Origins of oscillatory dynamics in the model of reactive oxygen species in the rhizosphere

Oscillatory processes are essential for normal functioning and survival of biological systems, and reactive oxygen species have a prominent role in many of them. A mechanism representing the dynamics of these species in the rhizosphere is analyzed using stoichiometric network analysis with the aim to determine its capabilities to simulate various dynamical states, including oscillations. A detailed analysis has shown that unstable steady states result from four destabilizing feedback cycles, among which the cycle involving hydroquinone, an electron acceptor, and its semi-reduced form is the dominant one responsible for the existence of saddle-node and Andronov-Hopf bifurcations. This requires a higher steady-state concentration for the reduced electron acceptor compared to that of the remaining species, where the level of oxygen steady-state concentration determines whether the Andronov-Hopf or saddle-node bifurcation will occur.

Chemo-hydrodynamic pulsations in simple batch A + B → C systems

Spatio-temporal oscillations can be induced under batch conditions with ubiquitous bimolecular reactions in the absence of any nonlinear chemical feedback, thanks to an active interplay between the chemical process and chemically driven hydrodynamic flows. When two reactants A and B, initially separated in space, react upon diffusive contact, they can power convective flows by inducing a localized variation of surface tension and density at the mixing interface. These flows feedback with the reaction-diffusion dynamics, bearing damped or sustained spatio-temporal oscillations of the concentrations and flow field. By means of numerical simulations, we detail the mechanism underlying these chemohydrodynamic oscillations and classify the main dynamical scenarios in the relevant space drawn by parameters ΔM and ΔR, which rule the surface tension- and buoyancy-driven contributions to convection, respectively. The reactor height is found to play a critical role in the control of the dynamics. The analysis reveals the intimate nature of these oscillatory phenomena and the hierarchy among the different phenomena at play: oscillations are essentially hydrodynamic and the chemical process features the localized trigger for Marangoni flows unstable toward oscillatory instabilities. The characteristic size of Marangoni convective rolls mainly determines the critical conditions and properties of the oscillations, which can be further tuned or suppressed by the buoyancy competition. We finally discuss the possible experimental implementation of such a class of chemo-hydrodynamic oscillator and its implications in fundamental and applied terms.