Hopf bifurcations in an atypical p53 protein oscillator model with discrete delay or distributed delay
Human cells have a natural cancerous defense system, and p53 protein is at the core. It is well known that p53 relies on oscillatory dynamic behavior to perform tumor suppressor functions. However, the mechanism of its oscillation remains unclear. To reveal the effect of time lag on the onset of p53...
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| Format: | Article |
| Language: | English |
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Elsevier
2024-01-01
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| Series: | Results in Physics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S221137972301077X |
| _version_ | 1797350862758084608 |
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| author | Nan Liu Hongli Yang Liangui Yang |
| author_facet | Nan Liu Hongli Yang Liangui Yang |
| author_sort | Nan Liu |
| collection | DOAJ |
| description | Human cells have a natural cancerous defense system, and p53 protein is at the core. It is well known that p53 relies on oscillatory dynamic behavior to perform tumor suppressor functions. However, the mechanism of its oscillation remains unclear. To reveal the effect of time lag on the onset of p53 oscillations, we analytically and numerically investigate a possible scenario in which p53 oscillations are driven by a time lag. The model has only three nodes, two negative loops, and one delay. We focus on two types of time delays: discrete and distributed, use Hopf bifurcation theory to derive conditions for the occurrence of limit cycle oscillations, and confirm the properties of Hopf bifurcations by normal form and central manifold approaches. The analytical results are supported by numerical results. We suggest that discrete time lag promote p53 oscillations, while distributed time lag have a dual effect on p53 oscillations. These results imply that controlling the time lag in an appropriate range favors the inhibition of p53 on cancer cells. |
| first_indexed | 2024-03-08T12:52:10Z |
| format | Article |
| id | doaj.art-36f25c364fe54bcfb82883f34e8773ee |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-03-08T12:52:10Z |
| publishDate | 2024-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-36f25c364fe54bcfb82883f34e8773ee2024-01-20T04:45:18ZengElsevierResults in Physics2211-37972024-01-0156107284Hopf bifurcations in an atypical p53 protein oscillator model with discrete delay or distributed delayNan Liu0Hongli Yang1Liangui Yang2Faculty of Mathematics, Baotou Teachers’ College, Baotou 014030, ChinaSchool of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China; Corresponding author.School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, ChinaHuman cells have a natural cancerous defense system, and p53 protein is at the core. It is well known that p53 relies on oscillatory dynamic behavior to perform tumor suppressor functions. However, the mechanism of its oscillation remains unclear. To reveal the effect of time lag on the onset of p53 oscillations, we analytically and numerically investigate a possible scenario in which p53 oscillations are driven by a time lag. The model has only three nodes, two negative loops, and one delay. We focus on two types of time delays: discrete and distributed, use Hopf bifurcation theory to derive conditions for the occurrence of limit cycle oscillations, and confirm the properties of Hopf bifurcations by normal form and central manifold approaches. The analytical results are supported by numerical results. We suggest that discrete time lag promote p53 oscillations, while distributed time lag have a dual effect on p53 oscillations. These results imply that controlling the time lag in an appropriate range favors the inhibition of p53 on cancer cells.http://www.sciencedirect.com/science/article/pii/S221137972301077Xp53 oscillator modelHopf bifurcationFunctional differential equationLocal or non-local delayNormalization and central manifold methodsAnti-cancer strategy |
| spellingShingle | Nan Liu Hongli Yang Liangui Yang Hopf bifurcations in an atypical p53 protein oscillator model with discrete delay or distributed delay Results in Physics p53 oscillator model Hopf bifurcation Functional differential equation Local or non-local delay Normalization and central manifold methods Anti-cancer strategy |
| title | Hopf bifurcations in an atypical p53 protein oscillator model with discrete delay or distributed delay |
| title_full | Hopf bifurcations in an atypical p53 protein oscillator model with discrete delay or distributed delay |
| title_fullStr | Hopf bifurcations in an atypical p53 protein oscillator model with discrete delay or distributed delay |
| title_full_unstemmed | Hopf bifurcations in an atypical p53 protein oscillator model with discrete delay or distributed delay |
| title_short | Hopf bifurcations in an atypical p53 protein oscillator model with discrete delay or distributed delay |
| title_sort | hopf bifurcations in an atypical p53 protein oscillator model with discrete delay or distributed delay |
| topic | p53 oscillator model Hopf bifurcation Functional differential equation Local or non-local delay Normalization and central manifold methods Anti-cancer strategy |
| url | http://www.sciencedirect.com/science/article/pii/S221137972301077X |
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