Structural Effects of Single Mutations in a Filamentous Viral Capsid

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Structural effects of single mutations in a filamentous viral capsid across multiple length scales Gili Abramov, Rona Shaharabani, Omry Morag, Ram Avinery, Anat Haimovich, Inbal Oz, Roy Beck, and Amir Goldbourt Biomacromolecules, Just Accepted Manuscript • DOI: 10.1021/acs.biomac.7b00125 • Publication Date (Web): 28 Jun 2017 Downloaded from http://pubs.acs.org on July 4, 2017

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Structural effects of single mutations in a filamentous viral capsid across multiple length scales Gili Abramov1,#,‡, Rona Shaharabani1,‡, Omry Morag1, Ram Avinery2, Anat Haimovich1, Inbal Oz1, Roy Beck2,*, Amir Goldbourt1,*. 1

School of Chemistry and 2School of Physics and Astronomy, Tel Aviv University, Tel Aviv,

Israel. KEYWORDS. Magic-angle spinning; solid-state NMR; filamentous viruses; Small angle X-ray scattering; SAXS; M13 bacteriophage; fd phage; inter-molecular interactions.

ABSTRACT. Filamentous bacteriophage (phage) are single-stranded DNA viruses that infect bacteria. Single-site mutants of fd phage have been studied by magic-angle spinning nuclear magnetic resonance and by small angle X-ray scattering. Detailed analysis has been performed that provides insight into structural variations on three length scales. The results, analyzed in conjunction with existing literature data, suggest that a single charge mutation on the capsid surface affects direct inter-viral interactions but not the structure of individual particles or the macro-scale organization. On the other hand, a single hydrophobic mutation located at the hydrophobic interface that stabilizes capsid assembly alters the atomic-structure of the phage mainly affecting inter-subunit interactions, affects its macro-scale organization, i.e. the pitch of

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the cholesteric liquid crystal formed by the particles, but skips the nano-scale hence does not affect direct inter-particle interactions. An X-ray scattering under osmotic pressure assay provides the effective linear charge density of the phage and we obtain values of 0.6 Å and

0.4 Å for fd and M13 phage, respectively. These values agree with a simple consideration of a

single cylinder with protein and DNA charges spread according to the most recent atomicresolution models of the phage.

INTRODUCTION Filamentous bacteriophage viruses are semi-flexible elongated biomolecular complexes consisting of a single stranded DNA (ssDNA) genome wrapped by thousands of copies of identical short coat protein subunits. They exhibit a highly symmetric organization on the atomic length scale and at high concentrations form cholesteric liquid crystals with micron-scale pitch size. Consequently, structural studies of these systems attract wide interest in a variety of disciplines including the basic understanding of virus infection and assembly1,2, of protein-DNA interactions, of complex systems' organization, the development of phage nanotechnology3,4 and phage-therapy5, the use of their DNA for the construction of expression vectors6 and of their capsids for phage display technology7,8, phenomenological studies of liquid crystal formation9,10, modeling interactions between charged rods11,12, and utilizing their self-organizational properties to create structures of higher hierarchies13–15. The Ff family of filamentous phage consists of M13, fd and f116,17. While fd and f1 share a similar 50 amino-acid-long coat protein sequence, that of M13 differs by a single amino acid; a charged aspartic acid in the N-terminal part of the fd coat protein is replaced with a non-charged asparagine in M13 (D12N). Sequence alterations in the DNA are minor18 (3% of 6407/8


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nucleotides, 0.2% when translated to amino acids) and both have a nucleotide to subunit (n/s) ratio of around 2.34 resulting in non-specific protein-DNA interactions19. Early structural studies by fiber diffraction suggested that the coat protein is mostly helical20,21, and that the capsid is arranged as pentamers that are related by a rise of ~16 Å and a rotation of approximately 36° resulting in the generation of an approximate two-fold screw axis22 (C5S2 symmetry). The complete structure determination of fd phage proved to be more complex due to fanning out of layer lines in the fiber diffraction data23 and broadening of lines in aligned static solid-state NMR (ssNMR) spectra24. It was shown that a single mutation of fd, in which tyrosine in position 21 is replaced with methionine (Y21M) generates phage particles that are better aligned providing better resolved layer lines (for fiber diffraction) and better resolved aligned ssNMR spectra. In addition, reduction of the pH below the isoelectric point of wild type (wt) fd to a value of 4.0 resulted in well aligned samples presumably due to the change in the overall particle charge. The structure of Y21M was then solved by both methods (protein data bank (PDB) structure 2C0W25 from fiber diffraction and 1NH426 from aligned ssNMR) as well as by mutually refining data from both experimental approaches resulting in the PDB model 2C0X25. This structure shows that the capsid of fd-Y21M is arranged as pentamers that are related by a rise of 16.15 Å and rotation of 36°. The structure of M13, which was shown by virtue of NMR chemical shift comparison to be similar to that of wt fd27, was solved28 (PDB 2MJZ) using magic angle spinning (MAS) NMR combined with Rosetta modeling. This model is somewhat different from that of Y21M, having a slightly larger rise of 16.6(.1) Å and a rotation per subunit of 36.3°(.3). On a much larger length scale, filamentous phage form liquid crystals at elevated concentrations of several tens of milligrams per milliliter9–11,29. Depending on the concentration


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and the charge of the viruses, they can adopt different liquid crystalline forms including smectic, cholesteric and nematic phases. This property made them very useful as alignment media for measuring residual couplings by solution NMR30,31. This property has also made them excellent candidates for testing and studying the theory of phase behavior of rod-like particle suspensions developed by Onsager32. Interestingly, it was shown by several studies that minor changes in the phage environment, or even single coat protein mutations, propagate and induce changes on a macroscopic scale, i.e. on the liquid crystalline form or on its cholesteric pitch. For example, the single Y21M mutation in fd changes the pitch of the cholesteric phase five-fold at concentrations of 80 mg/mL, and the persistence length increases by a factor of 3.5 (from 2.8 µm to 9.9 µm)29. Addition of perturbants such as sodium dodecyl sulfate (SDS) or positively charged metal ions of mercury and silver also alter the pitch of the cholesteric phase up to complete unwinding10. Interestingly the addition of silver ions does not change the structure of the coat protein but affects the dynamics of the residues involved in protein-DNA interactions, hence the properties of their interface33. Less is known on the direct interaction between the phage particles at the intermediate nanoscopic length scale. Small angle X-ray scattering (SAXS) studies already revealed hexagonal order in the packing of the fd virus34. Different concentrations result in generation of either columnar or crystalline hexagonal phases. It is not well established however, how environmental changes affect the density of such hexagonally-ordered particles and how such changes are linked with the atomic structure of the particles. In the following study, by combining MAS NMR and SAXS experiments, and by using prior experimental data, we link the three structural length scales discussed above – the atomic (NMR), nanometric (inter-particle spacing from SAXS) and the micron-scale (given from


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existing liquid crystalline studies). We choose to study the micro-scale by observing liquid crystal formation modalities due to the interest in liquid crystals across various disciplines, and since it is the most sensitive probe, to the best of our knowledge, occurring at this length scale. The use of these two complementary techniques have the advantage that the samples are prepared in a similar way, precipitated pellets, hence our conclusions are not based on differences due to sample preparation. We demonstrate that a single charged mutation (the difference between fd and M13) significantly affects the inter-particle interactions but not the atomic or the micron-scale arrangement. On the other hand, a single hydrophobic mutation (Y21M in fd) in a key binding pocket of the virus affects the atomic scale (the capsid structure changes), alters liquid crystalline formation, but skips the nano-scale hence it has no impact on virus-virus interactions. Therefore, our studies suggest that minor changes on the atomic scale at particular locations can have large impact on the macroscopic arrangement of rod-like particles. Such changes may impact the behavior of the particles, in this case viruses, in crowded environments such as cells. They can also direct the design of smart materials based on phage particle assembly. METHODS Preparation and purification of phage samples: Preparation of fd-Y21M for NMR: Small amounts of Y21M phage were obtained from Professor Stanley Opella, UCSD. This initial stock was used to infect a fresh culture of Escherichia Coli strain DH5αF'. Growth in minimal media was performed according to published procedures35 with a small modification: 200 µL of an overnight 3 ml starter was diluted into a new 5 mL rich lysogeny broth (LB) media and grown for 1-2 h until log phase (optical density of ~0.6). Shaking was reduced from 220 rpm to 60 rpm for 30 minutes, the


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culture was infected with phage stocks at a multiplicity of ten and left at 60 rpm for additional 30 minutes. This culture was then transferred to a one-liter M9 minimal medium (in a 4 liter flask), which was supplemented with 0.5 g

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N-labeled ammonium chloride and 4.0 g

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C-labeled

glucose. The culture was shaken at 240 rpm at a temperature of 37 °C for approximately 24 h, after which phage and bacteria were separated by centrifugation (8000 rpm, 40 minutes, FiberLite Piramoon rotor). Phage solution was precipitated with 5% w/v PEG8K (Polyethylene Glycol with average molecular weight of 8,000 daltons) and 0.5 M NaCl, and resuspended in 10 mM Tris buffer at pH 8. After discarding the remaining bacteria, the solution was brought to a density of 1.3 g/cm3 CsCl and span in an ultracentrifuge at 37K rpm for 48 h at 4 °C (Beckman Coulter rotor SW41). The phage band was extracted, precipitated, and diluted to ~1 mg/ml in a 10 mM Tris buffer at pH 8. For MAS NMR measurements, the samples were precipitated with either 5% or 40% w/w PEG8K and 5 mM MgCl2. The precipitated samples were then transferred to 4mm ZrO2 MAS rotors and sealed with HRMAS caps. It was experimentally verified that samples prepared with different PEG concentrations gave identical MAS NMR spectra (Fig. S3). Since high osmotic pressure increases the density of phage particles it may be useful to adopt the high-PEG precipitation technique to similar systems for MAS NMR studies. Preparation of wild-type fd, M13 and fd-Y21M for SAXS: M13 and fd were prepared according to published procedures, with the modification indicated above (reduced shaking during infection) using ampicillin and tetracycline antibiotics for M1327 and fd35, respectively, and using LB rich media. Y21M was prepared as described above using LB rich media. All samples for SAXS extracted from the ultracentrifuge tube were initially diluted to 1 mg/mL using Tris buffer, precipitated using 4-5% w/v PEG8K, diluted once more to DPBS buffer (pH ~7.5, 1-3


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mg/mL) in order to eliminate any remaining monovalent Cs+ ions, and divided to small aliquots containing 1-3 mg. Those samples were transferred to 1.5 mm quartz capillaries and precipitated using only 4-5% w/w PEG8K or PEG35K. After removal of the supernatant, the amount of PEG residuals is negligible. These samples were then subjected to different PEG20K/salt solutions in DPBS buffer as described below and those solutions were further used to calculate the osmotic pressures affecting the different samples. DPBS buffer contains 0.2 g/L of KCl, 0.2 g/L KH2PO4, 2.16 g/L Na2HPO4·7H2O and NaCl at a desired concentration. NMR: The assignment of fd-Y21M was obtained by acquiring homonuclear

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C-13C correlations

using the dipolar assisted rotational resonance (DARR) experiment36, heteronuclear 2D NCO and NCA DCP correlations37, 2D TEDOR NC correlations38, and 3D NCACX and NCOCX correlations39. Detailed experimental parameters are given in the supporting information (SI) Table S3. All experiments were acquired on a Bruker Avance III spectrometer operating at a 1H Larmor frequency of |600|MHz using a triple-resonance H/C/N Efree probe. The data were processed with the free software NMRPipe40 and analyzed using Sparky41. The chemical shifts of fd-Y21M were deposited in the Biomolecular Magnetic Resonance Bank (BMRB), accession number 26910. Small-angle X-ray scattering measurements: The viruses' pellets (around 2-3 mg) were centrifuged down to 1.5 mm quartz capillaries (Hilgenberg-GMBH) at 3500 rpm for less than one minute. This resulted in a few millimeters pellet at the bottom of the capillary. The supernatant was removed and about 50-70 µl of PEG20K solutions at the desired weight percentages and salt concentrations were added above the pellets. The capillaries were than flame-sealed and glued to prevent evaporation. All SAXS


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experiments were initially carried out in a home-built apparatus with a Cu ( = 1.54 Å) tube source (Xenocs), Pilatus 300K detector (Dectris), about 1 meter sample-to-detector distance, and a scatterless slit setup42. Synchrotron SAXS experiments were conducted in Diamond light source I22 (1.24 Å) beam line, using a Pilatus P3-2M (Silicon hybrid pixel detector, DECTRIS), at room temperature. Both fd and Y21M SAXS data where acquired with 5.2 meter sample to detector distance while M13 was measured at 3.7 meter. The scattering diffraction data of the samples were integrated azimuthally, using data reduction software (SAXSi) developed in our lab. The intensity was plotted versus reciprocal distance, , i.e. = (4/ )(/2), where

is the scattering angle and is the X-ray wavelength. Osmotic pressure techniques:

We measured the osmotic pressure of the viruses via the osmotic stress method43,44. The

osmotic pressure, Π, was determined by calibration of its w/w% in the solution using the formula log Π = −4.43 + 2.71 ( !"20# $/$%).& where Π is given in '()43. To overrule

osmolyte interference with the viruses, we also measured several representative samples with

smaller size PEG (PEG8K)45. After the proper osmotic pressure adjustments for both PEG sizes,

the scattering data resulted with almost identical inter-particle distances, '* , as shown in figure S4.

RESULTS AND DISCUSSION We characterized and compared wild type fd, the Y21M hydrophobic mutant of fd (Y21M), and M13, a wild-type electrostatic mutant of fd (D12N), by performing MAS NMR and SAXS measurements. The capsid of the three viruses is composed of ~3000 coat protein subunits, each consisting of 50 amino acids, the sequence of which is shown in Table 1. The charges of the


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amino acids, displayed above the sequences for a pH of ~8, show that the N-terminal part of the phage is mostly negatively charged and that the C-terminus is positively charged consisting of four lysine residues. Mostly these lysines form electrostatic interactions with the negatively charged ssDNA. The remaining residues in the center of the coat protein form a hydrophobic patch that enables tight packing of the phage capsid as well as its incorporation into the membrane during phage infection and assembly. We note here that due to the non-integer ratio of nucleotides to protein subunits, and considering the known structural models of these phages, charge compensation between the DNA and the capsid interior is not complete and in the intact particle this difference is probably compensated for by free ions in the solution. Table 1: amino acid sequences and charges of various fd phage mutants at physiological pH. The mutations discussed here are marked in bold.

Wild-type: Y21M: D12N (M13):

+------+-------------------------------+--++---+-AEGDDPAKAAFDSLQASATEYIGYAWAMVVVIVGATIGIKLFKKFTSKAS +------+-------------------------------+--++---+-AEGDDPAKAAFDSLQASATEMIGYAWAMVVVIVGATIGIKLFKKFTSKAS +------+-------------------------------+--++---+-AEGDDPAKAAFNSLQASATEYIGYAWAMVVVIVGATIGIKLFKKFTSKAS

The atomic scale: In order to investigate the impact of the mutations on the atomic scale, we used prior information from the MAS NMR-based structure of the M13 phage28 (PDB 2MJZ), from the structure of Y21M obtained by mutual refinement of static aligned NMR data and fiber diffraction25 (PDB 2C0X), and from the MAS chemical shift assignments data of fd35 and M1327. Based on the chemical shifts data of fd and M13 it can be safely stated that the packing and structure of both coat proteins is similar since the reported spectra were identical with the exception of a small change near the mutation site; the chemical shifts of K8 were altered due to the removal of the salt bridge it forms with D12 in wild-type fd27.


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An overlay of the structures of M13 and Y21M is shown in figure 1. While the coat protein subunits adopt a very similar helical shape, it is clear that they are not identical and in particular, the symmetry is slightly changed; the rise per pentamer in M13 (16.6 Å) is larger than that of Y21M (16.15 Å). Clear variations are also observed in the shape of the N-terminal loop as well as the overall curvature and exact position of the helices with respect to the viral axis. Since the structures of the two mutants have been solved with different techniques, and with samples prepared at somewhat different conditions, we decided to perform a comparison of chemical shifts between the two mutants, as was done for the comparison27 of fd and M13. Since chemical shifts are highly sensitive to the atomic structure, any changes of backbone shifts imply a significant secondary structure variation. For example, when M13 was compared to fd, the average change was below 0.1 ppm indicating high similarity. Those experiments have been performed on samples that were prepared using an identical protocol.

Figure 1. Comparison of M13 (2MJZ, green, fd-D12N) and fd-Y21M (2C0X, magenta) capsid structures. On the right, alignment of a single coat protein subunit. The backbone RMSD is 0.7 Å and the heavy atom RMSD is 0.9 Å. On the left, overlay of two pentamers generated by aligning


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the bottom pentamer. The RMSDs here increase to 1.4 Å and 1.8 Å for the backbone and heavy atoms, respectively. The dash lines indicate the clear shifted position of the C-terminus over a single pentamer rise (0.45 Å). This shift propagates and accumulates along the phage particle. The image was created, and the structures were aligned, by using the software PyMOL (https://www.pymol.org/) employing the coordinates from the PDB. Site-specific chemical shift assignments of Y21M were obtained by performing a set of twodimensional (2D) and three-dimensional (3D) experiments on two separate

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C,

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N uniformly

labeled samples as described in the Methods Section. A typical 2D spectrum from a Dipolar Assisted Rotational Resonance36 (DARR) experiment and strip plots from 3D heteronuclear NCC spectra39 are shown in Figure 2. The spectra show excellent resolution and dispersion suggesting a single conformation of the coat protein, despite the existence of a large number of copies in each phage. The complete assignment table appears in the SI, Table S1. We note here that 1H-detected experiments at fast MAS were reported on Y21M recently that showed highly resolved spectra. However, the shifts have not been reported46. Figure 3 shows an overlay of regions from the spectra of wild-type fd and the Y21M mutant of fd, prepared and purified under identical conditions. If any of the structural differences appearing in figure 1 were due to the different sample preparation conditions or due to different structure calculation protocols, the NMR spectra would exhibit negligible differences, as was demonstrated for M13 and fd. Yet, clear chemical shift perturbations (CSPs) can be observed that are not solely a result of the single site mutation. The CSPs are spread over many residues and are larger than the acceptable assignment error range we observe for the viruses discussed here. In the DARR spectra CSPs larger than 0.3 ppm appear for many key residues; for example alanine signals that belong to residues within the hydrophobic inter-subunit contact area are


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significantly shifted (e.g A7, A10). Also proline-6, which has been shown to contact the key tryptophan residue, is shifted.

Figure 2: (a) Strip plots from 3D NCACX (red) and NCOCX (blue) spectra of intact Y21M showing slices extracted at various

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N planes. The small spectral regions in the bottom are


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centered at Cβ shifts corresponding to the assigned amino acids. The strips demonstrate the excellent resolution and dispersion obtained for Y21M. (b)

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C-13C homonuclear Dipolar

Assisted Rotational Resonance36 (DARR) correlation spectrum of intact Y21M acquired with a mixing time of 100 ms, allowing for sequential contacts (residue i → residue i+1) to appear in the spectrum. The explicit atoms for each correlation are not shown for clarity and can be identified in the assignment list provided in the SI. A linkage between all proline atoms is indicated explicitly and demonstrates the appearance of single peaks for the single proline in the sequence. For comparison, an inset from an overlay of fd with M13 shows that in this case, no spectral changes for alanine residues occur at all (in the Cα/Cβ correlation region) demonstrating that our observed shifts are significant. The figure also shows differences in N-Cα and N-Cβ correlations collected in a single NCA experiment. Many, but not all changes are in the vicinity of the mutation site 21. In the bottom right, the N-Cβ correlation spectrum shows alanine residues that are significantly shifted in both C and N dimensions (A16, A18 circled). Also the changes in the vicinity of Y/M-21 extend beyond those observed for M13 and fd. There,

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N CSPs were

observed for residues 10-13 (for a D12N mutation) while in the current case, the direct stretch of 15

N CSPs is in residues 16-22 (see a complete list and a plot of the CSPs in Table S2 and Figure

S1 of the SI).


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Figure 3: (a) overlay of 13C-13C DARR spectra of fd (black) and Y21M (purple) acquired using a mixing time of 100 ms. In the inset, the alanine region from a spectral overlay of fd with M13 is shown for comparison. (b) Overlay of NCα (top) and NCβ (bottom) spectra of fd and Y21M. Both spectra were collected in a single NCA experiment. Spinning sidebands are marked 'ssb'. Residues with CSPs over 0.3 ppm are indicated explicitly. In order to better visualize the positions of these chemical shift changes, we plotted them on the structural model 2C0X shown in figure 4. Clearly the mutation site (residue 21), which is indicated by arrows in the figure, is located in the inter-subunit interface. A more detailed analysis of the CSPs shows two main features: (i) out of the seven residues that have been shown


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to contact with the DNA47 (V33, I37, K40, K43, K44, K48, and A49, noted by red circles in Fig. S1) only K44 and A49 show a single CSP. Others are not perturbed. This is also apparent in the colorless interior of the phage shown in the top view plot; (ii) if we note the residues with most observed inter-subunit contacts (three or more non-ambiguous contacts, Table S2 and Fig. S4 in the SI of Morag et al.28) we see that those are residues (green circles in Fig. S1) 5-8, 11, 20-21, 24, 26, 30, 33, 38, 39, 41, 42 and 45. L14 is also deep in the hydrophobic pocket although it shows only a single contact. Of those 17 residues, only F11 and V33 do not show any CSPs. However, A10, which is a neighboring residue of F11 and that could not be non-ambiguously resolved for the purpose of structure calculation, is located also in the binding pocket, and shows significant CSPs. Additional two such residues are A27 and V31, both showing CSPs, and A27 could not be used for obtaining non-ambiguous restraints. . Overall, these changes indicate that significant structural changes occur in the vicinity, but not only, of the mutation. While the large number of significant CSPs are directly related to variations in the secondary structure, we believe that due to the close proximity of the subunits (down to distances of 2Å as can be measured in the structure), and due to the clear link between residues with large CSPs and the inter-subunit interface, even a minor rearrangement of the subunit affects this interface, the hydrophobic binding pocket, and hence presumably drives the change in symmetry as shown in figure 1. A similar effect was observed upon a phase transition in Pf1 phage48. While it is not entirely clear how such changes may affect the macroscopic arrangement of the particles, our discussion below shows that such a link may exist, and we therefore propose that macroscopic parameters such as the persistence length and the pitch of the cholesteric liquid crystal, are influenced, at least partially, by symmetry changes that result from atomic structural variations.


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Figure 4: Chemical shift perturbation sites drawn on top of the 35-mer Y21M model 2C0X. From left to right CSPs are plotted on a single coat protein subunit, on a side view and on a top view of the phage capsid. On the single subunit, residues having at least 2 CSPs are colored in magenta while residues having a single CSP are colored with light pink. Others (unassigned or unperturbed) are in gray. CSPs on the 35-mer are colored differently on different pentamers and only for residues with at least 2 CSPs. The mutation site, indicated by the arrows, (methionine21) is colored blue. In the sideview most Met residues are hidden since they are located in the interface. Images were produced using PyMOL and with coordinates taken from the PDB. In conclusion, a single mutation in charge (D12N) on the surface of the protein has a negligible effect on the structure, while the single hydrophobic mutation Y21M affects the key inter-subunit contact surface hence affects the atomic-scale structure of the capsid. The nano scale:


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To directly quantify the inter-viral interactions for the various phage mutants we applied the well-established small-angle X-ray scattering (SAXS) under osmotic pressure (Π) assay. This technique has proved useful for identifying the inter-macromolecular interactions of DNA43,44,49, filamentous proteins50–56, and membranes57 to name a few. Briefly, SAXS can directly measure the nanoscopic inter-viral separation ('* ) and lattice symmetry in precipitated samples surrounded by buffer solutions. Osmotic pressures are regulated by inert osmolyte polymers such as polyethylene glycol (PEG). One advantage of this technique is the ability to measure the Π − '* diagrams at various buffer conditions, i.e. different salt and osmolyte concentrations, that

enable further comparisons with theoretical models addressing the inter-particle equation of state and the relevant inter-molecular forces43,55. In figure 5 we show representative SAXS intensity curves for the three filamentous viruses studied here at different osmotic pressures and buffer salinities. Indexing the correlation peaks for the three viral mutants indicates a single hexagonal packing symmetry, where the peak

positions follow *(+,) =

-.

√012

√ℎ& + ℎ4 + 4 & , with being the scattering wave-vector, and ℎ

and 4 are integers. The hexagonal packing was previously demonstrated for different virus concentrations34, and therefore '* is identified as the average nearest neighbor distance between

viruses in the pellets (see inset in Fig. 6). From the sharpness of the correlation peaks, the variation of the average distance is shown to be rather small. Here we show that the hexagonal

phase persists over a wide osmotic pressure range in equilibrium with a phase separated PEG20K solution in salinity ranging from 50 – 300 mM NaCl. All SAXS intensity curves for the three filamentous viruses at different osmotic pressures and buffer salinities can be seen in supplementary figure S2.


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To evaluate the dominant inter-viral interactions we follow the Π − '* diagrams shown in

figure 6. For high osmotic pressures (Π ≳ 10 '()) all data points collapse and approach a

minimal spacing of '* ≅ 67.5 Å. This value matches the expected virus diameter when

calculating a 67.7 Å average distance between the heavy atoms of the three terminal residues ala, glu, and gly in the model 2MJZ28. The data points of fd and Y21M follow an identical Π − '*

curve, which is slightly modulated at lower pressures by the buffer salinity due to electrostatic screening. On the other hand, the M13 inter-viral spacing is always smaller at a given osmotic

pressure and buffer salinity. These results are in-line with dominant electrostatic interactions governing the inter-viral spacing since both fd and Y21M viruses have identical charged residues while each coat protein subunit in M13 has one less positively charged amino acid (asparagine vs. aspartate), see Table 1.

Figure 5. High resolution SAXS profiles for fd (black), Y21M (red), and M13 (blue) viruses

under osmotic pressures of 0.18 '() (left) and 4.9 '() (right), in 50 mM (solid lines) and 300

mM (dashed lines) NaCl concentrations. For clarity, the profiles are vertically shifted. The characteristic correlation peaks (arrows) are indexed to a hexagonal phase. Both fd and Y21M

yield the same inter-viral distance as can be seen from the first order peak position, () . On the


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contrary, M13 results with smaller inter-viral distances at all NaCl concentrations and in particular at low osmotic pressures. In conclusion, in the nano-scale, a single mutation in charge (D12N) on the surface of the every protein in the capsid has a significant effect on the inter-particle interaction, while the single hydrophobic mutation Y21M, which affects the key inter-subunit contact surface, does not affect the inter-particle interactions.

To quantify the inter-viral forces we follow the cylindrical cell model formulation mentioned previously and demonstrated for DNA-DNA interactions44. There, the inter-viral forces are approximated with two additive terms of the osmotic pressure:

(1) Π('* ) = Π+ ('* ) + Π7 ('* ).

In Eq. 1, both the short-range hydration repulsion term (Π+ ) and the long-range electrostatic

term (Π7 ) follow the same mathematical format to a leading order:

& ' '* & # : * < # : 2ℓ < 2ℓ+ @ (2) Π+ ('* ) = 8+ 9 > ; Π7 ('* ) = 87 9 > , = = # : < # : < ℓ+ ℓ@

where = = 67.5 Å is the virus diameter, and # (B) and # (B) are the cylindrical Bessel

functions of the second kind. For the hydration part we may assume that both 8+ and ℓ+ are salt

independent (in the experimental range) and that the effective decay length (ℓ+ ) is of the order of

a few Ångströms44. For the electrostatic part a more rigorous argument can be applied to identify

the pre-factors where ℓ@ = 3.04Å/CD(M) is the Debye screening-length calculated from the

buffer's salt concentration taking into account the valence of all ions in the solution: D(F) = G H

∑K JK LK& where JK is the ion concentration in Molars (M) and LK is the ion charge. In addition,


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87 = M & /NN is directly related to the virus effective charge density (M) and the dielectric

permittivity of the medium (N is the vacuum permittivity and N = 80 for water). Given the

cylindrical symmetry, the effective charge density is usually discussed in the literature of filamentous viruses by an effective linear charge density, = =M⁄P, where P is the elementary charge.

Figure 6. Osmotic pressure vs. inter-viral separation curves at different NaCl concentrations for different viruses. Salt concentrations are marked with different colors and virus type by the symbol shape. Inter-viral separation, '* , is depicted from the X-ray data. Different osmotic

pressures were generated by controlling the PEG20K concentration43. Lines are fits of the data following equation (1). Each data set is fitted with a global fit model, where the pre-factors 87 , ℓ+ , and 8+ are the only free parameters. Given the identical Π − '* trends for both fd and

Y21M viruses, fitting (solid line) was performed on their averaged data sets. M13 Π − '* fit is marked with dashed lines. Inset depicts the hexagonal lattice of the viruses.

Following the fitting procedure of Yasar et al.44 we analyze the different inter-viral interaction contributions. The fits (lines in figure 6) reliably capture the overall observed osmotic pressure


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trend. A closer look on the fitted parameters (Table 2) indicates that the electrostatic interaction is indeed the dominating factor over most of the osmotic pressure/inter-viral spacing range as

ℓ@ > ℓ+ ~2Å. This also suggests that the hydration layer consists of 1-2 water molecules

decorating the virus exterior.

The effective linear charge density of fd virus and its mutants are commonly cited from the early work of Zimmermann et al.58 There, the surface charge of fd virus was measured using a polyelectrolyte titration setup. These measurements yielded a surface charge density, translated

to a linear charge density of TUVW = −1Å, that does not fit our results. Following the atomic

resolution structural models25,28, we can evaluate the effective charge density based on the protein sequence and ionized charged groups. We identify three main contributions to the overall

charge balance between: (1) the DNA, (2) charged groups exposed to the inner surface of the capsid and (3) charged groups exposed to the solution on the outer surface of the phage. This estimation assumes that all charged entities contribute to the effective electrostatic interaction between neighboring viruses and that ions are free to diffuse between the layers.

The DNA effective linear charge density @XY = Z[ [T TU /P \V is estimated by the measured

[T = 2.34 nucleotides per subunit protein19, TU = 5 subunits over a rise of \V , and Z[ = −1 is

the charge state of each nucleotide. For fd and M13 the ssNMR structure28 gives \V = 16.6 Å

while for Y21M25 it is \V = 16.16 Å. This yields @XY ≅ −0.71 ± 0.01 Å . Here the negative

sign reflects the acidic nature of the DNA. Similarly, the effective linear charge density of the capsid is calculated from the total charged ionized amino acids, TU

K[\_U`

= Zab TU /P \V . For fd

and Y21M the total number of charged groups (Zab ) facing the inner or outer surfaces is three

_U` _U` (Table 1) yielding K[ TU = − TU = 0.91 ± 0.01 Å . The latter estimation of TU alone is in line

with the measurements of Zimmermann et al.58 In M13, the mutation of the aspartic acid (in fd)


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K[ to asparagine results with an outer effective linear charge density _U` TU = −0.61 Å while TU does

not change.

Table 2. Osmotic pressure fitting results§. Virus

[NaCl] (mM)

fd/Y21M 50

M13

8+

ℓ+

(atm)

(Å)

30.1±8.5

2.1±0.6

87

(atm)

28.3±1.2

ℓ@

(Å)

dYed

(1/Å)

(1/Å)

10.9

-0.59±0.05

-0.7

-0.42±0.05

-0.4

150

7.2

300

5.3

50

34.9±3.1

2.3±0.2

13.8±0.6

10.9

150

7.2

300

5.3

a1fa

Assuming that within the virus capsid surrounding, the linear charge density is that of an

_U` effective charge resulting from all contributions g a1fa ≈ @XY + K[ TU + TU i, we get a1fa =

−0.7 Å for fd or Y21M, and a1fa = −0.4 Å for the M13 mutant with relatively small

uncertainty (

Structural Effects of Single Mutations in a Filamentous Viral Capsid

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