Adhirons to ɑ-actinin-2, the Z1Z2 epitope of titin, and ZASP

The Adhirons isolated to the calponin homology (CH) domains of ɑ-actinin-2, the Z1Z2 domains (N-terminal immunoglobulin tandem domains) of titin and ZASP have been briefly reported on in earlier work from our group [26,27]. Adhirons bind specifically to their target sequences as they recognise both sequence and structure of the domains they were raised against [24]. The structure of the co-crystal of the Adhiron bound to the calponin homology (CH) actin binding domains of ɑ-actinin-2 (6WST) shows its binding is mediated by salt bridges between Lys72 and Asp 80 in loop 1 of the Adhiron, with Glu217 and Lys221, respectively in the second CH domain of ɑ-actinin-2 [26]. While we do not have co-crystal structures for the remaining two Adhirons, Alphafold3 modelling [32] suggests that the main binding interaction of the Adhiron to Z1Z2 is through an arginine residue in loop 2 to Asp201 in the Z2 domain (S1A Fig). Alphafold3 also predicts that the ZASP Adhiron likely binds through an aspartate residue in loop 1 to a region between Trp13 and Gly14 in the PDZ domain (PDZ: postsynaptic density protein (PSD95), Drosophila disc large tumor suppressor (DlgA), and zonula occludens-1 protein (zo-1) (S1B Fig).

Pull-down assays demonstrated that the Adhirons bound specifically to their target epitopes. (S1C Fig). Although we saw a small amount of cross-reactivity between some Adhirons and their targets, we attribute this to the general stickiness of Adhirons in this type of assay, particularly when the binding loops contain many hydrophobic residues. It is unlikely that an Adhiron raised to the CH domain of ɑ-actinin-2 would recognise the PDZ domain of ZASP, which has both different sequence and structure. As the first few Ig domains of titin within the Z‑disc do show some sequence and structural conservation with Z1Z2, we also used pulldown assays to confirm that the Adhiron to Z1Z2 did not bind to these downstream Z-repeats (from Ala201 to Tyr598) (S1C Fig). Finally, we performed additional surface plasmon resonance (SPR) experiments for ZASP and Z1Z2 Adhirons to determine the binding affinity of these for their target proteins. These experiments showed that each Adhiron only bound to the target they were raised to. The apparent binding affinities for the ZASP Adhiron to the PDZ domain of ZASP was 0.215 nM. The apparent binding affinities for the Z1Z2 Adhiron binding to Z1/Z2 was 4.75 nM (S1D Fig).

iPALM generates high-precision localisations for Z-disc proteins in 3D

iPALM was used to image all three Z-disc proteins, ɑ-actinin-2, Z1Z2 and ZASP in cardiac myofibrils in rigor conditions, using Alexa647-labelled Adhirons (Fig 1). This generated high-precision localisations in 3D for all three proteins, with the greatest precision in z, followed by y then x (S2 Fig). The mean sarcomere length was estimated as 1.8 ± 0.1 µm (mean ± S.D.), in agreement with the expected sarcomere length for cardiac myofibrils. Interestingly, the density of localisations for ɑ-actinin-2 was higher than those for Z1Z2 and lowest for ZASP (Fig 1A). This may be explained by ɑ-actinin-2 being the most common Z-disc protein of the three, with ZASP the least.

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Fig 1. iPALM imaging of Z-disc proteins.

A: Example iPALM data for ɑ-actinin-2, Z1Z2 and ZASP in multiple Z-discs along a myofibril. The z axis is into the plane. B,C: Localisations for individual Z discs from A (blue arrows) in xy (B) and yz (C) planes. Yellow arrows: localisations removed from further analysis by Z-disc segmentation and denoising. Plots show maximum projection in the orthogonal plane to the view.

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The localisations for each Z-disc were extracted, allowing for per Z-disc characterisation and for subsequent modelling of protein organisation using PERPL (Fig 1B and 1C). As the orientation of the myofibrils varies across images, we developed a pipeline to segment the Z-discs and align each one to facilitate downstream pattern analysis (PERPL). Briefly, the iPALM data was converted to images and imported into Ilastik, an interactive semi-automatic segmentation tool, to segment the Z-discs in image space [33]. These segmentations were used to extract the point cloud data for each Z-disc [34], which were then aligned using principal component analysis (PCA) and denoised using DBSCAN (S3 Fig).

As in the unsegmented data, the localisation density for each Z-disc was greatest for ɑ‑actinin-2, followed by Z1Z2 and ZASP (Table 1). The lengths in x and y, together with the measured volume of the Z-discs was largest for ZASP, followed by Z1Z2 and then ɑ‑actinin‑2, which may indicate that ZASP has a broader distribution at the Z-disc. Dimensions in z were similar for all three proteins. It could also result from selection bias when segmenting the Z‑discs, an artefact of the smaller sample sizes for ZASP and Z1Z2 (Table 1). A further possibility is that the ZASP and Z1Z2 Adhirons were less specific to their target, although data from pulldowns suggest this is not the case (S1 Fig), and apparent binding affinities for ZASP and Z1Z2, measured by SPR, were in the low nanomolar range. For ZASP, the particularly small sample size (n_zdiscs = 5) resulted from fewer initial iPALM acquisitions and an increased difficulty in segmenting Z-discs from the lower density data.

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Table 1. iPALM Data characterisation. n_zdiscs: Number of Z-discs acquired. n_locs: Number of localisations per Z-disc. L: length of Z-disc in x, y and z. σ: localisation precision in x, y, and z. ρ: localisation density per Z-disc. Values are the mean ± S.D.

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PERPL reveals the organisation of ɑ-actinin-2, Z1Z2 and ZASP in Z-disc data

PERPL was used to infer the organisation of ɑ-actinin-2, Z1Z2 and ZASP in the axial (y) direction and transverse (x,z) plane, by modelling the relative position distributions (RPDs) for the localisations (Methods, S3 Fig) [26]. Model RPDs contained different numbers of characteristic distances, which could either be independent of one another, or dependent on one another (such as a linear repeat of a targeted protein domain along one direction). The model RPDs also contain different background models for distances unaccounted for by the combination of characteristic distances (e.g., a spatially random pattern of false positive localisations). For each protein, we swept through and selected pre‑processing settings for the localisation data to generate different experimental RPDs. For each RPD, we swept over a range of possible (user-defined models) to fit to the data. We then compared the relative likelihoods of the fitted models of axial and transverse organisation (S1-S2 Tables) [26]. Finally, we selected the fitted model best describing the axial and transverse structure underlying the experimental data in each case, as determined by the Akaike criterion (AICc) (S3-S5 Tables). In all cases except for the arrangement of Z1Z2 in the transverse plane, the best model was more than 100 times more likely as an explanation of the data than the second best as determined by the AICc.

In the axial direction (Fig 2A-2C), we found a linear repeat of between 16 and 18 nm to be the best model for the arrangement of all three proteins, with a variability (σ_broadening, fitted s.d. of the component peak) of 10–12 nm on the characteristic distances between instances of the same protein (Tables 2, S3-S5, Fig 3A). This arrangement is expected for ɑ-actinin-2 from the known structure of the Z-disc complex and its ɑ-actinin-2 repeated crosslinks [5,13]. The titin Z1Z2 domains and ZASP therefore apparently follow the same pattern as ɑ-actinin-2 in the axial direction. However, for ZASP localisations, the signal (peak amplitude) decreased more significantly at higher multiples of the repeat distance. Thus, although we fit 5 peaks, the localisations are more likely to be separated by only one repeat of the Z-disc structure (18 ± 10 nm, mean distance ± σ_broadening) (Fig 2C, S5 Table) in agreement with the lower density of localisations (Table 1). One possible explanation for this is that the PDZ domains of ZASP, labelled by the Adhiron, tend to be found in pairs (possibly resulting from ZASP dimerization [35]) separated by 16–18 nm, but the occurrence of this pairing occurs randomly throughout the Z-disc.

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Table 2. Characteristic axial distances and broadening in most likely models. Next most likely model in each case had a relative likelihood of < 0.01.

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Fig 2. Experimental and best model Relative Position Distributions (RPDs).

Total model RPD contains terms for the background from randomly distributed localisations, repeated localisation of the same dye molecule and the characteristic distances (d₁, d₂, d₃) between localisations (Tables 2,3, S3-S5). Ratios between modelled distances are shown (e.g., 2d₁, = 2 x d₁). 95% confidence intervals shown on total model RPD, only noticeable in A (*).

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Table 3. Characteristic transverse distances and broadening in most likely models. corresponds to previously reported distance between parallel actin filaments (d_p-fil). corresponds to expected distance between anti-parallel actin filaments (d_p-fil / √2). ^a √2 × d₁, ^b 2 × d₁.

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Fig 3. Model for organisation of ɑ-actinin-2, ZASP and titin Z1Z2 domains in the Z-disc (cardiac myofibrils).

A: Arrangement of actin, ɑ-actinin-2, ZASP and titin Z1Z2 in the axial view. The Z-disc in cardiac muscle contains 4-6 ɑ-actinin-2 repeats [5], and here 6 repeats are shown. The ɑ-actinin-2 molecules can also be organised into doublets of the homodimer, spaced 6 nm apart ([13] not illustrated here for simplicity). B: Arrangement of actin, ɑ‑actinin‑2, ZASP and titin Z1Z2 in the transverse view (basketweave lattice). The lattice constants for titin Z1Z2 and parallel actin filaments are stable across the Z-disc, while the sets of anti-parallel actin filaments may move relative to one another. The rotation of the square lattice between different locations on the Z-disc is also shown [5].

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A component describing repeated localisations of the same molecule was found in the best model for Z1Z2 and ZASP organisation, but not in the best ɑ-actinin-2 model. The overall fit at the shortest distances is also worse for ɑ-actinin-2. The most likely explanation for these two observations is the increased likelihood of nearby pairs of ɑ-actinin-2 molecules in the Z-disc structure, which add an extra, unmodelled distance that confounds the fit of a zero-distance component. This could be consistent with the presence of pairs of ɑ-actinin-2 dimers, seen in EM density maps [13], which are approximately 6 nm apart.

In the transverse plane (Fig 2D-2F), the most likely model for the arrangement of all three proteins included a characteristic distance of 27–30 nm, with a variability (σ_broadening) of 7–9 nm (Tables 3, S3-S5, Fig 3B). This distance also corresponds to the spacing of parallel actin filaments (d_p-fil) in this plane and the ɑ-actinin-2 binding sites on them in the basketweave lattice structure [5]. It is also in broad agreement with our previous estimate for the transverse distance of 24 nm measured in fixed cardiomyocytes using 3D dSTORM followed by PERPL analysis [26]. Interestingly, the Z-discs in the cardiomyocytes were more likely to have adopted the small square lattice form, as the cells were predominantly relaxed when fixed, and thus the lattice spacing would be expected to be about 10–20% smaller.

For ɑ-actinin-2, the best model also included a short characteristic distance at 10 ± 8 nm between localisations in the transverse plane. The Adhiron binds to the calponin homology (CH) domains of ɑ-actinin-2, which are located either side of the actin filament. Thus, the 10 nm distance could arise from by binding of Adhirons to either side of the actin filament (Fig 3A). However, we do not have an explanation for an additional characteristic distance of 51 ± 8 nm, a small component in the best ɑ-actinin-2 model (Table 3). We did not find a distance matching the spacing between anti-parallel actin filaments in the model, and the background term is a large contribution to the total RPD (Fig 2D). This suggests that the transverse separation between ɑ-actinin-2 binding sites is relatively consistent between binding sites on parallel filaments in a square lattice structure (d_p-fil), but less consistent between binding sites on anti-parallel filaments. A long-range variability of the displacement between the anti-parallel filament lattices may account for this (Fig 3B).

For Z1Z2, the best model also included distances at 1/√2 times (19 ± 7 nm; mean ± σ_broadening, fitted s.d.) and √2 times (38 ± 7 nm) the repeating value of 27 ± 7 nm between localisations in the transverse plane. These distances could arise from distances between anti-parallel actin filaments (1/√2 × lattice constant) and between second-nearest neighbour parallel filaments (√2 × lattice constant) in the small square lattice structure. The second most likely model for the transverse arrangement of Z1Z2, which was 3.5 times less likely to describe the true pattern, also contained the distances at 19 nm and 38 nm (between anti-parallel filaments) but lacked the distance at 27 nm (between parallel filaments) (S4 Fig). We conclude that the transverse distances between Z1Z2 titin domains are on a square lattice structure with a lattice constant of d_p-fil / √2 (Fig 3B).

Finally, for ZASP, the best model also included a second peak at twice the main distance of 28 ± 9 nm in the transverse plane, although it made a very small contribution to the total model RPD and its centre was beyond the maximum distance fitted. This peak may simply account for a very slightly higher density than a simple flat background at longer distance values. We therefore conclude that ZASP is most consistently found separated by the distance between parallel actin filaments in the transverse plane, similar to our conclusion for the ɑ-actinin-2 -actin binding site.

Adhirons – labelling and specificity

Three different Adhirons were used, raised against the calponin homology (CH) domains of ɑ‑actinin-2, the Z1Z2 repeats of titin, and the protein ZASP. We have briefly reported on these Adhirons previously [27]. Once isolated, the coding sequence is subcloned into a bacterial expression vector containing a unique C-terminal cysteine. The Adhirons were expressed in BL21 STAR (DE3) E. coli (Life Technologies, Invitrogen) and affinity purified using Ni-NTA resin (Thermo Scientific) as previously described [25,27]. Briefly, a single colony was used to inoculate a 2 ml overnight culture of LB media supplemented with 100 µg/mL carbenicillin. Then, 50 ml LB media plus antibiotic was inoculated with 1 ml of the overnight culture and grown at 37 °C and 230 rpm to an OD₆₀₀ between 0.6–0.8. Protein production was induced by addition of IPTG 0.1 mM and incubated for a further 20–22 hr, at 25°C and 150 rpm before harvesting. His-tagged proteins were lysed in 1 ml Adhiron lysis buffer (50 mM NaH₂PO₄, 300 mM NaCl, 30 mM Imidazole, 10% Glycerol, 1% Triton X-100, pH 7.4) supplemented with 0.1 mg/ml lysozyme, Halt protease inhibitor cocktail and 10 U/ml benzonase nuclease (Millipore, Burlington, MA). The lysate was then incubated with 200 µl of washed NiNTA His-Pur slurry (ThermoFisher Scientific) for 2 hr, washed with Adhiron wash buffer (50 mM NaH₂PO₄, 500 mM NaCl, 20 mM Imidazole, pH 7.4) and eluted in Adhiron elution buffer (50 mM NaH₂PO₄, 500 mM NaCl, 300 mM Imidazole, 20% glycerol, pH 7.4).

For iPALM, the Adhirons were labelled with AlexaFluor647, via a maleimide linkage to a unique cysteine residue at the C-terminus, and then further purified to remove extraneous dye as previously described [25]. Briefly, 150 µl of 40 µM Adhiron solutions were incubated with agitation at room temperature with 150 µl tris (2-carboxyethyl)phosphine (TCEP) immobilised resin (ThermoFisher Scientific) for 1 h. The solution was centrifuged (1 min at 1500 x g) and 130 µl of the supernatant transferred to a fresh tube containing 6 µl of 2 mM dye-maleimide (AlexaFluor-647-C2 maleimide, A20347 Invitrogen) and incubated at room temperature for 2 h. The reaction was quenched with 1.3 µl β-mercaptoethanol for 15 min at room temperature. Excess label was removed using Zeba dye and biotin removal columns (Thermo Scientific) as per the manufacturer’s instructions, followed by dialysis into PBS.

Target protein production

The calponin homology (CH) domains of ɑ-actinin-2 were expressed and purified as previously described [53], the Z1Z2 repeats of titin (residues 1–200) [27], the end of Z2 repeat to the beginning of the Zr5 domain of titin (residues 201–598) and the protein ZASP PDZ (residues 1–89) [27] were subcloned in pGEX-6P-1 between the BamHI and EcoRI sites. Target proteins were expressed in Escherichia coli BL21 Rosetta 2 (Novagen) and purified using GST-tag affinity chromatography. Briefly, a single colony was used to inoculate a 7 ml overnight culture of 2YT media supplemented with 100 µg/mL carbenicillin and 34 µg/mL chloramphenicol. Then, 400 ml LB (ɑ-actinin-2) or 500 ml TB media plus antibiotics was inoculated with 5 ml of the overnight culture and grown at 37 °C and 230 rpm to an OD600 between 0.6–0.8. Protein production was induced by addition of IPTG 0.5 mM and incubated for a further 3 h at 37 °C and 230 rpm or 2 h at 25 °C and 150 rpm before the temperature was reduced to 25°C for a further 16–18 h. Cells were harvested at 4000 x g at 4 °C for 20 mins. Harvested pellets were lysed in GST lysis buffer (50 mM Tris-HCl, 500mM NaCl, 1 mM DTT, 1 mM EDTA, 1% Triton X-100, pH 7.4) supplemented with 1x HALT protease inhibitor cocktail, 1 mg/ml lysozyme and 3U/mL benzonase followed by sonication (6 cycles of 10 s on/off pulses), centrifuged (20,000 x g, 30 min). Lysates were then incubated with 1.25 mL washed Glutathione Resin (Amintra) for 1hr. Resin was washed five times with GST Wash buffer (50 mM Tris-HCl, 500 mM NaCl, 1 mM DTT, 1 mM EDTA, pH8.0) and proteins eluted with GST Elution buffer (50 mM Tris-HCl, 500 mM NaCl, 1 mM DTT, 1 mM EDTA, 20 mM reduced glutathione, pH 7.4).

Immunoprecipitation and immunoblotting

Immunoprecipitations used His-Tag Dynabeads (ThermoFisher). Dynabeads were incubated with 50 µg Adhirons in 1x casein blocking buffer (SigmaAldrich) in wash buffer (100 mM sodium-phosphate, pH 8.0, 600 mM NaCl, 0.02% Tween-20) for 10 min and rinsed with wash buffer. Beads were then incubated with target proteins at a 1:1 molar ratio for 1 h at room temperature. Following three washes, proteins were eluted by incubation in His elution buffer (300 mM Imidazole, 50 mM sodium phosphate, pH 8.0, 300 mM NaCl, 0.01% Tween-20) for 10 min. Immunoprecipitants were heated in 4x SDS-sample buffer (200 mM Tris-HCl, 8% SDS, 20% glycerol, 10% mercaptoethanol, 0.1% (w/v) bromophenol blue, pH 7) and run on a 15% SDS-PAGE gel at 120V before transfer to nitrocellulose membrane using the BioRad Transblot Turbo. Membranes were then blocked in 5% milk in tris-buffered saline – 0.1% Tween 20 (TBS-T) incubation with rabbit anti-GST-HRP (1:10,000; Abcam, ab3416) or rabbit anti-6xHisTag-HRP (1:10,000; Abcam, ab1187) for 1 h at room temperature. Membranes were rinsed three times with TBS-T before development using Immunoblot Forte Western HRP (Millipore), according to the manufacturer’s instructions. Blots were imaged using an Amersham Imager 600 (GE Healthcare, Chicago, IL).

SPR analysis

The affinities of ZASP-Adhiron 6 and Z1/Z2-Adhiron 12 for GST-ZASP PDZ, GST-Z1/Z2, GST-α-actinin-2 CH domains and GST-end Z2 to Zr5 were determined by surface plasmon resonance (SPR) using a BIAcore 1K+ (Cytiva). Adhiron proteins with a C-terminal cysteine residue were biotinylated with biotin-maleimide (SigmaAldrich) as previously described [25]. Biotinylated Adhirons (10nM) were captured on streptavidin chips (Biacore) to a density for a predicted Rmax binding signal of <100RUs. Binding assays were performed at 25°C in PBS plus tween 20 (0.05% v/v). GST-Z1/Z2, GST-ZASP PDZ, GST-α-actinin-2 and GST-End Z2 to Zr5 were injected at 0.0, 1.5625, 3.125, 6.25, 12.5, 25, 50, 100, 200 and 400nM at a flow rate of 30μl min-1, for 3 minutes followed by a 5 min dissociation phase and a 30 second regeneration step with K2CO3 0.1M. Sensorgrams were processed by “double referencing” with subtraction of the signals from a reference flow-cell and from the zero concentration blank. The on- and off-rates and KD parameters were obtained from a fit to the lowest three concentrations using a 1:1 Langmuir model, using the BIAevaluation software.

Myofibril sample preparation

Frozen pig hearts were obtained from Pel-Freez Biologicals. The heart was allowed to thaw, small pieces (approximately 200–300 mg each) were excised from the left ventricular muscle wall using a scalpel and used to generate myofibrils using a similar approach to those used to generate mouse heart myofibrils [54]. Briefly, ~ 250 mg of muscle was placed into 1 ml of K60 buffer + BDM in an eppendorf and rinsed 2–3 times until the buffer was mostly clear. K60 buffer contains 1 x Protease inhibitor cocktail (Sigma P8340). The muscle was then transferred into 1 ml of K60 buffer in a 5 ml Eppendorf tube on ice and homogenised using a tissue tearor, at max speed (~21K RPM) for ~30s, repeated twice until no visible intact tissue remained. The mixture was then transferred to a 1.7 ml Eppendorf tube, and centrifuged at 4°C, 1000 g for 10 minutes. The supernatant was removed, and the pellet resuspended in K60 buffer containing 1% Triton X-100, then incubated on ice for 30 minutes. The mixture was vortexed twice during this incubation. The mixture was then centrifuged at 4°C, 1000 g for 5 minutes, the supernatant removed and the pellet resuspended in 1 ml K60 buffer. This mixture was then centrifuged at 4°C, 1000 g for 5 minutes, the supernatant removed, and the pellet resuspended in K60 buffer supplemented with 0.1% BSA, 10mM DTT and 1 mM EGTA. If not used immediately, myofibrils were stored for up to a week in the final K60 buffer containing 50% glycerol at -20°C. We thank David Warshaw’s group for sharing this detailed protocol with us [54].

To stain myofibrils, ~ 50 µl of resuspended myofibrils in K60 buffer (containing 0.1% BSA) were added to a 25 mm diameter round coverslip (CS-25R17, #1.5 thickness; Warner Instruments) embedded with gold nanorod fiducial markers (A12-40–600-CTAB; Nanopartz) and allowed to attach for ~2 minutes. If using myofibrils stored in glycerol, ~ 50 µl was removed and placed in a 1.7 ml Eppendorf, 450 µl of PBS was added, and the mixture was centrifuged at 2000 rpm for 5 minutes at 4°C. The supernatant was removed, and the pellet resuspended in 50 µl of PBS containing 0.1% BSA and then added to the coverslip. The coverslip was washed gently once with phosphate buffered saline (PBS), before fixing the myofibrils using 4% paraformaldehyde in PBS for 5 minutes. The coverslip was washed once with PBS, excess liquid removed, and PBS containing 2% BSA was added to the coverslip (blocking step) for 10 minutes. Excess solution was removed, and the fluorescent Adhiron added, diluted 1/10–1/20 depending on the concentration of the Adhiron, in PBS containing 0.2% Triton X 100. The coverslip was incubated at room temperature with the Adhiron for ~20–30 minutes at room temperature, or overnight at 4°C. The coverslip was then washed twice with PBS containing 0.2% Triton X 100 and briefly stored in PBS before mounting in the imaging chamber.

17mg/mL Catalase (C100-50MG, Sigma-Aldrich) and 70mg/mL Glucose Oxidase (G-2133–50KU, Sigma-Aldrich) solutions were prepared in Buffer A (10mM Tris pH 8.0 + 50mM NaCl). Both were mixed in a 1:4 volume ratio to prepare GLOX solution. This was centrifuged and only the supernatant was used. 1M cysteamine (30070-50G, Sigma-Aldrich) solution was prepared in 0.25N HCl. The STORM buffer was prepared by combining GLOX solution, 1M cysteamine, and Buffer B (50mM Tris pH 8.0 + 10mM NaCl + 10% Glucose) in 1:10:90 volume ratio. The sample coverslip was covered with STORM-buffer. An 18 mm diameter round coverslip (CS-18R17, #1.5 thickness; Warner Instruments) was placed centrally on top of the sample and the boundary was sealed with Valap (https://cshprotocols.cshlp.org/content/2015/2/pdb.rec082917) to create a sandwich mounting.

Sample imaging

iPALM imaging was performed similarly to as described in previous work [18,20,55–57]. The Alexa Fluor 647-labelled samples were excited using 647 nm laser (Opto Engine LLC) excitation at ca. 2–3 kW/cm² intensity in TIRF conditions. The gold fiducials embedded in the coverslip were used for calibrating interferometry. 100,000 images were collected through dual Nikon Apo TIRF 60x/1.49NA objective lenses coupled to a 647 nm long-pass filter (LP02–647RU, Semrock), and acquired via three EMCCD cameras (DU987E, Andor) at 30 ms exposure. The field-of-view (FOV) varied from 30–40 µm.

iPALM data preprocessing

As described in [18,20,55–57], the iPALM data was processed/localized using PeakSelector software (Janelia Research Campus). The gold fiducials embedded in the coverslip were used for drift correction. We used the grouped xyz position output as final localisation coordinates. z is depth through the sample along the optical axis.

Z-disc segmentation

Z-discs were segmented from iPALM reconstructions as reported previously [34]. Briefly, the point cloud data from each FOV was rendered as a 3D histogram with 50-nm bin size in x, y and z. The Z-discs in each image were then segmented using Ilastik’s pixel classification and object classification workflow, implemented through the graphical user interface (see Supplementary Videos 1–8) [33]. The underlying localisations (point-cloud data) for each Z-disc were then extracted from these segmented histograms. Z-disc dimensions and volume were then calculated respectively using principal component analysis (PCA) and the convex hull of the localisations. Sarcomere length was measured using the line selection tool in Fiji.

PERPL modelling

The organisation of each protein in the Z-disc in both the axial direction (cell axis, y) and in the transverse plane (x,z) was modelled using PERPL [26] (S3 Fig). Briefly, PERPL calculates the relative position distribution (RPD) for the proteins, fits RPD models generated from hypothetical models of organisation in real space and gives relative likelihoods for these models. Each model RPD is constructed by summing terms for: the background from randomly distributed localisations, N_peaks number of peaks for the characteristic distances of type, d_type, between the localisations; and the independent RPD resulting from repeated localisation of the same dye molecule (repeats).

The point-cloud for each Z-disc was pre-processed in preparation for PERPL analysis. First, the line of each Z-disc in its x,y view was aligned along x using 2D PCA, leaving z unchanged. Next, density-based spatial clustering of applications with noise (DBSCAN) was applied to each Z-disc to remove outlier localisations far from the main body of the Z-disc, implemented in visualisation software Open3D [42,58]. The two parameters for DBSCAN, epsilon (ε) and minimum points (minPts), were separately optimised for each Z-disc between ε: 50 – 150 nm and minPts: 3 – 7 by visually assessing the clustering result.

To generate the experimental RPD, the data was filtered by removing localisations with x, y or z precision above a threshold, σ_loc-max. The Euclidean distances between the resulting localisations were calculated up to 150 nm in the direction or plane being modelled. No limit was placed on the distances between localisations in the orthogonal directions, as this significantly reduced the number of distances available for modelling. From this set of distances, the final RPD was calculated as a kernel density estimate using Churchman's distributions for distances between localisations in 1D or 2D [59], up to a maximum distance, L_fit. To minimise the impact of edge effects in the transverse direction, L_fit was set well below the extent of the data in x,z (Tables 1, S2).

Background terms were a function of the relative distance (d) between localisations, including linear_1D (Ad + B, A ≤ 0, B ≥ 0), linear_flat (Ad + B, A ≤ 0, B ≥ 0 for 0 ≤ d < -B/A; 0 for d ≥ -B/A), linear_2D (Ad + B, A ≥ 0, B ≥ 0), linear_2D,int=0 (Ad, A ≥ 0), quad_2D (Ad + Bd², A ≥ 0, B ≤ 0), cubic_2D (Ad + Bd² + Cd³, A ≥ 0, B ≤ 0, C ≥ 0), None (no background term) or constant background level. A, B and C were optimised during fitting. 2D background options were extensions to PERPL based on the theoretical distribution of distances for randomly sampled points within a finite rectangle [60].

Peak type in the model RPD, d_type, was “int”, where peaks were at integer multiples of a single characteristic distance, a; “sq”, where peaks were at a, a√2, 2a; or “ind”, where characteristic distances were independent of one another. These peaks have a width defined by a Gaussian-like broadening term, σ_broadening, which is optimised for each model (rather than per-peak) during model fitting, to reflect experimental noise and biological variability [59, 26]. The characteristic distance values were optimised during model fitting. The term for repeat localisations of the same molecule (zero-distance) has a separate σ_broadening.

Model RPDs were fit to each experimental RPD by adjusting the model parameters to minimise the mean-squared error (MSE), having specified initial guesses and bounds for the parameter values. In the transverse plane, the count in the experimental and model RPD was divided by the distance, to avoid the fit being dominated by a parameter for a linearly increasing count as expected for a random 2D distribution (ignoring edge effects) [26,36].

We extended PERPL to allow the model RPDs to be procedurally generated. This allowed us to sweep over multiple pre-processing parameters and models to explore variability and inform final model selection in each case (S1 Table, S1 Data). Pre-processing filters were strengthened until remaining data was insufficient to generate a usable experimental RPD. For each protein and 3D model component (axial or transverse), we selected the lowest σ_loc-max (most precise localisations) at which models appeared to fit well and the longest L_fit for final model selection (Tables 1, S2, S1 Data).

For each experimental RPD, we selected the model with the lowest corrected Akaike information criterion (AIC_c) as the most likely, as in previous work [26]. AIC_c measures differences in information loss between different models for the same data, and therefore the relative likelihood that the models describe the true distribution from which the data is sampled. It penalises overfitting:

for models fitted by minimising MSE, where n is the number of datapoints, k is the number of free parameters, y is the experimental RPD and ŷ is the model RPD [61]. Models that had a relative likelihood ≥ 0.01 compared with the most likely model (∆AIC_c ≤ 9.21) were also identified [61]. Models with a fitted parameter value at its permitted bounds, negative background (not physically real) or large uncertainty on the parameter value (parameter uncertainty > parameter value) were rejected. AIC_c may not be used to compare models fitted to different data, so between different localisation filtering settings.