Influenza A virus surface proteins are organized to help penetrate host mucus

Influenza A virus (IAV) enters cells by binding to sialic acid on the cell surface. To accomplish this while avoiding immobilization by sialic acid in host mucus, viruses rely on a balance between the receptor-binding protein hemagglutinin (HA) and the receptor-cleaving protein neuraminidase (NA). Although genetic aspects of this balance are well-characterized, little is known about how the spatial organization of these proteins in the viral envelope may contribute. Using site-specific fluorescent labeling and super-resolution microscopy, we show that HA and NA are asymmetrically distributed on the surface of filamentous viruses, creating a spatial organization of binding and cleaving activities that causes viruses to step consistently away from their NA-rich pole. This Brownian ratchet-like diffusion produces persistent directional mobility that resolves the virus’s conflicting needs to both penetrate mucus and stably attach to the underlying cells, potentially contributing to the prevalence of the filamentous phenotype in clinical isolates of IAV.


Introduction
For a virus to infect a cell, it must reach receptors on the cell surface while avoiding neutralization or clearance by 'decoy' receptors in the surrounding environment. For viruses that bind to sialic acid, a receptor that is abundant both on the surface of cells and in the secreted extracellular mucosal environment, attachment and detachment is controlled by receptor-binding and receptor-destroying activities on the viral surface (Rosenthal et al., 1998;Zeng et al., 2008). Influenza A viruses (IAVs), respiratory pathogens that contribute to seasonal flu and have pandemic potential, achieve this balance with hemagglutinin (HA)-mediated receptor binding and neuraminidase (NA)-catalyzed receptor destruction (Air and Laver, 1989;Skehel and Wiley, 2000). Although the importance and genetic basis of the functional balance between HA and NA in IAV has been thoroughly characterized (Wagner et al., 2002;Xu et al., 2012;Yen et al., 2011), it is becoming clear that transmissibility of influenza viruses within and between hosts depends on factors beyond the sequence of these two genes (Chou et al., 2011;Herfst et al., 2012;Neumann and Kawaoka, 2015).
Mucosal barriers present the first line of defense against IAV infection. To infect the underlying epithelium, viral particles must first pass through a~1-10 mm thick layer of mucus that is being steadily transported towards the pharynx where it can be swallowed, neutralizing any virus immobilized within it (Bustamante-Marin and Ostrowski, 2017;Wanner et al., 1996;Zanin et al., 2016). Viruses that bind too tightly to sialic acid will pass through the mucus barrier very slowly, and will thus be unable to reach the surface of an airway epithelial cell before mucociliary clearance. In contrast, viruses that bind only very weakly to sialic acid (or which rapidly destroy it through excessive NA activity [Cohen et al., 2013;Yang et al., 2014]) will quickly penetrate mucus, but may be unable to stably attach to the surface of the underlying epithelium once it is reached. Adaptations that help the virus to overcome both of these conflicting challenges, such as changes in virus morphology or a particular spatial organization of envelope proteins, could be evolutionarily favored during in vivo replication.
Interestingly, one feature of IAV that tends to diverge when clinical isolates are cultured in a laboratory environment, or when animals are infected with laboratory-grown strains, is particle morphology. While clinical isolates of IAV -samples adapted to transmission in a mucosal environmentform filamentous particles with a consistent diameter but widely varying length, laboratory-adapted strains tend to produce more uniform, spherical particles (Badham and Rossman, 2016;Chu, 1949;Dadonaite et al., 2016;Seladi-Schulman et al., 2013). Recent evidence from the 2009 pandemic suggests that filamentous morphology, conferred by the virus's M segment, may play a role in transmission (Campbell et al., 2014;Lakdawala et al., 2011). However, whether or not virus morphology contributes directly to virus transmission -and if so, how -remains unclear. Similarly, although the two major envelope proteins of IAV, HA and NA, have been observed by electron microscopy to cluster non-uniformly on both the viral and pre-viral envelope (Calder et al., 2010;Harris et al., 2006;Leser and Lamb, 2017), whether and how the spatial organization of HA and NA affects virus transmission also remains unclear.
Motivated by these observations, we reasoned that virus shape, together with the packaging and organization of HA and NA in the viral membrane, could influence the balance of attachment and detachment in ways that promote efficient virus penetration through mucus. To test this idea, we sought to characterize the organization of proteins in filamentous IAV particles while simultaneously observing their engagement with sialic acid -a measurement that requires a non-destructive approach. To make this measurement possible, we recently developed strains of influenza A virus that are amenable to fluorescence microscopy through site-specific tags introduced into the viral genome (Vahey and Fletcher, 2019). Here we show that filamentous particles frequently contain asymmetric distributions of HA and NA in their membranes, and that this distinctive organization biases the diffusion of these particles in a persistent direction over distances of several microns. By enhancing the effective diffusion of a viral particle without reducing the stability of its attachment to the viral receptor, this mechanism could promote virus penetration across mucosal barriers.

Results
HA and NA are distributed asymmetrically on the surface of IAV particles We first sought to characterize the organization and dynamics of proteins in the viral membrane. By labeling HA and NA, along with the viral nucleoprotein, NP, we are able to measure features of virus organization on intact, infectious particles that corroborate and extend previous observations made using electron microscopy (Calder et al., 2010;Chlanda et al., 2015;Harris et al., 2006;Leser and Lamb, 2017). For these experiments, we use a tagged variant of the strain A/WSN/1933 with M1 from A/Udorn/1972, which differs from WSN M1 at six residues and confers filamentous morphology (Elleman and Barclay, 2004). Consistent with our prior observations, this virus produces filamentous particles that vary widely in size, from sub-diffraction limited spots to particles > 10 mm in length (Vahey and Fletcher, 2019). In viruses with fluorescently-labeled HA and NA, we observe a pronounced tendency for NA to be enriched at one end of the virus ( Figure 1A, inset). To quantify this enrichment, we measured the relative intensities of HA and NA within~400 nm of each viral pole in filamentous particles > 1 mm in length. Across 20344 such particles, approximately one third have NA intensities at least 5-fold higher on one pole than on the other ( Figure 1A, left). Similarly, viruses with labeled NP (the most abundant protein in vRNP complexes and a proxy for the virus genome) reveal individual foci that localize to one end of the virus. Aligning filamentous particles with polarized NP foci (4805 in total) reveals a tendency for NA to colocalize with NP ( Figure 1A, right). For the subset of these particles > 4.5 mm in length (540 in total), we created a composite image showing the average densities of viral proteins within 2 mm of each viral pole (Figure 1-figure supplement 1). On average, NA is enriched~2 x relative to HA at the NP-containing pole in these particles, as compared to the middle region of the particle and the opposite pole ( Approximately one third of filamentous particles have NA intensities five-fold higher on one pole than the other, as indicated by the vertical dashed lines (distributions are symmetric in this case because poles are designated randomly). Inset images show a particle Figure 1 continued on next page filamentous particles do not recover fluorescence in either HA or NA over tens of minutes ( Figure 1B).
To investigate the finer details of protein organization and to determine if NA in fluorescent viruses is clustered, as suggested by electron microscopy (Calder et al., 2010;Harris et al., 2006), we use two-color stochastic optical reconstruction microscopy (STORM) to reconstruct images of HA and NA with resolution~10X better than the diffraction limit (~30 nm compared to~300 nm; Figure 1-figure supplement 2). At this resolution, we find that the tendency of NA to concentrate at one of the viral poles is pronounced even in particles smaller than 300 nm in length ( Figure 1C). We also find that the NA seen at low levels along the length of filamentous viruses without super-resolution imaging is actually organized into small NA clusters ( Figure 1D). Additionally, HA and NA distributions in these particles are modestly anti-correlated ( Figure 1E), suggesting that receptor-binding and receptor-destroying activities may be spatially segregated on some regions of the virus. Collectively, these measurements present a picture of a variegated IAV envelope whose spatial organization is stable and coupled to the presence and location of the viral genome, with~70% of NPcontaining viruses having NA biased to the proximal pole.
We next investigated whether spatial organization of the IAV envelope could have functional significance for virus binding and detachment. As a first test of this idea, we compared the spatial organization of viruses that were released from the cell surface with those that remained attached after challenging the virus with the neuraminidase inhibitor (NAI) oseltamivir carboxylate (He et al., 1999) (Materials and methods). To quantify virus spatial organization, we defined HA-NA polarity as the separation between the center of masses for HA and NA divided by the virus length. Interestingly, viruses that escaped the cell surface under NAI challenge showed higher HA-NA polarity (0.155; 95% confidence interval, CI = 0.139-0.171) than viruses released in the absence of NAI challenge, both before (0.123; 95% CI = 0.106-0.140) and after (0.100; 95% CI = 0.090-0.110) facilitating virus release by treating with exogenous sialidase ( Figure 1F & G). In comparison, viruses treated with both NAI and exogenous sialidase have polarities similar to the untreated virus (0.124; 95% CI = 0.111-0.136). These results suggest that viruses with NA concentrated at one of the viral poles may be more effective at navigating environments rich in sialic acid. with NA enrichment of~5.6 fold (~31 st percentile of particles). The plot to the right shows the same comparison for particles aligned to their NP-foci, designated as pole 1 (distributions are determined from a total of 4805 particles with polarized NP distributions). The prevalence of particles with NA ratios > 1 indicates a tendency for NA to be enriched at the virus's genome-containing pole. Inset images show a particle with NA enrichment of~3.3 fold (~48 th percentile of particles based on NA polarity). (See also (E) Distribution of HA-NA spatial correlation coefficients from regions of 24 filamentous particles following reconstruction at~30 nm resolution. (F) To compare populations of virus that are able to detach from infected cell to those that remain bound to the cell surface with or without NAIs, we collect virus in two separate stages: first, we harvest virus from media at 16hpi, followed by the addition of media supplemented with an exogenous, oseltamivir-resistant bacterial neuraminidase. After one hour of treatment with exogenous NA, we harvest virus that had previously remained bound to the cell surface. Polarized viruses step persistently away from their NA-rich pole To directly test how NA polarization might affect virus motion, we characterized interactions between fluorescently-labeled viruses and sialic acid coated coverslips, where the well-defined geometry and density of sialic acid allow straightforward analysis of virus diffusion (Materials and methods) (Figure 2A). Because our approach to fluorescently labeling NA preserves its activity (Figure 2-figure supplement 1) and viruses harboring fluorophores on both HA and NA preserve~85% of their infectivity (Vahey and Fletcher, 2019), we could carry out functional assays with the virus and at the same time visualize HA and NA distributions on the viral membrane. Surprisingly, the motion we observed did not resemble randomly-oriented diffusion of the viral particle, but rather persistent, Brownian ratchet-like diffusion, in which filamentous particles with polarized distributions of NA exhibited directed mobility away from their NA-rich pole ( Figure 2B, Video 1). Labeling coverslips with fluorescein-labeled Erythrina cristagalli lectin (ECL), which binds specifically to the terminal galactose exposed following sialic acid cleavage (Iglesias et al., 1982), revealed the history of virus trajectories and confirmed that virus motion is accompanied by receptor destruction ( Figure 2B). Aligning the trajectories of mobile particles (defined as those with diffusion coefficients > 100 nm 2 /s, comprising~68% of the population; Figure 2C) to the orientation of their HA-NA axis reveals that directional mobility can persist for several microns, many times the length of the particle itself ( Figure 2D). Consistent with the observation that polarized distributions of HA and NA serve as a determinant for persistent motion and enhanced diffusion, we find that non-mobile viruses have, on average, less polarized distributions of HA and NA than mobile ones ( Figure 2E).
To determine if polarized distributions of NA were necessary for persistent directional mobility, we disrupted the spatial organization of viral surface proteins by removing the cytoplasmic tail of NA (residues 2-6; Figure Figure 3A), indicating that spatial organization of NA at the poles is necessary for persistent mobility of IAV.
Correlations in the direction of successive steps in a random walk will increase the rate at which the walker explores its environment, analogous to how more rigid polymer chains typically have larger end-to-end distances than those with equivalent contour length but lower bending rigidity. To quantitatively compare the rate at which the less persistent NADCT viruses explore their environment to that of the more persistent wildtype virus, we determined mean squared displacements from observed trajectories of mobile viruses (diffusion coefficients > 100 nm 2 /s over the observation period) and simulated random walks in which the number of steps, the size of each step, and the time interval between steps all match the observed data, but the direction of each step is uncorrelated with previous steps ( Figure 3B). From this analysis, we estimate that the diffusion coefficients of mobile viruses are enhanced approximately five-fold as a result of directional correlations ( Figure 3B, left). In contrast, the diffusion of mobile NADCT viruses is only modestly influenced by directional correlations (~1.5 fold increase; Figure 3B, right). To further quantify the difference between viruses with wildtype NA and NADCT, we tracked the displacement of particles between subsequent frames acquired 30 s apart and plotted the distribution of the stepping angle relative to the orientation of the virus's HA-NA axis. Viruses with wildtype NA step in the direction of increasing HA (with the NA pole at the rear) roughly twice as frequently as the opposite direction, while NADCT viruses exhibit no correlation between orientation and stepping direction ( Figure 3C). Additionally, despite having lower amounts of NA in the viral membrane, NADCT viruses left significantly larger trails of cleaved receptors than their wildtype counterparts ( results demonstrate that the spatial organization and mobility of NA on the viral surface both play an important role in determining where and when it cleaves substrate.
Computational modeling suggests a mechanism for persistent directional mobility To investigate the mechanism of this persistent directional mobility, we modeled the diffusion of filamentous viruses with defined spatial organization of HA and NA as the viruses bind to sialic acid on a two-dimensional surface (Appendix, Figure 3-figure supplement 4). In this model, virus diffusion is constrained by the tens of attachments the HAs form with sialic acid at any instant in time (English and Hammer, 2004;Xu and Shaw, 2016). At the interface between HA-rich and NA-rich regions of the viral membrane, like those seen in fluorescence images ( Figure 1A-D), NA will periodically gain access to, and hydrolyze, sialic acid as the position of the virus thermally fluctuates. The binding partners available to HAs located close to this interface will therefore be asymmetrically distributed, with more potential binding partners located further away from areas of higher NA density. This concept is illustrated most clearly in the case where the virus is constrained to a one-dimensional path. As this case illustrates, the sialic acid density along the length of the virus is lowest in close proximity to NA (Figure 3-figure supplement 5A-C). When NA is confined to a single pole, this results in a gradient in sialic acid density along the length of the particle. Since the number of available binding partners is higher in one direction than another, newly-formed HA-sialic acid bonds will tend to be offset from previous bonds in this direction. This leads to the persistent motion we observe experimentally as well as in our simulations (Video 2). Consistent with this mechanism, persistent motion of the virus is lost when NA is no longer localized to a single virus pole and the sialic acid distribution beneath the particle becomes symmetric (Figure 3-figure supplement 5B-D). We note that virions with symmetric distributions of NA also occur in the virus population and would not be expected to exhibit persistent motion (for example, those particles with NA polar ratios of~1 in Figure 1A).
Since virus motion is dependent on the virus's ability to establish distinct regions with and without sialic acid, we expect that dynamic distributions of either NA or sialic acid will alter virus mobility. Consistent with our experimental observations with the NADCT virus, allowing NA to freely diffuse eliminates directional bias in virus motion in both experiments ( Figure 3C) and simulations ( Figure 3D). However, allowing surface-bound sialic acid to diffuse can either enhance or suppress directed motion, depending on the kinetic parameters of HA and NA, the diffusion coefficient of sialic acid (D SA ), and the size of the virus (Appendix). Although our experimental data corresponds to the case where sialic acid is immobilized (D SA~0 ), our simulations predict that polarized IAV bound to slowly-diffusing transmembrane glycoproteins or gel-forming mucins (D SA <0.01 mm 2 /s) will exhibit enhanced directed mobility, likely due to the biased spatial distributions of sialic acid binding partners that are available to HAs distal to the virus's NA-rich pole. In contrast, increasing the rate of sialic acid diffusion further (D SA >0.01 mm 2 /s) is expected to suppress persistent motion, by flattening the sialic acid gradient that is created beneath the virus ( Figure 3E, Video 3). Finally, we find that increasing the length of the virus in simulations increases the number of HA-sialic acid interactions, reducing virus mobility but increasing directional persistence (Figure 3-figure supplement 6). Thus, the organization of proteins on the viral surface, the size of the virus, and the nature of the receptor to which the virus is bound can each influence the persistence of a virus's motion.
Although our results focus on a two-dimensional geometry in which a virus adheres to a flat surface decorated with sialic acid (a model for the cell surface), we reasoned that they should generalize to three-dimensional systems, such as the secreted mucus gel through which IAV must penetrate to reach naïve cells to infect. To test this prediction, we cultured Calu-3 cells at an air-liquid interface, resulting in a~1-10 mm thick gel of secreted mucus overlaying the apical surface of the cells ( Figure 4A). Adding virus with labeled HA and NA to the mucus, followed by fixation and labeling with ECL, revealed tracks similar to those we observed on two-dimensional surfaces ( Figure 4B). This suggests that the asymmetry of NA and HA biases the direction of virus diffusion in three dimensions, producing trails of cleaved sialic acid that can reach several microns in length as the virus moves ( Figure 4C). This directional mobility is less prevalent in viruses with more uniformly distributed NA, though they nonetheless are capable of creating swaths of ECL-staining within the mucus that lack clear directionality ( Figure 4D). Similar to our observations on idealized two-dimensional surfaces ( Figure 3C), we find that viruses in mucus exhibit a slight tendency to align their HA-NA axis (captured at the moment of fixation) with the displacement of the virus relative to the center of ECL labeling ( Figure 4E). These results suggest that the spatial organization of HA and NA on the virus surface may also promote penetration of polarized IAV particles through mucus barriers in vivo.

Discussion
Advances in electron microscopy over the past several decades have presented an increasingly detailed picture of the morphology and organization of influenza A virus. This has revealed organizational features of filamentous IAV whose origins and functional significance remain unclear. By using site-specific fluorescent labeling to measure the organization of a virus while preserving its function, we are able to corroborate key observations of envelope protein non-uniformity obtained from electron microscopy and extend them to dynamic observations of both protein motion on the surface of the virus, as well as the directionally-persistent motion of influenza A virus particles as they engage with the virus receptor, sialic acid. These observations demonstrate that the morphology of a virus, the spatial organization of proteins in its membrane, and constraints on the diffusion of these proteins collectively confer the tendency for viral particles to exhibit persistent directional mobility, enhancing the virus's rate of diffusion without diminishing its strength of adhesion. Importantly, our simulations show that this feature of filamentous morphology would not be limited to the extremely large particles whose length is easily measured using diffraction limited microscopy, but rather extends to capsule-shaped particles < 200 nm in length (Figure 3-figure supplement 6), which are known to be produced by filamentous strains of IAV (Calder et al., 2010). In contrast, this effect may be suppressed in spherical particles, due both to the absence of a clear axis for polarization and  Video 3. Simulations of polarized filamentous viruses on surfaces with freely-diffusing sialic acid (green). Simulations correspond to D SA = 10 À7 mm 2 /s, D SA = 10 À5 mm 2 /s, and D SA = 10 À1 mm 2 /s, as plotted in Figure 3E.  their ability to roll on two-dimensional surfaces. However, super-resolution live imaging will be required to confirm these predictions experimentally.
Although more work is needed to understand if these characteristics of IAV organization enhance infectivity and are adaptive during in vivo replication, a simple model of viral transport suggests how the directional viral mobility we observe could contribute during host-to-host transmission. On first entering the respiratory tract, viruses must diffuse through the mucosal barrier to infect the underlying airway epithelial cells. Competing with this process is mucocilliary clearance, which carries particles bound to mucus towards the pharynx where they are neutralized (Figure 4-figure  supplement 1A). If the transport of a virus through a mucosal barrier is modeled as a first passage problem with a time limit imposed by the rate of mucociliary clearance, a five-fold increase in the diffusion coefficient (as predicted in Figure 3B) would lead to a proportional reduction in the first passage time. More dramatically, it would also increase the fraction of particles that reach the cell surface when the rate of mucociliary clearance is high and would normally prevent most particles from reaching the cell surface. Our experiments on two-dimensional sialic acid-coated surfaces suggest a diffusion coefficient of~800 nm 2 /s for polarized viruses; adapting this value for a one-dimensional first passage model suggests that persistent motion increases the number of particles that reach the epithelium before being cleared by several orders of magnitude (Appendix, Figure 4-figure supplement 1B). Although there are multiple ways that a virus's passage through mucus can be accelerated (reducing its size, decreasing the number of HAs on its surface, increasing the number of NAs, or making the spatial distribution of NA more uniform), each of these changes would likely reduce binding stability once the virus has managed to reach the cell surface. In contrast, the polarized distributions of NA on the viral surface that we observe increase virus diffusion without compromising binding stability.
Balancing the need to robustly attach to the cell surface with the need to escape immobilization in host mucus is a fundamental challenge for influenza and other viruses that use sialic acid to enter cells. Previous work has shown that influenza particles are not immobilized during their interactions with sialic acid (Guo et al., 2018;Sakai et al., 2017). Additionally, work characterizing the diffusion of influenza C virus, in which receptor-binding and receptor-destroying activities are combined in a single protein (HEF), has shown that the destruction of receptors on a 2D surface prevents virions from retracing their steps (Sakai et al., 2018). Our results show that influenza A virus accomplishes a similar feat through a different mechanism -asymmetric distribution of receptor-binding and receptor-destroying activities on the viral surface that results in persistent motion while maintaining stable attachment. The persistent directional mobility shown here orients filamentous virus motion parallel to its major axis, where it could further enhance the anomalous diffusion coefficients observed for cylindrical nanoparticles in mucus (Yu et al., 2016). Analogous to the combined importance of active motility and cell shape in mucosal bacteria (Bartlett et al., 2017;Sycuro et al., 2010), the directed mobility and cylindrical shape of IAV could help to explain the virus's ability to penetrate host mucus and contribute to the prevalence of filamentous morphology in clinical isolates of IAV.

Culturing and labeling virus
Strains of influenza A virus amenable to site specific labeling on HA, NA, and NP were designed and characterized as described previously (Vahey and Fletcher, 2019). Briefly, viruses expressing HA with five consecutive glycine residues following the signal sequence (for labeling via Sortase A [Theile et al., 2013]), NA with a c-terminal ybbR tag (for labeling via Sfp [Yin et al., 2006]), and NP with a c-terminal tetracysteine motif (for labeling via direct binding of the biarsenical dye FlAsH [Griffin et al., 1998]) were rescued using reverse genetics (Hoffmann et al., 2000) by transfecting co-cultures of HEK293T and MDCK-II cells with plasmids encoding each of the eight genomic segments under the control of bidirectional promoters. Cells used in this work were obtained and authenticated by the UC Berkeley Cell Culture Facility and tested negative for mycoplasma. All viruses used in this work are derived from A/WSN/1933, with the WSN M1 gene replaced by that of A/Udorn/1972, to establish the filamentous phenotype. MDCK-II cells used to propagate virus were maintained in DMEM supplemented with 10% fetal bovine serum (Thermo Fisher, 10438026) and 1x penicillin/streptomycin (Thermo Fisher, 15140122). Prior to infection, confluent monolayers of cells were washed once with PBS, and serum-containing growth media was replaced with virus growth media (MEM, 0.25% BSA, 1 mg/ml TPCK-treated trypsin, and penicillin/streptomycin). Viruses used for experiments were collected from cells following infection at MOI~1 and 16 hr of growth at 37˚C in virus growth media. Media containing virus was collected, centrifuged at 2000 Â g for five minutes to remove cell debris, and treated with 10mU/ml soluble sialidase (from C. Perfringens, Sigma N2876) to ensure that viruses were well dispersed. Viruses were labeled in solution for 90 min at room temperature using NTC buffer (100 nM NaCl, 20 mM Tris pH 7.6, 5 mM CaCl 2 ) supplemented with 5 mM MgCl 2 , Sortase A (180 mM enzyme, 50 mM CLPETGG peptide) and SFP synthase (5 mM enzyme, 5 mM CoA probe). Following labeling, Capto Core 700 beads (GE Healthcare;~1:1 resin volume to sample volume) were used to remove residual dyes and enzymes from the solution of labeled virus. For labeling NP with the biarsenical dye FlAsH, viruses were immobilized on coverslips, washed in NTC buffer, and incubated with 2 mM FlAsH for 30 min at room temperature.

Virus photobleaching
To qualitatively evaluate the mobility of HA and NA on the virion surface ( Figure 1B, Figure 3-figure supplement 2B), unfixed, immobilized viruses were imaged using total internal reflectance (TIRF) microscopy. Filamentous virus of sufficient length (>5 mm) were positioned within the field of view such that when the field stop was closed, only approximately half of the virus was exposed to illumination. This half of the virus was then bleached using maximum laser power and then imaged at lower power at 30 s intervals as the field stop was opened to monitor recovery. Representative results are shown in Figure 1B and Figure 3-figure supplement 2B.

STORM imaging and analysis
Samples for STORM imaging were prepared by binding labeled virus to antibody or sialic acid (i.e. fetuin) functionalized coverslips for one hour at 4˚C, followed by the incubation of Dragon Greenlabeled 220nm-diameter streptavidin coated beads. Viruses and beads were then fixed to the surfaces with 4% paraformaldehyde in PBS and washed 3x with buffer containing 1M Tris pH 8.0, 5% glucose, and 140 mM b-mercaptoethanol. Following these washes, the buffer was supplemented with glucose oxidase and catalase to final concentrations of 0.6 mg/ml and 0.035 mg/ml, respectively, and mounted on the microscope for imaging. STORM data was acquired in the following sequence. First, an image of the Dragon Green beads (serving as fiducial marks), HA (labeled with CF568-conjugated peptide and SrtA), and NA (labeled with AF647-CoA and SFP) was acquired, to enable registration. Next, a sequence of STORM images was acquired using a 640 nm laser at full power, with acquisition of the HA channel via a 560 nm laser at low power every 50 frames to correct for drift. After collecting 15000-35000 frames in this way, we performed STORM imaging on CF568-HA using a 560 nm laser. To correct for drift, we acquire an image every 50 frames using a 405 nm laser and 575/20 nm emission filter; these settings allow us to image the Dragon Green beads, while simultaneously accelerating blinking of the CF568 dye. For reconstructions of HA, we acquire 25000-35000 frames.
For quantification and localization of blinking events, we use the ImageJ plugin Thunderstorm (Ovesný et al., 2014), combined with custom Matlab scripts for additional drift correction and removal of fluorophores that remain in the 'on' state for more than one frame. This analysis results in a list of coordinates for each localization that we then use to reconstruct images of virus at varying resolutions. Reconstructed STORM images (e.g. Figure 1C & D) are displayed by representing each localization as a gaussian with a standard deviation of 30 nm.

NAI challenge assay
Challenge experiments with the neuraminidase inhibitor oseltamivir are performed as described previously (Vahey and Fletcher, 2019). The analysis from Figure 1E uses an image dataset from Vahey and Fletcher (2019), reanalyzed to measure the spatial organization of HA and NA on the surface of released virus particles. We infect a polarized monolayer of MDCK cells grown on a collagen gel at MOI of 1-3. After incubating cells with virus for one hour at 37˚C, we wash to remove excess virus, replacing media with virus growth media supplemented with or without a specified concentration of oseltamivir carboxylate (Toronto Research Chemicals O700980), but without TPCKtreated trypsin. At 16 hr post infection, we remove the virus containing media for labeling and imaging, and replace with media supplemented with 1 U/ml NanI from C. perfringens (Sigma N2876). After treating with this exogenous sialidase for one hour at 37˚C, we again collect cell culture media for virus labeling and imaging.
To measure the HA-NA polarization on viruses released in these experiments, we segment filamentous viruses with lengths > 1 mm and measure the intensity-weighted centroid (i.e. 'center of mass') for both the HA and NA channels. The vector connecting the NA centroid to the HA centroid defines the orientation of HA-NA polarity. Dividing the magnitude of this vector by the total particle length gives the HA-NA polarity metric plotted throughout this work.

Virus motility assay
Coverslips presenting sialic acid for virus attachment were prepared as described previously (Vahey and Fletcher, 2019). Briefly, NH2-PEG-OH (Rapp Polymere, 122000-2) supplemented with 2.5 mole-percent NH2-PEG-Biotin (Rapp Polymere, 133000-25-20) was conjugated to silanized coverslips for subsequent attachment of sialylated proteins. Following PEGylation, custom PDMS chambers were attached to coverslips, and chambers were incubated for 10 min at room temperature with streptavidin at 50 mg/ml in 150 mM NaCl, 25 mM HEPEs, pH 7.2, and washed 5X in the same buffer. Fetuin (Sigma F3004) labeled with NHS-biotin was then added at 100 nM and incubated~30 min at room temperature. Coverslips were then washed 5X in NTC buffer and equilibrated to 4˚C in preparation for virus binding. For surfaces functionalized in this way (Piehler et al., 2000), we expect a PEG density of~0.75 molecules/nm 2 , corresponding to roughly one PEG-Biotin per 7 nm x 7 nm area on the surface. If each biotin is bound by one streptavidin tetramer and subsequently one molecule of biotinylated fetuin (with~10 sialic acid residues per molecule), the surface density of sialic acid will be~0.2 SA/nm 2 .
Viruses with HA and NA enzymatically labeled as described previously were bound to coverslips equilibrated to 4˚C for one hour on ice. Immediately before imaging, excess virus was washed with pre-chilled NTC, and the sample was mounted on the microscope stage. After allowing the chamber to equilibrate to room temperature, the buffer in the chamber was exchanged to NA buffer (100 mM NaCl, 50 mM MES pH 6.5, 5 mM CaCl 2 ), and timelapse recordings were collected using TIRF microscopy at 30 s intervals. To visualize trails of cleaved sialic acid, fluorescein-labeled Erythrina cristagalli lectin (ECL; Vector Labs FL-1141) was added to each well at a concentration of 5 mg/ml in NTC buffer with 10 mg/ml BSA and incubated for 30 min at room temperature. During this incubation period, rapid multivalent binding of ECL to cleaved sialic acid on the viral surface effectively blocks further motion of the virus. Images of ECL trails were acquired using TIRF microscopy without washing unbound ECL from the chamber.
To analyze images of viruses, we separately segment each image according to the intensity in both the HA and NA channels. Merging the two sets of segmented images allows us to determine the position of each virus (i.e. the centroid of the combined HA and NA masks) as well as their morphological features. To determine the HA-NA polarization of each virus, we calculate the distance between the centroid of HA and NA intensity for a particular virus, divided by that virus's length. The data in Figure 2 and Figure 3 is compiled by extracting these features for each virus in each frame of a timelapse recording.
To analyze the trails of cleaved sialic acid left by mobile viruses, we segment images of samples labeled with fluorescent ECL according to the intensity of lectin staining. Because the virus itself contains high densities of sialic acid on its surface, we use a bandpass threshold to specifically quantify ECL bound to processed glycans on the coverslip (which produces a signal brighter than the background, but dimmer than the virus). Although viruses dissociate from some of the tracks, those that remain bound to the surface allow us to connect intensity of ECL labeling on the surface to intensities of HA and NA on the virus that generated the track. This data is plotted in Figure 3-figure supplement 3, with and without normalization to NA intensity.

Quantification of NA activity using MUNANA
For assays using the fluorogenic neuraminidase substrate MUNANA, 10 ml of solution containing labeled virus was diluted into 40 ml of NA buffer (100 mM NaCl, 50 mM MES pH 6.5, 5 mM CaCl 2 ) and incubated in a test tube at 37˚C. At time points of 0, 30, 60, 120, and 180 min, aliquots were collected and NA was inactivated by adding sodium carbonate to a final concentration of 100 mM, and fluorescence was measured by imaging a fixed volume of sample on a confocal microscope using excitation at 405 nm. The rate of turnover was then determined from the slope of the intensity versus time plot with the signal at 0 min subtracted from each timepoint. Because strains with wildtype NA and NADCT produce different titers of virus that also differ in their morphology and NA composition, we normalized samples to total NA content ( Figure 3-figure supplement 3A), measured by immobilizing viruses on coverslips, imaging them, and integrating the total NA intensity associated with the two samples. This yields an estimated 6-fold difference in total NA content between virus with wildtype NA and viruses with NADCT.

Virus imaging at air-liquid interface of Calu-3 cell cultures
Calu-3 cells grown on plastic dishes for fewer than 10 passages (DMEM, 10% FBS, 1x penicillin/ streptomycin, supplemented with 1 mM sodium pyruvate (Thermo Fisher, 11360070) and 1x nonessential amino acids (Thermo Fisher, 11140076)) were split at 80% confluence and seeded onto 6 mm transwell supports at 50000 cells per insert. Approximately 3 days after seeding, media from the apical compartment was removed (the 'airlift') and cells were provided with fresh media in the basal compartment every other day until being collected for experiments, 8-12 days following the airlift. Cells cultured in this way differentiated into a secretory phenotype, producing a layer of mucus~1-10 mm thick over the apical surface of the monolayer ( Figure 4A). To bind virus without washing away secreted mucus, 5-10 ml of labeled virus was added to the apical side of each transwell insert (enough to just coat the surface), and immediately removed, leaving~1 ml of residual virus-containing solution that is approximately evenly distributed on the surface of the monolayer. The cells were then returned to the incubator for 3-6 hr, allowing virus to bind and diffuse, and allowing some of the residual moisture to dry before the cells are collected and fixed on ice for 20 min using 4% paraformaldehyde in PBS supplemented with 1 mM CaCl 2 . Following fixation, cells and mucus were labeled with MUC5AC monoclonal antibody (45M1; MA5-12178 ThermoFisher) and Erythrina cristagalli lectin labeled with FITC (5 mg/ml; Vector Laboratories, FL-1141). Following labeling, the transwell insert was carefully excised with a razor blade and inverted onto a coverslip for imaging.
To quantify alignment between the HA-NA axis of a virus particle and the direction of its displacement from the associated ECL track ( Figure 4E), fluorescent images of HA, NA, and ECL were segmented in both HA (to identify virus particles) and ECL (to identify regions of cleaved sialic acid) channels. For each segmented virus particle, we calculate the HA-NA axis (defined as the vector displacement between the center of masses for HA and NA) and the ECL displacement (defined as the vector displacement between the center of masses for HA and ECL) ( Figure 4B, right). Cases where multiple particles contact the same ECL track are excluded from analysis.

Statistics and replicates
Replicates referenced throughout this paper refer to biological replicates, defined as virus collected from separate infected cell cultures, labeled, and assayed as indicated. No statistical methods were used to predetermine sample size. Image data was excluded from analysis in rare cases if the sample drifted on the microscope stage, or if coverslip preparations showed non-specific virus binding. Statistical tests and the number of replicates used in specific cases are described in figure captions. All statistical tests were performed in Matlab R2017b using the Statistics and Machine Learning Toolbox. Confidence intervals for the data in Figure 1G were calculated using a critical value of the Student's t distribution of 3.182 (95% confidence interval for n-1 = 3 degrees of freedom). Data availability All data generated or analysed during this study are included in the manuscript and supporting files.

Additional information
For the typical time steps used in our simulations (~0.2 s), this amounts to instantaneous cleavage of any SA residues within reach of NA. Using these three probabilities, we calculate at each instant in time the number and location of each point of attachment between the virus and the surface and we remove any cleaved sialic acid residues for the remainder of the simulation. Note that we do not prohibit multiple SAs from binding to a single HA centroid; although this would be inaccurate at high densities of SA, under the conditions of these simulations it results in each HA centroid being bound to 0,1, or 2 SAs at any particular instant in time -reasonable values for a trimeric molecule.

Modeling virus diffusion
To model diffusion of the virus, we use expressions derived for dilute suspensions of cylindrical rods (Brenner, 1974): axisymmetric, rotations about j do not appreciably change the number or location of HA and NA molecules that are proximal to the surface. As a result, we do not expect that omitting this rotational degree of freedom from our simulations would qualitatively affect the results for cylindrical, axisymmetric particles. However, these simplifying approximations could not be extended to a spherical particle, which could rotate more freely on the surface, altering the number and location of NA molecules capable of cleaving sialic acid.

Origin of directed motion
In this model, rectification of virus motion comes from asymmetries in the location of HA relative to the SA that are available for binding. At the boundary between regions where NA activity has cleaved SA and regions where it has not, HA molecules will have more potential binding partners in the direction of the uncleaved region. The constraints introduced by binding to these SAs will leave the virus with greater likelihood to step in the direction of the uncleaved region. Although this asymmetrically distributed freedom of motion will only apply to a subset of all HAs, over the course of~10 6 simulation steps, it is sufficient to bias the direction of virus diffusion. This establishes a form of Brownian ratchet, where the input energy could derive from the hydrolysis of sialic acid by NA. Any change in NA organization that gets rid of this asymmetry in the orientation of the HA-NA interface (e.g. placing NA at both poles, in a single band away from the poles, spatially separated from HA, or in a uniform distribution over the surface of the virus) abolishes the rectified motion ( Figure 3-figure supplement 5).

Effects of sialic acid diffusion
So far, these simulations have used static distributions of SA. Allowing SA to diffuse on the surface will act to dissipate steep gradients in receptor density created by the activity of NA on the virus, resulting in shallower gradients that extend beyond the localized distributions of NA on the viral surface. The extent of this concentration gradient in available receptors will depend on the balance between the catalytic rate of NA, the rate of diffusion of SA, and the size and rate of motion of the virus. These relationships can be parameterized using a nondimensional Dahmkohler number: where k cat is the catalytic rate of NA as before (~100 s À1 ), D SA is the diffusion coefficient of sialic acid on the surface, and L is a characteristic length for the reaction-diffusion system. Taking L~100 nm, k cat~1 00 s À1 , and D SA~0 .01-0.1 mm 2 /s (reasonable values for large glycoproteins [Freeman et al., 2018;Jiang et al., 2015]) gives Da~10-100. The larger this value is, the better able a virus would be to maintain gradients in sialic acid density to support directional mobility. To test this prediction, we performed simulations where the diffusion coefficient of SA is varied while k cat remains constant and new SA residues are generated at the simulation boundary every time one is cleaved (to prevent complete removal of SA when its diffusion coefficient is high). Consistent with the prediction, simulations of virus motion at Da~100 or greater show preferential diffusion along the axis of the virus, while simulations at Da < 100 do not ( Figure 3E). Interestingly, for IAV this transition corresponds to a sialic acid diffusion coefficient of~0.01 mm 2 /s, characteristic of some membrane-anchored glycoproteins (Jacobson et al., 1984), but considerably slower than measured values for gangliosides (Komura et al., 2016). Although sialic acid diffusion can attenuate persistent virus motion if it is too rapid, it can also increase the rate of motion relative to immobile sialic acid by allowing HAs distal to the HA-NA interface to also sample from asymmetric distributions of receptors ( Figure 3E). Thus, the nature of the sialic acid receptors to which a virus is bound will likely influence how the virus moves -with greater persistent directional mobility on mucin gels of anchored glycoproteins, and with less persistence once it reaches glycolipids closer to the cell surface.