Investigation of a Biochemical Model with Recycling in Case of Negative Cooperativity
The objective of this paper is to find new dynamic perspectives in a well-known two dimensional nonlinear system which is a modification of the phosphofructo kinase model by incorporating recycling of the product, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" di...
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2025-01-01
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| author | Svetoslav G. Nikolov Vassil M. Vassilev Momchil I. Nenov |
| author_facet | Svetoslav G. Nikolov Vassil M. Vassilev Momchil I. Nenov |
| author_sort | Svetoslav G. Nikolov |
| collection | DOAJ |
| description | The objective of this paper is to find new dynamic perspectives in a well-known two dimensional nonlinear system which is a modification of the phosphofructo kinase model by incorporating recycling of the product, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>p</mi></semantics></math></inline-formula>, into the substrate, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>s</mi></semantics></math></inline-formula>. Specifically, we investigate the affect of the negative cooperativity on the number of equilibria and their stability. Moreover, in the parameter space, we analyze analytically and numerically the number of periodic oscillations (solutions) and their stability using Lyapunov coefficients (in other words, quantities and focus values). Thus, we obtain that three different dynamical conditions (regimes) take place: (1) structurally unstable, (2) the existence of an unstable limit cycle with an external stable limit cycle, and (3) the existence of a stable limit cycle with an external unstable limit cycle. Moreover, for a zero rate of product synthesis (due to e.g., defective enzyme), we obtain that the modified system has a first integral. |
| format | Article |
| id | doaj-art-a9cfdd362cdd40b8b35d19e485ffa675 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-a9cfdd362cdd40b8b35d19e485ffa6752025-01-24T13:39:56ZengMDPI AGMathematics2227-73902025-01-0113226010.3390/math13020260Investigation of a Biochemical Model with Recycling in Case of Negative CooperativitySvetoslav G. Nikolov0Vassil M. Vassilev1Momchil I. Nenov2Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, BulgariaInstitute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, BulgariaInstitute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, BulgariaThe objective of this paper is to find new dynamic perspectives in a well-known two dimensional nonlinear system which is a modification of the phosphofructo kinase model by incorporating recycling of the product, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>p</mi></semantics></math></inline-formula>, into the substrate, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>s</mi></semantics></math></inline-formula>. Specifically, we investigate the affect of the negative cooperativity on the number of equilibria and their stability. Moreover, in the parameter space, we analyze analytically and numerically the number of periodic oscillations (solutions) and their stability using Lyapunov coefficients (in other words, quantities and focus values). Thus, we obtain that three different dynamical conditions (regimes) take place: (1) structurally unstable, (2) the existence of an unstable limit cycle with an external stable limit cycle, and (3) the existence of a stable limit cycle with an external unstable limit cycle. Moreover, for a zero rate of product synthesis (due to e.g., defective enzyme), we obtain that the modified system has a first integral.https://www.mdpi.com/2227-7390/13/2/260biochemical modelnegative cooperativitybifurcation analysisLyapunov coefficients |
| spellingShingle | Svetoslav G. Nikolov Vassil M. Vassilev Momchil I. Nenov Investigation of a Biochemical Model with Recycling in Case of Negative Cooperativity Mathematics biochemical model negative cooperativity bifurcation analysis Lyapunov coefficients |
| title | Investigation of a Biochemical Model with Recycling in Case of Negative Cooperativity |
| title_full | Investigation of a Biochemical Model with Recycling in Case of Negative Cooperativity |
| title_fullStr | Investigation of a Biochemical Model with Recycling in Case of Negative Cooperativity |
| title_full_unstemmed | Investigation of a Biochemical Model with Recycling in Case of Negative Cooperativity |
| title_short | Investigation of a Biochemical Model with Recycling in Case of Negative Cooperativity |
| title_sort | investigation of a biochemical model with recycling in case of negative cooperativity |
| topic | biochemical model negative cooperativity bifurcation analysis Lyapunov coefficients |
| url | https://www.mdpi.com/2227-7390/13/2/260 |
| work_keys_str_mv | AT svetoslavgnikolov investigationofabiochemicalmodelwithrecyclingincaseofnegativecooperativity AT vassilmvassilev investigationofabiochemicalmodelwithrecyclingincaseofnegativecooperativity AT momchilinenov investigationofabiochemicalmodelwithrecyclingincaseofnegativecooperativity |