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Polymyxin Binding to the Bacterial Outer Membrane Reveals Cation Displacement and Increasing Membrane Curvature in Susceptible but not in Resistant LPS Chemotypes Denys Ewerton da Silva Santos, Laércio Pol-Fachin, Roberto D. Lins, and Thereza A. Soares J. Chem. Inf. Model., Just Accepted Manuscript • DOI: 10.1021/acs.jcim.7b00271 • Publication Date (Web): 14 Aug 2017 Downloaded from http://pubs.acs.org on August 15, 2017

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Journal of Chemical Information and Modeling

Polymyxin Binding to the Bacterial Outer Membrane Reveals Cation Displacement and Increasing Membrane Curvature in Susceptible but not in Resistant LPS Chemotypes

Denys E. S. Santosa, Laércio Pol-Fachina,b, Roberto D. Linsb and Thereza A. Soaresa,c,* a

Department of Fundamental Chemistry, Federal University of Pernambuco, 50740-560 Recife, Brazil b

c

Aggeu Magalhães Institute, Oswaldo Cruz Foundation, 50740-465 Recife, Brazil

Department of Chemistry, Umeå Center for Microbial Research, Umeå University, 90.187,

Umeå, Sweden.

Corresponding author e-mail address: [email protected]

ACS Paragon Plus Environment

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Lipid-A is the causative agent of Gram-negative sepsis and responsible for increasingly high mortality rate among hospitalized patients. Compounds that bind Lipid-A can limit this inflammatory process. The cationic antimicrobial peptide polymyxin B (Pmx-B) is one of the simplest molecules capable of selectively bind to Lipid-A, and may serve as a model for further development of Lipid-A binding agents. Gram-negative bacteria resistance to Pmx-B relies on the upregulation of a number of regulatory systems, which promote chemical modifications of the LPS structure, and leads to major changes in the physical-chemical properties of the outer membrane. A detailed understanding of how the chemical structure of the LPS modulates macroscopic properties of the outer membrane is paramount for the design and optimization of novel drugs targeting clinically relevant strains. We have performed a systematic investigation of Pmx-B binding to outer membrane models composed of distinct LPS chemotypes experimentally shown to be either resistant or susceptible to the peptide. Molecular dynamics simulations were carried out for Pmx-B bound to the penta- and hexa-acylated forms of Lipid-A (more susceptible) and Lipid-A modified with 4-amino-4-deoxy-L-arabinose (resistant) as well as the penta-acylated form of LPS Re (less susceptible). The present simulations show that upon binding to the bacterial outer membrane surface, Pmx-B promotes cation displacement and structural changes in membrane curvature and integrity as function of the LPS chemotype susceptibility or resistance to the antimicrobial peptide.

KEYWORDS. Molecular Dynamics, 3JHN,H coupling constant, GROMOS Force Field, NMRbased validation of simulations, Antimicrobial Peptides, Lipopolysaccharides, Lipid-A


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Introduction Lipopolysaccharide (LPS) is the major cell surface molecule of Gram-negative bacteria, and a powerful activator of the mammalian immune system at fmol amounts.1 The LPS molecule consists of a backbone containing a variable number of fatty acid chains termed lipid A, covalently linked to a long polysaccharide chain.2-4 LPS of varying oligosaccharide length or number of acyl chains with distinct biological properties constitute different chemotypes. Gramnegative bacteria evolved different strategies to fend off antimicrobial agents, including chemical modifications of the LPS (e.g. addition of phosphoethanolamine and/or 4-amino-4-deoxy-Larabinose) along with the use of efflux pumps, the production of outer membrane vesicles and overexpression of the outer membrane protein OprH.5-9 The harmful effects of LPS can be limited by the action of compounds acting on it. Polymyxin B (Pmx-B) is a cationic antimicrobial peptide capable of selectively binding to lipid A.10 Polymyxins are pentacationic polypeptides consisting of a cyclic heptapeptide, a linear tripeptide and a fatty acid tail linked to the N-terminal of the tripeptide (Figure 1). The presence of the positively charged L-diaminobutyric acid (positions 1, 3, 5, 8, and 9) and hydrophobic residues impart the amphiphatic nature of polymyxins. There has not been a new antibiotic scaffold for Gram-negative bacteria in the last decades.11-13 This issue is arguably more critical due to the emergence of multidrug-resistant (MDR) Gram-negative bacteria, in particular strains of Pseudomonas aeruginosa, Acinetobacter baumannii and Klebsiella pneumonia.14, 15 Polymyxins have become front-line therapy in recent years, although these natural antibiotics were deemed as too toxic when discovered 40 years ago.16-18 However, the low rate of acquired resistance to Pmx-B in Gram-negative bacteria compared to conventional antibiotics makes it a unique


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prototype for the development of novel therapeutic compounds targeting the structurally invariant Lipid-A toxin.19 The mechanism of action of polymyxins is not fully understood. Cationic antimicrobial peptides such as polymyxins appear to act as a “dirty” drug, which disrupts several biological functions with modest potency rather than inhibiting  a specific high-affinity target.20, 21 It has been proposed that polymyxins permeabilize the bacterial outer membrane via a self-promoted uptake mechanism where positively charged residues in the peptide would disrupt the negatively charged LPS head groups through competitive displacement of divalent cations.22-26 The selfpromoted uptake mechanism has not yet been demonstrated by direct measurements. This is partially due to experimental difficulties such as the conformational heterogeneity of polymyxins (see below), the low solubility of Lipid-A in water and the inhomogeneity of Lipid-A preparations. Furthermore, isothermal titration calorimetry measurements indicate different PmxB binding mechanisms depending on the chemotypes.27 On the other hand, computational simulations can overcome some of the above issues, and have recently been performed at the coarse-grain and atomistic levels for Pmx-B in presence of the chemotype LPS Re from Escherichia coli in the outer leaflet and a mixture of phospholipids in the inner leaflet.28, 29 These simulations have provided detailed insights into the interaction of Pmx-B with bacterial outer membrane at different temporal and spatial scales. Therefore, the full understanding of the molecular mechanism by which Pmx-B disrupts the bacterial outer membrane will ultimately benefit from methods that account for atomic-level properties while simultaneously coupling temporal and spatial scales.30, 31 NMR spectroscopy has been previously applied to the structural characterization of polymyxin variants in water and bound to Lipid-A aggregates from Escherichia coli.32, 33 These


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measurements have shown that polymyxin variants exist in equilibria of fast exchanging conformations in solution, and less so upon binding to LPS/Lipid-A aggregates. However, the NMR measurements did not yield NOE restraints in sufficient numbers and adequate intensities to allow the assignment of full three-dimensional structures.32,

33

Notwithstanding, a set of 10

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JHN,Hα coupling constants were obtained for polymyxins B and E which were used in

conjunction with molecular modeling to estimate the overall ring conformation of these cyclic peptides. We have performed atomistic MD simulations of Pmx-B in presence of five LPS chemotype bilayers representative of bacterial outer membrane with different levels of resistancesusceptibility to this antimicrobial peptide. In order to account for possible inaccuracies in the physical description of the system, we have built on NMR-derived vicinal constants to explore the conformational dynamics of polymyxin B in solution and upon binding to lipopolysaccharide (LPS) chemotype membranes via atomistic molecular dynamics (MD) simulations. A series of exploratory simulations were performed using two different force field sets for peptides (GROMOS 53A6 and GROMOS 54A7), two types of electrostatics treatment (particle mesh Ewald and reaction-field) and two sampling approaches (conventional MD and simulated annealing SA/MD). The present simulations provide an atom-level depiction of the initial steps of the Pmx-B uptake process, which is shown to take place through cation displacement from the outer membrane with the concomitant increase of membrane curvature in susceptible, but not in resistant LPS chemotypes.

Computational Procedure


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Atomic Parameters. MD simulations were performed for the cyclic peptide polymyxin B (Pmx-B) in explicit solvent and in presence of the five LPS chemotypes (Table 1). Atomic coordinates for the initial conformations of the peptides were modeled from the dihedral angles ϕ and ψ obtained from the 3JHN,Hα-coupling constants for polymyxin B in water via distance geometry optimization.33 Energy minimization was performed until a mean force of lesser than 100 kJ.mol-1.nm-1 was achieved. The NMR-derived conformations are characterized by a distorted type II’β-turn extending from residues 5-8 or an inverse γ-turn around residue 10.33 Ionization states of residues were chosen according to pH 7.0, which led to a total charge of +5e. The GROMOS parameter set 54A734 was used to represent Pmx-B in solution and in the LPS bilayers. Five LPS chemotype membranes were constructed: Lipid-A and Lipid-AAra4N, each one in the penta- and hexa-acylated forms, and LPS Re in the penta-acylated form (Figure SI-1). The parameter set 53A6GLYC35, 36 was used for the LPS carbohydrate moieties whereas the acyl chain parameters were taken from the GROMOS 53A6 force field37, 38 adapted and validated for LipidA.39 The GROMOS 53A6GLYC parameter set contains dihedral potential corrections for hexopyranoses with all the remaining atomic parameters being the same as for parameter set 54A7.34 Atomic charges for new chemical groups and new torsional potentials (e.g. for the Pglycosidic linkage and all C-C-C-O dihedrals) in the LPS chemotypes were calculated to maintain the compatibility with previous versions of GROMOS force fields.40-42 Atomic parameters for van der Waals interaction terms were retrieved from GROMOS 45A4/53A6 functional form for carbohydrates.40 The topologies and atomic parameters used to represent the LPS chemotypes are presented in supplementary information (Table SI-1: atomic charges, dihedral torsional potentials, potentials for bond stretching, bond-angle bending and improper


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dihedral deformation). Equilibrated atomic coordinates and topologies for all LPS chemotypes and different variants of polymyxin (B, M and E) are available for download at dqfnet.ufpe.br/BioMat or upon request. Simulated Systems and Setup. The SPC water model was used in all the simulations.43 Each polymyxin variant was placed in a cubic water box with a vector size of 4.0 nm. Counterions were added by replacing water molecules with the highest electrostatic potential by ions. LPS chemotype bilayers were comprised of 128 lipid molecules equally distributed in an 8 × 8 arrangement layer. When necessary, the charge of lipid molecules was neutralized with Ca2+ cations in order for the whole system to be neutral. The LPS bilayers were equilibrated for 100 ns when the area per lipid molecule converged.39 Subsequently, six molecules of Pmx-B were placed onto the surface of bilayers composed of the penta and hexa-acylated forms of Lipid-A and Lipid-AAra4N, and the hexa-acylated LPS Re, respectively. This setup corresponds to a peptide concentration of ca. 3 mM. An additional simulation of the penta-acylated Lipid-A bilayer (Pmx6+LipApenta-mM) was also performed at 150 mM NaCl to assess the effect of ionic strength on counter-ion diffusion. The simulated systems are presented in Table 1. MD simulations were performed in the NpT ensemble with a time step of 2 fs. Initial velocities were taken from a Maxwell distribution at 300 K and 1 bar. Bond lengths within the solute and the geometry of water molecules were constrained using the LINCS algorithm.44 The temperatures of solute and solvent were controlled by separately coupling them to a velocity rescaling thermostat with a relaxation time of 0.4 ps.45 The pressure was maintained at 1 bar through the Berendsen pressure coupling algorithm with a coupling constant of 1 ps and an isothermal compressibility of 4.5 × 10−5 bar-1 as appropriate for water.46 Isotropic and semiisotropic coordinate scaling coupling was applied to the simulations of the peptides in solution


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and in the bilayers, respectively. Long-range electrostatic interactions were calculated using the reaction-field approach47 with a relative dielectric permittivity constant of 66.48, 49 The reactionfield correction was applied to the electrostatic interactions beyond a cutoff of 1.4 nm. Nonbonded interactions were treated with a cutoff of 1.4 nm and pair list updates at every 10 fs. MD simulations coupled to the simulated annealing (MD/SA) technique were also employed in order to improve conformational sampling of polymyxin in solution. The same setup used in the MD simulations was kept for the MD/SA. The annealing was performed throughout the 100 ns of simulations with a periodic behavior alternating between 300 K and 600 K during 500 ps per loop. After equilibration, data production was carried out for 100 ns for MD and MD/SA simulations of Pmx-B in solution, and for 200 ns for Pmx-B in the LPS bilayers. Trajectories were recorded at every 2 ps. All simulations were performed using the GROMACS 4.5.4 suite of programs.50 Analysis. Trajectory analyses were performed with GROMACS 4.5.4 and in-house built codes. Three-bond 3JHN,Hα-coupling constants have been calculated from the MD ensemble of Pmx-B in solution using the Karplus equation51

= + +

(1)

where 3J is the spin-spin coupling constant for atoms HN and Hα, θ is the dihedral angle between atoms HN-N-Cα-Hα, and A, B and C are empirically calibrated parameters obtained from NMR measurements for globular proteins. We have used the parameters a = 6.51, b = 1.76, c = 1.6 Hz.52 The Karplus equation establishes a general relation between the dimension of the spin-spin coupling constant 3J and the molecular conformations of a molecule as defined by the dihedral angle in consideration. The time-averaged

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JHN,Hα-coupling constants were


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computed from the φ dihedral angle sampled over 100 ns MD simulations of the polymyxins and taking into account the chirality of the amino acids (D or L). The membrane surface curvature angle θ was estimated through a grid containing a normal vector per cell, i.e. a local normal vector. The curvature angle θ is given by the angle between the z-axis and each local vector per within the grid cells. To distinguish between two different phases (or orders) of the membrane surface curvature, we have calculated the curvature order parameter S by solving the second order Legendre polynomial for the cosine of the curvature angle θ:

= 3 − 1

(2)

Therefore, in the phase where S=1, the local membrane surface is normal to the z axis, i.e. θ = 0° whereas for S = -0.5, the local surface is parallel to the z axis, i.e. θ = 90°.

Results and Discussion Conformational landscape of Pmx-B from comparisons between MD- and NMR-derived 3

JHN,Hαα coupling constants in solution and LPS chemotype membranes The experimental 3JHN,Hα values for Pmx-B are in the range of average values expected for

fairly flexible molecules. 33 Therefore, it was necessary to ensure that our computational protocol and force field parameters would capture such flexibility, and reproduce the experimental structural ensemble for Pmx-B in solution and bound to the Lipid-A aggregate. Two different parameter sets of the GROMOS force field (53A6 and 54A7) and two different approaches to treat long-range electrostatic interactions (particle mesh Ewald and reaction field) have been used to simulate Pmx-B in solution (Table 2). The systematic comparison of force field and simulation conditions between MD- and NMR-generated structural ensembles was performed


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through assessment of 3JHN,Hα coupling constants obtained from experiment and simulations. The MD-derived vicinal constants obtained for Pmx-B in solution and using different simulation protocols reproduce the experimental values with maximum root mean square deviation (RMSD) of 1.32 Hz. On average, standard deviation varies between 1.65 and 2.30 in the four simulations. Residues R-6 (D-Phe) and R-7 (L-Leu) exhibit larger differences from the experimental values, and are the main source of deviation between average experimental and computational Jcoupling constants. Improved agreement is observed for values concerning R-6 with the parameter set 54A7 whereas R-7 responds better to the RF treatment compared to PME. Therefore, the most accurate combination was given by the GROMOS 54A7 parameter set plus the RF treatment. An increased conformational sampling performance of the RF over PME approach has been previously reported for simulations using the GROMOS force field.53 MD-derived 3J coupling constants can be directly compared to the experimental data as these quantities are directly related to the geometrical form of the molecule. Hence, it can be used to describe how well the simulated ensemble of structures represents the experimental one. Comparison of the MD- and NMR-derived 3JHN,Hα coupling constants for Pmx-B shows an excellent agreement as expressed by the RMSD values (Table 2). We have further investigated the consistency between calculated and experimental conformational ensembles through comparisons of the three-dimensional structures obtained from the experimental and computational 3J coupling constants (Figure 2A). The 10 lowest energy structures of Pmx-B in solution obtained from NMR spectroscopy can be divided in two families of conformations whose backbone atoms can be superimposed with a RMSD ranging from 0.18 to 0.50 Å (members of the same family) and from 1.00 to 1.18 Å (members from different families).33. Comparison of the NMR-derived structures against the MD-derived ones using the parameter set


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54A7 and the RF approach shows that one region of the Ramachandran plot is not well sampled during the simulations (Figure 2A). This sampling issue has been solved by performing simulated annealing MD (SA/MD) simulations of Pmx-B while maintaining the same choice of force field parameters and long-range electrostatic treatment (Figure 2B). As result, the 3J coupling constants calculated from the MD/SA simulations have an RMSD of 0.8621 Hz from the respective experimental values (Table 3). The same force field and long-range electrostatic scheme was also applied to the MD simulations of Pmx-B in the LPS chemotype membranes (Figure 3). It should be noticed that experimental 3JHN,Hα coupling constants are available only for Pmx-B in Lipid-A aggregates.33

Structural changes of the outer membrane surface upon Pmx-B binding All simulated LPS chemotype bilayers maintain the lamellar arrangement upon binding of Pmx-B (Figure 4). However, comparisons between LPS chemotype membranes before and upon Pmx-B binding reveal noticeable structural alterations. Pmx-B leads to an increase in membrane average thickness, which is more accentuated in the antibiotic susceptible chemotypes (Figure 5). Projection of the average thickness over the atomic coordinates of the respective bilayers shows regions of increased thickness at the Pmx-B binding sites (Figure 6a-6i). Previous coarse-grained simulations of Pmx-B binding to the chemotype LPS Re from Escherichia coli in the outer leaflet and phospholipids in the inner leaflet shows the appearance of highly ordered, crystalline patches.28, 29 Since an increase in membrane thickness presupposes an increase in the acyl chain order, the CG and atomistic simulations are quite consistent even if the phase space sampled with the two representations are not necessarily the same.


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The average membrane curvature angles have also been calculated for the simulated systems. These values are presented as frequency distributions averaged over every grid cell and every trajectory frame (Figure 7). Curvature angle distributions for LPS membranes in the absence of Pmx-B are centered on ca. 10° as expected for a liquid-crystalline flat bilayer. Upon Pmx-B binding, the curvature angle distribution broadens up increasingly with the chemotype susceptibility to the antibiotic (Figure 7). Projection of the curvature order parameter S over the atomic coordinates of the respective bilayers reproduces the pattern seen already for the membrane thickness representation (Figure 8). These parameters are representative of two states; for S = 1 the local membrane surface is normal to the z-axis (flat surface) whereas for S= -0.5 the local membrane is parallel to the z-axis (bent surface). The projection maps show that regions of higher curvature order parameter correspond the Pmx-B binding regions on the membrane surface. The conspicuous exception for the effect of Pmx-B binding on bilayer thickness and curvature is Lipid-AAra4N, which does not exhibit any significant structural changes in the presence or absence of the antibiotic (Figure 7 and Figure 8). The more susceptible the chemotype is to Pmx-B, the higher is the membrane curvature as result of Pmx-B binding to the outer membrane (Figure 9). Pmx-B binding takes place after peptide aggregation and via electrostatic interactions with the same functional groups of different chemotypes, mostly phosphate groups, and in minor degree carboxylates when present in the chemotype structure (Figure SI-1 and Table SI-3). These functional groups are also the binding sites for divalent cations in LPS membranes.54, 55

Counter-ion behavior in the outer membrane surface upon Pmx-B binding


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We have investigated the diffusional behavior of Ca2+ counter-ions in the simulated LPS bilayers. Calculated diffusion coefficients are presented in Table 4. These analyses point to three major trends. First, diffusion coefficients for Ca2+ ions increase at about two-fold rate or higher upon Pmx-B binding to the respective LPS chemotype. Further, counter-ion displacement takes place very early in the simulations, ensuing Pmx-B adsorption to the membrane surface (Figure 10). Second, Ca2+ displacement occurs mostly along the membrane surface (xy plane), and less noticeably along the z-axis. This behavior is expected given the significantly higher charge density of the LPS membrane compared to the aqueous environment outside it. However, this diffusion pattern could be affected by the ionic strength of aqueous medium surrounding the bilayer. Hence, we have performed an additional simulation of the system Pmx6+LipApenta in presence of 150 NaCl (Pmx6+LipApenta-mM). We observe that Ca2+ diffusion coefficients along the xy-plane and z-axis are two- and three-fold, respectively, larger for Pmx6+LipApenta-mM than for Pmx6+LipApenta (Table 4, Figure 10). Nevertheless, counter-ion displacement takes place chiefly along the bilayer surface, regardless of the ionic strength (Table 4). Third, Ca2+ diffusion coefficients are significantly larger for most susceptible LPS chemotypes (Table 4). Divalent cations have been shown to act as modulators of outer membrane hydration, fluidity and aggregate structure55, 56 Increased Ca2+ diffusion coefficients are associated to destabilization of the lamellar arrangement and increase of the outer membrane fluidity.39, 56-61 The larger diffusion rates for Ca2+ upon Pmx-B binding to susceptible LPS chemotypes provides atom-level evidence for the role of divalent counterions in the self-uptake of this antimicrobial peptide.

Conclusion


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It is increasingly apparent that LPS remodeling is a major survival strategy for Gram-negative bacteria. Chemical modifications of lipid A phosphates with positively charged groups, such as 4-amino-4-deoxy-L-arabinose and/or phosphoethanolamine are the most common polymyxin resistance mechanism in Pseudomonas aeruginosa, Salmonella enterica serovar Typhimurium, Escherichia coli, Acinetobacter baumannii and Klebsiella pneumoniae.17, 62 The mechanism of action of polymyxin remains disputable, and a number of models have been proposed based on biophysical studies.11 These models have in common the view that polymyxins act on the bacterial outer membrane surface, targeting Lipid A. One of the most accepted models is the self-promoted uptake22, which relies on the amphipathic nature of polymyxins to enable the uptake process across the outer membrane. In this model, the positively charged diaminobutyric acid residues bind to the anionic LPS phosphate groups leading to the competitive displacement of divalent cations.22-25 The present simulations depict the initial stages of such process upon polymyxin binding to an outer membrane model. However, it further shows that cation displacement is accompanied by alterations of the outer membrane curvature and stability. Remarkably, diffusion coefficients and membrane curvature angles are increasingly large for the most susceptible chemotypes while unnoticeable for the resistant chemotype containing 4-amino4-deoxy-L-arabinose. Divalent cations are the main interactions stabilizing the lamellar structure of the LPS leaflet. Hence, the polymyxin induced cation displacement across the outer membrane surface has a twofold effect. It allows for the insertion of the hydrophobic tail and hydrophobic residues into the outer membrane, thus weakening lipid packing in the LPS leaflet, and inducing membrane expansion. However, it also generates a fluidity gradient across the outer membrane surface, which appears to trigger changes in the outer membrane surface curvature. It is significant that


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polymyxin is able to induce the formation of outer membrane vesicles and high curvature bodies on the outer membrane surfaces of treated bacteria strains.63,

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Although the temporal-spatial

scales of the present simulations do not allow for the discussion of membrane vesiculation processes, it signals that such processes may be related to local fluidity gradients due to cation displacement whether in response to extracellular stimuli or intracellular regulation mechanisms.

Acknowledgment. This work was supported by the Brazilian funding agencies FACEPE (APQ-0732-1.06/14 and APQ-0398-1.06/13), BioMol/CAPES (BioComp 23038.004630/201435), CNPq (INCT-FCx 465259/2014-6) and by the Swedish funding agency STINT (IG20112048). Computational resources were partially provided by the High Performance Computing Center North (HPC2N) and the Santos Dumont Supercomputer Center at the Brazilian National Laboratory of Scientific Computing (LNCC). TAS was the recipient of a visiting professorship from the Umeå Centre for Microbial Research (UCMR) Linnaeus Program. The authors wish to acknowledge the anonymous reviewer for calling our attention to ref. 29. Supporting information. GROMOS atomic parameters (atom type, bond, angle, and torsion parameters) and topologies for simulated LPS chemotypes (Lipid-A, Lipid A containing 4amino-4-deoxy-l-arabinose (LipAAra4N) and LPS Re in the penta- and hexa-acylated forms polymyxin) and for polymyxin and calculated vicinal 3JHN,Hα coupling constants and associated values of the dihedral angle φ for PmxB molecules on a Lipid-A bilayer, radial distribution functions and coordination numbers are available in the supporting information.

References


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24. Zhang, L.; Dhillon, P.; Yan, H.; Farmer, S.; Hancock, R. E., Interactions of Bacterial Cationic Peptide Antibiotics with Outer and Cytoplasmic Membranes of Pseudomonas Aeruginosa. Antimicrob. Agents Chemother. 2000, 44, 3317-3321. 25. Wiese, A.; Munstermann, M.; Gutsmann, T.; Lindner, B.; Kawahara, K.; Zahringer, U.; Seydel, U., Molecular Mechanisms of Polymyxin B-Membrane Interactions: Direct Correlation between Surface Charge Density and Self-Promoted Transport. J. Membr. Biol. 1998, 162, 12738. 26. Hermsen, E. D.; Sullivan, C. J.; Rotschafer, J. C., Polymyxins: Pharmacology, Pharmacokinetics, Pharmacodynamics, and Clinical Applications. Infect Dis Clin N Am 2003, 17, 545-564. 27. Brandenburg, K.; Moriyon, I.; Arraiza, M. D.; Lewark-Yvetot, G.; Koch, M. H. J.; Seydel, U., Biophysical Investigations into the Interaction of Lipopolysaccharide with Polymyxins. Thermochim. Acta 2002, 382, 189-198. 28. Berglund, N. A.; Piggot, T. J.; Jefferies, D.; Sessions, R. B.; Bond, P. J.; Khalid, S., Interaction of the Antimicrobial Peptide Polymyxin B1 with Both Membranes of E. Coli: A Molecular Dynamics Study. PLoS. Comput. Biol. 2015, 11, e1004180, 1-17. 29. Jefferies, D.; Hsu, P. C.; Khalid, S., Through the Lipopolysaccharide Glass: A Potent Antimicrobial Peptide Induces Phase Changes in Membranes. Biochemistry 2017, 56, 16721679. 30. van Gunsteren, W. F.; Bakowies, D.; Baron, R.; Chandrasekhar, I.; Christen, M.; Daura, X.; Gee, P.; Geerke, D. P.; Glattli, A.; Hunenberger, P. H.; Kastenholz, M. A.; Ostenbrink, C.;


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Schenk, M.; Trzesniak, D.; van der Vegt, N. F. A., Biomolecular Modeling: Goals, Problems, Perspectives. Angewandt. Chem.-Intl. Ed. 2006, 45, 4064-4092. 31. van Gunsteren, W. F.; Bakowies, D.; Burgi, R.; Chandrasekhar, I.; Christen, M.; Daura, X.; Gee, P.; Glattli, A.; Hansson, T.; Oostenbrink, C.; Peter, C.; Pitera, J.; Schuler, L.; Soares, T. A.; Yu, H. B., Molecular Dynamics Simulation of Biomolecular Systems. Chimia 2001, 55, 856860. 32. Mares, J.; Kumaran, S.; Gobbo, M.; Zerbe, O., Interactions of Lipopolysaccharide and Polymyxin Studied by NMR Spectroscopy. J. Biol. Chem. 2009, 284, 11498-11506. 33. Pristovsek, P.; Kidric, J., Solution Structure of Polymyxins B and E and Effect of Binding to Lipopolysaccharide: An NMR and Molecular Modeling Study. J. Med. Chem. 1999, 42, 4604-4613. 34. Schmid, N.; Eichenberger, A. P.; Choutko, A.; Riniker, S.; Winger, M.; Mark, A. E.; van Gunsteren, W. F., Definition and Testing of the Gromos Force-Field Versions 54a7 and 54b7. Eur. Biophys. J. 2011, 40, 843-856. 35. Pol-Fachin, L.; Rusu, V. H.; Verli, H.; Lins, R. D., Gromos 53a6(Glyc), an Improved Gromos Force Field for Hexopyranose-Based Carbohydrates. J. Chem. Theory Comput. 2012, 8, 4681-4690. 36. Pol-Fachin, L.; Verli, H.; Lins, R. D., Extension and Validation of the Gromos 53a6(Glyc) Parameter Set for Glycoproteins. J. Comput. Chem. 2014, 35, 2087-2095. 37. Oostenbrink, C.; Soares, T. A.; van der Vegt, N. F.; van Gunsteren, W. F., Validation of the 53a6 Gromos Force Field. Eur. Biophys. J. 2005, 34, 273-284.


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38. Oostenbrink, C.; Villa, A.; Mark, A. E.; van Gunsteren, W. F., A Biomolecular Force Field Based on the Free Enthalpy of Hydration and Solvation: The Gromos Force-Field Parameter Sets 53a5 and 53a6. J. Comput. Chem. 2004, 25, 1656-1676. 39. Pontes, F. J. S.; Rusu, V. H.; Soares, T. A.; Lins, R. D., The Effect of Temperature, Cations and Number of Acyl Chains on the Lamellar to Non-Lamellar Transition in Lipid-a Membranes: A Microscopic View. J. Chem. Theory Comput. 2012, 8, 3830–3838. 40. Lins, R. D.; Hunenberger, P. H., A New Gromos Force Field for Hexopyranose-Based Carbohydrates. J. Comput. Chem. 2005, 26, 1400-1412. 41. Soares, T. A.; Hunenberger, P. H.; Kastenholz, M. A.; Krautler, V.; Lenz, T.; Lins, R. D.; Oostenbrink, C.; van Gunsteren, W. F., An Improved Nucleic Acid Parameter Set for the Gromos Force Field. J. Comput. Chem. 2005, 26, 725-37. 42. 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. 43. Berendsen, H. J. C., Grigera, J. R., Straatsma, T. P., The Missing Term in Effective Pair Potentials. J. Phys. Chem. 1987, 91. 44. Hess, B.; Bekker, H.; Berendsen, H. J. C.; Fraaije, J. G. E. M., Lincs: A Linear Constraint Solver for Molecular Simulations. J. Comput. Chem. 1997, 18, 1463-1472. 45. Bussi, G.; Donadio, D.; Parrinello, M., Canonical Sampling through Velocity Rescaling. J. Chem. Phys. 2007, 126, 014101.


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46. Berendsen, H. J. C.; Postma, J. P. M.; DiNola, A.; Haak, J. R., Molecular Dynamics with Coupling to an External Bath. J. Chem. Phys. 1984, 81, 3684-3691. 47. Tironi, I. G.; Sperb, R.; Smith, P. E.; van Gunsteren, W. F., A Generalized Reaction Field Method for Molecular Dynamics Simulations. J. Chem. Phys. 1995, 102, 5451-5459. 48. Essex, J. W., The Application of the Reaction-Field Method to the Calculation of Dielectric Constants. Mol. Simul. 1998, 20, 159-178. 49. Glattli, A.; Daura, X.; van Gunsteren, W. F., Derivation of an Improved Simple Point Charge Model for Liquid Water: Spc/a and Spc/L. J. Chem. Phys. 2002, 116, 9811-9828. 50. Hess, B.; Kutzner, C.; van der Spoel, D.; Lindahl, E., Gromacs 4: Algorithms for Highly Efficient, Load-Balanced, and Scalable Molecular Simulation. J. Chem. Theory Comput. 2008, 4, 435-447. 51. Karplus, M., Contact Electron-Spin Coupling of Nuclear Magnetic Moments. J. Chem. Phys. 1959, 30, 11-15. 52. Vuister, G. W.; Bax, A., Quantitative J Correlation - a New Approach for Measuring Homonuclear 3-Bond J(H(N)H(Alpha) Coupling-Constants in N-15-Enriched Proteins. J. Am. Chem. Soc. 1993, 115, 7772-7777. 53. Lins, R. D.; Rothlisberger, U., Influence of Long-Range Electrostatic Treatments on the Folding of the N-Terminal H4 Histone Tail Peptide. J. Chem. Theory Comput. 2006, 2, 246-250. 54. Dias, R. P.; da Hora, G. C. A.; Ramstedt, M.; Soares, T. A., Outer Membrane Remodeling: The Structural Dynamics and Electrostatics of Rough Lipopolysaccharide Chemotypes. J. Chem. Theory Comput. 2014, 10, 2488-2497.


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55. Nascimento, A.; Pontes, F. J.; Lins, R. D.; Soares, T. A., Hydration, Ionic Valence and Cross-Linking Propensities of Cations Determine the Stability of Lipopolysaccharide (Lps) Membranes. Chem. Commun. 2014, 50, 231-233. 56. Garidel, P.; Rappolt, M.; Schromm, A. B.; Howe, J.; Lohner, K.; Andra, J.; Koch, M. H. J.; Brandenburg, K., Divalent Cations Affect Chain Mobility and Aggregate Structure of Lipopolysaccharide from Salmonella Minnesota Reflected in a Decrease of Its Biological Activity. Biochim. Biophys. Acta 2005, 1715, 122-131. 57. Brandenburg, K.; Koch, M. H.; Seydel, U., Phase Diagram of Lipid a from Salmonella Minnesota and Escherichia Coli Rough Mutant Lipopolysaccharide. J. Struct. Biol. 1990, 105, 11-21. 58. Seydel, U.; Brandenburg, K.; Koch, M. H.; Rietschel, E. T., Supramolecular Structure of Lipopolysaccharide and Free Lipid a under Physiological Conditions as Determined by Synchrotron Small-Angle X-Ray Diffraction. Eur. J. Biochem. 1989, 186, 325-332. 59. Seydel, U.; Koch, M. H. J.; Brandenburg, K., Structural Polymorphisms of Rough Mutant Lipopolysaccharides Rd to Ra from Salmonella Minnesota. J. Struct. Biol. 1993, 110, 232-243. 60. Jeworrek, C.; Evers, F.; Howe, J.; Brandenburg, K.; Tolan, M.; Winter, R., Effects of Specific Versus Nonspecific Ionic Interactions on the Structure and Lateral Organization of Lipopolysaccharides. Biophys. J. 2011, 100, 2169-2177. 61. Snyder, S.; Kim, D.; McIntosh, T. J., Lipopolysaccharide Bilayer Structure: Effect of Chemotype, Core Mutations, Divalent Cations, and Temperature. Biochemistry 1999, 38, 1075810767.


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62. Raetz, C. R.; Reynolds, C. M.; Trent, M. S.; Bishop, R. E., Lipid a Modification Systems in Gram-Negative Bacteria. Annu. Rev. Biochem. 2007, 76, 295-329. 63. Brown, P.; Dawson, M. J., Development of New Polymyxin Derivatives for Multi-Drug Resistant Gram-Negative Infections. J. Antibiot. (Tokyo) 2017, 70, 386-394. 64. Deris, Z. Z.; Swarbrick, J. D.; Roberts, K. D.; Azad, M. A.; Akter, J.; Horne, A. S.; Nation, R. L.; Rogers, K. L.; Thompson, P. E.; Velkov, T.; Li, J., Probing the Penetration of Antimicrobial Polymyxin Lipopeptides into Gram-Negative Bacteria. Bioconjug. Chem. 2014, 25, 750-760.


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TABLES Table 1. Simulated Systems. MD simulations were performed for polymyxin B (Pmx-B) in solution and in presence of the penta- and hexa-acylated forms of the LPS chemotypes Lipid A (LipA), Lipid A containing 4-amino-4-deoxy-l-arabinose (LipAAra4N) and LPS Re (LPSRe). Systems

Number of Molecules

Simulation Length

Pmx-B

Lipid

Solvent Ions

Pmx

1

--

2106

5 Cl-

200 ns

LipApenta

0

256

44050

256 Ca2+

200 ns

LipAhexa

0

256

38266

256 Ca2+

200 ns

LPSRepenta

0

256

47516

512 Ca2+

200 ns

LipAAra4N,penta

0

256

50002

0

200 ns

LipAAra4N,hexa

0

256

48644

0

200 ns

Pmx2+LipA

2

256

65761

10 Cl-, 256 Ca2+

200 ns

Pmx6+LipApenta

6

256

61204

30 Cl-, 256 Ca2+

200 ns

Pmx6+LipAhexa

6

256

73168

30 Cl-, 256 Ca2+

200 ns

Pmx6+LPSRe

6

256

64050

30 Cl-, 512 Ca2+

200 ns

Pmx6+LipAAra4N,penta

6

256

73587

30 Cl-

200 ns

Pmx6+LipApenta-mM

6

256

60766

249 Cl-, 256 Ca2+, 219 Na+

200 ns

Pmx6+LipAAra4N,hexa

6

256

79770

30 Cl-

200 ns


25


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Page 26 of 41

Table 2. Vicinal 3JHN,Hα coupling constants for polymyxin B as measured by NMR33 and computed from MD trajectories using different parameter sets of the GROMOS force field (53a6 versus 54a7) and long-range electrostatic treatments (reaction field versus particle mesh Ewald). Coupling constants are in Hz. Residues

Exp. 3JHN,Hαα 3

Calc. 3JHN,Hαα

Jexp

53a6/PME

54a7/PME

53a6/RF

54a7/RF

DAB1

7.0

7.76 ± 1.99

6.46 ± 1.95

8.10 ± 1.94

6.46 ± 2.02

THR2

7.0

7.39 ± 2.29

6.43 ± 2.03

7.62 ± 2.30

6.66 ± 1.98

DAB3

7.5

7.96 ± 1.92

6.93 ± 1.86

7.81 ± 2.05

5.84 ± 2.00

DAB4

6.9

7.87 ± 2.18

7.06 ± 1.96

8.11 ± 1.98

6.14 ± 1.68

DAB5

7.0

7.68 ± 2.01

7.97 ± 1.69

7.52 ± 2.16

7.79 ± 1.94

R-6

5.2

8.07 ± 2.22

4.81 ± 1.76

7.06 ± 2.27

5.63 ± 2.59

R-7

8.2

7.24 ± 2.11

5.96 ± 1.62

8.26 ± 1.77

7.17 ± 2.01

DAB8

5.9

5.26 ± 2.02

7.38 ± 1.93

8.33 ± 2.00

6.39 ± 2.19

DAB9

7.4

6.98 ± 2.42

6.09 ± 0.64

5.29 ± 1.83

5.78 ± 2.16

THR10

7.2

8.46 ± 1.69

5.56 ± 1.37

6.88 ± 2.18

5.97 ± 0.84

1.17

1.17

1.32

1.06

RMSD


26

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Table 3. Vicinal 3JHN,Hα coupling constants for polymyxin variants as measured by NMR33, and computed from SA/MD trajectories using the GROMOS parameter set 54a7 and the RF longrange electrostatic treatment. Coupling constants are in Hz. Residues

Pmx in solution 3

3

DAB1

7.0

6.39 ± 2.03

THR2

7.0

7.14 ± 2.09

DAB3

7.5

6.79 ± 2.12

DAB4

6.9

6.54 ± 1.72

DAB5

7.0

7.41 ± 1.93

R-6

5.2

5.07 ± 2.35

R-7

8.2

6.01 ± 1.96

DAB8

5.9

6.24 ± 2.04

DAB9

7.4

7.29 ± 1.76

THR10

7.2

6.06 ± 1.94

Jexp

RMSD

Jcalc

0.8621


27


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Page 28 of 41

Table 4. Diffusion coefficients for Ca2+ counterions in Lipid A (LipA) and LPS Re (LPSRe) membranes in the presence and absence of polymyxin B and at different ionic strengths. The LipAAra4N membranes do not contain Ca2+ counterions. Chemotype

Diffusion coefficient [10-7 cm2/s] xy plane

z axis

Total

LipApenta

2.51 +/- 0.25

1.00 +/- 0.17

2.00 +/- 0.22

LipAhexa

1.02 +/- 0.14

0.51 +/- 0.02

0.85 +/- 0.08

LPSRe

1.29 +/- 0.36

0.93 +/- 0.21

1.17 +/- 0.17

Pmx6+LipApenta

11.58 +/- 7.10

2.60 +/- 0.06

8.59 +/- 4.75

Pmx6+LipApenta-mM

21.28 +/- 0.72

6.46 +/- 1.51

16.34 +/- 0.02

Pmx6+LipAhexa

4.26 +/- 1.50

2.73 +/- 0.01

3.75 +/- 1.00

Pmx6+LPSRe

2.41 +/- 0.83

1.46 +/- 0.32

2.09 +/- 0.44


28

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Figure Captions Figure 1. Chemical structure of a) polymyxin-B and LPS chemotypes b) Lipid-A, c) LipidAAra4N and d) LPS Re. The cyclic decapeptide is composed of a methyl octanoate tail, several α,γ-diaminobutyric acid (DAB) and α-amino acids. Polymyxin variants differ with respect to the identity of residues at position 6 and 7. These residues correspond to D-Phe and L-Leu in PmxB. The penta-acylated forms of the LPS chemotypes are shown. Figure 2. Ramachandran diagram calculated from MD simulations of polymyxin-B (Pmx-B) in solution. Trajectories were generated using the GROMOS parameter set 54a7 and the RF longrange electrostatic treatment through a) MD or b) MD/SA simulations. Violet and orange squares correspond to ϕ and ψ values derived from NMR spectroscopic measurements for Pmx-B.33 Figure 3. Ramachandran diagrams obtained from MD simulations of six copies of polymyxin B on

LPS

chemotype

bilayers

(a)

Pmx6+LipApenta,

(b)

Pmx6+LPSRepenta

and

(c)

Pmx6+LipAAra4N,penta. Violet and orange squares correspond to ϕ and ψ values derived from NMR spectroscopic measurements for Pmx-B in Lipid-A.33 NMR measurements for Pmx-B in presence of LPS Re or Lipid-A containing 4-amino-4-deoxy-l-arabinose are not available. Figure 4. Bilayer density profiles for (a) LipApenta, (b) Pmx6+LipApenta, (c) LipAhexa, (d) Pmx6+LipAhexa, (e) LPSRepenta, (f) Pmx6+LPSRepenta, (g) LipAAra4N,penta and Pmx6+ LipAAra4N,penta (h). Profiles for Ca2+ ions and Pmx-B have been increased by a factor of 20 and 5 respectively. Figure 5. Bilayer thickness as a function of time for LPS membranes in the absence (A) and in the presence (B) of Pmx-B, respectively. LPS membrane chemotypes are represented in black (LipApenta), red (LipAhexa), green (LPSRepenta) and blue (LipAAra4N,penta).


29


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Page 30 of 41

Figure 6. Time-averaged bilayer thickness projected on the membrane surface in a) LipApenta, b) LipAhexa, c) LPSRepenta, d) LipAAra4N,penta, e) Pmx6+LipApenta, f) Pmx6+LipAhexa, g) Pmx6+LPSRepenta, h) Pmx6+LipAAra4N,penta. Density maps for Pmx-B atomic coordinates in i) Pmx6+LipApenta, j) Pmx6+LipAhexa, k) Pmx6+LPSRepenta, l) Pmx6+LipAAra4N,penta. Figure 7. Frequency distribution of average membrane curvature angles LPS chemotype bilayers in the absence and presence of Pmx-B. Figure 8. Time-averaged curvature order parameters projected onto the membrane surface a) LipApenta, b) LipAhexa, c) LPSRepenta, d) LipAAra4N,penta, e) Pmx6+LipApenta, f) Pmx6+LipAhexa, g) Pmx6+LPSRepenta, h) Pmx6+LipAAra4N,penta. Figure 9. Snapshots of simulated systems a) Pmx6+LipApenta, b) Pmx6+LPSRepenta, c) Pmx6+LipAhexa and d) Pmx6+LipAAra4N. Atomic coordinates averaged over the final 10 ns of the respective simulation. LPS chemotypes are represented in lines (acyl chains) and sticks (carbohydrate moieties) with carbon atoms colored grey. Pmx peptides are represented by the respective van der Waals radii with carbon atoms in light blue and Ca2+ ions in orange. Nitrogen, oxygen, hydrogen and phosphorus atoms are shown in dark blue, red, white, and phosphorous in dark gold, respectively. Figure 10. Diffusion coefficients for Ca2+ counterions in LPS chemotype membranes calculated at different time intervals. Bars are colored in black and blue for membranes in the absence and the presence of Pmx-B, respectively. Bar in red represents a simulation at 150mM. Depicted systems are a) LipApenta, Pmx6+LipApenta, and Pmx6+LipApenta-mM, b) LipAhexa and Pmx6+LipAhexa, c) LPSRepenta and Pmx6+LPSRepenta. LipAAra4N does not have Ca2+ counterions.


30

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Graphical abstract 88x35mm (300 x 300 DPI)



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4

3.9

3.9

3.8

3.8

3.7

3.7

3.6

3.6

3.5

3.5

3.4

3.4

3.3

3.3

3.2

3.2

3.1

3.1

3

3

2.9 2.8

2.9 0

20

40 60 Time [ns]

80

100 0

20


40 60 Time [ns]

80

2.8 100

Average Thickness [nm]

4

Average Thickness [nm]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

Page 36 of 41

0.0

nm

g i

16.4

y axis [nm] y axis [nm]

y axis [nm]

x axis [nm] Thickness 0.0nm nm 16.4 0.0 2.0Thickness 16.4 Density 5.0


y axis [nm]

2.0Thickness 5.0

x axis [nm]

-0 0

x axis [nm] axis[nm] [nm] xxaxis 0.0 nm 16.4 Density 2.0 0.0 nm nm 5.0 16.4

x axis [nm] 0.0

2.0Thickness 5.0 2.0

5.0

k

Density

x axis [nm] xxaxis axis[nm] [nm] axis [nm] 0.0 xnm 16.4 x axis [nm] 2.0Thickness 5.0 0.0 nm^-3 nm 16.4 0.0 0.0 Density nm 16.4 16.4

x Thickness axis x axis[nm] [nm] 0.02.0Thickness nm 16.4 5.0 Density

x axis [nm]

-0

x axis [nm] x axis [nm]

2.0Thickness 5.0

x axis 0.02.0Thickness nm [nm] 16.4 5.0 2.0 0.0 nm^-3 19.4

l

Density

y axis [nm]

Density

y axis [nm]

y axis [nm]

j

nm

2.0Thickness 5.0 16.4

y axis [nm]

y axis [nm]

y axis [nm]

h j

0

x axis [nm]

Density

-0

0

x axis [nm]

x axis [nm]

x axis [nm]

0.0 Density nm 16.4 16.4 0.0 nm^-3

Density

Density

0

0

k

Thickness

-0

-0

i

y axis [nm]

y axis [nm]

y axis [nm]

Thickness x axis [nm]

Thickness

y axis [nm]

f

0

Density Density Density x x axis axis [nm][nm]


x axis [nm]

d

y axis [nm]

x axis [nm] Thickness axis[nm] [nm] xxaxis 0.0 nm 16.4 0.0 nm 5.0 16.4 2.0Thickness

Thickness

y axis [nm]

y axis [nm]

y axis [nm]

Density


c


Thickness

Density Density

y axis [nm]

e

Thickness

b

y axis [nm]

y axis y axis [nm][nm]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Thickness

y axis [nm]

a

Page 37 of 41

0.0 nm^-3 19.4

l

Density

x axis [nm]

x axis [nm]

0.0

0.0 ACS Paragon Plus Environment

nm

nm

17.5

16.4

x axis [nm] 0.0 nm^-3 20.3

5.0


Surface Curvature Angle 5 LipA LipAHexa LPSRe LipAAra4N LipAHexa-Ara4N LipA+Pmx6 LipAHexa+Pmx6 LPSRe+Pmx6 LipAAra4+Pmx6 LipAHexa-Ara4+Pmx6

4

3 %

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

Page 38 of 41

2

1

0

0

20

40 o Angle [ ] ACS Paragon Plus Environment

60

80

Order Parameter

a

Page 39 of 41

b

Order Parameter

Order Parameter

c

Order Parameter

d


1 11.2 2

9.5

7.5

5.5

y axis [nm]

y axis [nm]

y axis [nm]

y axis [nm]

y axis [nm]

y axis [nm]

y axis [nm]

retemaraP redrO

y axis [nm]

2.

3.5

1.5

1

2.5

e

Density Density

Density

5.5 x axis [nm]7 x axis [nm] x axis [nm] Order Parameter -0.5 1.0 0.0 nm 16.4 0.0 nm 16.4

x axis [nm]

4

f

Density

Order Parameter x axis [nm]

8.1

1.5

16.2

x axis x axis [nm][nm]

Order Parameter x axis [nm]1.0 -0.5

g

0.0 -0.5 nm order 16.41.0

Density

Density

0

3.5

6

8

x axis [nm] x axis [nm]

10.5

Order -0.5 Parameter 1.0

h

0.0 0.0nm nm 16.416.4

4.

0.0

nm

16.4

17.2 16.4

9.6

6

y axisy [nm] axis [nm]

7.2

y axis [nm]

y axis [nm]

y axis [nm]

y axis [nm]

y axis [nm]

8.4

y axis [nm]

3 4 5 6 78.4 8 9 10 116 12 13 14 15 16 3.2 17 18 19 20 0.8 21 22 23 24 25 26 27 28 10.6 29 10 30 31 9.4 32 33 34 35 7.2 36 6.6 37 386 39 40 41 42 3.8 43 3.2 44 2.6 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

11.2 10.4

2.

4 5.2

2.8

8. 1.6

0.5

2

8.5 x axis5.5[nm] 7 x axis [nm] x axis [nm] -0.5 1.0 0.0 nm 16.4 0.0 nm 16.4

7

0

-0 0

1.2

x axis [nm] 0.0

x axis [nm]

nm

16.4

-0.5 order

1.0

2.8

7.2

11.6

x axis [nm] 0.0

x axis [nm]1.0 -0.5

nm 16.4 x axis [nm]

0.0


nm

16.4

13.2

2.4

x axis [nm] ]mn[ 4.4

0.1

6.4

x axis [nm]1.0 -0.5

0.0-0.5nm

16.4

5.5

4

sixa 5x.07.6

9.6

1.0

5.2

1


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Page 40 of 41

Page 41 of 41

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47


aa

a

bb

cc


Polymyxin Binding to the Bacterial Outer ... - ACS Publications

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