Stochastic thermodynamics of separation process in space and time: from kinetic proofreading to chromatography

In both living cells and chemical plants, the ability to recognize and discern molecules of similar properties is crucial. Separation of similar molecules can happen in both space and time. We model separation as random walks on graphs equipped with an inlet node and one or more outlet nodes. If the graphs represent chemical reaction networks, each node denotes an intermediate product of the reaction (i.e., a chemical-reaction state). If the graphs represent distillation or chromatography, each node corresponds to a physical location (spatial state). This work provides a unified description of various separations: kinetic proofreading as separation in the chemical space, distillation tower as a spatial separation, and chromatography as separation in the time domain. By performing kinetic Monte Carlo simulation of various designs of graphs, we can compare the performance of kinetic proofreading, chromatography, and some novel designs for accurate separation. Here we demonstrate that nonequilibrium cycles borrowed from the kinetic proofreading can significantly improve the separation performance of chromatography in the time domain.