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PubMed1994

Cycles, chaos, and evolution in virus cultures: a model of defective interfering particles.

Defective interfering particles (DIP) are spontaneous deletion mutants of viruses that replicate at the expense of the parent virus. DIP have complex effects on the growth of viruses in vitro, including the establishment of persistent infection, cyclical variation in virus titer, eradication of replicating virus, and rapid evolution of the virus. We show here that a simple mathematical model, based only on experimental observations, can explain all of the major effects of DIP on the population dynamics of virus growth. The variation in virus titer caused by DIP has many features that are characteristic of deterministic chaos: it follows that the quantitative effects of DIP are intrinsically unpredictable beyond a short time. We conclude (i) that other factors, such as temperature-sensitive virus mutants or interferons, need not be invoked to explain the complex effects of DIP; and (ii) that dominantly interfering viruses should only be used with great caution for therapeutic purposes, since their effects are, in principle, unpredictable.

Biological Evolution↗

PubMed2004

Yeast as a model organism for studying the evolution of non-standard genetic codes.

During the last 30 years, a number of alterations to the standard genetic code have been uncovered both in prokaryotes and eukaryotic nuclear and mitochondrial genomes. But, the study of the evolutionary pathways and molecular mechanisms of codon identity redefinition has been largely ignored due to the assumption that non-standard genetic codes can only evolve through neutral evolutionary mechanisms and that they have no functional significance. The recent discovery of a genetic code change in the genus Candida that evolved through an ambiguous messenger RNA decoding mechanism is bringing that naive assumption to an abrupt end by showing, in a rather dramatic way, that genetic code changes have profound physiological and evolutionary consequences for the species that redefine codon identity. In this paper, the recent data on the evolution of the Candida genetic code are reviewed and an experimental framework based on forced evolution, molecular genetics and comparative and functional genomics methodologies is put forward for the study of non-standard genetic codes and genetic code ambiguity in general. Additionally, the importance of using Saccharomyces cerevisiae as a model organism for elucidating the evolutionary pathway of the Candida and other genetic code changes is emphasised.

Candida↗

PubMed2004

Genomic data support the hominoid slowdown and an Early Oligocene estimate for the hominoid-cercopithecoid divergence.

Several lines of indirect evidence suggest that hominoids (apes and humans) and cercopithecoids (Old World monkeys) diverged around 23-25 Mya. Importantly, although this range of dates has been used as both an initial assumption and as a confirmation of results in many molecular-clock analyses, it has not been critically assessed on its own merits. In this article we test the robusticity of the 23- to 25-Mya estimate with approximately 150,000 base pairs of orthologous DNA sequence data from two cercopithecoids and two hominoids by using quartet analysis. This method is an improvement over other estimates of the hominoid-cercopithecoid divergence because it incorporates two calibration points, one each within cercopithecoids and hominoids, and tests for a statistically appropriate model of molecular evolution. Most comparisons reject rate constancy in favor of a model incorporating two rates of evolution, supporting the "hominoid slowdown" hypothesis. By using this model of molecular evolution, the hominoid-cercopithecoid divergence is estimated to range from 29.2 to 34.5 Mya, significantly older than most previous analyses. Hominoid-cercopithecoid divergence dates of 23-25 Mya fall outside of the confidence intervals estimated, suggesting that as much as one-third of ape evolution has not been paleontologically sampled. Identifying stem cercopithecoids or hominoids from this period will be difficult because derived features that define crown catarrhines need not be present in early members of these lineages. More sites that sample primate habitats from the Oligocene of Africa are needed to better understand early ape and Old World monkey evolution.

Animals↗

PubMed2001

Deterministic numerical model for treating the three elastic constants in nematic liquid-crystalline polymers.

In this paper, a deterministic model, which considers the three Frank elastic constants, is introduced. It is based on a lattice model and a director is used to represent the orientation of the liquid crystals in each cell. A tensor expression of the so-called "texture field" is deduced so that the nematic symmetry is conserved automatically. In the current model, the evolution of the director field can be viewed as a process towards the state of zero elastic torque. The model forms the basis for an improved understanding of the mesoscale structures and rheological phenomena of nematic liquid-crystalline polymers. It has been tested in its ability to reproduce the Fréedericksz transitions, and simulations of thin liquid crystalline polymer films clearly show the effect of unequal elastic constants on the director microstructure evolution.

Journal Article↗

PubMed1999

Parasitic plant responses to host plant signals: a model for subterranean plant-plant interactions.

The ability of plants to fulfill nutritional needs by parasitizing neighboring plants has originated several times in angiosperm evolution. Molecular tools are now being exploited to investigate the evolutionary origins of plant parasitism and to dissect the genetic mechanisms governing parasitic plant-host plant interactions. Investigating the nature of signal exchanges between parasitic plants and their hosts serves as a tractable system for understanding how plants in general communicate in the environment. This work should also lead to the development of novel strategies for minimizing the devastation caused by parasitic weeds in international agriculture.

Biological Evolution↗

PubMed1998

Somite number and vertebrate evolution.

Variation in segment number is an important but neglected feature of vertebrate evolution. Some vertebrates have as few as six trunk vertebrae, while others have hundreds. We examine this phenomenon in relation to recent models of evolution and development. Surprisingly, differences in vertebral number are foreshadowed by different somite counts at the tailbud stage, thought to be a highly conserved (phylotypic) stage. Somite number therefore violates the 'developmental hourglass' model. We argue that this is because somitogenesis shows uncoupling or dissociation from the conserved positional field encoded by genes of the zootype. Several other systems show this kind of dissociation, including limbs and feathers. Bmp-7 expression patterns demonstrate dissociation in the chick pharyngeal arches. This makes it difficult to recognise a common stage of pharyngeal development or 'pharyngula' in all species. Rhombomere number is more stable during evolution than somite number, possibly because segmentation and positional specification in the hindbrain are relatively interdependent. Although developmental mechanisms are strongly conserved, dissociation allows at least some major evolutionary changes to be generated in phylotypic stages.

Animals↗

PubMed1984

Transmembrane electron transport and the neutral theory of evolution.

Based on the concept of "pairs of basic functional states" the evolution of the first chemiosmotic mechanism of energy conversion is discussed in terms of point mutations, gene duplications and of the neutral theory of evolution. A model for estimating the overall probability of the evolutionary step in question is presented, both for the "selectionist" and "neutralist" position. It is concluded that, concerning the present stage of knowledge, the evolution of transmembrane electron transport is an unsolved problem in evolutionary biology.

Adenosine Triphosphatases↗

PubMed1991

On the divergence of species.

Speciation may be considered as a kind of non-equilibrium phase transition which is caused by bifurcation at a critical point of instability. It can be shown that multiple branching of an evolutionary tree is highly improbable, since non-degenerate mathematical models describe only binary branchings.

Biological Evolution↗

PubMed2002

Evolution of enzymes in metabolism: a network perspective.

Several models have been proposed to explain the origin and evolution of enzymes in metabolic pathways. Initially, the retro-evolution model proposed that, as enzymes at the end of pathways depleted their substrates in the primordial soup, there was a pressure for earlier enzymes in pathways to be created, using the later ones as initial template, in order to replenish the pools of depleted metabolites. Later, the recruitment model proposed that initial templates from other pathways could be used as long as those enzymes were similar in chemistry or substrate specificity. These two models have dominated recent studies of enzyme evolution. These studies are constrained by either the small scale of the study or the artificial restrictions imposed by pathway definitions. Here, a network approach is used to study enzyme evolution in fully sequenced genomes, thus removing both constraints. We find that homologous pairs of enzymes are roughly twice as likely to have evolved from enzymes that are less than three steps away from each other in the reaction network than pairs of non-homologous enzymes. These results, together with the conservation of the type of chemical reaction catalyzed by evolutionarily related enzymes, suggest that functional blocks of similar chemistry have evolved within metabolic networks. One possible explanation for these observations is that this local evolution phenomenon is likely to cause less global physiological disruptions in metabolism than evolution of enzymes from other enzymes that are distant from them in the metabolic network.

Databases, Protein↗

PubMed1984

On the evolution of altruism by kin selection.

A general model for the evolution of altruism is formulated. Central to the model is a pair of local fitness functions, which prescribe the fitness of the altruist and selfish phenotypes as functions of the composition of local groups into which prereproductives are subdivided. When the local groups are sibships or other kin groups, the model is one for kin selection. Functions for cost and benefit of altruism are derived from the fitness functions. Conditions for evolution of altruism are then determined in terms of cost and benefit. It is shown that the Hamilton rule has quantitative validity only in the special case of linear fitness functions. Sufficient conditions are found for qualitative validity of the Hamilton rule. Qualitative violation of the rule is also possible.

Journal Article↗

PubMed1994

Substitution processes in molecular evolution. III. Deleterious alleles.

The substitution processes for various models of deleterious alleles are examined using computer simulations and mathematical analyses. Most of the work focuses on the house-of-cards model, which is a popular model of deleterious allele evolution. The rate of substitution is shown to be a concave function of the strength of selection as measured by alpha = 2N sigma, where N is the population size and sigma is the standard deviation of fitness. For alpha < 1, the house-of-cards model is essentially a neutral model; for alpha > 4, the model ceases to evolve. The stagnation for large alpha may be understood by appealing to the theory of records. The house-of-cards model evolves to a state where the vast majority of all mutations are deleterious, but precisely one-half of those mutations that fix are deleterious (the other half are advantageous). Thus, the model is not a model of exclusively deleterious evolution as is frequently claimed. It is argued that there are no biologically reasonable models of molecular evolution where the vast majority of all substitutions are deleterious. Other models examined include the exponential and gamma shift models, the Hartl-Dykhuizen-Dean (HDD) model, and the optimum model. Of all those examined, only the optimum and HDD models appear to be reasonable candidates for silent evolution. None of the models are viewed as good candidates for protein evolution, as none are both biologically reasonable and exhibit the variability in substitutions commonly observed in protein sequence data.

Alleles↗

PubMed2005

Comparative cytogenetics of human chromosome 3q21.3 reveals a hot spot for ectopic recombination in hominoid evolution.

Fluorescence in situ hybridization mapping of fully integrated human BAC clones to primate chromosomes, combined with precise breakpoint localization by PCR analysis of flow-sorted chromosomes, was used to analyze the evolutionary rearrangements of the human 3q21.3-syntenic region in orangutan, siamang gibbon, and silvered-leaf monkey. Three independent evolutionary breakpoints were localized within a 230-kb segment contained in BACs RP11-93K22 and RP11-77P16. Approximately 200 kb of the human 3q21.3 sequence was not present on the homologous orangutan, siamang, and Old World monkey chromosomes, suggesting a genomic DNA insertion into the breakpoint region in the lineage leading to humans and African great apes. The breakpoints in the orangutan and siamang genomes were narrowed down to 12- and 20-kb DNA segments, respectively, which are enriched with endogenous retrovirus long terminal repeats and other repetitive elements. The inserted DNA segment represents part of an ancestral duplication. Paralogous sequence blocks were found at human 3q21, approximately 4 Mb proximal to the evolutionary breakpoint cluster region; at human 3p12.3, which contains an independent orangutan-specific breakpoint; and at the subtelomeric and pericentromeric regions of multiple human and orangutan chromosomes. The evolutionary breakpoint regions between human chromosome 3 and orangutan 2 as well their paralogous segments in the human genome coincide with breaks of chromosomal synteny in the mouse, rat, and/or chicken genomes. Collectively our data reveal reuse of the same short recombinogenic DNA segments in primate and vertebrate evolution, supporting a nonrandom breakage model of genome evolution.

Animals↗

PubMed1999

Gene duplication: past, present and future.

Gene duplication is of central interest to evolutionary developmental biology, having been implicated in evolutionary increases in complexity. These ideas stem principally from the Lewis model for the evolution of the BX-C and Ohno's proposal for genome duplications during chordate evolution. Here I revisit these models and show how recent data have confirmed their essential features, but forced some important revisions. These include revised dates for homeotic gene duplications and for widespread gene duplication in vertebrate evolution. I also outline the major unresolved questions in the study of gene duplication, and its relevance to evolution and development.

Animals↗

PubMed1999

Power of the concentrated changes test for correlated evolution.

The concentrated changes test (CCT) calculates the probability that changes in a binary character are distributed randomly on the branches of a cladogram. This test is used to examine hypotheses of correlated evolution, especially cases where changes in the state of one character influence changes in the state of another character. The test may be sensitive to the addition of branches that lack either trait of interest (white branches). To examine the effects of the proportion of white branches and of tree topology on the CCT probability, we conducted a simulation analysis using a series of randomly generated 100-taxon trees, in addition to a nearly perfectly balanced (symmetrical) and a completely imbalanced (asymmetrical) 100-taxon tree. Using two models of evolution (gains only, or gains and losses), we evolved character pairs randomly onto these trees to simulate cases where (1) characters evolve independently (i.e., no correlation among the traits) or (2) all changes in the dependent character occur on branches containing the independent trait (i.e., a strong correlation among the traits). This allowed us to evaluate the sensitivity of the CCT to type I and type II errors, respectively. In the simulations, the CCT did not appear to be overly sensitive to the inclusion of white branches (low likelihood of type I error with both CCT probabilities < 0.05 and < 0.01). However, the CCT was susceptible to type II error when the proportion of white branches was < 20%. The test was also sensitive to tree shape and was positively correlated to Colless's tree imbalance statistic I. Finally, the CCT responded differently for simulations where only gains were allowed and those where both gains and losses were permitted. These results indicate that the CCT is unlikely to detect a correlation between characters when no such correlation exists. However, when a trait can be gained but not lost, the CCT is conservative and may fail to detect true correlations among traits (increased type II error). Determination of the sampling universe (the taxa included in the comparative analysis) can strongly influence the probability of making such type II errors. We suggest guidelines to circumvent these limitations.

Biological Evolution↗

PubMed2005

Modeling gene and genome duplications in eukaryotes.

Recent analysis of complete eukaryotic genome sequences has revealed that gene duplication has been rampant. Moreover, next to a continuous mode of gene duplication, in many eukaryotic organisms the complete genome has been duplicated in their evolutionary past. Such large-scale gene duplication events have been associated with important evolutionary transitions or major leaps in development and adaptive radiations of species. Here, we present an evolutionary model that simulates the duplication dynamics of genes, considering genome-wide duplication events and a continuous mode of gene duplication. Modeling the evolution of the different functional categories of genes assesses the importance of different duplication events for gene families involved in specific functions or processes. By applying our model to the Arabidopsis genome, for which there is compelling evidence for three whole-genome duplications, we show that gene loss is strikingly different for large-scale and small-scale duplication events and highly biased toward certain functional classes. We provide evidence that some categories of genes were almost exclusively expanded through large-scale gene duplication events. In particular, we show that the three whole-genome duplications in Arabidopsis have been directly responsible for >90% of the increase in transcription factors, signal transducers, and developmental genes in the last 350 million years. Our evolutionary model is widely applicable and can be used to evaluate different assumptions regarding small- or large-scale gene duplication events in eukaryotic genomes.

Arabidopsis↗

PubMed2004

A maximum likelihood method for detecting functional divergence at individual codon sites, with application to gene family evolution.

The tailoring of existing genetic systems to new uses is called genetic co-option. Mechanisms of genetic co-option have been difficult to study because of difficulties in identifying functionally important changes. One way to study genetic co-option in protein-coding genes is to identify those amino acid sites that have experienced changes in selective pressure following a genetic co-option event. In this paper we present a maximum likelihood method useful for measuring divergent selective pressures and identifying the amino acid sites affected by divergent selection. The method is based on a codon model of evolution and uses the nonsynonymous-to-synonymous rate ratio (omega) as a measure of selection on the protein, with omega = 1, < 1, and > 1 indicating neutral evolution, purifying selection, and positive selection, respectively. The model allows variation in omega among sites, with a fraction of sites evolving under divergent selective pressures. Divergent selection is indicated by different omega's between clades, such as between paralogous clades of a gene family. We applied the codon model to duplication followed by functional divergence of (i) the epsilon and gamma globin genes and (ii) the eosinophil cationic protein (ECP) and eosinophil-derived neurotoxin (EDN) genes. In both cases likelihood ratio tests suggested the presence of sites evolving under divergent selective pressures. Results of the epsilon and gamma globin analysis suggested that divergent selective pressures might be a consequence of a weakened relationship between fetal hemoglobin and 2,3-diphosphoglycerate. We suggest that empirical Bayesian identification of sites evolving under divergent selective pressures, combined with structural and functional information, can provide a valuable framework for identifying and studying mechanisms of genetic co-option. Limitations of the new method are discussed.

Amino Acids↗

PubMed2005

Chaotic behavior of semigroups related to the process of gene amplification-deamplification with cell proliferation.

In the last few years there has been a renewed interest in infinite systems of differential equations, similar to the classical birth-and-death system of population dynamics, due to their rôle in modelling the evolution of drug resistance in cancer cells. In [J. Banasiak, M. Lachowicz, Topological chaos for birth-and-death models with proliferation, Math. Models Methods Appl. Sci. 12 (6) (2002) 755] such systems were shown to generate a chaotic dynamics under, however, very restrictive assumptions on the growth of coefficients. In this paper, using recently developed concept of subspace chaos [J. Banasiak, M. Moszyński, A generalization of Desch-Schappacher-Webb criteria for topological chaos with applications, Discrete Contin. Dyn. Syst. - A 12 (5) (2005) 959], we show that for a linear growth of the coefficients, which are more acceptable from biological point of view, the dynamics of these systems is chaotic in some subspaces of the original state space.

Algorithms↗

PubMed2001

Host switching in Lyssavirus history from the Chiroptera to the Carnivora orders.

Lyssaviruses are unsegmented RNA viruses causing rabies. Their vectors belong to the Carnivora and Chiroptera orders. We studied 36 carnivoran and 17 chiropteran lyssaviruses representing the main genotypes and variants. We compared their genes encoding the surface glycoprotein, which is responsible for receptor recognition and membrane fusion. The glycoprotein is the main protecting antigen and bears virulence determinants. Point mutation is the main force in lyssavirus evolution, as Sawyer's test and phylogenetic analysis showed no evidence of recombination. Tests of neutrality indicated a neutral model of evolution, also supported by globally high ratios of synonymous substitutions (d(S)) to nonsynonymous substitutions (d(N)) (>7). Relative-rate tests suggested similar rates of evolution for all lyssavirus lineages. Therefore, the absence of recombination and similar evolutionary rates make phylogeny-based conclusions reliable. Phylogenetic reconstruction strongly supported the hypothesis that host switching occurred in the history of lyssaviruses. Indeed, lyssaviruses evolved in chiropters long before the emergence of carnivoran rabies, very likely following spillovers from bats. Using dated isolates, the average rate of evolution was estimated to be roughly 4.3 x 10(-4) d(S)/site/year. Consequently, the emergence of carnivoran rabies from chiropteran lyssaviruses was determined to have occurred 888 to 1,459 years ago. Glycoprotein segments accumulating more d(N) than d(S) were distinctly detected in carnivoran and chiropteran lyssaviruses. They may have contributed to the adaptation of the virus to the two distinct mammal orders. In carnivoran lyssaviruses they overlapped the main antigenic sites, II and III, whereas in chiropteran lyssaviruses they were located in regions of unknown functions.

Adaptation, Physiological↗