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# Design of biologically active binary protein 2D materials

An Author Correction to this article was published on 02 March 2021

## Abstract

Ordered two-dimensional arrays such as S-layers1,2 and designed analogues3,4,5 have intrigued bioengineers6,7, but with the exception of a single lattice formed with flexible linkers8, they are constituted from just one protein component. Materials composed of two components have considerable potential advantages for modulating assembly dynamics and incorporating more complex functionality9,10,11,12. Here we describe a computational method to generate co-assembling binary layers by designing rigid interfaces between pairs of dihedral protein building blocks, and use it to design a p6m lattice. The designed array components are soluble at millimolar concentrations, but when combined at nanomolar concentrations, they rapidly assemble into nearly crystalline micrometre-scale arrays nearly identical to the computational design model in vitro and in cells without the need for a two-dimensional support. Because the material is designed from the ground up, the components can be readily functionalized and their symmetry reconfigured, enabling formation of ligand arrays with distinguishable surfaces, which we demonstrate can drive extensive receptor clustering, downstream protein recruitment and signalling. Using atomic force microscopy on supported bilayers and quantitative microscopy on living cells, we show that arrays assembled on membranes have component stoichiometry and structure similar to arrays formed in vitro, and that our material can therefore impose order onto fundamentally disordered substrates such as cell membranes. In contrast to previously characterized cell surface receptor binding assemblies such as antibodies and nanocages, which are rapidly endocytosed, we find that large arrays assembled at the cell surface suppress endocytosis in a tunable manner, with potential therapeutic relevance for extending receptor engagement and immune evasion. Our work provides a foundation for a synthetic cell biology in which multi-protein macroscale materials are designed to modulate cell responses and reshape synthetic and living systems.

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## Data availability

Rosetta build, Rosetta build database, and all scripts used in this work are available upon request.

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## Acknowledgements

This work has been supported by the Medical Research Council (MC_UP_1201/13 to E.D.), HFSP (Career Development Award CDA00034/2017-C to E.D. and Cross-Disciplinary Fellow LT000162/2014-C to A.J.B.-S.), HHMI (D.B.), NIGMS and NHLBI (R01GM12764 and R01GM118396 to J.M.K. and 1P01GM081619, R01GM097372, R01GM083867, 1P01GM081619, U01HL099997 and UO1HL099993 to H.R.-B.), NCI (R35 CA220340 to S.C.B.) and a grant from AHA (19IPLOI34760143 to H.R.-B). We thank L. McKeane for artwork in Figs. 3 and 4, N. Chiaruttini for help with image segmentation and supported bilayers; A. Colomb for sharing his expertise in AFM on supported bilayers; H. McMahon, R. Mittal and F. Perez for their help with EGFR trafficking; A. Picco for help with microscope calibration; D. Levi for discussions; the Arnold and Mabel Beckman CryoEM Center at the University of Washington for access to electron microscopy equipment; the Mike and Lynn Garvey Cell Imaging Laboratory at the Institute for Stem Cell and Regenerative Medicine, University of Washington. AFM imaging was supported by the Department of Energy (DOE) Office of Basic Energy Sciences (BES) Biomolecular Materials Program (BMP) at Pacific Northwest National Laboratory (PNNL). PNNL is a multi-program national laboratory operated for DOE by Battelle under contract no. DE-AC05-76RL01830. Analysis of AFM data was supported by the DOE BES BMP at the University of Washington (DE-SC0018940). High speed AFM/SIM in the laboratory of C.F.K. was supported by the MRC (MR/K015850/1/ MR/K02292X/1), the Engineering and Physical Sciences Research Council (EP/ H018301/1, EP/L015889/1), Wellcome Trust (089703/Z/ 09/Z and 3‐3249/Z/16/Z), MedImmune and Infinitus. C.F.K. and I.M. acknowledge Bruker Nanosurfaces for the kind support for the Bioscope Resolve. We thank the Nikon Imaging Center at Harvard Medical School, in particular J. Waters, A. Jost and G. Campbell. SAXS at SIBYLS was made possible by the IDAT grant from DOE BER and NIH ALS-ENABLE (P30 GM124169) with support from beamline staff J. Bierma and J. Holton. We thank I. Xavier Raj for support to L.S. We thank L. Carter, C. Chow and the Institute for Protein Design (IPD) protein production core for support in expressing and purifying some of the design and experimental components.

## Author information

Authors

### Contributions

A.J.B.-S. and D.B. designed the research and experimental approach for protein assemblies. A.J.B.-S. and W.S. wrote program code and performed the docking and design calculations. A.J.B.-S. performed the experimental designs screening, electron microscopy, UV-vis and CD characterization. A.J.B.-S., M.C.J. and J.M.K. designed and analysed the results of electron microscopy, and M.C.J. performed electron microscopy sample preparation, imaging and image processing. F.J. and J.C. performed AFM imaging on mica substrates. F.J., J.C. and J.J.D.Y. analysed AFM data and contributed to manuscript preparation. A.J.B.-S., E.D., J.L.W., H.R.-B., S.C.B. and D.B. designed and developed experimental approach for arrays–synthetic membranes and arrays–cells assemblies. J.L.W. performed the imaging and analysis of array assembly onto supported lipid bilayers and living cells and all calibration measurements. E.D. developed image processing methods for arrays-membrane characterization. I.M. and C.F.K. performed correlative AFM–SIM on supported bilayers and subsequent analysis. A.B. performed the EGFR endocytic block experiments. G.L.H. and A.J.B.-S. performed the SAXS experiments and analysis. L.S. performed the TIE2 F domain–arrays binding and optical characterization with J.D. and with guidance from H.R.-B. S.M.J. prepared the spyTag–DLL4 protein, A.J.B.-S. and A.A.D. prepared the A–DLL4 conjugate, and A.A.D. performed the NOTCH1–A–DLL4 experiments and analysis. A.J.B.-S., E.D. and D.B. wrote the manuscript and produced the figures. All authors discussed the results and commented on the manuscript.

### Corresponding authors

Correspondence to Emmanuel Derivery or David Baker.

## Ethics declarations

### Competing interests

S.C.B. receives funding for unrelated projects from the Novartis Institutes for Biomedical Research and from Erasca. He is on the Scientific Advisory Board for Erasca, and is a consultant on unrelated projects for IFM and Ayala Therapeutics.

Peer review information Nature thanks Philippe Bastiaens and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Extended data figures and tables

### Extended Data Fig. 1 Dihedral building blocks inherent advantage for planar assemblies.

a, Model of two dihedral homooligomers, a D3 hexamer (left panel, four monomers in grey and a pair of monomers constituting a single interface are coloured in purple and magenta) and a D2 tetramer (right panel, two monomers in grey, with a pair of jointly interfacing monomers coloured in green shades). Both components are positioned such that their highest order rotation symmetry axis is perpendicular to the plane (blue arrows) and an additional two-fold (C2) in plane rotation symmetry axis of each component is aligned with the other component in plane C2 symmetry axis (red dashed line). b, Top, front, and diagonal views of the D2 homooligomer showing the symmetric nature of the interface. Due to the C2 rotation symmetry of the interface (within each building block) it can be considered as two smaller interfaces, this is illustrated by the two diagrams showing the rotated origin. c, At each monomeric interface (each monomeric interface constitutes exactly half of the full contact area between two interacting homooligomer) there are 6 ways for the interacting monomer pairs two deviate from the predicted, designed, conformation. These are the 6 DOFs between each two free objects in a 3D space, and could be classified to 3 translational and 3 angular DOFs. In c, the six panels decompose the six DOFs to show the outcome of local deviations at the monomeric interface on the homooligomeric interface geometry. It shows that due to the dihedral homooligomers C2 symmetry alignment all angular deviations (lower row) and cell spacing (this is the distance between the components and illustrated here with red arrows, upper left panel) are being counterweighted, as a result those would not propagate along the symmetric assembly. The remaining two translation DOFs, orthogonal to the cell spacing (two rightmost upper panels) would result in an in-plane twist (red curved arrow) that if too large may hinder correct propagation.

### Extended Data Fig. 2 Designed component solubility nearest neighbour (NN) model versus assembled array geometry.

a, Unit cell description. In the p6m plane symmetry unit cell there are exactly 2 C3 rotation centres (green triangles) and 3 C2 rotation centres (1 fully within the unit cell and 4 halves, blue small rectangles); for illustration purposes the design model is overlaid on top of the unit cell diagram. Unit cell length is X = 31 nm, and the distance between each two nearest A components or B components is denoted by dAarray and dBarray, respectively, and are equal to ~15nm and 17.5nm, respectively. b, Mean Nearest Neighbour distance in nm as a function of component concentrations. Based on the law of distribution of the nearest neighbour in a random distribution of particles we derive the average inter particle distance for a given component concentration, dANN and dBNN (ref. 65). The mean distance is given by $$D=0.55396\cdot {n}^{-1/3}$$ where $$n=\frac{N}{V\cdot Nd}$$, N is the number of monomers, V is volume in nm3, and Nd is the number of monomers in each homooligomer: 6 and 4 for D3 and D2, respectively. The vertical lines show the components distance upon assembly (dAarray and dBarray). Typically in our work co-assembly is initiated at components concentration around 5μM and below (range indicated by the red ellipse). The graph shows that under these concentrations the co-assembly process brings the components much closer to each other, as indicated by the two horizontal arrows. c, NN mean distance of components stored at high concentration (D3:[2.6μM,dANN = 8.7nm], D2:[2.2μM,dBNN = 8.0nm], see Supplementary Table 6) is shown with a full circle markers to the left of the vertical lines thus in these concentrations dANN< dAarray and dBNN< dBarray. This situation is interesting because here co-assembly practically draws the components apart, somewhat analogous to the ice/water expansion anomaly, and is substantially different from the typical process that occurs in one-component materials that assemble around a nucleation centre (we note that the components are drawn apart only within the plane, unlike the situation in ice). This unique phenomenon stems from the designable system properties: interface orthogonality, components stabilization, and sparse assembly geometry. d, Illustration of stock solution volumes required to generate a total of 1m2 of arrays. We note that in current processes multiple μm scale arrays or smaller are formed.

### Extended Data Fig. 3 In vitro assembly kinetics and AFM edge analysis.

a, Kinetics of array formation in solution monitored by light scattering, (mean ± SD; n = 3 experimental replicates; see methods for details). bh, AFM characterization of arrays on freshly cleaved mica substrates in fluid cell from a solution containing components at equimolar concentrations of 7μM. Arrays were assembled from A+B components or A–GFP+B as indicated. b, Left panel: height section profile along the white dashed line of an AFM image of growing A+B arrays (right panel). Note that this picture is the same as the one in Fig. 2e, reproduced here for convenience. c, Close up of the area in blue in b showing healing of lattice vacancy defects and growth (dashed to solid white circles). Elapsed time in minutes. Note that the left and middle pictures are the same as the ones in Fig. 2f, reproduced here for convenience. d, Structural comparison of A+B arrays (left panel) and A–GFP+B arrays (right panel). To extract the unit cell length, we further processed five images of arrays assembled from A+B components and fives images of arrays assembled from A–GFP+B components. Five pixels width Gaussian blur filter was applied to smooth the images (low pass filter) and a cross-section along the crystal lattice direction was used to assess the length of every five unit cells. A+B and A–GFP+B arrays unit cell length and standard deviation are calculated to be 31.51 ± 0.41nm (n = 14) and 31.57 ± 0.53nm (n = 20), respectively. e, High magnification detail of a A+B array. f, g, Edge analysis based on our ability to characterize edge states. By comparing arrays formed from A+B components (left panels) vs. arrays formed from A–GFP+B components (right panel). By analysing the profile along crystal lattice directions (indicated with white lines in f and as the white or red curves in g a measurable signal for the GFP fusions or the lack of it, can be measured. Lattice edge state analysis for the co-assembly of A–GFP units and B units assume the images capture equilibrium distributions of edge sites and are based on ∆G(i - j) = -kTln(pi/pj). We assume equilibrium states because assembly kinetics is significantly faster (see panel a and Extended Data Fig. 5f, g) than the experimental setup. This is further supported by the set of images in Fig. 2e, f and panel c above where we follow the dynamics of a single array at time points ranging from “zero” to 91 min which demonstrate mostly defects healing, and reshaping. For the edge state statistics we analysed 9 and 2 images for the A+B pair in liquid and air, respectively, and 6 and 3 images for the A–GFP+B pair in liquid and air, respectively. The calculated free energy differences between different edge states: ∆G(AGFP-II - AGFP-I) = -5.5 kJ/mol, ∆G(B-1 - AGFP-I) = -5.2 kJ/mol, and ∆G(AGFP-II - B) = -0.3 kJ/mol. Unit cell spacing, the distance between the centres of each two hexagons, is calculated by measuring the distance over a number of unit cells (white arrow in (f left panel) corresponding to the black arrow in (g left panel)). The arrow length is estimated at 215nm and unit cell spacing at 315Å (see methods) in close agreement with the design model 310Å). h, Lattice edge state statistics. Scale bars: (b, d) 200 nm, (c, e, f) 100 nm.

### Extended Data Fig. 4 Arrays ordered stacking.

a, In multiple TEM images either single or stacks of arrays are observed. Averaging the apparently indistinguishable conformations (four left panels) and pattern illustration of each (right four panels) revealed that in all cases arrays interact through a single contact point shown in the lowest panel (number 5, middle) which illustrates the lattice packing arrangements diagram on top of a.2. This diagram shows that those contact points are all between the vertical faces of the B component. Because the B component alone is soluble at mM concentrations (Supplementary Table 6 and Extended Data Fig. 2c) we assume that the stacking is an artefact of TEM grid preparation and that array assembly in solution proceeds solely in two dimensions (this is shown later by solution SAXS in Fig 2d, and Extended Data Fig. 5). b, Interacting B components from different arrays share the vertical rotation axis and are rotated around that axis by 60°, top and bottom panels show the alignment geometry from top and side views, respectively. c, Assuming this observation defines the way the system predominantly performs means that hexagon belonging to vertically interacting arrays can interact in three different ways, all including that similar B–B interaction at exactly two contact points, rendering those three interaction options to be energetically equivalent. Thus, we assume that when arrays interact all three possible options have the same probability. When an array is added to a single array all three contacting options will result in a similar outcome (panel a.2 and c.2). When a third and fourth layers are added, three different outcomes could be obtained (panels a and c 2-4). d, Definition: the probabilities to observe a certain pattern given the number of arrays in a stack. This analysis supports the assumption that given a hexagonal lattice is observed only a single layer is layered. e, Definition: given a pattern observation, the probability the observed pattern comprises a certain number of arrays. Again, observing a hexagonal array means that only a single array is layered, while observing a square lattice does not mean that only 2 layers are stacked, even though that is the situation with the highest probability. This also shows that an observation of pattern (4) does not provide any information about the number of stacked layers. The equations above each panel describe the different probability distributions.

### Extended Data Fig. 5 SAXS analysis.

a, Left and middle panels: Components A and B SAXS measurements (black curves) analysed using the Scatter program and SAXS profiles (magenta and blue for components A and B model (shown in insets), respectively) calculated using FOXS (ref. 66) and demonstrating excellent agreement (A: χ2 = 0.18, B: χ2 = 0.20) and no concentration dependence. Right panel: A+B mixture SAXS measurement (black curves) and ASU scattering profile (brown). Bragg peaks shown in the A+B SAXS data correlate with the p6 symmetry model and spacing of 303 Angstrom (see Supplementary Table 8) in close agreement with TEM data and design model. The ASU model (top right panel corner) comprises 12 monomers, 6 belonging to a single A component (D3 hexamer in magenta) and 6 more belonging to 3 halves of the B component (half of a D2 tetramer in blue). b, Negative stain TEM assembly validation for the components used for the SAXS experiments demonstrating the local expected order. c, Array models with increasing size, increasing number of ASUs, and 3D crystal model of stacked arrays as inferred from TEM analysis shown in Extended Data Fig. 4d. d, Scattering profiles of array models consisting of an increasing number of ASUs ([6, 9, 12, 15, 30, 36, 72, 108, 180] grey scale intensity corresponds to ASUs #) and selected models. A+B mixture SAXS measurement profile (as shown in a right panel) is shown as a black curve and circle markers demonstrating close agreement between the computational design model of the p6 array and structures formed in solution. e, Interpolation of measured arrays ASUs number and dimensions (assuming circular arrays) based on the fit to the models’ SAXS profiles intensity difference between the first peak minimum and maximum (see method) suggesting that in solution (unsupported) the two components form 2D arrays which constitute about 6,000 ASUs (tera-Da scale flat assembly) and are 1.8 μm in diameter. f, SAXS profiles collected directly after the mixture of array components at time points ranging from 30 s to 15 min. Each measurement was collected from a separate well to avoid accumulated damage to the samples. It is notable that within the first 30 s after components mixture at 10μM, distinctive Bragg peaks emerge. g, Time-resolved analysis of array dimensions using SAXS profiles from f based on the computational model analysis in ce. These newly formed arrays constitute only a few hexagons; however, this suggests that SAXS measurements enable a thorough kinetics study and potentially the construction of phase diagrams of macroscale 2D binary systems. Scale bars: (b) 500 nm.

### Extended Data Fig. 6 Preformed arrays cluster transmembrane proteins in stable assemblies.

a, b, Preformed arrays clusters characterization. a, 2D arrays formed in-vitro by mixing A–GFP+B in equimolar concentration (5 μM) in buffer (25 mM Tris-HCl, 150 mM NaCl, 5% glycerol) supplemented with 500 mM imidazole followed by overnight incubation at room temperature in eppendorf tube (total volume of 200 μl). After polymerization, solution is centrifuged, supernatant is discarded, and pellet is resuspend the same buffer. b, Negative stain TEM images of the resuspended array pellet (tenfold dilution, see methods). c, d, Clustering of transmembrane proteins by preformed arrays. c, Principle of the experiment: NIH/3T3 cells expressing GBP-TM-mScarlet are incubated with A–GFP+B arrays for 30 min leading to clustering of the mScarlet construct. This is the same scheme as in Fig. 3a reproduced here for clarity. d, After incubation with preformed arrays, live cells are processed for imaging by spinning-disk confocal microscopy. 3D z-stacks are acquired (11 μm, Δz = 0.2 μm) and processed for 3D reconstruction. Note that the intracellular mScarlet protein signal overlaps perfectly with the extracellular GFP signal of the array. e, f, mScarlet constructs clustered by the arrays are not dynamic. e, Cells were incubated with A–GFP+B arrays for 1 h at 37 °C, then the mScarlet signal was bleached and its fluorescence recovery monitored. The GFP signal was used to delineate the bleaching area. f, Quantification of the effect seen in a (see methods). The mScarlet signal (magenta curve) does not recover, suggesting that GBP-TM-mScarlet molecules are stably trapped by the A–GFP+B array. As a control that binding of A–GFP alone (that is, not in an array) does not affect fluorescence recovery of GBP-TM-mScarlet (meaning that the array does not recover because all the GBP-TM-mScarlet is trapped by the A–GFP+B array), we also performed FRAP experiments of GBP-TM-mScarlet in cells incubated with A–GFP alone (purple curve). As expected, these recovers. Scale bars: (d) 12 μm; (e) 6 μm.

### Extended Data Fig. 7 TIE2 receptor clustering and CD31/VE-Cad recruitment.

ac, Clustering of TIE2 receptors. Imaging of cells incubated for 60 min with GFP-positive arrays functionalized with the F domain of the angiogenesis promoting factor Ang1 (a, c), or not (b), then fixed and processed for immunofluorescence with TIE2 antibodies (a, b), CD31 (c, left two panels) or VE-CAD (c, right two panels) antibodies. Note that TIE2 signal is dramatically reorganized and colocalizes with the array (compare a and b). c, Recruitment of CD31 and VE-Cad under the F domain array (arrows), together with the extensive Actin remodelling (Fig. 3f and inset to a left panel), suggests that the structure induced by the array is a precursor to adherens junction. d, Negative stain TEM validation of arrays formation using pre-functionalized components A–SC–ST–fD+BcGFP A component with a genetically fused spyCatcher peptide fused to spyTag-fDomain (see Supplementary Table 10 for sequences), and cyclic B component with genetically fused GFP). e, Assembly of TIE2 cluster via on-cell assembly of arrays is as potent at inducing AKT signalling as preformed arrays. The A(c)fD alone elicits much less AKT phosphorylation alone than when assembled into arrays by the B subunits on cells. Assembly here is done sequentially as in Fig. 4 by first incubating with A(c)fD followed by extensive washing of unbound A(c)fD, then by adding the B subunit. As a reference, cells were treated with preformed A(c)Fd+B arrays. Induction of phospho AKT is similar between A(c)fD+B arrays assembled on cells or pre assembled. Scale bars: (ac) 2.5 μm, (d) 500 nm.

### Extended Data Fig. 8 Component desymmetrization.

ad, B-component desymmetrization. a, left panel: model of the B component dihedral homooligomer (grey, with the arrays forming interfaces in purple) with GFP fusions (green), blue arrow pointing towards a perpendicular direction to the plane. Right panel: model of a cyclic B component with only two GFP fusions both facing to one vertical direction, note the purple region remain unchanged. b, Left panel: illustration of the consequences of the binding of a dihedral homooligomer to a flat surface like a lipid bilayer through GFP/GBP interactions: array interfaces are either blocked or facing a direction which is not parallel to the plane. This thereby may induce membrane wrapping and assembly block because propagation interfaces are facing the membrane. Right panel: Ideal binding conformation with the purple arrows indicating the propagation direction when a cyclic component binds to the same membrane. This does not induce any membrane remodelling. c, Schematics of the linker insertion protocol. In the D2 dimer, C- and N-terminal ends are adjacent (left panel, arrows pointing on the terminals). A linker is designed to connect the two (middle panel) resulting in approximately twice as big a monomer which forms a C2 homooligomer (right panel). d, Negative stain EM images of arrays made of B(c) or B(c)GFP and various A components. eh, A component desymmetrization. e, Left panel: A component dihedral (D3) model, two monomers (coloured green to red) and red arrow pointing on the designed array interface direction. Middle panel: Various fragments build between the C-term of one monomer to different positions near the N-term of the second monomer. Right panel: Model of the cyclic A components with the new linkers indicated in blue, note that again arrays interfaces remain unchanged. f, Negative stain EM screening for hexagonal assemblies. Top panel shows cyclic A components genetically fused to GFP (A(c)GFP) with dihedral B components, while in the bottom panel both components are cyclic. g, h, Cyclisation of the A component enables array assembly on cells. Stable NIH/3T3 cells constitutively expressing GBP-TM-mScarlet were incubated with 1 μM A-GFP (g) or 1 μM A(c)GFP (h), rinsed in PBS, then 1μM unlabelled B was added and cells were imaged by spinning-disk confocal microscopy. Images correspond to a single confocal plane of the GFP channel. On the contrary to dihedral A, cyclic A enables rapid array assembly on cells, as seen by the characteristic appearance of diffraction limited, GFP-positive spots (see inserts and also Fig. 4 and main text). See also Supplementary Fig. 7 for additional discussion, rationale of component desymmetrization, and computational protocol. Scales bars: (d) 500 nm (100 nm in inserts); (g, h) 10 μm, 2 μm for insets.

### Extended Data Fig. 9 Correlative SIM/AFM of arrays assembled onto supported bilayers.

a, Design of the assay (see also methods): a supported lipid bilayer containing 5% biotinylated lipids and 0.2% fluorescent lipids is formed onto a glass coverslip in a flow cell. B(c)mSA2 (200 nM) is then injected into the chamber to bind to biotinylated lipids. After washing the excess of unbound B, A–GFP (20 nM) is injected into the chamber. After assembly for 5 min, the chamber is extensively washed and the sample fixed. The top lid of the chamber is then removed, and the sample is imaged by Super-resolution structured illumination microscopy (SIM) imaging from the bottom and atomic force microscopy (AFM) from the top. This correlative imaging allows one to find the arrays by light microscopy, before increasing the magnification to determine their degree of order by AFM. Note that the sequential mode of assembly used here is conceptually identical to the assembly of arrays onto cells (Fig. 4). Indeed, the cyclic B component B(c) is used to anchor the array to the membrane via its monovalelent functionalization moiety (mSA2 here compared to GFP on cells), and assembly can only happen on the membrane, as there is no free B(c)mSA2 in solution. Accordingly, arrays assembled onto supported bilayers by this method are very similar to arrays assembled on cells when imaging with diffraction-limited microscopy (see b, left panel). b, Low magnification image of arrays assembled as above obtained by correlative Widefield microscopy (left panel), SIM super resolution microscopy (middle panel) and AFM (right panel). Super-resolution imaging indicates that arrays appearing as diffraction-limited spots by widefield microscopy can actually be somewhat elongated structures. This is in remarkable agreement with our observation that arrays assembled on cell membranes can fuse post-assembly (Fig. 4b, c for quantification). This further confirms that assembly on supported bilayers and on cells are similar. c, Examples of topography in the image presented in the b-right panel. Note that height measured by AFM is uniform at about 3-4 nm, confirming 2D growth. d, High-magnification images of arrays seen in c by fast AFM, demonstrating high hexagonal order of the polymer onto supported bilayers (see methods; Note that the bottom right panel is identical to Fig. 4f, reproduced here for convenience). Lookup table corresponds to amplitude between 0 and 455, 475 and 410 p.m. for the top, bottom left and bottom right panels, respectively. From bd, we conclude that the height and the size of the lattice on membranes is exactly as expected from the design model (Fig. 1), the EM imaging of arrays assembled in solution (Fig. 2a–c, Extended Data Fig. 8), the SAXS measurements of arrays assembled in solution (Fig. 2e, Extended Data Fig. 5) and the AFM measurements on mica substrates (Fig. 3, Extended Data Fig. 3). This confirms that assembly on membranes leads to ordered arrays and also validates that our quantitative light microscopy measurements (Fig. 5e, Extended Data Fig. 10) are a valid proxy for bulk order evaluation. Scale bars: 5 μm (b) 50 nm (d).

### Extended Data Fig. 11 Control of array size, and 2D/3D EGFR clustering.

ae, Array size controls the extent of their endocytosis block. a, Measurement of the surface density of GBP-TM-mScarlet as a function of GBP-TM-mScarlet expression levels. Stable NIH/3T3 cells expressing GBP-TM-mScarlet under Doxycycline (Dox)-inducible promoter where treated with increasing doses for Dox for 24h, then briefly incubated with purified GFP and the amount of immobilized GFP per cell was assessed by flow cytometry (mean fluorescence per cell, n > 4000 cells/sample). b, c, Cells as in a were incubated with 1 μM B(c)GFP, rinsed in PBS, then 0.2 μM unlabelled A was added and cells were imaged by spinning-disk confocal microscopy. The average number of B(c)GFP molecules per array was then estimated (median ± error, b), as well as the GFP/mScarlet intensity ratio (c). Number of spots/cells analysed, respectively: 0.1 μg/mL Dox: 4602/41 ; 0.5 μg/mL Dox: 2670/32 ; 2 μg/mL Dox: 6439/55. Dox induction increases the number of B(c)GFP, meaning array size can be modulated by controlling receptor density at the cell surface. Clustering activity scales accordingly. d, Cells as in b were treated with increasing doses of Dox for 24h, then incubated with 0.5 μM B(c)GFP, rinsed in PBS, then 0.5 μM unlabelled A was added (or not). After 60 min, cells were briefly incubated with Alexa-633-coupled Wheat Germ Agglutinin to label cell membranes, then cells were fixed and imaged by spinning-disk confocal microscopy. Images correspond to single confocal planes. Images correspond to quantification displayed in Fig. 4i. e, Graphical summary illustrating the extent of the endocytic block (d) as a function of the initial mean number of B(c)GFP per array (see b). For reference, the apparent diameter of arrays as a function of their B(c)GFP content, the size of 60mer nanocages (I3) and Clathrin Coated Pits (CCP) are also figured. (f, g) Clustering of EGFR into a 3D spherical geometry does not induce endocytic block. f, Endogenous EGF receptors (EGFR) on HeLa cells were clustered using a fusion protein binding both GFP and EGFR (GBP–EGFR DARPIN) and either 3D icosahedral nanocages functionalized with GFP, or trimeric GFP unassembled building block as a control. After varying chase time, cells were fixed, processed for immunofluorescence with anti-LAMP1 antibodies and imaged by spinning-disk confocal microscopy. Images correspond to single confocal planes, and side panels correspond to split-channel, high-magnification of the indicated regions. g, Automated quantification of the colocalization between GFP and LAMP1 in the samples described in f. n indicates number of cells analysed per condition. Statistics were performed using an ANOVA1 test (P < 0.001) followed by Tukey’s post hoc test (P value of each comparison test indicated in panel). There is very little (if any) endocytic block for EGF receptors clustered with the 60mer nanocages as the percentage of colocalization is similar between control GFP trimers and GFP 60mer icosahedron. hk, Clustering of EGF receptors via arrays induces endocytic block. h, Experiment scheme: Serum-starved HeLa cell were incubated with 20 μg/mL GBP–EGFR DARPIN in DMEM-0.1% serum, then washed in DMEM-0.1% serum, then incubated with 0.5 μM B(c)GFP in DMEM-0.1% serum, then washed in DMEM-0.1% serum, then 0.5 μM A in DMEM-0.1% serum is added. Cells are then either imaged live (i) or incubated in DMEM-0.1% serum for 40 min before fixation and processing for immunofluorescence using anti-LAMP1 antibodies (k). i, Addition of A induces rapid clustering of EGFR, in a similar fashion to the GBP-TM-mScarlet construct (see Fig. 4b). j, Automated quantification of the number of tracks of arrays as a function of time reveals that the dynamics of array formation is fast and quantitatively similar to the GBP-TM-mScarlet construct (compare with Fig. 4c). This suggests that the fast kinetics seen in Fig. 4a–c are not due to the properties of this single-pass synthetic model receptor, but are rather a property of the arrays themselves. k, EGF receptors on HeLa cells were clustered (or not) as in h. Cells were then fixed and processed for immunofluorescence using LAMP1 antibodies and imaged by spinning-disk confocal microscopy. After 40 min chase, unclustered EGFR extensively colocalizes with the lysosomal marker LAMP1, while clustered EGFR stays at the plasma membrane, suggesting that array-induced 2D clustering of EGFR inhibits its endocytosis. Images correspond to maximum-intensity z-projections across entire cells (insets correspond to single confocal planes). Images correspond to split channels of Fig. 4g. EGFR clustering did not trigger EGF signalling, presumably because the distance between receptors in the cluster is longer than within EGF-induced dimers (data not shown). Scale bars: 10 μm (d, f, i, left panel and k) and 1 μm (f, k insets and i, right panel).

## Supplementary information

### Supplementary Information

This file contains Supplementary Methods, Supplementary Figures 1-9, Supplementary Tables 1-10, and Supplementary References.

### Supplementary Video 1

Design strategy PyMOL illustration: dock, design, and propagation PyMOL illustration demonstrating the docking process, benefits of dihedral components for planar assemblies, and the propagation of ordered structure.

### Supplementary Video 2

Instantaneous gelation upon components mixing Mixture of 10 μL dihedral A component at 2 mM into 10 μL of 1 mM B(c)mScarlet (note mixture ratio of 1:2 due to symmetry differences). Upon addition of the second component, the mixture goes through immediate gelation which impairs further pipetting.

### Supplementary Video 3

Clustering of intracellular mScarlet constructs by preformed arrays NIH/3T3 cells expressing GBP-TM-mScarlet were incubated with 10 μl/mL of preformed A–GFP+B arrays and were imaged immediately by spinning disk confocal microscopy. Upon landing onto the cells, AGFP+B arrays quickly cluster the GBP-TM-mScarlet construct.  This movie corresponds to Fig. 3b, c. Scale bar: 6 µm.

### Supplementary Video 4

3D rendering of cell incubated with preformed arrays NIH/3T3 cells expressing GBP-TM-mScarlet were incubated with 10 μl/mL of preformed A-GFP+B arrays and were imaged immediately by spinning disk confocal microscopy after 30 minutes. 3D stacks were then processed for 3D reconstruction. This movie corresponds to Fig. 3d and Extended Data Fig. 6d.

### Supplementary Video 5

Stability of receptor clustering assessed by FRAP GBP-TM-mScarlet expressing NIH/3T3 cells were incubated with the A–GFP+B arrays for 1 hour at 37 °C, then the mScarlet signal was bleached and its fluorescence recovery monitored by spinning disk confocal microscopy. Left panel, quantification (see methods). mScarlet signal does not recover, suggesting that arrays cluster stably the GBP-TM-mScarlet construct. This movie corresponds to Figure Extended Data Fig. 6e, f. Scale bar: 6 µm.

### Supplementary Video 6

Growth of arrays onto cells NIH/3T3 cells expressing GBP-TM-mScarlet were incubated with 1 µM B–GFP, rinsed in PBS, then 0.2 µM unlabelled A was added and cells were imaged by spinning disk confocal microscopy. Upon addition of A, numerous foci positive for extracellular B–GFP and intracellular mScarlet appear and subsequently fuse with each other. This movie corresponds to Fig. 4a–c. Scale bar: 12 µm.

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Ben-Sasson, A.J., Watson, J.L., Sheffler, W. et al. Design of biologically active binary protein 2D materials. Nature 589, 468–473 (2021). https://doi.org/10.1038/s41586-020-03120-8

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• ### Ordering protein arrays on cells

• Lei Tang

Nature Methods (2021)