Non-normality and non-monotonic dynamics in complex reaction networks
Complex chemical reaction networks, which underlie many industrial and biological processes, often exhibit non-monotonic changes in chemical species concentrations. Such non-monotonic dynamics are in principle possible even in a linear model if the matrix defining the model is non-normal, as charact...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2020-10-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.2.043059 |
| _version_ | 1797211210286891008 |
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| author | Zachary G. Nicolaou Takashi Nishikawa Schuyler B. Nicholson Jason R. Green Adilson E. Motter |
| author_facet | Zachary G. Nicolaou Takashi Nishikawa Schuyler B. Nicholson Jason R. Green Adilson E. Motter |
| author_sort | Zachary G. Nicolaou |
| collection | DOAJ |
| description | Complex chemical reaction networks, which underlie many industrial and biological processes, often exhibit non-monotonic changes in chemical species concentrations. Such non-monotonic dynamics are in principle possible even in a linear model if the matrix defining the model is non-normal, as characterized by a necessarily non-orthogonal set of eigenvectors. However, the extent to which non-normality is responsible for non-monotonic behavior remains an open question. Here, using a master equation to model the reaction dynamics, we derive a general condition for observing non-monotonic dynamics of individual species, establishing that non-normality promotes non-monotonicity but is not a requirement for it. In contrast, we show that non-normality is a requirement for non-monotonic dynamics to be observed in the Rényi entropy. Using hydrogen combustion as an example application, we demonstrate that non-monotonic dynamics under experimental conditions are supported by a linear chain of connected components, at variance with the dominance of a single giant component observed in typical random reaction networks. The exact linearity of the master equation enables development of a rigorous theory and simulations for dynamical networks of unprecedented sizes (approaching 10^{5} dynamical variables, even for a network of only 20 reactions and involving less than 100 atoms). Our conclusions are expected to hold for other combustion processes, and the general theory we develop is applicable to all chemical reaction networks, including biological ones. |
| first_indexed | 2024-04-24T10:22:52Z |
| format | Article |
| id | doaj.art-6e9be1eb827348a1805cd2abd2820d68 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:22:52Z |
| publishDate | 2020-10-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-6e9be1eb827348a1805cd2abd2820d682024-04-12T17:02:12ZengAmerican Physical SocietyPhysical Review Research2643-15642020-10-012404305910.1103/PhysRevResearch.2.043059Non-normality and non-monotonic dynamics in complex reaction networksZachary G. NicolaouTakashi NishikawaSchuyler B. NicholsonJason R. GreenAdilson E. MotterComplex chemical reaction networks, which underlie many industrial and biological processes, often exhibit non-monotonic changes in chemical species concentrations. Such non-monotonic dynamics are in principle possible even in a linear model if the matrix defining the model is non-normal, as characterized by a necessarily non-orthogonal set of eigenvectors. However, the extent to which non-normality is responsible for non-monotonic behavior remains an open question. Here, using a master equation to model the reaction dynamics, we derive a general condition for observing non-monotonic dynamics of individual species, establishing that non-normality promotes non-monotonicity but is not a requirement for it. In contrast, we show that non-normality is a requirement for non-monotonic dynamics to be observed in the Rényi entropy. Using hydrogen combustion as an example application, we demonstrate that non-monotonic dynamics under experimental conditions are supported by a linear chain of connected components, at variance with the dominance of a single giant component observed in typical random reaction networks. The exact linearity of the master equation enables development of a rigorous theory and simulations for dynamical networks of unprecedented sizes (approaching 10^{5} dynamical variables, even for a network of only 20 reactions and involving less than 100 atoms). Our conclusions are expected to hold for other combustion processes, and the general theory we develop is applicable to all chemical reaction networks, including biological ones.http://doi.org/10.1103/PhysRevResearch.2.043059 |
| spellingShingle | Zachary G. Nicolaou Takashi Nishikawa Schuyler B. Nicholson Jason R. Green Adilson E. Motter Non-normality and non-monotonic dynamics in complex reaction networks Physical Review Research |
| title | Non-normality and non-monotonic dynamics in complex reaction networks |
| title_full | Non-normality and non-monotonic dynamics in complex reaction networks |
| title_fullStr | Non-normality and non-monotonic dynamics in complex reaction networks |
| title_full_unstemmed | Non-normality and non-monotonic dynamics in complex reaction networks |
| title_short | Non-normality and non-monotonic dynamics in complex reaction networks |
| title_sort | non normality and non monotonic dynamics in complex reaction networks |
| url | http://doi.org/10.1103/PhysRevResearch.2.043059 |
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