Tradeoff between short-term and long-term adaptation in a changing environment

We investigate the competition dynamics of two microbial or viral strains that live in an environment that switches periodically between two states. One of the strains is adapted to the long-term environment, but pays a short-term cost, while the other is adapted to the short-term environment and pays a cost in the long term. We explore the tradeoff between these alternative strategies in extensive numerical simulations, and present a simple analytic model that can predict the outcome of these competitions as a function of the mutation rate and the time scale of the environmental changes. Our model is relevant for arboviruses, which alternate between different host species on a regular basis.Comment: 9 pages, 3 figures, PRE in pres

The look-ahead effect of phenotypic mutations

The evolution of complex molecular traits such as disulphide bridges often requires multiple mutations. The intermediate steps in such evolutionary trajectories are likely to be selectively neutral or deleterious. Therefore, large populations and long times may be required to evolve such traits. We propose that errors in transcription and translation may allow selection for the intermediate mutations if the final trait provides a large enough selective advantage. We test this hypothesis using a population based model of protein evolution. If an individual acquires one of two mutations needed for a novel trait, the second mutation can be introduced into the phenotype due to transcription and translation errors. If the novel trait is advantageous enough, the allele with only one mutation will spread through the population, even though the gene sequence does not yet code for the complete trait. The first mutation then has a higher frequency than expected without phenotypic mutations giving the second mutation a higher probability of fixation. Thus, errors allow protein sequences to ''look-ahead'' for a more direct path to a complex trait.Comment: Submitted to "Genetics

Ergosterol Effect on the Desaturation of 14C-Cis-Vaccenate in Tetrahymena

Supplement of ergosterol to the growth medium of the ciliated protozoan Tetrahymena pyriformis W leads to incorporation of the foreign sterol within cell membranes and suppression of synthesis of the native sterol-like compound tetrahymanol, as well as to changes in the fatty acid compositions of several major classes of membrane lipid. Alteration of fatty acid composition is thought to represent a regulatory mechanism whereby optimum membrane fluidity is maintained when the slightly dissimilar foreign sterol is added into the phospholipid bilayer of the membranes. The present study, using several different conditions of growth temperature, substrate concentrations and incubation time, and ergosterol concentrations and exposure time, is an attempt to provide evidence supporting a hypothetical regulatory mechanism. This mechanism proposes that there is a feedback regulation by membrane-bound sterol on an enzyme or enzymes involved in synthesis of the long chain fatty acids contained in membrane phospholipid. Such a mechanism could account for the balance between sterol and fatty acid content of membrane. The data presented here show that a statistically significant increase in desaturation of 14C-cis-vaccenate can be demonstrated in Tetrahymena cell cultures whose membranes contain the foreign sterol, when growth temperature is maintained at 20° or 29.5°. Tetrahymena desaturated 14C-cis-vaccenate substrate in both ergosterol supplemented and normal cultures. The 14C labeled product, 6,11-18:2 was recovered and separated by silver nitrate-Unisil column chromatography

Zero-frequency anomaly in quasiclassical ac transport: Memory effects in a two-dimensional metal with a long-range random potential or random magnetic field

We study the low-frequency behavior of the {\it ac} conductivity $\sigma(\omega)$ of a two-dimensional fermion gas subject to a smooth random potential (RP) or random magnetic field (RMF). We find a non-analytic $\propto|\omega|$ correction to ${\rm Re} \sigma$, which corresponds to a $1/t^2$ long-time tail in the velocity correlation function. This contribution is induced by return processes neglected in Boltzmann transport theory. The prefactor of this $|\omega|$-term is positive and proportional to $(d/l)^2$ for RP, while it is of opposite sign and proportional to $d/l$ in the weak RMF case, where $l$ is the mean free path and $d$ the disorder correlation length. This non-analytic correction also exists in the strong RMF regime, when the transport is of a percolating nature. The analytical results are supported and complemented by numerical simulations.Comment: 12 pages, RevTeX, 7 figure

On quasilinear parabolic evolution equations in weighted Lp-spaces II

Our study of abstract quasi-linear parabolic problems in time-weighted L_p-spaces, begun in [17], is extended in this paper to include singular lower order terms, while keeping low initial regularity. The results are applied to reaction-diffusion problems, including Maxwell-Stefan diffusion, and to geometric evolution equations like the surface-diffusion flow or the Willmore flow. The method presented here will be applicable to other parabolic systems, including free boundary problems.Comment: 21 page

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