Design principles of selective transport through biopolymer barriers

Abstract

In biological systems, polymeric materials block the movement of some macromolecules while allowing the selective passage of others. In some cases, binding enables selective transport, while in others the most inert particles appear to transit most rapidly. To study the general principles of filtering, we develop a model motivated by features of the nuclear pore complex (NPC) which are highly conserved and could potentially be applied to other biological systems. The NPC allows selective transport of proteins called transport factors, which transiently bind to disordered flexible proteins called phenylalanine-glycine-nucleoporins. While the NPC is tuned for transport factors and their cargo, we show that a single feature is sufficient for selective transport: the bound-state motion resulting from transient binding to flexible filaments. Interchain transfer without unbinding can further improve selectivity, especially for cross-linked chains. We generalize this observation to model nanoparticle transport through mucus and show that bound-state motion accelerates transport of transient nanoparticle application, even with clearance by mucus flow. Our model provides a framework to control binding-induced selective transport in biopolymeric materials.

Figure 8.

(a) Selectivity as a function of diffusion coefficient ratio, with varying dissociation constant in the linear approximation. (b) Selectivity as a function of dissociation constant, with varying diffusion coefficient ratio, in the linear approximation. The full nonlinear solution should be used to the left of the dotted line.

Figure 9.

The blue curve shows the selectivity in the linear regime where we have explicitly considered tethered diffusion (L_c = 120 nm). In contrast, in the red curve we have assumed local chemical equilibrium to test whether simply including tethered diffusion into that model can be a good approximation for the solutions to the full binding model. This leads to quantitatively different predicted fluxes. With local chemical equilibrium, the boundary conditions must be incorrect - bound complex leaves the gel and the flux of transport factor on either end of the gel is not equal.

Figure 10.

(a) Selectivity as a function of diffusion coefficient ratio, with varying dissociation constant in the full nonlinear model (b) Selectivity S as a function of diffusion coefficient ratio using the model described in Yang et al. [22]. The transport factor concentration in the reservoir is T_L = 1 μM and the total Nup concentration is N_t = 1 mM.

Figure 11.

(a) Examples of mean-squared displacement (MSD) of a simulated TF in the inter-chain transfer model, with varying transfer rate. (b) Examples of MSD distributions ρ_MSD(t) used in estimating the diffusion coefficient, with varying unbinding rate. Tethers have 40 nm contour length; other parameters are as discussed in the main text.

Figure 12.

Diffusion constant ratio D_B/D_F (top) and selectivity S (bottom) for model incorporating tethered diffusion and inter-chain transfer. Polymer contour lengths of L_c = 4, 12, 40, and 120 nm are shown with a number of transfer rates k_t.

Figure 1.

Schematics of the nuclear pore complex and model. (a) The nuclear pore complex (grey) is filled with FG Nups (green polymers) that selectively passage transport factors that bind to FG Nups (blue) while blocking non-binding proteins (red). The central channel of the pore has length L. Protein concentration is high on the left (inlet) and low on the right (outlet). (b) Selectivity quantifies the degree of selective transport through the pore. A non-selective pore with S = 1 has the same flux for a transport factor as for a non-binding protein (top). A selective pore with S > 1 has a larger flux for a transport factor than a non-binding protein (lower).

Figure 2.

Flux through the pore and selectivity for transport factors with varying bound mobility. (a) Flux as a function of time when transport factors are immobile while bound, with varying binding affinity as in (b). (b) Flux as a function of time when transport factors are mobile while bound with D_B = D_F , with varying binding affinity. Note change in y-axis scale. (c) Selectivity as a function of dissociation constant with varying bound diffusion coefficient.

Figure 3.

(a) Schematic of the flexible tether model of bound-state diffusion. FG Nups are treated as entropic springs that constrain the motion of TFs more (top and center left, longer FG Nup) or less (top and center right, shorter Nup), which corresponds to changing width of the harmonic potential well (lower). (b) Ratio of bound to free diffusion coefficient as a function of dissociation constant, with varying polymer length in the tethered-diffusion model. (c) Selectivity as a function of K_D, with varying polymer length in the tethered-diffusion model.

Figure 4.

Selectivity as a function of K_D with and without inter-chain transfer for FG Nup contour lengths L_c = 4 nm and L_c = 40 nm. FG Nups are entropic springs that constrain the motion of transport factors, and inter-chain transfer allows a transport factors to move from one FG Nup to another without unbinding at rate k_t, which corresponds to switching from one harmonic well to another.

Figure 5.

(a) Schematic of simulated transient drug application showing binding (blue) and inert (red) particles introduced to the fluid above a mucus layer (green) and subsequently washed away. Some particles are retained in the mucus layer for a time, and some of those enter the cells below (grey). Figure adapted from [74]. (b) Accumulation for a 2-s application followed by a 200-s accumulation period.

Figure 6.

Normalized flux for a 2-s application followed by a 200-s accumulation period, shown for several values of bound diffusion constant ratio D_B/D_F . Inset: Total accumulated flux after 200 s as a function of D_B/D_F .

Figure 7.

Total accumulation for a 2-s application followed by a 200-s accumulation period as a function of dissociation constant K_D, shown for several values of the flow velocity v away from the barrier.