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 FG Nups. 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 crosslinked 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 bipolymeric materials.

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 FG Nups. 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. Inter-chain transfer without unbinding can further improve selectivity, especially for crosslinked 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 bindinginduced selective transport in biopolymeric materials.

Crowded environments modify the diffusion of macromolecules, generally slowing their movement and inducing transient anomalous subdiffusion. The presence of obstacles also modifies the kinetics and equilibrium behavior of tracers. While previous theoretical studies of particle diffusion have typically assumed either impenetrable obstacles or binding interactions that immobilize the particle, in many cellular contexts bound particles remain mobile. Examples include membrane proteins or lipids with some entry and diffusion within lipid domains and proteins that can enter into membraneless organelles or compartments such as the nucleolus. Using a lattice model, we studied the diffusive movement of tracer particles which bind to soft obstacles, allowing tracers and obstacles to occupy the same lattice site. For sticky obstacles, bound tracer particles are immobile, while for slippery obstacles, bound tracers can hop without penalty to adjacent obstacles. In both models, binding significantly alters tracer motion. The type and degree of motion while bound is a key determinant of the tracer mobility: slippery obstacles can allow nearly unhindered diffusion, even at high obstacle filling fraction. To mimic compartmentalization in a cell, we examined how obstacle size and a range of bound diffusion coefficients affect tracer dynamics. The behavior of the model is similar in two and three spatial dimensions. Our work has implications for protein movement and interactions within cells.

kinesin-II delays its recycling to the basal body and kinesin-II accumulates in a concentration gradient in the flagellum. As a result, kinesin-II is depleted at the flagellar base as the flagellum elongates. When the flagellum is elongated via Li þ treatment, or when the cell regrows flagella in the presence of protein synthesis inhibitor, the base is similarly depleted of kinesin-II. These results suggest that accumulation in the flagellum acts as a negative-feedback mechanism to limit the number of kinesin-II available for moving cargo on IFT trains, and limits the growth of flagella when they reach longer lengths.