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A Deficiency-Based Approach to Parametrizing Positive Equilibria of Biochemical Reaction Systems

February 18 @ 1:00 pm - 2:00 pm KST

B378 Seminar room, IBS, 55 Expo-ro Yuseong-gu
Daejeon, 34126 Korea, Republic of
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Speaker

Bryan Hernandez
IBS Biomedical Mathematics Group

We will discuss about “A Deficiency-Based Approach to Parametrizing Positive Equilibria of Biochemical Reaction Systems”, Johnston, Müller, and Pantea, Bulletin of Mathematical Biology, 2019

We present conditions which guarantee a parametrization of the set of positive equilibria of a generalized mass-action system. Our main results state that (1) if the underlying generalized chemical reaction network has an effective deficiency of zero, then the set of positive equilibria coincides with the parametrized set of complex-balanced equilibria and (2) if the network is weakly reversible and has a kinetic deficiency of zero, then the equilibrium set is nonempty and has a positive, typically rational, parametrization. Via the method of network translation, we apply our results to classical mass-action systems studied in the biochemical literature, including the EnvZ–OmpR and shuttled WNT signaling pathways. A parametrization of the set of positive equilibria of a (generalized) mass-action system is often a prerequisite for the study of multistationarity and allows an easy check for the occurrence of absolute concentration robustness, as we demonstrate for the EnvZ–OmpR pathway.

Details

Date:
February 18
Time:
1:00 pm - 2:00 pm KST
Event Category:

Organizer

Jae Kyoung Kim
Email:
jaekkim@kaist.ac.kr

Venue

B378 Seminar room, IBS
55 Expo-ro Yuseong-gu
Daejeon, 34126 Korea, Republic of
+ Google Map
IBS 의생명수학그룹 Biomedical Mathematics Group
기초과학연구원 수리및계산과학연구단 의생명수학그룹
대전 유성구 엑스포로 55 (우) 34126
IBS Biomedical Mathematics Group (BIMAG)
Institute for Basic Science (IBS)
55 Expo-ro Yuseong-gu Daejeon 34126 South Korea
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