Laurent Pujo-Menjouet

In this paper, we study the global well-posedness of a reaction–diffusion–advection system with time-dependent coefficients that models the interaction of ATM and ApoE proteins in cells under Alzheimer’s disease. We prove the existence and uniqueness of a non-negative global solution to this system considering in particular a non-autonomous advective term by demonstrating the existence of a local-in-time solution both with an autonomous and non-autonomous approach. The non-negativity of the solution is proven in the non-autonomous case and passed to the solution of the autonomous setting, and we compute energy estimates that show that this solution is in fact global.

To understand the dynamics of Alzheimer’s disease, we formulate a generalized mathematical model based on three events: aggregation of disease-related proteins, activation of immune cells and initiation of inflammation. We incorporate functional forms in the model to represent the complex biological interactions between components related to Alzheimer’s disease. We take explicit forms depending on the properties of functions in the model. We describe the system dynamics by locating biologically feasible steady states, determining stability properties and identifying the effective parameters. Parameters are estimated using two methods: biological literature and data fitting. We perform sensitivity and uncertainty analyses to identify the most influential parameters. Partial Rank Correlation Coefficient and scatter plots are used to visualize global sensitivity. Our results reveal that lower activation rate and higher proliferation rate of microglia may contribute to a reduction in toxic protein aggregate levels, thus slowing the disease’s early progression.

Since 2014, a model of the individual response to ionizing radiation (IR), based on the radiation-induced nucleoshuttling of the ATM protein kinase (RIANS), has been developed by our lab: after irradiation, ATM dimers monomerize in cytoplasm and diffuse into the nucleus to trigger both recognition and repair of DNA double-strand breaks (DSB), the key-damage of IR response. Moderate radiosensitivity is generally caused by heterozygous mutations of ATM substrates (called X-proteins) that are over-expressed in cytoplasm and form complexes with ATM monomers, which reduces and/or delays the RIANS and DSB recognition. Here, we asked whether molecules, rather than X-proteins, can also influence RIANS. Caffeine was chosen as a potential “X-molecule” candidate. After incubation of cells with caffeine, cutaneous fibroblasts from an apparently healthy radioresistant donor, a patient suffering from Alzheimer’s disease (AD) and another suffering from neurofibromatosis type 1 (NF1) were exposed to X-rays. The functionality of ATM-dependent DSB repair and signaling was evaluated. We report here that caffeine molecule interaction with ATM leads to the inhibition of DSB recognition. This effect is significant in radioresistant cells. Conversely, in the AD and NF1 cells, the DSB recognition is already so low that caffeine does not provide any additional molecular effect.

We propose a novel multi-scale modeling framework for infectious disease spreading, borrowing ideas and modeling tools from the so-called Refractory Density (RD) approach. We introduce a microscopic model that describes the probability of infection for a single individual and the evolution of the disease within their body. From the individual-level description, we then present the corresponding population-level model of epidemic spreading on the mesoscopic and macroscopic scale. We conclude with numerical illustrations, taking into account either a white Gaussian noise or an escape noise to showcase the potential of our approach in producing both transient and asymptotic complex dynamics as well as finite-size fluctuations consistently across multiple scales. A comparison with the epidemiology of coronaviruses is also given to corroborate the qualitative relevance of our new approach.

To understand the dynamics of Alzheimer's disease, we formulate a generalized mathematical model based on three events: aggregation of disease-related proteins, activation of immune cells, and initiation of inflammation. We incorporate functional forms in the model to represent the complex biological interactions between components related to Alzheimer's disease. We take explicit forms depending on the properties of functions in the model. We describe the system dynamics by locating biologically feasible steady states, determining stability properties, and identifying the effective parameters. Parameters are estimated using two methods: biological literature and data fitting. We perform sensitivity and uncertainty analyses to identify the most influential parameters. Partial Rank Correlation Coefficient and scatter plots are used to visualize global sensitivity. Our results reveal that lower activation rate and higher proliferation rate of microglia may contribute to a reduction in toxic protein aggregate levels, thus slowing the disease progression.

Radiation impacting astronauts in their spacecraft come from a “bath” of high-energy rays (0.1–0.5 mGy per mission day) that reaches deep tissues like the heart and bones and a “stochastic rain” of low-energy particles from the shielding and impacting surface tissues like skin and lenses. However, these two components cannot be reproduced on Earth together. The MarsSimulator facility (Toulouse University, France) emits, thanks to a bag containing thorium salts, a continuous exposure of 120 mSv/y, corresponding to that prevailing in the International Space Station (ISS). By using immunofluorescence, we assessed DNA double-strand breaks (DSB) induced by 1–5 weeks exposure in ISS of human tissues evoked above, identified at risk for space exploration. All the tissues tested elicited DSBs that accumulated proportionally to the dose at a tissue-dependent rate (about 40 DSB/Gy for skin, 3 times more for lens). For the lens, bones, and radiosensitive skin cells tested, perinuclear localization of phosphorylated forms of ataxia telangiectasia mutated protein (pATM) was observed during the 1st to 3rd week of exposure. Since pATM crowns were shown to reflect accelerated aging, these findings suggest that a low dose rate of 120 mSv/y may accelerate the senescence process of the tested tissues. A mathematical model of pATM crown formation and disappearance has been proposed. Further investigations are needed to document these results in order to better evaluate the risks related to space exploration.

Context: Although carcinogenesis is a multi-factorial process, the mutability and the capacity of cells to proliferate are among the major features of the cells that contribute together to the initiation and promotion steps of cancer formation. Particularly, mutability can be quantified by hyper-recombination rate assessed with specific plasmid assay, hypoxanthine-guanine phosphoribosyltransferase (HPRT) mutations frequency rate, or MRE11 nuclease activities. Cell proliferation can be assessed by flow cytometry by quantifying G2/M, G1 arrests, or global cellular evasion. Methods: All these assays were applied to skin untransformed fibroblasts derived from eight major cancer syndromes characterized by their excess of relative cancer risk (ERR). Results: Significant correlations with ERR were found between hyper-recombination assessed by the plasmid assay and G2/M arrest and described a third-degree polynomial ERR function and a sigmoidal ERR function, respectively. The product of the hyper-recombination rate and capacity of proliferation described a linear ERR function that permits one to better discriminate each cancer syndrome. Conclusions: Hyper-recombination and cell proliferation were found to obey differential equations that better highlight the intrinsic bases of cancer formation. Further investigations to verify their relevance for cancer proneness induced by exogenous agents are in progress.