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Title: Polyhedral geometry and combinatorics of an autocatalytic ecosystem
Developing a mathematical understanding of autocatalysis in reaction networks has both theoretical and practical implications. We review definitions of autocatalytic networks and prove some properties for minimal autocatalytic subnetworks (MASs). We show that it is possible to classify MASs in equivalence classes, and develop mathematical results about their behavior. We also provide linear-programming algorithms to exhaustively enumerate them and a scheme to visualize their polyhedral geometry and combinatorics. We then define cluster chemical reaction networks, a framework for coarse-graining real chemical reactions with positive integer conservation laws. We find that the size of the list of minimal autocatalytic subnetworks in a maximally connected cluster chemical reaction network with one conservation law grows exponentially in the number of species. We end our discussion with open questions concerning an ecosystem of autocatalytic subnetworks and multidisciplinary opportunities for future investigation.  more » « less
Award ID(s):
2218817
PAR ID:
10523800
Author(s) / Creator(s):
; ; ;
Publisher / Repository:
Springer
Date Published:
Journal Name:
Journal of Mathematical Chemistry
Volume:
62
Issue:
5
ISSN:
0259-9791
Page Range / eLocation ID:
1012-1078
Subject(s) / Keyword(s):
Chemical reaction networks Autocatalysis Linear Programming Polyhedral Geometry
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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