Robustness and epistasis in mutation-selection models

We investigate the fitness advantage associated with the robustness of a phenotype against deleterious mutations using deterministic mutation-selection models of quasispecies type equipped with a mesa shaped fitness landscape. We obtain analytic results for the robustness effect which become exact in the limit of infinite sequence length. Thereby, we are able to clarify a seeming contradiction between recent rigorous work and an earlier heuristic treatment based on a mapping to a Schr\"odinger equation. We exploit the quantum mechanical analogy to calculate a correction term for finite sequence lengths and verify our analytic results by numerical studies. In addition, we investigate the occurrence of an error threshold for a general class of epistatic landscape and show that diminishing epistasis is a necessary but not sufficient condition for error threshold behavior.Comment: 20 pages, 14 figure

Rif1 controls DNA replication by directing Protein Phosphatase 1 to reverse Cdc7-mediated phosphorylation of the MCM complex

Peer reviewedPublisher PD

Do bilinguals have different concepts? The case of shape and material in Japanese L2 users of English

An experiment investigated whether Japanese speakers’ categorisation of objects and substances as shape or material is influenced by acquiring English, based on Imai and Gentner (1997). Subjects were presented with an item such as a cork pyramid and asked to choose between two other items that matched it for shape (plastic pyramid) or for material (piece of cork). The hypotheses were that for simple objects the number of shape-based categorisations would increase according to experience of English and that the preference for shape and material-based categorisations of Japanese speakers of English would differ from mono¬lingual speakers of both languages. Subjects were 18 adult Japanese users of English who had lived in English-speaking countries between 6 months and 3 years (short-stay group), and 18 who had lived in English-speaking countries for 3 years or more (long-stay group). Both groups achieved above criterion on an English vocabulary test. Results were: both groups preferred material responses for simple objects and substances but not for complex objects, in line with Japanese mono¬linguals, but the long-stay group showed more shape preference than the short-stay group and also were less different from Americans. These effects of acquiring a second language on categorisation have implications for conceptual representation and methodology

Evolutionary dynamics of the most populated genotype on rugged fitness landscapes

We consider an asexual population evolving on rugged fitness landscapes which are defined on the multi-dimensional genotypic space and have many local optima. We track the most populated genotype as it changes when the population jumps from a fitness peak to a better one during the process of adaptation. This is done using the dynamics of the shell model which is a simplified version of the quasispecies model for infinite populations and standard Wright-Fisher dynamics for large finite populations. We show that the population fraction of a genotype obtained within the quasispecies model and the shell model match for fit genotypes and at short times, but the dynamics of the two models are identical for questions related to the most populated genotype. We calculate exactly several properties of the jumps in infinite populations some of which were obtained numerically in previous works. We also present our preliminary simulation results for finite populations. In particular, we measure the jump distribution in time and find that it decays as $t^{-2}$ as in the quasispecies problem.Comment: Minor changes. To appear in Phys Rev

In the light of directed evolution: Pathways of adaptive protein evolution

Directed evolution is a widely-used engineering strategy for improving the stabilities or biochemical functions of proteins by repeated rounds of mutation and selection. These experiments offer empirical lessons about how proteins evolve in the face of clearly-defined laboratory selection pressures. Directed evolution has revealed that single amino acid mutations can enhance properties such as catalytic activity or stability and that adaptation can often occur through pathways consisting of sequential beneficial mutations. When there are no single mutations that improve a particular protein property experiments always find a wealth of mutations that are neutral with respect to the laboratory-defined measure of fitness. These neutral mutations can open new adaptive pathways by at least 2 different mechanisms. Functionally-neutral mutations can enhance a protein's stability, thereby increasing its tolerance for subsequent functionally beneficial but destabilizing mutations. They can also lead to changes in “promiscuous” functions that are not currently under selective pressure, but can subsequently become the starting points for the adaptive evolution of new functions. These lessons about the coupling between adaptive and neutral protein evolution in the laboratory offer insight into the evolution of proteins in nature

Records and sequences of records from random variables with a linear trend

We consider records and sequences of records drawn from discrete time series of the form $X_{n}=Y_{n}+cn$, where the $Y_{n}$ are independent and identically distributed random variables and $c$ is a constant drift. For very small and very large drift velocities, we investigate the asymptotic behavior of the probability $p_n(c)$ of a record occurring in the $n$th step and the probability $P_N(c)$ that all $N$ entries are records, i.e. that $X_1 < X_2 < ... < X_N$. Our work is motivated by the analysis of temperature time series in climatology, and by the study of mutational pathways in evolutionary biology.Comment: 21 pages, 7 figure

The Effect of Mobile Element IS10 on Experimental Regulatory Evolution in Escherichia coli

Mobile genetic elements are widespread in bacteria, where they cause several kinds of mutations. Although their effects are on the whole negative, rare beneficial mutations caused by insertion sequence elements are frequently selected in some experimental evolution systems. For example, in earlier work, we found that strains of Escherichia coli that lack the sigma factor RpoS adapt to a high-osmolarity environment by the insertion of element IS10 into the promoter of the otsBA operon, rewiring expression from RpoS dependent to RpoS independent. We wished to determine how the presence of IS10 in the genome of this strain shaped the evolutionary outcome. IS10 could influence the outcome by causing mutations that confer adaptive phenotypes that cannot be achieved by strains without the element. Alternatively, IS10 could influence evolution by increasing the rate of appearance of certain classes of beneficial mutations even if they are no better than those that could be achieved by a strain without the element. We found that populations evolved from an IS10-free strain did not upregulate otsBA. An otsBA-lacZY fusion facilitated the recovery of a number of mutations that upregulate otsB without involving IS10 and found that two caused greater fitness increases than IS10 insertion, implying that evolution could have upregulated otsBA in the IS10-free strain. Finally, we demonstrate that there is epistasis between the IS10 insertion into the otsBA promoter and the other adaptive mutations, implying that introduction of IS10 into the otsBA promoter may alter the trajectory of adaptive evolution. We conclude that IS10 exerts its effect not by creating adaptive phenotypes that could not otherwise occur but by increasing the rate of appearance of certain adaptive mutations

Canalization of the evolutionary trajectory of the human influenza virus

Since its emergence in 1968, influenza A (H3N2) has evolved extensively in genotype and antigenic phenotype. Antigenic evolution occurs in the context of a two-dimensional 'antigenic map', while genetic evolution shows a characteristic ladder-like genealogical tree. Here, we use a large-scale individual-based model to show that evolution in a Euclidean antigenic space provides a remarkable correspondence between model behavior and the epidemiological, antigenic, genealogical and geographic patterns observed in influenza virus. We find that evolution away from existing human immunity results in rapid population turnover in the influenza virus and that this population turnover occurs primarily along a single antigenic axis. Thus, selective dynamics induce a canalized evolutionary trajectory, in which the evolutionary fate of the influenza population is surprisingly repeatable and hence, in theory, predictable.Comment: 29 pages, 5 figures, 10 supporting figure

Maximally-localized generalized Wannier functions for composite energy bands

We discuss a method for determining the optimally-localized set of generalized Wannier functions associated with a set of Bloch bands in a crystalline solid. By ``generalized Wannier functions'' we mean a set of localized orthonormal orbitals spanning the same space as the specified set of Bloch bands. Although we minimize a functional that represents the total spread sum_n [ _n - _n^2 ] of the Wannier functions in real space, our method proceeds directly from the Bloch functions as represented on a mesh of k-points, and carries out the minimization in a space of unitary matrices U_mn^k describing the rotation among the Bloch bands at each k-point. The method is thus suitable for use in connection with conventional electronic-structure codes. The procedure also returns the total electric polarization as well as the location of each Wannier center. Sample results for Si, GaAs, molecular C2H4, and LiCl will be presented.Comment: 22 pages, two-column style with 4 postscript figures embedded. Uses REVTEX and epsf macros. Also available at http://www.physics.rutgers.edu/~dhv/preprints/index.html#nm_wan

Teleportation of geometric structures in 3D

Simplest quantum teleportation algorithms can be represented in geometric terms in spaces of dimensions 3 (for real state-vectors) and 4 (for complex state-vectors). The geometric representation is based on geometric-algebra coding, a geometric alternative to the tensor-product coding typical of quantum mechanics. We discuss all the elementary ingredients of the geometric version of the algorithm: Geometric analogs of states and controlled Pauli gates. Fully geometric presentation is possible if one employs a nonstandard representation of directed magnitudes, formulated in terms of colors defined via stereographic projection of a color wheel, and not by means of directed volumes.Comment: typos corrected, one plot remove