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. Interestingly, adaptation occurs with a delayed timing compared with repair and shows a large variation in time, two properties that may provide a survival advantage at the population level without interfering with repair. Here, we explore this idea by mathematically modelling cell survival in response to DNA damage and focusing on adaptation parameters. We find that the delayed adaptation timing indeed maximizes survival, but its heterogeneity is beneficial only in a fluctuating damage-inducing environment. Finally, we show that adaptation does not only contribute to survival but also to genome instability and mutations, which might represent another criterion for its selection throughout evolution. Overall, we propose that adaptation can act as a bet-hedging mechanism for cell survival in response 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. We then analyse the model in the framework of adaptive dynamics. More precisely, we study single Dirac mass steady states, their linear stability and we investigate the role of parameters in the model on the nature of the evolutionary stable distributions (ESDs) such as monomorphism, dimorphism and the uniqueness properties. We also study the dominant phenotypes by an asymptotic approach and we obtain the equation for dominant phenotypes. Numerical simulations are employed to illustrate our analytical results. In particular, we represent the case of the invasion of malignant cells as well as the case of co-existence of cancerous cells and healthy 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]. How these elements may adapt polarity domain size to cellular geometry is not known. Here, by tracking the width of successive oscillating Cdc42-GTP domains in fission yeast spores [9], we find that domain width scales with local cell-surface radii of curvature over an 8-fold range, independently of absolute cell volume, surface, or Cdc42-GTP concentration. This local scaling requires formin-nucleated cortical actin cables and the fusion of secretory vesicles transported along these cables with the membrane. These data suggest that reaction-diffusion may set a minimal domain size and that secretory vesicle transport along actin cables may dilute and extend polarity domains to adapt their size to local cell-surface curvature. This work reveals that actin networks may act as micrometric curvature sensors and uncovers a generic morphogenetic principle for how polarity domains define their size according to cell morphologies.

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. In another extension of the argument, we treat a weakly nonlinear case and prove total desynchronization in the network. For greater nonlinearities, we present a numerical study of the impact of the fragmentation term on the appearance of synchronization of neurons in the network using two "extreme" cases. Mathematics Subject Classification (2000)2010: 35B40, 35F20, 35R09, 92B20.