Speaker
Description
Reaction-diffusion equations provide a framework for understanding how spatial patterns emerge from biochemical networks. In quantitative biology, however, parameter values are frequently accompanied by large confidence intervals due to measurement uncertainty and limited experimental repetitions. This necessitates the study of entire families of parametrized PDEs to determine their qualitative behavior.
In this talk, we focus on a reaction-diffusion model of distributive double phosphorylation with unknown parameters. As numerical exploration of high-dimensional parameter spaces is often computationally prohibitive, we present an analytical approach to identify regions of the parameter space where the system exhibits Turing-like instabilities.
We derive a polynomial inequality — depending only on the catalytic constants and the diffusion constants of the enzyme-substrate complexes — that guarantees the existence of positive eigenvalues in the linearization of the PDE system, regardless of the values of the remaining constants. Notably, this description is structurally similar to the semi-algebraic conditions characterizing multistationarity in the corresponding ODE setting.
This is joint work with Maya Mincheva and Hannes Uecker.
