Table 1.
Systems simulated.
Figure 1.
Initial and final configuration of simulated wild-type Nsp1-FGs grafted to a gold ring (simulation wild-type_ring).
(a) Initial configuration. Shown are fully-extended, wild-type Nsp1-FGs grafted on the ring, the geometry of which matches that of an experimentally constructed nanodevice mimicking an NPC as reported in [21], [29]. Colors distinguish 120 wild-type Nsp1-FGs grafted on the ring in three concentric rows. (b) Close-up view of grafted ends of the Nsp1-FG chains. The gold nano-ring is cut open to expose the C-termini, shown as red spheres, fixed to the gold ring, as well as the terminal parts of the Nsp1-FG chains. (c) Snapshot of the () end of simulation wild-type_ring. One can recognize that the Nsp1-FG chains, shown in surface representation, have formed brush-like bundles. (d) Close-up view of the structure in (a). Shown is a region as marked. The close-up view reveals the initially straight conformation of the Nsp1-FG chains; bumps in the surface of the individual chains correspond to amino acid side groups. (e) Close-up view of a segment of (c). The view reveals the brush-like bundles formed by the Nsp1-FG chains. Arrows point to cross-links between bundles formed when single Nsp1-FG chains cross from one bundle to another bundle. As a result of such cross-links the bundles form a mesh of thick (bundles made of several Nsp1-FG chains) and thin (cross-links made of single Nsp1-FG chains) segments. Video S1 shows how during simulation wild-type_ring the initially completely extended Nsp1-FG chains assume random conformations and form bundles as those seen here. Video S2 provides a three-dimensional view, reached through rotating the system in front of the viewer, of the conformation reached in simulation wild-type_ring after
, namely the conformation depicted in (c) and (e).
Figure 2.
Bundle thickness distribution.
Bundle thickness is determined by the number of Nsp1-FG chains involved in a bundle. Shown is here the distribution of these numbers for the simulations carried out. The frequencies with which chain numbers arise were averaged for the last 30 ns of the four simulations wild-type_ring, mutant_ring, random_array, and random_bath. Bundles with fewer than ten Nsp1-FG chains favor a mesh-like structure, namely bundles with frequent cross-links, whereas bundles with more than ten Nsp1-FG chains exhibit brush-like structures with relatively few cross-links. Green represents the frequency distribution of Nsp1-FGs for simulation wild-type_ring, red for mutant_ring, cyan for random_array, and purple for random_bath.
Figure 3.
Initial and final configuration of a simulated array of wild-type Nsp1-FGs grafted to a gold substrate (simulation random_array).
(a) Initial configuration. Shown is the 5×5 array of wild-type Nsp1-FGs grafted with their C-terminal ends to a gold substrate. The proteins are placed initially in random polymer-like conformations obtained computationally through a description of non-overlapping worm-like chains. Colors distinguish the 25 grafted wild-type Nsp1-FGs. (b) Close-up view of grafted ends of the Nsp1-FG chains in an array. Shown as red spheres are C-terminal ends of the Nsp1-FG chains fixed to the gold substrate, as well as the terminal segments of the Nsp1-FG chains. (c) Snapshot of the () end of simulation random_array. One can see that the end-tethered, randomly placed (matching a worm-like chain model) Nsp1-FGs, shown in surface representation, form brush-like structures as in case of simulation wild-type_ring, but with a higher density of cross-links compared to the gold ring case shown in Figure 1. (d) Close-up view of a segment of (c). The view reveals cross-linked Nsp1-FG bundles. Arrows point to cross-links between bundles formed when Nsp1-FG chains cross from one bundle to another bundle. Video S3 shows how during simulation random_array the initially completely random conformation of Nsp1-FG chains assume a mesh-like structure by cross-linking between thin bundles as those seen here. Video S4 provides a 360-degree view of the conformation reached in simulation random_array after
, namely the conformation depicted in (c) and (d).
Figure 4.
(a) Time evolution of the average height. The height is shown for simulations for the end-tethered Nsp1-FGs in simulations wild-type_ring (green line), mutant_ring (red line), and random_array (cyan line). The heights are calculated as the average end-to-end distance in the
-direction, the average being taken over all chains in a given simulation system. (b) Snapshot of the (
) end of simulation wild-type_ring (see also Figure 1(c)), mutant_ring, and random_array (see also Figure 3(c)). Videos show how during simulation wild-type_ring, the fully extended Nsp1-FG chains form brush-like, strongly cross-linked bundles (Video S1) and how in simulation random_array, the worm-like chain Nsp1-FGs form non-brush-like bundles (Video S3). The mutated Nsp1-FG chains (FG-to- AA) arising in simulation mutant_ring form brush-like bundles with similar average brush height as seen to arise for wild-type Nsp1-FGs in simulation wild-type_ring.
Figure 5.
Initial and final configuration of simulated wild-type Nsp1-FGs in a solvent bath (simulation random_bath).
(a) Initial configuration. Shown is the periodic (see simulation conditions as described in Methods) system of wild-type Nsp1-FGs, freely floating in a solvent bath (water and ions). The initial random conformations match a polymer melt modeled from worm-like chains. Colors distinguish 120 freely floating Nsp1-FG chains. Neighboring boxes in - and
- directions are shown with the Nsp1-FGs colored in grey. (b) Snapshot of the (
) end of simulation random_bath. The Nsp1-FG chains, shown in surface representations, are seen to form a porous mesh of cross-linked Nsp1-FG bundles. (c) Close-up view of the structure in (b). Shown is a region as marked. The view reveals a system of short bundles that are frequently cross-linked; arrows point to the cross-links between bundles. Video S5 shows how during simulation random_bath, the initially completely random Nsp1-FGs assume the final structure seen here. Video S6 provides a 360-degree view of the conformation reached in simulation random_bath after
, namely of the conformation depicted in (b).
Figure 6.
Structural features of bundle regions and cross-linking regions observed in coarse-grained and all-atom molecular simulations.
(a) Probability of amino acids to form inter-chain backbone-backbone hydrogen bonds (HB) when located inside the bundle regions (brown bars) or inside the cross-linking regions (blue bars). Shown are the results obtained from the all-atom simulation. All amino acids located outside the bundle regions are considered to be inside the cross-linking regions. The bars labelled FG and FxFG denote the probabilities for the first phenylalanine residues in FG and FxFG motifs, respectively. (b) Solvent accessible surface area (SASA) of the first phenylalanine residues that are located either inside the bundle regions (labeled “bundle regions”) or inside the cross-linking regions (labeled “cross-linking regions”). SASA values from CG simulations wild-type_ring, random_array and random_bath (summarized in Table 1) are compared with SASA values from the all-atom simulation fragment_AA (Table 1) which comprises of eleven Nsp1-FG fragments of the final cross-linked bundle structure resulting from the CG simulation wild-type_ring.
Figure 7.
Schematic algorithm for calculating pore sizes.
The figure shows a schematic depiction of the algorithm employed in calculating the pore sizes listed in Table 2. The pore size is defined through the radius of the largest spherical cargo capable of passing through the final structure resulting from a simulation of a system of Nsp1-FGs. A search for the largest cargo starts on one side of the system, the latter shown in grey. The cargo (black sphere) of a certain size moves towards the other side while the algorithm probes if the cargo can pass. The panel at right illustrates what is measured by the algorithm, namely the radius of the largest cargo that can pass through along a probing direction. As shown in this panel, there are two bottlenecks, the second smaller one of which determines how large a ball can pass through the obstacles and, therefore, characterizes the pore size of obstacles.
Table 2.
Average pore size.
Figure 8.
Schematic model for the structural assembly of nups in the NPC channel.
The strands in black represent bundles of two or more Nsp1-FG chains. The frequency of cross-linking is higher in the central region, a feature that can be identified with the assembly of nups formed in simulation random_bath (inset in purple) characterized as a sieve-like mesh; in the periphery, brush-like bundles with less cross-linking arise and the respective structure can be identified with the ones developed in simulations random_array (inset in blue) and wild-type_ring (inset in green).