The selectivity and speed of many biological transport processes transpire from a 'reduction of dimensionality' that confines diffusion to one or two dimensions instead of three. This behaviour remains highly sought after on polymeric surfaces as a means to expedite diffusional search processes in molecular engineered systems. Here, we have reconstituted the two-dimensional diffusion of colloidal particles on a molecular brush surface. The surface is composed of phenylalanine-glycine nucleoporins (FG Nups)--intrinsically disordered proteins that facilitate selective transport through nuclear pore complexes in eukaryotic cells. Local and ensemble-level experiments involving optical trapping using a photonic force microscope and particle tracking by video microscopy, respectively, reveal that 1-µm-sized colloidal particles bearing nuclear transport receptors called karyopherins can exhibit behaviour that varies from highly localized to unhindered two-dimensional diffusion. Particle diffusivity is controlled by varying the amount of free karyopherins in solution, which modulates the multivalency of Kap-binding sites within the molecular brush. We conclude that the FG Nups resemble stimuli-responsive molecular 'velcro', which can impart 'reduction of dimensionality' as a means of biomimetic transport control in artificial environments.