In nature, microorganisms are continuously facing nutrient availability changes in the environment, and thus they have evolved to dynamically adapt their physiology to cope with this phenomenon, by dynamically allocating resources to different cellular functions. In order to study their behaviours, the fitness of such microorganisms can be represented as a dynamical growth maximization strategy, which is formulated as an OCP (Optimal Control Problem) in coarse-grained selfreplicator systems. This study inspired the use of biotechnological engineering to maximize the production of a metabolite of interest in E. coli by means of both analytical and computational techniques. Motivated by this approach, we incorporate the metabolite production scheme in a CSTR (Continuous Stirred-Tank Reactor) Bioreactor, which can be interpreted as a general case of the preceding models. We then derive two particular cases and study the associated OCP, so as to stress the importance of singular regimes and chattering arcs in optimal solutions. From a biological point of view, our results show that the natural allocation of resources of bacteria has to be modified in order to achieve optimal metabolite production. Finally, we go over the computations of the second order singular arc, and provide a numerical check of the Legendre-Clebsch condition.

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Looming-sensitive neurons (LSNs) are motion-sensitive neurons tuned for detecting imminent collision. Their main characteristic is the selectivity to looming (a 2D representation of an object approach), rather than to receding stimuli. We studied a set of LSNs by performing surface extracellular recordings in the optic nerve of Neohelice granulata crabs, and characterized their response against computer-generated visual stimuli with different combinations of moving edges, highlighting different components of the optical flow. In addition to their selectivity to looming stimuli, we characterized other properties of these neurons, such as low directionality; reduced response to sustained excitement; and an inhibition phenomenon in response to visual stimuli with dense optical flow of expansion, contraction, and translation. To analyze the spatio-temporal processing of these LSNs, we proposed a biologically plausible computational model which was inspired by previous computational models of the locust lobula giant motion detector (LGMD) neuron. The videos seen by the animal during electrophysiological experiments were applied as an input to the model which produced a satisfactory fit to the measured responses, suggesting that the computation performed by LSNs in a decapod crustacean appears to be based on similar physiological processing previously described for the LGMD in insects.

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