Mathematical Models of Quasi-Species Theory and Exact Results for the Dynamics

Saakian, David B.; Hu, Chin‐Kun

doi:10.1007/82_2015_471

Cited by 8 publications

(5 citation statements)

References 43 publications

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“…Since then, several extensions of the theory to non-equilibrium conditions with stochastic components have been developed, with the aim of finding general solutions for multi-peak fitness landscapes. These objectives approximate quasispecies to the real case of RNA viruses, which are compelled to deal with dramatic variations in population size and environment (reviewed in [19]). Research on quasispecies has proceeded through several theoretical and experimental avenues that include continuing studies on evolutionary optimization and the origin of life, RNA-RNA interactions and replicator networks, the error threshold in variable fitness landscapes, consideration of chemical mutagenesis and proofreading mechanisms, evolution of tumor cells, bacterial populations or stem cells, chromosomal instability, drug resistance, and conformation distributions in prions (a class of proteins with conformation-dependent pathogenic potential; in this case the quasispecies is defined by a distribution of conformations) [16,20].…”

Section: Historical Originsmentioning

confidence: 99%

Viral quasispecies

2019

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Viral quasispecies refers to a population structure that consists of extremely large numbers of variant genomes, termed mutant spectra, mutant swarms or mutant clouds. Fueled by high mutation rates, mutants arise continually, and they change in relative frequency as viral replication proceeds. The term quasispecies was adopted from a theory of the origin of life in which primitive replicons) consisted of mutant distributions, as found experimentally with present day RNA viruses. The theory provided a new definition of wild type, and a conceptual framework for the interpretation of the adaptive potential of RNA viruses that contrasted with classical studies based on consensus sequences. Standard clonal analyses and deep sequencing methodologies have confirmed the presence of myriads of mutant genomes in viral populations, and their participation in adaptive processes. The quasispecies concept applies to any biological entity, but its impact is more evident when the genome size is limited and the mutation rate is high. This is the case of the RNA viruses, ubiquitous in our biosphere, and that comprise many important pathogens. In virology, quasispecies are defined as complex distributions of closely related variant genomes subjected to genetic variation, competition and selection, and that may act as a unit of selection. Despite being an integral part of their replication, high mutation rates have an upper limit compatible with inheritable information. Crossing such a limit leads to RNA virus extinction, a transition that is the basis of an antiviral design termed lethal mutagenesis.

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Section: Historical Originsmentioning

confidence: 99%

Viral quasispecies

2019

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“…The introduction of quasispecies to virology initially described the mutant spectrum nature of RNA virus populations and subsequently emphasized internal interactions among components of the mutant distributions (reviewed in references 4, 11, and 12). The connection of this view of RNA viruses with theoretical quasispecies has been strengthened by several recent developments: (i) extensions of quasispecies theory to finite populations of replicating entities under nonequilibrium conditions (13,14), (ii) quantifications of mutant spectrum complexity by deep-sequencing methodologies (15), and (iii) experimental evidence of the existence of an error threshold for virus survival in realistic fitness landscapes (4,16). Several questions that bear on the general understanding of viral quasispecies and disease features of viral pathogens remain.…”

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confidence: 99%

Internal Disequilibria and Phenotypic Diversification during Replication of Hepatitis C Virus in a Noncoevolving Cellular Environment

Moreno

Gallego

Gregori

et al. 2017

J Virol

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Viral quasispecies evolution upon long-term virus replication in a noncoevolving cellular environment raises relevant general issues, such as the attainment of population equilibrium, compliance with the molecular-clock hypothesis, or stability of the phenotypic profile. Here, we evaluate the adaptation, mutant spectrum dynamics, and phenotypic diversification of hepatitis C virus (HCV) in the course of 200 passages in human hepatoma cells in an experimental design that precluded coevolution of the cells with the virus. Adaptation to the cells was evidenced by increase in progeny production. The rate of accumulation of mutations in the genomic consensus sequence deviated slightly from linearity, and mutant spectrum analyses revealed a complex dynamic of mutational waves, which was sustained beyond passage 100. The virus underwent several phenotypic changes, some of which impacted the virus-host relationship, such as enhanced cell killing, a shift toward higher virion density, and increased shutoff of host cell protein synthesis. Fluctuations in progeny production and failure to reach population equilibrium at the genomic level suggest internal instabilities that anticipate an unpredictable HCV evolution in the complex liver environment. Long-term virus evolution in an unperturbed cellular environment can reveal features of virus evolution that cannot be explained by comparing natural viral isolates. In the present study, we investigate genetic and phenotypic changes that occur upon prolonged passage of hepatitis C virus (HCV) in human hepatoma cells in an experimental design in which host cell evolutionary change is prevented. Despite replication in a noncoevolving cellular environment, the virus exhibited internal population disequilibria that did not decline with increased adaptation to the host cells. The diversification of phenotypic traits suggests that disequilibria inherent to viral populations may provide a selective advantage to viruses that can be fully exploited in changing environments.

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“…Another mathematical approach to the quasispecies models with permutation invariant fitness landscapes is based on the limiting procedure that transform the original system of ordinary differential equations into one first order partial differential equation of Hamilton-Jacobi type. There is a recent review of results obtained with this approach [28], therefore here we just mention the main idea. Again, for simplicity, we only present the results for model (3.1), (3.2).…”

Section: The Ising Model the Maximum Principle And The Hamilton-jacmentioning

confidence: 99%

Rigorous Mathematical Analysis of the Quasispecies Model: From Manfred Eigen to the Recent Developments

Bratus

Novozhilov

Semenov

2019

Advanced Mathematical Methods in Biosciences and Applications

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We review the major progress in the rigorous analysis of the classical quasispecies model that usually comes in two related but different forms: the Eigen model and the Crow-Kimura model. The model itself was formulated almost 50 years ago, and in its stationary form represents an easy to formulate eigenvalue problem. Notwithstanding the simplicity of the problem statement, we still lack full understanding of the behavior of the mean population fitness and the quasispecies distribution for an arbitrary fitness landscape. Our main goal in this review is two-fold: First, to highlight a number of impressive mathematical results, including some of the recent ones, which pertain to the mathematical development of the quasispecies theory. Second, to emphasize that, despite these 50 years of vigorous research, there are still very natural both biological and mathematical questions that remain to be addressed within the quasispecies framework. Our hope is that at least some of the approaches we review in this text can be of help for anyone embarking on further analysis of the quasispecies model.

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Mathematical Models of Quasi-Species Theory and Exact Results for the Dynamics

Cited by 8 publications

References 43 publications

Viral quasispecies

Viral quasispecies

Internal Disequilibria and Phenotypic Diversification during Replication of Hepatitis C Virus in a Noncoevolving Cellular Environment

Rigorous Mathematical Analysis of the Quasispecies Model: From Manfred Eigen to the Recent Developments

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