(A) The mathematical model used in the main text corresponds to the simplest case where the density of available NTR binding sites within the FG network is uniform throughout the channel (i.e. has no dependence on the position along the NPC axis). In reality, accumulating evidence indicates that the density of the FG motifs, and consequently the free energy profile, vary along the pore (Lowe et al., 2010; Tagliazucchi et al., 2013; Tu et al., 2013; Lowe et al., 2015). The top panel depicts one such experimentally motivated density profile, which includes a high density 'barrier' region of high FG Nup density at the centre of the pore () (which also increases the cost of insertion in this region [Ghavami et al., 2016; Tagliazucchi et al., 2013]); the low density ( cytoplasmic 'docking/vestibule' region with no insertion cost (dashed line), and the transition region between the two with intermediate FG Nup density (). In this case, the effective free energy in the central region is given by while in the transition regions the effective free energy is , where is the 'bare' free energy of NTR interaction with an FG motif. The effective free energy in the 'vestibule' is . The initial flux is where are the lengths of the central, peripheral and vestibule regions respectively and . Compared with the uniform model in the main text (Figure 5B), . Bottom panel: Red, green, blue schematically depict effective free energy profiles for N=35 for MS2S37P, I53-47, MS2 respectively. (B) Top panel: for non-uniform effective free energy, the data for all capsid sizes can be described by a single value of the bare interaction energy . Parameter values are: = 30 nm, = 5 nm, nm, = 0.01, = 0.001, , = 15.1 . For MS2S37P: F() = 5.5 , F() = 0.9 ; for I53-47: F() = 5.7 , F() = 3.3 ; and for MS2 F() = 6.5 , F() = 6.0 . We emphasize that this density profile and the parameter values are just one possible combination consistent with the data, and the results are robust with respect to parameter choice. Bottom panel: overlay of the model with the experimental data.