Spatial dynamics of floral organ formation

Epigenetic forest and flower morphogenesis

This paper studies the epigenetic process that leads to Angiosperms' flower architecture (flowering plants). As a case study, we analyze the flower Arabidopsis thaliana's GRN obtained during cell fate determination in the early stages of the flower's development, which was constructed in a previous work using experimental data. We start by constructing and analyzing the Epigenetic Forest, a discrete representation of Waddington's Epigenetic Landscape, obtained as the transition graph of the discrete dynamical system associated with the GRN. Next, we propose an optimization problem to model morphogenesis by defining a biologically meaningful function that accounts for the work involved in cell specialization. Finally, the problem is solved using a genetic algorithm. The optimal solution found by the algorithm correctly recovers the flower's architecture, as observed in wild type flowers and recovered in other theoretical works. Even though the case study addresses this specific problem, the method is directly applicable to other GRN's with attractors consisting of equilibrium points only and could be extended to the situation where there are periodic attractors.

Information Processing in the Brain as Optimal Entropy Transport: A Theoretical Approach

We consider brain activity from an information theoretic perspective. We analyze the information processing in the brain, considering the optimality of Shannon entropy transport using the Monge–Kantorovich framework. It is proposed that some of these processes satisfy an optimal transport of informational entropy condition. This optimality condition allows us to derive an equation of the Monge–Ampère type for the information flow that accounts for the branching structure of neurons via the linearization of this equation. Based on this fact, we discuss a version of Murray’s law in this context.