Prologue to the special issue of JTB dedicated to the memory of René Thomas (1928-2017): A journey through biological circuits, logical puzzles and complex dynamics

Pillars of biology: Boolean modeling of gene-regulatory networks

Boolean modeling is a mathematical modeling framework used for defining and studying gene-regulatory networks (GRNs). It serves as a means to develop mechanistic models, offering insights into the trajectories and dynamic properties of GRNs. In this review, I delve into seminal papers published in the Journal of Theoretical Biology that have spearheaded this field. Additionally, I explore the application of these modeling methods in the current era of data-intensive science.

Time-keeping and decision-making in living cells: Part I

To survive and reproduce, a cell must process information from its environment and its own internal state and respond accordingly, in terms of metabolic activity, gene expression, movement, growth, division and differentiation. These signal–response decisions are made by complex networks of interacting genes and proteins, which function as biochemical switches and clocks, and other recognizable information-processing circuitry. This theme issue of Interface Focus (in two parts) brings together articles on time-keeping and decision-making in living cells—work that uses precise mathematical modelling of underlying molecular regulatory networks to understand important features of cell physiology. Part I focuses on time-keeping: mechanisms and dynamics of biological oscillators and modes of synchronization and entrainment of oscillators, with special attention to circadian clocks.

Labyrinth chaos: Revisiting the elegant, chaotic, and hyperchaotic walks

Labyrinth chaos was discovered by Otto Rössler and René Thomas in their endeavor to identify the necessary mathematical conditions for the appearance of chaotic and hyperchaotic motion in continuous flows. Here, we celebrate their discovery by considering a single labyrinth walk system and an array of coupled labyrinth chaos systems that exhibit complex, chaotic behavior, reminiscent of chimera-like states, a peculiar synchronization phenomenon. We discuss the properties of the single labyrinth walk system and review the ability of coupled labyrinth chaos systems to exhibit chimera-like states due to the unique properties of their space-filling, chaotic trajectories, which amounts to elegant, hyperchaotic walks. Finally, we discuss further implications in relation to the labyrinth walk system by showing that even though it is volume-preserving, it is not force-conservative.