The Error and Repair Catastrophes: A Two-Dimensional Phase Diagram in the Quasispecies Model

This paper develops a two gene, single fitness peak model for determining the equilibrium distribution of genotypes in a unicellular population which is capable of genetic damage repair. The first gene, denoted by $\sigma_{via}$, yields a viable organism with first order growth rate constant $k > 1$ if it is equal to some target ``master'' sequence $\sigma_{via, 0}$. The second gene, denoted by $\sigma_{rep}$, yields an organism capable of genetic repair if it is equal to some target ``master'' sequence $\sigma_{rep, 0}$. This model is analytically solvable in the limit of infinite sequence length, and gives an equilibrium distribution which depends on \mu \equiv L\eps , the product of sequence length and per base pair replication error probability, and \eps_r , the probability of repair failure per base pair. The equilibrium distribution is shown to exist in one of three possible ``phases.'' In the first phase, the population is localized about the viability and repairing master sequences. As \eps_r exceeds the fraction of deleterious mutations, the population undergoes a ``repair'' catastrophe, in which the equilibrium distribution is still localized about the viability master sequence, but is spread ergodically over the sequence subspace defined by the repair gene. Below the repair catastrophe, the distribution undergoes the error catastrophe when $\mu$ exceeds \ln k/\eps_r , while above the repair catastrophe, the distribution undergoes the error catastrophe when $\mu$ exceeds $\ln k/f_{del}$, where $f_{del}$ denotes the fraction of deleterious mutations.Comment: 14 pages, 3 figures. Submitted to Physical Review

Mutator Dynamics on a Smooth Evolutionary Landscape

We investigate a model of evolutionary dynamics on a smooth landscape which features a ``mutator'' allele whose effect is to increase the mutation rate. We show that the expected proportion of mutators far from equilibrium, when the fitness is steadily increasing in time, is governed solely by the transition rates into and out of the mutator state. This results is a much faster rate of fitness increase than would be the case without the mutator allele. Near the fitness equilibrium, however, the mutators are severely suppressed, due to the detrimental effects of a large mutation rate near the fitness maximum. We discuss the results of a recent experiment on natural selection of E. coli in the light of our model.Comment: 4 pages, 3 figure

Nonlinear deterministic equations in biological evolution

We review models of biological evolution in which the population frequency changes deterministically with time. If the population is self-replicating, although the equations for simple prototypes can be linearised, nonlinear equations arise in many complex situations. For sexual populations, even in the simplest setting, the equations are necessarily nonlinear due to the mixing of the parental genetic material. The solutions of such nonlinear equations display interesting features such as multiple equilibria and phase transitions. We mainly discuss those models for which an analytical understanding of such nonlinear equations is available.Comment: Invited review for J. Nonlin. Math. Phy

Population genomics of domestic and wild yeasts

The natural genetics of an organism is determined by the distribution of sequences of its genome. Here we present one- to four-fold, with some deeper, coverage of the genome sequences of over seventy isolates of the domesticated baker's yeast, _Saccharomyces cerevisiae_, and its closest relative, the wild _S. paradoxus_, which has never been associated with human activity. These were collected from numerous geographic locations and sources (including wild, clinical, baking, wine, laboratory and food spoilage). These sequences provide an unprecedented view of the population structure, natural (and artificial) selection and genome evolution in these species. Variation in gene content, SNPs, indels, copy numbers and transposable elements provide insights into the evolution of different lineages. Phenotypic variation broadly correlates with global genome-wide phylogenetic relationships however there is no correlation with source. _S. paradoxus_ populations are well delineated along geographic boundaries while the variation among worldwide _S. cerevisiae_ isolates show less differentiation and is comparable to a single _S. paradoxus_ population. Rather than one or two domestication events leading to the extant baker's yeasts, the population structure of _S. cerevisiae_ shows a few well defined geographically isolated lineages and many different mosaics of these lineages, supporting the notion that human influence provided the opportunity for outbreeding and production of new combinations of pre-existing variation

Aneuploidy Drives Genomic Instability in Yeast

Aneuploidy decreases cellular fitness, yet it is also associated with cancer, a disease of enhanced proliferative capacity. To investigate one mechanism by which aneuploidy could contribute to tumorigenesis, we examined the effects of aneuploidy on genomic stability. We analyzed 13 budding yeast strains that carry extra copies of single chromosomes and found that all aneuploid strains exhibited one or more forms of genomic instability. Most strains displayed increased chromosome loss and mitotic recombination, as well as defective DNA damage repair. Aneuploid fission yeast strains also exhibited defects in mitotic recombination. Aneuploidy-induced genomic instability could facilitate the development of genetic alterations that drive malignant growth in cancer

Mutation Size Optimizes Speciation in an Evolutionary Model

The role of mutation rate in optimizing key features of evolutionary dynamics has recently been investigated in various computational models. Here, we address the related question of how maximum mutation size affects the formation of species in a simple computational evolutionary model. We find that the number of species is maximized for intermediate values of a mutation size parameter μ; the result is observed for evolving organisms on a randomly changing landscape as well as in a version of the model where negative feedback exists between the local population size and the fitness provided by the landscape. The same result is observed for various distributions of mutation values within the limits set by μ. When organisms with various values of μ compete against each other, those with intermediate μ values are found to survive. The surviving values of μ from these competition simulations, however, do not necessarily coincide with the values that maximize the number of species. These results suggest that various complex factors are involved in determining optimal mutation parameters for any population, and may also suggest approaches for building a computational bridge between the (micro) dynamics of mutations at the level of individual organisms and (macro) evolutionary dynamics at the species level

Changes in intraocular pressure in study and fellow eyes in the IVAN trial

PURPOSE: To describe changes in intraocular pressure (IOP) in the 'alternative treatments to Inhibit VEGF in Age-related choroidal Neovascularisation (IVAN)' trial (registered as ISRCTN92166560). DESIGN: Randomised controlled clinical trial with factorial design. PARTICIPANTS: Patients (n=610) with treatment naïve neovascular age-related macular degeneration were enrolled and randomly assigned to receive either ranibizumab or bevacizumab and to two regimens, namely monthly (continuous) or as needed (discontinuous) treatment. METHODS: At monthly visits, IOP was measured preinjection in both eyes, and postinjection in the study eye. OUTCOME MEASURES: The effects of 10 prespecified covariates on preinjection IOP, change in IOP (postinjection minus preinjection) and the difference in preinjection IOP between the two eyes were examined. RESULTS: For every month in trial, there was a statistically significant rise in both the preinjection IOP and the change in IOP postinjection during the time in the trial (estimate 0.02 mm Hg, 95% CI 0.01 to 0.03, p<0.001 and 0.03 mm Hg, 95% CI 0.01 to 0.04, p=0.002, respectively). There was also a small but significant increase during the time in trial in the difference in IOP between the two eyes (estimate 0.01 mm Hg, 95% CI 0.005 to 0.02, p<0.001). There were no differences between bevacizumab and ranibizumab for any of the three outcomes (p=0.93, p=0.22 and p=0.87, respectively). CONCLUSIONS: Anti-vascular endothelial growth factor agents induce increases in IOP of small and uncertain clinical significance

Complex Adaptations Can Drive the Evolution of the Capacitor [PSI+], Even with Realistic Rates of Yeast Sex

The [PSI+] prion may enhance evolvability by revealing previously cryptic genetic variation, but it is unclear whether such evolvability properties could be favored by natural selection. Sex inhibits the evolution of other putative evolvability mechanisms, such as mutator alleles. This paper explores whether sex also prevents natural selection from favoring modifier alleles that facilitate [PSI+] formation. Sex may permit the spread of “cheater” alleles that acquire the benefits of [PSI+] through mating without incurring the cost of producing [PSI+] at times when it is not adaptive. Using recent quantitative estimates of the frequency of sex in Saccharomyces paradoxus, we calculate that natural selection for evolvability can drive the evolution of the [PSI+] system, so long as yeast populations occasionally require complex adaptations involving synergistic epistasis between two loci. If adaptations are always simple and require substitution at only a single locus, then the [PSI+] system is not favored by natural selection. Obligate sex might inhibit the evolution of [PSI+]-like systems in other species

Evolutionary connectionism: algorithmic principles underlying the evolution of biological organisation in evo-devo, evo-eco and evolutionary transitions

The mechanisms of variation, selection and inheritance, on which evolution by natural selection depends, are not fixed over evolutionary time. Current evolutionary biology is increasingly focussed on understanding how the evolution of developmental organisations modifies the distribution of phenotypic variation, the evolution of ecological relationships modifies the selective environment, and the evolution of reproductive relationships modifies the heritability of the evolutionary unit. The major transitions in evolution, in particular, involve radical changes in developmental, ecological and reproductive organisations that instantiate variation, selection and inheritance at a higher level of biological organisation. However, current evolutionary theory is poorly equipped to describe how these organisations change over evolutionary time and especially how that results in adaptive complexes at successive scales of organisation (the key problem is that evolution is self-referential, i.e. the products of evolution change the parameters of the evolutionary process). Here we first reinterpret the central open questions in these domains from a perspective that emphasises the common underlying themes. We then synthesise the findings from a developing body of work that is building a new theoretical approach to these questions by converting well-understood theory and results from models of cognitive learning. Specifically, connectionist models of memory and learning demonstrate how simple incremental mechanisms, adjusting the relationships between individually-simple components, can produce organisations that exhibit complex system-level behaviours and improve the adaptive capabilities of the system. We use the term “evolutionary connectionism” to recognise that, by functionally equivalent processes, natural selection acting on the relationships within and between evolutionary entities can result in organisations that produce complex system-level behaviours in evolutionary systems and modify the adaptive capabilities of natural selection over time. We review the evidence supporting the functional equivalences between the domains of learning and of evolution, and discuss the potential for this to resolve conceptual problems in our understanding of the evolution of developmental, ecological and reproductive organisations and, in particular, the major evolutionary transitions

Chemical Vapor Deposition Coating for Micromachines

Two major problems associated with Si-based MEMS devices are stiction and wear. Surface modifications are needed to reduce both adhesion and friction in micromechanical structures to solve these problems. In this paper, the authors will present a process used to selectively coat MEMS devices with tungsten using a CVD (Chemical Vapor Deposition) process. The selective W deposition process results in a very conformal coating and can potentially solve both stiction and wear problems confronting MEMS processing. The selective deposition of tungsten is accomplished through silicon reduction of WF{sub 6}, which results in a self-limiting reaction. The selective deposition of W only on polysilicon surfaces prevents electrical shorts. Further, the self-limiting nature of this selective W deposition process ensures the consistency necessary for process control. Selective tungsten is deposited after the removal of the sacrificial oxides to minimize process integration problems. This tungsten coating adheres well and is hard and conducting, requirements for device performance. Furthermore, since the deposited tungsten infiltrates under adhered silicon parts and the volume of W deposited is less than the amount of Si consumed, it appears to be possible to release stuck parts that are contacted over small areas such as dimples. Results from tungsten deposition on MEMS structures with dimples will be presented. The effect of wet and vapor phase cleanings prior to the deposition will be discussed along with other process details. The W coating improved wear by orders of magnitude compared to uncoated parts. Tungsten CVD is used in the integrated-circuit industry, which makes this approach manufacturable