A thermodynamic force generated by chemical gradient and adsorption reaction

Biological units such as macromolecules, organelles, and cells are directed to a proper location under gradients of relevant chemicals. By considering a macroscopic element that has binding sites for a chemical adsorption reaction to occur on its surface, we show the existence of a thermodynamic force that is generated by the gradient and exerted on the element. By assuming local equilibrium and adopting the grand potential from thermodynamics, we derive a formula for such a thermodynamic force, which depends on the chemical potential gradient and Langmuir isotherm. The conditions under which the formula can be applied are demonstrated to hold in intracellular reactions. The role of the force in the partitioning of bacterial chromosome/plasmid during cell division is discussed.