nanoscale imaging reveals laterally expanding antimicrobial pores in lipid bilayers

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  • 7/27/2019 Nanoscale imaging reveals laterally expanding antimicrobial pores in lipid bilayers

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    Nanoscale imaging reveals laterally expandingantimicrobial pores in lipid bilayersPaulina D. Rakowskaa,b,1, Haibo Jiangc,1, Santanu Raya,1, Alice Pynea,d, Baptiste Lamarrea, Matthew Carre,Peter J. Judgef, Jascindra Ravia, Ulla I. M. Gerlingg, Beate Kokschg, Glenn J. Martynah, Bart W. Hoogenboomd,i,Anthony Wattsf, Jason Craina,e, Chris R. M. Grovenorc, and Maxim G. Ryadnova,e,2

    aNational Physical Laboratory, Teddington TW11 0LW, United Kingdom; bDepartment of Chemistry, University College London, London WC1H 0AJ, UnitedKingdom; cDepartment of Materials, University of Oxford, Oxford OX1 3PH, United Kingdom; dLondon Centre for Nanotechnology, University CollegeLondon, London WC1H 0AH, United Kingdom; eSchool of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom; fDepartmentof Biochemistry, University of Oxford, Oxford OX1 3QU, United Kingdom; gInstitut fr Chemie und Biochemie, Freie Universitt Berlin, 14195 Berlin, Germany;hIBM T. J. Watson Research Center, Yorktown Heights, NY 10598; and iDepartment of Physics and Astronomy, University College London, London WC1E 6BT,United Kingdom

    Edited by Hiroshi Nikaido, University of California, Berkeley, CA, and approved April 16, 2013 (received for review January 2, 2013)

    Antimicrobial peptides are postulated to disrupt microbial phospho-

    lipid membranes. The prevailing molecular model is based on the

    formation of stable or transient pores although the direct observa-

    tion of the fundamental processes is lacking. By combining rationalpeptide design with topographical (atomic force microscopy) and

    chemical (nanoscale secondary ion mass spectrometry) imaging on

    the same samples, we show that pores formed by antimicrobial

    peptides in supported lipid bilayers are not necessarily limited toa particular diameter, nor theyare transient, but can expand laterally

    at the nano-to-micrometer scale to the point of complete membrane

    disintegration. The results offer a mechanistic basis for membraneporation as a generic physicochemical process of cooperative and

    continuous peptide recruitmentin the available phospholipid matrix.

    innate host defense | de novo protein design | nanometrology |antibiotics | nanoscopy

    Structurally compromised phospholipid membranes can leadto premature cell death, which is particularly critical forunicellular microorganisms (1, 2). Multicellular organisms takethe full advantage of such vulnerability by using host defense orantimicrobial peptides (AMPs) (16). Although there are >1,000

    AMPs known to date (7), only a few have been studied to exposethe molecular mechanisms of action. The proposed barrel-stavepore (4, 8), torroidal pore (3), and carpet models (9) differ ac-cording to the ways in which AMPs interact within phospholipidbilayers, but all are believed to involve two distinct peptidelipidstatesan inactive surface-bound S-state and a pore-like insertionI-state (1, 10, 11). However, the link between these two statesand membrane disintegration remains unresolved.

    Despite their apparent diversity in structure and modes of ac-tion, AMPs share common features that make their modulation inmodel sequences possible. The peptides preferentially target an-ionic microbial surfaces, upon binding to which (S-state) theyadopt amphipathic conformations by partitioning polar and hy-drophobic amino acid side chains (2, 12, 13). Neutron diffraction

    and solid-state nuclear magnetic resonance (ssNMR) spectros-copy suggest that these conformations assemble into perpendicularstacks that close into the pore-like (I-state) structures (5, 11, 14).Here, positive curvature strains (15) and membrane thinning (16)are induced and may precede poration. In lipid vesicles (17, 18)and supported bilayers (16), kinetic studies imply the formation oftransient pores (6), suggesting that antimicrobial peptides mayexpand through the monolayers of the lipid bilayers (1518).Much research has focused on small and stabilized pores (5, 14,15, 17). Growth arrest and uniform sizes of pores conform to thefunctional and structural rationale of specialized transmembraneproteins but may not be consistent with that of antimicrobialpeptides.

    Indeed, bacterial protein toxins such as -hemolysins oligo-merize into small 2- to 4-nm pores of defined structure, which is

    sufficient to cause the rapid discharge of vital resources (ions,ATP) from host cells (19, 20). Cell death in this case is a con-sequence, but not an aim. In contrast, AMPs are designed to killmicrobial cells, not necessarily specifically (21), but rapidly

    within the time limits of their proteolytic stability. The behaviorof other protein toxins is somewhat similar to these two sce-narios. For example, perforins (22) that activate intrinsic suicide

    programs (apoptosis) of various cells, thus mediating cell lysisrather than causing it directly, use different avenues for mem-brane targeting and can form heterogeneous transmembranepores (23). Heterogeneity in pore formation for AMPs may de-rive from the fact that, unlike the case of membrane proteins(24), there are no a priori topological constraints on assembledstructures that the peptides must adopt in bilayers. Therefore,their pore sizes may be governed as much by progressive peptideaggregation as they are by local energetics. Because AMPs aretypically cationic, free-energy changes in the edges of pores canbe affected by peptide positions and local variations in the di-electric medium between peptide molecules, suggesting strongelectrostatic repulsion. In this light, poration can be described asa physical phenomenon accommodating peptide diffusion in the

    membrane matrix with no strict predisposition for a particularpore size, but with sufficient freedom of movement for lateralexpansion. To address this phenomenon in a sufficient moleculardetail, the direct observation of pore architecture and dynamicsis needed, but thus far has been lacking.

    One reason for the lack of direct observation is the intrinsiccomplexity of imaging poration in live cells. Membrane binding of

    AMPs is kinetically driven and, in live cells, occurs over timescalesof microseconds to minutes (2, 25). Pores need not expand sub-stantially because cell death can occur concomitantly as a result ofmembrane leakage and swelling under osmotic pressure and be-cause AMPs can reach and bind to intracellular targets or disruptprocesses that are crucial to cell viability (protein, DNA, or cell-

    wall syntheses) within the same timescales (2, 25). Furthermore,microbial membranes are curved 3D architectures whose diame-

    ters do not exceed 2 m. Pore formation in these membranes cancause significant variations in membrane tension, which can lead to

    Author contributions: B.W.H., A.W., J.C., C.R.M.G., and M.G.R. designed research; P.D.R.,

    H.J., S.R., A.P., B.L., M.C., P.J.J., J.R., U.I.M.G.,and G.J.M. performed research; U.I.M.G. and B.K.

    contributed new reagents/analytic tools; P.D.R., H.J., S.R., A.P., B.L., M.C., P.J.J., J.R., B.K.,

    G.J.M., B.W.H., A.W., J.C., C.R.M.G., and M.G.R. analyzed data; and M.G.R. wrote the paper.

    The authors declare no conflict of interest.

    This article is a PNAS Direct Submission.

    Freely available online through the PNAS open access option.

    1P.D.R., H.J., and S.R. contributed equally to this work.

    2To whom correspondence should be addressed. E-mail: [email protected].

    This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.

    1073/pnas.1222824110/-/DCSupplemental.

    www.pnas.org/cgi/doi/10.1073/pnas.1222824110 PNAS Early Edition | 1 of 6

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    mailto:[email protected]://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1222824110/-/DCSupplementalhttp://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1222824110/-/DCSupplementalhttp://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1222824110/-/DCSupplementalhttp://www.pnas.org/cgi/doi/10.1073/pnas.1222824110http://www.pnas.org/cgi/doi/10.1073/pnas.1222824110http://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1222824110/-/DCSupplementalhttp://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1222824110/-/DCSupplementalmailto:[email protected]
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    premature membrane rupture before individual pores can ex-pand substantially. A visible expansion in live cells depends onthese interrelated factors, which makes its direct observationproblematic.

    In contrast, longer time and length scale studies are accessiblein supported lipid bilayers (SLBs) (26). SLBs provide ideal ex-perimental models for fluid-phase membranes and can be im-aged by atomic force microscopy (AFM) (27, 28). Combining

    AFM with high-resolution secondary-ion mass spectrometry

    (SIMS), which has been shown to provide compositional chem-ical imaging of small lipid domains with lateral resolution of

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    homogeneous and stable bilayers maintained in the fluid phase atroom temperature and (ii) avoid charge build-up during SIMSmeasurements, which is necessary as SIMS relies on the detectionof secondary ions extracted from the surface by a focused beam ofprimary ions (133Cs+) rastered across the sample (29).

    The SLB samples were incubated with solutions containingamhelin, which was 15N-labeled at all alanine and leucine residuesand washed to remove excess peptide. To arrest poration andpreserve structural changes in the membrane, the hydrated sam-

    ples were then rapidly frozen and freeze-dried (29). Secondary ionimages of the 12C14N and 12C15N signals, which are commonlyused in imaging SIMS experiments of biological materials (38),revealed pores of varied forms and sizes supporting the conjectureof pore expansion across the whole scanned area (Fig. 2A andFig. S3).

    In these samples, we expect a higher signal intensity fromregions of the surface rich in peptide because each unlabeledresidue in amhelin contributes to 12C14N, but the 12C15N signals

    will come predominantly from the labeled residues. Thus, SIMSimages have a strong degree of component specificity providingdirect evidence for the location of the peptide, which prompts theconclusion that the observed pores are peptide-specific. Theconclusion was reinforced by the images of the 12C15N/12C14N

    ratio and hue saturation intensity (HSI) images (Fig. 2B

    and Fig.S3). Complementary images of control samples (bare and non-AMP-treated SLBs and bare and amhelin-treated silicon wafersubstrates) were featureless (Fig. 2C and Figs. S4 and S5).

    Firstly, all these images suggest that the interior of the pores inthe amhelin-exposed samples is completely free of peptide, as arethe control samples, as expected. Secondly, 12C15N/12C14N ra-tios far above natural abundance values (0.37%) are recordedfrom the surface of the sample away from the pores and areparticularly evident at the edges of the pores, where the peptidecontent appears to be highest (40%) and increases with increasingpore sizes (Fig. 2B). Thirdly, high peptide accumulations can beseen running across the NanoSIMS images, presumably pore-connecting ridges that are spread across the imaged area sug-gesting peptide migration dynamics (Fig. 2 A and B and Fig. S3).

    It should be emphasized here that SIMS measurements relateto the chemical composition of the surface with only a minorcontribution from topography. Therefore, AFM measurements

    on the same samples were performed to support the SIMS data(Fig. 3). AFM-scanned pore sizes revealed that the pore edgesprotruded from the surface to the heights of4 nm (Fig. 3A). Thelong axis of the peptide can account for 3.2 nm whereas theremaining is consistent with the size of a lipid head group (Fig.3B). Although other explanations are possible, the height differ-ence could be interpreted as due to a staggered arrangement ofthe peptides at the pore edges, with every other peptide beingshifted slightly upward, while retaining their roughly vertical

    alignment on the edge (4, 5) and maximizing the contact with thehydrophic lipid tails (Fig. 3B). In addition, small white-dotdeposits observed predominantly inside the pores and on theiredges are most likely due to the aggregation of peptidelipidmaterial ejected from the membrane. These observations alto-gether (i) suggest that the peptide incorporates into the bilayerby distorting and partially displacing the lipids of the outerleaflet and (ii) imply an efficient migration mode of lipidpeptideassemblies through fluidic pores and ridges in a highly coop-erative manner.

    An intriguing question provoked by the observations is thepeaking of pore edges. Although the heights of the edges werefairly consistent, the depth values of the perforations could notbe determined reliably. The holes would appear as deep as 2

    nm in relation to the surrounding surfaces, but an explicit cross-section analysis was hampered by high noise levels from thesurfaces in the 1- to 2-nm range. The peaking itself may becomenegligible under equilibrium conditions at which outer leafletlipids detach irreversibly and too fast to be observed withoutdeliberately arresting the system by freezing. An insight into thisscenario can be obtained only in solution.

    Therefore, we monitored real-time changes of SLBs incubatedwith amhelin by time-lapse AFM in water (25). Amhelin solutionat low concentration was directly introduced into a liquid cell thatcontained an AUV lipid bilayer assembled on flat mica. After thefirst 10 min of incubation, small pores started forming on thesurface and continued to grow in size and numbers over the pe-riod of 2 h, culminating in the total removal of the lipid from themica surface (Fig. 4A). The lipids are likely to dissolve in the form

    of micelles, possibly including peptides. On removal of largeramounts of the SLB, material increasingly precipitates on thesurface (Fig. 4A and Fig. S6). As expected, the pores appeared as

    Fig. 2. SIMS analysis of amhelin-treated supported lipid bilayers. (A) SIMS images of 12C14N, 12C15N, and 12C15N/12C14N signals from the supported lipid

    bilayers treated with the isotopically labeled peptide. (B) 12C15N/12C14N ratio expressed as HSI images. The rainbow scale changes from blue (natural

    abundance ratio of 0.37%) to red (40%, >100 times the natural ratio). This image is the sum of several sequential images to enhance the statistical significance

    of the measured ratios. (C) SIMS images of 12C14N, 12C15N, and 12C15N/12C14N signals from the supported lipid bilayers with no peptide. Incubation con-

    ditions: 10 M, pH 7.4, 20 C.

    Rakowska et al. PNAS Early Edition | 3 of 6

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    http://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1222824110/-/DCSupplemental/pnas.201222824SI.pdf?targetid=nameddest=SF3http://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1222824110/-/DCSupplemental/pnas.201222824SI.pdf?targetid=nameddest=SF3http://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1222824110/-/DCSupplemental/pnas.201222824SI.pdf?targetid=nameddest=SF3http://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1222824110/-/DCSupplemental/pnas.201222824SI.pdf?targetid=nameddest=SF4http://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1222824110/-/DCSupplemental/pnas.201222824SI.pdf?targetid=nameddest=SF5http://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1222824110/-/DCSupplemental/pnas.201222824SI.pdf?targetid=nameddest=SF3http://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1222824110/-/DCSupplemental/pnas.201222824SI.pdf?targetid=nameddest=SF6http://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1222824110/-/DCSupplemental/pnas.201222824SI.pdf?targetid=nameddest=SF6http://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1222824110/-/DCSupplemental/pnas.201222824SI.pdf?targetid=nameddest=SF3http://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1222824110/-/DCSupplemental/pnas.201222824SI.pdf?targetid=nameddest=SF5http://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1222824110/-/DCSupplemental/pnas.201222824SI.pdf?targetid=nameddest=SF4http://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1222824110/-/DCSupplemental/pnas.201222824SI.pdf?targetid=nameddest=SF3http://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1222824110/-/DCSupplemental/pnas.201222824SI.pdf?targetid=nameddest=SF3http://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1222824110/-/DCSupplemental/pnas.201222824SI.pdf?targetid=nameddest=SF3
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    expanding holes, suggesting the displacement of outer lipids fromthe surface into the water, which is characteristic of equilibratedsystems (17). The depths of perforations reached 2.7 nm, con-forming to the amhelin spanning the bound hydrophobic core ofthe bilayer (Fig. 4B). Similar real-time changes were observed foranother amphipathic AMP (AMP2) whose pore expansion inSLBs provides an additional example (Figs. S1 and S6).

    Discussion

    Collectively our findings provide evidence for pore expansion, oran E-state, of amphipathic antimicrobial peptides in lipid bilay-ers (Fig. 5). The E-state promotes cooperative peptide migrationthrough the lipid matrix and can persist to complete membrane

    disintegration. Our proposed model of pore expansion is thesynergistic interplay of two physical processes.

    In the first, peptide adsorption induces surface tension onmembrane surfaces, which, when sufficiently large, leads to pora-tion. The pore formation promotes peptide migration from thesurface to the edges of the pores. This variation of surface tension

    with composition (Gibbs surface excess) is driven by amphipathicpeptides having higher affinity to the membrane edges (3, 4). Theprocess is likely to reduce the tension between peptide and lipidbilayers, thereby stabilizing the formed pores. However, it ischallenged by strong electrostatic repulsion between insertedhelices in the pore edges (3, 4). In live cells, this conflict can beavoided both because excess peptide on cell membranes canmigrate through small pores directly into the cytoplasm targetingintracellular components and because continuous peptide in-corporation and diffusion in lipid bilayers can be preempted bymembrane swelling (6, 12, 22). For flat and extended 2D lipidmatrices, pore expansion is more thermodynamically favorableand is determined by both incorporation and repulsion of pep-tides to the pore edges. In this way, inserting helices can be viewedas charged equipotential surfaces with a degree of translationalfreedom (4, 14) conforming to toroidal type poration, which ischaracterized by shallow energy minima leading to substantial var-iations in pore sizes (4, 6, 18).

    Pores of 10 m in size can be physically generated in giantunilamellar vesicles (100 m in diameter) by strong optical illu-mination in a viscous medium (39). The edges of the generatedpores make up a line of lipid bilayer edges that, unless stabi-lized or expanded, reseal due to the line tension (17, 18). De-tergent molecules (e.g., Tween 20) can reduce the tension andpartially stabilize the line (17, 39) but cannot fold and propagate.Instead, they form micellar aggregates above a critical concen-tration. In contrast, antimicrobial peptides become amphipathiconly upon folding, which, in conjunction with sustained hydro-phobic and electrostatic interactions, enables their progressiveself-assembly in lipid bilayers. Pore expansion is also differentfrom mechanisms of fusion and transmembrane proteins whose

    conserved topologies impose specific self-assembly modes andpore architectures (22). For example, HIV glycoprotein 41 (gp41)controls each step in fusion, including pore nucleation, througha sequence of highly specialized conformations rendering thedimensions and lifetime of induced pores precisely optimized for

    viral entry.

    Fig. 3. Amhelin-treated supported lipid bilayers. (A) In-air AFM topographic

    images with a cross-section along the highlight line. (B) Schematic represen-

    tation of pore edges showing the thickness of the SLB (3.2 nm), the maximumobserved height (4 nm), and the difference between the two (0.50.8 nm)

    accounted for by possible protrusion variants, three shown. For clarity, only

    one peptide (blue cylinder) and one phospholipid per layer are shown (ali-

    phatic chains in gray, headgroups in pink). Incubation conditions: 10 M, pH

    7.4, 20 C.

    Fig. 4. In-water AFM imaging of amhelin-treated supported lipid bilayers. (A) Topography of supported lipid bilayers during incubation with amhelin. Color

    scale (see Inset, 0 min): 3 nm (020 min); 9 nm (30120 min). (B) Topography image after 40 min incubation with cross-sections along the highlighted lines.

    Incubation conditions: 0.5 M, pH 7.4, 20 C.

    4 of 6 | www.pnas.org/cgi/doi/10.1073/pnas.1222824110 Rakowska et al.

    http://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1222824110/-/DCSupplemental/pnas.201222824SI.pdf?targetid=nameddest=SF1http://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1222824110/-/DCSupplemental/pnas.201222824SI.pdf?targetid=nameddest=SF6http://www.pnas.org/cgi/doi/10.1073/pnas.1222824110http://www.pnas.org/cgi/doi/10.1073/pnas.1222824110http://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1222824110/-/DCSupplemental/pnas.201222824SI.pdf?targetid=nameddest=SF6http://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1222824110/-/DCSupplemental/pnas.201222824SI.pdf?targetid=nameddest=SF1
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    Thus, our findings support the biological rationale of antimi-crobial peptides as nonspecific and fast-reacting molecules thattarget microbial membranes and whose action depends on con-centration and matrix availability rather than on pore uniformityand global structural parameters such as folding topology.

    Materials and Methods

    Peptide Design and Synthesis. Amhelin and a non-AMP control,

    QIAALEQEIAALEQEIAALQ and AMP2 were designed, synthesized, and char-

    acterized according to protocols published elsewhere (33) (SI Materials and

    Methods).15

    N-amhelin labeled at all alanine and leucine residues was pur-chased from AnaSpec. All peptides were identified by reverse phase high

    performance liquid chromatography (RP-HPLC) and MALDI-TOF mass spec-

    trometry. MS [M+H]+: amhelin, m/z2448.2 (calculated), 2447.7 (found); non-

    AMP, m/z 2152.4 (calculated), 2152.4 (found); 15N-amhelin, m/z 2458.2 (cal-

    culated), 2458.1 (found); AMP2, m/z2319.1 (calculated), 2320.1 (found). [M+

    Na]+ and [M+K]+ were also found.

    Circular and Linear Dichroism Spectroscopy. All CD spectra were recorded on

    a JASCOJ-810spectropolarimeterfittedwith a Peltiertemperaturecontroller.All

    measurements were taken in ellipticities in mdeg and converted to molar

    ellipticities ([], deg cm2dmol1) by normalizing for the concentration of pep-

    tide bonds. Aqueous peptide solutions (300L,20M) were prepared infiltered

    (0.22 m) 10 mM phosphate buffer, pH 7.4. CD spectrarecorded in thepresence

    of synthetic membranes are for lipid:peptide molar ratio of 100:1. Solution-

    phase flow LD spectra were recorded on a Jasco-810 spectropolarimeter using

    a photo-elastic modulator 1/2 wave plate, and a microvolume quartz cuvetteflow cell with0.25 mm annular gapand quartzcapillaries(all from Kromatec).

    Molecular alignment was achieved through the constant flow of the sample

    solution between two coaxial cylindersa stationary quartz rod and a rotating

    cylindrical capillary. LD spectra were acquired with laminar flow obtained by

    maintaining a cell rotation speed of 3,000 rpm and processed by subtracting

    nonrotating baseline spectra. LD spectra recorded in the presence of synthetic

    membranes were prepared at a lipid:peptide molar ratio of 100:1 (2 mM total

    lipid, 20 M peptide).

    Solid-State NMR Spectroscopy. ssNMR experiments were carried out on

    a VarianInfinityplus 500MHz spectrometerequippedwitha 4 mm MAStriple

    resonance (HXY) probe at 30 C. 31P ssNMR spectra were acquired at 202

    MHz. A single 4 s 90 pulse was used to excite directly the 31P nuclei, and

    broadband proton decoupling of 20 kHz was applied during the acquisition

    period. Samples were rotated at 8 kHz MAS at 20 C. The 8k scans were

    collected, and the pulse delay was 4 s. Spectra were referenced to NH4

    H2

    PO4

    .

    Molecular Dynamics Simulations. Molecular dynamics simulations were per-

    formed using the CHARMM36 force field using chloride counter ions for

    charge neutralization. The initial helical configuration was obtained using

    the XPlor-NIH structure determination algorithm (http://nmr.cit.nih.gov/

    xplor-nih/). DLPC/DLPG (3:1) membranes were constructed with dimensions

    of 12 12nm and simulated with a semiisotopic moles, pressure, tempera-

    ture (NPT) ensemble with equilibrations of 20 ns. Production runs were then

    performed for 100 ns.

    In-Air Atomic Force Microscopy Imaging. Topographic, amplitude, and phaseAFM images were recorded using tapping mode AFM on an MFP-3D Asylum

    AFM instrument (for imaging bacteria) and on a Cypher Instrument (Asylum

    Research) (for imaging supported lipid bilayers). All AFM images were flat-

    tened with a first-order line-wise correction fit. AFM tips used were super-

    sharp silicon probes (Nanosensors; resonant frequency 330 kHz, tip radius

    of curvature

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