How the quasispecies evolution depends on the topology of the genome space

Kolář, Michal; Slanina, František

doi:10.1016/s0378-4371(02)00970-6

Cited by 3 publications

(5 citation statements)

References 49 publications

(74 reference statements)

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“…Compare it, for example, with the celebrated Eigen model of biological evolution in the space of heteropolymer sequences [37]. There, the localization-delocalization phase transition, known as the "error catastrophe", separates two states, where the genotype is localized in the vicinity of a preferred pattern, and where it is completely random [38][39][40]. The transition occurs due to an interplay between the attraction to a point-like potential well and the entropic repulsion from this well due to the exponential growth of the number of states with increasing the Hamming distance from the well.…”

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confidence: 99%

Islands of Stability in Motif Distributions of Random Networks

et al. 2014

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We consider random non-directed networks subject to dynamics conserving vertex degrees and study analytically and numerically equilibrium three-vertex motif distributions in the presence of an external field, h, coupled to one of the motifs. For small h the numerics is well described by the "chemical kinetics" for the concentrations of motifs based on the law of mass action. For larger h a transition into some trapped motif state occurs in Erdős-Rényi networks. We explain the existence of the transition by employing the notion of the entropy of the motif distribution and describe it in terms of a phenomenological Landau-type theory with a non-zero cubic term. A localization transition should always occur if the entropy function is non-convex. We conjecture that this phenomenon is the origin of the motifs' pattern formation in real evolutionary networks. One particular topological characteristic, which seems to be very instructive in providing detailed information about local network topology, is the distribution of small subgraphs (motifs). The presence of motifs of specific type is tightly linked to the network function. For example, the transcriptional regulatory networks have excess of auto-regulation loops with respect to randomly connected graphs with the same vertex degree distribution [15,16]. Some authors [17] connect the prevalence of specific motif types in the transcription factor networks of E.coili and S.cerevisiae with a network evolution, which might lead to self-consistent optimal circuit design [18][19][20]. It is known, that protein interaction networks have many short cycles and completely connected subgraphs [21]. This can be thought as a feature necessary for a signal transduction by feed-back loops [18]. These and many other examples clearly demonstrate that the existence of specific motifs in networks strongly correlate with the network function.The statistical analysis of motifs distribution (MD) in various naturally observed directed networks demonstrates [22,23] that the simplest three-vertex motifs (triads) of oriented graphs can be split into four broad superfamilies, and the networks within the same superfamily tend to have similar functions. However, to the best of our knowledge, still there is no common opinion about the mechanism behind the separation of MDs into a particular preferred stable state. In this letter we put forward a hypothesis which may give at least a partial answer to this question.

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Islands of Stability in Motif Distributions of Random Networks

et al. 2014

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“…As in the previous paper [39] we investigate the formation of a localized state, now interpreted as a quasispecies…”

Section: Partitioningmentioning

confidence: 99%

“…Recently, [39] we have modelled evolution in a holey landscape using the regular Bethe lattice. Now we will try to represent it in a more precise way and take into account the irregularity of the lattice.…”

Section: Modelmentioning

confidence: 99%

“…which can be calculated using the partitioning (projector) method [47], explained in more detail in [39]. The loopless structure of the Bethe lattice greatly simplifies the treatment.…”

Section: Partitioningmentioning

confidence: 99%

“…in [38]. In our previous work we have studied several similar models of the fitness landscape, too [39].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Selective advantage of topological disorder in biological evolution

Kolář

Slanina

2003

The European Physical Journal B - Condensed Matter

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Abstract. We examine a model of biological evolution of Eigen's quasispecies in a so-called holey fitness landscape, where the fitness of a site is either 0 (lethal site) or a uniform positive constant (viable site). The evolution dynamics is therefore determined by the topology of the genome space which is modelled by the random Bethe lattice. We use the effective medium and single-defect approximations to find the criteria under which the localized quasispecies cloud is created. We find that shorter genomes, which are more robust to random mutations than average, represent a selective advantage which we call "topological". A way of assessing empirically the relative importance of reproductive success and topological advantage is suggested.

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The tangled nature model as an evolving quasi-species model

Collobiano

Christensen

Jensen

2003

J. Phys. A: Math. Gen.

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We show that the Tangled Nature model can be interpreted as a general formulation of the quasi-species model by Eigen et al. in a frequency dependent fitness landscape. We present a detailed theoretical derivation of the mutation threshold, consistent with the simulation results, that provides a valuable insight into how the microscopic dynamics of the model determine the observed macroscopic phenomena published previously. The dynamics of the Tangled Nature model is defined on the microevolutionary time scale via reproduction, with heredity, variation, and natural selection. Each organism reproduces with a rate that is linked to the individuals' genetic sequence and depends on the composition of the population in genotype space. Thus the microevolutionary dynamics of the fitness landscape is regulated by, and regulates, the evolution of the species by means of the mutual interactions. At low mutation rate, the macro evolutionary pattern mimics the fossil data: periods of stasis, where the population is concentrated in a network of coexisting species, is interrupted by bursts of activity. As the mutation rate increases, the duration and the frequency of bursts increases. Eventually, when the mutation rate reaches a certain threshold, the population is spread evenly throughout the genotype space showing that natural selection only leads to multiple distinct species if adaptation is allowed time to cause fixation.

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How the quasispecies evolution depends on the topology of the genome space

Cited by 3 publications

References 49 publications

Islands of Stability in Motif Distributions of Random Networks

Islands of Stability in Motif Distributions of Random Networks

Selective advantage of topological disorder in biological evolution

The tangled nature model as an evolving quasi-species model

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