-dose. It is found that the drug-induced compressibilitychange is prominent in the LE–LC transition zone. Effect of pH on drug-induced ‘softening’ is found to be consistent with the results of mechanical stability with pH. Drug-induced ‘softening’ with drug-dose shows there is an optimum dose of drug for attaining maximum compressibility. The softening of the monolayer is found to increase its stability. Molecular dynamics simulation of DMPC monolayer shows that there is a significant number of gauche conformations with low lipid tail ordering in LE-phase and the alltrans conformations dominate in LC-phase of the lipid monolayer. The part of the chain near the headgroup region is found to be more ordered. The alkyl chains of the lipids are less ordered in the presence of drug with D/L ratio 0.025. The drug-induced change in the lipid tail ordering is found to be more prominent near the headgroup region. Both the chains become ordered as D/L ratio is increased from 0.025 to 0.100 indicating an anomalous behaviour of drug–lipid interaction with drug concentration as seen in our compressibility studies. Our proposed model has been borne out of Molecular Dynamics studies. Acknowledgements UKB thanks University Grants Commission (UGC) for their financial support and Department of Atomic Energy (DAE) for giving permission to carry out research under the aegis of Saha Institute of Nuclear Physics (SINP). References [1] S. Kundu, H. Chakraborty, M. Sarkar, A. Datta, Colloids Surf. B: Biointerfaces 70 (1) (2009) 157–161. [2] M. Lúcio, F. Bringezu, S. Reis, J.L. Lima, G. Brezesinski, Langmuir 24 (8) (2008) 4132–4139. [3] C. Nunes, G. Brezesinski, C. Pereira-Leite, J.L. Lima, S. Reis, M. Lúcio, Langmuir 27 (17) (2011) 10847–10858. [4] K. Czapla, B. Korchowiec, E. Rogalska, Langmuir 26 (5) (2009) 3485–3492. [5] M.K. Ratajczak, Y. Chris Ko, Y. Lange, T.L. Steck, K.Y.C. Lee, Biophys. J. 93 (6) (2007) 2038–2047. [6] J.M. Holopainen, H.L. Brockman, R.E. Brown, P.K. Kinnunen, Biophys. J. 80 (2) (2001) 765–775.
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Colloids and Surfaces B: Biointerfaces journal homepage: www.elsevier.com/locate/colsurfb
Stability and softening of a lipid monolayer in the presence of a pain-killer drug Uttam Kumar Basak a , Alokmay Datta a , Dhananjay Bhattacharyya b a b
Surface Physics and Material Science Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar City, Kolkata 700064, India Computational Sciences Division, Saha Institute of Nuclear Physics, Kolkata 700064, India
a r t i c l e
i n f o
Article history: Received 23 December 2014 Received in revised form 24 April 2015 Accepted 27 April 2015 Available online 8 May 2015 PACS: 68.18.−g 83.60.Bc 87.14.Cc 83.10.Mj Keywords: Langmuir monolayer Algebraic relaxation Softening DMPC NSAID Chain disordering Molecular dynamics
a b s t r a c t The aim of this study is to investigate the interaction of a drug (Piroxicam, 4-hydroxy-2-methyl-N-(2pyridinyl)-2H-1,2-benzothiazine-3-carboxamide 1,1 dioxide) with a lipid (DMPC) monolayer used as a membrane-mime in terms of drug-induced changes in stability and compressibility with variation in temperature, surface-pressure, drug-dose and ionic states of the monolayers. Drug-induced fluidization is noticed in the − A isotherms through increase in phase-transition pressure at constant temperature. The long-term dynamics of the lipid-monolayer is characterized by algebraic decays in surface-energy E with time t, E ∼ t−p1,2,3 , with an initial decay exponent p1 that changes to p2 after ∼1000 s, and, at high surface pressures and/or drug-dose, to a third exponent p3 after ∼3500 s, suggesting structural reorganizations in the monolayer. With increasing drug–lipid ratio (D/L), p1 shows a decrease ending at an almost constant value after 0.05, p2 shows an almost negligible lowering while p3 shows a monotonic and considerable increase. The reorganization is summarized by proposing two mechanisms: (a) ‘charging–discharging’ where drug-molecules sitting parallel to the interface increase headgroup separations and (b) ‘discharging–charging’ where drug-molecules sitting roughly perpendicular to the interface bring headgroups closer. Drug-induced softening of lipid-monolayers is characterized by the compressibilites of pure and mixed lipid monolayers. Compressibility-change (i.e., compressibility difference between drug/lipid and pure lipid monolayer) with pressure is maximum in the LE–LC transition zone and compressibility-change with drug-dose reveals an optimum dose of drug for maximum increase in compressibility. Molecular dynamics simulation shows that the ordering in the different parts of the lipid chains is changed to different extents in the presence of drugs with maximum change near the headgroups and again points to an optimum dose for maximum disorder. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Non-steroidal anti-inflammatory drugs (NSAIDs), the most common group of drugs used as anti-inflammatory, antipyretic and analgesic agents work by targeting and assembling with the enzyme cyclooxygenase-2 (COX-2) in the cell-membrane, thereby inhibiting the inflammatory function of the latter. This process involves extensive drug–membrane interaction and, since lipids constitute the major structural and active component of the cellmembrane, interactions between NSAIDs and phospholipids has become a focus of research. The complexity of this interaction becomes apparent if we consider the series of ionization states assumed by the drugs and the phospholipid-headgroups at the different pH-values under physiological (pH = 7.4) and pathological
E-mail address: [email protected] (U.K. Basak). http://dx.doi.org/10.1016/j.colsurfb.2015.04.059 0927-7765/© 2015 Elsevier B.V. All rights reserved.
conditions (pH ≈ 5.0), ambient temperatures, interfacial pressures and drug/lipid-headgroup concentration ratios (i.e., drug-dose). The major question from a structural point of view that surely affects bio-functionality is regarding the position and orientation of drug-molecules relative to the lipid-headgroups, how this is affected by the above factors and what effects do the changes in position and orientation have on the mechanical properties of the cell-membrane. It is very important to gain detailed insight into the NSAID-membrane interaction because the therapeutic ability of the drugs is related to this complex event. Langmuir monolayer (LM) has an advantage over other model membranes because of its easy tunability over packing density, lateral pressure, thermal and ionic conditions. Recently there have been few attempts to understand the drug-membrane interaction using LM as a model membrane [1–4]. Marlene et al. have reported NSAID-induced perturbations in the liquid-crystalline phase of DPPC monolayer. Kundu et al. [1] have found an anomalous dependence of NSAID/lipid-monolayer interaction on drug-dose. The
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drug-induced cooperativity of the phase-transition in DPPC monolayer is changed with the ionic states of drugs and lipids [3]. Thus the drug-molecules may change the physical properties of a lipidmonolayer. This modification is, again, decided by the position and orientation of drug-molecules with respect to the lipid-molecules, and in particular, to the phospholipid-headgroups, while its expression is, among others, in the mechanical properties of the lipid assembly. In our specific example of lipid-monolayers in presence of NSAIDs, the major effects of the drug are expected in the mechanical stability of the monolayer over long time scale and in its rigidity. Both these effects have important consequences for biofunctionality of the cell-membrane. The stability of a lipid-monolayer in presence of an NSAID under inflammatory and extreme pH conditions may indicate the long-term stability or otherwise of the membrane under similar conditions in vivo. On the other hand, as mentioned above, NSAID biofunction involves penetration of the cell-membrane and the penetrability of the drug depends on the softening or otherwise of the membrane due to its presence. The effect of NSAIDs on the compressibility of the lipid-monolayer serves as a membrane-mime in this case, too. In this communication, we present the drug-monolayer interaction in terms of drug-induced stability and compressibility-change for varying temperatures, surface densities, drug-doses and ionic states of Piroxicam/DMPC monolayers. At the same time, we try to reveal the microscopic picture of this interaction from molecular ordering using united-atom molecular dynamics (MD) simulations. 2. Experimental details DMPC (dimyristoylphosphatidylcholine), Piroxicam (4-hydroxy-2-methyl-N-(2-pyridinyl)-2H-1,2-benzothiazine-3-carboxamide 1,1-dioxide, C15 H13 N3 O4 S), Chloroform and methanol used are of quoted purity >99%. 115 L of DMPC–Piroxicam solution in chloroform/methanol (9:1, v/v) of four different drug/lipid (D/L, w/w) ratios 0.000 (i.e., pure DMPC), 0.025, 0.050, 0.100 was spread in Langmuir trough on Milli-Q water (resistivity 18.2 M) and compressed with a speed of 5 cm2 /min after solvent evaporation and equilibration. Surface-pressure was measured by a Whilhelmy plate during compression to obtain surface pressure-specific molecular area ( − A) isotherms. Data was collected at 15 ◦ C, 20 ◦ C, 25 ◦ C, 30 ◦ C, 35 ◦ C and 40 ◦ C by maintaining subphase temperature using Julabo Recirculating Cooler (FL300). Data was also collected for different subphase-pH’s, low pH’s (2.5, 3.0, 3.5 and 4.5) using hydrochloric acid (HCl) and high pH’s (6.0, 6.5, 7.0 and 7.5) using sodium bicarbonate (NaHCO3 ). Relaxation (area-fraction vs. time) curves were obtained by recording monolayer area with time at constant surface-pressures of = 20 mN/m to 40 mN/m (at 5 mN/m intervals) and at 43 mN/m and pH = 2.5, 3.5, 4.5 and 5.5 for D/L = 0.000 and 0.025. 3. Experimental results 3.1. LE/LC phase-transition in presence of drug DMPC monolayer undergoes a liquid-expanded (LE) to liquidcondensed (LC) phase transition (t ) as the surface-pressure () is increased [5,6] which corresponds, respectively, to the more fluid ‘gel’ phase and the denser ‘solid’ phase of lipid membranes. Table 1a shows the values of t ’s obtained from surface pressure-specific molecular area ( − A) isotherms of pristine DMPC and Drug/DMPC monolayers at different temperatures. t of pure DMPC monolayers is increased as its temperature is raised. In the LE-phase the hydrocarbon chains of lipids are disordered between the trans and gauche conformations [7] while in the LC-phase they are all-trans in conformation. Thermal movements of lipids prevents the condensation in
35
the monolayer resulting in increase in t with temperature. However, what is more interesting is that t is also increased due to the presence of drugs in DMPC monolayer for a constant temperature except at the high temperature of 40 ◦ C. This indicates that the drug-molecules break the ordering in the lipids making the monolayer more fluid. Our studies of stability and softening of DMPC monolayer by Piroxicam are centred around t . 3.2. Stability of monolayers and effects of drug 3.2.1. Reorganization of the monolayers Fig. 2a presents typical − A isotherms of a pure DMPC monolayer at 25 ◦ C (ambient), on water with unadjusted pH (≈5.5) as the reference isotherm; mixture of DMPC with Piroxicam at drug/lipid (D/L) of 0.025 at ambient temperature and unadjusted pH (R = D/L); pure DMPC at 15 ◦ C and unadjusted pH and pure DMPC at 25 ◦ C and pH = 2.5. The area-fraction vs. time (An − t) curves at a particular were obtained by maintaining the monolayer at that -value while recording the monolayer area as a function of time (t) and finally normalizing the area-values with the initial area [8]. The An − t curves were then converted to the surface-energy (E) vs. time (t) curves using the expression E = An , being the surface-pressure corresponding to each An − t curve. Fig. 2b and c shows, again as typical curves, the log E − log t plots for DMPC monolayer at 25 ◦ C and subphase pH = 2.5 for different ’s, in absence and presence of Piroxicam (D/L = 0.025), respectively, while Fig. 1d shows the data of Fig. 1b in a log E − t curve. The effect of drug dosage is shown in Fig. 1e and f where the log E − log t curves for D/L = 0.0, 0.025, 0.05 and 0.1 are shown for 25 ◦ C and subphase pH = 2.5 at = 30 mN/m and 40 mN/m, respectively. From these curves it is clear that, in contrast to DPPC [9] or polymer [10] monolayers, the DMPC monolayer does not show an exponential decay in surface-energy (or surface-area) with time but rather an algebraic decay given by E ∼ t−p where the p-values extracted from Fig. 2b and c, and from Fig. 1e and f are given in Table 1b and c, respectively. This algebraic nature of the decay strongly suggests that it entails neither desorption into the subphase nor nucleation in air [8]. This is confirmed from results of Brewster Angle Microscopy (BAM) carried out on the monolayer using an Imaging Ellipsometer (EP3, Accurion GmbH) and presented for the pristine monolayer at = 40 mN/m after t = 0 s and 2 h in Fig. 2a and b, respectively, while the corresponding BAM images for the mixed-monolayer (D/L = 0.025) are shown in Fig. 2c and d, respectively. The small bright patches on otherwise uniformly dark background show no perceptible change in shape, size or number in any of BAM images. Thus they cannot be taken to signify any observable phase change or clustering. We feel that (a) these are either artefacts or surface structures formed as the lipid monolayer is spread on water surface and (b) both the LE and LC domains have sizes below the in-plane resolution of BAM. The algebraic decay of surface energy with time is consistent with similar decays in two-dimensional systems, especially of complex liquids near the gelation transition [11]. Even in diffusion limited cluster aggregation of droplets in two-dimension the mean field rate equation leading to a sigmoidal growth becomes invalid and the mean cluster size grows algebraically with time [12]. In our system, on the other hand, the surface-area (or surface-energy) of the monolayer decays algebraically. In absence of structural data, we propose that surface-energy change with time corresponds to some structural relaxations whereby the monolayer assumes a closer packing. Stability with surface pressure and drug dosage. It is expected that the ionization states of the lipid-headgroups and the drugs at different subphase-pH’s will affect such structural relaxations. This is borne out from the changes in the p exponents in Table 1b
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Table 1 Results from isotherm studies. (a) Liquid expanded–liquid condensed (LE–LC) phase-transition pressures of drug/lipid (D/L, w/w) monolayers at different temperatures on pure aqueous subphase Temperature (◦ C)
Phase transition pressure t (mN/m)
15 20 25 30 35 40
For D/L = 0.0
For D/L = 0.025
36.5 37.0 41.0 42.0 42.5 45.0
43.3 40.1 43.7 44.1 44.1 42.8
(b) Values of decay exponents at different surface-pressures for D/L = 0.000 and 0.025 for subphase pH = 2.5 Pressure
Decay exponent p1
20 25 30 35 40 43
Decay exponent p2
Decay exponent p3
D/L = 0.000
D/L = 0.025
D/L = 0.000
D/L = 0.025
D/L = 0.000
D/L = 0.025
0.767 0.861 0.797 0.691 0.903 0.891
0.716 0.819 0.912 0.761 0.743 0.691
0.361 0.601 0.423 0.591 0.517 0.578
0.531 0.497 0.431 0.413 0.414 0.322
– – – – 0.312 0.479
– – – – 0.513 0.191
(c) Values of decay exponents at = 30 mN/m and 40 mN/m for D/L = 0.000, 0.025, 0.050 and 0.100 for subphase pH = 2.5 D/L ratio
Decay exponent p1
0.000 0.025 0.050 0.100
Decay exponent p2
Decay exponent p3
= 30 mN/m
= 40 mN/m
= 30 mN/m
= 40 mN/m
= 30 mN/m
= 40 mN/m
0.797 0.912 0.671 0.672
0.903 0.743 0.671 0.679
0.423 0.431 0.449 1.188
0.517 0.414 0.357 0.418
– – 0.789 1.372
– 0.513 1.445 3.239
(d) Values of decay exponents at = 30 mN/m and 40 mN/m for subphase pH = 2.5, 3.5, 4.5 and 5.5 for D/L = 0.025. (w, m, s) z = (weakly, moderately, strongly) zwitterionic, u = undissociated pH
2.5 3.5 4.5 5.5
Ionic state (probable)
Decay exponent p1
Decay exponent p2
Lipid
Drug
= 30 mN/m
= 40 mN/m
= 30 mN/m
= 40 mN/m
= 30 mN/m
= 40 mN/m
u wz wz sz
wz wz mz sz
0.912 0.764 0.731 0.970
0.743 1.000 0.671 0.863
0.431 0.502 0.385 0.699
0.414 0.646 0.637 0.707
– – – 0.273
0.513 0.470 0.419 0.413
and, more emphatically, in Table 1c. The major feature of both these tables and the corresponding curves is the separation of the stabilization dynamics into more than one temporal regime, each with its characteristic p exponent. We also find that the number of such regimes is 2 (with p1 and p2 ) for < 40 mN/m or D/L < 0.05 and 3 (with p1 , p2 and p3 ) for higher values of and D/L, thereby indicating an equivalence of the response of the monolayer to these two quantities on one hand and corresponding with the LE–LC transition, on the other. Table 1c shows that the effect of drug on p1 is a progressive decrease with D/L ending at an almost constant value after 0.05, that on p2 is a smaller lowering (almost negligible) while that on p3 is a monotonic and considerable increase. Stability with pH. The ionization states of the interacting partners depend on the pH of the aqueous subphase. Hence, to understand the effect of these states on the stability of the system, we have presented the p exponents at pH = 2.5, 3.5, 4.5, and 5.5 for the system at D/L = 0.025 and at 25 ◦ C, in Table 1d. Some general comparisons that maybe drawn between the systems at 40 mN/m (purportedly LC phase) with D/L ratio (Table 1c) and pH (Table 1d) are: (1) while p1 decreases with increasing D/L, it oscillates with pH, reaching high values at 3.5 and 5.5, (2) p2 decreases with increasing D/L but increases with pH, and (3) p3 increases with D/L but decreases with increasing pH. The probable ionization states of the
Decay exponent p3
lipid headgroups and the drug, as discussed in a subsection below, are also given in Table 1d. 3.2.2. ‘Charging’ and ‘discharging’ of the monolayers To bring out the drug-induced modifications to the monolayer stability, we have plotted E = EDMPC+Piroxicam − EDMPC vs. time for D/L = 0.025 at pH = 2.5, 3.5, 4.5 and 5.5 and presented them for different ’s in Figs. 4a and 3d, in the respective order. These curves show two classes of behaviour – (a) a swing from increase to decrease in surface-energy as is increased and (b) a reverse swing from decrease to increase with increase in . This variation is almost entirely within the -range of 35 mN/m to 43 mN/m, i.e., the LE–LC transition zone, while basically nothing happens below = 25 mN/m. If we call (a) as ‘charging-discharging’ and (b) as ‘discharging-charging’ then it is interesting to note that there is an alternation in these actions with pH increase – at pH = 2.5 we have a ‘charging-discharging’ between = 40 mN/m and 43 mN/m, at pH = 3.5 this goes to a ‘discharging–charging’ between 35 mN/m and 40 mN/m, at pH = 4.5 continues to be ‘discharging-charging’ between 35 mN/m and 40 mN/m but at pH = 5.5 the ‘chargingdischarging’ reappears between 35 mN/m and 43 mN/m. Structural charges at the headgroup of the lipid-monolayer cause the maximum changes in the monolayer packing and, consequently, the surface-energy and mechanical properties. The
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Fig. 1. (a) Typical − A isotherms of dimyristoyl-phosphatidylcholine (DMPC) under different conditions (see text for details). log(surface-energy, mJ/m2 ) vs. log(time, s) plots for (b) pure DMPC monolayer and (c) DMPC–Piroxicam (D/L, w/w) ratio 0.025, at pH = 2.5 and different surface-pressures and at (e) = 30 mN/m and (f) = 40 mN/m and different drug/lipid ratios, (d) log(surface-energy, mJ/m2 ) vs. time for the same data as in (b).
drug-molecule can change the lipid-headgroup separation and the orientation of drugs and headgroups are decided by their ionization states as controlled by subphase-pH. Our observations suggest that the drug-headgroup morphology undergoes an alternation between two ionization states. In the ‘charging–discharging’ state
drug-molecules probably increase headgroup separations while in the ‘discharging–charging’ state they bring them closer. This scenario is possible if drug-molecules in the former state sit with their rings parallel to the water surface and in the latter with the rings roughly perpendicular to this surface. If we accept this scheme then
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Fig. 2. Brewster angle microscopy (BAM) images of DMPC/Piroxicam monolayers captured at t = 0 s ((a), (c)) and after 2 h ((b), (d)) for D/L = 0.000 and 0.025 respectively at = 40 mN/m.
it is apparent that these two positions of the drug-molecules relative to water surface are decided by the ionization states of the rings through a control of the ring hydrophilicity. The role of drug-dosage is brought out in Fig. 3e and f, where E is plotted against time at 25 ◦ C and subphase pH = 2.5 for D/L = 0.025, 0.05 and 0.1 at = 30 mN/m and 40 mN/m, respectively. At the lower pressure, which corresponds to the LE phase, the drugdosage hugely enhances the ‘charging’ of the monolayer and this ‘charging’ increases with the dose, whereas at the higher pressure, which is near the LE–LC phase boundary, there is a drop in the ‘charging’ at D/L = 0.1, suggesting an overdose. This is consistent with the above model since at higher headgroup concentration (higher ) an increase in drug concentration at the drug–lipid interface above a certain limit may force out-of-plane motion of the rings. 3.3. Drug-induced ‘softening’ of monolayers 3.3.1. Effect of temperature The most relevant physical parameter regarding the drugmembrane interaction which involves penetration of membrane by drug-molecules is the compressibility [13]. We are using the change in compressibility in the lipid-monolayer as a simple model for the situation obtained at the membrane interface. Compressibilities () were calculated using the expression, = − (1/A)(∂A/∂)T . The compressibility-change, (= DMPC+Piroxicam − DMPC ) in DMPC monolayers at pH = 5.5, due to D/L = 0.025, are given as functions of temperature (T ◦ C) and in the contour plot of Fig. 4a. We find that the only significant changes are in the temperature-range of 15–20 ◦ C and the -range of 40–43 mN/m (the LE–LC transition zone) and there is an increase in compressibility going up above 20 m/mN. The corresponding gelation transition temperature for DMPC membrane is 23 ◦ C, hence the compressibility-change
observed for the monolayer transition region due to the drug has strong relevance for membranes, too. The interaction of drugmolecules with lipid-molecules thus seems to prevent rigidity or long-range ordering in lipid-monolayers. In the vicinity of t , the presence of both the gauche and all-trans conformations most probably provides a favourable environment for drug-molecules to enter the cell and express their biofunctionality. 3.3.2. Effect of pH The conformation and the ionic state of DMPC containing an anionic phosphate and a cationic quaternary ammonium groups are very much dependent on the subphase-pH. It has been reported that two ionizable groups, pyridine moiety and enolate group, lead to different pH dependent ionic states in Piroxicam [14,15]. Thus it is important to understand the drug-membrane interaction over the range of extreme pH-values, from ∼2.5 to ∼4.5, inflamed condition (pH ∼ 5.5) and normal physiological condition (pH ∼ 7.5). As seen in the previous section, the drug-membrane interaction is very weak away from t and hence we focus on the pH dependence of drug-membrane interaction around t . Fig. 4b shows through contour plots, the as a function of pH due to the presence of drugs in the DMPC monolayer at 25 ◦ C. The behaviour is very much consistent with the results of mechanical stability with pH. There are essentially two regions of major ‘softening’ at pH ∼ 5.5, while there is a wide region of minor ‘softening’ from 20 mN/m to 35 mN/m, i.e., the LE-phase at pH ∼ 2.5 to 3.5 and two regions of minor ‘softening’ in the LE-phase at pH ∼ 5.5 and 7.5, away from and near t , respectively. The major softening zones are interspersed with a ‘hardening’ zone around pH = 4.5 and spread over = 36 mN/m to 42 mN/m. We can identify the ‘softening’ zones with the ‘charging–discharging’ and the ‘hardening’ zone with the ‘discharging–charging’ zones, respectively and thus are led to conclude that softening of the monolayer increases its stability.
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Fig. 3. E = EDMPC+Piroxicam − EDMPC vs. time at different surface-pressures for D/L = 0.025 and (a) pH = 2.5, (b) pH = 3.5, (c) pH = 4.5 and (d) pH = 5.5, and for different D/L (R) ratios at (e) = 30 and (f) = 40 mN/m.
The repulsion between lipids increases with pH due to deprotonation of the phosphate groups. The anionic form of Piroxicam is dominant for pH > 7. Rozoue et al. observed that the concentration of the zwitterionic Piroxicam increases with pH up to pH ∼ 6.0 while at the same time its lipophilicity increases as a result of the neutralization of the charges due to the dimerization of
zwitterions [14]. Thus the strong drug–lipid interaction at pH = 5.5 may represent a turning point, since at this pH the concentration of zwitterionic nature of headgroups probably reach maximum values whereas at pH > 5.5, the drug-membrane interaction decreases due to the dimerization of zwitterions. At pH = 2.5, there is again a strong affinity of drug-molecules to form ionic associations with
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increased. At ’physiological pH (=7.5) the drug repels the lipidmonolayer and pushes its together resulting in hardening of the monolayer. 3.3.3. Effect of drug-dose The complicated electrostatic interaction between drug and lipid, each containing two ionizable charged groups makes it a complex system. Kundu et al found the anomalous dependence of drug membrane interaction on drug concentration [1]. Similar anomalous behaviour of drug-induced softening with drug-dose is seen in our compressibility studies. The compressibility-change as a function of pressure for three D/L ratios (0.025, 0.050 and 0.100) is shown in Fig. 4c. These results show clearly that while the lipid-monolayer is softened moderately in the LE-phase for all drug-doses, it is softened considerably at the LE–LC transition zone only for D/L = 0.025 and is in fact hardened at this zone for higher drug-dose. This result thus may indicate an optimum dose of drug for cell-membrane penetration and bioefficiency. In extension of our model of the drug dynamics at the interface we suggest that the drug-molecules lie flat on the water surface at low concentration but are aligned with the rings out of the water surface due to mutual repulsion at higher concentrations. This is again effective at high , i.e., high lipid-headgroup concentration at the interface while at low , the drug-headgroup interaction is much reduced and the drugs lead to an average small increase in the headgroup separation. Hence from both the results of pH and drug-dose on druginduced softening of lipid-monolayer, the emerging idea is that of drug-molecule changing its orientation relative to the lipid–water interface with changes in the mean field caused either by pH or by the presence of other drug-molecules. Of these the physiologically more relevant effect is that of drug-dose since that can be externally controlled. However, experimental verification of the orientation of drug-molecules at the lipid–water interface can be aided considerably if the changes in the hydrocarbon chain (tail) ordering due to these changes in molecular orientation are estimated from some other means. To this end, we have carried out molecular dynamics (MD) simulations of the dynamics of a DMPC monolayer in presence of different concentrations of Piroxicam and this is presented in the next section. 4. Simulation details
Fig. 4. Contour plots of compressibility-change ( = DMPC+Piroxicam−DMPC ) as a function of (a) temperature, (b) pH and (c) D/L ratio due to the presence of drug in the DMPC monolayer.
the undissociated, dipolar headgroups of the lipids leading to fluidization of lipid-monolayer. Based on these considerations, we have indicated the probable ionization states of the lipid headgroups and the drug in Table 1d. These considerations and our results reinforce our model of the drug-molecule alternating in the positions of its rings relative to the water surface as pH is
Nine different DMPC/Piroxicam systems with different areal densities and D/L ratios, each containing two monolayers of 120 DMPC molecules around a water block, consistent with the periodic boundary conditions [16], were constructed with Packmol [17,18]. Four reference systems of pure DMPC monolayers with areas per lipid of 49.5, 53.0, 60.5 and 81.5 nm2 /molecule and four DMPC/Piroxicam systems with D/L ratio of 0.025 at the same areal densities and one DMPC/Piroxicam system with D/L ratio of 0.100 and areal density of 60.5 were simulated. The different areal densities were obtained by adjusting the size of the simulation cell in the x- and y-directions. The number of water molecules added to the water block ranged from 1822 to 3998, depending on the size of the simulation cell. Periodic boundary conditions were applied along three spatial dimensions. All the simulation were performed using Groningen Machine for Chemical Simulations (GROMACS-4.5) package [19] with the GROMOS-53a6 parameter set [20,21]. The parameters of the force field for DMPC lipids used for the simulation have been described elsewhere [22,23]. Initial structure and GROMOS-53A6 [24] topology of Piroxicam were obtained using the Automated Topology Builder (ATB) server [25]. All bond lengths were kept constant to
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Fig. 5. Initial and final configurations of lipid ((a), (b)) and drug ((c), (d)) systems show lipid forms monolayer on water whereas drug does not and for drug/lipid system ((e), (f)) drug-molecules come to the interface of the stable monolayers. The drug-molecules are selectively enlarged.
their equilibrium values by LINCS algorithm [26]. The non-bonded Lennard–Jones interaction cut-off was set to a distance of 1.2 nm. A Particle-Mesh Ewald (PME) algorithm with 1.2 nm cut-off and 0.16 Fast-Fourier spacing was used to calculate electrostatic interactions [27]. The equations of motions were integrated using leap-frog integrator with a time step of 2 fs. The system temperature was set to 298 K by Nose–Hoover thermostat [28,29] with a coupling time constant of 0.5 ps and pressure was maintained at 1 bar using the semi-isotropic pressure coupling to a Parinnello–Rahman barostat [30,31] with a time constant of 2.0 ps. Each system was initially energy minimized using the steepest-descent method. After energy minimization, NPT (constant number of particles, pressure and temperature) and NVT (constant number of particles, volume and temperature) equilibration of 20 ns each were conducted prior to the actual MD-run. Although our interest was on the short term equilibrium properties and the MD-run simulations were performed for 400 ns to investigate their long-term stability. We used first 20 ns of MD-run simulations to extract deuterium order parameters. We should point out that since the periodic boundary used has a maximum length of 70 nm, it is expected that only
intra-molecular and intra-domain dynamics can be simulated through this procedure, and in fact inter-domain dynamics could not be visualized. We have also limited our simulations to a situation at ambient pH ( 5.5).
Fig. 6. Snapshots of the lipid-monolayers at (a) A = 81.5 nm2 /molecule and (b) A = 49.5 nm2 /molecule showing gauche to all-trans transformation of lipid alkyl chains with surface density.
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Fig. 7. (a) Deuterium order parameter (Scd) for the two hydrocarbon chains (sn1, blue, sn2, red) along the carbon numbering for the areal densities (A, nm2 /molecule) of 49.5 (square), 60.5 (circle) and 81.5 (up triangle); change in Scd (Scd=ScdDMPC+Piroxicam - ScdDMPC ) with carbon numbering at A = 49.5, D/L = 0.025 (square), A = 53.0, D/L = 0.025 (circle), A = 60.5, D/L = 0.025 (up triangle), A = 81.5, D/L = 0.025 (diamond) and A = 60.5, D/L = 0.100 (down triangle) for (b) sn1 chain and (c) sn2 chain. Orientation of typical Piroxicam molecule (enlarged for better viewing) at water–liquid interface for (d) low and (e) high drug concentration for the same areal density A = 60.5 nm2 /molecule.
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5. Simulation results 5.1. Comparison of experimental and simulation results on the monolayers: consistency check Fig. 5a depicts the snapshot of the initial lipid-monolayer configuration on water before energy minimization. In the initial configuration there is a gap between the water block and lipidheadgroups. The gap has disappeared and lipids have formed a stable monolayer on water after 400 ns of MD-run (Fig. 5b). This is consistent with the experimental studies of DMPC lipids forming a stable monolayer at air/water interface [1,32,33]. Fig. 5c and d shows that the drug-molecules do not form a stable monolayer but aggregate to form clusters inside water. This is again consistent with our experimental results of isotherm studies, where no pressure-rise is noticed during compression and BAM studies where no change in reflectivities is found after spreading drug solution on water. The drug can stay at the interface when both drug and lipid-molecules are spread on water (Fig. 5e and f), again consistent with the experimentally obtained results. Fig. 6a and b depicts the snapshots of the lipid-monolayers respectively at low (A = 81.5 nm2 /molecule) and high 2 (A = 50 nm /molecule) surface densities. At low pressure lipidmolecules are loosely packed and the alkyl chains are in gauche conformations (Fig. 6a). At high pressure, molecules become closely packed and the alkyl chains are in all-trans conformations (Fig. 6b). This is consistent with the experimental studies of Gang et al [34]. They have reported the DPPC lipid chains are conformationally disordered with a significant number of gauche configurations in the LE-phase. The hydrocarbon chains are in an all-trans conformation and are tilted from the surface normal by 25◦ in the LC-phase.
5.2. Drug-induced molecular disorder The intrusion of drugs into lipid-membrane changes molecular ordering in lipid chains. The deuterium order parameter as a function of carbon atom index along the lipid tail (carbon number one is the carbonyl carbon closest to the headgroup) gives the ordering details of the tails in the lipid-membrane [35–37]. The drug-induced softening should be reflected in the change in deuterium order parameter values. The deuterium order parameter (Scd) is defined as S = (1/2)(cos 2 − 1) where is the angle between the molecular vector and the membrane normal and the brackets denote average over time and molecules. g order tool of GROMACS has been used to extract order parameter values of carbon atom Ci by using the molecular vector Ci−1 to Ci+1 of lipid chains from mdrun simulations. No order parameter value is calculated for the first and last carbon atom of the tails. Scd profiles of sn1 and sn2 chains in pure lipid-membranes for different areal densities are shown in Fig. 7a. The order parameter profile of sn1 chain is seen to have a plateau region in the lower and middle part of the chains in which the order parameter remains almost constant, and a drop in order parameter towards 0 at the end of the chain. The order parameter profile for the other chain shows a more ordered region in the middle of the chain only. Both the chains are disordered at low lipid density (A = 81.5 nm2 /molecule). The order parameter value of sn2 chain is increased with lipid density. The order parameter value of sn1 chain for carbon atoms close to the headgroup is increased with lipid density. The ordering of sn1 chains away from the headgroup is maximum at A = 60 nm2 /molecule. This disordering of different parts of the tails are consistent with the experimental observation on the bilayer where the part of the chain near the headgroup region is found to be more ordered [3].
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Both chains become disordered at very high lipid density (A = 49.5 nm2 /molecule). Although chains are close packed and ordered at A = 49.5 nm2 /molecule the calculated order parameter value is low due to membrane deformation. In general, the monolayers with the larger areal density remained planar throughout the simulations and the monolayers with smaller areal density get deformed sometimes with partial loss of molecules into subphase [16,38]. At A = 49.5 nm2 /molecule lipid membrane buckled and few lipid-molecules were observed to emerge out of the monolayer into the subphase during the molecular dynamics simulation. Fig. 7b and c shows the change in order parameters in the presence of drug in lipid-monolayers. For each case, the alkyl chains become disordered in the presence of drug except at A = 49.5 nm2 /molecule. The unusual behaviour at A = 49.5 nm2 /molecule is due to extreme deformation of lipid membrane and material loss from the interface to water subphase. For sn1 chain Scd is maximum at 11th carbon atom for A = 53.0 nm2 /molecule, at 9th carbon atom for A = 60.5 nm2 /molecule and at 8th for A = 81.5 nm2 /molecule. For sn2 chain Scd is maximum at 10th carbon atom for A = 53.0 nm2 /molecule, at 11th for A = 60.5 nm2 /molecule and at 8th for A = 81.5 nm2 /molecule. Thus the drug-induced disordering effect on the alkyl chains is minimum near the headgroup region. This is consistent with the drug-induced change in cooperativity in a lipid bilayer [3]. Both the chains become ordered as D/L ratio is increased from 0.025 to 0.100. This is consistent with the anomalous behaviour on drug concentration observed in our compressibility studies. Again this is analogous to the order parameter value of both chains increasing with lipid density and shows the equivalence of high surface pressure and high drug-dose, consistent with the experimental data on stability and compressibility. Fig. 7d and e shows the orientation of drug-molecules at the interface for D/L = 0.025 and 0.100, respectively. It is clear that in the former case the molecule has its rings roughly parallel to the interface which in the latter they are roughly perpendicular, bearing out the proposed model to explain the stability and compressibility variations with drug dosage. Hence we can temporarily assign this model for the drug–lipid interaction.
6. Conclusion Isotherms of pure-lipid monolayers show that LE–LC phase transition pressure (t ) is raised as the temperature is increased. The increase in t at constant temperature in the presence of drug indicates drug-induced fluidization in drug/lipid monolayers. This is reflected in the − A isotherm of drug/lipid monolayer with the variation of pressure, temperature, subphase-pH and drug-dose. The long-term dynamics of the lipid-monolayer are studied to investigate monolayer stability. DMPC monolayer is found to be very stable and unlike DPPC or polymer monolayers, follows an algebraic decay in surface-area or surface-energy E with time t, given by E ∼ t−p , where p is the decay exponent. Each decay curve has two distinct temporal regions at low surface pressure and/or drug-dose and three at high values of these quantities. This nature of decay suggests that the decay entails neither desorption into the subphase nor nucleation on the subphase as confirmed by BAM studies. Drug-induced modifications to the monolayer stability are tentatively modelled by introducing two opposite mechanisms: (a) ‘charging–discharging’ where the drug-molecule sitting with its rings parallel to the water surface increases the separation between the headgroups and (b) ‘discharging–charging’ where the rings sitting roughly perpendicular to the water surface bring the headgroups closer. The orientations of drugs relative to water surface in the above two mechanisms are found to be decided by the molecular ionization states. Drug-induced softening of lipid-monolayer is
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characterized by obtaining the compressibilities of pure and mixed monolayers as a function of surface-pressure, temperature, pH and drug-dose. It is found that the drug-induced compressibilitychange is prominent in the LE–LC transition zone. Effect of pH on drug-induced ‘softening’ is found to be consistent with the results of mechanical stability with pH. Drug-induced ‘softening’ with drug-dose shows there is an optimum dose of drug for attaining maximum compressibility. The softening of the monolayer is found to increase its stability. Molecular dynamics simulation of DMPC monolayer shows that there is a significant number of gauche conformations with low lipid tail ordering in LE-phase and the alltrans conformations dominate in LC-phase of the lipid monolayer. The part of the chain near the headgroup region is found to be more ordered. The alkyl chains of the lipids are less ordered in the presence of drug with D/L ratio 0.025. The drug-induced change in the lipid tail ordering is found to be more prominent near the headgroup region. Both the chains become ordered as D/L ratio is increased from 0.025 to 0.100 indicating an anomalous behaviour of drug–lipid interaction with drug concentration as seen in our compressibility studies. Our proposed model has been borne out of Molecular Dynamics studies. Acknowledgements UKB thanks University Grants Commission (UGC) for their financial support and Department of Atomic Energy (DAE) for giving permission to carry out research under the aegis of Saha Institute of Nuclear Physics (SINP). References [1] S. Kundu, H. Chakraborty, M. Sarkar, A. Datta, Colloids Surf. B: Biointerfaces 70 (1) (2009) 157–161. [2] M. Lúcio, F. Bringezu, S. Reis, J.L. Lima, G. Brezesinski, Langmuir 24 (8) (2008) 4132–4139. [3] C. Nunes, G. Brezesinski, C. Pereira-Leite, J.L. Lima, S. Reis, M. Lúcio, Langmuir 27 (17) (2011) 10847–10858. [4] K. Czapla, B. Korchowiec, E. Rogalska, Langmuir 26 (5) (2009) 3485–3492. [5] M.K. Ratajczak, Y. Chris Ko, Y. Lange, T.L. Steck, K.Y.C. Lee, Biophys. J. 93 (6) (2007) 2038–2047. [6] J.M. Holopainen, H.L. Brockman, R.E. Brown, P.K. Kinnunen, Biophys. J. 80 (2) (2001) 765–775.
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