In budding yeast, overcoming of a critical size to enter S phase and the mitosis/mating switch—two central cell fate events—take place in the G1 phase of the cell cycle. Here we present a mathematical model of the basic molecular mechanism controlling the G1/S transition, whose major regulatory feature is multisite phosphorylation of nuclear Whi5. Cln3–Cdk1, whose nuclear amount is proportional to cell size, and then Cln1,2–Cdk1, randomly phosphorylate both decoy and functional Whi5 sites. Full phosphorylation of functional sites releases Whi5 inhibitory activity, activating G1/S transcription. Simulation analysis shows that this mechanism ensures coherent release of Whi5 inhibitory action and accounts for many experimentally observed properties of mitotically growing or conjugating G1 cells. Cell cycle progression and transcriptional analyses of a Whi5 phosphomimetic mutant verify the model prediction that coherent transcription of the G1/S regulon and ensuing G1/S transition requires full phosphorylation of Whi5 functional sites.

The transcriptome in a cell is finely regulated by a large number of molecular mechanisms able to control the balance between mRNA production and degradation. Recent experimental findings have evidenced that fine and specific regulation of degradation is needed for proper orchestration of a global cell response to environmental conditions. We developed a computational technique based on stochastic modeling, to infer condition-specific individual mRNA half-lives directly from gene expression time-courses. Predictions from our method were validated by experimentally measured mRNA decay rates during the intraerythrocytic developmental cycle of Plasmodium falciparum. We then applied our methodology to publicly available data on the reproductive and metabolic cycle of budding yeast. Strikingly, our analysis revealed, in all cases, the presence of periodic changes in decay rates of sequentially induced genes and co-ordination strategies between transcription and degradation, thus suggesting a general principle for the proper coordination of transcription and degradation machinery in response to internal and/or external stimuli.

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. The model-based control law is conceived for medical and health-care frameworks and, indeed, is applied to synthesize a feedback antiangiogenic tumor therapy. To cope with unavailable or temporally sparse measurements, the control law benefits of 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 are identified from experimental data taken from the literature. In silico results are encouraging and pave the way to further clinical verifications.

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This work investigates the state prediction problem for nonlinear stochastic differential systems, affected by multiplicative state noise. This problem is relevant in many state-estimation frameworks such as filtering of continuous-discrete systems (i.e. stochastic differential systems with discrete measurements) and timedelay systems. A very common heuristic to achieve the state prediction exploits the numerical integration of the deterministic nonlinear equation associated to the noise-free system. Unfortunately this methods provide the exact solution only for linear systems. Instead here we provide the exact state prediction for nonlinear system in term of the series expansion of the expected value of the state conditioned to the value in a previous time instant, obtained according to the Carleman embedding technique. The truncation of the infinite series allows to compute the prediction at future times with an arbitrary approximation.Simulations support the effectiveness of the proposed state-prediction algorithm in comparison to the aforementioned heuristic method.

Impulsive systems model continuous-time frameworks with control actions occurring at discrete time instants. Among the others, such models assume relevance in medical situations, where the physical system under control evolves continuously in time, whilst the control therapy is instantaneously administered, e.g. by means of intravenous injections. This note proposes a discretization algorithm for an impulsive system, whose methods relies on the Carleman embedding techinique. The discretization times are given by the impulsive control action and do not require to have a fixed discretization period. On the ground of the resulting discrete-time system (which can be computed with arbitrary level of accuracy) we propose an optimal control algorithm on a finite horizon. Simulations are carried out on a model exploited for anti-angiogenic tumor therapies and show the effectiveness of the theoretical results.

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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.