Volume 110, Issue 3, Pages 646-660 (February 2016) Principles Governing the Self-Assembly of Coiled-Coil Protein Nanoparticles  Giuliana Indelicato, Newton Wahome, Philippe Ringler, Shirley A. Müller, Mu-Ping Nieh, Peter Burkhard, Reidun Twarock  Biophysical Journal  Volume 110, Issue 3, Pages 646-660 (February 2016) DOI: 10.1016/j.bpj.2015.10.057 Copyright © 2016 Biophysical Society Terms and Conditions

Figure 1 The monomeric building blocks underlying the SAPN self-assembly. (A) One domain on the monomer encodes an N-terminal pentamer (green), which aligns along the fivefold symmetry axis, and a C-terminal trimer (blue) centered at a threefold symmetry axis. (B) An archetypical monomer (from SAPN-K) with a molecular mass of 12,587.53 Da is shown, containing an N-terminal histidine tag, a pentameric oligomerization domain (green), a glycine linker (black), and a C-terminal trimeric oligomerization domain (blue). (C) The monomer’s domains allow a geometric fit along the symmetry axes of the five- and threefold rotational symmetry axes of an icosahedron or a dodecahedron. To see this figure in color, go online. Biophysical Journal 2016 110, 646-660DOI: (10.1016/j.bpj.2015.10.057) Copyright © 2016 Biophysical Society Terms and Conditions

Figure 2 Transmission electron micrograph of negatively stained SAPN-K. Projections of selected negatively stained SAPN-K particles sorted (left to right, top to bottom) according to their dimensions. (Asterisk) Average diameter of the 20 particles in these rows: 28 ± 3 nm. (Hash mark) Particle aggregates; (arrowhead) possible aggregate. Scale bar = 50 nm. See Fig. S2 for the entire gallery. Biophysical Journal 2016 110, 646-660DOI: (10.1016/j.bpj.2015.10.057) Copyright © 2016 Biophysical Society Terms and Conditions

Figure 3 Molecular weight and 2D morphology of SAPN-K derived by STEM. (A) Mass histogram. The distribution is described by six Gaussian curves. Particles with masses in the corresponding ranges are shown adjacent to the peaks; projection dimensions increase with particle mass. This can be seen more clearly in Fig. S2 where all of the particles measured are shown, similarly sorted according to mass. The two most predominant species have masses of 3.93 and 4.63 MDa (±0.37 MDa) (blue peak). The projections of these particles are generally circular; compare (A). (B) Comparison of the number of chains present in the STEM peaks with those of canonical Caspar-Klug T-number series particles. (C) Average circularity versus molecular weight of SAPN-K. Circularity is defined as 4π(area/perimeter2), with the upper and lower limits of acceptable 2D morphologies being defined as circles associated with vertices of a decagon and pentagon, respectively. To see this figure in color, go online. Biophysical Journal 2016 110, 646-660DOI: (10.1016/j.bpj.2015.10.057) Copyright © 2016 Biophysical Society Terms and Conditions

Figure 4 3D morphology and form factor of SAPN-R derived from SANS. (A) SANS data of the three SAPN-R samples (0.119, 0.289, and 0.435 mg/mL), best fitted by a polydisperse spherical core-shell form factor (solid lines). (B) A schematic of the PSS model, where t is the thickness of the shell layer. Here, rc is the radius of the core, and ρc and ρs represent the neutron scattering length density of the core and the shell, respectively. The solvent scattering length density (ρsolv) is considered to be the same as ρc. (C–E) DLS volume size plots (left) and negative stain TEM micrographs (right) for the three SAPN-R concentrations. (C) 0.119 mg/mL SAPN-R. DLS-derived particle size = 32.97 nm; peak width = 9.888 nm. (D) 0.289 mg/mL SAPN-R. Particle size = 33.58 nm; peak width = 9.450 nm. (E) 0.435 mg/mL SAPN-R. Particle size = 32.80 nm, peak width = 11.28 nm. The number of particles in the three micrographs correlates to the sample concentration, and the proportion of larger species present is about the same. Most imaged particles have roughly circular projections. Amino acid sequence of the SAPN species: MGHHHHHHGDWKWDGGLVPRGSDEMLRELQETNAALQDVRELLRQQVKQITFLRALLMGGRLLARLEELERRLEELERRLEELERAINTVDLELAALRRRLEELAR. To see this figure in color, go online. Biophysical Journal 2016 110, 646-660DOI: (10.1016/j.bpj.2015.10.057) Copyright © 2016 Biophysical Society Terms and Conditions

Figure 5 Geometric principles underlying the symmetric locations of SAPN. (A) The monomeric building block of the SAPN, containing trimeric (blue) and pentameric (green) oligomerization domains, is shown positioned with reference to a dodecahedron (with vertices on icosahedral threefold axes) and icosahedron (with vertices on icosahedral fivefold axes), and as a 60-chain assembly with icosahedral symmetry. (B) A 360-chain SAPN is shown in comparison with the all-pentamer scaffold used in viral tiling theory to model the surface structure of polyomavirus, where five-coordinated vertices in the tiling mark the centers of the fivefold protein clusters. Putative trimer locations of the SAPN are superimposed as blue dots, given by the central positions of three triangulated pentameric vertices. The 12 icosahedral fivefold symmetry axes are shown in gold, while the pentameric vertices proposed by viral tiling theory are in cyan. The middle image demonstrates that the trimeric locations are equivalent to the vertices of a T = 7d icosadeltahedral particle in Caspar-Klug theory. The 20 icosahedral threefold symmetry axes are shown in gray, while the trimeric vertices proposed by Caspar and Klug are in blue. (C) Adaptation of Twarock’s tiling model for tubular assemblies of viral capsid proteins with all-pentamer clusters. In the virus model, pentamers are positioned at the five-coordinated vertices; in the case of a SAPN particle, threefold clusters occur in addition at the positions marked as blue dots. Amino acid sequence of the SAPN species: MGHHHHHHGDWKWDGGLVPRGSDEMLRELQETNAALQDVRELLRQQVRQITFLRALLMGGRLLARLEELERRLEELERRLEELERAINTVDLELAALRRRLEELAR. To see this figure in color, go online. Biophysical Journal 2016 110, 646-660DOI: (10.1016/j.bpj.2015.10.057) Copyright © 2016 Biophysical Society Terms and Conditions

Figure 6 Graphical representation of the surface tessellation. (A) Spherical graph representations of the 240-, 300-, and 360-chain particles, indicating the positions of trimeric and pentameric clusters at the three- and five-coordinated vertices, respectively. (B) A planar representation of the surface tessellation corresponding to one triangular face (red triangle) of a tetrahedron in the 240- and 300-chain case, and icosahedron in the 360-chain case, corresponding to the spherical graphs in (A): small blue triangles denote trimeric clusters, while green circles denote pentameric clusters. The red triangle corresponds to the triangle identified in Step 3 in analogy to the Caspar-Klug approach for viruses. A representative asymmetric unit of the symmetry group is highlighted in dark-blue in each triangle. (C) The structures of the SAPNs are obtained by fitting the monomeric chains into the graph-theoretical models. To see this figure in color, go online. Biophysical Journal 2016 110, 646-660DOI: (10.1016/j.bpj.2015.10.057) Copyright © 2016 Biophysical Society Terms and Conditions

Figure 7 Spherical representation of the tessellation of the 120- and 180-chain models. (A) Spherical graphs corresponding to the 120- and 180-chain particles. (B) The corresponding SAPNs obtained by fitting the monomeric chains into the graph-theoretical models. To see this figure in color, go online. Biophysical Journal 2016 110, 646-660DOI: (10.1016/j.bpj.2015.10.057) Copyright © 2016 Biophysical Society Terms and Conditions