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Synthetic genetic oscillators can serve as internal clocks within engineered cells to program periodic expression. However, cell-to-cell variability introduces a dispersion in the characteristics of these clocks that drives the population to complete desynchronization. Here, we introduce the optorepressilator, an optically controllable genetic clock that combines the repressilator, a three-node synthetic network in E. coli, with an optogenetic module enabling to reset, delay, or advance its phase using optical inputs. We demonstrate that a population of optorepressilators can be synchronized by transient green light exposure or entrained to oscillate indefinitely by a train of short pulses, through a mechanism reminiscent of natural circadian clocks. Furthermore, we investigate the system’s response to detuned external stimuli observing multiple regimes of global synchronization. Integrating experiments and mathematical modeling, we show that the entrainment mechanism is robust and can be understood quantitatively from single cell to population level.

Down syndrome (DS) is one of the most frequent genetic disorders and represents the first cause of intellectual disability of genetic origin. While the majority of patients with DS follow a harmonious evolution, an unusual neurodevelopmental regression may occur, distinct from that described in the context of autism spectrum disorders, called down syndrome regression disorder (DSRD). Based on four patients, two males and two females, with age range between 20 and 24, treated at the Reference Center for Rare Psychiatric Disorders of the GHU Paris Psychiatry and Neurosciences [Pôle hospitalo-universitaire d’Évaluation Prévention et Innovation Thérapeutique (PEPIT)], we describe this syndrome, discuss its etiologies and propose therapeutic strategies. DSRD often occurs in late adolescence. There is a sudden onset of language disorders, loss of autonomy and daily living skills, as well as behavioral symptoms such as depression, psychosis, or catatonia. These symptoms are non-specific and lead to an overlap with other diagnostic categories, thus complicating diagnosis. The etiologies of the syndrome are not clearly identified but certain predispositions of patients with trisomy 21 have suggested an underlying immune-mediated mechanism. Symptomatic therapeutic approaches (serotonergic antidepressants, atypical antipsychotics, benzodiazepines) were not effective, and generally associated with poor tolerance. Etiological treatments, including anti-inflammatory drugs and corticosteroids, led to partial or good recovery in the four cases. Early recognition of regressive symptoms and rapid implementation of adapted treatments are required to improve the quality of life of patients and their families.

AbstractUnruptured cerebral aneurysms are increasingly identified in elderly patients as the global life expectancy continues to rise and non-invasive vascular imaging becomes more prevalent. The optimal management of unruptured aneurysms in elderly patients remains controversial. Variability in life expectancy, comorbidities and rupture risk coupled with heterogenous endovascular and surgical treatments contribute to a paucity of clear guidelines, and current management is highly individualized. Elderly patients present unique considerations including frailty, cognitive dysfunction, vasculopathy, reduced life expectancy and overall worse prognosis in case of rupture which shape the risks and likelihood of success of endovascular and microsurgical treatment. In this review, we provide a comprehensive overview of unruptured cerebral aneurysms in the elderly, with a particular focus on the natural history, key challenges associated with advanced age, management and future innovations to further refine treatment.Key MessagesThe management of unruptured cerebral aneurysms in elderly patients remains controversial.Key challenges including frailty, cognitive dysfunction, reduced life expectancy, vasculopathy and poor prognosis with aneurysm rupture add complexity to endovascular and surgical decision making not encountered with younger demographics.A thorough understanding of available treatment options, likelihood of treatment success and associated risks weighed against the risk of aneurysm rupture informs patient discussion and management.

We derive necessary optimality conditions for minimizers of regular functionals in the calculus of variations under smooth state constraints. In the literature, this classical problem is widely investigated. The novelty of our result lies in the fact that the presence of state constraints enters the Euler-Lagrange equations as a local feedback, which allows to derive the C1;1-smoothness of solutions. As an application, we discuss a constrained Mean Field Games problem, for which our optimality conditions allow to construct Lipschitz relaxed solutions, thus improving an existence result due to the first two authors.

We study a two-layer energy balance model that allows for vertical exchanges between a surface layer and the atmosphere. The evolution equations of the surface temperature and the atmospheric temperature are coupled by the emission of infrared radiation by one level, that emission being partly captured by the other layer, and the effect of all non-radiative vertical exchanges of energy. Therefore, an essential parameter is the absorptivity of the atmosphere, denoted ε a. The value of ε a depends critically on greenhouse gases: increasing concentrations of CO 2 and CH 4 lead to a more opaque atmosphere with higher values of ϵ a. First, we prove that global existence of solutions of the system holds if and only if ε a ∈ (0 , 2) and blow up in finite time occurs if ε a > 2. (Note that the physical range of values for ε a is (0 , 1 ].) Next, we explain the long time dynamics for ε a ∈ (0 , 2) , and we prove that all solutions converge to some equilibrium point. Finally, motivated by the physical context, we study the dependence of the equilibrium points with respect to the involved parameters, and we prove, in particular, that the surface temperature increases monotonically with respect to ε a. This is the key mathematical manifestation of the greenhouse effect. [ABSTRACT FROM AUTHOR]

Hemorrhage in the central nervous system (CNS), including intracerebral hemorrhage (ICH), intraventricular hemorrhage (IVH), and aneurysmal subarachnoid hemorrhage (aSAH), remains highly morbid. Trials of medical management for these conditions over recent decades have been largely unsuccessful in improving outcome and reducing mortality. Beyond its role in creating mass effect, the presence of extravasated blood in patients with CNS hemorrhage is generally overlooked. Since trials of surgical intervention to remove CNS hemorrhage have been generally unsuccessful, the potent neurotoxicity of blood is generally viewed as a basic scientific curiosity rather than a clinically meaningful factor. In this review, we evaluate the direct role of blood as a neurotoxin and its subsequent clinical relevance. We first describe the molecular mechanisms of blood neurotoxicity. We then evaluate the clinical literature that directly relates to the evacuation of CNS hemorrhage. We posit that the efficacy of clot removal is a critical factor in outcome following surgical intervention. Future interventions for CNS hemorrhage should be guided by the principle that blood is exquisitely toxic to the brain.

This article is devoted to the study of null controllability properties for two systems of coupled one dimensional degenerate parabolic equations. The first system consists of two forward equations, while the second one consists of one forward equation and one backward equation. Both systems are in cascade, that is, the solution of the first equation acts as a control for the second equation and the control function only acts directly in the first equation. We prove positive null controllability results when the control and coupling sets have nonempty intersection and 0 does not belong to the coupling set.

In this paper we study controllability properties for semilinear degenerate parabolic equations with nonlinearities involving the first derivative in a bounded domain of R. Due to degeneracy, classical null controllability results do not hold in general. Thus we investigate results of 'regional null controllability', showing that we can drive the solution to rest at time T on a subset of the space domain, contained in the set where the equation is nondegenerate.

A simple exit time problem with degenerate cos is here considered. Using a new technique for constructing admissible trajectories, a semiconcavity result for the value function ν is obtained. Such a property of ν is then applied to obtain optimality conditions.