Thermodynamic Paradigm for Solution Demixing Inspired by Nuclear Transport in Living Cells

Abstract

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.

Physics of the nuclear pore complex: Theory, modeling and experiment

“…[335,339,344,345] Similar uncertainty remains on how the relative concentrations of cargo in nucleus and cytoplasm depend on the numbers of transport proteins, Ran, RanGAP/GEF and various other adaptor proteins in the cell. Timney et al [86] found that the nucleo-cytoplasmic concentration ratio increases with cytoplasmic concentration of the transport proteins, while Elbaum and coworkers predict a non-monotonic function of the transport protein concentration [342,345]. Finally, [87,337] observed that the import rate is decreasing with the concentration of Importin-β (due to the depletion of RanGTP), although the connection between the initial accumulation rate and the relative concentrations at saturation is nontrivial [87,337].…”

“…Given the low efficiency of the transport cycle, it is possible that the import-export system is simply hitch-hiking on the RanGTP/GDP de-mixing cycle, which has other important roles, such as nucleosome positioning during cell division [335,340], and therefore is not necessarily optimized to facilitate cargo de-mixing between the nucleus and the cytoplasm. This point of view, which defines the ''futile cycle'' [341] of RanGTP/RanGDP conversion as a primary driver of the nucleocytoplasmic transport cycle, has been useful in conceptualizing the principles of nucleocytoplasmic de-mixing using the methods of non-equilibrium thermodynamics [342].…”

“…In principle, all the reactions involved in the nucleocytoplasmic exchange can be computationally described with appropriate rate equations, but understanding of the full picture remains complicated due to the large number of various molecular complexes involved. Therefore, the predictions remain sensitive to the choice of parameters and assumptions, and are often at variance with each other, both on the computational and experimental fronts [86,87,335,337,339,[342][343][344][345]. All these experimental and computational studies mostly agree that the initial accumulation of import cargo in the nucleus follows simple first order kinetics, and the initial accumulation rate/flux is linearly proportional to the cargo concentration in the cytoplasm.…”

Protein Transport by the Nuclear Pore Complex: Simple Biophysics of a Complex Biomachine

“…Macroscopically, NPCs can efficiently import and export macromolecular cargoes into and out of the nucleus against the cargoes' apparent concentration gradients. From the thermodynamic standpoint, this requires energy input, which is provided by GTP hydrolysis during the transport cycle (4,22). In many other types of transporters (such as ion exchangers or proton pumps), GTP/ATP hydrolysis is directly coupled to directional substrate transport via conformational changes of the transporter (1,23).…”

“…In the nucleus, RanGDP is converted to RanGTP by a chromatin-associated guanine exchange factor RanGEF. Overall, directional transport is driven by the energy released from irreversible GTP hydrolysis in the cytoplasm (22) and maintained by the localization gradient of RanGTP; RanGTP concentration is higher in the nucleus relative to the cytoplasm. In turn, this gradient relies on the constitutive localizations of RanGEF in the nucleus, RanGAP1 in the cytoplasm, and the NTF2mediated transport of RanGDP (4).…”