Retroactivity attenuation through signal transduction cascades

This paper considers the problem of attenuating retroactivity, that is, the effect of loads in biological networks and demonstrates that signal transduction cascades incorporating phosphotransfer modules have remarkable retroactivity attenuation ability. Uncovering the biological mechanisms for retroactivity attenuation is relevant in synthetic biology to enable bottom-up modular composition of complex circuits. It is also important in systems biology for deepening our current understanding of natural principles of modular organization. In this paper, we perform a combined theoretical and computational study of a cascade system comprising two phosphotransfer modules, ubiquitous in eukaryotic signal transduction, when subject to load from downstream targets. Employing singular perturbation on the finite time interval, we demonstrate that this system implements retroactivity attenuation when the input signal is sufficiently slow. Employing trajectory sensitivity analysis about nominal parameters that we have identified from in vivo data, we further demonstrate that the key parameters for retroactivity attenuation are those controlling the timescale of the system.