How do cyclic antibiotics with activity against Gram-negative bacteria permeate membranes? A machine learning informed experimental study

Abstract

All antibiotics have to engage bacterial amphiphilic barriers such as the lipopolysaccharide-rich outer membrane or the phospholipid-based inner membrane in some manner, either by disrupting them outright and/or permeating them and thereby allow the antibiotic to get into bacteria. There is a growing class of cyclic antibiotics, many of which are of bacterial origin, that exhibit activity against Gram-negative bacteria, which constitute an urgent problem in human health. We examine a diverse collection of these cyclic antibiotics, both natural and synthetic, which include bactenecin, polymyxin B, octapeptin, capreomycin, and Kirshenbaum peptoids, in order to identify what they have in common when they interact with bacterial lipid membranes. We find that they virtually all have the ability to induce negative Gaussian curvature (NGC) in bacterial membranes, the type of curvature geometrically required for permeation mechanisms such as pore formation, blebbing, and budding. This is interesting since permeation of membranes is a function usually ascribed to antimicrobial peptides (AMPs) from innate immunity. As prototypical test cases of cyclic antibiotics, we analyzed amino acid sequences of bactenecin, polymyxin B, and capreomycin using our recently developed machine-learning classifier trained on α-helical AMP sequences. Although the original classifier was not trained on cyclic antibiotics, a modified classifier approach correctly predicted that bactenecin and polymyxin B have the ability to induce NGC in membranes, while capreomycin does not. Moreover, the classifier was able to recapitulate empirical structure–activity relationships from alanine scans in polymyxin B surprisingly well. These results suggest that there exists some common ground in the sequence design of hybrid cyclic antibiotics and linear AMPs.

1. Introduction

It is difficult to overestimate the problem posed by antibiotic-resistant bacteria to global human health. Approximately 70% of hospital acquired infections in the United States are resistant to at least one antibiotic. Currently, over 2.8 million people acquire antibiotic-resistant infections in the U.S. each year, of which >35,000 die as a result [1]. Unfortunately, progress on antibiotic development has been slow. In the last 20 years, only two new classes of antibiotics, oxazolidinones and lipopeptides, have been approved for use, and there is already resistance to both [2–4]. Indeed, the economic dimension of the problem cannot be ignored. The costs associated with these infections in terms of annual health care costs and productivity losses are estimated to be upwards of $20 billion and $35 billion, respectively [5]. Moreover, it takes over $500 million to develop an antibiotic but typically only a few years elapse before the emergence of resistant strains, so the present version of discovery-based approach to antibiotic development is not necessarily sustainable. The growing gap between the decline of antibiotic development and the escalating emergence of bacterial drug resistance has become one of the most salient challenges for human health.

We aim to discover design principles implicit in cyclic antibiotics, a growing class of promising antibiotics with activity against recalcitrant Gram-negative bacteria. All antibiotics have to engage bacterial amphiphilic barriers by disrupting them outright and/or permeating them and thereby allowing the antibiotic to get into bacteria: these barriers include the lipopolysaccharide-rich outer membrane and the phospholipid-based inner membrane. We study a diverse collection of these cyclic antibiotics, some of bacterial origin and some synthetic, in order to identify what they have in common when they interact with bacterial membranes. These cyclic antibiotics include bactenecin, polymyxin B, octapeptin, capreomycin, and Kirshenbaum peptoids, with some of these being hybrid molecules that include peptide-based and non-peptide-based components. We find that these cyclic antibiotics virtually all have the ability to induce negative Gaussian curvature (NGC) in bacterial membranes, the type of curvature geometrically required for permeation mechanisms such as pore formation, blebbing, and budding. Interestingly, this ability to permeate bacterial membranes is a common feature of antimicrobial peptides (AMPs), which have retained antimicrobial activity despite prolonged co-evolution with bacteria and comprise a key component of the eukaryotic innate immune system [6]. We adapted our method for implementing a recently developed machine-learning classifier trained on α-helical AMP sequences [7] so that it can approximately account for non-proteinogenic amino acids and non-amino acid-based hydrophobic structural elements. Using this modified classifier, we examine three prototypical cyclic antibiotics: bactenecin, polymyxin B, and capreomycin. The first two exhibit NGC-inducing ability experimentally, while the third does not. The first and third are cyclic peptides, with the former using proteinogenic amino acids and the latter using both proteinogenic and non-proteinogenic amino acids. The second of the three is a hybrid, a lipopeptide that contains a fatty acid chain and a cyclic peptide composed of both proteinogenic and non-proteinogenic amino acids. Although the classifier was not trained specifically on cyclic antibiotics, it predicted that bactenecin and polymyxin B have the ability to induce NGC in membranes, whereas capreomycin does not, in agreement with experiments. Furthermore, the classifier was able to recapitulate published empirical structure–activity relationships from alanine scans in polymyxin B surprisingly well. Taken together, these results suggest that there exists some common ground in the sequence design of hybrid cyclic antibiotics and linear AMPs.

Before we describe our results, we provide a summary description of the various cyclic antibiotics used in this study:

Bactenecin is a 12-residue cathelicidin AMP that is found in the granules of bovine neutrophils and contains a disulfide bond, forming a cyclic structure. It is the smallest known cationic AMP and exhibits broad antimicrobial activity. Bactenecin has been shown to bind to LPS and permeabilize both outer and inner bacterial membranes [8]. Although bactenecin displays activity against both Gram-positive and Gram-negative bacteria, it has greater potency against the latter [9].

A member of the polymyxins, polymyxin B is a natural cationic lipopeptide antibiotic produced by Bacillus polymyxa and has been clinically used as a last line of defense against multidrug-resistant Gram-negative bacterial infections. Its structure consists of a peptide ring that has a peptide side chain with a fatty acid tail. Like bactenecin, polymyxin B has been shown to kill Gram-negative bacteria by binding to the LPS of their outer membrane and permeabilizing both the outer and inner membranes [10,11].

Octapeptins are a family of natural cyclic lipopeptide antibiotics isolated from Bacillus circulans that have broad antimicrobial activity against both Gram-positive and Gram-negative bacteria [12]. Despite their discovery >40 years ago, octapeptins remain largely un-characterized. The general octapeptin scaffold consists of a cyclic peptide ring linked to a D-amino acid and a fatty acid tail.

The structures of both polymyxins and octapeptins feature a cyclic peptide core that is linked to an N-terminal fatty acid chain. Both are also characterized by a hydrophobic motif in their peptide ring. As octapeptins generally possess fewer charges than polymyxins, they feature increased hydrophobicity relative to the polymyxins.

A vast number of synthetic peptidomimetic compounds have been developed to capture the conformations and functions of natural AMPs. Among these are a class of sequence-specific oligomers of N-substituted glycine called “peptoids” that feature cationic and hydrophobic side chains similar to natural peptides [13]. Kirshenbaum peptoids C3 and C124 are two potent antimicrobial cyclic peptoids that cause cell-surface damage and form pores in bacterial membranes [14,15]. However, additional antimicrobial mechanisms may also be involved.

Capreomycin is a natural polypeptide antibiotic from Streptomyces capreolus that has been used in the treatment of tuberculosis. It is believed to exert its antimicrobial effects by inhibiting ribosomal protein synthesis. For instance, studies suggest that capreomycin binds to and inhibits the 16S rRNA of the 30S ribosomal subunit in Mycobacterium tuberculosis [16,17]. Due to having similar intracellular activity and nephrotoxic side effects, capreomycin is often compared and grouped with animoglycosides. Accordingly, as aminoglycosides are unable to freely cross cell membranes and thus must enter cells via endocytosis [18–20], it is proposed that capreomycin similarly translocates through a cellular uptake pathway [16]. Indeed, recent studies have found that disruption of uptake regulators in Mycobacterium smegmatis result in greater membrane permeability and susceptibility to aminoglycosides and capreomycin [21].

2. Materials and methods

2.1. Preparation of lipid vesicles

Lyophilized phospholipids 1,2-dioleoyl-sn-glycero-3-phospho-(1′-rac-glycerol) (sodium salt) (DOPG), 1,2-dioleoyl-sn-glycero-3-phospho-l-serine (sodium salt) (DOPS), and 1,2-dioleoyl-sn-glycero-3-phosphoethanolamine (DOPE) were purchased from Avanti Polar Lipids and dissolved in chloroform at 20 mg/mL to produce individual lipid stock solutions. Lipid compositions were prepared from the lipid stock solutions as mixtures at specified molar ratios, evaporated under nitrogen, and desiccated under vacuum overnight to form a dry lipid film. Lipid films were resuspended in aqueous 140 mM NaCl, 10 mM N-(2-hydroxyethyl)piperazine-N′-ethanesulfonic acid (HEPES) (pH 7.4) to a concentration of 20 mg/mL. Lipid suspensions were incubated overnight at 37 °C, sonicated until clear, and extruded through a 0.2 μm pore size Anopore membrane filter (Whatman) to form unilamellar vesicles (ULVs).

2.2. SAXS experiments

Solubilized antibiotic compounds were mixed with ULVs at specified antibiotic-to-lipid charge ratios (A_c/L_c) and hermetically sealed into quartz capillaries (Hilgenberg GmbH, Mark-tubes) for high-resolution small-angle X-ray scattering (SAXS) measurements taken at the Stanford Synchrotron Radiation Lightsource (SSRL, beamline 4–2) using monochromatic X-rays with an energy of 9 keV. A DECTRIS PILATUS3 X 1M detector (172 μm pixel size) was used to collect the scattered radiation and the resulting 2D SAXS power patterns were integrated using the Nika 1.50 [22] package for Igor Pro 6.31 and FIT2D [23].

The integrated scattering intensity I(q) was plotted against q. The phases present in each sample were determined by comparing the ratios of measured peak positions, q_measured, with those of the permitted reflections for different crystal phases. The linear regression through points corresponding to the peaks was then used to calculate the lattice parameter, a, of each identified phase. For powder-averaged cubic phases, each peak was represented by a point having coordinates of the assigned reflection, in terms of Miller indices (h, k, l), and q_measured. For a cubic phase, $q=(2\pi /a)\sqrt{(h^2+k^2+l^2)}$. The slope of the regression of q_measured vs $\sqrt{(h^2+k^2+l^2)}$ is 2π/a, which can then be used to calculate a.

2.3. Membrane activity predictions by an SVM classifier

Sequences listed in Tables 2 and 3 were evaluated for membrane disruption activity using a previously validated support vector machine (SVM) classifier [7]. The classifier outputs a probability value, P(+1), for the peptide sequence to be membrane active. (Note that the original classifier was trained with amino acid sequences only containing the 20 standard proteinogenic amino acids.) We approximated each cyclic antibiotic using a linear peptide sequence based on the standard proteinogenic amino acids. For antibiotic compounds that contain non-proteinogenic residues, each non-proteinogenic residue is approximated with a proteinogenic amino acid that best represents the original side chain (e.g., α,γ-diaminobutyric acid (Dab) was approximated with lysine). The results from the SVM classifier are presented in Fig. 3A, Tables 2 and 3.

Table 2. Peptide analogs for cyclic antibiotics and their P(+1) outputs from the SVM classifier.

Cyclic antibiotics were modeled using linear peptide sequences composed of standard proteinogenic amino acids and evaluated by the SVM classifier. As bactenecin is a peptide naturally composed of only proteinogenic amino acids, its native sequence was used.

Antibiotic modeled	Peptide analog variant name	Peptide sequence	P(+ 1)
Bactenecin	N/A	RLCRIVVIRVCR (native)	0.981884801
Polymyxin B (without fatty acid chain)	Polymyxin B-v0	KTKAKFLKKT	0.008487151
Polymyxin B	Polymyxin B-v1	IKTKAKFLKKT	0.601030492
Polymyxin B	Polymyxin B-v2	IIKTKAKFLKKT	0.829476546
Capreomycin	Capreomycin-v1	AKASKRKA	0.000295565
Capreomycin	Capreomycin-v2	AKASKRNA	0.000272803

Table 3. SVM predictions compared with empirical observations for alanine scans of polymxin B.

Alanine scan sequences for peptide analog polymyxin B–v2 with their corresponding analogous substitutions in polymyxin B [70] (if available) and corresponding P(+1) outputs from the SVM classifier. Each alanine substitution is indicated in bold. The SVM classifier predictions agree well with the experimental antimicrobial activities of the alanine substitutions [70]. Alanine substitutions at positions 2, 5, and 9 of polymyxin B, which led to the most notable reductions in observed antimicrobial activity, correspond to peptide sequences (#2, #5, and #9, respectively) with decreased P(+1) values. Furthermore, alanine substitutions at positions 3, 7, and 10 resulted in little to no change in antimicrobial activity and correspond to peptide sequences (#3, #7, and #10, respectively) that maintain high P(+1) values.

Peptide sequence index	Peptide sequence	Analogous substitution in polymyxin B [70]	P(+ 1)	Changes in empirically observed antimicrobial activity [70]
1	IIATKAKFLKKT	Dab1A	0.592073833
2	IIKAKAKFLKKT	T2A	0.755870297	Reduction
3	IIKTAAKFLKKT	Dab3A	0.869940844	Minimal to no change
4 (polymyxin B-v2)	IIKTKAKFLKKT		0.829476546
5	IIKTKAAFLKKT	Dab5A	0.597315289	Large reduction
6	IIKTKAKALKKT	(d-F)6(d-A)	0.784859991
7	IIKTKAKFAKKT	L7A	0.814938477	Minimal to no change
8	IIKTKAKFLAKT		0.645279651
9	IIKTKAKFLKAT	Dab9A	0.463844949	Reduction
10	IIKTKAKFLKKA	T10A	0.906324927	Minimal to no change

Fig. 3. Machine-learning predictions align with empirical membrane activity.

(A) The SVM classifier output P(+1) values for the peptide analogs of bactenecin, polymyxin B, and capreomycin. Polymyxin B–v0, a peptide analog representing the peptide component of polymyxin B, was not predicted to have membrane activity. However, peptide analogs polymyxin B–v1 and polymyxin B–v2, which represent both the peptide and fatty acid chain components of polymyxin B, resulted in high P (+1) values and are predicted to induce NGC. From their P(+1) values, bactenecin and polymyxin B, but not capreomycin, were predicted to induce NGC in membranes. (B) The SVM predictions are in good agreement with the observed NGC-generating ability of the compounds and suggest that the hydrophobic fatty acid chain in polymyxin B increases its membrane activity. Indeed, we observed a broader stoichiometric range (A_c/L_c = 1/2 and 1/1, A/L = 1/50 and 1/25) over which polymyxin B generates NGC, in comparison with that of bactenecin (A_c/L_c = 1/1, A/L = 1/20 only). NGC values for A_c/L_c = 1/2 and 1/1 are depicted as solid and striped bars, respectively.

3. Results and discussion

In this work, we studied experimentally seven cyclic antibiotics with potent activity against Gram-negative bacteria: bactenecin, capreomycin, polymyxin B, two octapeptin isomers, and two Kirshenbaum peptoids (Fig. 1). Specifically, we investigated whether there are any unifying features in how these cyclic antibiotics interact with membranes. Using high-resolution synchrotron SAXS, we quantitatively characterized the deformations induced by the antibiotics in model bacterial membranes. ULVs were prepared from phospholipid mixtures of DOPG, DOPS, and DOPE at distinct molar ratios to mimic the different lipid compositions of bacterial plasma membranes. Each antibiotic was incubated with ULVs at specified A_c/L_c charge ratios relative to the isoelectric point, at which the charge of the antibiotic neutralizes that of the membrane, and the resulting membrane structures were characterized using SAXS. For each antibiotic, an A_c/L_c charge ratio can be converted to a corresponding stoichiometric antibiotic-to-lipid molar ratio (A/L). At a given A_c/L_c, the corresponding A/L value depends on the net charge of the antibiotic. For the antibiotics in this study, A_c/L_c of 1/2 and 1/1 (electroneutral) correspond to A/L ranges of 1/25 to 1/15 and 1/50 to 1/30, respectively.

Fig. 1.

Chemical structures of the cyclic antibiotics in this study.

3.1. Cyclic antibiotics generate negative Gaussian curvature in bacterial membranes

We found that at physiologically relevant conditions, all tested antibiotics, except for capreomycin, restructured the lipid vesicles into bicontinuous cubic phases rich in NGC (Fig. 2A,B). In contrast, the control samples of ULVs only showed a broad characteristic feature consistent with the form factor of ULVs (Fig. S1A). A large number of AMPs have been recognized to exert their bactericidal effects by disrupting bacterial membranes to form pores [24–28] and induce blebbing [29,30], which can lead to membrane depolarization, leakage, and cell lysis. A topological requirement shared by such membrane-destabilizing processes is the generation of NGC in membranes. At a given point on a surface, the maximum and minimum curvatures, which are in orthogonal directions, are called the two principal curvatures, c₁ and c_2· Curvature is defined as c = 1/r, with r being the radius of a circle that best approximates the curve at that point. (By convention, a membrane monolayer that bends to form a convex hydrophilic surface is described as having positive curvature, whereas, a monolayer that bends to form a concave hydrophilic surface is described as having negative curvature.) Gaussian curvature, K, is the product of the principal curvatures (K = c₁c₂) and becomes negative when one principal curvature is positive and the other is negative. Thus, NGC characterizes a surface that bends upward along one direction and bends downward along the orthogonal direction, forming a saddle shape (Fig. 2C). NGC is the specific type of curvature geometrically required in transmembrane pores (Fig. 2D), fusion pores, and along the necks of budding vesicles. AMPs have been observed to generate NGC in a large number of studies [31–36]. NGC has been experimentally observed in other contexts where peptide–membrane or protein–membrane interactions result in membrane topological changes, such as cell-penetrating peptides (CPPs), viral fusion peptides, viral budding proteins, metaphilic peptides, and mitochondrial remodeling proteins [37–41].

Fig. 2. Cyclic antibiotics generate NGC in model bacterial membranes.

SAXS spectra from membranes incubated with each cyclic antibiotic: (A) 20/80 DOPG/DOPE at A_c/L_c = 1/2 (A/L = 1/50–1/30) (left) and A_c/L_c = 1/1 (A/L = 1/25–1/15) (right), (B) 20/80 DOPS/DOPE at A_c/L_c = 1/2 (A/L = 1/50–1/30) (left) and A c/L_c = 1/1 (A/L = 1/25–1/15) (right). Correlation peaks found in the low q region indexed to cubic phases. For clarity, expanded views of low intensity cubic reflections (dashed box regions) for A_c/L_c = 1/1 are provided alongside the spectra plots for 20/80 DOPG/DOPE and 20/80 DOPS/DOPE. Indexing of the identified cubic phases are shown below each spectra plot. Each plotted point corresponds to an indexed cubic peak, with its associated cubic lattice denoted by the marker symbol (square = Pn3m, circle = Im3m, and triangle = Ia3d). (C) NGC characterizes a saddle-shaped surface, which bends upward along one direction and bends downward along the orthogonal direction, and is defined by principal curvatures c₁ and c₂ that are opposite in sign. (D) NGC is found along the inner curved surface of a transmembrane pore. The directions of the principal curvatures for the curved membrane surface are indicated by black arrows. Different pore diameters (d_pore) are characterized by different magnitudes of NGC. (E) Schematic of the Ia3d bicontinuous cubic phase.

Inverse bicontinuous cubic phases (Q_II) are among the range of lyotropic liquid-crystalline phases that can be formed by lipid systems. Of these, the Pn3m, Im3m, and Ia3d symmetries are three cubic phases most commonly observed in biological membranes [42] (Fig. 2E). Each of these cubic phases consists of two interpenetrating, but non-intersecting, aqueous volumes that are separated by a single continuous lipid bilayer. For the Pn3m, Im3m, and Ia3d, the bilayer mid-plane traces the D, P, and G minimal surfaces, respectively, and has NGC at all points on its surface [43]. For a cubic phase, the average Gaussian curvature, <K>, can be calculated from the equation <K> = (2πχ)/(A₀a²), where the Euler characteristic, χ, and the dimensionless surface area per unit cell, A₀, are geometric characteristics unique to each cubic phase, and a is the lattice parameter of the unit cell. Specifically, for the Pn3m, Im3m, and Ia3d cubic phases, χ = −2, −4, −8 and A₀ = 1.919, 2.345, 3.091, respectively.

Membranes of many Gram-negative bacteria, such as Escherichia coli, Klebsiella pneumoniae, and Pseudomonas aeruginosa often contain high concentrations of phosphatidylethanolamine (PE) lipids [44–50]. ULVs with a representative lipid composition of 20/80 DOPG/DOPE to model Gram-negative bacterial membranes were exposed to each antibiotic compound (A_c/L_c = 1/1, A/L = 1/25–1/15) and measured using SAXS (Fig. 2A, Table 1). For bactenecin, the SAXS spectra exhibited correlation peaks with q-ratios of √2:√3:√4:√6:√8:√9, which index to a Pn3m cubic phase with a lattice parameter of 23.11 nm and average Gaussian curvature of −1.23 × 10⁻² nm⁻². For polymyxin B, we observed peaks with q-ratios of √6:√8:√14, corresponding to an Ia3d cubic phase (a = 37.67 nm, <K> = −1.15 × 10⁻² nm⁻²). Octapeptin isomers 1 and 2 both generated Ia3d cubic phases with respective lattice parameters of 35.76 nm and 35.85 nm, and average Gaussian curvatures of −1.27 × 10⁻² nm⁻² and −1.27 × 10⁻² nm⁻². Kirshenbaum peptoids C3 and C124 induced Ia3d (a = 37.32 nm, <K> = −1.17 × 10⁻² nm⁻²) and Pn3m (a = 16.67 nm, <K> = −2.36 × 10⁻² nm⁻²) cubic phases, respectively. These six antibiotics that generated cubic phases also each induced a lamellar phase with a low repeat distance (4.80–5.40 nm), indicative of a condensed lamellar aggregate. Interestingly, the formation of such aggregates has been suggested to facilitate the development of cubic phases [51].

Table 1. Cubic phases induced by cyclic antibiotics.

The symmetries and lattice parameters of the cubic phases generated by the cyclic antibiotics in 20/80 DOPG/DOPE and 20/80 DOPS/DOPE membranes, at both A_c/L_c = 1/2 (A/L = 1/50–1/30) and 1/1 (A/L = 1/25–1/15). Empty cells indicate the absence of cubic phases.

Antibiotic	20/80 DOPG/DOPE		20/80 DOPS/DOPE
	Ac/Lc = 1/2 (A/L = 1/50–1/30)	Ac/Lc = 1/1 (A/L = 1/25–1/15)	Ac/Lc = 1/2 (A/L = 1/50–1/30)	Ac/Lc = 1/1 (A/L = 1/25–1/15)
Bactenecin		Pn3m: 23.11 nm		Pn3m: 17.30 nm
Polymyxin B	Pn3m: 25.06 nm	Ia3d: 37.67 nm	Pn3m: 24.03 nm	Ia3d: 37.47 nm
Octapeptin isomer 1	Pn3m: 20.61 nm Im3m: 26.38 nm	Ia3d: 35.76 nm	Pn3m: 24.15 nm	Ia3d: 35.76 nm
Octapeptin isomer 2	Pn3m: 28.18 nm	Ia3d: 35.85 nm	Pn3m: 22.26 nm Im3m: 28.49 nm	Ia3d: 35.96 nm
Kirshenbaum peptoid C3		Ia3d: 37.32 nm		Ia3d: 37.51 nm
Kirshenbaum peptoid C124 Capreomycin		Pn3m: 16.67 nm		Ia3d: 37.36 nm

Additional PE-rich lipid compositions also produced similar results when incubated with the antibiotics (A_c/L_c = 1/1, A/L = 1/25–1/15). For 20/80 DOPS/DOPE ULVs (Fig. 2B, Table 1), the scattering spectrum for bactenecin contained peaks with q-ratios of √2:√3:√4, indicating the presence of a Pn3m cubic phase (a = 17.30 nm, <K> = −2.19 × 10⁻² nm⁻²). Polymyxin B yielded peaks with q-ratios of √6:√8:√14, which indexed to an Ia3d cubic phase (a = 37.47 nm, <K> = −1.16 × 10⁻² nm⁻²). Octapeptin isomers 1 and 2 both generated Ia3d cubic phases (a = 35.76 nm, <K> = −1.27 × 10⁻² nm⁻² and a = 35.96 nm, <K> = −1.26 × 10⁻² nm⁻², respectively). Similarly, the SAXS spectra of Kirshenbaum peptoids C3 and C124 exhibited peaks that indexed to Ia3d cubic phases with lattice parameters of 37.51 nm and 37.36 nm, and average Gaussian curvatures of −1.16 × 10⁻² nm⁻² and −1.17 × 10⁻² nm⁻², respectively.

Remarkably, the calculated amounts of average Gaussian curvature, <K>, on the surfaces of the cubic phases induced by these six antibiotic compounds were comparable to those induced by many AMPs [35,36]. Moreover, the capacity of these compounds to generate NGC is consistent with their ability to kill bacteria via membrane disruption, a trend that was previously identified among canonical AMPs and their analogs [35,40,52–54]. This new finding supports the generality of NGC-mediated bactericidal activity in structurally diverse natural and synthetic antimicrobial molecules. Furthermore, all seven tested antibiotic compounds did not generate NGC in low-PE membranes (data not shown), which more closely mimic those of mammalian cells [55,56]. Together, these results suggest that their preferential activity against bacterial membranes is at least in part due to membrane composition differences among cell types.

Most strikingly, we found that of the tested antibiotics, capreomycin did not generate NGC in the range of membrane compositions at physiologically realistic conditions. While this result may at first seem at odds with the behavior typical of AMPs and the other six tested compounds, capreomycin’s low membrane activity is in fact consistent with its proposed mechanism of action. Similar to the aminoglycoside class of antibiotics, capreomycin exerts its antimicrobial effects intracellularly by inhibiting protein synthesis [16,17] and is believed to gain entry into cells through a cellular uptake pathway [16,21]. Because neither of these processes would require antibiotic-mediated membrane restructuring, it is not surprising that capreomycin was not found to induce NGC and is therefore the “exception that proves the rule.” However, the precise mechanism of action for capreomycin is not fully understood, as the antibiotic is able to remain active against non-replicating dormant bacteria with significantly reduced cellular uptake [57].

3.2. Comparison of machine-learning predictions and empirical membrane activity

We previously developed a machine-learning SVM classifier trained to identify α-helical peptide sequences that have the capacity to remodel membranes via NGC generation [7]. Moreover, the SVM has been shown to be able to detect the existence of potential membrane-active regions within larger protein sequences [41,58]. The classifier exemplifies how computational methods can be used to predict the function of a peptide or protein based on its sequence-derived physicochemical properties, independent of sequence or structural homology. This type of approach can therefore promote efficient, high-throughput identification and design of new membrane-active peptide sequences with effective antimicrobial activity. To explain briefly, from a given amino acid sequence, based on 12 optimized physicochemical descriptors, the SVM outputs a score, σ, that specifies the distance of the sequence from an 11-dimensional hyperplane trained to separate known α-helical NGC-generating sequences from decoy sequences. A sequence with a high positive σ score indicates a high probability that it has the ability to induce NGC in membranes, while a large negative σ score indicates a high probability that it lacks this membrane-restructuring ability. The σ score can then be converted to a probability 0 < P(+1) < 1 that the sequence is able to induce NGC. A strong correlation was found to exist between P(+1) and the magnitude of NGC generated [7].

At present, there is no known machine-learning classifier for evaluating cyclic peptide antibiotics that are composed of both proteinogenic and non-proteinogenic amino acids. Moreover, there is not enough available data to train such a classifier. Here, we explored the possibility of adapting the SVM classifier we previously trained using natural AMP sequences to estimate the membrane activity of cyclic peptide-based antibiotic compounds via a few approximations. In alignment with their in vitro bactericidal membrane-disruptive effects, we have shown that the six cyclic antibiotics, bactenecin, polymyxin B, octapeptin isomers 1 and 2, and Kirshenbaum peptoids C3 and C124, are indeed capable of inducing NGC in model bacterial membranes. While bactenecin is a short eukaryotic peptide with a disulfide bond, polymyxin B, capreomycin, and octapeptin isomers 1 and 2 are nonribosomal polypeptide antibiotics that are composed of both standard proteinogenic amino acids and non-proteinogenic amino acids, some of which are further modified with additional functional groups. For instance, polymyxin B and octapeptins make extensive use of non-amino acid hydrocarbon-based hydrophobic tails [11,12]. Kirshenbaum peptoids C3 and C124 are synthetic peptidomimetics characterized by having different structures based on poly-N-substituted glycines, and are quite different from regular polypeptides. Therefore, to see how well the SVM trained on AMPs can capture empirical trends of cyclic antibiotics, we focus on three: bactenecin, polymyxin B, and capreomycin. The first two exhibit NGC inducing ability experimentally, while the third does not. We aimed to evaluate the antibiotic compounds with the SVM classifier by approximating each cyclic molecule using a linear peptide sequence with a composition limited to the 20 standard proteinogenic amino acids (e.g., Dab, a non-proteinogenic lysine analog, is substituted with lysine [59]), and incorporating hydrophobic residues to account for additional hydrophobic functional groups (e.g., progressive incorporation of isoleucine to approximate alkyl chains) (Table 2). For example, polymyxin B is a mixture of polymyxins, with the main components being polymyxins B1 and B2 [60], which are characterized by terminal fatty acids with hydrocarbon chains containing 8 and 7 carbons, respectively. In the peptide analog of polymyxin B, we represented the fatty acid chain by using two consecutive isoleucine residues, each of which has a 4-carbon hydrocarbon side chain. Using the SVM classifier on the peptide analogs for bactenecin, polymyxin B, and capreomycin, we found that both bactenecin and polymyxin B resulted in relatively high values of P(+1), indicating a high likelihood of inducing NGC in membranes (Fig. 3A, Table 2). On the contrary, the peptide analogs for capreomycin were not predicted to be able to generate NGC, as reflected by their low P(+1) values. Although the classifier is not trained on cyclic molecules, the SVM predictions for the peptide analogs are in surprising agreement with the observed membrane-restructuring and NGC-generating ability of the compounds (Fig. 3B).

3.3. The role of hydrophobic tails on the membrane activity of lipopeptide antibiotics: polymyxin B as a case study

For the peptide-based cyclic antibiotics, utilizing simple linear peptide analogs as inputs for the SVM yielded reasonable predictions of their membrane activity. This finding thus introduces potential new applications for the SVM as an informative tool for the analysis and understanding of existing molecules and the rational design of new ones. For instance, we can specifically examine polymyxin B, which features a cyclic peptide core that is characterized by a high proportion of cationic Dab residues and is linked to an N-terminal fatty acyl tail (Fig. 1). To probe why polymyxin B contains a hydrophobic alkyl chain in addition to a main peptide core, we modeled its peptide core using a linear peptide analog and screened it for membrane activity with the SVM classifier. The 10-amino acid long linear sequence (polymyxin B–v0) representing the peptide component of polymyxin B was not predicted to have a very high P(+1) score, in contrast with the substantially higher P(+1) values for the peptide analogs that contain additional hydrophobic residues to account for the hydrophobicity contributions from the alkyl chain (polymyxin B–v1, polymyxin B–v2) (Fig. 3A, Table 2). This suggests that the peptide core of polymyxin B alone is not capable of inducing the membrane disruption necessary for bactericidal activity, but incorporation of the hydrophobic alkyl chain will substantially raise the P(+1) values to the range in which that the molecule is likely to generate NGC and can facilitate a broader stoichiometric range over which it exhibits membrane activity (Fig. 3B). In fact, this finding is consistent with previous work that has shown that the removal of the fatty acid component of polymyxin B results in significant loss of antimicrobial activity [61–64]. Accordingly, the increase in antimicrobial activity as a result of greater hydrophobicity is a well-documented general effect in both natural AMPs and their analogs [25,65–69].

3.4. Machine-learning predictions of structure–activity relationships in polymyxin B mutants and comparison with empirical alanine scans

The contribution of each amino acid to a given peptide’s function is often inferred by performing an alanine scan on the sequence. In this manner, the peptide length is maintained while the predominant physicochemical contributions of each native amino acid are sequentially removed. Given that the SVM classifier evaluates a peptide using key learned physicochemical properties for membrane activity, it is natural to ask whether such classifications are sensitive to in silico alanine scan substitutions. As a case in point, we performed an alanine scan on the polymyxin B peptide analog, polymyxin B–v2, sequence (IIKTKAKFLKKT) starting at the first lysine. The P(+1) outputs from the classifier reflect the importance of cationic charges for membrane activity, as indicated by the decreased scores when positively charged lysines are substituted with alanines (Table 3). Interestingly, the scores agree with the previously reported in vitro results of single alanine substitutions in polymyxin B and their effects on antimicrobial activity. Specifically, alanine substitutions of cationic Dab residues at positions 5 or 9 were found to greatly reduce bactericidal activity of polymyxin B against E. coli, as demonstrated by the increased minimum inhibitory concentrations (MICs) of 16 nmol/mL and 4 nmol/mL, respectively, as compared to native polymyxin B, which has an MIC of 1 nmol/mL [70]. Our SVM classifier also predicted similar changes to antimicrobial activity, with corresponding sequences #5 and #9 having lower P(+1) values of ~0.60 and ~0.46, respectively, in comparison with ~0.83 for sequence #4 (Table 3). In addition, alanine substitution of Dab at position 3 of polymyxin B was observed to have less impact on antimicrobial activity, as evidenced by its MIC of 1 nmol/mL [70]. Our SVM prediction for sequence #3 also shows this effect, with a P(+1) value of ~0.87. Furthermore, SVM classifier predictions for alanine substitutions of other polymyxin B residues also tracked well with their experimental antimicrobial activities. Alanine substitution of threonine at position 2 led to a higher MIC [70], which is consistent with the lower P(+1) value of peptide sequence #2. Alanine substitutions of leucine and threonine at positions 7 and 10, respectively, resulted in little to no change in MIC [70] and correspond to respective peptide sequences #7 and #10, which maintain high P(+1) values. Collectively, these results indicate that our improvised SVM classifier is able to recapitulate empirical structure–activity relationships from alanine scans in polymyxin B surprisingly well.

3.5. Comparative analysis of cyclic antibiotics with prototypical linear membrane-active peptides

CPPs are peptides that are capable of efficient direct translocation across cell membranes without causing lytic membrane damage. Like AMPs, most CPPs are short, positively charged peptides that interact with negatively charged membranes [71–76]. Both AMPs and CPPs feature a high proportion of cationic residues and exert their membrane-permeating effects via mechanisms that engage NGC generation [35,37,77]. Due to their similarities, many have questioned whether AMPs and CPPs actually should be categorized as two unrelated classes [78,79]. In fact, increasing evidence indicates that some AMPs, including LL-37 and magainin 2, possess the ability to cross cell membranes [79–81], and certain CPPs, such as penetratin, display significant antimicrobial activity [82,83]. This cross-functionality suggests that AMPs and CPPs may not belong to two distinct peptide classes, but rather comprise a larger family of membrane-active peptides that exhibit a diverse range of antimicrobial activity and translocation ability.

If we consider AMPs and CPPs collectively, we can identify key behavioral trends relating to their physicochemical properties and induced membrane curvature. Studies have observed that on average, AMPs are more hydrophobic than CPPs [37,84] (Table 4). Interestingly, we found that the average magnitude of NGC, |<K>|, generated by CPPs tends to be greater than that induced by AMPs. (For uniformity, these comparisons are made typically with model membranes at lipid compositions with 20% anionic lipids and 80% PE lipids with negative intrinsic curvature.) Taken together, these trends point to an inverse relationship between hydrophobicity and |<K>| among membrane-active peptides. More specifically, we noted that AMPs, which are characterized by greater hydrophobicity, most often generate modest magnitudes of NGC, whereas CPPs typically have lower hydrophobicity and higher magnitudes of NGC. Then by comparing the hydrophobicities and NGCs of the peptide-based cyclic antibiotics (bactenecin and polymyxin B) with those of known AMPs and CPPs, we find that the antibiotics indeed are more AMP-like than CPP-like. But can these trends tell us more about the differences in behavior between AMPs and CPPs? It has been suggested that for a membrane-active peptide, increased hydrophobicity is associated with increased stability of the membrane pore, presumably as a result of having longer membrane residence times [37,85,86]. Therefore, it would make sense that AMPs, being more hydrophobic and thereby forming stable pores, are generally found to be more lytic, in contrast to CPPs, which tend to create transient pores and do not cause significant membrane damage [65,87,88]. As we have found that the level of hydrophobicity can offer temporal information about the produced membrane pore, we hypothesize that the magnitude of NGC can provide clues about the spatial character of the pore, given that additional hydrophobic insertion can have steric consequences for the curvature of the resultant pore. Previous groups have studied the effects of inserting a peptide or protein into a membrane and have found that, in response, a membrane will typically alter its thickness to match that of the inclusion in order to prevent energetically unfavorable exposure of its hydrophobic regions to a hydrophilic environment and to relieve intramembrane stresses and strains. This effect will often lead to changes in the membrane thickness and curvature by stretching, compressing, or tilting the constituent lipids [89–93]. However, we hypothesize there to be less freedom for dimensional changes in the direction normal to the membrane surface than laterally along the membrane surface due to the inherent limitations of membrane thickness changes. Thus, for membrane pores induced by AMPs or CPPs, we anticipate different magnitudes of NGC to be predominantly reflected in differences in pore size (Fig. 2D). For example, we speculate that between two given peptides, the one that induces a lower magnitude of NGC will exhibit a structural tendency to produce a larger pore. Hence, in general, we would expect larger pores for AMPs and smaller pores for CPPs. Remarkably, we discover that this is in fact consistent with empirical measurements of pore sizes for AMPs and CPPs. AMPs have been observed to create a wide range of pore sizes, with diameters of 1.3–3 nm for melittin [94,95], 2–5 nm for magainin [96,97], 2.3–3.3 nm for LL-37 [98], 2.5 nm for defensin human neutrophil peptide-2 [99], 4 nm for cecropin [100], 4.6 nm for lacticin Q [101], and 9 nm for protegrin-1 [102]. In contrast, CPPs exhibit seemingly smaller pores, with HIV-TAT producing 1.3–2 nm pores [103], 0.66 nm for polyarginine-9 [104], and no detectable pores for pep-1 [105].

Table 4. Antibiotic membrane activity relative to that of known AMPs and CPPs.

In general, AMPs are more hydrophobic than CPPs. However, we observe that the average magnitudes of NGC, |<K>|, generated by CPPs tend to be greater than that of AMPs. Together, this suggests an inverse relationship between hydrophobicity and NGC. Comparing the |<K>| induced by the cyclic antibiotics (in bold) and the average hydrophobicities of their respective peptide analogs, we see that their membrane activities are more AMP-like than CPP-like.

Molecule	|<K>| (10−2 nm−2) 20/80 DOPG/DOPE Ac/Lc = 1/1	|<K>| (10−2 nm−2) 20/80 DOPS/DOPE Ac/Lc = 1/1	Peptide Analog Variant (for antibiotics) see Table 2 for sequences	Peptide <Hydrophobicity> (Eisenberg Consensus Scale)
Melittin (AMP)		1.85		−0.09
Polymyxin B	1.15	1.16	Polymyxin B-v1	−0.34
			Polymyxin B-v2	−0.25
Bactenecin	1.23	2.19		−0.29
RTD-1 (cyclic AMP)	2.56			−0.35
BTD-1 (cyclic AMP)	2.56			−0.35
Crp-4 (AMP)		5.31		−0.36
HBD-3 (AMP)		5.02		−0.38
PG-1 (AMP)	4.62			−0.44
Penetratin (CPP)		2.59		−0.55
HIV TAT (CPP)		5.72		−1.23

4. Conclusions

We examined a diverse collection of cyclic antibiotics, consisting of bactenecin, polymyxin B, octapeptin, capreomycin, and Kirshenbaum peptoids, in order to identify what they have in common when they interact with bacterial lipid membranes, using synchrotron X-ray diffraction and machine-learning methods. We found that all except capreomycin have the ability to induce NGC in bacterial membranes, the type of curvature geometrically required for permeation mechanisms such as pore formation, blebbing, and budding. To examine their usage of amino acids compared to that in AMPs, we analyzed amino acid sequences of bactenecin, polymyxin B, and capreomycin using a machine-learning classifier trained on α-helical AMP sequences. Although the classifier was not trained on cyclic antibiotics or peptides containing non-proteinogenic amino acids, a modified implementation correctly predicted that bactenecin and polymyxin B have the ability to induce NGC in membranes, while capreomycin does not. Moreover, a modified approach to implementing the classifier was able to recapitulate empirical structure–activity relationships from alanine scans in polymyxin B surprisingly well. Taken together, these results suggest that the sequence design of hybrid cyclic antibiotics and linear AMPs are cognate.

Abbreviations:

NGC

negative Gaussian curvature

AMP

antimicrobial peptide

DOPG

1,2-dioleoyl-sn-glycero-3-phospho-(1′-rac-glycerol)

DOPS

1,2-dioleoyl-sn-glycero-3-phospho-l-serine

DOPE

1,2-dioleoyl-sn-glycero-3-phosphoethanolamine

ULV

unilamellar vesicle

A_c/L_c

antibiotic-to-lipid charge ratio

SAXS

small-angle X-ray scattering

SVM

support vector machine

Dab

α,γ-diaminobutyric acid

A/L

antibiotic-to-lipid molar ratio

CPP

cell-penetrating peptide

Q_II

inverse bicontinuous cubic phase

PE

phosphatidylethanolamine

MIC

minimum inhibitory concentration