UNified FramewOrk for reguLatory Dynamics (UNFOLD): Dissecting robustness, plasticity, evolvability and canalisation of biological function.

A unique balance of seemingly contradictory properties like robustness and plasticity, or evolvability and functional canalisation, characterises biological systems. To understand the basis of these properties, we investigate gene regulation, which is at the core of biological function. We simulate dynamical models of over 190 million genetic circuits covering all possible three-gene circuit structures. Our computational pipeline classifies these circuits into functional clusters by matching their temporal response shapes. Thus, we generate a dataset linking circuit structure, parameters and a corresponding functional label. Our key finding is a finite list of 20 functions that three-node genetic circuits can perform under step input and within the explored parameter space. Moreover, the structure-parameter space for these circuits tends to be primed for responses that stabilise over time following a perturbation. Every structure exhibits potential for multifunctionality with a range of 2-17 functions contingent upon parameters. We quantify network degeneracy, showing that many structural changes can be made to circuits without altering function. We define three quantities: structural, parametric, and functional diversities. Using these diversities, we construct a UNified FramewOrk for reguLatory Dynamics (UNFOLD) to analyse four key biological properties-robustness, plasticity, evolvability, and functional canalisation. Using UNFOLD, and within the explored parameter space, we identify that only 6.5% of network structures are non-plastic, while parameter sets enabling parametric robustness exist for every three-node network. We identify functionally canalised circuits from structure pairs that can be interchanged for a large number of parameter sets without a change in function. Overall, our framework offers insights into the fundamental organisation of biological networks by thorough analysis of three-node networks.