Bifunctional enzyme action as a source of robustness in biochemical reaction networks: a novel hypergraph approach

Abstract: Substrate modification networks are ubiquitous in living, biochemical systems. We use a directed hypergraph, a generalization of a directed graph where a directed edge connects a nonempty set of nodes to another nonempty set of nodes, to model the substrate modifications. This substrate ''skeleton'' portrays information about changes to the substrates while not showing the detailed reaction steps, the identity of enzymes or that of substrate-enzyme compounds. One skeleton can underlie multiple different detailed models and reaction mechanisms. We show that certain dynamical properties, such as the existence of positive steady states or presence of concentration robustness can be inferred directly from the substrate skeleton. Concentration robustness is the property where the concentration of one species or a positive-integer linear combination of species is invariant across all positive steady states. We introduce the notion of ''current'' on a directed hypergraph, which is one of the two crucial ingredients along with bifunctional enzyme action required to produce concentration robustness. This approach is a departure from previous deficiency based results as it applies to arbitrary substrate modification networks. This is joint work with Tung Nguyen.

algebraic geometrydynamical systemsprobability

Audience: researchers in the topic

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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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