No abstract

A signaling pathway transmits information from an upstream system to downstream systems, ideally in a unidirectional fashion. A key obstacle to unidirectional transmission is retroactivity, the additional reaction flux that affects a system once its species interact with those of downstream systems. This raises the fundamental question of whether signaling pathways have developed specialized architectures that overcome retroactivity and transmit unidirectional signals. Here, we propose a general procedure based on mathematical analysis that provides an answer to this question. Using this procedure, we analyze the ability of a variety of signaling architectures to transmit one-way (from upstream to downstream) signals, as key biological parameters are tuned. We find that single stage phosphorylation and phosphotransfer systems that transmit signals from a kinase show a stringent design tradeoff that hampers their ability to overcome retroactivity. Interestingly, cascades of these architectures, which are highly represented in nature, can overcome this tradeoff and thus enable unidirectional transmission. By contrast, phosphotransfer systems, and single and double phosphorylation cycles that transmit signals from a substrate, are unable to mitigate retroactivity effects, even when cascaded, and hence are not well suited for unidirectional information transmission. These results are largely independent of the specific reaction-rate constant values, and depend on the topology of the architectures. Our results therefore identify signaling architectures that, allowing unidirectional transmission of signals, embody modular processes that conserve their input/output behavior across multiple contexts. These findings can be used to decompose natural signal transduction networks into modules, and at the same time, they establish a library of devices that can be used in synthetic biology to facilitate modular circuit design.

Page 734, column 2, line 7 should read: However, if X T (and M T ) is made small, the system cannot attenuate the retroactivity to the output, since as the output X** is sequestered by the downstream system, there is not enough substrate available for the signaling system.

Single phosphorylation cycles have been found to have insulation device abilities, that is, they attenuate the effect of retroactivity applied by downstream systems and hence facilitate modular design in synthetic biology. It was recently discovered that this retroactivity attenuation property comes at the expense of an increased retroactivity to the input of the insulation device, wherein the device slows down the signal it receives from its upstream system. In this paper, we demonstrate that insulation devices built of cascaded phosphorylation cycles can break this tradeoff, allowing to attenuate the retroactivity applied by downstream systems while keeping a small retroactivity to the input. In particular, we show that there is an optimal number of cycles that maximally extends the linear operating region of the insulation device while keeping the desired retroactivity properties, when a common phosphatase is used. These findings provide optimal design strategies of insulation devices for synthetic biology applications.