From the Belousov-Zhabotinsky reaction to biochemical clocks, traveling waves and cell cycle regulation

From biological data to oscillator models using SINDy

Periodic changes in the concentration or activity of different molecules regulate vital cellular processes such as cell division and circadian rhythms. Developing mathematical models is essential to better understand the mechanisms underlying these oscillations. Recent data-driven methods like SINDy have fundamentally changed model identification, yet their application to experimental biological data remains limited. This study investigates SINDy's constraints by directly applying it to biological oscillatory data. We identify insufficient resolution, noise, dimensionality, and limited prior knowledge as primary limitations. Using various generic oscillator models of different complexity and/or dimensionality, we systematically analyze these factors. We then propose a comprehensive guide for inferring models from biological data, addressing these challenges step by step. Our approach is validated using glycolytic oscillation data from yeast.

Periodical alternation between precipitation and dissolution of camphor solid film on an ethanol solution

Rhythmic behaviors are generally observed in nonlinear chemical reactions such as the Belousov-Zhabotinsky reaction and enzymatic reactions. Similarly, a simple phase change can also lead to rhythmic behavior. It has been reported previously that camphor solid films alternate between generation and disappearance on ethanol (EtOH) solution, and a phenomenological mechanism has been suggested for this. The evaporation of EtOH decreases the temperature on the surface of the solution via vaporization heat and induces precipitation in the camphor solid film. At this time, the film prevents evaporation, and thus, the surface temperature increases due to thermal diffusion from the atmosphere, resulting in dissolution of the solid film. To verify the previously suggested phenomenological mechanism, we controlled the evaporation rate of EtOH using a porous plastic cover. As a result, the period of oscillation increased with decreasing pore diameter, and finally, the oscillation did not occur without pore in the cover, where the camphor solid film was not observed. Additionally, a new mathematical model was proposed, and the numerical calculations agreed well with experimental observations. Linear stability and bifurcation analyses revealed the detailed mechanism of this phenomenon, which agreed well with the phenomenological explanation mentioned above.

The ups and downs of biological oscillators: a comparison of time-delayed negative feedback mechanisms

Many biochemical oscillators are driven by the periodic rise and fall of protein concentrations or activities. A negative feedback loop underlies such oscillations. The feedback can act on different parts of the biochemical network. Here, we mathematically compare time-delay models where the feedback affects production and degradation. We show a mathematical connection between the linear stability of the two models, and derive how both mechanisms impose different constraints on the production and degradation rates that allow oscillations. We show how oscillations are affected by the inclusion of a distributed delay, of double regulation (acting on production and degradation) and of enzymatic degradation.

Hydrodynamics of a confined active Belousov-Zhabotinsky droplet

Self-sustained locomotion of synthetic droplet swimmers has been of great interest due to their ability to mimic the behavior of biological swimmers. Here we harness the Belousov-Zhabotinsky (BZ) reaction to induce Marangoni stresses on the fluid-droplet interface and elucidate the spontaneous locomotion of active BZ droplets in a confined two-dimensional channel. Our approach employs the lattice Boltzmann method to simulate a coupled system of multiphase hydrodynamics and BZ-reaction kinetics. Our investigation reveals the mechanism underlying the propulsion of active BZ droplets, in terms of convective and diffusive fluxes and deformation of the droplets. Furthermore, we demonstrate that by manipulating the degree of confinement, strength, and nature of coupling between surface tension and active species' concentration, the motion of the BZ droplet can be directed. In addition, we are able to capture two different kinds of droplet behaviors, namely, sustained and stationary, and establish conditions for the sustained long-time motion. We envisage that our findings can be used not only to understand the mechanics of biological swimmers but also to design reaction-driven self-propelled systems for a variety of biomimetic applications.

Nucleation of stem cell domains in a bistable activator-inhibitor model of the shoot apical meristem

Shoot apical meristems (SAMs) give rise to all above-ground tissues of a plant. Expansion of meristematic tissue is derived from the growth and division of stem cells that reside in a central zone of the SAM. This reservoir of stem cells is maintained by expression of a transcription factor WUSCHEL that is responsible for the development of stem cells in the central zone. WUSCHEL expression is self-activating and downregulated by a signaling pathway initiated by CLAVATA proteins, which are upregulated by WUSCHEL. This classic activator-inhibitor network can generate localized patterns of WUSCHEL activity by a Turing instability provided certain constraints on reaction rates and diffusion constants of WUSCHEL and CLAVATA are satisfied, and most existing mathematical models of nucleation and confinement of stem cells in the SAM rely on Turing's mechanism. However, Turing patterns have certain properties that are inconsistent with observed patterns of stem cell differentiation in the SAM. As an alternative mechanism, we propose a model for stem cell confinement based on a bistable-switch in WUSCHEL-CLAVATA interactions. We study the bistable-switch mechanism for pattern formation in a spatially continuous domain and in a discrete cellularized tissue in the presence of a non-uniform field of a rapidly diffusing hormone. By comparing domain formation by Turing and bistable-switch mechanisms in these contexts, we show that bistable switching provides a superior account of nucleation and confinement of the stem cell domain under reasonable assumptions on reaction rates and diffusion constants.

OSCILLATORS IN THE MICROVASCULATURE - GLYCOCALYX AND BEYOND

The growing recognition of abundance of oscillating functions in biological systems has motivated this brief overview which narrows down on the microvasculature. Specifically, it encompasses self-sustained oscillations of blood flow, hematocrit and viscosity at bifurcations; their effects on the oscillations of endothelial glycocalyx, mechanotransduction and its termination to prime endothelial cells for the subsequent mechanical signaling event; oscillating affinity of hyaluronan-CD44 binding domain; spontaneous contractility of actomyosin complexes in the cortical actin web, its effects on the tension of the plasma membrane; reversible effects of sirtuin-1 on endothelial glycocalyx; and effects of plasma membrane tension on endo-and exocytosis. Some potential interactions between those oscillators - their coupling - are discussed together with their transition into chaotic movements. Future in-depth understanding of the oscillatory activities in the microvasculature could serve as a guide to its chronotherapy under pathological conditions.