5 papers
An integrative phenotype-structured partial differential equation model for the population dynamics of epithelial-mesenchymal transition
Jules Guilberteau, Paras Jain, Mohit Kumar Jolly +2
Phenotypic heterogeneity along the epithelial-mesenchymal (E-M) axis contributes to cancer metastasis and drug resistance. Recent experimental efforts have collated detailed time-c…
A particle method for non-local advection-selection-mutation equations
Frank Ernesto Alvarez, Jules Guilberteau
The well-posedness of a non-local advection-selection-mutation problem deriving from adaptive dynamics models is shown for a wide family of initial data. A particle method is then…
Bistability and oscillatory behaviours of cyclic feedback loops
Jules Guilberteau
In this paper, we study the stability of an Ordinary Differential Equation (ODE) usually referred to as Cyclic Feedback Loop, which typically models a biological network of molecul…
Long-time behaviour of an advection-selection equation
Jules Guilberteau, Camille Pouchol, Nastassia Pouradier Duteil
We study the long-time behaviour of the advection-selection equation $$\partial_tn(t,x)+\nabla \cdot \left(f(x)n(t,x)\right)=\left(r(x)-ρ(t)\right)n(t,x),\quad ρ(t)=\int_{\mathbb{R…
Monostability and bistability of biological switches
Nastassia Pouradier Duteil, Jules Guilberteau, Camille Pouchol +1
Cell-fate transition can be modeled by ordinary differential equations (ODEs) which describe the behavior of several molecules in interaction, and for which each stable equilibrium…