### October 17, 2018

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### PhD Seminars I

**Talk 1**

Lucie Chambon (BIOCORE)

**Title**

A new qualitative control strategy for the genetic Toggle Switch.

**Abstract**

Positive feedback loops, such as the "Toggle Switch", are recurrent building blocks of gene regulatory networks. They are known to be essential for cell differentiation and cell decision making. In a mathematical formalism, they are classically described with a two-dimensional smooth non-linear differential system. The bistability of this classical model captures the decision properties of these biological motifs. This talk presents a new control strategy based on the measurement and control of a unique gene within the loop, in order to stabilize the system around its unstable fixed point. The quantized nature of genetic measurements and the new synthetic control approaches available in biology encourage the use of a piecewise constant control law. Interestingly, this approach may lead to a cell dedifferentiation process.

**Talk 2**

**Speaker**

**Title
**On a mean-field model of interacting neurons

**Abstract**

How to understand macroscopic phenomena in the brain - such as the emergence of oscillatory activity - using models at the scale of the neurons?

I will present a simple mathematical model of neurons. It consists of N neurons modeled by the time evolution of their membrane potential.

The dynamic of each neuron is not deterministic: each neuron can emit a spike with a probability which depends on its membrane potential.

This spike induces a jump in the membrane potential of the post-synaptic neurons connected with the spiking neuron.

I will discuss the mathematical tools needed to study the model. Emphasis will be given on how this model can capture collective effects such as oscillations of the mean activity. Numerical simulations will be presented to illustrate the theoretical results.