Chemical Kinetics and Mass Action in Coexisting Phases

Abstract

The kinetics of chemical reactions are determined by the law of mass action, which has been successfully applied to homogeneous, dilute mixtures. At nondilute conditions, interactions among the components can give rise to coexisting phases, which can significantly alter the kinetics of chemical reactions. Here, we derive a theory for chemical reactions in coexisting phases at phase equilibrium. We show that phase equilibrium couples the rates of chemical reactions of components with their diffusive exchanges between the phases. Strikingly, the chemical relaxation kinetics can be represented as a flow along the phase equilibrium line in the phase diagram. A key finding of our theory is that differences in reaction rates between coexisting phases stem solely from phase-dependent reaction rate coefficients. Our theory is key to interpreting how concentration levels of reactive components in condensed phases control chemical reaction rates in synthetic and biological systems.

Dynamical control enables the formation of demixed biomolecular condensates

“…Proposals based on purely thermodynamic considerations focus on relative interfacial tensions, and hence relative solubilities, as the main determinants of condensate demixing or spatially organized structures of condensates 20,29–35 . Sequence-intrinsic 7,20,36,37 interactions, emulsification 38 , chemical reactions 39 , and elastic networks within cells 40,41 have also been proposed as regulators of the sizes and compositional specificities of coexisting ribonucleoprotein condensates. Our work adds sequence-intrinsic non-equilibrium dynamical complexities of ribonucleoprotein mixtures to the list of possible controllers of condensate sizes and compositional specificities.…”

Nonlinear chemical reaction induced abnormal pattern formation of chemotactic particles

“…Similar phenomena can be seen in systems where active chemical reactions and phase separation are combined. 37,38 Notably, we demonstrate a mechanism that the consumption of certain substance triggers the nonlinearity effect of reaction, which drives the system towards a heterogeneous state. We also consider other parameter regions and find the dynamic pattern of the system which can also be understood in a similar mechanism.…”

The interplay between biomolecular assembly and phase separation

“…Following the concepts developed in Ref. [56], in each phase, the kinetics of the respective volume fractions of the assembly of size i, ϕ is the total volume fraction of all assemblies. Consistently, assembly kinetics conserves ϕ tot in both phases.…”

“…Building upon the thermodynamic framework discussed in the previous sections, we devise a non-equilibrium kinetic theory for molecular assembly at non-dilute conditions, where the interactions can give rise to coexisting phases. Here, we restrict ourselves to the case where each phase is homogeneous and at phase equilibrium but not at assembly equilibrium [56], i.e., Eq. (6) is fulfilled during the kinetics while Eq.…”