We study families of chemical reaction networks , with toric steady states . Larger family members are constructed algorithmically from a smallest networkand we show that many results about the entire family can be obtained by studying the small family members only. In particular, we prove that if a small family member is multistationary, then so are all of its larger members . Further, we address the questions of model selection and experimental design  by investigating the algebraic dependencies of the chemical concentrations at positive steady state. To this end we define the positive steady state matroid as one of our central objects of study. We show that, given a family with toric steady states and a constant number of conservation relations, we can build a chain of matroids that encodes important algebraic information regarding the steady state behaviour of the entire family  .
We study families of chemical reaction networks whose positive steady states are toric, and therefore can be parameterized by monomials. Families are constructed algorithmically from a core network; we show that if a family member is multistationary, then so are all subsequent networks in the family . Further, we address the questions of model selection and experimental design for families by investigating the algebraic dependencies of the chemical concentrations using matroids. Given a family with toric steady states and a constant number of conservation relations, we construct a matroid that encodes important information regarding the steady state behaviour of the entire family . Among other things, this gives necessary conditions for the distinguishability of families of reaction networks with respect to a data set of measured chemical concentrations. We illustrate our results using multi-site phosphorylation networks .
R
, with toric steady states . Larger family members
whose positive steady states are toric, and therefore can be parameterized by monomials. Families
R
smallest networkand
core network;
R
many results about the entire family can be obtained by studying the small family members only. In particular, we prove that if a small
if a
R
of its larger members
subsequent networks in the family
A
for families
R
at positive steady state. To this end we define the positive steady state matroid as one of our central objects of study. We show that, given
using matroids. Given
R
can build a chain of matroids
construct a matroid
D
algebraic
A
. Among other things, this gives necessary conditions for the distinguishability of families of reaction networks with respect to a data set of measured chemical concentrations. We illustrate our results using multi-site phosphorylation networks