Vol. 13, No. 5, 2020

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Mixed volume of small reaction networks

Nida Obatake, Anne Shiu and Dilruba Sofia

Vol. 13 (2020), No. 5, 845–860
Abstract

An important invariant of a chemical reaction network is its maximum number of positive steady states. This number, however, is in general difficult to compute. Nonetheless, there is an upper bound on this number — namely, a network’s mixed volume — that is easy to compute. Moreover, recent work has shown that, for certain biological signaling networks, the mixed volume does not greatly exceed the maximum number of positive steady states. Continuing this line of research, we further investigate this overcount and also compute the mixed volumes of small networks, those with only a few species or reactions.

Keywords
chemical reaction network, steady state, Newton polytope, mixed volume
Mathematical Subject Classification
Primary: 52A39, 12D10, 37C10
Secondary: 65H04, 80A30
Milestones
Received: 1 May 2020
Revised: 10 September 2020
Accepted: 20 September 2020
Published: 5 December 2020

Communicated by Suzanne Lenhart
Authors
Nida Obatake
Department of Mathematics
Texas A&M University
College Station, TX
United States
Anne Shiu
Department of Mathematics
Texas A&M University
College Station, TX
United States
Dilruba Sofia
Department of Mathematics and Statistics
University of Massachusetts
Amherst, MA
United States