Toward an Early Diagnosis for Alzheimer's Disease Based on the Perinuclear Localization of the ATM Protein.

Alzheimer's disease (AD) is the most common neurodegenerative dementia, for which the molecular origins, genetic predisposition and therapeutic approach are still debated. In the 1980s, cells from AD patients were reported to be sensitive to ionizing radiation. In order to examine the molecular basis of this radiosensitivity, the ATM-dependent DNA double-strand breaks (DSB) signaling and repair were investigated by applying an approach based on the radiation-induced ataxia telangiectasia-mutated (ATM) protein nucleoshuttling (RIANS) model. Early after irradiation, all ten AD fibroblast cell lines tested showed impaired DSB recognition and delayed RIANS. AD fibroblasts specifically showed spontaneous perinuclear localization of phosphorylated ATM (pATM) forms. To our knowledge, such observation has never been reported before, and by considering the role of the ATM kinase in the stress response, it may introduce a novel interpretation of accelerated aging. Our data and a mathematical approach through a brand-new model suggest that, in response to a progressive and cumulative stress, cytoplasmic ATM monomers phosphorylate the APOE protein (pAPOE) close to the nuclear membrane and aggregate around the nucleus, preventing their entry in the nucleus and thus the recognition and repair of spontaneous DSB, which contributes to the aging process. Our findings suggest that pATM and/or pAPOE may serve as biomarkers for an early reliable diagnosis of AD on any fibroblast sample.

Theoretical evidence of osteoblast self-inhibition after activation of the genetic regulatory network controlling mineralization.

Bone is a hard-soft biomaterial built through a self-assembly process under genetic regulatory network (GRN) monitoring. This paper aims to capture the behavior of the bone GRN part that controls mineralization by using a mathematical model. Here, we provide an advanced review of empirical evidence about interactions between gene coding (i) transcription factors and (ii) bone proteins. These interactions are modeled with nonlinear differential equations using Michaelis-Menten and Hill functions. Compared to empirical evidence - coming from osteoblasts culture -, the two best systems (among 126=2,985,984 possibilities) use factors of inhibition from the start of the activation of each gene. It reveals negative indirect interactions coming from either negative feedback loops or the recently depicted micro-RNAs. The difference between the two systems also lies in the BSP equation and two ways for activating and reducing its production. Thus, it highlights the critical role of BSP in the bone GRN that acts on bone mineralization. Our study provides the first theoretical evidence of osteoblast self-inhibition after activation of the genetic regulatory network controlling mineralization with this work.

Parameter estimation and prediction for coronavirus disease outbreak 2019 (COVID-19) in Algeria.

BACKGROUND: The wave of the coronavirus disease outbreak in 2019 (COVID-19) has spread all over the world. In Algeria, the first case of COVID-19 was reported on 25 February, 2020, and the number of confirmed cases of it has increased day after day. To overcome this difficult period and a catastrophic scenario, a model-based prediction of the possible epidemic peak and size of COVID-19 in Algeria is required. METHODS: We are concerned with a classical epidemic model of susceptible, exposed, infected and removed (SEIR) population dynamics. By using the method of least squares and the best fit curve that minimizes the sum of squared residuals, we estimate the epidemic parameter and the basic reproduction number ℜ 0. Moreover, we discuss the effect of intervention in a certain period by numerical simulation. RESULTS: We find that ℜ 0 = 4.1, which implies that the epidemic in Algeria could occur in a strong way. Moreover, we obtain the following epidemiological insights: the intervention has a positive effect on the time delay of the epidemic peak; the epidemic size is almost the same for a short intervention; a large epidemic can occur even if the intervention is long and sufficiently effective. CONCLUSION: Algeria must implement the strict measures as shown in this study, which could be similar to the one that China has finally adopted.

Mathematical Modeling Predicts That Strict Social Distancing Measures Would Be Needed to Shorten the Duration of Waves of COVID-19 Infections in Vietnam.

Coronavirus disease 2019 (COVID-19) emerged in Wuhan, China in 2019, has spread throughout the world and has since then been declared a pandemic. As a result, COVID-19 has caused a major threat to global public health. In this paper, we use mathematical modeling to analyze the reported data of COVID-19 cases in Vietnam and study the impact of non-pharmaceutical interventions. To achieve this, two models are used to describe the transmission dynamics of COVID-19. The first model belongs to the susceptible-exposed-infectious-recovered (SEIR) type and is used to compute the basic reproduction number. The second model adopts a multi-scale approach which explicitly integrates the movement of each individual. Numerical simulations are conducted to quantify the effects of social distancing measures on the spread of COVID-19 in urban areas of Vietnam. Both models show that the adoption of relaxed social distancing measures reduces the number of infected cases but does not shorten the duration of the epidemic waves. Whereas, more strict measures would lead to the containment of each epidemic wave in one and a half months.

Global stability of an age-structured epidemic model with general Lyapunov functional.

In this paper, we focus on the study of the dynamics of a certain age structured epidemic model. Our aim is to investigate the proposed model, which is based on the classical SIR epidemic model, with a general class of nonlinear incidence rate with some other generalization. We are interested to the asymptotic behavior of the system. For this, we have introduced the basic reproduction number R0 of model and we prove that this threshold shows completely the stability of each steady state. Our approach is the use of general constructed Lyapunov functional with some results on the persistence theory. The conclusion is that the system has a trivial disease-free equilibrium which is globally asymptotically stable for R0 < 1 and that the system has only a unique positive endemic equilibrium which is globally asymptotically stable whenever R0 > 1. Several numerical simulations are given to illustrate our results.

Global dynamics of a differential-difference system: a case of Kermack-McKendrick SIR model with age-structured protection phase.

In this paper, we are concerned with an epidemic model of susceptible, infected and recovered (SIR) population dynamic by considering an age-structured phase of protection with limited duration, for instance due to vaccination or drugs with temporary immunity. The model is reduced to a delay differential-difference system, where the delay is the duration of the protection phase. We investigate the local asymptotic stability of the two steady states: disease-free and endemic. We also establish when the endemic steady state exists, the uniform persistence of the disease. We construct quadratic and logarithmic Lyapunov functions to establish the global asymptotic stability of the two steady states. We prove that the global stability is completely determined by the basic reproduction number.

A Novel Multiscale Mathematical Model for Building Bone Substitute Materials for Children.

Bone is an engineering marvel that achieves a unique combination of stiffness and toughness exceeding that of synthesized materials. In orthopedics, we are currently challenged for the child population that needs a less stiff but a tougher bone substitute than adults. Recent evidence suggests that the relationship between inter-molecular connections that involve the two main bone building blocks, TropoCollagen molecules (TC) and carbonated Hydroxyapatite (cAp), and bone macroscopic mechanical properties, stiffness and toughness, are key to building bone substitute materials for children. The goal of our study is to establish how inter-molecular connections that occur during bone mineralization are related to macroscopic mechanical properties in child bones. Our aim is to link the biological alterations of the TC-cAp self assembly process happening during bone mineralization to the bone macroscopic mechanical properties' alterations during aging. To do so, we have developed a multiscale mathematical model that includes collagen cross links (TC⁻TC interface) from experimental studies of bone samples to forecast bone macroscopic mechanical properties. Our results support that the Young's modulus cannot be a linear parameter if we want to solve our system. In relation to bone substitute material with innovative properties for children, our results propose values of several biological parameters, such as the number of crystals and their size, and collagen crosslink maturity for the desired bone mechanical competence. Our novel mathematical model combines mineralization and macroscopic mechanical behavior of bone and is a step forward in building mechanically customized biomimetic bone grafts that would fit children's orthopedic needs.