Identification and immunological characterization of cuproptosis-related molecular clusters in Alzheimer's disease

IntroductionAlzheimer's disease is the most common dementia with clinical and pathological heterogeneity. Cuproptosis is a recently reported form of cell death, which appears to result in the progression of various diseases. Therefore, our study aimed to explore cuproptosis-related molecular clusters in Alzheimer's disease and construct a prediction model.MethodsBased on the GSE33000 dataset, we analyzed the expression profiles of cuproptosis regulators and immune characteristics in Alzheimer's disease. Using 310 Alzheimer's disease samples, we explored the molecular clusters based on cuproptosis-related genes, along with the related immune cell infiltration. Cluster-specific differentially expressed genes were identified using the WGCNA algorithm. Subsequently, the optimal machine model was chosen by comparing the performance of the random forest model, support vector machine model, generalized linear model, and eXtreme Gradient Boosting. Nomogram, calibration curve, decision curve analysis, and three external datasets were applied for validating the predictive efficiency.ResultsThe dysregulated cuproptosis-related genes and activated immune responses were determined between Alzheimer's disease and non-Alzheimer's disease controls. Two cuproptosis-related molecular clusters were defined in Alzheimer's disease. Analysis of immune infiltration suggested the significant heterogeneity of immunity between distinct clusters. Cluster2 was characterized by elevated immune scores and relatively higher levels of immune infiltration. Functional analysis showed that cluster-specific differentially expressed genes in Cluster2 were closely related to various immune responses. The Random forest machine model presented the best discriminative performance with relatively lower residual and root mean square error, and a higher area under the curve (AUC = 0.9829). A final 5-gene-based random forest model was constructed, exhibiting satisfactory performance in two external validation datasets (AUC = 0.8529 and 0.8333). The nomogram, calibration curve, and decision curve analysis also demonstrated the accuracy to predict Alzheimer's disease subtypes. Further analysis revealed that these five model-related genes were significantly associated with the Aβ-42 levels and β-secretase activity.ConclusionOur study systematically illustrated the complicated relationship between cuproptosis and Alzheimer's disease, and developed a promising prediction model to evaluate the risk of cuproptosis subtypes and the pathological outcome of Alzheimer's disease patients

Analysis of large amplitude shock profiles for non-equilibrium radiative hydrodynamics: formation of Zeldovich spikes

International audienceWe consider a model for the interaction of a gas with photons. In a former article, smooth traveling wave solutions called shock profiles have been constructed under a suitable smallness assumption between the asymptotic states. In this work, we construct piecewise smooth traveling wave solutions that connect two asymptotic states with a large jump. In particular, we give a rigorous mathematical justification to the formation of the so-called Zeldovich spike

Shock Profiles for Non Equilibrium Radiating Gases

We study a model of radiating gases that describes the interaction of an inviscid gas with photons. We show the existence of smooth traveling waves called 'shock profiles', when the strength of the shock is small. Moreover, we prove that the regularity of the traveling wave increases when the strength of the shock tends to zero

Modèles mathématiques de la théorie du transfert radiatif

We are interested in various different models arising in radiative transfer, which describe the interactions between the medium and the photons. The radiation is described in terms of energy and energy flux in the macroscopic view, the material being described by the Euler equations (radiative hydrodynamic model). In another way, the radiation can be seen as a collection of photons, in the microscopic view point ; the photons can be absorbed or emitted by the material. The absorption and the emission of photons depend on the internal excitation and ionization state of the material. We begin with the local existence (in time) of smooth solutions to a system coupling the Euler equations and the transfer equation. This system describes the exchange of energy and moment between the radiation and the material. Next, we give an asymptotic discussion for this model in the NON-LTE regime and get a simple system : coupling the Euler equations with an elliptic equation. We show the existence of (smooth) shock profiles to this system and the regularity of the shock profile as a function of the strength of the shock. Then we study the asymptotic stability of the shock profile. Finally, we study a system describing the radiation and the internal state of the material, in the microscopic view point.We prove the existence of the solution to this system and study the convergence towards the statistical equilibrium. The theoretical results are illustrated by numerical simulations.On s'intéresse dans ce travail à différents modèles de transfert radiatif, décrivant les interactions entre la matière et les photons. Les radiations sont décrites en termes d'énergie et flux d'énergie, dans le cas macroscopique, le flfluide environnant est quant à lui décrit par les équations d'Euler (modèle d'hydrodynamique radiative). Dans le cas microscopique, le champ radiatif est vu comme une collection des photons interagissant avec la matière par des mécanismes d'absorption-émission. Ces mécanismes dépendent des états d'excitation interne et d'ionisation de la matière. On commence par monter l'existence locale de solutions régulières pour un système couplant les équations d'Euler et l'équation du transfert radiatif. Ce système est obtenu à partir du bilan d'énergie et d'impulsion totale. Puis on fait une discussion asymptotique pour ce modèle dans le régime hors équilibre et on obtient un système simple couplant les équations d'Euler et une équation elliptique. On montre l'existence des profifils de choc (réguliers) pour ce système, et la régularité de ces profils en fonction de l'amplitude du choc. Puis on étudie la stabilité asymptotique de ces profifils. Enfifin, on présente une étude d'un système décrivant le champ radiatif et les états internes de la matière. On montre l'existence de solutions pour ce système et on établit rigoureusement la convergence vers l'équilibre statistique. Les résultats théoriques sont illustrés par des simulations numériques

Global existence to the equilibrium diffusion model in radiative hydrodynamics

International audienceThis paper is devoted to the analysis of the Cauchy problem for a system of PDEs arising in radiative hydrodynamics. This system, which comes from the so-called equilibrium diffusion regime, is a variant of the usual Euler equations, where the energy and pressure functionals are modified to take into account the effect of radiation and the energy balance containing a nonlinear diffusion term acting on the temperature. The problem is studied in the multi-dimensional framework. The authors identify the existence of a strictly convex entropy and a stability property of the system, and check that the Kawashima-Shizuta condition holds. Then, based on these structure properties, the well-posedness close to a constant state can be proved by using fine energy estimates. The asymptotic decay of the solutions are also investigated

Mathematicals models of the theory of the radiative transfer

On s'intéresse dans ce travail à différents modèles de transfert radiatif, décrivant les interactions entre la matière et les photons. Les radiations sont décrites en termes d'énergie et flux d'énergie, dans le cas macroscopique, le fluide environnant est quant à lui décrit par les équations d'Euler (modèle d'hydrodynamique radiative). Dans le cas microscopique, le champ radiatif est vu comme une collection des photons interagissant avec la matière par des mécanismes d'absorption-émission. Ces mécanismes dépendent des états d'excitation interne et d'ionisation de la matière. On commence par monter l'existence locale de solutions régulières pour un système couplant les équations d'Euler et l'équation du transfert radiatif. Ce système est obtenu à partir du bilan d'énergie et d'impulsion totale. Puis on fait une discussion asymptotique pour ce modèle dans le régime hors équilibre et on obtient un système simple couplant les équations d'Euler et une équation elliptique. On montre l'existence des profils de choc (réguliers) pour ce système, et la régularité de ces profils en fonction de l'amplitude du choc. Puis on étudie la stabilité asymptotique de ces profils. Enfin, on présente une étude d'un système décrivant le champ radiatif et les états internes de la matière. On montre l'existence de solutions pour ce système et on établit rigoureusement la convergence vers l'équilibre statistique.LILLE1-BU (590092102) / SudocSudocFranceF

The strong relaxation limit of the multidimensional Euler equations

International audienceThis paper is devoted to the analysis of global smooth solutions to the multidimensional isentropic Euler equations with sti relaxation. We show that the asymptotic behavior of the global smooth solution is governed by the porous media equation as the relaxation time tends to zero. The results are proved by combining some classical energy estimates with the so-called Shizuta-Kawashima condition