pH-Responsive Virus-Based Colloidal Crystals for Advanced Material Platforms

Abstract

Bacteriophages have a well-defined nanoscale size, shape, and surface chemistry, making them promising candidates for creating advanced biomaterials for applications including biocatalysis, drug delivery, and biosensing. This study demonstrates the self-assembly of the ≈29 nm diameter bacteriophage Qbeta (Qubevirus durum) with the synthetic polycation, poly [2-(methacryloyloxy)ethyl] trimethylammonium chloride (pMETAC), into compartmentalized colloidal crystals. The pH and the polymer chain length tune their self-assembly and the resulting structure, with the potential for further chemical modification or loading with bioactive molecules. Small angle X-ray scattering (SAXS), multi-angle dynamic light scattering (DLS), and atomic force microscopy (AFM) are used for studying the Qbeta self-assembly into the geometrically ordered aggregates. The suprastructures form at pH > 7.0 and disassemble at pH < 7.0. Zeta potential measurements and X-ray photoelectron spectroscopy (XPS) show pMETAC adsorption onto the negatively charged Qbeta surface. The colloidal crystal formation is achieved without chemically modifying the Qbeta surface. Additionally, the Qbeta/pMETAC suprastructures can be easily separated from the suspension as macroscopic aggregate, maintaining their activity. Their simple preparation allows for large-scale production of advanced materials in food and health science applications and nanotechnology. The insights from this study will further advance the tailored design and production of novel colloidal materials.

1 Introduction

Nature uses colloidal structurization to customize material properties and biological function. Examples include collagen structurization in bone and dental tissues or actin structures in the cytoskeleton and muscles.^[1-6] Drawing inspiration from this to design novel structured materials allows for innovations across diverse fields, spanning health sciences, food technology, and energy research. They can be used, for instance, as vehicles for enzyme and drug delivery, electrodes for energy conversion, antimicrobial surfaces, and nanoreactors.^[7-9]

Peptides and lipids have been used to create various structured materials.^[10-13] Applying pre-assembled viruses in this process could facilitate the design of complex hierarchical functional material. For example, exploiting viral particles such as bacteria viruses (phages) as foundational elements for novel structures offers a notable advantage due to their well-defined nanoscale surface characteristics, shapes, sizes, mechanical stability, and biological functions.^[14] Viruses are precision-designed by nature, built from the self-assembly of peptide monomers into a highly organized protein nanocage. Their shapes span from cylindrical and tailed to spherical, depending on the specific phage variant.^[14] Their intrinsic biocompatibility and the active research on scalable production make them prime candidates for designing advanced biomaterials.^[15-17] Their well-defined structural and functional properties can be bioengineered on demand.^[18] Tailoring the functional groups on the protein nanocage surface can enable them to immobilize in precise orientations onto surfaces.^[19] The manipulation of the protein nanocage self-assembly process is also achievable through surface modification of these functional groups.^{[20, 21]} An alternate route for tailoring the ordered assembly of virus capsids is based on DNA templating.^[22] These materials are promising therapeutic agents in phage therapy.^{[16, 23-25]} Expanding their scope, they can be utilized as energy generators or biosensors within the food industry, exemplifying their far-reaching potential.

The phage Qbeta (Qubevirus durum), belonging to the Fiersviridae family, consists of an icosahedral protein capsid containing single-strand RNA and replicates selectively in Escherichia coli.^[26-28] Qbeta has been widely studied and used as a model system for pathogenic viruses such as norovirus and rotavirus due to their structural similarities.^{[29, 30]} It has a diameter of 29.4 nm with a net negative charge at pH values above its isoelectric point (IEP) of ≈4.3.^[31] Any interaction properties should be governed mainly by its surface properties and size due to its isotropic shape. Therefore, Qbeta potentially serves as a simple and solid foundation for protein-based nanostructured material due to its well-known properties and small size.

The fundamental understanding of the interaction between the viral particles and other involved building blocks will guide the design and development of advanced structured materials. Extensive research has been reported on the interaction mechanisms between polyelectrolytes and charged nanoparticles.^[32-35] However, most focus has been on homogenous spherical particles, with few studies on heterogeneously charged, core-shell particles such as phages.^{[36, 37]} The insights from investigations on homogeneous particles may not seamlessly translate to viral particles exhibiting a core-shell structure, intricate surface charge distribution, and heterogeneously exposed functional groups.^[31]

In this study, the control over the interaction of Qbeta is achieved with a custom-designed polyelectrolyte, the polycation poly [2-(methacryloyloxy)ethyl] trimethylammonium chloride (pMETAC, refer to Figure S1, Supporting Information). It is synthesized at defined chain lengths through atom transfer radical polymerization (ATRP) and contains a cationic quaternary ammonium group per repeating unit. pMETAC is widely used in different fields, for instance, as a flocculant in wastewater treatment, for developing antimicrobial surfaces, or in gene delivery vectors.^[38-40]

To our knowledge, this study demonstrates the first formation of highly geometrically organized colloidal crystals through the self-assembly of Qbeta mediated by a polycationic polymer. The study comprehensively examines how composition, polymer chain length, and pH influence supramolecular structures, providing insights into protein nanocage self-assembly with polyelectrolytes. This understanding is key for controlling material parameters, including morphology, size, and structure. These resulting biocompatible and degradable materials are promising for various potential applications in the biomedical and nanotechnology fields.

2 Results and Discussion

2.1 Synthesis and Characterization of pMETAC

Two different chain lengths of pMETAC were synthesized via ATRP. The primary chosen molecular weight of 3.3 kDa aligns with the size range typically observed for antimicrobial peptides, whereas the 16.5 kDa variant represents a comparably larger structure,^[41] refered to as pMETAC1 and pMETAC2, respectivly. After synthesis, a comprehensive pMETAC characterization was performed using gel permeation chromatography (GPC), nuclear magnetic resonance (NMR), and Raman spectroscopy.

¹H-NMR confirmed the polymerization of the METAC monomers to pMETAC. The hydrogen signal associated with the C = C double bonds at δ 6.31 ppm and 5.94 ppm disappeared after the reaction (see Figure S1B, Supporting Information).^[42] This finding agrees with the Raman analysis, where the C = C vibration and its associated hydrogen vibrations at 1640 cm⁻¹ (C═C stretch), 1409 cm⁻¹ (C═C-H₂ bending, in-plane), and at 895 cm⁻¹ (C═C-H₂ bending, out of plane) are absent in the pMETAC spectrum (see Figure S1C, Supporting Information). pMETAC polymers were assessed via aqueous GPC. pMETAC1 displayed a dispersity index (DI) defined as the ratio of the weight averaged (Mw) and number averaged molecular weight (Mn) of the polymer with DI = Mw/Mn = 3.3 kDa /2.65 kDa = 1.26. For pMETAC2, the DI = 16.5 kDa/11.04 kDa = 1.49. The repeat unit length (RU) was approximated at 1.75 ± 0.17 Å through hexamer simulations (simulation details can be found in the supporting information). Utilizing the degree of polymerization extracted from Mn (refer to Equation S3, Supporting Information), the estimated lengths for pMETAC1 and pMETAC2 were calculated as 20.7 and 91.4 Å, respectively.

The polymers were further studied with small angle X-ray scattering (SAXS) in virus dilution buffer (VDB, composition see Materials and Methods in the supporting information) at different pH values between 3.0 and 9.0, see Figure S2 (Supporting Information). A broad peak with a maximum at scattering vector magnitude, q ≈ 1.1 nm⁻¹ for pMETAC1 and q ≈ 0.8 nm⁻¹ for pMETAC2 was observed. These peaks, corresponding to real-space dimensions of d  =  2π/q = 5.7 and 7.9 nm, respectively, can be associated with the apparent center-to-center distance between the positively charged polymer coils in solution.^[43] The larger d value for pMETAC2 compared to pMETAC1 agrees qualitatively with the differences in the molecular weight determined by GPC analysis. The peak position and scattering profiles do not change with pH between 3.0 and 9.0. This finding suggests that the inter-polymer interaction and polymer conformation remain mostly unchanged in this pH range (see Figure S2, Supporting Information), as the quaternary ammonium cation remains positively charged at all these pH values.

2.2 Qbeta/pMETAC Self-Assembly in Water

The colloidal structure of Qbeta in VDB was analyzed before and after adding pMETAC at different pH values between 3.0 and 9.0. Figure S3A (Supporting Information) shows the SAXS curve for Qbeta in VDB at pH 3.0 and 9.0 at optimized Qbeta concentrations for the SAXS study. The Qbeta concentration was estimated by plague forming unit (PFU) counting, measuring the infective particles per milliliter (PFU/ml). A Qbeta sample at ≈10¹³ PFU/ml gave a signal with reasonable signal-to-noise and negligible scattering from inter-particle correlations in SAXS. The Qbeta concentration in this sample was estimated to ≈1 mg mL⁻¹, in agreement with a previous study.^[44] This concentration estimate was further validated with SAXS using a protein of known molecular weight as standard (see supporting information).

The SAXS patterns are characteristic of nanoscale particles with a Guinier region below q ≈ 0.2 nm⁻¹. At higher q values (0.2 < q < 1 nm⁻¹), the scattering curves show maxima and minima, characteristic of the quasi-spherical (icosahedral) virus particles. A modified low-q (q < 0.2 nm⁻¹) scattering has been observed for suspensions of viruses only at pH 3.0. This SAXS curve shows a power-law behavior with an exponent of ≈ −3.0 at this pH and no Guinier region. This curve shape results from aggregates larger than the maximum dimension that can be accurately resolved with the SAXS setup (π/q_min ≈ 45 nm). The low-q aggregation behavior of Qbeta agrees with previous reports.^[30]

The size and shape of Qbeta were obtained from the SAXS data using the generalized-independent Fourier transformation (GIFT) method (details can be found in the Materials and Method section in the supporting information). The resulting pair-distance distribution (p(r)) function is characteristic of spherical particles with diameters ≈29 nm at pH 7.0 (see Figure S3B, Supporting Information). The representative cryogenic-transmission electron microscopy (cryo-TEM) image of the Qbeta at pH 7.0, presented in Figure 1C, confirms the results on size and shape from SAXS, showing an icosahedral particle with diameters ≈29 nm. These findings agree with previous reports on the size and shape of Qbeta.^{[30, 45, 46]} At pH 9.0, a shift in the p(r) function can be observed that arises due to changes in the electron density of the buffer media after pH adjustments.^[47]

Figure 1

Qbeta/pMETAC1 (1:50 weight ratio) self-assembly at pH 7.0. The curves were displaced vertically for better visibility. A) Black squares represent the experimental SAXS data; red lines are the best possible fits of Equation S9 (Supporting Information) to the experimental SAXS data of Qbeta and the Qbeta/pMETAC1 assembly. The peaks in the SAXS curve are further identified by their Miller indices (hkl). B) is an artistic representation of the data showing the Qbeta in a hexagonal arrangement, marked in yellow, with polymers on the surface and in the voids. It is worth noting that the icosahedral Qbeta is represented as spheres. C) Cryo-TEM image showing icosahedral Qbeta with a diameter of ≈29 nm at pH 7.0 in VDB. The zoomed-out overview image is presented in Figure S5 (Supporting Information).

Supramolecular Qbeta materials were created for the first time by adding pMETAC1 or pMETAC2 to the Qbeta suspension. The structure and pH-responsive interactions between Qbeta and pMETAC1, and pMETAC2 were systematically investigated in VDB at pH values between 3.0 and 9.0. The SAXS curves of Qbeta/pMETAC1 and Qbeta/pMETAC2 at a mass ratio of 1:50 in this pH range are presented in Figure S4A,B (Supporting Information). The scattering of Qbeta aggregates dominates the sample Qbeta/pMETAC1 at pH 5.0 and 3.0. At pH 7.0 and 9.0, Bragg reflections of colloidal crystals appear in the presence of pMETAC1, see Figure 1A. The q-positions of the peaks are at 0.27, 0.44, 0.48, 0.70, 0.81, and 0.95 nm⁻¹. The corresponding peak ratio of 1/√3/√4/√7/√9/√12 is characteristic of a 2-dimensional (D) hexagonal structure as represented in Figure 1B. The lattice constant, a, calculated from the first-order reflection using Equation (4), is 27.8 ± 1.4 nm. This agrees with the dimensions of Qbeta of ≈29 nm from the SAXS and cryo-TEM analysis reported above.

To further analyze the structures of the highly geometrically ordered Qbeta/pMETAC1 composite material at pH 7.0, model-dependent fitting of the SAXS data was performed. A spherical core-shell model with added Gaussian coil scattering (P_G(q)) to account for the polymer scattering contributions from the Qbeta sample (protein and RNA) was used (see Equation S9, Supporting Information, where S_hex(q) = 1 and N = 0). The best possible fit of this equation to the experimental data of Qbeta alone is presented in Figure 1A. The inner radius was 10.1 ± 1.2 nm, and the protein shell thickness was 2.7 ± 0.1 nm. The calculated scattering from the analytical model agrees well with the experimental data, given that the SAXS signal provides statistical information on all components in the sample, including impurities. These impurities may be responsible for the smearing of the local minima in the experimental scattering curve, which is not accounted for in the analytical model. Minor fractions of coexisting bacteria- and virus fragments with sizes in the nanometer-range, are seen in some TEM images (see Figure S6, Supporting Information).

For the highly ordered Qbeta/pMETAC1 structures, the spherical core-shell form factor model was multiplied with the structure factor of a 2D hexagonal lattice (S_hex(q)). (see Equations S6 and S10, Supporting Information). For the model to represent the overall scattering curve, an additional power law model was included to account for the contribution of larger aggregates at low q values (see Equation S9, Supporting Information). Detailed fitting parameters can be found in Table S1 (Supporting Information). For the assembly, a core radius of 16.2 ± 0.2 nm with a shell thickness of 1.6 ± 0.5 nm and lattice constant of 27.8 ± 0.1 nm was obtained from the best possible fit of the model to the experimental data (see Figure 1). The fitted radius of Qbeta in the assembly, with an overall radius of 17.8 ± 0.5 nm, is larger when compared to the obtained radius of 12.8 ± 1.2 nm, for Qbeta alone. This increase in the radius with apparently larger core dimensions and reduced shell thickness indicates the adsorption of pMETAC1 to the virus surface with related modifications in the excess electron density in this region.

Atomic force microscopy (AFM) images of the assemblies were acquired in buffer to further analyze the Qbeta/pMETAC1 suprastructures at pH 7.0 (see Figure 2). In Figure 2A and Figure S7 (Supporting Information), the representative topographical AFM images reveal a hexagonal pattern with a center-to-center distance of ≈29 nm from the AFM height profile. The hexagonal lattice spacing obtained at the 2D interface from the AFM image is consistent with the one obtained from the SAXS analysis of 3D bulk structures.

Figure 2

A) Representative AFM image shows the ordered Qbeta-pMETAC1 assembly measured in VDB at pH 7.0. The inset shows an enlarged area with the hexagonal arrangement of the Qbeta marked in yellow. B) FFT spectrum of the image area, marked with a red square in (A). C) The scattering pattern was obtained from the radial integration of the intensities in the FFT image (blue line) and the experimental SAXS data (orange line). The vertical lines guide the eye to compare selected peak positions between the curves, and scattering patterns were displaced vertically.

A fast Fourier transformation (FFT) algorithm was used to calculate the 2D Fourier spectrum of the AFM image (Figure 2B). This spectrum is related to the SAXS data, which are also in the reciprocal space. The radial integration of the 2D spectrum into a 1D scattering curve allowed us to directly compare the structure in the AFM image with the experimental SAXS data of the same sample in buffer (Figure 2C). The calculated scattering pattern agrees reasonably with the experimental SAXS data. The smearing of the FFT peaks from the AFM data can be attributed to factors including compromised statistics on the image, the limited contrast of the image, and imaging artifacts. All those effects, in combination with the cross-terms of the form factor of the spherical particles, contribute to frequency overlay from the imaging process, leading to smeared features and insufficient statistics for a higher resolution scattering pattern in the overall q range.

The influence of the ratio Qbeta/pMETAC1 on the structure formation was evaluated on weight ratios of 0:1, 1:100, 1:50, 1:20, 1:10, 1:5, 1:2, 1:1, 1:0.5, 1:0.2, and 1:0 as shown in Figure 3. In Figure 3A, the SAXS curves corresponding to Qbeta/pMETAC1 ratios between 1:1 and 1:50 show a low-q power-law decay of the I(q) with an exponent of −3.5 to −4, which is characteristic of attractive inter-particle interactions (aggregation).^[48] Additionally, Bragg reflections are evident in the SAXS patterns for the ratios of 1:5 to 1:20, with peak maxima at q values of 0.26, 0.46, 0.69, and 0.95 nm⁻¹. These peaks result from a 2D hexagonal structure with a lattice parameter of 27.7 nm, similar to the sample at Qbeta/pMETAC1 at 1:50 ratio presented in Figure 1. Referring to Figure 3A, for ratios 1:1 and 1:2, an upturn at low-q but no Bragg reflections can be seen. This observation indicates that this Qbeta/pMETAC1 ratio is a threshold for forming colloidal crystals. Upon increasing the ratio to 1:100, the Bragg peaks and the low-q upturn diminish in the scattering. The low-q region of the I(q) showed a power-law decay with an exponent of ≈−2.1, comparable to that of the pMETAC1 alone (sample 0:1). This implies that the number of aggregates present is insignificant. Likely, charge inversion occurs at this high pMETAC1 concentration, stabilizing the pMETAC-coated Qbeta.

Figure 3

A) SAXS data of Qbeta/pMETAC1 at pH 7.0 at varying composition. For better comparison, the curves have been shifted vertically on the arbitrary unit axis. B) Zeta potential (black squares) and conductivity (orange circles) of Qbeta/pMETAC1 at pH 7.0 at different weight ratios with the artistic views of the structure at different Qbeta/pMETAC1 ratios. A hexagonal arrangement of Qbeta within the suprastructures is observed in the composition range highlighted in blue. and the hexagonal lattice is marked in yellow in the corresponding graphical representation.

To study this effect, zeta potential and conductivity measurements were conducted on Qbeta/pMETAC1 samples at pH 7.0, employing a range of ratios (1:0, 1:0.2, 1:0.5, 1:1, 1:5, 1:10, 1:50, 1:100) as illustrated in Figure 3B. The zeta potential of Qbeta was −21.4 ± 1.3 mV, consistent with previous reports.^{[30, 31]} Until Qbeta/pMETAC1 of 1:1, the zeta potential was relatively constant at ≈−20 mV. As the quantity of pMETAC1 increased, an incremental rise in zeta potential from −18.3 to 3.9 mV was evident. At the 1:5 ratio, charge inversion was observed. This goes with a slow, gradual increase until an inflection point, indicating a change in adsorption behavior. A steeper conductivity increase is followed due to the overcharging of the Qbeta until saturation, with additional free pMETAC1 ions in the surrounding water phase. This effect has been observed previously when adding polyelectrolytes to functionalized polystyrene particle suspension.^[49]

The onset of aggregation aligned closely with the zeta potential values reaching a magnitude of <10 mV upon pMETAC1 addition. Further increasing the pMETAC concentration to Qbeta/pMETAC1 at 1:100 led to charge inversion and a significant amount of free pMETAC1 with the zeta potential increasing to 13 mV. Repulsive interactions between the now positively charged particles trigger de-aggregation and free pMETAC1. This behavior agrees with the observations from the SAXS analysis. While the scattering of virus particles dominates the signal at low and high pMETAC1, Bragg peaks from colloidal crystals appear when the zeta potential magnitude is below 10 mV (see Figure 3).

SAXS was used to analyze the stability of the Qbeta and the Qbeta/pMETAC1 at 1:50 colloidal crystals upon heating and salt addition. The SAXS patterns for Qbeta are comparable up to ≈60 °C (see Figure S8A, Supporting Information). At 80 °C, changes in the low-q region of I(q) are observed due to temperature-triggered structural modifications that are irreversible upon cooling to 20 °C. This agrees with previous reports on the protein capsid alteration, with an onset at ≈60 °C, depending on the environment.^{[50, 51]} A similar behavior is reflected in the Qbeta/pMETAC1 at 1:50 colloidal crystals. The hexagonal structure was stable between 20 and 60 °C, with no major change in SAXS curves (see Figure S8B, Supporting Information). However, the scattering patterns change significantly with a decrease in the intensity of the Bragg reflections, when heated to 80 °C.

Increasing the ionic strength of the suspension by adding NaCl had a major effect on the colloidal structure of the Qbeta/pMETAC self-assemblies. The Bragg reflections of the hexagonal Qbeta self-assemblies at 10 mm NaCl disappeared ≥ 30 mm NaCl (see Figure S9, Supporting Information). This shows that electrostatic interactions between the Qbeta and pMETAC mainly control the structure formation in this system. Therefore, stable conditions for the suprastructures are at low ionic strength.

The influence of the polymer chain length was studied by mixing Qbeta with the roughly 4–5x longer pMETAC2 (3.3 kDa vs 16.5 kDa) at mass-ratio 1: 50 at varying pH from 3.0 to 9.0. Based on Figure S4B (Supporting Information), the SAXS curves indicate the presence of Qbeta/pMETAC2 aggregates as there is an upturn in low-q scattering across all measured pH values from attractive interactions. As the pH value increases, the intensities of the minima and maxima in the scattering curve decrease at higher q-values, suggesting a change in scattering contrast within the Qbeta/pMETAC aggregates due to the higher intensity of the Gaussian chain scattering. At pH 7.0 and 9.0, the SAXS curves displayed a broad peak ≈0.26 nm⁻¹ and relatively weak reflections with maxima ≈0.46, 0.68, and 0.92 nm⁻¹. The broad and weak reflections make it challenging to determine the structure type accurately. The positions of the broad peaks were comparable to the sharper reflections from the hexagonal phase in the Qbeta/pMETAC1 assembly discussed above. This indicates that less ordered colloidal crystals were formed in the presence of pMETAC2 compared to pMETAC1.

Inorganic salts were added to Qbeta suspensions at pH 7.0 to analyze whether simple charge screening can induce colloidal crystal formation. The ionic strength upon the salt addition was aligned with that of the pMETAC-containing samples at pH 7.0. The pMETAC1 charge was calculated from the number-averaged molecular mass (2.65 kDa) by assuming that each repeating unit holds one cationic quaternary amine for interaction (see Equations S3 and S12–S17, Supporting Information and in the Experimental Section part of the supporting information). Therefore, NaCl (0.25, 0.5, and 1 m) and MgCl₂ (0.125, 0.25, and 0.5 m) were added instead of pMETAC. The lowest salt concentration at 0.25 m matches the estimated charges from when pMETAC is added.

Figure S10 (Supporting Information) shows that as the salt concentrations increase, the maxima and minima in the SAXS curve of the Qbeta form factor scattering become less pronounced. This behavior may result from the increased electron density of the buffer from salt addition, which decreases the excess electron density (scattering contrast) of Qbeta. No Bragg reflections were observed in the Qbeta samples with the mono- and divalent cations, even at concentrations exceeding the theoretical charge available from pMETAC. These findings demonstrate that charge screening induced by inorganic salt is insufficient for colloidal crystal formation. Specific interactions between Qbeta and the polycations are necessary.

It has been shown that low valency ions tend to induce instability of latex particles by charge screening, while polyelectrolytes adsorb onto the particle surface.^[52] The combination of charge interactions and the linear arrangement of the charges induces the formation of the colloidal structure. In the case of Qbeta/pMETAC1, the electrostatically driven self-assembly is stable over up to more than 50 °C but susceptible to changes in the ionic strength.

Further investigation into the chain-length dependent mechanism shows that pMETAC1 is sufficiently short (≈21 Å), likely allowing the locally flat attachment onto the virus surface in a so-called train conformation.^[53] When a particle interacts with a considerably smaller polymer, the polymers can wrap around it,^{[34, 35]} likely the case for this study's Qbeta/pMETAC structures. Even though pMETAC2 is roughly 4.5–5 times longer (≈91 Å) than pMETAC1, it is still short compared to the size of the virus particle. The finding that Qbeta can aggregate into colloidal crystals with pMETAC1 and less organized structures with pMETAC2 shows that the length of the polycation is important in the structure formation.

The small polymer chain length of pMETAC1 and 2, compared to the Qbeta, differs from previous works, where polyelectrolyte-patchy-charged particle interactions were mainly studied with a chain length similar to or larger than the nanoscale-sized spherical particles.^{[34, 37, 54-56]} The polyelectrolyte chain length influenced the attachment onto spherical particles such as silica or poly(styrene sulfate) latex particles.^{[32, 57]}

The 2D hexagonal structure observed in the Qbeta/pMETAC aggregates suggests that the interactions among the pMETAC and viruses are anisotropic. For homogeneously interacting spheres, the attractive interaction may prefer the formation of closed cubic hard-sphere packing. The hexagonal structure in this system may result from the inhomogeneous charge distribution on the Qbeta surface.^{[29, 31]} The inhomogeneous charge distribution from various polyelectrolytes on different polymer particles, such as amidine or sulfate latex surfaces, was shown before.^[58] The specific adsorption of pMETAC onto Qbeta sufficiently screens its surface charge, bringing them close enough that attractive forces, such as van der Waals forces, start to dominate and structures aggregate forms.^[32] The heterogeneous charge distribution on the Qbeta surface may also allow pMETAC to connect between particles. Such “specific” polymer bridging could explain why pMETAC2 forms assemblies with reduced order. Similar observations were made when simulating the interaction of polyelectrolytes with globular proteins.^{[36, 56]} However, we can not exclude that the hexagonal structure is a secondary minimum on the complex energy hypersurface of such a system. Weak interactions may hinder the system from reaching a potentially lower energy state, allowing it to form face-centered cubic (fcc) structures.^{[59, 60]} Furthermore, the order of the structure can be reduced by longer bridging segments.

2.3 In Situ Dynamic Light Scattering Study of Qbeta pMETAC Aggregation

The assembly mechanism of Qbeta/pMETAC structures is studied with in situ multi-angle dynamic light scattering (DLS). The aggregation rate constants are calculated from the change in the apparent R_H with time.^[61] The multi-angle approach provides additional information on the homogeneity of the process, as the signal at each scattering angle is weighted with the particle size (large particles scatter to smaller angles; small particles to larger ones). The scattering angles were chosen to analyze the aggregation simultaneously at 39° for large particles, at 90 ° as intermediate, and at 124° for small particles.

For the Qbeta/pMETAC1 sample at a mass ratio 1:1 in a total concentration of 0.005 wt% (Qbeta and pMETAC1) at pH 7.0, the aggregation started within seconds after mixing (see Figure 4). Lowering the mass ratio to Qbeta/pMETAC 1:1 was chosen to achieve aggregation kinetics within the DLS time-resolution range. The initial step of the aggregation process was fast, reaching ∼400 nm within the first 10 min, and slowed down to plateau at an apparent R_H of ≈1000 nm after one hour. All measured scattering angles (39, 90, 124°) show comparable aggregation behavior, and the calculated polydispersity index (PDI) values fluctuated around 0.5. This highlights the relative homogeneity of the Qbeta/pMETAC aggregation process. Similar behavior was observed for the Qbeta/pMETAC aggregation at both chain lengths at pH 9.0 and Qbeta/pMETAC2 at pH 5.0 (see Figure S12, Supporting Information).

Figure 4

Aggregation kinetics of Qbeta with pMETAC at a fixed ratio of 1:1 and pH 7.0 studied in situ using time-resolved DLS at different scattering angles. A) Evolution of R_H over time for Qbeta in the presence of pMETAC1; B) pMETAC2; C) and D) show the corresponding polydispersity plots. The DLS autocorrelation curves are presented in Figure S11 (Supporting Information).

In contrast, the DLS results for Qbeta/pMETAC1 at pH 5.0 and 3.0, and pMETAC2 at pH 3.0 did not show the formation of large aggregates. An apparent R_H of up to 200 nm is observed at the smallest scattering angle (39°), giving weight to large aggregates (see Figure S12, Supporting Information). The signal at larger scattering angles reflects R_H values < 150 nm for these samples. Based on the results, the interaction between Qbeta and pMETAC1 is not very strong when the pH is at or below 5.0. These pH values are close to the isoelectric point of Qbeta, and the electrostatic interaction of Qbeta with pMETAC is reduced. Only minor aggregation can be observed when focusing on large particles at the lowest scattering angles. The aggregation reaction's equilibrium appears to have shifted toward Qbeta/pMETAC oligomers that remain static over time and do not exhibit further growth. This observation agrees with the findings from the SAXS analysis. Large and compact aggregates containing multiple repeat units are essential for generating Bragg reflections in the scattering patterns, as demonstrated by the samples at pH 7.0 and 9.0, but not for pH 5.0.

Qbeta/pMETAC2 exhibits comparable aggregation behavior across the pH range from 5.0 to 9.0 from DLS. A noticeable disparity arises in the SAXS analysis when the pH is lowered to 5.0, revealing a reduction in order and aggregation. These results suggest that the pMETAC chain length is critical in the Qbeta aggregation and structurization process.

To gain more insight into the detailed kinetics and to investigate the influence of the Qbeta/pMETAC1 ratio, the self-assembly process was further studied at pH 7.0. When the ratio of Qbeta to pMETAC1 was changed from 1:1 to 1:0.5, 1:0.2, to 1:0.1, the R_H increase was less homogeneous over the observed scattering angles (see Figure 4; Figure S14, Supporting Information), indicating multi-modal particle size distributions. Additionally, the formation of smaller aggregates at a R_H range of 600 nm for 1:0.5, 50 nm for 1:0.2, and 25 nm for 1:0.1, was observed, suggesting an insufficient amount of polymers for forming larger aggregates. As the SAXS experiment has shown (see Figure 3), at ratios below 1:2, no Bragg reflection could be observed. The low-q upturn becomes less pronounced at these low polymer concentrations, indicating the formation of less and smaller aggregates, in agreement with DLS.

For Qbeta/pMETAC2 the ratio was varied from 1:1, 1:0.5, 1:0.2 to 1:0.1 (see Figure 4; Figure S14, Supporting Information), analogous to pMETAC1. The main difference was that even for the ratio 1:0.5, a homogeneous time-dependent aggregation, yielding large aggregates of R_H ≈ 1000 nm, was observed. This behavior contradicts the heterogenous 600 nm-sized aggregates for Qbeta/pMETAC1 at a 1:0.5 ratio. It can be concluded that large aggregates can be formed at a broader range of conditions for pMETAC2. Therefore, longer chains promote the formation of aggregates. This observation agrees with the revisited Schulze–Hardy rule, where the critical coagulation concentration (CCC) decreases with increasing valence for multivalent counterions.^[62]

For more quantitative analysis, the time-resolved DLS data were fitted for all samples at a 1:1 ratio at pH 7.0 and 9.0 and the Qbeta /pMETAC2 1:0.5 ratio at pH 7.0 (see Table S2, Supporting Information). The diffusion-limited cluster aggregation (DLCA) model was chosen because the primary driving force behind the aggregation process is considered to be the charge interactions of the anionic Qbeta with the cationic pMETAC at sufficiently high concentrations. From the fitting parameter A (see Equation S22, Supporting Information), the aggregation rate is similar for Qbeta/pMETAC1 at 1:1 and Qbeta/pMETAC2 at 1:1 at the same pH, resulting in apparent average R_H values ≈1000 nm. This finding implies that the aggregation rate depends mainly on the pH and, thus, the surface charge of Qbeta but less on the difference in the pMETAC chain length. An exception can be seen for Qbeta/pMETAC2 1:0.5 at pH 7.0, where the aggregation rate is higher than at a 1:1 ratio. At a 1:0.5 ratio, the charge modification is lower due to the lower amount of pMETAC, as observed from the zeta potential (Figure 3B). Still, the lower ionic strength could benefit the aggregation of longer chains. It has been shown that the interaction between cationic polymers and functionalized latex particles with heterogeneous charge distributions increased aggregation rates at low ionic strength.^{[33, 63]}

For the Qbeta/pMETAC1 system, fitting the DLCA model to the DLS data results in a D_f between 1.9 and 2.36. The calculated D_f values are larger than typical D_f, 1.75 −1.85, obtained from DLCA and indicate reaction-limited cluster aggregation (RLCA).^[64] This can result from thermally-driven restructuring to the denser cluster, especially if the inter-particle interactions are weak. A similar behavior has been observed with gold nanoparticles interacting with cationic surfactant.^[65]

A further cause for denser clusters has been shown by increased concentration of polyelectrolytes such as poly(allylamine hydrochloride) or poly-diallyldimethylammonium chloride to screen the charges of silica nanoparticles.^[37] This charge screening effect also applies to Qbeta/pMETAC aggregates and can explain the higher D_f than expected from the DLCA model for simple particle aggregation. For Qbeta, the higher surface charge at pH above 7.0 leads to a stronger attraction between the patchy regions, favoring rearrangement to reduce repulsion between the adsorbed pMETAC.^{[30, 31]}

The DLS results demonstrate the effect of the Qbeta/pMETAC1 ratio and their self-assembly into suprastructures. For Qbeta/pMETAC1, an optimal ratio is found based on charge balance, which agrees with the zeta potential analysis. The particle size increases at sufficiently high pMETAC1 concentration (from Qbeta/pMETAC = 1:0.5), leading to large aggregates. At low particle concentrations, this process is slow enough to be studied by DLS. Upon increasing the particle concentration, the rate at which the particles collide increases, and the aggregation rate increases, however, the mechanism stays the same.

In summary, pMETAC induces charge screening and destabilization of Qbeta in suspension and tailors the structure of the aggregates with a given chain length. Rearrangement into a more efficient packing, crucial to forming colloidal crystals, is likely due to repulsive forces between Qbeta/pMETAC1 assemblies and free pMETAC1 in solution. Therefore, the analysis of the DLS data completes the conclusions on the aggregation from SAXS, zeta potential analysis, and AFM with additional kinetic information.

2.4 Qbeta/pMETAC of Surface Chemistry

X-ray photoelectron spectroscopy (XPS) provides the chemical composition of the outermost surface of a sample, with a typical information depth of <10 nm ^{[66, 67]} Thus, in the case of Qbeta, primarily the protein capsid is probed by XPS analysis.^[67] Cryogenic XPS was performed to detect any alterations in the chemical composition on the surface of the phage after exposure to the polymer. These measurements were conducted with the assembly Qbeta/pMETAC at 1:50 at pH 7.0 (see Figures S16 and S17, and Table S3, Supporting Information) and comparing its surface chemistry to its pure components. Survey spectra of the phages in the buffer showed the presence of O, N, C, Na, Cl, and P. However, Na, Cl, and P mainly originated from the buffer, while O was from the buffer and the phage surface. N and C originated only from the phages. The C 1s spectrum was fitted with four components relating to aliphatic C at 285.0 eV, C atoms with an O or N neighbor at 286.4 eV, C in peptide bonds at 288.2 eV, and C with two O neighbors, e.g., in esters, at 288.7 eV (Figure S17, Supporting Information). The N 1s spectrum of the phage sample showed a main peak at 400.1. eV, which corresponds to N in amides or peptide bonds.^[68] This peak had a shoulder at 401.5 eV arising from protonated groups (Figure S17, Supporting Information). Survey spectra of the polymer samples showed the presence of C, N, O, and Cl. For samples with the shorter polymer, Br was also detected. C 1s spectra for pMETAC were fitted with three peaks representing aliphatic C at 285.0 eV, C with N or O neighbor at 286.4 eV, and C in esters at 289.1 eV. The quaternary ammonium groups in the polymer were observed in N 1s spectra at 402.6- 402.7 eV (Figures S1 and S17, Supporting Information). The spectra acquired from phages with polymer show the presence of both species in the analysis volume, in line with the observations from DLS and SAXS of an overlayer of polymers coating the surface of the phages. Three peaks can be observed in N 1s spectra from the assembly corresponding to NH and protonated NH at the phage surface, at low binding energy, and quaternary ammonium groups from the polymer at higher binding energy (see Figure S17 and Table S3, Supporting Information). A unique peak relating to the phage is also observed in the C 1s spectra of the assembly since the polymer does not contain C in peptide bonds (at 288.2 eV). Furthermore, the COO peak corresponds to esters, observed in the phages at 288.7 eV, shifts to 289.1 eV, similar to that of the polymer, when the polymer is present in the sample and coats the phage surface. The similarity of the XPS data between the pure phage and the assembled phage-polymer system suggests that no significant alteration in the form of surface reorganization of Qbeta takes place during the adsorption of the polymer onto the surface of the phage, confirming a physical adsorption process.

2.5 Infectivity of Qbeta and Qbeta pMETAC1 Aggregates

The Qbeta suprastructures were formed at Qbeta/pMETAC1 at 1:50 and separated as macroscopic aggregate from the liquid using centrifugation. The gel-like aggregate was resuspended in VDB buffer at pH 7.0 by gentle mixing with a pipette. The viral infectivity was studied by using a plaque assay (a detailed procedure can be found in the methods section of the supporting information). The infectivity of Qbeta/pMETAC1 at 1:50 after centrifugation and separation was comparable to the original suspension. Compared to the unbound Qbeta, a 2.2 log reduction was observed (see Figure S18, Supporting Information). This results from the fact that Qbeta is bound in the aggregates, hence the assay allows to count the number of infectious aggregate particles rather than infectious Qbeta particles. Overall, this proof of concept experiment demonstrates the separation of bactericidal Qbeta/pMETAC1 = 1:50 suprastructured aggregates from the buffer. This opens future opportunities to develop novel phage-based materials, such as antimicrobial films. The aggregates' response to their environment, such as ionic strength and pH, may open the possibility of tailoring the suprastructures into a functional phage delivery system. Additionally, the fast and simple method of separating intact phages in the presence of pMETAC1 as macroscopic aggregates could be further developed into a virus extraction technology.

3 Conclusion

This study demonstrates advanced nanopatterned biomaterials from the self-assembly of the 29 nm protein nanocage Qbeta with a polycationic polymer. Upon interacting with pMETAC, Qbeta self-assembles into pH- and composition-responsive colloidal crystals. The pMETAC chain length is shown to influence the self-assembly process and structure strongly.

SAXS analysis confirms the formation of highly ordered, nanopatterned materials when Qbeta is combined with pMETAC of 3.3 kDa at a ratio of ≈1:50 (w/w). The Qbeta structure and surface chemistry are not modified in this process, and cryoXPS indicates non-covalent adsorption of the polymer onto the phage surface. Analysis of the SAXS and liquid AFM data demonstrate the formation of hexagonally packed Qbeta structures at pH > 7.0. The pH of the suspension triggers structural transformation in the suprastructures. At pH < 7.0, the long-range order of the suprastructures reduces, and the aggregates eventually disassemble at and below pH 5.0.

When the pMETAC chain length is increased to 16.5 kDa, the crystal-like ordering of the Qbeta decreases, as seen by the smearing of the Bragg reflections in the SAXS data. Zeta potential analysis demonstrates specific adsorption of the pMETAC, with charge inversion and disintegration of structures at elevated pMETAC content. Time-resolved light scattering studies showed that the self-assembly of the viruses with the polymers is homogenous and follows the diffusion-limited aggregation process. Rearrangement into the ordered structure is enabled due to the patchy-charge surface nature of Qbeta, which gets enhanced by the adsorbed pMETAC.

The thermodynamically stable Qbeta self-assemblies are mainly controlled by electrostatic interaction and are highly susceptible to changes in the ionic strength and temperature at or above 60 °C. The Qbeta/pMETAC suprastructures could be separated from the liquid using centrifugation. The solid aggregate maintained its biological activity, albeit in a reduced form compared to free Qbeta in suspension.

Further optimizations of the composition may be required based on the desired conditions. Nevertheless, the versatility of bacteriophage provides inherent advantages, such as the scalability of synthesis and the customizability by bioengineering its surface properties. Pursuing suprastructured materials typically involves multiple steps in the synthesis. The simple production process presented in this work is transferrable to other systems. It is feasible for large-scale production, targeting applications in biomedicine, food, and nanotechnology. The suprastructures can be further encapsulated or dispersed as particles with various loadings of, for instance, drugs and nutrients in the core of the protein cage.

4 Experimental Section

Synthesis and Virus Propagation

Poly [2-(methacryloyloxy)ethyl] trimethylammonium chloride (pMETAC) was synthesized with the activator generated by electron transfer (AGET) ATRP.^{[69, 70]} Details on the synthesis and the material used can be found in the Materials and Methods part of the supporting information. Qbeta was propagated in Escherichia coli strain W1485 and purified using ultra-centrifugation filtration. A detailed protocol can be found in the supporting information.

Small-Angle X-Ray Scattering

SAXS measurements were conducted in the laboratory and at the Austrian SAXS beamline at Elettra (Trieste, Italy) at two beamtimes. Laboratory SAXS measurements were conducted on the SAXSpoint 5.0 (Anton Paar, Graz, Austria) coupled to a MetalJet D2 X-ray source (Excillum, Kista, Sweden). An X-ray beam with a wavelength, λ, of 0.134 nm (9.3 keV) and sample-to-detector distance was 1608.1 mm, providing a q-range from 0.04 – 2.4 nm⁻¹. The scattering vector magnitude q was calculated with Eq. 1, where n is the refractive index, which is virtually unity for X-rays in this study, θ is the scattering angle.

$$$$\begin{equation}q\ = \ \ \frac{{4\pi n}}{\lambda }\ sin\ \left( {\frac{\theta }{2}} \right)\end{equation}$$$$(1)

The scattering and diffraction images were recorded using a 2D EIGER R 1M detector (Dectris Ltd., Baden, Switzerland) with a total area of 77.10 × 79.65 mm² and pixel size of 75 × 75 µm2. The resulting 2D scattering patterns were radially integrated into the 1D I(q) functions using SAXSanalysis 4.20 (Anton Paar, Graz, Austria) The temperature was kept at 25 °C if not mentioned otherwise. Measurements were done in sextet to check for beam damage, and the average of the results was used. No beam damage was observed. The scattering curves were corrected for transmittance. Buffer scattering was measured with all samples and subtracted as background from the scattering curves.

For temperature scans, the sample was heated to the desired temperature and equilibrated for 5 min in a sample holder for vertical capillaries, which is temperature controlled by a Peltier device. The measurement was taken over a time span of 2 h.

At the Austrian SAXS beamline, an X-ray beam with a wavelength of 0.154 nm (8 keV) and sample-to-detector distance was 1753 mm and 906.2 mm was used, providing a q-range from 0.05 to 4.2 nm⁻¹ and 0.07 to 7.4 nm⁻¹. The scattering patterns were recorded using a Pilatus3 1M detector (Dectris Ltd., Baden, Switzerland) with a total area of 169 × 179 mm² and pixel size of 172 × 172 µm². The resulting 2D scattering patterns were azimuthally integrated into the 1D I(q) functions using SAXSDOG.^[71] The temperature was kept at 25 °C. Measurements were done in quadruplets to check for beam damage, and the average of the results was used. No beam damage was observed. The scattering curves were corrected for transmittance using a semitransparent beam stop. Buffer scattering was subtracted as background from all samples as background.

SAXS Data Analysis

The SAXS data were analyzed using the generalized indirect Fourier transformation (GIFT) method^{[72, 73]} and further analyzed with model-dependent fitting with SASfit.^[74]

The scattering intensity I(q) of N monodisperse, homogeneous, and spherical particles is described by the product of the form factor P(q) and the structure factor S(q):

$$$$\begin{equation}I\ \left( q \right) = \ N\ S\left( q \right)P\left( q \right)\end{equation}$$$$(2)

The GIFT method allows the simultaneous fitting of P(q) and S(q) by selecting a suitable S(q) model.^{[72, 75-77]} With this method direct information on the size, shape of the particles, and their internal structure are obtained.^[78-81] Further details on the GIFT method can be found in the supporting information.

The virus structure before and after interaction with pMETAC was also analyzed with the spherical core-shell form factor model (see Equation S6, Supporting Information) combined with a structure factor model for hexagonal structures (see Equation S10, Supporting Information) to obtain the overall scattering intensity of the assembly I_assembly(q), taking into account of additional factors (see Equation S9, Supporting Information).^[82-84] The detailed model and fitting procedure are described in the supporting information. The data were fitted up to q = 0.89 nm^–1 due to the low signal-to-noise ratio above that value.

For samples showing diffraction patterns, the Bragg peaks in the scattering curves, which correspond to the reflections from the planes defined by their hkl Miller indices, were assigned to the space groups of the liquid crystalline structures.

$$$$\begin{equation} \ {d}_{h}=\frac{2\pi}{{q}_{h}}\ \end{equation}$$$$(3)

$$$$\begin{equation}\ \frac{1}{{{{d}^2}_{hkl}}} = \frac{4}{3}\ \frac{{\left( {{{h}^2} + hk + {{k}^2}} \right)}}{{{{a}^2}}}\end{equation}$$$$(4)

where q_hkl is the q-value of the Bragg peak corresponding to the reflection from the hkl Miller planes and d_hkl is the corresponding interplanar spacing. The lattice constant a was calculated from d_hkl using Equations (3) and (4), assuming a 2D hexagonal close-packed system. This structure provided the best possible fit to all peaks out of all the tested symmetries.^[85]

Cryogenic Transmission Electron Microscopy

Qbeta has been prepared for cryogenic transmission electron microscopy and for negative staining TEM. Samples for cryo-TEM were prepared on Quantifoil Holey Carbon Grids of Type R 2/2 Cu 300 (Quantifoil Micro Tools GmbH, Großlöbichau, Germany). Negative glow discharging for 30 s at 25 mA was performed in PELCO easiGlow (Ted Pella, inc., USA). Vitrifying of 4 µl sample was performed on Vitrobot, FEI (ThermoFisher Scientific) at 20 °C under 95% relative humidity. The sample suspension was adsorbed for 10 s, blotted for 5 s and plunge frozen into liquid ethane. All samples were stored under liquid nitrogen until imaging.

Grids were loaded by the autoloader system into Titan Krios G2 300 kV TEM (FEI). Images were recorded with K2 BioQuantom, energy filtered direct electron detector using Digital Micrograph software (Gatan, Inc. USA). 33 000x magnification resulted in a recorded pixel size of 4.37 Å.

Atomic Force Microscopy

The colloidal Qbeta-pMETAC assemblies were deposited onto ultra-flat Au surfaces for AFM imaging in VDB at pH 7.0. Au substrates were fabricated by a template-assisted procedure ^{[86, 87]} based on silicon wafers (CrysTec, Berlin, Germany) to create an ultra-flat and fresh Au surface for every experiment. The Qbeta (1 mg ml⁻¹) and pMETAC1 5 wt% solution were mixed in a volumetric 1:1 ratio by vortexing for 2 × 10 s until a turbid liquid had formed. Tiny droplets of the suspension were incubated on a fresh ultra-flat Au surface for 10 min. The VDB, prepared as described above, was exchanged several times to remove unbound components. The samples were equilibrated in the buffer in the AFM overnight to reduce thermal drift.

AFM images were acquired on a Dimension ICON equipped with a Nanoscope V controller (Bruker, Santa Barbara, USA) in PeakForce Tapping mode. Silicon nitride cantilevers SNL-A (Bruker, Santa Barbara, USA) with a typical resonance frequency of 65 kHz and a nominal spring constant of 0.35 N m⁻¹ were operated at a PeakForce frequency of 1 kHz, a PeakForce setpoint of 8 mV, Peak Force Amplitude of 10 nm and a tip velocity of 300 nm s⁻¹ in VDB.

AFM Data Processing

A first-order plane fit and first-order flattening procedure was applied to the height sensor channel of the AFM images in NanoscopeAnalysis (version 1.80, Bruker, Santa Barbara, USA). A fast Fourier transform (FFT) of a 926 nm x 926 nm sized image section and its azimuthal integration was performed using Python (NumPy package fft.fft2) to obtain the calculated 1D scattering pattern from the AFM data. A filter (Tukey window) was priory applied to avoid edge effects leading to artifacts during the FFT.

Electrophoretic Mobility Analysis

The electrophoretic mobility, µ_e, was determined by phase analysis light scattering on a Litesizer 500 (Anton Paar, Graz, Austria). The wavelength of the laser was 658 nm, the laser power was 40 mW, and the scattering angle was either 15° or 175°, optimized automatically through the build-in algorithm of the device. The temperature was 25 °C for all measurements. The zeta-potential, ζ, was calculated with Henry's equation.^[88]

$$$$\begin{equation}\ {{\mu }_e} = \frac{{2{{\varepsilon }_r}{{\varepsilon }_0}{\mathrm{\zeta \ f}}\left( {{\mathrm{ka}}} \right)}}{{3\eta }}\ \end{equation}$$$$(5)

ε_r is the relative permittivity of VDB of 76.64, ε_r is the permittivity of vacuum of 8.854 × 10⁻¹² C V⁻¹ m⁻¹, f(ka) is the Henry function, approximated to 1.5 by the Smoluchowski approximation,^[89] and η is the viscosity of the solvent (VDB, 0.904 mPa s). The samples were diluted 20-fold and vortexed before being measured five times, applying a voltage of 50 V.

At the same time, the current I was measured on the same samples at the applied voltage V. From this, the conductivity σ is calculated (Equation (6)), where L is the distance between the electrodes and S is the surface area.

$$$$\begin{equation}\sigma \ = \frac{I}{V}\ *\frac{L}{S}\end{equation}$$$$(6)

Dynamic Light Scattering

Multi-angle DLS measurements were carried out with a light scattering goniometer (CGS-8F, ALV Langen, Germany) and a solid-state laser (Coherent Verdi V5, with a wavelength, λ, of 532 nm and max. power of 5 W) with single-mode fiber detection optics (OZ from GMP, Zurich, Switzerland), 8 fiber-optic detectors and ALV 7004 correlators with fast expansion (ALV, Langen, Germany). Measured angles were in the range between 34.0 and 144.5°.

Qbeta and pMETAC in VDB were separately adjusted to pH 3.0, 5.0, 7.0, and 9.0. Immediately before the measurement, the components were mixed with a 1 mL pipette by 10x loading and unloading in a 5 mL DLS vial. Time-dependent DLS measurements were conducted with 10 s of accumulation over 1 h to monitor the kinetics of aggregation. The total volume of the sample was 2 mL at an estimated total concentration of 0.002 – 0.005 wt%, depending on the ratio of Qbeta to pMETAC (1:1, 1:0.5, 1:0.2, 1:0.1). The refractive index and viscosity of water, n = 1.33 and η = 0.89 × 10⁻³ Pa s and temperature of 25 °C were used for all measurements.

The DLS autocorrelation functions were fitted with the Cumulant method. The apparent hydrodynamic radius (R_H) was determined from the diffusion coefficient using the Stokes-Einstein equation (see Materials and Methods in the Supporting Information for details).^[90] The diffusion-limited cluster aggregation (DLCA) model was used to compare the aggregation behavior of the Qbeta under different conditions based on the time-dependent DLS data (see Materials and Methods in the Supporting Information for details).^[91]

X-ray Photoelectron Spectroscopy

XPS spectra were acquired on a Kratos Axis Ultra DLD spectrometer with a monochromated Al K_alpha source operated at 150 W as previously described.^[67] All spectra were acquired with a hybrid lens system, an analysis area of 0.3 by 0.7 mm, and using the inbuilt charge neutralizing system of the spectrometer. The binding energy scale was referenced to aliphatic carbon at 285.0 eV. The survey spectra were collected using an analyzer pass energy of 160 eV, while high-resolution spectra were collected using a pass energy of 20 eV. The polymeric samples were measured as a powder at room temperature (21 °C), while samples containing the phages were measured as a suspension in VDB at pH 7.0 under cryogenic conditions. For cryo-XPS, a small quantity of the liquid samples (15-20 µl) was placed with an automatic pipette onto the pre-cooled copper stub (−170 °C) inside the loading chamber, which immediately froze the droplet. The sample holder was transferred into the analyzing chamber, and analyzed under cryogenic conditions using liquid nitrogen cooling. Data analysis was performed in CasaXPS, Casa Software Ltd. using a Shirley background and Gaussian-Lorentzian (GL30) peak shapes.^[92]

Acknowledgements

The Swiss National Science Foundation funded this work through project no. 186251 and the National Center of Competences in Research (NCCR) Bioinspired Materials. The authors thank the CERIC-ERIC Consortium for access to the Austrian SAXS beamline at the Elettra Synchrotron (outstation of the Institute of Inorganic Chemistry, Graz University of Technology) and Heinz Amenitsch for technical support. The authors further acknowledge Nico Bruns and Sara R. Velasquez for the technical support with GPC measurements and Linda Sandblad with electron microscopy.

Open access funding provided by Universite de Fribourg.

Conflict of Interest

The authors declare no conflict of interest.

Open Research

Data Availability Statement

The data that support the findings of this study are available in the supplementary material of this article.