A stochastic version of the Brusselator model is proposed and studied via the system size expansion. The mean-field equations are derived and shown to yield to organized Turing patterns within a specific parameters region. When determining the Turing condition for instability, we pay particular attention to the role of cross-diffusive terms, often neglected in the heuristic derivation of reaction-diffusion schemes. Stochastic fluctuations are shown to give rise to spatially ordered solutions, sharing the same quantitative characteristic of the mean-field based Turing scenario, in term of excited wavelengths. Interestingly, the region of parameter yielding to the stochastic self-organization is wider than that determined via the conventional Turing approach, suggesting that the condition for spatial order to appear can be less stringent than customarily believed.

Various systems in physics, biology, social sciences and engineering have been successfully modeled as networks of coupled dynamical systems, where the links describe pairwise interactions. This is, however, too strong a limitation, as recent studies have revealed that higher-order many-body interactions are present in social groups, ecosystems and in the human brain, and they actually affect the emergent dynamics of all these systems. Here, we introduce a general framework to study coupled dynamical systems accounting for the precise microscopic structure of their interactions at any possible order. We show that complete synchronization exists as an invariant solution, and give the necessary condition for it to be observed as a stable state. Moreover, in some relevant instances, such a necessary condition takes the form of a Master Stability Function. This generalizes the existing results valid for pairwise interactions to the case of complex systems with the most general possible architecture.

We study a simplified scheme of k coupled autocatalytic reactions, previously introduced by Togashi and Kaneko. The role of stochastic fluctuations is elucidated through the use of the van Kampen system-size expansion and the results compared with direct stochastic simulations. Regular temporal oscillations are predicted to occur for the concentration of the various chemical constituents, with an enhanced amplitude resulting from a resonance which is induced by the intrinsic graininess of the system. The associated power spectra are determined and have a different form depending on the number of chemical constituents k . We make detailed comparisons in the two cases k=4 and k=8 . Agreement between the theoretical and numerical results for the power spectrum is good in both cases. The resulting spectrum is especially interesting in the k=8 system, since it has two peaks, which the system-size expansion is still able to reproduce accurately.

It is commonly thought that when multiple carbon sources are available, bacteria metabolize them either sequentially (diauxic growth) or simultaneously (co-utilization). However, this view is mainly based on analyses in relatively simple laboratory settings. Here we show that a heterotrophic marine bacterium, Pseudoalteromonas haloplanktis, can use both strategies simultaneously when multiple possible nutrients are provided in the same growth experiment. The order of nutrient uptake is partially determined by the biomass yield that can be achieved when the same compounds are provided as single carbon sources. Using transcriptomics and time-resolved intracellular 1 H-13 C NMR, we reveal specific pathways for utilization of various amino acids. Finally, theoretical modelling indicates that this metabolic phenotype, combining diauxie and co-utilization of substrates, is compatible with a tight regulation that allows the modulation of assimilatory pathways.