a, Short DNA oligos (22 bp) were covalently conjugated to the envelope proteins of herpes simplex virus type 1 (HSV-1) virions via hydrazone formation, which allows labelling transfer across multiple hydrogels, amplification based on branched DNA, and fluorescence readout based on hybridization of fluorescent oligos. b, Schematic illustration of TG- (top) and PAAG-based (bottom) iterative expansion of HSV-1 virions with the direct oligo-conjugation as in a. PAAG-based re-embedding and expansion was used for all expansion rounds after the first round, reasoning that most of the error of an iterative expansion protocol is introduced in the first round of expansion (see text for details). c, HSV-1 virions with directly labelled envelope proteins, expanded by TG- (left) and PAAG-based (right) 2-round iterative expansion. Scale bar, 1 µm (TG, 10.3 µm; PAAG, 15.3 µm). Expansion factor, 10.3x (TG) and 15.3x (PAAG). Results are representative of 3 separately acquired fields of view from a single hydrogel preparation for each gel type, using virions from the same single batch of live HSV-1 preparation. d, Single-particle averaged images of HSV-1 virions after TG (top)- and PAAG-based (bottom) 2-round iterative expansion (TG, n = 396; PAAG, n = 362 virions; virions from the same single batch of live HSV-1 preparation). Full width half maximum (FWHM) of the radial intensity profile (the line intensity profile from the particle centre to the edge of the particle), 73.6 nm (TG) and 91.0 nm (PAAG). Scale bars, 100 nm. e, Single-particle averaged images of HIV virions expanded by TG- (top) and PAAG-based (bottom) 2-round iterative expansion (TG, n = 61; PAAG, n = 73 virions; virions from the same single batch of live HIV preparation). FWHM of the radial intensity profile, 49.1 nm (TG) and 119.0 nm (PAAG). Scale bars, 100 nm. f, Top left and middle, representative single xy-plane images of HSV-1 virions expanded by TG- and PAAG-based 2-round iterative expansion. White lines indicate the 8 directions along which the virion’s radii (R) were measured. Scale bars, 100 nm. Top right, representative line intensity profile (circles) along a single direction (Direction 1) of the TG-expanded virion and the fitted Gaussian (red line). Distance from the centre of the Gaussian to the centre of the virion was defined as R along that direction. Bottom, histogram of the particle-mean-normalized R (Rn) for all the measured line profiles [TG, n = 1977; PAAG, n =1889 profiles; from 352 (TG) and 330 (PAAG) virions from the same single batch of live HSV-1 preparation]. g, Standard deviation (σ) of HSV-1 virion radii (R) within individual virions for TG- and PAAG-based iterative expansion (p = 2.4 × 10−24, 2-sided Wilcoxon rank sum test; TG, n = 352; PAAG, n = 330 virions; virions from the same single batch of live HSV-1 preparation). Data are presented as box plots with ends of whiskers representing maximum and minimum values of the distribution after outlying points (values above 75th percentile + 1.5 × interquartile range, or below 25th percentile – 1.5 × interquartile range) are excluded, upper line of box representing 75th percentile, middle line of box representing 50th percentile (median), lower line of box representing 25th percentile, and plus signs representing individual values for the outlying points.