Adaptation to DNA damage as a bet-hedging mechanism in a fluctuating environment.

In response to DNA damage, efficient repair is essential for cell survival and genome integrity. In eukaryotes, the DNA damage checkpoint is a signalling pathway that coordinates this response and arrests the cell cycle to provide time for repair. However, when repair fails or when the damage is not repairable, cells can eventually bypass the DNA damage checkpoint and undergo cell division despite persistent damage, a process called adaptation to DNA damage.

Adaptive dynamics of hematopoietic stem cells and their supporting stroma: a model and mathematical analysis.

We propose a mathematical model to describe the evolution of hematopoietic stem cells (HSCs) and stromal cells in considering the bi-directional interaction between them. Cancerous cells are also taken into account in our model. HSCs are structured by a continuous phenotype characterising the population heterogeneity in a way relevant to the question at stake while stromal cells are structured by another continuous phenotype representing their capacity of support to HSCs.

Actin-Based Transport Adapts Polarity Domain Size to Local Cellular Curvature.

Intracellular structures and organelles such as the nucleus, the centrosome, or the mitotic spindle typically scale their size to cell size [1]. Similarly, cortical polarity domains built around the active form of conserved Rho-GTPases, such as Cdc42p, exhibit widths that may range over two orders of magnitudes in cells with different sizes and shapes [2-6]. The establishment of such domains typically involves positive feedback loops based on reaction-diffusion and/or actin-mediated vesicle transport [3, 7, 8].

Adaptation and fatigue model for neuron networks and large time asymptotics in a nonlinear fragmentation equation.

Motivated by a model for neural networks with adaptation and fatigue, we study a conservative fragmentation equation that describes the density probability of neurons with an elapsed time s after its last discharge. In the linear setting, we extend an argument by Laurençot and Perthame to prove exponential decay to the steady state. This extension allows us to handle coefficients that have a large variation rather than constant coefficients.