An optimal control algorithm is proposed for impulsive differential systems, i.e., systems evolving according to ordinary differential equations between any two control actions, occurring impulsively at discrete-time instants. Measurements are as well acquired at discrete-time instants. A model-based control law is conceived for medical and healthcare frameworks and, indeed, is applied to synthesize a feedback antiangiogenic tumor therapy. To cope with unavailable or temporally sparse measurements, the control law benefits a state observer properly designed for continuous-discrete systems by suitably exploiting recent results on observers for time-delay systems. The closed-loop algorithm is validated by building up an exhaustive simulation campaign on a population of virtual subjects, each sampled from a multivariate Gaussian distribution whose mean and covariance matrix is identified from experimental data taken from the literature. In silico results are encouraging and pave the way to further clinical verifications.

A tumor growth model accounting for angiogenic stimulation and inhibition is here considered, and a closed-loop control law is presented with the aim of tumor volume reduction by means of anti-angiogenic administration. To this end the output-feedback linearization theory is exploited, with the feedback designed on the basis of a state observer for nonlinear systems. Measurements are supposed to be acquired at discrete sampling times, and a novel theoretical development in the area of time-delay systems is applied in order to derive a continuous-time observer in spite of the presence of sampled measurements. The overall control scheme allows to set independently the control and the observer parameters thanks to the structural properties of the tumor growth model. Simulations are carried out in order to mimic a real experimental framework on mice. These results seem extremely promising: they provide very good performances according to the measurements sampling interval suggested by the experimental literature, and show a noticeable level of robustness against the observer initial estimate, as well as against the uncertainties affecting the model parameters.

In this study, the formation of the adult sea urchin shape is ra-tionalized within the Turing's theory paradigm. The emergence of protrusions from the expanding underlying surface is described through a reaction-diffusion model with Gray-Scott kinetics on a growing oblate spheroid. The case of slow exponential isotropic growth is considered. The model is first studied in terms of the spatially homogenous equilibria and of the bifurcations involved. Tur-ing diffusion-driven instability is shown to occur and the impact of the slow exponential growth on the resulting Turing regions adequately discussed. Nu-merical investigations validate the theoretical results showing that the com-bination between an inhibitor and an activator can result in a distribution of spot concentrations that underlies the development of ambulacral tentacles in the sea urchin's adult stage. Our findings pave the way for a model-driven ex-perimentation that could improve the current biological understanding of the gene control networks involved in patterning.

Timing and synchronization mechanisms are ubiquitous in living systems, and in many cases involve switch-like regulators that control complex molecular pathways and cellular functions. The switching of such regulators is often irreversible and controlled by the co-activation of a set of concurrent independent enabling events. Despite the random nature of each individual switch, the timing in the onset of the controlled process has a rather small variability. This note introduces a mathematical framework for the description of the collective behavior of populations of interconnected stochastic switches. The main contribution of this note is to explain how the connecting mode (series/parallel) of switches affects the behavior of the entire switch population and in particular the degree of synchronization. We describe the switch model for the G ₁ /S phase transition in yeast and briefly discuss the general utility of this class of models in systems biology.