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Article ; Online: Generalized quasispecies model on finite metric spaces: isometry groups and spectral properties of evolutionary matrices.

Semenov, Yuri S / Novozhilov, Artem S

2018 Volume 78, Issue 3, Page(s) 837–878

Abstract: The quasispecies model introduced by Eigen in 1971 has close connections with the isometry group of the space of binary sequences relative to the Hamming distance metric. Generalizing this observation we introduce an abstract quasispecies model on a ... ...

Abstract	The quasispecies model introduced by Eigen in 1971 has close connections with the isometry group of the space of binary sequences relative to the Hamming distance metric. Generalizing this observation we introduce an abstract quasispecies model on a finite metric space X together with a group of isometries [Formula: see text] acting transitively on X. We show that if the domain of the fitness function has a natural decomposition into the union of tG-orbits, G being a subgroup of [Formula: see text], then the dominant eigenvalue of the evolutionary matrix satisfies an algebraic equation of degree at most [Formula: see text], where R is the orbital ring that is defined in the text. The general theory is illustrated by three detailed examples. In the first two of them the space X is taken to be the metric space of vertices of a regular polytope with the natural "edge" metric, these are the cases of a regular m-gon and of a hyperoctahedron; the final example takes as X the quotient rings [Formula: see text] with p-adic metric.
MeSH term(s)	Biological Evolution ; Genetic Fitness ; Mathematical Concepts ; Models, Biological ; Mutation ; Species Specificity ; Systems Biology
Language	English
Publishing date	2018-09-05
Publishing country	Germany
Document type	Journal Article
ZDB-ID	187101-8
ISSN	1432-1416 ; 0303-6812
ISSN (online)	1432-1416
ISSN	0303-6812
DOI	10.1007/s00285-018-1294-y
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Book ; Online: On a hypercycle equation with infinitely many members

Bratus, Alexander S. / Chmereva, Olga S. / Yegorov, Ivan / Novozhilov, Artem S.

2022

Abstract: A hypercycle equation with infinitely many types of macromolecules is formulated and studied both analytically and numerically. The resulting model is given by an integro-differential equation of the mixed type. Sufficient conditions for the existence, ... ...

Abstract	A hypercycle equation with infinitely many types of macromolecules is formulated and studied both analytically and numerically. The resulting model is given by an integro-differential equation of the mixed type. Sufficient conditions for the existence, uniqueness, and non-negativity of solutions are formulated and proved. Analytical evidence is provided for the existence of non-uniform (with respect to the second variable) steady states. Finally, numerical simulations strongly indicate the existence of a stable nonlinear wave in the form of the wave train. Comment: 21 pages, 5 figures
Keywords	Quantitative Biology - Populations and Evolution
Publishing date	2022-07-11
Publishing country	us
Document type	Book ; Online
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Book ; Online: Food webs and the principle of evolutionary adaptation

Bratus, Alexander S. / Korushkina, Anastasiia V. / Novozhilov, Artem S.

2021

Abstract: A principle of evolutionary adaptation is applied to the Lotka--Volterra models, in particular to the food webs. We present a relatively simple computational algorithm of optimization with respect to a given criterion. This algorithm boils down to a ... ...

Abstract	A principle of evolutionary adaptation is applied to the Lotka--Volterra models, in particular to the food webs. We present a relatively simple computational algorithm of optimization with respect to a given criterion. This algorithm boils down to a sequence of easy to solve linear programming problems. As a criterion for the optimization we use the total weighted population size of the given community and an ecological fitness, which is an analogue of the potential energy in physics. We show by computational experiments that it is almost always possible to substantially increase the total weighed population size for an especially simple food web -- food chain; we also show that food chains are evolutionary unstable under the given optimization criteria and, if allowed, evolve into more complicated structures of food webs. Comment: 14 pages, 7 figures
Keywords	Quantitative Biology - Populations and Evolution
Publishing date	2021-09-02
Publishing country	us
Document type	Book ; Online
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Article ; Online: How trait distributions evolve in populations with parametric heterogeneity.

P Karev, Georgy / S Novozhilov, Artem

Mathematical biosciences

2019 Volume 315, Page(s) 108235

Abstract: We consider the problem of determining the time evolution of a trait distribution in a mathematical model of non-uniform populations with parametric heterogeneity. This means that we consider only heterogeneous populations in which heterogeneity is ... ...

Abstract	We consider the problem of determining the time evolution of a trait distribution in a mathematical model of non-uniform populations with parametric heterogeneity. This means that we consider only heterogeneous populations in which heterogeneity is described by an individual specific parameter that differs in general from individual to individual, but does not change with time for the whole lifespan of this individual. Such a restriction allows obtaining a number of simple and yet important analytical results. In particular we show that initial assumptions on time-dependent behavior of various characteristics, such as the mean, variance, or coefficient of variation, restrict severely possible choices for the exact form of the trait distribution. This fact must be taken into account for both model formulation and, especially, for testing theoretical models against available real world data. We illustrate our findings by in-depth analysis of the variance evolution and specific examples from population ecology and mathematical epidemiology. We also reanalyze a well known mathematical model for gypsy moth population and show that the knowledge of how trait distributions evolve allows producing oscillatory behaviors for highly heterogeneous populations.
MeSH term(s)	Animals ; Ecosystem ; Models, Theoretical ; Moths/physiology ; Statistical Distributions ; Trees/physiology
Language	English
Publishing date	2019-07-24
Publishing country	United States
Document type	Journal Article ; Research Support, N.I.H., Intramural
ZDB-ID	1126-5
ISSN	1879-3134 ; 0025-5564
ISSN (online)	1879-3134
ISSN	0025-5564
DOI	10.1016/j.mbs.2019.108235
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Article ; Online: Origin and Evolution of the Universal Genetic Code.

Koonin, Eugene V / Novozhilov, Artem S

Annual review of genetics

2017 Volume 51, Page(s) 45–62

Abstract: The standard genetic code (SGC) is virtually universal among extant life forms. Although many deviations from the universal code exist, particularly in organelles and prokaryotes with small genomes, they are limited in scope and obviously secondary. The ... ...

Abstract	The standard genetic code (SGC) is virtually universal among extant life forms. Although many deviations from the universal code exist, particularly in organelles and prokaryotes with small genomes, they are limited in scope and obviously secondary. The universality of the code likely results from the combination of a frozen accident, i.e., the deleterious effect of codon reassignment in the SGC, and the inhibitory effect of changes in the code on horizontal gene transfer. The structure of the SGC is nonrandom and ensures high robustness of the code to mutational and translational errors. However, this error minimization is most likely a by-product of the primordial code expansion driven by the diversification of the repertoire of protein amino acids, rather than a direct result of selection. Phylogenetic analysis of translation system components, in particular aminoacyl-tRNA synthetases, shows that, at a stage of evolution when the translation system had already attained high fidelity, the correspondence between amino acids and cognate codons was determined by recognition of amino acids by RNA molecules, i.e., proto-tRNAs. We propose an experimentally testable scenario for the evolution of the code that combines recognition of amino acids by unique sites on proto-tRNAs (distinct from the anticodons), expansion of the code via proto-tRNA duplication, and frozen accident.
MeSH term(s)	Amino Acids/genetics ; Amino Acids/metabolism ; Amino Acyl-tRNA Synthetases/genetics ; Amino Acyl-tRNA Synthetases/metabolism ; Anticodon/chemistry ; Anticodon/metabolism ; Biota/genetics ; Codon/chemistry ; Codon/metabolism ; Evolution, Molecular ; Extinction, Biological ; Gene Transfer, Horizontal ; Genetic Code ; Genome ; Models, Genetic ; Phylogeny ; Protein Biosynthesis ; RNA, Transfer/genetics ; RNA, Transfer/metabolism
Chemical Substances	Amino Acids ; Anticodon ; Codon ; RNA, Transfer (9014-25-9) ; Amino Acyl-tRNA Synthetases (EC 6.1.1.-)
Language	English
Publishing date	2017-08-30
Publishing country	United States
Document type	Journal Article ; Review ; Research Support, N.I.H., Intramural
ZDB-ID	207928-8
ISSN	1545-2948 ; 0066-4170 ; 0066-4197
ISSN (online)	1545-2948
ISSN	0066-4170 ; 0066-4197
DOI	10.1146/annurev-genet-120116-024713
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Article ; Online: On Eigen's Quasispecies Model, Two-Valued Fitness Landscapes, and Isometry Groups Acting on Finite Metric Spaces.

Semenov, Yuri S / Novozhilov, Artem S

Bulletin of mathematical biology

2016 Volume 78, Issue 5, Page(s) 991–1038

Abstract: A two-valued fitness landscape is introduced for the classical Eigen's quasispecies model. This fitness landscape can be considered as a direct generalization of the so-called single- or sharply peaked landscape. A general, non-permutation invariant ... ...

Abstract	A two-valued fitness landscape is introduced for the classical Eigen's quasispecies model. This fitness landscape can be considered as a direct generalization of the so-called single- or sharply peaked landscape. A general, non-permutation invariant quasispecies model is studied, and therefore the dimension of the problem is [Formula: see text], where N is the sequence length. It is shown that if the fitness function is equal to [Formula: see text] on a G-orbit A and is equal to w elsewhere, then the mean population fitness can be found as the largest root of an algebraic equation of degree at most [Formula: see text]. Here G is an arbitrary isometry group acting on the metric space of sequences of zeroes and ones of the length N with the Hamming distance. An explicit form of this exact algebraic equation is given in terms of the spherical growth function of the G-orbit A. Motivated by the analysis of the two-valued fitness landscapes, an abstract generalization of Eigen's model is introduced such that the sequences are identified with the points of a finite metric space X together with a group of isometries acting transitively on X. In particular, a simplicial analog of the original quasispecies model is discussed, which can be considered as a mathematical model of the switching of the antigenic variants for some bacteria.
MeSH term(s)	Genetic Fitness ; Mathematical Concepts ; Models, Genetic ; Mutation ; Selection, Genetic
Language	English
Publishing date	2016-05
Publishing country	United States
Document type	Journal Article
ZDB-ID	184905-0
ISSN	1522-9602 ; 0007-4985 ; 0092-8240
ISSN (online)	1522-9602
ISSN	0007-4985 ; 0092-8240
DOI	10.1007/s11538-016-0172-2
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Article ; Online: Exact solutions for the selection-mutation equilibrium in the Crow-Kimura evolutionary model.

Semenov, Yuri S / Novozhilov, Artem S

Mathematical biosciences

2015 Volume 266, Page(s) 1–9

Abstract: We reformulate the eigenvalue problem for the selection-mutation equilibrium distribution in the case of a haploid asexually reproduced population in the form of an equation for an unknown probability generating function of this distribution. The special ...

Abstract	We reformulate the eigenvalue problem for the selection-mutation equilibrium distribution in the case of a haploid asexually reproduced population in the form of an equation for an unknown probability generating function of this distribution. The special form of this equation in the infinite sequence limit allows us to obtain analytically the steady state distributions for a number of particular cases of the fitness landscape. The general approach is illustrated by examples; theoretical findings are compared with numerical calculations.
MeSH term(s)	Biological Evolution ; Gene Frequency ; Models, Biological ; Mutation ; Selection, Genetic
Language	English
Publishing date	2015-08
Publishing country	United States
Document type	Journal Article ; Research Support, U.S. Gov't, Non-P.H.S.
ZDB-ID	1126-5
ISSN	1879-3134 ; 0025-5564
ISSN (online)	1879-3134
ISSN	0025-5564
DOI	10.1016/j.mbs.2015.05.002
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Article: On the spread of epidemics in a closed heterogeneous population.

Novozhilov, Artem S

Mathematical biosciences

2008 Volume 215, Issue 2, Page(s) 177–185

Abstract: Heterogeneity is an important property of any population experiencing a disease. Here we apply general methods of the theory of heterogeneous populations to the simplest mathematical models in epidemiology. In particular, an SIR (susceptible-infective- ... ...

Abstract	Heterogeneity is an important property of any population experiencing a disease. Here we apply general methods of the theory of heterogeneous populations to the simplest mathematical models in epidemiology. In particular, an SIR (susceptible-infective-removed) model is formulated and analyzed when susceptibility to or infectivity of a particular disease is distributed. It is shown that a heterogeneous model can be reduced to a homogeneous model with a nonlinear transmission function, which is given in explicit form. The widely used power transmission function is deduced from the model with distributed susceptibility and infectivity with the initial gamma-distribution of the disease parameters. Therefore, a mechanistic derivation of the phenomenological model, which is believed to mimic reality with high accuracy, is provided. The equation for the final size of an epidemic for an arbitrary initial distribution of susceptibility is found. The implications of population heterogeneity are discussed, in particular, it is pointed out that usual moment-closure methods can lead to erroneous conclusions if applied for the study of the long-term behavior of the models.
MeSH term(s)	Algorithms ; Animals ; Communicable Diseases/epidemiology ; Communicable Diseases/transmission ; Disease Outbreaks ; Disease Susceptibility/epidemiology ; Humans ; Models, Biological ; Models, Statistical ; Nonlinear Dynamics ; Population Density ; Population Dynamics ; Social Behavior ; Statistical Distributions
Language	English
Publishing date	2008-08-03
Publishing country	United States
Document type	Journal Article ; Research Support, N.I.H., Intramural
ZDB-ID	1126-5
ISSN	1879-3134 ; 0025-5564
ISSN (online)	1879-3134
ISSN	0025-5564
DOI	10.1016/j.mbs.2008.07.010
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Book ; Online: Epidemiological models with parametric heterogeneity

Novozhilov, Artem S.

Deterministic theory for closed populations

2012

Abstract: We present a unified mathematical approach to epidemiological models with parametric heterogeneity, i.e., to the models that describe individuals in the population as having specific parameter (trait) values that vary from one individuals to another. ... ...

Abstract	We present a unified mathematical approach to epidemiological models with parametric heterogeneity, i.e., to the models that describe individuals in the population as having specific parameter (trait) values that vary from one individuals to another. This is a natural framework to model, e.g., heterogeneity in susceptibility or infectivity of individuals. We review, along with the necessary theory, the results obtained using the discussed approach. In particular, we formulate and analyze an SIR model with distributed susceptibility and infectivity, showing that the epidemiological models for closed populations are well suited to the suggested framework. A number of known results from the literature is derived, including the final epidemic size equation for an SIR model with distributed susceptibility. It is proved that the bottom up approach of the theory of heterogeneous populations with parametric heterogeneity allows to infer the population level description, which was previously used without a firm mechanistic basis; in particular, the power law transmission function is shown to be a consequence of the initial gamma distributed susceptibility and infectivity. We discuss how the general theory can be applied to the modeling goals to include the heterogeneous contact population structure and provide analysis of an SI model with heterogeneous contacts. We conclude with a number of open questions and promising directions, where the theory of heterogeneous populations can lead to important simplifications and generalizations. Comment: 26 pages, 6 figures, submitted to Mathematical Modelling of Natural Phenomena
Keywords	Quantitative Biology - Populations and Evolution
Subject code	612
Publishing date	2012-02-11
Publishing country	us
Document type	Book ; Online
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Book ; Online: On Eigen's quasispecies model, two-valued fitness landscapes, and isometry groups acting on finite metric spaces

Semenov, Yuri S. / Novozhilov, Artem S.

2015

Abstract: A two-valued fitness landscape is introduced for the classical Eigen's quasispecies model. This fitness landscape can be considered as a direct generalization of the so-called single or sharply peaked landscape. A general, non permutation invariant ... ...

Abstract	A two-valued fitness landscape is introduced for the classical Eigen's quasispecies model. This fitness landscape can be considered as a direct generalization of the so-called single or sharply peaked landscape. A general, non permutation invariant quasispecies model is studied, therefore the dimension of the problem is $2^N\times 2^N$, where $N$ is the sequence length. It is shown that if the fitness function is equal to $w+s$ on a $G$-orbit $A$ and is equal to $w$ elsewhere, then the mean population fitness can be found as the largest root of an algebraic equation of degree at most $N+1$. Here $G$ is an arbitrary isometry group acting on the metric space of sequences of zeroes and ones of the length $N$ with the Hamming distance. An explicit form of this exact algebraic equation is given in terms of the spherical growth function of the $G$-orbit $A$. Sufficient conditions for the so-called error threshold for sequences of orbits are given. Motivated by the analysis of the two-valued fitness landscapes an abstract generalization of Eigen's model is introduced such that the sequences are identified with the points of a finite metric space $X$ together with a group of isometries acting transitively on $X$. In particular, a simplicial analogue of the original quasispecies model is discussed, which can be considered as a mathematical model of the switching of the antigenic variants for some bacteria. Comment: 38 pages, 7 figures, several typos were fixed
Keywords	Quantitative Biology - Populations and Evolution ; 92D15 ; 92D25
Subject code	612
Publishing date	2015-03-11
Publishing country	us
Document type	Book ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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