Figure 4:

(A) Shell radius as a function of the shell spontaneous curvature radius R₀ and scaffold unperturbed size R_scaf (normalized by the shell elastic energy length scale R_E), calculated by numerically minimizing Eq. 1, with scaffold chemical potential Δμ = −10k_BT, R_E = 30, subunit area $a=2.5r_{\ast }^2$, and excluded volume parameter ν = 0. The dashed line encompasses parameter values that lead to efficient scaffold packaging (see SI Fig. S1 for the amount of packaged scaffold as a function of these parameters). Outside of this region σ_s ≈ 0, leading to assembly of nearly empty shells (with a surface layer of scaffold and cargo) with sizes approximately equal to R₀, incomplete shells, or no assembly. The heat map in this region corresponds to the size of the complete but nearly empty shells. (B) Examples of incomplete assemblies that form in the dynamics simulations with overly short (top) or long (bottom) scaffold molecules. Parameters are (top) R₀ > 300 and L_s = 34, (bottom) R₀ = 4.5 and L_s = 84. Other parameters are as in Fig. 3. (C) The minimum and maximum shell radius (normalized by the shell elastic energy length scale R_E) that lead to assembly and cargo packaging, predicted by the theory for varying the scaffold length as a function of the scaffold packaging driving force Δμ, for fixed shell spontaneous curvature R₀ = 50. The left y-axis shows the shell size, while the right y-axis shows the corresponding scaffold length, showing that the shell size closely tracks the scaffold preferred size in this regime. The symbols correspond to maximum and minimum shell sizes obtained by numerically minimizing Eq. 1, and the lines show the asymptotic results (Eq. 7). For scaffold lengths above the maximum length, shells would be either incomplete or empty, whereas below the minimum length, shells will either be incomplete or have low packaging of scaffold and cargo. (D) The minimum and maximum shell radius (normalized by R_E) in the high intrinsic shell curvature regime (R₀ < R_E), calculated by numerically minimizing Eq. 1 (symbols) and from the asymptotic analysis Eq. (11) (lines) for R₀ = 8, R_E = 30, and ν = 0. Other parameters in (C) and (D) are the same as in (A).