Necessary conditions for ACR in Reaction Networks

Abstract: A biological system has absolute concentration robustness (ACR) for some molecular species if the concentration of this species does not vary among the different steady states that the network admits. In particular, this concentration is independent of the initial conditions. This interesting feature confers the system a highly desirable property in order to adapt to environmental conditions, which makes it useful, for instance, in synthetic biology. While some classes of networks with ACR have been described (Shinar and Feinberg 2010; Karp et al. 2012), as well as some techniques to check a network for ACR (Pérez Millán 2011; Kuwahara et al. 2017), finding networks with this property is a difficult task in general.

Motivated by this problem, we studied local and global notions of robustness on the set of (real positive) solutions of a system of polynomial equations, and in particular on the set of steady states of a reaction network. Algebraic geometry allowed us to provide a practical test on necessary conditions for ACR. Properties of real and complex algebraic varieties are necessary for the results, while the test ends up being a linear algebra computation.

algebraic geometrydynamical systemsprobability

Audience: researchers in the topic

( paper | 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!

The organizers.

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