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SOCIAL NEUROSCIENCE

# Oxytocin and the altruistic ‘Goldilocks zone’

When choosing whether to act altruistically, people may compare the current option to an idiosyncratic ideal. Prosocial individuals seem to represent deviations from that ideal in the amygdala, but selfish individuals do not. Oxytocin administration makes selfish individuals look more like prosocial individuals, behaviorally and neurally.

Imagine that you and a friend receive a windfall inheritance from a rich acquaintance (lucky you!). The deceased was a bit peculiar and made a very specific bequest. Of $10,000, you get$5,532 and your friend gets $4,468. How would you feel? What if instead you received$9,999, and your friend got only $1? Or your friend got$9,999 and you got $1?$5,000 and $5,000? If you felt best about that first option, you wouldn’t be alone. It’s just a bit better for you, but not so much so that you feel too guilty to enjoy it. In other words, it’s hit the ‘Goldilocks zone’ for balancing what you’d like for yourself and what you’d want for your friend. Of course, not everyone would feel the same way. Some would be much happier with$9,999 for themselves. What explains such stark individual differences? New research from Liu et al.1 suggests that the amygdala, a region of the brain important for emotion and arousal2, might be key. In people who are relatively prosocial, but not in people who are relatively selfish, this area encodes outcomes in reference to that Goldilocks zone split. Moreover, administering oxytocin, a neuropeptide widely thought to be important for social bonding, moves the Goldilocks zone for selfish individuals closer to that of prosocial people and amps up the amygdala response when proposed outcomes deviate from it. This research has important implications for a number of important outstanding questions about human sociality.

In the experiments, people rated how much they liked different proposed distributions of money to themselves and their assigned partner. To capture the pattern of preferences, the authors propose a model in which people calculate a ratio of their partner’s outcomes to their own and are sensitive to the difference between this ratio and an ‘ideal’ or reference ratio. Importantly, Liu and colleagues also find that individuals vary widely in what that ideal ratio is. For someone generous, it might be close to 1:1, while for someone selfish, it might be skewed 5:1 or even 500:1 in favor of the self. They succinctly describe this ratio as the angle φ of a line drawn from the origin to the point representing the ideal combination of self and other. Deviations from φ reduced liking for an outcome. Remarkably, this ‘reference point’ account provided a more parsimonious fit to the data than many other popular accounts of altruistic choice, including models based on inequality3.

The impact of reference points on choice has a long history of study4. In the social domain, researchers often assume that reference dependence is expressed as a concern for equality: outcomes for one party in reference to the other should be the same, and deviations from inequality are disliked. Importantly, inequality can be computed objectively as the difference in outcomes for self and other. Liu et al. give a new perspective by arguing that social preferences about resource distributions may also be processed in relation to subjectively-defined reference points. The deviation from that reference point was represented neurally across multiple structures, including the posterior cingulate cortex and the middle frontal gyrus, regions recently associated with context-sensitive representations of others5 and moral preferences6.

However, other brain regions encoding deviations from this reference point depended on whether people tend toward selfish or prosocial choices. In individualist participants (who favored distributions skewed toward the self), deviations from the reference were more strongly represented in lateral orbitofrontal cortex (lOFC). In prosocial subjects (who favored more equal ratios) these deviations appeared more strongly in the amygdala. The researchers also found that in prosocial individuals, trial-by-trial fluctuations in amygdala response were associated with decreases in liking, even after controlling for model predictions. Moreover, the amygdala was functionally connected with an area of the ventromedial prefrontal cortex (vmPFC) thought to be important in constructing preferences. This suggests that the amygdala provides an important altruism-promoting input to the valuation process.

Liu and colleagues then went a step further. Some research suggests that individual differences in prosocial disposition result in part from differences in the action of the neuropeptide oxytocin (OT) and its receptor expression in the amygdala7. The authors thus hypothesized that administering OT might shift individualist participants’ ideal reference point. Remarkably, this was exactly what they found. In the between-subjects functional MRI study and then again in a larger, within-subjects replication study, OT shifted the reference points of a priori individualist participants toward more equitable monetary divisions, but had no effect on prosocial people (Fig. 1). The same pattern was observed in a modified version of the task that evoked competitive motives. Moreover, OT increased individualist subjects’ amygdala representations of reference point deviance and functional connectivity with the vmPFC.

These striking results expand our understanding of how contextual and dispositional factors can modulate the behavioral effects of OT administration8. Previous findings regarding OT’s effect on social behavior have been decidedly mixed, and the literature has been the target of deeply-worrying statistical9 and physiological10 criticisms. Liu and colleagues’ work features larger-than-typical sample sizes and includes a separate well-powered replication experiment. This adds considerably to the strength of their conclusions. Thus, the work by Liu and colleagues exemplifies how concerns over the replicability of OT results should be met. Of course, questions of exactly how intranasal OT influences choice remain, and the results pose several interesting questions for how social preferences are expressed during decision-making.

For example, this new ‘social referencing’ model suggests that choices arise from a comparison process that evaluates potential outcomes relative to a ratio of self and other outcomes rather than their absolute magnitude. This implies that the size of outcomes may be less consequential than their relative distribution. Individuals may similarly like receiving $3 while their partner receives$2 and receiving $6 when their partner receives$4. This also makes the counterintuitive prediction that people may sometimes prefer that both parties receive less money, as long as the ratio is more even. Future work will need to more directly test the idea that social preferences are scale-independent.

These results also raise important questions about how to conceptualize the amygdala’s computational role in prosocial decision making. This area is strongly implicated in the production of emotional, autonomic and visceral responses, and prior work also points to its importance in prosocial choice11. The current findings conceptualize it as a type of comparator that, in conjunction with the vmPFC, integrates multiple factors relative to a holistic social reference point. Such a role is consistent with research suggesting that the amygdala influences attentional deployment after unexpected events12, which here might be represented by deviations from a social reference.

Considering the influence of OT raises more intriguing possibilities. Some theories13 argue that OT attenuates the precision or salience of interoceptive signals, permitting attention to turn outward, away from the self. This outward deployment of attention then enables incoming social signals to be incorporated into predictions about desired outcomes. In the studies presented here, OT may have attenuated interoceptive signals in individualist subjects that otherwise lead to an overly self-focused reference point. Shifting reference point ‘predictions’ from egocentric to more egalitarian appears to also alter brain regions that encode deviations, from lOFC to amygdala, respectively. This raises the intriguing possibility that a more prosocial reference might be a default14 that is released when interoceptive inputs to the lOFC are attenuated. Future studies measuring physiological arousal and linking those responses to choice could test such currently speculative hypotheses and provide support for the social predictive-coding interpretation suggested by Liu and colleagues.

Future work should also be targeted at integrating these findings with previous results. For example, whereas OT increased the prosociality of individualist participants in the current study, it has decreased trusting behavior in people with borderline personality disorder15. This suggests that a fruitful avenue for exploration might be to compare social reference points and effects of oxytocin in individualist people and in people with borderline personality disorder, as well as in people with other disorders that have sometimes been tied to oxytocin, such as autism13.

A final key set of questions concerns how the amygdala computes social reference signals, which require considerations of self and other to construct. Previous work suggests that computations related to these quantities may be partially dissociable, with others’ outcomes being represented in the temporoparietal junction and posterior cingulate cortex or precuneus5. Is there a functional connection between these regions and the amygdala? Does this connection depend on OT? Future research answering these questions would provide a clearer map of the computations carried out by different components of a distributed brain network during prosocial choice.

How people make social decisions, and what produces changes in prosocial behavior, has occupied philosophers, economists and psychologists for decades. More recently, interest has also grown in understanding how the brain is implicated in these complex social decisions. Liu and colleagues’ work points to the important idea that people’s social behavior depends on their reference point, which can be manipulated by oxytocin. In making this case, we suspect their work will itself serve as a reference point in the field of social neuroscience.

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## Author information

Authors

### Corresponding author

Correspondence to Cendri A. Hutcherson.

## Rights and permissions

Reprints and Permissions

Roberts, I.D., Teoh, Y.Y. & Hutcherson, C.A. Oxytocin and the altruistic ‘Goldilocks zone’. Nat Neurosci 22, 510–512 (2019). https://doi.org/10.1038/s41593-019-0362-y


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# Antimicrobial peptide capsids of de novo design

## Abstract

The spread of bacterial resistance to antibiotics poses the need for antimicrobial discovery. With traditional search paradigms being exhausted, approaches that are altogether different from antibiotics may offer promising and creative solutions. Here, we introduce a de novo peptide topology that—by emulating the virus architecture—assembles into discrete antimicrobial capsids. Using the combination of high-resolution and real-time imaging, we demonstrate that these artificial capsids assemble as 20-nm hollow shells that attack bacterial membranes and upon landing on phospholipid bilayers instantaneously (seconds) convert into rapidly expanding pores causing membrane lysis (minutes). The designed capsids show broad antimicrobial activities, thus executing one primary function—they destroy bacteria on contact.

## Introduction

Antibiotic resistance presents significant challenges for healthcare1. Conventional antimicrobial strategies that target individual intracellular processes continue facing the same barriers of rapidly acquired resistance2, impermeable bacterial membranes3 and the tolerance of quiescent bacteria to antibiotic treatments4. These are just a few factors that prompt the development of novel antimicrobial agents that would be compatible with mammalian immune systems, would not differentiate between growing and dormant bacteria and whose activity does not rely on reaching intracellular targets. In this regard, host defense peptides provide a promising source of antimicrobial agents5. These molecules are evolutionarily conserved components of the innate immunity that are found in all living organisms. Despite their apparent diversity, the peptides share common characteristics. They fold into amphipathic structures in response to membrane binding, are cationic and cause disrupting pores, channels or carpets in microbial phospholipid bilayers6. To realise these modes of action, the peptides must translate from an inactive surface-bound (“S”) state to an active and antimicrobial pore-like insertion (“I”) state7. This transition necessitates the localised oligomerisation of individual peptides in membranes that would be able to overcome a threshold barrier—a critical local concentration above which antimicrobial effects become apparent. Removing this barrier by locally delivering concentrations that greatly exceed the threshold concentrations may introduce strategies with potentially faster and more profound antimicrobial responses that are less subject to acquired resistance.

Here, we show that artificial virus-like capsids assembled from de novo antimicrobial peptide sequences provide such a strategy. These designed capsids assemble as 20-nm hollow shells that favour attack on bacterial membranes and upon landing on phospholipid bilayers instantaneously convert into rapidly expanding pores causing bacterial lysis within minutes. We demonstrate that these capsids exhibit broad antimicrobial activities, thus executing one primary biological function. They destroy bacteria on contact.

## Results

### Capsid design principles

Our approach is a retro design that aims to encode a pore-forming oligomerisation state into a discrete pre-assembly of antimicrobial peptides. Since membrane-disrupting pores need not exceed tens of nanometres, the resulting assembly has to be structurally confined to avoid aggregation, an order of magnitude smaller than a bacterial cell (0.2–2 µm) to instantaneously convert into membrane-lysing pores, and functionally inert (non-toxic) to mammalian cells. The viral capsid architecture offers a suitable self-assembly form that is symbiotic to mammalian host cells and can meet all of these requirements. Viruses do not disrupt microbial membranes, are not typically antimicrobial, but their capsids offer an ideal, amenable architectural platform for designing artificial capsids assembled from antimicrobial sequences. Such synthetic capsids have a primary biological function of destroying bacterial membranes on contact.

Native capsid proteins assemble according to an n-fold rotational symmetry, which imposes geometric constraints on allowed protein folds and interactions. Often it means that more protein subunits or subunit proteins are used in a capsid. Any capsid can be described using the concept of quasi-equivalent positions. The concept offers an approach whereby capsid proteins are packed around the surface of a sphere with a cubic symmetry, may be positioned in similar environments (quasi-equivalent) with respect to each other, and are clustered into closed supramolecular networks8. These principles are universal and pertinent to viruses from different taxonomic groups: human (adenoviruses), plant (cowpea mosaic viruses), animal (porcine parvovirus), algal (phycodnavirus) or bacterial (tailless phage) capsids are all proteinaceous icosahedra9. An icosahedron consists of 20 flat faces of equilateral triangles arranged around a sphere with 5/2 3 symmetry (Fig. 1a).

Each face is subdivided into smaller triangles, facets, and their number is reflected in a triangulation number T, which can be found graphically from an equilateral triangular net and using a simple equation:

$$T = k^2 + k \times h + h^2,$$
(1)

where k and h are any integers with no common factor (Fig. 1b).

Capsids with low triangulation numbers would have low numbers of different polypeptide sequences and subunits in the assembly (Fig. 1c). Indeed, a T = 1 capsid has 20 triangular faces and each triangle can be subdivided into three equal portions each hosting one protein (Fig. 1a). A total of 60 identical proteins would make up a T = 1 capsid (Fig. 1d). Any T > 1 icosahedron has 20 × T faces, 12 pentamers (five-fold vertices) and 10 × (T–1) hexamers. As a consequence, protein numbers in capsids increase with increasing T numbers, e.g. T = 3 (180 proteins), T = 4 (240) and so on. The capsid symmetry is ensured by the arrangement of protein subunits around five- and six-fold vertices into pentameric and hexameric supramolecular units, respectively (Fig. 1b). Capsid proteins interface via precisely matched orthogonal interactions10, which remain challenging to emulate de novo.

To mitigate the need for such orthogonal fitting, the same protein motif can be placed at each triangular vertex, whereas each triangle must retain the three-fold symmetry (Fig. 1a). To accommodate this requirement, we designed a rigid C 3-triskelion to occupy a triangle (Fig. 1e). Two triskelion arrangements within a triangle are possible, leading to two different propagation modes, “starburst” and “honeycomb” (Fig. 1e). Each adapts a classical 5/2 3 capsid symmetry, and each requires the triskelion to propagate at its termini. However, the “honeycomb” propagation, albeit successfully exploited for the design of peptide shells, relies on interfacial “sticky” interactions, oblique or orthogonal11,12,13,14,15,16,17. These use naturally occurring peptides, typically forming β-pleated structures, that assemble into amyloid-like aggregates11,15,16,17, and artificial helices whose assembly depends fully on stabilisation via disulphide bridging13 or benefits from it12,14. Three-arm dendrimers or three-directional, non-covalent branching hubs in this mode propagate at two-fold axes of symmetry, with agglomeration and fibrillogenesis being common side reactions13,14,15. Strong binding at two-fold axes is crucial as the five- and six-fold vertices are deemed largely hollow and redundant18. Therefore, only short triskelions or orthogonal C 3-branching can afford tight packing supporting this mode of propagation. By contrast, the “starburst” arrangement is better suited to direct a capsid-like assembly. It is enabled by all three C 3-termini clustering at five- and six-fold axes and can readily translate into any T > 1 assembly. The three equivalent legs of each triskelion provide the three altitudes of a triangle. Therefore, the edge of a triangular unit is a common integer for all units in an icosahedron face, irrespective of their number (Fig. 1b, c). Based on these principles, we engineered an antimicrobial protein motif arranged into a C 3-triskelion that by clustering at its leg termini with other triskelion copies assembles into capsid-like shells.

### An elementary C1-subunit

To provide a triangular unit, each leg of a triskelion must be a rigid, rod-like structure. A protein folding motif to provide this property is an α-helical coiled coil19. The motif is ubiquitous for different viral processes ranging from capsid assembly (hepatitis B virus) to membrane fusion (HIV)20,21. Coiled coils are bundles of interdigitated α-helices, the number of which can be rationally controlled. In viruses, however, the motif is predominantly heterodimeric and packs further forming four- and six-helix bundles20,21,22. Canonical coiled coils are characterised by heptad repeats of hydrophobic and polar residues, typically designated abcdefg, in which a and d form hydrophobic interfaces23. In order to form contiguous interfaces, the a/d patterns of corresponding helices must be in register. Yet, the average spacing of hydrophobic residues along a coiled-coil sequence is 3.5 residues, which is less than one complete turn (3.6 residues) of a monomeric α-helix19. To rectify this discrepancy, a/d patterns impose a slight left-handed twist, enabling left-handed helix-crossing angles in the coiled-coil bundle. This permits stable coiled-coil formation. Complementary electrostatic interactions at e and g sites of successive heptads between partner strands (i.e. ge′ interactions: g of one heptad and e′ of the following heptad on the other helix) stabilise the coiled coil24. Recently, we have expanded the assignment of coiled-coil patterns into naturally occurring and de novo antimicrobial sequences25,26,27.

For engineering antimicrobial coiled coils, it is necessary to consider hydrophobic a/d pairs in conjunction with charged g/e′ pairs25. In this case, a coiled-coil heterodimer would have an antimicrobial cationic strand and a complementary anionic strand. To enable such a dimer, we made a/d pairs isoleucine/leucine, thus emulating native leucine-zipper structures, while cationic lysines (antimicrobial strand) and anionic glutamates (antagonistic strand) were used for complementary g/e′ pairs supporting parallel heterodimers. Additional lysine residues were introduced into the solvent-exposed c sites of the antimicrobial strand to facilitate coiled-coil disassembly upon binding to microbial membranes. The other solvent-exposed positions, b and f, were occupied by alternating neutral polar glutamines and small alanines. In the anionic strand, serine residues alternating with alanines in b and c positions were used to promote peptide solubility, with f sites taken up by glutamines. Given the minimum requirement of three contiguous heptads to form stable coiled coils28, and that antimicrobial sequences of similar lengths are appreciably strong29, each strand was made as a 21-mer (Fig. 2a–d, Supplementary Fig 1 and 2). This dimeric coiled coil offered an elementary geometric building block—an anisotropic, rod-shaped 3.2 × 2-nm C 1-subunit (Fig. 2e).

Circular dichroism (CD) spectroscopy revealed that individually the peptides remain unfolded in solution, while helix formation was essentially complete (>90%) for their equimolar mixtures (Supplementary Fig 3a). The folding of the C 1-subunit proved to be highly cooperative as gauged by nearly sigmoidal unfolding curves30 with a dominating transition midpoint (T M) of ~50 °C (Supplementary Fig 3b), and by the constant signal intensity at 202 nm during thermal denaturation, which provided a clear isodichroic point typical of a two-state, helix-to-coil, transition (Supplementary Fig 3c). The transition was also fully reversible as spectra recorded before and after the melt were nearly identical (Supplementary Fig 3d). As expected, no assemblies were observed for this elementary subunit by transmission electron microscopy (TEM) (Supplementary Fig 4a). For it to be placed at the triangular vertices and to endow it with a capsid-like symmetry, further modifications were necessary.

### A capsid C3-subunit

First of all, three copies of the C 1 (+) strand were conjugated onto a triskelial hub (Fig. 2f and Supplementary Fig 1). Each leg of the resulting structure folded with the C 1 (–) strand giving rise to a rigid C 3-triskelion (Fig. 3a).

All three legs are folded and identical, all carry a large positive net charge, which provides electrostatic repulsions, all have polar solvent-exposed faces with no complementary interactions and none can support anti-parallel coiled-coil formation. This rigid C 3-subunit firmly fits into a triangular face, but cannot yet assemble. In accord with this, particulate structures with sizes of the subunit (5.3 ± 1.5 nm), and without higher order assemblies, were observed by TEM (Supplementary Fig 4b, c). Dynamic Light Scattering (DLS) provided complementary evidence by revealing an average hydrodynamic diameter of 5.25 ± 0.61 nm for the subunit in solution (Supplementary Fig 4d, e). Therefore, we set out to promote a directed aggregation of triskelions via their termini.

To enable this, the N-terminus of the C 1 (−) strand was extended with a cysteine cap (Figs. 2a, e and 3a and Supplementary Fig 1). Cysteines, in both reduced and oxidised forms, have the highest hydrophobicity among the proteinogenic amino acids, possess high propensity for secondary structure and are capable of localised, proximity-driven cross-linking14,31. Buried, unpaired cysteines are known to induce particle formation in antibodies providing interfacial hydrophobic clustering accompanied by non-native cystine formation32. Similarly, viruses, in which native disulphide bonds are reduced or replaced, retain their ability to assemble into wild-type forms33,34. Collectively, these factors suggest that C 3-oriented N-terminal cysteines of the triskelions should promote hydrophobic clustering at the vertices of triangular facets resulting in a capsid-like assembly. Consistent with this, DLS measurements gave average diameters of 21.2 ± 5.3 nm indicating the formation of higher order assemblies with a relatively narrow size distribution (Supplementary Fig 4f, g). It should be noted, however, that DLS is limited in size resolution by the factor of 3, which may not be sufficient to resolve complex and narrow distributions. Therefore, we sought more accurate evidence. The assembled capsids were analysed by high-resolution TEM, which showed broadly uniform paracrystalline phases with an average diameter of 18 nm (Fig. 3b). The importance of this finding is three fold.

Firstly, it supports a structural plasticity of the assembled capsids within a narrow size range. Such polymorphism is indeed common among viruses that can tune packaging symmetry to compensate for size variations35. As a rule, these changes are reflected in different T numbers36. For example, cowpea chlorotic mottle virus can repack from T = 3 (28 nm) into T = 1 (18 nm) capsids37. In our design, each leg of the folded triskelion (from the centre of the dendrimer hub to the acetylated N-terminus of C 1 (−) strand) spans approximately 4 nm (Fig. 3a). This makes the side of an equilateral triangle ~6.1 nm, which falls within the sizes observed by TEM (Supplementary Fig 4b, c). A T = 1 assembly is deemed unstable and geometrically disfavoured as the triskelions cannot arrange around six-fold axes in this capsid (Fig. 1e and Supplementary Fig 5). Therefore, smaller assemblies observed by TEM are likely to be aberrant or incomplete capsids (Fig. 3b, c). Since the triskelions can only pack into equilateral triangular facets, the next possible assembly, in which triskelia termini cluster into clearly defined six- and five-fold symmetries, is a T = 4 capsid of ~20 nm in diameter (Fig. 3d, e and Supplementary Fig 5). Triskelions readily fit into this capsid (Fig. 3e), which is amply complemented by the most abundant diameters observed by TEM (Fig. 3b, c).

Secondly, regardless of size variations, viral capsids maintain their shell-like morphology. To gain a better insight into this for the design, C 3-capsids were analysed using cryo-TEM and tomography that revealed hollow shells having diameters in the same range observed by high-resolution TEM (Fig. 4a, Supplementary Fig 6). It should be noted that cryo-EM reconstructions provide attainable resolution in the 5–10-nm range38, which borders the size of the triskelion shells. Therefore, three-dimensional (3D) volume reconstructions of the obtained images were fitted into 24-nm spheres39, matching predominant diameters of 20–24 nm, and were benchmarked against larger (>100 nm) shells of the HIV-1 core assembly used for comparison40. Returned reconstructions confirmed the assembly of C 3-capsids as spherical, hollow shells (Fig. 4b–d). In accord with the data, atomic force microscopy (AFM), which provides an ideal probe for the analysis of morphologically defined assemblies, revealed globular capsids with a similarly narrow size distribution under both in-air and in-solution imaging conditions (Supplementary Fig 7a, b). Notably, sizes measured by AFM in solution closely matched those observed by DLS (Supplementary Fig 7b and 4f).

Thus, thirdly, the geometrically conserved shells established for the design manifest a synergy between the assembly and folding of C 3-subunits. Consistent with this, C 3-capsids were found to retain the strong helicity of the elementary C 1-subunit (Supplementary Figs 3a and 8a). Both CD and Fourier transform infra-red spectroscopy (FTIR) spectra for the capsids were characteristic of α-helical conformations, with elements of a β-turn structure that could be assigned in the FTIR spectra being attributable to the dendrimer hub (Supplementary Fig 8b). In particular, the amide I band in the spectra appeared to be red-shifted (1650 ± 2 cm−1) from the values expected for a monomeric α-helix (1656 ± 2 cm−1), indicating helical adjustments for the coiled-coil formation in the C 3-subunits (Supplementary Fig 8b)41. These adjustments proved to be cooperative as reflected in gradual increases in helicity as a function of increasing concentrations of the C 1 (–) strand titrated into the C 3 (+) strand (Supplementary Fig 8c)42,43. Plotting these increases versus the concentrations revealed a saturation ratio of 3 for the C 1 (–) to C 3 (+) strands and a single binding affinity value (K D) of 32 ± 5.6 µM44 (Supplementary Fig 8d). At this ratio, the assembly thermally denatured (20–90 °C) returned sigmoidal unfolding curves, with helical spectra recorded every 1 °C sharing the same signal intensity at 202 nm (Supplementary Fig 8e, f), which indicates a clear one-state transition comparable to that observed for the elementary unit (Supplementary Fig 3). Taken together, these findings confirm the cooperative assembly of the C 3-capsids and the complementarity of coiled-coil interactions and cysteine-promoted hydrophobic clustering. More specifically, complementarity ensures that each C 3-subunit is stabilised as a rigid, autonomous structure, while cysteine caps encourage the formation of a hydrophobic network at vertices. Proximity-driven cross-linking of the caps can accompany the clustering, but is not necessary, with the variation of odd and even numbers of cysteines available at the vertices. Indeed, comparative quantifications by Ellman’s test gave up to 25% reductions in the concentration of free thiols in the capsids, confirming a partial disulphide formation. Such a dual stabilisation function—clustering and cross-linking—allows the assembly to maintain the anisotropic packing of spatially restricted C 1-subunits at the vertices facilitating the formation of a well-hydrated shell.

### Antimicrobial activity and mechanism of C3-capsids

To elicit the biological activity, the design has two main modes of folding, each supporting a specific function. The assembly is stable in solution as well as in the presence of mammalian cell membranes. The capsids, however, are expected to bind to microbial membranes, which is followed by their disassembly into two independent components—the antimicrobial C 3 (+) triskelion that folds and inserts in the microbial phospholipid matrix, and the C 1 (−) strand, the anionic antagonist, which cannot bind to cellular membranes, and instead converts into a random coil remaining in solution. This renders the capsids differential in attacking microbial, but not mammalian, membranes. To probe this behaviour in isolation from intracellular processes45,46, which may indirectly involve in the antimicrobial activity, the folding of the components was measured in the presence of zwitterionic and anionic unilamellar vesicles (ZUVs and AUVs) mimicking mammalian and bacterial membranes, respectively. Two lipid types, saturated and unsaturated, were used to assemble the vesicles. 1,2-Dilauroyl-sn-glycero-3-phosphocholine (DLPC) and its 3:1 molar mixtures with 1,2-dilauroyl-sn-glycero-3-phospho-(1′-rac-glycerol) (DLPG) were used for the corresponding assembly of ZUVs and AUVs. Thicker, unsaturated and more asymmetric membranes were assembled from 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) and 1-hexadecanoyl-2-(9Z-octadecenoyl)-sn-glycero-3-phospho-(1′-rac-glycerol) (POPG) lipids. All these compositions give fluid-phase membranes at both room and physiological temperatures, allowing for the direct assessment of membrane-disrupting effects in solution. As expected, the C 3 (+) triskelion folded only in AUVs, while the C 1 (−) strand did not fold at all (Supplementary Fig 9). These differences correlated with biological activities. Namely, the C 3 (+) triskelion and the assembled capsids were strongly antimicrobial with no apparent haemolytic activities at micromolar concentrations. Minimum inhibitory concentrations (MICs) were typical of polypeptide antibiotics within the phenotypic tolerance of bacteria to antibiotics47, while the C 1 (−) strand was biologically inactive (Table 1).

The seemingly lower MICs of C 3-capsids are for the total peptide concentrations; that is, for 1:3 molar ratios of C 3 (+) triskelions co-assembled with C 1 (−) strands. Therefore, the actual active concentration of the triskelions in the assembled capsids is decreased by to a factor of 4 (Table 1). In principle, higher MICs for the capsids could also be accounted for by a partial antagonistic action of the C 1 (−) strand on the C 1 (+) strand inhibiting membrane binding. To be apparent, however, this action requires substantially higher ratios25. Nonetheless, for the reasons of avoiding strong antagonistic effects of the C 1 (−) strand, each heptad of the C 1 (+) strand incorporates an additional lysine residue contributing a positive charge that is not engaged in coiled-coil formation, is solvent exposed and hence is available for binding to microbial membranes (Fig. 2a-d). Since in their native environments antimicrobial peptides are secreted to act within their proteolytic life time (minutes), the antimicrobial action of capsids should be evident within similar timescales. MIC assays cannot access such timescales because these tests are optical density measurements performed over much longer periods of time (24 h).

To gain a better insight into killing kinetics at the cellular level, we monitored the lysis of Gram-negative Escherichia coli and Gram-positive Bacillus subtilis using one-stain (propidium iodide) and two-stain (LIVE/DEAD® BacLightTM) bacterial viability assays in conjunction with fluorescence microscopy (Supplementary Fig 10). For both bacteria, the capsids used at the MIC (3 µm) caused progressive lysis of up to 80% of the total number of cells within the first 20 min reaching nearly complete killing rates in 30 min (Supplementary Fig 10). Collectively, the results of the biological tests indicate strong and rapid antimicrobial responses of the C 3-capsids, suggesting a physical, membrane-mediated mechanism of action. Indeed, once in membranes C 1 (+) strands are meant to refold and insert in phospholipid bilayers in a transmembrane manner46. Because all three legs in the C 3 (+) triskelion are identical, each has the same ability to bind and insert. Because the length of each strand matches the thickness of the phospholipid bilayers (3–4 nm), this ability is not restricted, but facilitated by the other two strands of the triskelion that remain lipid bound. Finally, given that in membranes all the strands would have the same orientational preference, for which they compete, triskelions are anticipated to inflict an immediate membrane damage leading to the progressive removal of the bilayer. Consequently, C 3-capsids are predicted to porate phospholipid bilayers with the formation of large and expanding transmembrane pores.

It should be noted, however, that microbial membranes are curved 3D structures that do not exceed 2 µm in size. Poration in these membranes can lead to rapid membrane rupture and collapse before individual pores can expand visibly. Longer time and length scale studies are necessary to observe the predicted effect, which can be accessed in supported lipid bilayers (SLBs). These preparations give ideal models for fluid-phase membranes and are flat (to within ~0.1 nm) in their unperturbed state, thereby ensuring the most accurate depth measurements of forming pores in real time by AFM45. With this in mind, we visualised the effect of C 3-capsids on SLBs prepared by the surface deposition of AUVs in aqueous solution46, using an AFM adapted for high-speed scanning48 and compiling videos (Supplementary Movie 1) based on sequences of rapidly acquired AFM images49. Upon the addition of the capsids, poration was apparent within seconds of incubation, indicating the instantaneous disassembly of the capsids on the membranes (Fig. 5a and Supplementary Movie 1). The formed pores grew in size and merged resulting in the complete removal of the available phospholipid matrix under 5 min (Fig. 5a). The depths of the pores were consistently ~3 nm, indicating that C 1 (+) strands spanned the bilayer (Fig. 5b and Supplementary Movie 1).

The data prompt a mechanism according to which C 3-capsids at once disassemble upon landing on membranes, whereupon C 3-triskelions re-assemble into transmembrane pores—all within several minutes. The orientation of C 1 (+) strands incorporated into the bilayer is likely to be in a dynamic equilibrium with the other strands in the same C 3 (+) triskelion whose membrane binding must be equally satisfied. On the one hand, such a demand for each C 1 (+) strand to bind and fold with the lipids promotes profound membrane disruption manifesting in rapidly expanding pores (Fig. 5). On the other hand, a thicker peptidoglycan layer on the surface of Gram-positive bacteria that is rich in anionic teichoic polymers might initiate the premature disassembly of the capsids, while inhibiting the migration of folded triskelions to the cytoplasmic membrane50. Partly, this may explain the less pronounced activities of the capsids against Gram-positive Staphylococcus aureus and Enterococcus faecalis (Table 1). By contrast, Gram-positive B. subtilis, whose peptidoglycan undergoes continuous transformations from thick to thin layers51, was noticeably more susceptible to the treatment of the capsids (Table 1). Encouragingly, this property of the capsids to respond differentially to bacterial membranes can be harnessed for targeting Gram-negative membranes, in which case membrane-selective capsids could be developed.

## Discussion

The demonstrated concept offers a molecular platform for engineering bespoke antimicrobial capsids that can be assembled from relatively short amino-acid sequences. Given that there are thousands of antimicrobial peptides reported in the literature5,6, each of these may be used to construct a self-assembling capsid protomer. Antimicrobial sequences are certainly not limited to stand-alone peptides, naturally occurring or designed, and can be sourced from native proteins exhibiting complementary properties. For example, short peptide fragments of transmembrane proteins or bacteriostatic proteins from biological fluids can be redesigned to assemble into biologically functional nanoscale shells17,52. The use of antagonistic sequences that co-fold with antimicrobial sequences introduces another level of control when compared to structures assembled exclusively from antimicrobial components17. Resulting hetero-oligomers give rise to discrete protomers for which number in a final assembly can be pre-defined in a manner similar to the aggregation number of capsids used to describe viruses9. Not only this supports geometrically conserved structures with a narrow size distribution, as demonstrated here, but can also provide a means of tuning discrete capsids or their ensembles within close T > 1 ranges.

In principle, this ability would be important in addressing broader aspects of antimicrobial activity including the targeting of intracellular pathogens. Conventional antibiotics are of little help against these, and particularly against dormant forms that are phenotypically tolerant to antibiotic treatments53. Similar to antimicrobial peptides, which, unlike antibiotics, attack both growing and mature bacteria29, the designed peptide capsids may prove effective in this regard: their differential membrane binding is directly related to their ability to traverse mammalian membranes and reach the cytoplasm without cytotoxicity. Antimicrobial sequences have built-in cell-penetrating properties, so do the designed capsids. Furthermore, the capsids may encapsulate genetic cargo or a reporter and deliver it into the cytoplasm of human cells, which may provide a dual function of cell penetration and delivery. To probe the feasibility of intracellular delivery, the capsids were co-assembled with a model RNA that was fluorescently labelled. The resulting capsids promoted an active RNA delivery into HeLa cells within hours (Supplementary Fig 11a). The fluorescent RNA appeared as particulate cytoplasmic spreads in the cytoplasm suggesting an endocytic uptake14. Flow cytometry measurements showed that the transfection efficiency of the capsids was at least comparable with that of commercial transfection reagents (Supplementary Fig 11b, c), whereas RNA mixed with the C 1 (−) strand, as a negative control, showed no transfection (Supplementary Fig 11d). Thus, the capsids are effectively infectious agents whose cellular and intracellular targeting can be enhanced by incorporating specialist moieties allowing for receptor-mediated delivery.

In more practical terms, whereas better antibiotics inevitably lead to a fitter resistance, the concept entails a promising discovery paradigm. The clinical potential of antimicrobial capsids owes to the lack of widespread microbial resistance to antimicrobial sequences5. Membrane disrupters impose a prohibitive cost for bacterial resistance to develop6, but yet their action is bound to the same “S”-to-“I” transition of individual peptide monomers. By contrast, pre-concentrating the monomers into capsids introduces a principally more challenging scenario of virtually built-in pores that can instantaneously convert into irreparable membrane lesions in bacterial cells.

Indeed, the designed capsids are weakly cationic, which might allow them to cross biological barriers more effectively (Supplementary Table 1). For example, particles with strong cationic surfaces are not effective in crossing blood–brain barrier, which remains a major obstacle for their therapeutic uses14. Native viruses have isoelectric points (pI) below 8, but which can extend due to sorption processes, while for highly infectious viruses such as polioviruses pI can be >854. The designed capsids possess a weak positive charge that is sufficient to bind to anionic bacterial surfaces, and upon binding the capsids disassemble with a rapid increase in pI (to 11 as that of the C 3 (+) strand), thus effectively binding membrane phospholipids and disrupting the bilayer.

Most peptide-based antibiotics destroy bacterial cell membranes (colistin) or inhibit their construction (vancomycin). With the increasing usage of membrane-active antibiotics in clinic (daptomycin, polymyxins) and a stronger drive towards antibiotics effective against Gram-negative bacteria, there is a pressing need to extend search strategies to alternative approaches involving macromolecules that are different from antibiotics altogether and may build upon similar, membrane-disrupting mechanisms. For all these reasons, the described mechanistic design lends itself to emerging classes of antimicrobial agents and materials with a rich repertoire of exploitable properties.

## Methods

### Peptide synthesis

All the peptides were assembled on a Liberty microwave peptide synthesiser (CEM Corp.) using standard Fmoc/tBu solid-phase protocols with HBTU/DIPEA as coupling reagents (Supplementary Fig 1). Rink amide 4-methylbenzhydrylamine resin was used throughout. Standard Allyl-based orthogonal protocols were employed for the synthesis of the C 3-triskelion on resin, with Fmoc-Lys(Alloc)-OH used to generate the C 3-dendrimer hub (Supplementary Fig 1). The hub and the C 1 (−) strand were acetylated using a solution containing acetic anhydride (5%, v/v) and pyridine (5%, v/v) in DMF. Upon cleavage and deprotection of cysteine-free peptides (95% TFA, 2.5% TIS, 2.5% water) and the C 1 (−) strand (95% TFA, 2.5% TIS, 2.5% EDT), the peptide identities were confirmed by analytical RP-HPLC and MALDI-ToF (Supplementary Fig 2).

MS [M+H]+: C 1 (−) strand—m/z 2545.8 (calc.), 2546.1 (observed); Cys-free C 1 (−) strand—m/z 2371.6 (calc.), 2372.5 (observed); C 1 (+) strand—m/z 2447.1 (calc.), 2447.3 (observed); C 3-triskelion—m/z 8302.6 (calc.), 8302.6 (observed). MS [M+Na]+: C 1 (−) strand—m/z 2568.8 (calc.), 2569.3 (observed); Cys-free C 1 (−) strand—m/z 2394.6 (calc.), 2394.6 (observed); C 3-triskelion—m/z 8325.5 (calc.), 8324.9 (observed).

### High-performance liquid chromatography

Analytical and semi-preparative gradient RP-HPLC was performed on a JASCO HPLC system using Vydac C18 analytical (5 μm) and semi-preparative (5 μm) columns. Both analytical and semi-preparative runs used a 10–60% B gradient over 40 min at 1 and 4.7 mL min–1, respectively, with detection at 230 and 220 nm. Buffer A—5% and buffer B—95% aqueous CH3CN, 0.1% TFA.

### CD spectroscopy

CD spectra were recorded on a Chirascan Plus spectropolarimeter (Applied Photophysics Ltd.) equipped with a Peltier temperature controller. All measurements were taken in millidegrees using 1 nm step, 1 nm bandwidth, 1 s time/point and four acquisitions. All measurements were recorded in a quartz cuvette with 0.05 cm pathlength. Aqueous peptide solutions (300 µL, 100 µM total peptide, unless stated otherwise) were prepared in filtered (0.22 µm) 10 mM 3-(N-morpholino)propanesulfonic acid (MOPS), pH 7.4, room temperature. After baseline subtraction, the spectra were converted to mean residue ellipticities (MRE, deg cm2 dmol−1 res−1) by normalising for the concentration of peptide bonds and the cell pathlength. CD spectra at variable temperature were recorded with a 1-°C step from 20 to 90 °C with 180 s equilibration time for each spectrum. Thermal denaturation curves were obtained by plotting the MRE at 222 nm as a function of temperature, the first derivative of which provided T M values. Binding titrations were performed using module B end-station spectrophotometer at B23 beamline (Diamond Light Source, UK) and a cylindrical cuvette with a 0.01-cm path. All measurements were performed by titrating the C 1 (−) strand into the C 3-triskelion (25 µM). Each sample for a specific molar ratio was incubated for 15 min prior to measurement. All measurements were taken in ellipticities and K D values were calculated using Hills equation44. The thermal denaturation curve was fitted to standard two-state denaturation equations (dose response and Hills equations). The calculations returned a nearly sigmoidal curve (Supplementary Fig 3)30. The coefficient of determination (R 2) used as the measure of goodness of fit was 0.999 for the data versus 1 for an ideal fit. CD spectra in the presence of ZUVs and AUVs are for lipid–peptide (L/P) molar ratios of 100.

### FTIR spectroscopy

All FTIR spectra were collected using a Tensor-37 series FTIR spectrophotometer with a BioATR II unit (Bruker Optics, UK) as the sampling platform with a photovoltaic mercury cadmium telluride (MCT) detector and a Bruker Optics workstation, which was equipped with OPUS software. Low volume (20 μL) peptide samples (100 μM) were placed in a circular sampling area of radius 2 mm with a pathlength of 6 μm. The temperature of the sample was maintained at 20 °C by means of flow connectors to a circulating water bath. All FTIR spectra were collected between 4000 and 850 cm−1 with a resolution of 4 cm−1, scanner velocity 20 kHz, 128 scans, phase resolution 32 and zero filling factor 4.

### Lipid vesicle preparation

The lipids DLPC and DLPG, and POPC and POPG used for liposome construction were from Avanti Polar Lipids. The lipids were weighted up, dissolved in chloroform–methanol (2:1, v/v), dried under a nitrogen stream and placed under vacuum overnight. The resulting film was hydrated to 10 mg mL–1 total lipid concentration in 10 mM phosphate buffer, pH 7.4. The suspension was then extensively vortexed, sonicated (30 °C) and extruded (15 times) through polycarbonate filters (0.05 μm) using a hand-held extruder (Avanti Polar Lipids) to give a clear solution containing small unilamellar vesicles (SUV), which were analysed (50 nm) by photon correlation spectroscopy using a Zetasizer Nano (ZEN3600, Malvern Instruments, UK) following the re-suspension of vesicles to a final concentration of 1 mg mL−1. DLS batch measurements were carried out in a low-volume disposable cuvette at 25 °C. Hydrodynamic radii were obtained through the fitting of autocorrelation data using the manufacture’s software, Dispersion Technology Software (DTS version 5.10).

### Determination of free thiols

A stock solution of 5,5′-dithio-bis(2-nitrobenzoic acid) (Ellman’s reagent from Pierce) was prepared to a final concentration of 2 mM in LC-MS grade water with 50 mM sodium acetate. Fifty microlitres of the solution was mixed with 10 mM MOPS (pH 7.4, 100 µL) and LC-MS grade water (840 µL), to take background absorbance. Pre-assembled capsids (10 µL, 100 µM, without TCEP) were then added to the solution (final volume of 1 mL); 200 µL of the final solution was scanned in the 280–600 nm region (automatic background subtraction) with recording absorbance at 412 nm. The absorbance for each sample was calculated and the results were averaged and divided by 14,150 M−1 cm−1 (extinction coefficient of 2-nitro-5-thiobenzoate) and 1 (number of thiols in peptide) to obtain the final concentrations. Free thiol was quantified using a cysteine standard curve prepared according to the proprietary protocol.

### High-resolution TEM

Electron micrographs were recorded using a FEI Tecnai 20 twin lens scanning transmission electron microscope, operated at 200 kV. Droplets of solution (8 µL) were placed on glow discharged Cu grids coated with pioloform and carbon film. After 1 min, the excess solvent was removed using a blotting paper and the grid was stained with uranyl acetate (1%, wt) for 15 s before blotting the excess stain. High-resolution images were recorded using a proprietary FEI Eagle 4k × 4k CCD.

### Cryo-TEM

Cryo-TEM samples were prepared by plunge freezing performed using a VITROBOT mark IV (FEI Company)—into liquid N2-cooled liquid ethane. Droplets (5 µL) of peptide solutions (100 µM) were placed on glow discharged lacey carbon grids and left for 2 s before blotting (2 s) and plunging. This yielded samples in which peptide capsids are embedded in the vitreous ice suspended inside the holes of the carbon. The sample grid was then transferred (without warming) into a Gatan 626 cryo-holder and visualised at 200 kV in a Tecnai T20 (FEI company) transmission electron microscope fitted with an Eagle 4k × 4k camera (FEI).

### Cryo-TEM tomography

The samples were prepared as above and tilt series were collected automatically at 3° increments over an angular range of −42° to 55°. The electron dose was 2.75 electrons per square Ångstrom per second per image. Projection alignment, reconstruction and image processing were done using IMOD. Visualisation, surface reconstruction and final segmentation were performed in Amira 3.0 (TGS, San Diego, CA).

### In-air AFM

AFM images were obtained for a drop of peptide solution (8 µL, 100 µM) placed on a clean silicon wafer with the buffer excess removed by blotting. All measurements were carried out on a Cypher instrument (Asylum research) in a tapping mode using super-sharp PPP-NCHR type cantilevers (Nanosensors™: resonant frequency ~330 kHz, tip radius of curvature <5 nm, force constant 42 N m−1). Images were flattened via line-by-line subtraction of first-order fits to the background, using SPIP software, version 6.0.2.

### Preparation of SLBs for AFM in water

SLBs were formed on mica as described elsewhere45 from a vesicle solution of 4 mg mL−1 DLPC/DLPG (3:1, molar ratio) and for POPC/POPG (3:1, molar ratio) SLBs. The vesicle solution was incubated on cleaved mica for 30 min in 10 mM MOPS pH 7.2, with 5 mM MgCl2 and 5 mM CaCl2. After absorption, the solution was washed 10 times with 10 mM MOPS pH 7.2, with 150 mM NaCl, to remove unfused vesicles from the solution. Mica discs (Agar Scientific, Stansted, UK) were glued to a metal puck, and freshly cleaved prior to lipid deposition.

### In-water AFM on SLBs

Topographic images of SLBs in water were recorded on a Multimode 8 AFM (Bruker AXS, CA, USA) with a modified AFM head designed for the photothermal actuation of miniaturised cantilevers46. Bruker FASTSCAN-D probes (0.25 N/m) (Bruker AFM probes, CA, USA) were photothermally driven for Tapping mode at ~90 kHz with a typical amplitude setpoint of ~300 mV. Capsids were introduced into the sample volume via a channel in the custom fluid cell and diluted in the existing buffer solution (150 mM NaCl, 10 mM MOPS pH 7.2) to the final concentration stated. A negative Tapping mode setpoint was applied to raise the cantilever above the sample surface during capsid injection. Images of 2 μm size (256 × 256 pixels) were captured in alternate scan directions at a line rate of 19.3 Hz. Images were processed using Gwyddion (http://gwyddion.net/) for zeroth-order flattening to centre data, and first- or second-order plane fitting to remove tilt or bow. The time-lapse AFM video was generated from the image sequence by using Fiji—Image J47. Cross-section measurements were carried out using NanoScope Analysis or Gwyddion (http://gwyddion.net/) and plotted using Origin (OriginLab, MA, USA).

### MIC assay

MICs were determined by broth microdilution on different bacteria according to the Clinical and Laboratory Standards Institute. Typically, 100 μL of 0.5–1 × 106 CFU mL–1 of each bacterium in Mueller Hinton media broth (Oxoid) were incubated in 96-well microtitre plates with 100 μL of serial two-fold dilutions of the peptides (from 100 to 0 μM) at 37 °C on a 3D orbital shaker. The absorbance was measured after peptide addition at 600 nm using a Victor 2 plate reader (Perkin-Elmer). MICs were defined as the lowest peptide concentration after 24 h at 37 °C. All tests were done in triplicate and the results are summarised in Table 1.

### Haemolysis assay

Haemolysis was determined by incubating a 10% (vol/vol) suspension of human erythrocytes with peptides. Erythrocytes were rinsed four times in 10 mM phosphate buffer saline (PBS), pH 7.2, by repeated centrifugation and re-suspension (3 min at 3000×g). Erythrocytes were incubated at room temperature for 1 h in either deionised water (fully haemolysed control), PBS, or with peptide in PBS. After centrifugation at 10,000×g for 5 min, the supernatant was separated from the pellet, and the absorbance was measured at 550 nm. Absorbance of the suspension treated with deionised water defined complete haemolysis. The values given in Table 1 correspond to concentrations needed to kill a half of the sample population (50% lysis of human erythrocytes) and are expressed as median lethal concentrations—LC50. All tests were done in triplicate and the results are summarised in Table 1.

### Fluorescence imaging of bacteria

Bacterial cultures were centrifuged to give a cell pellet, which was washed twice with 10 mM phosphate buffer (pH 7.4) before being reconstituted in the buffer. One-hundred microlitres of the solution was dispensed in an 8-well chamber (LabTek) with diluted (1/500) propidium iodide (PI) (1 mg mL–1, Invitrogen CA, USA). The chambers with surface-settled bacteria were mounted on a confocal microscope (IX 81, Olympus) equipped with an incubation chamber at 37 °C. PI fluorescence emission was monitored at 625 nm for 60 min after the addition of the peptide to a final concentration of 10 µM. Recorded images were processed by ImageJ (NIH, USA, http://imagej.nih.gov/ij/) to plot the number of fluorescent (stain-dead) cells as a function of time. The values are expressed as a percentage of the total number of cells (taken as 100% for each point).

### Bacterial viability LIVE/DEAD® BacLight™ assays

Bacterial cultures (1 mL) were centrifuged to give a cell pellet, which was washed twice with 10 mM phosphate buffer (pH 7.4) before being reconstituted in the same buffer to give OD600 nm = 0.008. A 100-µL aliquot of the solution was dispensed in an 8-well glass chamber (LabTek) with LIVE/DEAD® BacLight™ bacterial viability kit (Invitrogen). The chambers with surface-settled bacteria (20 min) were mounted on a confocal microscope (Olympus) equipped with an incubation chamber at 37 °C. SYTO®9 and the fluorescence emission of PI were monitored at 515 and 625 nm, respectively, at different time points for 50 min after the addition of the capsids. Recorded images (XY) were analysed using Fiji software to plot the number of dead cells as a percentage of the total number of cells (taken as 100% for each point) after subtracting the total number of dead cells in buffer alone (with no capsids added).

### Flow cytometry

Quantification of labelled siRNA uptake was performed by flow cytometry. AF647-siRNA was assembled with the capsids by immediately adding to the buffered capsid components at a peptide/nucleic acid (P/N) charge (+) ratio of 8:1 as previously described14. For a negative control, AF647-siRNA was incubated with the C 1 (−) strand at the same charge (−) ratio. For a positive control, AF647-siRNA was assembled with Lipofectamine® RNAiMax (Lipo) according to the proprietary protocols. After 4-h incubations with the obtained preparations, cells were trypsinised and re-suspended in 200 µL PBS. AF647 fluorescence was measured by flow cytometry on a Cytek DxP8 FACScan (USA) and analysed using FlowJo software (USA). At least 105 events were gated from each ≥106 subset measured for each sample by forward scatter and side scatter on the 488 or 633 nm lasers to extract and analyse 104 single viable cells. From the untreated control cells, incubated with 200 µL Opti-MEM containing no siRNA and no peptide, a negative population was taken as 0% negative. This gate was then used on all other samples to measure the relative population of negative (no siRNA) and positive (siRNA) cells, which was expressed in percentage.

### Data availability

The authors declare that the data supporting the findings of this study are available within this paper and its supplementary information files as well as from the authors.

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Glasgow, J. & Tullman-Ercek, D. Production and applications of engineered viral capsids. Appl. Microbiol. Biotechnol. 98, 5847–5858 (2014).

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## Acknowledgements

We acknowledge funding from the UK’s Department for Business, Energy and Industrial Strategy and the European Metrology Research Programme (EMRP) projects. The EMRP is jointly funded by the EMRP participating countries within EURAMET and the European Union. We thank the BBSRC for funding (BB/M503113/1), the staff of beamline B23 at Diamond Light Source for access to their facilities (experiment number: SM12739), Judith Mantell from the Wolfson Bioimaging Facility at the University of Bristol for assistance with TEM experiments, Adrian Nievergelt and Georg Fantner (École Polytechnique Fédérale de Lausanne) for providing the design of the modified AFM head and advice on the assembly and operation thereof, and Adrian Hodel (University College London) for assistance with the rendering of 3D structures.

## Author information

Authors

### Contributions

E.D.S., A.B., B.L., S.R., B.W.H. and M.G.R. designed the research. E.D.S., H.A., B.L., N.F., A.B., J.E.N., N.M., S.R., J.R.B. and A.R.Y. performed the research. B.W.H and M.G.R. supervised the research. E.D.S., H.A., B.L., N.F., A.B., J.E.N., N.M., S.R., J.R.B., A.R.Y., B.W.H. and M.G.R. analysed the data. M.G.R wrote the paper.

## Ethics declarations

### Competing interests

The authors declare no competing financial interests.

Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Rights and permissions

Reprints and Permissions

De Santis, E., Alkassem, H., Lamarre, B. et al. Antimicrobial peptide capsids of de novo design. Nat Commun 8, 2263 (2017). https://doi.org/10.1038/s41467-017-02475-3

• Accepted:

• Published:

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text:
## College Physics (4th Edition)

The frequency of the oscillations is $0.25~s$
In general: $y(t) = A~sin(\omega~t+\phi)$ In this case: $y(t) = (8.0~cm)~sin~[~(1.57~rad/s)~t~]$ We can see that $\omega = 1.57~rad/s$. We can find the frequency of the oscillations: $f = \frac{\omega}{2\pi}$ $f = \frac{1.57~rad/s}{2\pi}$ $f = 0.25~s$ The frequency of the oscillations is $0.25~s$.


text:
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>> Home >> Bookstore >> Books on Stata >> Essential Medical Statistics, Second Edition

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See the back cover

## Essential Medical Statistics, Second Edition

$54.00 each Buy  Authors: Betty R. Kirkwood and Jonathan A. C. Sterne Publisher: Blackwell Science Copyright: 2003 ISBN-13: 978-0-86542-871-3 Pages: 501; paperback Price:$54.00

### Comment from the Stata technical group

This text gives an excellent overview of the basics of medical statistics and achieves a good balance between classic methodology, such as contingency tables, and more sophisticated models, such as Cox regression. As personal computers become more powerful, the use of complex models in leading medical journals is becoming more prevalent, and the second edition of this text follows this shift by focusing more on these models. A very nice section on basic meta-analysis is also included.

Covered in the text are the basics of normal-based tests and inference, including linear regression, contingency tables and logistic regression, longitudinal analysis, Poisson regression, survival analysis (including the Cox model), likelihood theory, meta-analysis, Bayesian statistics, basic design, sample-size calculations, and measurement error.


text:
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How can I multiply list items in a dict with another list in Python

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Optimizing parsing of massive python dictionary, multi-threading

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# ListPointPlot3D with connected points?

With the command ListPlot[data,Joined -> True] I can visually connect adjacent data points in the array with lines. However, this option appears to be missing in ListPointPlot3D? Is there some manner with which to join with to join (with a line) adjacent three-dimensional points? There will be a large number of points in my data structure, and I'd really like to keep the standard output format of ListPointPlot3D.

-
'Adjacent can have a rather fuzzy meaning. Are the points on one surface or segregated to some fixed number of surfaces? If so, you can just use ListPlot3D. – ciao Jan 24 '14 at 5:15
@rasher Adjacent just means that the elements in the array are next to one another, e.g. {A,B,C,D,...} would have "A" next to "B", "B" is next to both "A" and "C", and so forth. – 110110 Jan 24 '14 at 5:17
@rasher The problem with ListPlot3D is that I don't want a surface, I just want a "chain" of connected points like this: mars.cs.umn.edu/projects/current/VisionAidedINS_MSCKF/… – 110110 Jan 24 '14 at 5:26

pts = RandomReal[{0, 1}, {19, 3}];
Show[ListPointPlot3D@pts, Graphics3D@Line@pts]

Edit:

Something slightly more useful as an example:

data = RandomFunction[RandomWalkProcess[0.3], {0, 10^2}, 3];
pts = Transpose@data["States"];
Show[ListPointPlot3D@#, Graphics3D@Line@#] &@pts

-
Very very nice. – 110110 Jan 24 '14 at 5:35
Why not Graphics3D[{Point@pkt, Line@pkt}]? Because of axes etc? – Kuba Jan 24 '14 at 8:09
@Kuba The OP said "I'd really like to keep the standard output format of ListPointPlot3D", and I think he better way to keep the format of ListPointPlot3D[] is by using it :) – Dr. belisarius Jan 24 '14 at 11:13
oh, right :) +1 :P – Kuba Jan 24 '14 at 11:21

One can use ListPointPlot3D and then replace Point with Line. By this way, the plot can enjoy options of ListPointPlot3D:

ListPointPlot3D[...]/. Point[a___] :> {Thick, Line[a]}
`
-
This is great!! I think your answer is better than Dr. belisarius. belisarius's method join points with black lines. However, if there are groups of curve data, your method gives consistent color in each curve, fantastic! – matheorem Apr 1 at 15:08


text:
# The joint equation of bisectors of angles between lines x = 5 and y = 3 is ___________

more_vert

The joint equation of bisectors of angles between lines x = 5 and y = 3 is ___________

A) (x – 5) (y – 3) = 0

B) x2 – y2 – 10x + 6y + 16 = 0

C) xy = 0

D) xy – 5x – 3y + 15 = 0

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text:
Two trains started at $7$AM from the same point. The first train travelled north at a speed of $80$km/h and the second train travelled south at a speed of $100$ km/h. The time at which they were $540$ km apart is ________ AM.

1. $9$
2. $10$
3. $11$
4. $11.30$