  Living cells display a remarkable capacity to compartmentalize their
functional biochemistry. A particularly fascinating example is the cell
nucleus. Exchange of macromolecules between the nucleus and the surrounding
cytoplasm does not involve traversing a lipid bilayer membrane. Instead, large
protein channels known as nuclear pores cross the nuclear envelope and regulate
the passage of other proteins and RNA molecules. Beyond simply gating
diffusion, the system of nuclear pores and associated transport receptors is
able to generate substantial concentration gradients, at the energetic expense
of guanosine triphosphate (GTP) hydrolysis. In contrast to conventional
approaches to demixing such as reverse osmosis or dialysis, the biological
system operates continuously, without application of cyclic changes in pressure
or solvent exchange. Abstracting the biological paradigm, we examine this
transport system as a thermodynamic machine of solution demixing. Building on
the construct of free energy transduction and biochemical kinetics, we find
conditions for stable operation and optimization of the concentration gradients
as a function of dissipation in the form of entropy production.
