Figure 1.
A schematic representation of the NPC structure with the cargo-complex indicated as a kap-β-bound blue sphere inside the central channel.
For more excellent descriptive figures of the NPC along with different biochemical agents see the recent comprehensive review by Jamali et al., 2011 [18].
Figure 2.
Dimensions of different subunits of the Xenopus oocyte NPC that were used in our model.
Dimensions taken from Akey 1989 and Stoffler et al. 2003 [37], [38].
Figure 3.
Our discretized model of the NPC structure includes three different groups of nups.
a) Poms are responsible for anchoring the structure to the NE. They are modeled as a set of linear springs fixed at one end to the NE and at the other end to the central channel. b) The main scaffold includes cytoplasmic filaments, central channel, and nuclear basket, and is modeled by linear and angular springs. While the linear springs account for the elastic extension in the NPC backbone, angular springs explain the bending rigidity. c) FG-repeat domains are modeled as discrete wormlike chains (WLC) with the persistence length measured by AFM force-extension [39].
Figure 4.
The energy and force-law of different springs between consecutive beads in the structural component of the NPC.
a) Extensional elastic potential energy between two consecutive beads in the pom or main scaffold regions, representing the elastic extension. b) Angular potential energy between two consecutive springs representing bending rigidity of the main scaffold and the FG-repeat domains. Y-axis on the left shows values of the angular potential energy for the main scaffold, while the right y-axis shows those values for FG-repeat domains. c) The force-law of the wormlike chain (WLC). Discrete WLC models the FG-repeat domains.
Figure 5.
The nonbonded potential energies employed in the model.
a) Hydrophobic potential energy is applied between FG-beads localized to the central channel (dashed line). The same potential, a bit stronger, is applied between kap and FG-beads (solid line). b) Pairwise repulsive potential.
Figure 6.
The structural components of the NPC and their equivalences in our model.
a) The NPC structure is composed of three different groups of nups, namely poms (yellow), structural proteins (green), and FG-nups (red). b) In our model, we consider all these components with the appropriate set of bead-spring elements representing their in-vivo functions.
Figure 7.
The cargo-complex interacting with FG-repeat domains via hydrophobic patches on the convex surface of the kap-β[46], [73].
Kap-β has a boat-like shape [8] and the localization of the binding spots on its surface has led to the idea of a “coherent FG-binding stripe” instead of discrete binding spots [46]. In our model, we take into account this fact by considering a ‘hydrophobic arc with limited capacity’ on the cargo surface. This arc possesses eight hydrophobic binding spots, and thus, is able to simultaneously interact with up to eighth FG-motifs. The magnification on the right shows a closer depiction of the cargo-complex with the crystal structure of the kap-β (blue) interacting with FG-repeats (red) on its convex surface (1F59, pdb bank). Also, the average path of a 15 nm cargo-complex during translocation is shown in purple. The path is averaged over 150 independent simulations. As it can be seen, the cargo-complex is primarily attached to the FG-layer during its translocation.
Table 1.
Different values used in the coarse-grained model.
Figure 8.
The mean transport time of a 15 nm diameter cargo complex is ms (
SEM) that is averaged over 150 independent runs.
As it can be seen, the transport time is scattered over a wide range from 0.5 ms to 8 ms. The transport time can be viewed as the first passage time [80] if an absorbing wall is imagined in the nuclear compartment where the cargo is released. The histograms show the distribution of the first passage time that obeys the inverse Gaussian. Red dashed lines show the best fitted inverse Gaussian distribution with the scale parameter and the mean value 2.6 ms. Solid black line shows the cumulative distribution function (cdf) obtained from simulation results and blue dash lines represent cdf of the inverse Gaussian that is in a good agreement with simulation results.
Table 2.
The different cargo-complex sizes.
Figure 9.
The histograms on left show the radial probability distribution of the cargo-complex versus the channel radius (the bin size is 1 nm).
The cargo diameter is indicated inside the plot area. Each diagram is averaged over 50 independent simulations. Histograms are fit with Gaussian distributions (red dash line). The peak ± SD is recorded on top of histograms for each cargo size. Color bars on the right side show the radial probability distribution inside the central channel geometry. The more reddish, the higher the probability density. As it can be seen both in histograms and color bars, the large cargo is more likely to attach to the wall and less likely to disperse in the channel as opposed to the smaller cargo. This is partly due to its larger surface area and smaller diffusion coefficient, which make it less mobile compared the smaller cargo.
Figure 10.
The y-component of a cargo-complex trajectory during ∼2.5 ms transport through the pore.
The NPC structure is sketched on the right to illustrate the corresponding location of the cargo-complex within the NPC. It can be seen that the cargo-complex jumps back and forth tens of times before it released in the nuclear basket. The majority of its time is spent in the central channel.