Re-Examination of the Sel’kov Model of Glycolysis and Its Symmetry-Breaking Instability Due to the Impact of Diffusion with Implications for Cancer Imitation Caused by the Warburg Effect
We revisit the seminal model of glycolysis first proposed by Sel’kov more than fifty years ago. We investigate the onset of instabilities in biological systems described by the Sel’kov model in order to determine the conditions of the model parameters that lead to bifurcations. We analyze the glycol...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-11-01
|
| Series: | Biophysica |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2673-4125/4/4/36 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1846105570620211200 |
|---|---|
| author | Miljko V. Satarić Tomas Nemeš Jack A. Tuszynski |
| author_facet | Miljko V. Satarić Tomas Nemeš Jack A. Tuszynski |
| author_sort | Miljko V. Satarić |
| collection | DOAJ |
| description | We revisit the seminal model of glycolysis first proposed by Sel’kov more than fifty years ago. We investigate the onset of instabilities in biological systems described by the Sel’kov model in order to determine the conditions of the model parameters that lead to bifurcations. We analyze the glycolysis reaction under the circumstances when the diffusivity of both ATP and ADP reactants are taken into account. We estimate the critical value of the model’s single compact dimensionless parameter, which is responsible for the onset of reaction instability and the system’s symmetry breaking. It appears that it leads to spatial inhomogeneities of reactants, leading to the formation of standing waves instead of a homogeneous distribution of ATP molecules. The consequences of this model and its results are discussed in the context of the Warburg effect, which signifies a transition from oxidative phosphorylation to glycolysis that is correlated with the initiation and progression of cancer. Our analysis may lead to the selection of therapeutic interventions in order to prevent the symmetry-breaking phenomenon described in our work. |
| format | Article |
| id | doaj-art-7c48a41aea854b80b67f9938be00bd9d |
| institution | Kabale University |
| issn | 2673-4125 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Biophysica |
| spelling | doaj-art-7c48a41aea854b80b67f9938be00bd9d2024-12-27T14:14:06ZengMDPI AGBiophysica2673-41252024-11-014454556010.3390/biophysica4040036Re-Examination of the Sel’kov Model of Glycolysis and Its Symmetry-Breaking Instability Due to the Impact of Diffusion with Implications for Cancer Imitation Caused by the Warburg EffectMiljko V. Satarić0Tomas Nemeš1Jack A. Tuszynski2Branch in Novi Sad, Serbian Academy of Sciences and Arts, Nikole Pasica 6, 21101 Novi Sad, SerbiaFaculty of Technical Sciences, University of Novi Sad, Trg Dositeja Obradovica 6, 21102 Novi Sad, SerbiaDepartment of Physics, University of Alberta, Edmonton, AB T6G 2E1, CanadaWe revisit the seminal model of glycolysis first proposed by Sel’kov more than fifty years ago. We investigate the onset of instabilities in biological systems described by the Sel’kov model in order to determine the conditions of the model parameters that lead to bifurcations. We analyze the glycolysis reaction under the circumstances when the diffusivity of both ATP and ADP reactants are taken into account. We estimate the critical value of the model’s single compact dimensionless parameter, which is responsible for the onset of reaction instability and the system’s symmetry breaking. It appears that it leads to spatial inhomogeneities of reactants, leading to the formation of standing waves instead of a homogeneous distribution of ATP molecules. The consequences of this model and its results are discussed in the context of the Warburg effect, which signifies a transition from oxidative phosphorylation to glycolysis that is correlated with the initiation and progression of cancer. Our analysis may lead to the selection of therapeutic interventions in order to prevent the symmetry-breaking phenomenon described in our work.https://www.mdpi.com/2673-4125/4/4/36glycolysisATPADPdiffusionsymmetry-breaking instability |
| spellingShingle | Miljko V. Satarić Tomas Nemeš Jack A. Tuszynski Re-Examination of the Sel’kov Model of Glycolysis and Its Symmetry-Breaking Instability Due to the Impact of Diffusion with Implications for Cancer Imitation Caused by the Warburg Effect Biophysica glycolysis ATP ADP diffusion symmetry-breaking instability |
| title | Re-Examination of the Sel’kov Model of Glycolysis and Its Symmetry-Breaking Instability Due to the Impact of Diffusion with Implications for Cancer Imitation Caused by the Warburg Effect |
| title_full | Re-Examination of the Sel’kov Model of Glycolysis and Its Symmetry-Breaking Instability Due to the Impact of Diffusion with Implications for Cancer Imitation Caused by the Warburg Effect |
| title_fullStr | Re-Examination of the Sel’kov Model of Glycolysis and Its Symmetry-Breaking Instability Due to the Impact of Diffusion with Implications for Cancer Imitation Caused by the Warburg Effect |
| title_full_unstemmed | Re-Examination of the Sel’kov Model of Glycolysis and Its Symmetry-Breaking Instability Due to the Impact of Diffusion with Implications for Cancer Imitation Caused by the Warburg Effect |
| title_short | Re-Examination of the Sel’kov Model of Glycolysis and Its Symmetry-Breaking Instability Due to the Impact of Diffusion with Implications for Cancer Imitation Caused by the Warburg Effect |
| title_sort | re examination of the sel kov model of glycolysis and its symmetry breaking instability due to the impact of diffusion with implications for cancer imitation caused by the warburg effect |
| topic | glycolysis ATP ADP diffusion symmetry-breaking instability |
| url | https://www.mdpi.com/2673-4125/4/4/36 |
| work_keys_str_mv | AT miljkovsataric reexaminationoftheselkovmodelofglycolysisanditssymmetrybreakinginstabilityduetotheimpactofdiffusionwithimplicationsforcancerimitationcausedbythewarburgeffect AT tomasnemes reexaminationoftheselkovmodelofglycolysisanditssymmetrybreakinginstabilityduetotheimpactofdiffusionwithimplicationsforcancerimitationcausedbythewarburgeffect AT jackatuszynski reexaminationoftheselkovmodelofglycolysisanditssymmetrybreakinginstabilityduetotheimpactofdiffusionwithimplicationsforcancerimitationcausedbythewarburgeffect |