Anionic Form of Usnic Acid Promotes Lamellar to Nonlamellar

Mar 21, 2014 - Fundamental Chemistry Department, Federal University of Pernambuco, Recife PE 50.740-540, Brazil. J. Phys. Chem. B , 2014, 118 (14), ...
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Anionic Form of Usnic Acid Promotes Lamellar to Nonlamellar Transition in DPPC and DOPC Membranes Daniela Nadvorny, Joaõ Bosco P. da Silva, and Roberto D. Lins* Fundamental Chemistry Department, Federal University of Pernambuco, Recife PE 50.740-540, Brazil ABSTRACT: Usnic acid is a secondary metabolite found in several species of lichens, organisms resulting from the symbiosis between fungi and algae. This compound has been extensively studied because of its pharmacological properties. Despite its potential medicinal importance, it exhibits a high degree of toxicity. The confinement of the usnic acid within liposomes has been investigated as a possibility to reduce its toxicity. In this work, we characterize the interaction of usnic acid in its neutral and anionic states (usniate) with DPPC and DOPC by means of molecular dynamics simulations. A lamellar to nonlamellar transition is observed for both membranes upon contact with usniate within 100 ns time scale. The transition suggests the formation of a liposome-like structure encapsulating the metabolyte. Furthermore, such process occurs at a significantly shorter time frame for DOPC.

U

delivery systems make possible targeted administration of smaller dosages of a given compound, therefore mitigating eventual side effects.7 Encapsulation can take place via transport across the medium of by assembly of the material around the metabolyte. Therefore, encapsulation efficiency will depend on the molecular mechanism, that is, physicochemical interactions, between metabolyte and nanocapsule. The choice of the material used in delivery should ideally take into account biocompatibility and biodegradability issues. In vivo studies have shown that UA encapsulated into poly(lactic-co-glycolic-acid) (PLGA) has increased antitumor activity and overall lower cytotoxicity.1,6 In addition, the metabolyte was shown to remain considerably longer inside of the cells compared to the delivery of its free form. Liposomes have also been used as an alternative biomaterial for the encapsulation of UA as their components are the main constituents of biological membranes.8 Aiming to understand the interaction between UA and lipid membranes, thermodynamic analyses from Langmuir films of monolayers of DOPC, DMPC, and DPPC in the presence of different molar rations of UA have been performed.9 Although analysis of excess free energies (ΔGE) revealed that UA interacts with all three membranes, a better association was observed for DOPC. The favored interaction between the DOPC and UA was attributed to the presence of an unsaturation in the DOPC chain. To test this hypothesis, we have performed computer simulations of the interactions of UA, in its anionic and neutral forms (UAI and UAN, respectively), with model lipid bilayers of DPPC and DOPC. DOPC differs from the former by an unsaturation on carbon-9 and acyl chains formed by 18 carbons, compared to 16 carbons

snic acid (UA) (Figure 1) is a secondary metabolite found in several species of lichens, organisms resulting

Figure 1. Structure of usnic acid in its most stable (enolic) form: (a) Neutral and (b) anionic. (The enolic group having the strongest acidic character is highlighted in red.)

from the symbiosis between algae and fungi.1 This compound has been extensively studied because of their pharmacological properties such as analgesic activity, antimicrobial, and antitumoral, for example.1,2 The ability of UA to cross biological membranes has been attributed to the possibility of this largely apolar compound to modulate its solubility by protonation/deprotonation of a hydroxyl group.3 Previous studies indicate that, among the three hydroxyl groups in UA, the enolic 3-OH has the strongest acidic character (pKa 4.4), followed by 9-OH (pKa 8.8) and 6-OH (pKa 10.7).4 Thus, it has been postulated that in physiological environment UA can assume its usniate form through a deprotonation at 3-OH (as illustrated in Figure 1). Despite its potential medical applications, the use of UA as a drug has been prevented due to its strong hepatotoxicity in mammals.5 As an example, in 2006, Roach and co-workers have demonstrated that the ingestion of lichen Xanthoparmelia chlorochroa resulted in the death of 328 elk in the Red Kidney region, Wyoming. Severe lesions were identified in the livers of these animals.5 In an attempt to overcome UA hepatotoxicity, nanocapsules have been used as UA deliver systems.1,6 Drug © 2014 American Chemical Society

Received: December 12, 2013 Revised: March 20, 2014 Published: March 21, 2014 3881

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in DPPC. The molecular level associations of these binary systems were assessed in aqueous solutions, and the influence of UA on the stability of the model membranes discussed. In addition, the present results provide insights into the encapsulation mechanism of UA by biological lipids.

membrane phase transitions. This parameter can be calculated as

METHODOLOGY AND COMPUTATIONAL DETAILS Usnic acid atomic coordinates were generated with the GaussView program and subsequently geometry optimized at the B3LYP/6-31++G(d,p) level with the Gaussian 03 program.10 The resulting structures (neutral and deprotonated forms) were submitted to a RESP fitting11 to obtain partial atomic charges that were used in conjunction with the GROMOS 53A6 parameter set.12−15 Starting from previously equilibrated DPPC and DOPC lipid bilayer membranes, systems comprising a larger membrane slab with 256 lipids per leaflet and 196 UA molecules were generated. The ratio of ca. 2.6:1 lipid/UA was arbitrarily chosen. The UA molecules were initially placed at a distance of at least 10 Å from the membrane surface. The systems were solvated using the SPC water model16 and counterions added, if necessary to maintain system neutrality (systems dimensions are summarized in Table 1). Initial system dimensions were set to ca. 127 × 127 × 120

Figure 2 shows the area per lipid for each system as a function of time. The graph shows a stable behavior for both membranes

area per lipid =



time of simulation (ns) no. of atoms no. of UA molecules no. of lipid molecules no. of water molecules no. of Na+ ions

DPPCI

DOPCN

DOPCI

100 129 959 196 512 32 957

190 129 371 196 512 32 761 196

100 167 881 196 512 44 915

100 185 368 196 512 50 744 196

(1)

Figure 2. Area per lipid in function of time for DPPC and DOPC in the presence of neutral (DPPCN, DOPCN) and anionic (DPPCI, DOPCI) UA.

Table 1. Description of the System Dimensions and Simulation Time DPPCN

(box length in x)(box length in y) number of lipids in a leaflet

in the presence of UA in its neutral form throughout the entire 100 ns of simulation. In addition, UAN does not seem to interfere with the membrane structure. Previous simulations of pure DPPC and DOPC, using the same force field, have reported values nearly identical to ones obtained in the presence of UAN. The average values of the current simulation over the entire 100 ns trajectory are 0.62 and 0.65 nm2 (at 310 K) for DPPC and DOPC, respectively (Table 2). These values compare to 0.64 nm2 (at 325 K) for pure DPPC and 0.66 nm2 (at 310 K) for pure DOPC. It is noticeable that while the force field is capable to reproduce correctly the experimentally measured area per lipid for DPPC (0.63 nm2), it slightly underestimates this property for DOPC (0.72 nm2) (Table 2).23,24 In contrast, the anionic form of UA leads to a perturbation of the area per lipid of both membranes. A dramatic decrease of the area per lipid suggests that UAI promotes a lamellar to nonlamellar transition. Such behavior is more pronounced in DOPC at shorter time scales. After 100 ns, the area per lipid for DOPC is ca. 0.34 nm2, while for DPPC this value is ca. 0.48 nm2. The latter requires twice the amount of simulation time to display a similar area per lipid (Figure 2). Such a disturbance indicates an effective interaction of the membrane with UAI. (It is worth noting that both systems are overall neutral, since mobile counterions are present in the simulations containing UAI.) This result is consistent with previous experimental observation where a decrease in area per lipid of DPPC, DOPC, and DBPC monolayers was observed as a function of increasing the concentration of UA.9 The authors have proposed that hydrogen bond interactions between the UA molecules would reduce their ability to anchor the membranes. Density Profile. To evaluate the lamellar integrity and UA distribution, the transmembrane electron density profile was calculated for the last 25 ns period of each simulation. Figure 3a,b and e,f shows a symmetric profile for DPPC and DOPC at the beginning and at the end of the simulations, respectively, when in the presence of the neutral form of UA. Such

Å3 for the DPPC membranes and 130 × 130 × 140 Å3 for the DOPC membranes. The four systems (DPPC-UAN, DPPCUAI, DOPC-UAN, DOPC-UAI) were submitted to molecular dynamics simulations using the GROMACS 4.0.717 in conjunction with the GROMOS force field parameter set 53A6.12−15 The leapfrog algorithm18 was used with an integration time step of 2 fs. The temperature was kept at 310 K via the v-rescale thermostat19 with a relaxation time of 0.1 ps coupled separately for solvent and solute. Pressure was maintained at 1 bar using the Berendsen barostat20 in a semiisotropic scheme with a coupling constant of 1.0 ps and a compressibility of 4.5 × 10−5 bar−1. Periodic boundary conditions were applied in all three dimensions. A shortrange cutoff of 14 Å was used for all nonbonded interactions, and the reaction field treatment21 was applied to long-range electrostatic interactions with ε = 66. LINCS constraints22 were applied to all bonds.



RESULTS AND DISCUSSION The structure and dynamical stability of DPPC and DOPC membranes in the presence of both forms of UA, that is, neutral and anionic, were probed by their area per lipid, density profile, deuterium order parameter, and the interactions between the lipids UA. Area per Lipid Headgroup. The time-dependence of the area per lipid can be used a metric to determine structural equilibrium in a simulation as well as to monitor eventual 3882

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Table 2. Experimental and Theoretical Average Values for Area Per Lipid pure experimental (nm2) DPPC DOPC a

a

0.63 (323 K) 0.72 (303 K)c

pure theoretical (nm2) b

0.64 (325 K) 0.66 (310 K)d

UAN theoretical (nm2) e

0.62 (310 K) 0.65 (310 K)e

UAI theoretical (nm2) nonlamellare nonlamellare

Nagle and Tristram-Nagle.24 bTieleman and Berendsen.26 cLiu and Nagle.23 dSiu et al.30 eThis work.

Figure 4. Representation of the different steps of the simulations performed. (a, b) DPPC with UAN at 100 ns of simulation, (c) DPPC with UAI at 100 ns of simulation, (d) DPPC with UAI at 190 ns of simulation, (e) DOPC with UAN at 100 ns of simulation, and (f) DOPC with UAI at 100 ns of simulation. The z-axis denotes the transmembrane axis; (b) is rotated 90° over the z−y plane and shows the distribution of the UA from a top view. Membrane atoms are shown in gray, except for the ester group oxygen atoms, which are shown in red; UA molecules are shown in blue. (Systems (d) and (f) were laterally replicated (×1) to better convey the liposome-like arrangement.)

area per lipid (Figure 2) displayed by the DOPC-UAI system. The nonsymmetrical density profile is characteristic of a nonlamellar membrane structure. In addition, all profiles show a correspondence in the distribution of UA and the phosphate groups of the lipids (Figure 3). In fact, visual inspections of the molecular systems reveal a disruption of the lamellar state of both DPPC and DOPC when in presence of UA in its anionic form (Figure 4). While UA in its anionic form causes membrane disruption to both DPPC and DOPC systems, the time required to observe such transition is much longer for DPPC. It took ca. 40 ns for the anion to disrupt the DOPC membrane, which occurred abruptly and a total absence of a lamellar structure was observed within the next 60 ns (see area per lipid behavior in Figure 2). On the other hand, usniate caused a slow and continuous lamellar to nonlamellar transition in the DPPC membrane. Upon contact with the metabolite, the latter quickly undergoes to ripple-like phase (Figure 4c) during the first ca. 90 ns and progressively looses its lamellar arrangement over the remaining 110 ns (see area per lipid behavior in Figure 2). This finding suggests that such transition is thermodynamically more favorable for DOPC, which corroborates previously published studies by Andrade and co-workers.9 In this study mixed floating monolayers of DPPC, DBPC, and DOPC and (UA) were used to analyze quantities such as excess areas, excess free energy, and free energy. As a result, it was observed that the UA interacts with the three phospholipids. However, based on the results of excess free energies, a better association with DOPC

Figure 3. Density profiles of the first and last 25 ns of simulation with the UA neutral and deprotonated in DPPC (a−d) and DOPC (e−h). The black, red, green and blue lines represent the density profile of the usnic acid, lipid, oxygen atom of the water molecules, and phosphates groups, respectively. ((a) first 25 ns DPPC-UAN; (b) last 25 ns DPPCUAN; (c) first 25 ns DPPC-UAI; (d) last 25 ns DPPC-UAI; (e) first 25 ns DPPC-UAN; (f) last 25 ns DPPC-UAN; (g) first 25 ns DPPC-UAI; (h) last 25 ns DPPC-UAI.)

distribution is characteristic of a lamellar system. The neutral form of UA lies on the polar−nonpolar membrane interface in both cases (Figure 3b and f). It is also interesting to note that the metabolyte presents a broader distribution in DOPC, compared to DPPC (Figure 3b and f). This is likely due to the increased DOPC area per lipid. On the other hand, the ionic form of UA causes a perturbation of both systems (Figure 3d and h) toward a nonsymmetrical profile. The distribution of water molecules, as well as UA, can be seen throughout the entire normal axis as defined with respect to the initial lamellar membrane structure. The disturbance is more pronounced at the early stages of the simulation for DPPC (Figure 3c and g), as expected from the behavior of the area per lipid (Figure 2). However, after 100 ns of simulation, the UA and water molecules are more evenly distributed in the DOPC system (see Figure 3d and h). An additional 100 ns is necessary for the DPPC-UAI system to reach similar arrangement (Figure 4) and 3883

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DOPC is a unsaturated phospholipid, which results in some difficulties with the isotopic labeling of a double bond and therefore in the determination of their experimental order parameter.29 Hydrogen Bond Analyses. Monitoring of hydrogen bonds can reveal the differential interaction of UA with DPPC and DOPC as a function of its protonation state. The number of hydrogen bonds and their corresponding average lifetime were calculated, over the last 25 ns interval, for four group pairs: UA−UA, UA−lipid phosphate group, UA−lipid SN1 ester and UA−lipid SN2 ester. A hydrogen bond donor-hydrogen··· acceptor (DH···A) is assumed to be present when the distance H···A is smaller than 0.35 nm and the angle DH···A is larger than 135°. Figure 6 shows the average number of hydrogen bond formed between the UA and the lipid components during the

was observed. In these analyses, only the DOPC presented negative values of free energy indicating a more stable system. For mixed DPPC/UA and DOPC/UA, low pressures are required to have a system thermodynamically favored. The more favorable interaction for the system DOPC-UA was associated to the presence of the double bond in the alkyl chain.9 Deuterium Order Parameter. The order parameter, SCD, provides a measurement of the degree of ordering in a system. Such quantity has been widely used to validate and calibrate molecular dynamics simulations.25 The expression used to calculate this parameter is given by SCD =

1 3cos 2 sin aθi − 1 2

(2)

where θi is the angle formed by the resulting vector along the lipid acyl chain and the normal to the bilayer. The brackets denote an average over the ensemble. Therefore, ordered systems will have higher values, while values closer to zero are typical from disordered systems. Figure 4 shows the calculated order parameter for SN1 and SN2 chains in all simulations. A dramatic decrease in the deuterium order parameter is observed for the membranes in the presence of UA in its ionic form, confirming the adoption of a nonlamellar state for theses systems. Average values for the membranes in the presence of UA in its neutral form do not differ significantly from previous simulations of the systems in absence of cosolutes,26,27 as well as the average experimental value for DPPC (0.212 at 41 °C for its SN2 chain).28 To our knowledge, detailed deuterium order parameter experimental data for DOPC is not available in the literature. However, values for C9, C10 (32 °C), and C11 (30 °C) in pure DOPC have been measured.29 These atoms correspond to C8, C9, and C10 in Figure 5. As expected from the obtained smaller area

Figure 6. Number of hydrogen bonds formed during simulations between the UA in its neutral and ionic form and the usnic acid, phosphate group, ester group SN1 and SN2. In blue is the simulation of UA neutral in DPPC, red the simulation of UA neutral in DOPC, green the simulation of UA ionic in DPPC, and purple the simulation of UA ionic in DOPC.

simulations. The number of hydrogen bonds of UA with itself in its ionic form is higher compared to its neutral counterpart. As expected, once the compound becomes soluble, the electrostatic interactions should play a more important role in the UA−UA interactions. This increase in the number of UA− UA hydrogen bonds comes at the expense of a decrease of the interaction between UA and the lipid phosphate groups (Figure 6). Despite the lower number of hydrogen bonds between lipid-UAI, the lifetime of these interactions are significantly stronger compared to the UA in its neutral form (Table 3). The relative increased UA−UA interaction in its anionic form is explained by the confinement of UA molecules into pockets formed by a liposome-like arrangement (Figure 4). Figure 6

Figure 5. Order parameter for SN1 and SN2 chain to (a) DPPC and (b) DOPC in the presence of usnic acid in its neutral and anionic forms. (Values shown as averages of 5 ns over the last 25 ns simulation for each system. Standard deviations per carbon atom are represented as error bars.)

per lipid for DOPC compared to the experimental value, the calculated order parameters are slightly higher. Experimental values for above-mentioned carbons are 0.10, 0.02, and 0.05,29 which compares to ca. 0.11, 0.07, and 0.10 as obtained from our simulations. Moreover, the overall shape and amplitude of calculated order parameters for DOPC in the presence of neutral UA are similar to those of a number of previously published simulations for pure DOPC. In our simulations, differences in the behavior of SN1 and SN2 chains are nearly negligible. Small differences can be seen for the carbon atoms closer to the lipid headgroup, due to the asymmetry of the ester groups with respect to the headgroup. As expected, values decrease along the chain in all systems since the atoms located in the end of the chain have more freedom of movement.

Table 3. Average Hydrogen Bond Lifetimes (given in ps)a UAN AUS-AUS AUS-PO4 AUS-est-SN1 AUS-est-SN2

UAI

DPPC

DPPC

DPPC

DOPC

5.12 19.64 36.88 11.83

5.24 15.60 42.50 9.74

91.77 63.23 135.10 29.58

106.73 74.22 202.81 23.03

a

Hydrogen bond lifetime (or residence time) is expressed as the integral of the autocorrelation function. Data shown were calculated for the last 25 ns interval.

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(7) Pinto Reis, C.; Neufeld, R. J.; Ribeiro, A. J.; Veiga, F. Nanoencapsulation Ii. Biomedical Applications and Current Status of Peptide and Protein Nanoparticulate Delivery Systems. Nanomed. Nanotech. Biol. Med. 2006, 2, 53−65. (8) Lira, M. C. B.; Ferraz, M. S.; Silva, D. G. V. C.; Cortes, M. E.; Teixeira, K. I.; Caetano, N. P.; Sinisterra, R. D.; Ponchel, G.; SantosMagalhães, N. S. Inclusion Complex of Usnic Acid with BetaCyclodextrin: Characterization and Nanoencapsulation into Liposomes. J. Inclusion Phenom. Macrocyclic Chem. 2009, 64, 215−224. (9) Andrade, C. A. S.; Santos-magalhães, N. S.; Melo, C. P. D. Thermodynamic Characterization of the Prevailing Molecular Interactions in Mixed Floating Monolayers of Phospholipids and Usnic Acid. J. Colloid Interface Sci. 2006, 298, 145−153. (10) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. J. A.; Vreven, T.; Kudin, K. N.; Burant, J. C., et al. Gaussian 03, Revision E.01; Gaussian, Inc.: Wallingford, CT, 2004. (11) Bayly, C. I.; Cieplak, P.; Cornell, W. D.; Kollman, P. A. A WellBehaved Electrostatic Potential Based Method Using Charge Restraints for Deriving Atomic Charges - the Resp Model. J. Phys. Chem. 1993, 97, 10269−10280. (12) Chandrasekhar, I.; Kastenholz, M.; Lins, R. D.; Oostenbrink, C.; Schuler, L. D.; Tieleman, D. P.; van Gunsteren, W. F. A Consistent Potential Energy Parameter Set for Lipids: Dipalmitoylphosphatidylcholine as a Benchmark of the Gromos96 45a3 Force Field. Eur. Biophys. J. 2003, 32, 67−77. (13) Oostenbrink, C.; Soares, T. A. Validation of the 53a6 Gromos Force Field. Eur. Biophys. J. 2005, 273−284. (14) Soares, T. A.; Daura, X.; Oostenbrink, C.; Smith, L. J.; van Gunsteren, W. F. Validation of the Gromos Force-Field Parameter Set 45a3 against Nuclear Magnetic Resonance Data of Hen Egg Lysozyme. J. Biomol. NMR 2004, 30, 407−422. (15) van Gunsteren, W.; Bakowies, D.; Burgi, R.; Chandrasekhar, I.; Christen, M.; Daura, X.; Gee, P.; Glattli, A.; Hansson, T.; Oostenbrink, C.; et al. Molecular Dynamics Simulation of Biomolecular Systems. Chimia 2001, 55, 856−860. (16) Berendsen, H. J. C.; Postma, J. P. M.; van Gunsteren, W. F.; Hermans, J. Interaction Models for Water in Relation to Protein Hydration. In Intermolecular Forces; Pullman, B., Ed.; Reidel: Dordrecht, 1981; pp 331−342. (17) Hess, B.; Kutzner, C.; van der Spoel, D.; Lindahl, E. Gromacs 4: Algorithms for Highly Efficient, Load-Balanced, and Scalable Molecular Simulation. J. Chem. Theor. Comput. 2008, 4, 435−447. (18) Hockney, R. W. The Potential Calculation and Some Applications. In Methods in Computational Physics; Alder, B., Fernbach, S., Rotenberg, M., Eds.; Academic Press: New York/ London, 1970; Vol. 9. (19) Bussi, G.; Donadio, D.; Parrinello, M. Canonical Sampling through Velocity Rescaling. J. Chem. Phys. 2007, 126, 014101−014101. (20) Berendsen, H. J. C.; Postma, J. P. M.; Van Gunsteren, W. F.; Dinola, A.; Haak, J. R. Molecular-Dynamics with Coupling to an External Bath. J. Chem. Phys. 1984, 81, 3684−3690. (21) Tironi, I. G.; Sperb, R.; Smith, P. E.; Van Gunsteren, W. F. A Generalized Reaction Field Method for Molecular-Dynamics Simulation. J. Chem. Phys. 1995, 102, 5451−5459. (22) Hess, B.; Bekker, H.; Berendsen, H. J. C.; Fraaije, J. Lincs: A Linear Constraint Solver for Molecular Simulations. J. Comput. Chem. 1997, 18, 1463−1472. (23) Liu, Y.; Nagle, J. Diffuse Scattering Provides Material Parameters and Electron Density Profiles of Biomembranes. Phys. Rev. E 2004, 69, 040901−040901. (24) Nagle, J. F.; Tristram-Nagle, S. Structure of Lipid Bilayers. Biochim. Biophys. Acta 2000, 1469, 159−195. (25) Vermeer, L. S.; de Groot, B. L.; Réat, V.; Milon, A.; Czaplicki, J. Acyl Chain Order Parameter Profiles in Phospholipid Bilayers: Computation from Molecular Dynamics Simulations and Comparison with 2h Nmr Experiments. Eur. Biophys. J. 2007, 36, 919−931. (26) Tieleman, D. P.; Berendsen, H. J. C. Molecular Dynamics Simulations of a Fully Hydrated Dipalmitoylphosphatidylcholine

also shows that the interaction between UA and the ester groups plays a less important role, indicating that this association takes place at the membrane surface/head groups (as illustrated in Figure 4). The slightly higher number of hydrogen bonds between UA and the ester group in SN1 chain over SN2 occurs due to the presence of one more methylene group in the chain of the SN2 ester group. Thus, the UA is spatially closer to the ester group in SN1. Figure 6 and Table 3 also show that an overall higher number and persistence of UA−lipid hydrogen bonds for DOPC, compared to DPPC. This observation suggests an increased affinity between UA and DOPC, consistent with the observation of a thermodynamically more favorable phase transition for DOPC than DPPC.9



CONCLUSIONS The simulations presented here indicate that DPPC and DOPC undergo a lamellar to nonlamellar transition in the presence of the anionic form of UA. The membranes assume a liposomelike structure where the UA molecules are kept confined within the supramolecular arrangement. Despite of its lipophilicity UA molecules were distributed along the membrane headgroups, independent of its protonation state, within the simulation time of this study. These findings calls for experiments, such as differential scanning calorimetry, that can further characterize the association between usnic acid and model biological membranes.



AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.



ACKNOWLEDGMENTS This work was developed with financial support from FACEPE, NanoBiotec-BR/CAPES, CNPq, INCT-INAMI, and nBioNet. The authors thank Prof. Thereza Soares for her valuable comments. Partial computational resources were provided by Argonne Leadership Computing Facility, an U.S. Department of Energy scientific user facility located at Argonne National Laboratory.



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