Synthesis of the Dynamical Properties of Feedback Loops in Bio-Pathways

Feedback loops regulate various biological functions such as oscillations, bistability, and robustness. They play a significant role in developmental signalling and failure of feedback can lead to disease. Systematic analysis of feedback loops could be useful in understanding their properties and biological effects. We propose here a method to automatically analyze feedback loops in bio-pathways and synthesize temporal logic properties which describe their dynamics. Starting with an ordinary differential equations (ODEs) based model of a bio-pathway, for a chosen feedback loop present in the pathway, we use a convolutional neural network to classify the behaviours of the key components of the feedback according to templates specified in bounded linear temporal logic (BLTL). Once a template has been identified, we instantiate the symbolic variables appearing in the template and synthesize properties using a parameter estimation procedure based on sequential hypothesis testing. We have applied this framework to a number of bio-pathway models and validated that the synthesized properties faithfully describe the behaviours of the feedback loops.