Marie-Aimée Dronne

Role of astrocytes in grey matter during stroke: a modelling approach.

The astrocytic response to stroke is extremely complex and incompletely understood. On the one hand, astrocytes are known to be neuroprotective when extracellular glutamate or potassium is slightly increased. But, on the other hand, they are considered to contribute to the extracellular glutamate increase during severe ischaemia. A mathematical model is used to reproduce the dynamics of the membrane potentials, intracellular and extracellular concentrations and volumes of neurons and astrocytes during ischaemia in order to study the role of astrocytes in grey matter during the first hour of a stroke. Under conditions of mild ischaemia, astrocytes are observed to take up glutamate via the glutamate transporter, and potassium via the Na/K/Cl cotransporter, which limits glutamate and potassium increase in the extracellular space. On the contrary, under conditions of severe ischaemia, astrocytes appear to be unable to maintain potassium homeostasis. Moreover, they are shown to contribute to the excitotoxicity process by expelling glutamate out of the cells via the reversed glutamate transporter. A detailed understanding of astrocytic function and influence on neuron survival during stroke is necessary to improve the neuroprotective strategies for stroke patients.

Modelling methodology in physiopathology.

Diseases are complex systems. Modelling them, i.e. systems physiopathology, is a quite demanding, complicated, multidimensional, multiscale process. As such, in order to achieve the goal of the model and further to optimise a rather-time and resource-consuming process, a relevant and easy to practice methodology is required. It includes guidance for validation. Also, the model development should be managed as a complicated process, along a strategy which has been elaborated in the beginning. It should be flexible enough to meet every case. A model is a representation of the available knowledge. All available knowledge does not have the same level of evidence and, further, there is a large variability of the values of all parameters (e.g. affinity constant or ionic current) across the literature. In addition, in a complex biological system there are always values lacking for a few or sometimes many parameters. All these three aspects are sources of uncertainty on the range of validity of the models and raise unsolved problems for designing a relevant model. Tools and techniques for integrating the parameter range of experimental values, level of evidence and missing data are needed.

Exploration of beneficial and deleterious effects of inflammation in stroke: dynamics of inflammation cells

The inflammatory process during stroke consists of activation of resident brain microglia and recruitment of leucocytes, namely neutrophils and monocytes/macrophages. During inflammation, microglial cells, neutrophils and macrophages secrete inflammatory cytokines and chemokines, and phagocytize dead cells. The recruitment of blood cells (neutrophils and macrophages) is mediated by the leucocyte–endothelium interactions and more specifically by cell adhesion molecules. A mathematical model is proposed to represent the dynamics of various brain cells and of immune cells (neutrophils and macrophages). This model is based on a set of six ordinary differential equations and explores the beneficial and deleterious effects of inflammation, respectively phagocytosis by immune cells and the release of pro-inflammatory mediators and nitric oxide (NO). The results of our simulations are qualitatively consistent with those observed in experiments in vivo and would suggest that the increase of phagocytosis could contribute to the increase of the percentage of living cells. The inhibition of the production of cytokines and NO and the blocking of neutrophil and macrophage infiltration into the brain parenchyma led also to the improvement of brain cell survival. This approach may help to explore the respective contributions of the beneficial and deleterious roles of the inflammatory process in stroke, and to study various therapeutic strategies in order to reduce stroke damage.

A numerical study of the blocking of migraine by Rolando sulcus.

Migraine with aura is a complex phenomena, which remains still not completely understood. A striking fact is that its clinical manifestations may change from one patient to another. Migraine with aura may only consist in visual hallucinations, but may as well go on to temporary aphasy. However, for all the patients it always stops before it goes from area 3 to area 4, thus just before crossing Rolando sulcus. In this paper, we give arguments showing that the detailed geometry of Rolando sulcus in human cortex may by itself explain that migraine attack never crosses Rolando sulcus.

Examples of the influence of the geometry on the propagation of progressive waves

In this paper, we give examples of the influence of the domain of propagation on progressive waves. More precisely, we numerically investigate the propagation of reaction diffusion waves in cylinders with variable radius. We show that, when the radius rapidly expands from a very small radius to a larger one, depending on the viscosity and the nonlinearity, the travelling wave may be blocked. The aim of this paper is to give numerical illustrations and quantifications of this effect, and to propose some conjectures which could be interesting subjects for further mathematical investigations. This work is linked to the study of spreading depression (SD), a propagative mechanism in brain and various tissues which has been observed in vivo and in vitro in many species since their discovery in 1944 by Leao. As a matter of fact, their direct observation in Man is still controversial. The complex structure of gray and white matter in humans may block the propagation of SD over large distances in brain and thus explain the difficulty of observing it. Medical consequences of the current numerical studies are detailed in [M.A. Dronne, et al., Influence of brain geometry on spreading depressions: A computationnal study, Progress in Biophysics and Molecular Biology 97 (1) (2008) 54-59] and a first mathematical approach given in [M.A. Dronne, E. Grenier, H. Gilquin, Modelization of spreading depressions following Nedergaard, preprint, 2003].

In Silico Study of the Influence of Intensity and Duration of Blood Flow Reduction on Cell Death Through Necrosis or Apoptosis During Acute Ischemic Stroke

Ischemic stroke involves numerous and complex pathophysiological mechanisms including blood flow reduction, ionic exchanges, spreading depressions and cell death through necrosis or apoptosis. We used a mathematical model based on these phenomena to study the influences of intensity and duration of ischemia on the final size of the infarcted area. This model relies on a set of ordinary and partial differential equations. After a sensibility study, the model was used to carry out in silico experiments in various ischemic conditions. The simulation results show that the proportion of apoptotic cells increases when the intensity of ischemia decreases, which contributes to the model validation. The simulation results also show that the influence of ischemia duration on the infarct size is more complicated. They suggest that reperfusion is beneficial when performed in the early stroke but may be either inefficacious or even deleterious when performed later after the stroke onset. This aggravation could be explained by the depolarisation waves which might continue to spread ischemic damage and by the speeding up of the apoptotic process leading to cell death. The effect of reperfusion on cell death through these two phenomena needs to be further studied in order to develop new therapeutic strategies for stroke patients.

Transcriptional regulation of CRMP5 controls neurite outgrowth through Sox5

Transcriptional regulation of proteins involved in neuronal polarity is a key process that underlies the ability of neurons to transfer information in the central nervous system. The Collapsin Response Mediator Protein (CRMP) family is best known for its role in neurite outgrowth regulation conducting to neuronal polarity and axonal guidance, including CRMP5 that drives dendrite differentiation. Although CRMP5 is able to control dendritic development, the regulation of its expression remains poorly understood. Here we identify a Sox5 consensus binding sequence in the putative promoter sequence upstream of the CRMP5 gene. By luciferase assays we show that Sox5 increases CRMP5 promoter activity, but not if the putative Sox5 binding site is mutated. We demonstrate that Sox5 can physically bind to the CRMP5 promoter DNA in gel mobility shift and chromatin immunoprecipitation assays. Using a combination of real-time RT-PCR and quantitative immunocytochemistry, we provide further evidence for a Sox5-dependent upregulation of CRMP5 transcription and protein expression in N1E115 cells: a commonly used cell line model for neuronal differentiation. Furthermore, we report that increasing Sox5 levels in this neuronal cell line inhibits neurite outgrowth. This inhibition requires CRMP5 because CRMP5 knockdown prevents the Sox5-dependent effect. We confirm the physiological relevance of the Sox5–CRMP5 pathway in the regulation of neurite outgrowth using mouse primary hippocampal neurons. These findings identify Sox5 as a critical modulator of neurite outgrowth through the selective activation of CRMP5 expression.