The selectivity and speed of many biological transport processes(1) transpire from a 'reduction of dimensionality'(2) that confines diffusion to one or two dimensions instead of three(3). This behaviour remains highly sought after on polymeric surfaces(4) 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 phenylalanineglycine nucleoporins (FG Nups)(5)-intrinsically disordered proteins that facilitate selective transport through nuclear pore complexes in eukaryotic cells(6). Local and ensemble-level experiments involving optical trapping using a photonic force microscope(7) and particle tracking by video microscopy(8), respectively, reveal that 1-mu m-sized colloidal particles bearing nuclear transport receptors(9) 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(10). We conclude that the FG Nups resemble stimuli-responsive(11) molecular 'velcro', which can impart 'reduction of dimensionality' as a means of biomimetic transport control in artificial environments.