Cells express genes when they respond to environmental changes, differentiate to different cell fates, or develop into a healthy organism. Gene expression is often regulated by externally supplied cues, such as changing transcription factor concentrations. The expression in response to a changing concentration can be viewed as a type of decision that can be analyzed in terms of an information-theoretic framework. In this talk, I will show, on the examples of early development in the fruit fly and in cultured mouse stem cells, how an information-theoretic inference approach can help us understand features of a complex signalling apparatus that may be difficult to model, due to the complexity of the contributing regulatory factors. One inference approach, the information bottleneck, simplifies for molecular sensing, where signals are smooth; I will show how this can be used to understand binding site architectures. Finally, I will discuss our work on modelling and inference on noisy molecular signals in the context of wnt signalling.

Living systems exhibit various robust dynamics during system regulation, growth, and motility. However, how robustness emerges from stochastic components remains unclear. Towards understanding this, I develop topological theories that support robust edge currents and localization, effectively reducing the system function to a lower-dimensional subspace. I will introduce stochastic networks in molecular reaction space that model long and stable time scales, such as the circadian rhythm. More generally, we prove that unlike their quantum counterparts, stochastic topological systems require non-Hermiticity for edge states and strong localization. I will close by discussing experimental platforms for the detection and use of edge currents for self-assembly and replication in living systems.