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Edited by Hiroshi Nikaido, University of California, Berkeley, CA, and approved April 16, 2013 (received for review January 2, 2013)
Abstract
Antimicrobial peptides are postulated to disrupt microbial phospholipid membranes. The prevailing molecular model is based on the formation of stable or transient pores although the direct observation of the fundamental processes is lacking. By combining rational peptide 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 to a particular diameter, nor they are 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 membrane poration as a generic physicochemical process of cooperative and continuous peptide recruitment in the available phospholipid matrix.
Structurally compromised phospholipid membranes can lead to premature cell death, which is particularly critical for unicellular microorganisms (1, 2). Multicellular organisms take the full advantage of such vulnerability by using host defense or antimicrobial peptides (AMPs) (1⇓⇓⇓⇓–6). Although there are >1,000 AMPs known to date (7), only a few have been studied to expose the molecular mechanisms of action. The proposed barrel-stave pore (4, 8), torroidal pore (3), and carpet models (9) differ according to the ways in which AMPs interact within phospholipid bilayers, but all are believed to involve two distinct peptide–lipid states—an inactive surface-bound S-state and a pore-like insertion I-state (1, 10, 11). However, the link between these two states and membrane disintegration remains unresolved.
Despite their apparent diversity in structure and modes of action, AMPs share common features that make their modulation in model sequences possible. The peptides preferentially target anionic microbial surfaces, upon binding to which (S-state) they adopt amphipathic conformations by partitioning polar and hydrophobic amino acid side chains (2, 12, 13). Neutron diffraction and solid-state nuclear magnetic resonance (ssNMR) spectroscopy suggest that these conformations assemble into perpendicular stacks 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 of transient pores (6), suggesting that antimicrobial peptides may expand through the monolayers of the lipid bilayers (15⇓⇓–18). Much research has focused on small and stabilized pores (5, 14, 15, 17). Growth arrest and uniform sizes of pores conform to the functional and structural rationale of specialized transmembrane proteins but may not be consistent with that of antimicrobial peptides.
Indeed, bacterial protein toxins such as α-hemolysins oligomerize 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 consequence, but not an aim. In contrast, AMPs are designed to kill microbial cells, not necessarily specifically (21), but rapidly within the time limits of their proteolytic stability. The behavior of other protein toxins is somewhat similar to these two scenarios. For example, perforins (22) that activate intrinsic suicide programs (apoptosis) of various cells, thus mediating cell lysis rather than causing it directly, use different avenues for membrane targeting and can form heterogeneous transmembrane pores (23). Heterogeneity in pore formation for AMPs may derive from the fact that, unlike the case of membrane proteins (24), there are no a priori topological constraints on assembled structures that the peptides must adopt in bilayers. Therefore, their pore sizes may be governed as much by progressive peptide aggregation as they are by local energetics. Because AMPs are typically cationic, free-energy changes in the edges of pores can be affected by peptide positions and local variations in the dielectric medium between peptide molecules, suggesting strong electrostatic repulsion. In this light, poration can be described as a physical phenomenon accommodating peptide diffusion in the membrane matrix with no strict predisposition for a particular pore size, but with sufficient freedom of movement for lateral expansion. To address this phenomenon in a sufficient molecular detail, the direct observation of pore architecture and dynamics is needed, but thus far has been lacking.
One reason for the lack of direct observation is the intrinsic complexity of imaging poration in live cells. Membrane binding of AMPs is kinetically driven and, in live cells, occurs over timescales of microseconds to minutes (2, 25). Pores need not expand substantially because cell death can occur concomitantly as a result of membrane leakage and swelling under osmotic pressure and because AMPs can reach and bind to intracellular targets or disrupt processes 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 diameters do not exceed 2 μm. Pore formation in these membranes can cause significant variations in membrane tension, which can lead to “premature” membrane rupture before individual pores can expand substantially. A visible expansion in live cells depends on these interrelated factors, which makes its direct observation problematic.
In contrast, longer time and length scale studies are accessible in supported lipid bilayers (SLBs) (26). SLBs provide ideal experimental models for fluid-phase membranes and can be imaged by atomic force microscopy (AFM) (27, 28). Combining AFM with high-resolution secondary-ion mass spectrometry (SIMS), which has been shown to provide compositional chemical imaging of small lipid domains with lateral resolution of <100 nm (29), permits the detailed visualization of poration in SLBs.
To mitigate the complexities of direct live cell studies, we introduce and explore here a model system designed to expose the fundamental physicochemical processes relevant in the peptide–bilayer interactions. A model antimicrobial peptide, which combines main features of helical AMPs, was designed to integrate into SLBs that were then used as substrates for detailed nanoscale imaging and analysis by AFM and high resolution SIMS.
Results
To enable pore formation, a de novo amino acid sequence, KQKLAKLKAKLQKLKQKLAKL, dubbed amhelin (for “antimicrobial helix insert”), was generated as an archetypal model of transmembrane AMPs. The peptide comprises three PPPHPPH heptads, in which P is polar or small (alanine) and H is hydrophobic. This arrangement allows for the formation of a contiguous amphipathic helix in SLBs spanning ∼3.15 nm (0.54 nm per turn) to match the bilayer thickness of ∼3.2 nm (30, 31). The heptads in the sequence place i and i + 7 residues (32), which are of the same type, next to each other when viewed along the helical axis (Fig. 1A and Fig. S1). This order ensures the segregation of hydrophobic and polar residues onto distinct regions or faces, giving rise to an amphipathic helix. The hydrophobic face was kept short at the 1:1.5 ratio of hydrophobic (leucine) to cationic (lysine) residues to avoid hemolytic activities common for venom peptides that have broader hydrophobic clusters (4, 33). To support the ratio, small alanines and neutral glutamines, which do not contribute to membrane binding, were alternately arranged in the polar face as a neutral cluster opposite to the hydrophobic face (SI Text).
Fig. 1.
Peptide design and folding. (A) Amhelin sequence, linear and on a helical wheel, and as an amphipathic helix spanning ∼3.15 nm (in blue, 2ZTA PDB entry rendered with PyMoL). (B) CD spectra of amhelin (20 μM) in 10 mM phosphate buffer (red line), ZUVs (blue line), and AUVs (green line). (C) LD spectra of amhelin (solid line) and the non-AMP (dashed line) (both at 20 μM) in AUVs. (D) 31P MAS ssNMR spectra of AUVs mixed with amhelin at different lipid–peptide ratios, −0.9 ppm (large peak) and 0.2 ppm (small peak) resonances arise from the PC and PG headgroups, respectively. (E) The rmsd for the molecular dynamics simulation of a model octameric amhelin pore (initial configuration in Inset) in an AUV bilayer. (F) Initial (Left) and later stage (Right) configurations of a model hexameric amhelin pore in the bilayer.
Peptide folding in solution was probed using zwitterionic unilamellar vesicles (ZUVs) and anionic unilamellar vesicles (AUVs) mimicking mammalian and microbial membranes, respectively (33, 34). Dilauroylphosphatidylcholine (DLPC) was used to assemble ZUVs whereas its mixtures with dilaurylphosphatidylglycerol (DLPG) at 3:1 ratios were used to assemble AUVs (30, 33). These lipid compositions yield fluid-phase membranes at room and physiological temperatures (27, 30, 31). Circular dichroism (CD) spectroscopy revealed that amhelin did not fold in aqueous buffers or in the presence of ZUVs at micromolar concentrations. In contrast, an appreciable helical signal was recorded for the peptide in AUV samples (Fig. 1B). Linear dichroism (LD) spectroscopy, which gives a convenient probe for relative peptide orientation in membranes, showed band patterns comprising maxima at 190–195 nm and 220–230 nm, and a minimum at 205–210 nm, which are indicative of peptide insertion into AUVs in a transmembrane manner (Fig. 1C) (35). In contrast, no signal was observed for a designed non-AMP, which cannot bind and order in membranes (Fig. 1C) (33). 31P magic angle spinning ssNMR (MAS ssNMR) spectra of AUV mixed with amhelin revealed increasing broadening of phospholipid peaks as a function of decreasing lipid–peptide ratios (Fig. 1D). This broadening effect relates to an increase in line width caused by a decrease in the T2 relaxation time (36), which corresponds to an increase in correlation time of the phospholipid groups. This increase suggests a decrease in motion of phospholipid groups in contact with the peptide, which is more pronounced at higher peptide concentrations and is more noticeable in thicker membranes (Fig. S1). Taken together, the data is consistent with a transmembrane insertion of the peptide.
Early oligomers of helical inserts are believed to arrange into small pores whose projections can be obtained by crystallizing peptide–lipid assemblies in fluid bilayers as a function of hydration and temperature (14). Diffraction patterns of such assemblies show regular hexagonal arrays of pores comprising just a few helices. To probe the dynamics of poration and expansion, amhelin inserts in AUVs were explored with molecular dynamics simulations using the Chemistry at HARvard Macromolecular Mechanics (CHARMM)36 force field (37). Amhelin helices remained stable with slightly tilted orientations over timescales of 100 ns whereas rudimentary hexameric and octameric pores constructed in the bilayers expanded with the root-mean-square displacement (rmsd) separations doubling in diameter over timescales of order 100 ns (Fig. 1 E and F and Movies S1 and S2). These results imply that early oligomers have a tendency for expansion, which may occur at the expense of further peptide recruitment in the pores.
Consistent with the folding and simulation data, amhelin exhibited antimicrobial activity with minimum inhibitory concentrations typical of AMPs, while showing negligible hemolytic activity (Table S1 and Fig. S2) (1, 2, 12, 21). AFM revealed the surface corrugation of amhelin-treated bacterial cells (Escherichia coli) (Fig. S2). The analysis of pore-like structures was deemed ambiguous due to the considerable roughness of the cell surfaces (Fig. S2) (25). A comparative analysis was performed on SLBs prepared by the surface deposition of AUV in aqueous solution using adapted protocols (26, 29). Silicon wafers used as substrates were coated with a 9-nm layer of silicon dioxide to (i) support homogeneous and stable bilayers maintained in the fluid phase at room temperature and (ii) avoid charge build-up during SIMS measurements, which is necessary as SIMS relies on the detection of secondary ions extracted from the surface by a focused beam of primary ions (133Cs+) rastered across the sample (29).
The SLB samples were incubated with solutions containing amhelin, which was 15N-labeled at all alanine and leucine residues and washed to remove excess peptide. To arrest poration and preserve structural changes in the membrane, the hydrated samples were then rapidly frozen and freeze-dried (29). Secondary ion images of the 12C14N– and 12C15N– signals, which are commonly used in imaging SIMS experiments of biological materials (38), revealed pores of varied forms and sizes supporting the conjecture of pore expansion across the whole scanned area (Fig. 2A and Fig. S3).
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 conditions: 10 μM, pH 7.4, 20 °C.
In these samples, we expect a higher signal intensity from regions of the surface rich in peptide because each unlabeled residue in amhelin contributes to 12C14N–, but the 12C15N– signals will come predominantly from the labeled residues. Thus, SIMS images have a strong degree of component specificity providing direct evidence for the location of the peptide, which prompts the conclusion that the observed pores are peptide-specific. The conclusion 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 wafer substrates) were featureless (Fig. 2C and Figs. S4 and S5).
Firstly, all these images suggest that the interior of the pores in the amhelin-exposed samples is completely free of peptide, as are the control samples, as expected. Secondly, 12C15N–/12C14N– ratios far above natural abundance values (0.37%) are recorded from the surface of the sample away from the pores and are particularly evident at the edges of the pores, where the peptide content appears to be highest (40%) and increases with increasing pore sizes (Fig. 2B). Thirdly, high peptide accumulations can be seen running across the NanoSIMS images, presumably pore-connecting ridges that are spread across the imaged area suggesting peptide migration dynamics (Fig. 2 A and B and Fig. S3).
It should be emphasized here that SIMS measurements relate to the chemical composition of the surface with only a minor contribution 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 edges protruded from the surface to the heights of ∼4 nm (Fig. 3A). The long axis of the peptide can account for ∼3.2 nm whereas the remaining is consistent with the size of a lipid head group (Fig. 3B). Although other explanations are possible, the height difference could be interpreted as due to a staggered arrangement of the peptides at the pore edges, with every other peptide being shifted slightly upward, while retaining their roughly vertical alignment on the edge (4, 5) and maximizing the contact with the hydrophic lipid tails (Fig. 3B). In addition, small white-dot deposits observed predominantly inside the pores and on their edges are most likely due to the aggregation of peptide–lipid material ejected from the membrane. These observations altogether (i) suggest that the peptide incorporates into the bilayer by distorting and partially displacing the lipids of the outer leaflet and (ii) imply an efficient migration mode of lipid–peptide assemblies through fluidic pores and ridges in a highly cooperative manner.
Fig. 3.
Amhelin-treated supported lipid bilayers. (A) In-air AFM topographic images with a cross-section along the highlight line. (B) Schematic representation of pore edges showing the thickness of the SLB (3.2 nm), the maximum observed height (4 nm), and the difference between the two (0.5–0.8 nm) accounted for by possible protrusion variants, three shown. For clarity, only one peptide (blue cylinder) and one phospholipid per layer are shown (aliphatic chains in gray, headgroups in pink). Incubation conditions: 10 μM, pH 7.4, 20 °C.
An intriguing question provoked by the observations is the peaking of pore edges. Although the heights of the edges were fairly consistent, the depth values of the perforations could not be 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 the surfaces in the 1- to 2-nm range. The peaking itself may become negligible under equilibrium conditions at which outer leaflet lipids detach irreversibly and too fast to be observed without deliberately arresting the system by freezing. An insight into this scenario can be obtained only in solution.
Therefore, we monitored real-time changes of SLBs incubated with amhelin by time-lapse AFM in water (25). Amhelin solution at low concentration was directly introduced into a liquid cell that contained an AUV lipid bilayer assembled on flat mica. After the first 10 min of incubation, small pores started forming on the surface and continued to grow in size and numbers over the period of 2 h, culminating in the total removal of the lipid from the mica surface (Fig. 4A). The lipids are likely to dissolve in the form of micelles, possibly including peptides. On removal of larger amounts of the SLB, material increasingly precipitates on the surface (Fig. 4A and Fig. S6). As expected, the pores appeared as expanding holes, suggesting the displacement of outer lipids from the surface into the water, which is characteristic of equilibrated systems (17). The depths of perforations reached ∼2.7 nm, conforming to the amhelin spanning the bound hydrophobic core of the bilayer (Fig. 4B). Similar real-time changes were observed for another amphipathic AMP (AMP2) whose pore expansion in SLBs provides an additional example (Figs. S1 and S6).
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 (0–20 min); 9 nm (30–120 min). (B) Topography image after 40 min incubation with cross-sections along the highlighted lines. Incubation conditions: 0.5 μM, pH 7.4, 20 °C.
Discussion
Collectively our findings provide evidence for pore expansion, or an E-state, of amphipathic antimicrobial peptides in lipid bilayers (Fig. 5). The E-state promotes cooperative peptide migration through the lipid matrix and can persist to complete membrane disintegration. Our proposed model of pore expansion is the synergistic interplay of two physical processes.
Fig. 5.
Proposed pore expansion mechanism for amphipathic antimicrobial peptides. Antimicrobial peptides (blue cylinders) bind to the surface of the membrane (S-state), insert into lipid bilayers forming pores (I-state), which can then expand indefinitely (E-state).
In the first, peptide adsorption induces surface tension on membrane surfaces, which, when sufficiently large, leads to poration. The pore formation promotes peptide migration from the surface to the edges of the pores. This variation of surface tension with composition (Gibbs surface excess) is driven by amphipathic peptides having higher affinity to the membrane edges (3, 4). The process is likely to reduce the tension between peptide and lipid bilayers, thereby stabilizing the formed pores. However, it is challenged by strong electrostatic repulsion between inserted helices in the pore edges (3, 4). In live cells, this conflict can be avoided both because excess peptide on cell membranes can migrate through small pores directly into the cytoplasm targeting intracellular components and because continuous peptide incorporation and diffusion in lipid bilayers can be preempted by membrane swelling (6, 12, 22). For flat and extended 2D lipid matrices, pore expansion is more thermodynamically favorable and is determined by both incorporation and repulsion of peptides to the pore edges. In this way, inserting helices can be viewed as charged equipotential surfaces with a degree of translational freedom (4, 14) conforming to toroidal type poration, which is characterized by shallow energy minima leading to substantial variations in pore sizes (4, 6, 18).
Pores of 10 μm in size can be physically generated in giant unilamellar vesicles (100 μm in diameter) by strong optical illumination in a viscous medium (39). The edges of the generated pores make up a “line” of lipid bilayer edges that, unless stabilized or expanded, reseal due to the line tension (17, 18). Detergent molecules (e.g., Tween 20) can reduce the tension and partially stabilize the line (17, 39) but cannot fold and propagate. Instead, they form micellar aggregates above a critical concentration. In contrast, antimicrobial peptides become amphipathic only upon folding, which, in conjunction with sustained hydrophobic and electrostatic interactions, enables their progressive self-assembly in lipid bilayers. Pore expansion is also different from mechanisms of fusion and transmembrane proteins whose conserved topologies impose specific self-assembly modes and pore architectures (22). For example, HIV glycoprotein 41 (gp41) controls each step in fusion, including pore nucleation, through a sequence of highly specialized conformations rendering the dimensions and lifetime of induced pores precisely optimized for viral entry.
Thus, our findings support the biological rationale of antimicrobial peptides as nonspecific and fast-reacting molecules that target microbial membranes and whose action depends on concentration and matrix availability rather than on pore uniformity and 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 characterized according to protocols published elsewhere (33) (SI Materials and Methods). 15N-amhelin labeled at all alanine and leucine residues was purchased from AnaSpec. All peptides were identified by reverse phase high performance liquid chromatography (RP-HPLC) and MALDI-TOF mass spectrometry. MS [M+H]+: amhelin, m/z 2448.2 (calculated), 2447.7 (found); non-AMP, m/z 2152.4 (calculated), 2152.4 (found); 15N-amhelin, m/z 2458.2 (calculated), 2458.1 (found); AMP2, m/z 2319.1 (calculated), 2320.1 (found). [M+Na]+ and [M+K]+ were also found.
Circular and Linear Dichroism Spectroscopy.
All CD spectra were recorded on a JASCO J-810 spectropolarimeter fitted with a Peltiertemperature controller. All measurements were taken in ellipticities in mdeg and converted to molar ellipticities ([θ], deg cm2⋅dmol−1) by normalizing for the concentration of peptide bonds. Aqueous peptide solutions (300 μL, 20 μM) were prepared in filtered (0.22 μm) 10 mM phosphate buffer, pH 7.4. CD spectra recorded in the presence 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 cuvette flow cell with ∼0.25 mm annular gap and quartz capillaries (all from Kromatec). Molecular alignment was achieved through the constant flow of the sample solution between two coaxial cylinders—a 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 μM peptide).
Solid-State NMR Spectroscopy.
ssNMR experiments were carried out on a Varian Infinityplus 500 MHz spectrometer equipped with a 4 mm MAS triple resonance (HXY) probe at 30 °C. 31P ssNMR spectra were acquired at 202 MHz. A single 4 µs 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 NH4H2PO4.
Molecular Dynamics Simulations.
Molecular dynamics simulations were performed 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, temperature (NPT) ensemble with equilibrations of 20 ns. Production runs were then performed for ∼100 ns.
In-Air Atomic Force Microscopy Imaging.
Topographic, amplitude, and phase AFM 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 flattened with a first-order line-wise correction fit. AFM tips used were supersharp silicon probes (Nanosensors; resonant frequency ∼330 kHz, tip radius of curvature <5 nm, force constant 42 N/m). Images were processed using proprietary SPIP software, version 5.1.3.
In-Water Atomic Force Microscopy Imaging.
Topographic images of supported lipid bilayers in liquid were recorded in contact mode on a JPKNanoWizard I AFM, mounted on an Olympus IX71 inverted optical microscope, as well as in tapping mode on the Asylum Cypher mentioned above. The AFM probes used for all experiments in liquid were MSNL Silicon Nitride probes with spring constants of 0.005–0.03 N/m (Bruker AFM probes) for contact mode imaging, and Olympus BL-AC40 (∼0.1 N/m, Olympus) for tapping mode. Images were processed using Gwyddion (http://gwyddion.net) first-order line-wise flattening and cross-section measurements.
High Resolution Secondary Ion Mass Spectrometry.
SIMS images of chemical and isotopic distributions were acquired on a CAMECA NanoSIMS 50 with lateral resolution down to 50 nm. The instrument uses a 16 keV primary 133Cs+ beam to bombard the sample surface and collects five selected secondary negative ions using a Mauttach–Herzog mass analyzer with electrostatic sector and asymmetric magnet configuration. 12C14N– and 12C15N– secondary ions were collected. Three of the following signals were also recorded simultaneously to give information on sample morphology: 12C–, 13C–, 16O– and 31P–. The ratio images (12C15N–/12C14N–) (30 by 30 μm, 256 by 256 pixels) were collected with a large primary aperture to match the pixel size in the images with the incident ion beam diameter (∼120 nm). A smaller primary aperture was used to achieve higher lateral resolution images (10 by 10 μm). The data were collected without preliminary 133Cs+ implantation to avoid sputtering away the thin samples. The images were calculated and processed using OpenMIMS software (MIMS, Harvard University; www.nrims.harvard.edu), were multiplied by a scale factor 10,000, and processed by a median filter with one pixel radius. Ratios of the control samples were calculated as: ratio = 12C15N–/(12C14N– + 12C15N–) × 100%.
Acknowledgments
We thank Ian Gilmore and Alex Shard for their advice and support for the work. We acknowledge funding from the United Kingdom’s Department of Business, Innovation and Skills, European Metrology Research Programme Grant HLT10, the Strategic Research Programme of the National Physical Laboratory, the Scottish Universities Physics Alliance, IBM Research, Biotechnology and Biological Sciences Research Council Grant BB/G011729/1 (to B.W.H.), Engineering and Physical Sciences Research Council Grants EP/I029443/1 (to J.C.), EP/I029516/1 (to A.W. and P.J.J.), and EP/G036675/1 (to B.W.H. and A.P.), and a Chinese Scholarship Council Research Scholarship (to H.J.).
Footnotes
↵1P.D.R., H.J., and S.R. contributed equally to this work.
- ↵2To whom correspondence should be addressed. E-mail: max.ryadnov{at}npl.co.uk.
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.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1222824110/-/DCSupplemental.
Freely available online through the PNAS open access option.
References
Expanding antimicrobial pores
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