Fig. 2: A theoretical framework for RPA-achieving intein-based integral controllers.
From: A cybergenetic framework for engineering intein-mediated integral feedback control systems
The closed-loop network is formed of a controller network, comprised of M species Z1, ⋯, ZM, connected in a feedback configuration with the regulated network, comprised of L species X1, ⋯, XL. Following the general biomolecular control paradigm37, it is assumed that the controller interacts with the regulated network via X1 and XL only, referred to as the input and regulated output species, respectively. The objective of the controller network is to steer the concentration of the regulated output XL to a prescribed value, referred to as the setpoint, despite the presence of constant disturbances and uncertainties in the regulated network. The controller network is divided into three subnetwork classes according to the list of Species Rules. The allowed reactions within and between the three subnetworks are listed as Reaction Rules. The feedback controller network operates by “sensing” the abundance of the concentration of the regulated output XL(θixL), and “actuating” the input X1 by producing it (h+(z,xL)) or removing it (h−(z,xL)). The total control action u is given by h+(z,xL) − h−(z,xL)x1. Note that, throughout the paper, the diamond-shaped arrowhead denotes either an activation or repression. The setpoint and output-sensing mechanisms are jointly encoded in the vectors μ and θ to allow for multiple setpoint/sensing-encoding reactions.
