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

Friction in surface micromachined microengines

Understanding the frictional properties of advanced Micro-Electro- Mechanical Systems (MEMS) is essential in order to develop optimized designs and fabrication processes, as well as to qualify devices for commercial applications. We develop and demonstrate a method to experimentally measure the forces associated with sliding friction of devices rotating on a hub. The method is demonstrated on the rotating output gear of the microengine recently developed at Sandia National Laboratories. In-situ measurements of an engine running at 18300 rpm give a coefficient of friction of 0.5 for radial (normal) forces less than 4 {mu}N. For larger forces the effective coefficient of friction abruptly increases, suggesting a fundamental change in the basic nature of the interaction between the gear and hub. The experimental approach we have developed to measure the frictional forces associated with the microengine is generically applicable to other MEMS devices

Performance tradeoffs for a surface micromachined microengine

An electromechanical model of Sandia`s microengine is developed and applied to quantify critical performance tradeoffs. This is done by determining how forces impact the mechanical response of the engine to different electrical drive signals. To validate the theoretical results, model-based drive signals are used to operate actual engines, where controlled operation is achieved for the following cases: (1) spring forces are dominant, (2) frictional forces are dominant, (3) linear inertial forces are dominant, (4) viscous damping forces are dominant, and (5) inertial load forces are dominant. Significant improvements in engine performance are experimentally demonstrated in the following areas: positional control, start/stop endurance, constant speed endurance, friction load reduction, and rapid actuation of inertial loads

Failure modes in surface micromachined microelectromechanical actuators

In order for the rapidly emerging field of MicroElectroMechanical Systems (MEMS) to meet its extraordinary expectations regarding commercial impact, issues pertaining to how they fail must be understood. The authors identify failure modes common to a broad range of MEMS actuators, including adhesion (stiction) and friction induced failures caused by improper operational methods, mechanical instabilities, and electrical instabilities. Demonstrated methods to mitigate these failure modes include implementing optimized designs, model based operational methods, and chemical surface treatments

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

Wider Access to Genotypic Space Facilitates Loss of Cooperation in a Bacterial Mutator

Understanding the ecological, evolutionary and genetic factors that affect the expression of cooperative behaviours is a topic of wide biological significance. On a practical level, this field of research is useful because many pathogenic microbes rely on the cooperative production of public goods (such as nutrient scavenging molecules, toxins and biofilm matrix components) in order to exploit their hosts. Understanding the evolutionary dynamics of cooperation is particularly relevant when considering long-term, chronic infections where there is significant potential for intra-host evolution. The impact of responses to non-social selection pressures on social evolution is arguably an under-examined area. In this paper, we consider how the evolution of a non-social trait – hypermutability – affects the cooperative production of iron-scavenging siderophores by the opportunistic human pathogen Pseudomonas aeruginosa. We confirm an earlier prediction that hypermutability accelerates the breakdown of cooperation due to increased sampling of genotypic space, allowing mutator lineages to generate non-cooperative genotypes with the ability to persist at high frequency and dominate populations. This may represent a novel cost of hypermutability

Mutator dynamics in sexual and asexual experimental populations of yeast

<p>Abstract</p> <p>Background</p> <p>In asexual populations, mutators may be expected to hitchhike with associated beneficial mutations. In sexual populations, recombination is predicted to erode such associations, inhibiting mutator hitchhiking. To investigate the effect of recombination on mutators experimentally, we compared the frequency dynamics of a mutator allele (<it>msh2</it>Δ) in sexual and asexual populations of <it>Saccharomyces cerevisiae</it>.</p> <p>Results</p> <p>Mutator strains increased in frequency at the expense of wild-type strains in all asexual diploid populations, with some approaching fixation in 150 generations of propagation. Over the same period of time, mutators declined toward loss in all corresponding sexual diploid populations as well as in haploid populations propagated asexually.</p> <p>Conclusions</p> <p>We report the first experimental investigation of mutator dynamics in sexual populations. We show that a strong mutator quickly declines in sexual populations while hitchhiking to high frequency in asexual diploid populations, as predicted by theory. We also show that the <it>msh2Δ </it>mutator has a high and immediate realized cost that is alone sufficient to explain its decline in sexual populations. We postulate that this cost is indirect; namely, that it is due to a very high rate of recessive lethal or strongly deleterious mutation. However, we cannot rule out the possibility that <it>msh2</it>Δ also has unknown directly deleterious effects on fitness, and that these effects may differ between haploid asexual and sexual populations. Despite these reservations, our results prompt us to speculate that the short-term cost of highly deleterious recessive mutations can be as important as recombination in preventing mutator hitchhiking in sexual populations.</p

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