Figure 1.
Main Features of the NPC and of Nuclear Import
(A) Schematic of the nuclear import process. The karyopherins bind the cargo in the cytoplasm and transport it to the nucleus, where the cargo is released by RanGTP.
(B) Schematic of the NPC. The nucleus and the cytoplasm are connected by a channel, which is filled with flexible, mobile filamentous proteins termed FG nups. The karyopherins carrying a cargo enter from the cytoplasm and hop between the binding sites on the FG nups until they either reach the nuclear side of the NPC or return to the cytoplasm.
Figure 2.
Transport through the NPC Is Modeled as Diffusion in an Energy Landscape
The NPC channel is represented by a potential well U(x), shown in black. The complexes enter the NPC at x = R at an average rate J. A fraction of the entrance flux, JM, goes through to the nucleus. The rest return to the cytoplasm at an average rate, J0. The exit of the complexes from the channel into the nucleus occurs either due to thermal activation, with the rate JL, or by activated release by RanGTP, with the rate Je. Steady state particle density inside the channel, ρ(x), is shown in blue. It differs from what would be expected from equilibrium statistical mechanics as the complexes do not accumulate at the minimum of the potential but rather their density decreases toward the exit.
Figure 3.
Transport Efficiency Is Determined by the Interaction Strength
(A) Transport efficiency, as given by the probability to reach the nucleus, is shown as a function of the interaction strength. RanGTP activity in the nucleus is represented by using JranL2/(N2D) = 1.5. The curves correspond to four different values of the entrance rate, J (measured in units of 10−416D/R2); the red line is the low-rate limit of Equation 4. For any entrance rate, the transport efficiency is maximal at a specific value of the interaction strength, which provides a mechanism of selectivity.
(B) Optimal interaction strength of (A) as a function of the incoming rate J (in units of 10−416D/R2), for JranL2/(N2D) = 1.5; parabolic potential shape. See Discussion for the corresponding actual values of the flux through the pore. Black dots are simulation results.
Figure 4.
Karyopherins Efficiently Exclude Nonspecifically Binding Macromolecules from the NPC
Shown is the transport efficiency of particles across the NPC as a function of interaction strength with the FG-repeat regions, either in the presence or absence of competing particles. Gray line: transport efficiency of particles as a function of interaction strength in the absence of competition. Red line: transport efficiency of a weakly binding species in an equal mixture of weakly and strongly binding species, as a function of the interaction strength of the weakly binding species; the interaction strength for the strongly binding species is 12kBT. Translocation of the weakly binding species is sharply reduced in the presence of the strongly binding species, until its binding strength approaches that of the strongly binding species. No RanGTP activity was included in these simulations, hence lowering the transport efficiency compared with Figure 3.
Figure 5.
Discrete Overlapping FG-Repeat Regions Can Be Approximated by a Smooth Effective Potential
Transport through the NPC can be represented as diffusion in an array of potential wells (solid black lines) that represent flexible FG-repeat regions whose fluctuation regions overlap. The red dotted arrows correspond to the complexes unbinding from and rebinding to the FG-repeat regions. The solid blue line represents the unbound state. The solid red line shows the equivalent potential in the case when the unbinding of the complexes from the FG-repeat regions is much faster than the lateral diffusion across an individual well.
Figure 6.
The Number of FG nups Does Not Significantly Affect the Transport Properties of NPCs
(A) Effective potential for sparse flexible FG-repeat regions is shown as a blue line. Each well corresponds to an FG-repeat region. The transport properties in this multiwell potential are independent of the number of wells, and hence equivalent to those in the single-well potential, shown as a red line.
(B) Numerical simulations show essentially identical transport efficiencies in the multiwell potential (blue line) and in the single-well potential (red line).