We will discuss about “Absolute concentration robustness in networks with low-dimensional stoichiometric subspace”, Meshkat, Nicolette, Anne Shiu, and Angelica Torres., Vietnam Journal of Mathematics 50.3 (2022): 623-651.<\/p>\n
Abstract:<\/p>\n
A reaction system exhibits \u201cabsolute concentration robustness\u201d (ACR) in some species if the positive steady-state value of that species does not depend on initial conditions. Mathematically, this means that the positive part of the variety of the steady-state ideal lies entirely in a hyperplane of the form xi = c, for some c >\u20090. Deciding whether a given reaction system \u2013 or those arising from some reaction network \u2013 exhibits ACR is difficult in general, but here we show that for many simple networks, assessing ACR is straightforward. Indeed, our criteria for ACR can be performed by simply inspecting a network or its standard embedding into Euclidean space. Our main results pertain to networks with many conservation laws, so that all reactions are parallel to one other. Such \u201cone-dimensional\u201d networks include those networks having only one species. We also consider networks with only two reactions, and show that ACR is characterized by a well-known criterion of Shinar and Feinberg. Finally, up to some natural ACR-preserving operations \u2013 relabeling species, lengthening a reaction, and so on \u2013 only three families of networks with two reactions and two species have ACR. Our results are proven using algebraic and combinatorial techniques.<\/p>\n
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We will discuss about “Absolute concentration robustness in networks with low-dimensional stoichiometric subspace”, Meshkat, Nicolette, Anne Shiu, and Angelica Torres., Vietnam Journal of Mathematics 50.3 (2022): 623-651. Abstract: A reaction … <\/p>\n