Complete characterization of kinetics-independent robust perfect adaptation in biochemical reaction networks

Abstract: Biological cells must precisely regulate the levels of key biomolecular species to survive and perform their functions. A specific form of this regulation is Robust Perfect Adaptation (RPA), where certain species maintain certain levels despite external disturbances, without the need to fine-tune the system’s parameters. Although RPA has been extensively studied mathematically, identifying it in complex, high-dimensional networks—along with understanding the associated regulatory mechanisms—remains a significant challenge.

This talk introduces a novel approach to identifying all RPA properties that emerge independently of the network’s kinetics in general deterministic reaction networks. The approach demonstrates that each RPA property corresponds to a subnetwork with specific topological characteristics. By leveraging this connection, we show that these structures give rise to all kinetics-independent RPA properties, enabling the systematic identification of all these properties by enumerating such subnetworks. Additionally, we identify the integral feedback controllers responsible for realizing each RPA property, framing our findings within the control-theoretic framework of the Internal Model Principle.

This is joint work with Prof. Yuji Hirono (Osaka University) and Prof. Mustafa Khammash (ETH Zürich)

algebraic geometrydynamical systemsprobability

Audience: researchers in the topic

( video )

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Seminar on the Mathematics of Reaction Networks

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This seminar series focuses on progress in mathematical theory for the study of reaction networks, mainly in biology and chemistry. The scope is broad and accommodates works arising from dynamical systems, stochastics, algebra, topology and beyond.

We aim at providing a common forum for sharing knowledge and encouraging discussion across subfields. In particular we aim at facilitating interactions between junior and established researchers. These considerations will be represented in the choice of invited speakers and we will strive to create an excellent, exciting and diverse schedule.

The seminar runs twice a month, typically on the 2nd and 4th Thursday of the month, at 17:00 Brussels time (observe that this webpage shows the schedule in your current time zone). Each session consists of two 25-minute talks followed by 5-minute questions. After the two talks, longer discussions will take place for those interested. To this end, we will use breakout rooms. For this to work well, you need to have the latest version of Zoom installed (version 5.3.0 or higher), and use the desktop client or mobile app (not supported on ChromeOS).

We look forward hearing about new work and meeting many of you over zoom! Many of the talks are recorded; to see the recording, from Past Talks, open details of the listed talk for a video link.

The organizers.

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