Quasispecies dynamics with time lags and periodic fluctuations in replication
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911020778258432 |
|---|---|
| author | Turner, Edward A. Crespo, Francisco Sardanyés, Josep Morales, Nolbert |
| author_facet | Turner, Edward A. Crespo, Francisco Sardanyés, Josep Morales, Nolbert |
| contents | Quasispecies theory provides the conceptual and theoretical bases for describing the dynamics of biological information of replicators subject to large mutation rates. This theory, initially conceived within the framework of prebiotic evolution, is also being used to investigate the evolutionary dynamics of RNA viruses and heterogeneous cancer cells populations. In this sense, efforts to approximate the initial quasispecies theory to more realistic scenarios have been made in recent decades. Despite this, how time lags in RNA synthesis and periodic fluctuations impact quasispecies dynamics remains poorly studied. In this article, we combine the theory of delayed ordinary differential equations and topological Leray-Schauder degree to investigate the classical quasispecies model in the single-peak fitness landscape considering time lags and periodic fluctuations in replication. First, we prove that the dynamics with time lags under the constant population constraint remains in the simplex in both forward and backward times. With backward mutation and periodic fluctuations, we prove the existence of periodic orbits regardless of time lags. Nevertheless, without backward mutation, neither periodic fluctuation nor the introduction of time lags leads to periodic orbits. However, in the case of periodic fluctuations, solutions converge exponentially to a periodic oscillation around the equilibria associated with a constant replication rate. We check the validity of the error catastrophe hypothesis assuming no backward mutation; we determine that the error threshold remains sound for the case of time of periodic fitness and time lags with constant fitness. Finally, our results show that the error threshold is not found with backward mutations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_10475 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quasispecies dynamics with time lags and periodic fluctuations in replication Turner, Edward A. Crespo, Francisco Sardanyés, Josep Morales, Nolbert Populations and Evolution Dynamical Systems 92D25, 34K13, 47H11 Quasispecies theory provides the conceptual and theoretical bases for describing the dynamics of biological information of replicators subject to large mutation rates. This theory, initially conceived within the framework of prebiotic evolution, is also being used to investigate the evolutionary dynamics of RNA viruses and heterogeneous cancer cells populations. In this sense, efforts to approximate the initial quasispecies theory to more realistic scenarios have been made in recent decades. Despite this, how time lags in RNA synthesis and periodic fluctuations impact quasispecies dynamics remains poorly studied. In this article, we combine the theory of delayed ordinary differential equations and topological Leray-Schauder degree to investigate the classical quasispecies model in the single-peak fitness landscape considering time lags and periodic fluctuations in replication. First, we prove that the dynamics with time lags under the constant population constraint remains in the simplex in both forward and backward times. With backward mutation and periodic fluctuations, we prove the existence of periodic orbits regardless of time lags. Nevertheless, without backward mutation, neither periodic fluctuation nor the introduction of time lags leads to periodic orbits. However, in the case of periodic fluctuations, solutions converge exponentially to a periodic oscillation around the equilibria associated with a constant replication rate. We check the validity of the error catastrophe hypothesis assuming no backward mutation; we determine that the error threshold remains sound for the case of time of periodic fitness and time lags with constant fitness. Finally, our results show that the error threshold is not found with backward mutations. |
| title | Quasispecies dynamics with time lags and periodic fluctuations in replication |
| topic | Populations and Evolution Dynamical Systems 92D25, 34K13, 47H11 |
| url | https://arxiv.org/abs/2412.10475 |