Dynamics of a diffusive model for cancer stem cells with time delay in microRNA-differentiated cancer cell interactions and radiotherapy effects
Abstract Understand the dynamics of cancer stem cells (CSCs), prevent the non-recurrence of cancers and develop therapeutic strategies to destroy both cancer cells and CSCs remain a challenge topic. In this paper, we study both analytically and numerically the dynamics of CSCs under radiotherapy eff...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Nature Portfolio
2024-03-01
|
| Series: | Scientific Reports |
| Subjects: | |
| Online Access: | https://doi.org/10.1038/s41598-024-55212-4 |
| _version_ | 1797275118653669376 |
|---|---|
| author | Frank Eric Essongo Alain Mvogo Germain Hubert Ben-Bolie |
| author_facet | Frank Eric Essongo Alain Mvogo Germain Hubert Ben-Bolie |
| author_sort | Frank Eric Essongo |
| collection | DOAJ |
| description | Abstract Understand the dynamics of cancer stem cells (CSCs), prevent the non-recurrence of cancers and develop therapeutic strategies to destroy both cancer cells and CSCs remain a challenge topic. In this paper, we study both analytically and numerically the dynamics of CSCs under radiotherapy effects. The dynamical model takes into account the diffusion of cells, the de-differentiation (or plasticity) mechanism of differentiated cancer cells (DCs) and the time delay on the interaction between microRNAs molecules (microRNAs) with DCs. The stability of the model system is studied by using a Hopf bifurcation analysis. We mainly investigate on the critical time delay $$\tau _{c}$$ τ c , that represents the time for DCs to transform into CSCs after the interaction of microRNAs with DCs. Using the system parameters, we calculate the value of $$\tau _{c}$$ τ c for prostate, lung and breast cancers. To confirm the analytical predictions, the numerical simulations are performed and show the formation of spatiotemporal circular patterns. Such patterns have been found as promising diagnostic and therapeutic value in management of cancer and various diseases. The radiotherapy is applied in the particular case of prostate model. We calculate the optimum dose of radiation and determine the probability of avoiding local cancer recurrence after radiotherapy treatment. We find numerically a complete eradication of patterns when the radiotherapy is applied before a time $$t < \tau _{c}$$ t < τ c . This scenario induces microRNAs to act as suppressors as experimentally observed in prostate cancer. The results obtained in this paper will provide a better concept for the clinicians and oncologists to understand the complex dynamics of CSCs and to design more efficacious therapeutic strategies to prevent the non-recurrence of cancers. |
| first_indexed | 2024-03-07T15:09:44Z |
| format | Article |
| id | doaj.art-051b5e7e26024a358d0e78411a0758f5 |
| institution | Directory Open Access Journal |
| issn | 2045-2322 |
| language | English |
| last_indexed | 2024-03-07T15:09:44Z |
| publishDate | 2024-03-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj.art-051b5e7e26024a358d0e78411a0758f52024-03-05T18:43:11ZengNature PortfolioScientific Reports2045-23222024-03-0114111710.1038/s41598-024-55212-4Dynamics of a diffusive model for cancer stem cells with time delay in microRNA-differentiated cancer cell interactions and radiotherapy effectsFrank Eric Essongo0Alain Mvogo1Germain Hubert Ben-Bolie2Laboratory of Nuclear Physics, Dosimetry and Radiation Protection, Department of Physics, Faculty of Science, University of Yaounde ILaboratory of Biophysics, Department of Physics, Faculty of Science, University of Yaounde ILaboratory of Nuclear Physics, Dosimetry and Radiation Protection, Department of Physics, Faculty of Science, University of Yaounde IAbstract Understand the dynamics of cancer stem cells (CSCs), prevent the non-recurrence of cancers and develop therapeutic strategies to destroy both cancer cells and CSCs remain a challenge topic. In this paper, we study both analytically and numerically the dynamics of CSCs under radiotherapy effects. The dynamical model takes into account the diffusion of cells, the de-differentiation (or plasticity) mechanism of differentiated cancer cells (DCs) and the time delay on the interaction between microRNAs molecules (microRNAs) with DCs. The stability of the model system is studied by using a Hopf bifurcation analysis. We mainly investigate on the critical time delay $$\tau _{c}$$ τ c , that represents the time for DCs to transform into CSCs after the interaction of microRNAs with DCs. Using the system parameters, we calculate the value of $$\tau _{c}$$ τ c for prostate, lung and breast cancers. To confirm the analytical predictions, the numerical simulations are performed and show the formation of spatiotemporal circular patterns. Such patterns have been found as promising diagnostic and therapeutic value in management of cancer and various diseases. The radiotherapy is applied in the particular case of prostate model. We calculate the optimum dose of radiation and determine the probability of avoiding local cancer recurrence after radiotherapy treatment. We find numerically a complete eradication of patterns when the radiotherapy is applied before a time $$t < \tau _{c}$$ t < τ c . This scenario induces microRNAs to act as suppressors as experimentally observed in prostate cancer. The results obtained in this paper will provide a better concept for the clinicians and oncologists to understand the complex dynamics of CSCs and to design more efficacious therapeutic strategies to prevent the non-recurrence of cancers.https://doi.org/10.1038/s41598-024-55212-4Cancer cellsCancer stem cellsMicroRNAsHopf bifurcationTime delayCircular patterns |
| spellingShingle | Frank Eric Essongo Alain Mvogo Germain Hubert Ben-Bolie Dynamics of a diffusive model for cancer stem cells with time delay in microRNA-differentiated cancer cell interactions and radiotherapy effects Scientific Reports Cancer cells Cancer stem cells MicroRNAs Hopf bifurcation Time delay Circular patterns |
| title | Dynamics of a diffusive model for cancer stem cells with time delay in microRNA-differentiated cancer cell interactions and radiotherapy effects |
| title_full | Dynamics of a diffusive model for cancer stem cells with time delay in microRNA-differentiated cancer cell interactions and radiotherapy effects |
| title_fullStr | Dynamics of a diffusive model for cancer stem cells with time delay in microRNA-differentiated cancer cell interactions and radiotherapy effects |
| title_full_unstemmed | Dynamics of a diffusive model for cancer stem cells with time delay in microRNA-differentiated cancer cell interactions and radiotherapy effects |
| title_short | Dynamics of a diffusive model for cancer stem cells with time delay in microRNA-differentiated cancer cell interactions and radiotherapy effects |
| title_sort | dynamics of a diffusive model for cancer stem cells with time delay in microrna differentiated cancer cell interactions and radiotherapy effects |
| topic | Cancer cells Cancer stem cells MicroRNAs Hopf bifurcation Time delay Circular patterns |
| url | https://doi.org/10.1038/s41598-024-55212-4 |
| work_keys_str_mv | AT frankericessongo dynamicsofadiffusivemodelforcancerstemcellswithtimedelayinmicrornadifferentiatedcancercellinteractionsandradiotherapyeffects AT alainmvogo dynamicsofadiffusivemodelforcancerstemcellswithtimedelayinmicrornadifferentiatedcancercellinteractionsandradiotherapyeffects AT germainhubertbenbolie dynamicsofadiffusivemodelforcancerstemcellswithtimedelayinmicrornadifferentiatedcancercellinteractionsandradiotherapyeffects |