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

The Genetic coding style of digital organisms

Recently, all the human genes were identified. But understanding the functions coded in the genes is of course a much harder problem. We are used to view DNA as some sort of a computer code, but there are striking differences. For example, by using entropy, it has been shown that the DNA code is much closer to random code than written text, which in turn is less ordered than ordinary computer code. Instead of saying that the DNA is badly written, using common programming standards, we might say that it is written in a different style − an evolutionary style. In this paper the coding style of creatures from the artificial life platform Avida has been studied. Avida creatures that have evolved under different size merit methods and mutation rates have been analysed using the notion of stylistic measures. The analysis has shown that the evolutionary coding style depends on the environment in which the code evolved, and that the choice of size merit method and mutation probabilities affect different stylistic properties of the genome. A better understanding of Avida’s coding style, might eventually lead to insights of evolutionary codes in general

Solution of the Quasispecies Model for an Arbitrary Gene Network

In this paper, we study the equilibrium behavior of Eigen's quasispecies equations for an arbitrary gene network. We consider a genome consisting of $N$ genes, so that each gene sequence $\sigma$ may be written as $\sigma = \sigma_1 \sigma_2 ... \sigma_N$. We assume a single fitness peak (SFP) model for each gene, so that gene $i$ has some ``master'' sequence $\sigma_{i, 0}$ for which it is functioning. The fitness landscape is then determined by which genes in the genome are functioning, and which are not. The equilibrium behavior of this model may be solved in the limit of infinite sequence length. The central result is that, instead of a single error catastrophe, the model exhibits a series of localization to delocalization transitions, which we term an ``error cascade.'' As the mutation rate is increased, the selective advantage for maintaining functional copies of certain genes in the network disappears, and the population distribution delocalizes over the corresponding sequence spaces. The network goes through a series of such transitions, as more and more genes become inactivated, until eventually delocalization occurs over the entire genome space, resulting in a final error catastrophe. This model provides a criterion for determining the conditions under which certain genes in a genome will lose functionality due to genetic drift. It also provides insight into the response of gene networks to mutagens. In particular, it suggests an approach for determining the relative importance of various genes to the fitness of an organism, in a more accurate manner than the standard ``deletion set'' method. The results in this paper also have implications for mutational robustness and what C.O. Wilke termed ``survival of the flattest.''Comment: 29 pages, 5 figures, to be submitted to Physical Review

Does the Red Queen reign in the kingdom of digital organisms?

In competition experiments between two RNA viruses of equal or almost equal fitness, often both strains gain in fitness before one eventually excludes the other. This observation has been linked to the Red Queen effect, which describes a situation in which organisms have to constantly adapt just to keep their status quo. I carried out experiments with digital organisms (self-replicating computer programs) in order to clarify how the competing strains' location in fitness space influences the Red-Queen effect. I found that gains in fitness during competition were prevalent for organisms that were taken from the base of a fitness peak, but absent or rare for organisms that were taken from the top of a peak or from a considerable distance away from the nearest peak. In the latter two cases, either neutral drift and loss of the fittest mutants or the waiting time to the first beneficial mutation were more important factors. Moreover, I found that the Red-Queen dynamic in general led to faster exclusion than the other two mechanisms.Comment: 10 pages, 5 eps figure

Eigen model as a quantum spin chain: exact dynamics

We map Eigen model of biological evolution [Naturwissenschaften {\bf 58}, 465 (1971)] into a one-dimensional quantum spin model with non-Hermitean Hamiltonian. Based on such a connection, we derive exact relaxation periods for the Eigen model to approach static energy landscape from various initial conditions. We also study a simple case of dynamic fitness function.Comment: 10 pages. Physical Revew E vol. 69, in press (2004

On the Neutrality of Flowshop Scheduling Fitness Landscapes

Solving efficiently complex problems using metaheuristics, and in particular local searches, requires incorporating knowledge about the problem to solve. In this paper, the permutation flowshop problem is studied. It is well known that in such problems, several solutions may have the same fitness value. As this neutrality property is an important one, it should be taken into account during the design of optimization methods. Then in the context of the permutation flowshop, a deep landscape analysis focused on the neutrality property is driven and propositions on the way to use this neutrality to guide efficiently the search are given.Comment: Learning and Intelligent OptimizatioN Conference (LION 5), Rome : Italy (2011

Survival-extinction phase transition in a bit-string population with mutation

A bit-string model for the evolution of a population of haploid organisms, subject to competition, reproduction with mutation and selection is studied, using mean field theory and Monte Carlo simulations. We show that, depending on environmental flexibility and genetic variability, the model exhibits a phase transtion between extinction and survival. The mean-field theory describes the infinite-size limit, while simulations are used to study quasi-stationary properties.Comment: 11 pages, 5 figure

V I R O L O G Y More than efficacy revealed by single-cell analysis of antiviral therapeutics

Because many aspects of viral infection dynamics and inhibition are governed by stochastic processes, single-cell analysis should provide more information than approaches using population averaging. We have developed a microfluidic device composed of ~6000 wells, with each well containing a microstructure to capture single, infected cells replicating an enterovirus expressing a fluorescent reporter protein. We have used this system to characterize enterovirus inhibitors with distinct mechanisms of action. Single-cell analysis reveals that each class of inhibitor interferes with the viral infection cycle in a manner that can be distinguished by principal component analysis. Single-cell analysis of antiviral candidates not only reveals efficacy but also facilitates clustering of drugs with the same mechanism of action and provides some indication of the ease with which resistance will develop

Single-Cell Virology: On-Chip Investigation of Viral Infection Dynamics

We have developed a high-throughput, microfluidics-based platform to perform kinetic analysis of viral infections in individual cells. We have analyzed thousands of individual poliovirus infections while varying experimental parameters, including multiplicity of infection, cell cycle, viral genotype, and presence of a drug. We make several unexpected observations masked by population-based experiments: (1) viral and cellular factors contribute uniquely and independently to viral infection kinetics; (2) cellular factors cause wide variation in replication start times; and (3) infections frequently begin later and replication occurs faster than predicted by population measurements. We show that mutational load impairs interaction of the viral population with the host, delaying replication start times and explaining the attenuated phenotype of a mutator virus. We show that an antiviral drug can selectively extinguish the most-fit members of the viral population. Single-cell virology facilitates discovery and characterization of virulence determinants and elucidation of mechanisms of drug action eluded by population methods. Guo et al. use a microfluidics device installed on a fluorescence microscope to monitor the kinetics of viral infection in single cells. Between-cell variation in outcomes of infection exists at all phases of the life cycle. Cellular gene expression governs the eclipse phase; viral genetics govern replication rate and yield

Predicting evolution and visualizing high-dimensional fitness landscapes

The tempo and mode of an adaptive process is strongly determined by the structure of the fitness landscape that underlies it. In order to be able to predict evolutionary outcomes (even on the short term), we must know more about the nature of realistic fitness landscapes than we do today. For example, in order to know whether evolution is predominantly taking paths that move upwards in fitness and along neutral ridges, or else entails a significant number of valley crossings, we need to be able to visualize these landscapes: we must determine whether there are peaks in the landscape, where these peaks are located with respect to one another, and whether evolutionary paths can connect them. This is a difficult task because genetic fitness landscapes (as opposed to those based on traits) are high-dimensional, and tools for visualizing such landscapes are lacking. In this contribution, we focus on the predictability of evolution on rugged genetic fitness landscapes, and determine that peaks in such landscapes are highly clustered: high peaks are predominantly close to other high peaks. As a consequence, the valleys separating such peaks are shallow and narrow, such that evolutionary trajectories towards the highest peak in the landscape can be achieved via a series of valley crossingsComment: 12 pages, 7 figures. To appear in "Recent Advances in the Theory and Application of Fitness Landscapes" (A. Engelbrecht and H. Richter, eds.). Springer Series in Emergence, Complexity, and Computation, 201