Signaling architectures that transmit unidirectional information

A signaling pathway transmits information from an upstream system to downstream systems, ideally unidirectionally. A key bottleneck to unidirectional transmission is retroactivity, which is the additional reaction flux that affects a system once its species interact with those of downstream systems. This raises the question of whether signaling pathways have developed specialized architectures that overcome retroactivity and transmit unidirectional signals. Here, we propose a general mathematical framework that provides an answer to this question. Using this framework, we analyze the ability of a variety of signaling architectures to transmit signals unidirectionally as key biological parameters are tuned. In particular, we find that single stage phosphorylation and phosphotransfer systems that transmit signals from a kinase show the following trade-off: either they impart a large retroactivity to their upstream system or they are significantly impacted by the retroactivity due to their downstream system. However, cascades of these architectures, which are highly represented in nature, can overcome this trade-off and thus enable unidirectional information transmission. By contrast, single and double phosphorylation cycles that transmit signals from a substrate impart a large retroactivity to their upstream system and are also unable to attenuate retroactivity due to their downstream system. Our findings identify signaling architectures that ensure unidirectional signal transmission and minimize crosstalk among multiple targets. Our results thus establish a way to decompose a signal transduction network into architectures that transmit information unidirectionally, while also providing a library of devices that can be used in synthetic biology to facilitate modular circuit design. Author Summary Although signaling pathways in cells are typically viewed as transmitting information unidirectionally between an 1 upstream and downstream system, such a viewpoint is not accurate in general due to retroactivity. Retroactivity in the 2 added reaction flux that changes the behavior of the upstream system because of the reactions its species participate in to 3 transmit information to downstream processes. Large retroactivity effects are therefore a major bottleneck to 4 unidirectional signal transmission. Thus, a framework that can identify signaling architectures that overcome retroactivity 5 and transmit unidirectional signals (and those that do not) is required to accurately simplify and analyze signal 6 transduction networks. In this work, we develop such a framework and analyze several signaling architectures to test for 7 their ability to transmit unidirectional signals. We find that cascades of signaling cycles that transmit information via 8 kinases are well-suited to unidirectional transmission. In contrast, signaling systems that transmit information via 9 substrates are highly susceptible to effects of retroactivity. They are thus not well-suited to unidirectional signal 10 transmission, which may explain their low frequency of occurrence in natural systems. Our results thus provide key 11 insights into cellular signal transduction, as well as provide a library of devices for synthetic biology that could be used 12 for unidirectional signaling. 13