The zebrafish is a model organism for pattern formation in vertebrates. Understanding what drives the formation of its coloured skin motifs could reveal pivotal to comprehend the mechanisms behind morphogenesis. The motifs look and behave like reaction–diffusion Turing patterns, but the nature of the underlying physico-chemical processes is very different, and the origin of the patterns is still unclear. Here we propose a minimal model for such pattern formation based on a regulatory mechanism deduced from experimental observations. This model is able to produce patterns with intrinsic wavelength, closely resembling the experimental ones. We mathematically prove that their origin is a Turing bifurcation occurring despite the absence of cell motion, through an effect that we call differential growth. This mechanism is qualitatively different from the reaction–diffusion originally proposed by Turing, although they both generate the short-range activation and the long-range inhibition required to form Turing patterns.

Promoters are adsorbed mobile species which do not directly participate in a catalytic surface reaction, but can influence its rate. Often, they are characterized by strong attractive interactions with one of the reactants. We show that these conditions lead to a Turing instability of the uniform state and to the formation of reaction-induced periodic concentration patterns. Experimentally such patterns are observed in catalytic water formation on a Rh(110) surface in the presence of coadsorbed potassium.

In nonexcitable cells, global ${\mathrm{Ca}}^{2+}$ spikes emerge from the collective dynamics of clusters of ${\mathrm{Ca}}^{2+}$ channels that are coupled by diffusion. Current modeling approaches have opposed stochastic descriptions of these systems to purely deterministic models, while both paradoxically appear compatible with experimental data. Combining fully stochastic simulations and mean-field analyses, we demonstrate that these two approaches can be reconciled. Our fully stochastic model generates spike sequences that can be seen as noise-perturbed oscillations of deterministic origin, while displaying statistical properties in agreement with experimental data. These underlying deterministic oscillations arise from a phenomenological spike nucleation mechanism.

The construction of hypothetical environments to produce organic molecules such as metabolic intermediates or amino acids is the subject of ongoing research into the emergence of life. Experiments specifically focused on an anabolic approach typically rely on a mineral catalyst to facilitate the supply of organics that may have produced prebiotic building blocks for life. Alternatively to a true catalytic system, a mineral could be sacrificially oxidized in the production of organics, necessitating the emergent ‘life’ to turn to virgin materials for each iteration of metabolic processes. The aim of this perspective is to view the current ‘metabolism‐first’ literature through the lens of materials chemistry to evaluate the need for higher catalytic activity and materials analyses. While many elegant studies have detailed the production of chemical building blocks under geologically plausible and biologically relevant conditions, few appear to do so with sub‐stoichiometric amounts of metals or minerals. Moving toward sub‐stoichiometric metals with rigorous materials analyses is necessary to demonstrate the viability of an elusive cornerstone of the ‘metabolism‐first’ hypotheses: catalysis. We emphasize that future work should aim to demonstrate decreased catalyst loading, increased productivity, and/or rigorous materials analyses for evidence of true catalysis.

A stochastic thermodynamics of Brownian motion is set up in which state functions are expressed in terms of state variables through the same relations as in classical irreversible thermodynamics, with the difference that the state variables are now random fields accounting for the effect of fluctuations. Explicit expressions for the stochastic analog of entropy production and related quantities are derived for a dilute solution of Brownian particles in a fluid of light particles. Their statistical properties are analyzed and, in the light of the insights afforded, the thermodynamics of a single Brownian particle is revisited and the status of the second law of thermodynamics is discussed.