Persistence of species obeying difference equations

The question of persistence of interacting species is one of the most important in theoretical ecology; when the system is governed by difference equations this question is particularly difficult to resolve because of the complicated dynamics of the model. The problem has usually been tackled via the concepts of asymptotic stability and global asymptotic stability, however the first is not a strong enough restriction since only orbits starting near a rest point are guaranteed to converge to the rest point, while the second as well as usually being extremely difficult to establish is surely too strong a condition, since it rules out for example a stable limit cycle. It is proposed here that a more biologically realistic criterion, and incidentally one which turns out to be more tractable, is that of cooperativeness, where all orbits are required eventually to enter and remain in a region at a non-zero distance from the boundary (corresponding to a zero value of at least one population). A theorem is proved giving conditions for cooperativeness, and is applied to some examples of predator-prey interactions, simple conditions on the parameters being obtained even for some ranges of the parameters where the dynamics are chaotic.     

Cumulant dynamics of a population under multiplicative selection, mutation, and drift

We revisit the classical population genetics model of a population evolving under multiplicative selection, mutation, and drift. The number of beneficial alleles in a multilocus system can be considered a trait under exponential selection. Equations of motion are derived for the cumulants of the trait distribution in the diffusion limit and under the assumption of linkage equilibrium. Because of the additive nature of cumulants, this reduces to the problem of determining equations of motion for the expected allele distribution cumulants at each locus. The cumulant equations form an infinite dimensional linear system and in an authored appendix Adam Prügel-Bennett provides a closed form expression for these equations. We derive approximate solutions which are shown to describe the dynamics well for a broad range of parameters. In particular, we introduce two approximate analytical solutions: (1) Perturbation theory is used to solve the dynamics for weak selection and arbitrary mutation rate. The resulting expansion for the system's eigenvalues reduces to the known diffusion theory results for the limiting cases with either mutation or selection absent. (2) For low mutation rates we observe a separation of time-scales between the slowest mode and the rest which allows us to develop an approximate analytical solution for the dominant slow mode. The solution is consistent with the perturbation theory result and provides a good approximation for much stronger selection intensities.     

Human migrations and linkage disequilibrium ofHL-A system

A migration with admixture of genes in two populations inducesHL-A linkage disequilibrium or when gene frequencies in the two populations are dissimilar. Since theHL-A linkage disequilibrium disappears very slowly, this factor could be used to recognize some migrations. In the recent migration of American Negroes, a dilution of Caucasoid disequilibrium is noted. By the presence of values, a study of possible migrations around the world is reported and a brief comparison with other methods of research into population origins is discussed in connection with the European ecosphere: a well-known expansion axis is found from East to West (probably due to the Indo-European migration), which ends with admixture with various local Western European populations. Another expansion of genes is noted from the North of Europe towards the Southwest.     

Originator dynamics

We study the origin of evolution. Evolution is based on replication, mutation, and selection. But how does evolution begin? When do chemical kinetics turn into evolutionary dynamics? We propose "prelife" and "prevolution" as the logical precursors of life and evolution. Prelife generates sequences of variable length. Prelife is a generative chemistry that proliferates information and produces diversity without replication. The resulting "prevolutionary dynamics" have mutation and selection. We propose an equation that allows us to investigate the origin of evolution. In one limit, this "originator equation" gives the classical selection equation. In the other limit, we obtain "prelife." There is competition between life and prelife and there can be selection for or against replication. Simple prelife equations with uniform rate constants have the property that longer sequences are exponentially less frequent than shorter ones. But replication can reverse such an ordering. As the replication rate increases, some longer sequences can become more frequent than shorter ones. Thus, replication can lead to "reversals" in the equilibrium portraits. We study these reversals, which mark the transition from prelife to life in our model. If the replication potential exceeds a critical value, then life replicates into existence.     

Environment‐specific spectral modeling: A new tool for the analysis of biological specimens

The recent discovery of fluorescent dyes for improving pathologic tissues identification has highlighted the need of robust methods for performance validation especially in the field of fluorescence‐guided surgery. Optical imaging of excised tissue samples is the reference tool to validate the association between dyes localization and the underlying histology in a controlled environment. Spectral unmixing may improve the validation process discriminating dye from endogenous signal. Here, an innovative spectral modeling approach that weights the spectral shifts associated with changes in chemical environment is described. The method is robust against spectral shift variations and its application leads to unbiased spectral weights estimates as demonstrated by numerical simulations. Finally, spectral shifts values computed pixel‐wise from spectral images are used to display additional information with potential diagnostic value.      

An application of the central limit theorem to coalescence times in the structured coalescent model with strong migration

The structured coalescent describes the ancestral relationship among sampled genes from a geographically structured population. The aim of this article is to apply the central limit theorem to functionals of the migration process to study coalescence times and population structure. An application of the law of large numbers to the migration process leads to the strong migration limit for the distributions of coalescence times. The central limit theorem enables us to obtain approximate distributions of coalescence times for strong migration. We show that approximate distributions depend on the population structure. If migration is conservative and strong, we can define a kind of effective population size N _e ^*, with which the entire population approximately behaves like a panmictic population. On the other hand, the approximate distributions for nonconservative migration are qualitatively different from those for conservative migration. And the entire population behaves unlike a panmictic population even though migration is strong.     

Genetic structure and domains of DNA polymerase III of Bacillus subtilis

Summary We have determined the nucleotide sequence of the polC gene of Bacillus subtilis which codes for DNA polymerase III. Our recent analysis has revealed that the gene comprises 4311 nucleotides, from the start to the stop codon, 306 nucleotides more than we reported earlier. The plasmid reported by us and by N.C. Brown's laboratory contained a sequence at the end of the gene which is not related to the polC region of B. subtilis. We have isolated the rest of the gene, the sequence of which is presented in this paper. The new stop codon is followed by a hyphenated palindromic sequence of 13 nucleotides. The C-terminus' of the coding region contains the novel mutation, dnaF, which results in a defect in the initiation of replication due to a change in the codon TCC to TTC (serine to phenylalanine). The hypermutator mutation mut-1 is due to two point mutations in the 3 to 5 exonuclease domain, the proof reading function. The codon changes are GGA to GAA (glycine to glutamic acid) and AGC to AAC (serine to asparagine). The elongation defective mutation, polC26, affecting the catalytic site that adds nucleotides to the growing chain, is due to a change in the codon GTC to GAC (valine to aspartic acid). It is separated from the mutation reported earlier, azp-12, by 306 nucleotides. Knowing the locations of the mutational sites allowed us to deduce the domains of the gene and the enzyme it encodes, and permitted us to present a precise map of the gene at the molecular level.Abbreviations HPUra p-hydroxyphenyl azouracil - nt nucleotide - PCR polymerase chain reaction     

Viral Mutation Rates

Accurate estimates of virus mutation rates are important to understand the evolution of the viruses and to combat them. However, methods of estimation are varied and often complex. Here, we critically review over 40 original studies and establish criteria to facilitate comparative analyses. The mutation rates of 23 viruses are presented as substitutions per nucleotide per cell infection (s/n/c) and corrected for selection bias where necessary, using a new statistical method. The resulting rates range from 10⁻⁸ to10⁻⁶ s/n/c for DNA viruses and from 10⁻⁶ to 10⁻⁴ s/n/c for RNA viruses. Similar to what has been shown previously for DNA viruses, there appears to be a negative correlation between mutation rate and genome size among RNA viruses, but this result requires further experimental testing. Contrary to some suggestions, the mutation rate of retroviruses is not lower than that of other RNA viruses. We also show that nucleotide substitutions are on average four times more common than insertions/deletions (indels). Finally, we provide estimates of the mutation rate per nucleotide per strand copying, which tends to be lower than that per cell infection because some viruses undergo several rounds of copying per cell, particularly double-stranded DNA viruses. A regularly updated virus mutation rate data set will be available at www.uv.es/rsanjuan/virmut.The mutation rate is a critical parameter for understanding viral evolution and has important practical implications. For instance, the estimate of the mutation rate of HIV-1 demonstrated that any single mutation conferring drug resistance should occur within a single day and that simultaneous treatment with multiple drugs was therefore necessary (72). Also, in theory, viruses with high mutation rates could be combated by the administration of mutagens (1, 5, 21, 44, 53, 83). This strategy, called lethal mutagenesis, has proved effective in cell cultures or animal models against several RNA viruses, including enteroviruses (11, 39, 44), aphtoviruses (83), vesiculoviruses (44), hantaviruses (10), arenaviruses (40), and lentiviruses (15, 53), and appears to at least partly contribute to the effectiveness of the combined ribavirin-interferon treatment against hepatitis C virus (HCV) (13). The viral mutation rate also plays a role in the assessment of possible vaccination strategies (16), and it has been shown to influence the stability of live attenuated polio vaccines (91). Finally, at both the epidemiological and evolutionary levels, the mutation rate is one of the factors that can determine the risk of emergent infectious disease, i.e., pathogens crossing the species barrier (46).Slight changes of the mutation rate can also determine whether or not some virus infections are cleared by the host immune system and can produce dramatic differences in viral fitness and virulence (75, 90), clearly stressing the need to have accurate estimates. However, our knowledge of viral mutation rates is somewhat incomplete, partly due to the inherent difficulty of measuring a rare and random event but also due to several sources of bias, inaccuracy, and terminological confusion. One goal of our work is to provide an update of published mutation rate estimates, since the last authoritative reviews on viral mutation rates were published more than a decade ago (29, 30). We therefore present a comprehensive review of mutation rate estimates from over 40 original studies and 23 different viruses representing all the main virus types. A second, and perhaps more ambitious, goal of our study is to consolidate the published literature by dealing with what we regard as the two main problems in the field: the use of different units of measurement and the bias caused by selection.The problem of units is linked to the different modes of replication in viruses. Under “stamping machine” or linear replication, multiple copies are made sequentially from the same template and the resulting progeny strands do not become templates until the progeny virions infect another cell. In contrast, under binary replication, progeny strands immediately become templates and hence the number of molecules doubles in each cycle of strand copying, increasing geometrically. This basic distinction leads to two different definitions of the mutation rate: per strand copying or per cell infection. If replication is stamping machine-like, there is only one cycle of strand copying per infected cell and hence the two units are equivalent. However, binary replication means that the virus completes several cycles of strand copying per cell. The actual replication mode of most viruses is probably intermediate between these two idealized cases, and although it is known to be closer to linear in some viruses (9, 19) and closer to binary in others (26, 55), it is often unknown. This leads to uncertainties in mutation rate estimates. For instance, in the case of poliovirus 1, the estimated rate per strand copying can vary by 10-fold depending on whether stamping machine or binary replication is assumed (27). Typically this difference in the unit of measurement has been overlooked in comparative studies. Here, we express published estimates in the same unit.The other issue that we address is selection. In general, deleterious mutations tend to be eliminated and hence are less likely to be sampled than neutral ones, introducing a bias in mutation rate estimates. To avoid this problem, selective neutrality is sometimes enforced by the experimenter, such that the number of mutations increases linearly with time (58, 88). The opposite strategy is to focus on lethal mutations, which have necessarily appeared during the last cell infection cycle, thus establishing a direct and time-independent relationship between the observed mutation frequency and the underlying mutation rate (13, 37). In between these two special cases, an explicit correction for selection is needed. Even if the effect of each individual mutation on viral fitness is unknown, the effect of selection can be statistically accounted for as long as the number of mutations sampled for estimating mutation rates is large. We do this here using empirical information about the distribution of mutational fitness effects previously obtained for several viruses (6, 23, 73, 80). Importantly, the basic properties of this distribution appear to be well conserved (78), and hence the proposed method should be applicable to a wide variety of viruses.Using the resulting mutation rate data, we retest some previously accepted general patterns, suggest new ones, infer the mode of replication of some viruses, and compare the rates of mutation to substitutions with those to insertions/deletions (indels).     

Asymmetric directional mutation pressures in bacteria

Background

When there are no strand-specific biases in mutation and selection rates (that is, in the substitution rates) between the two strands of DNA, the average nucleotide composition is theoretically expected to be A = T and G = C within each strand. Deviations from these equalities are therefore evidence for an asymmetry in selection and/or mutation between the two strands. By focusing on weakly selected regions that could be oriented with respect to replication in 43 out of 51 completely sequenced bacterial chromosomes, we have been able to detect asymmetric directional mutation pressures.

Results

Most of the 43 chromosomes were found to be relatively enriched in G over C and T over A, and slightly depleted in G+C, in their weakly selected positions (intergenic regions and third codon positions) in the leading strand compared with the lagging strand. Deviations from A = T and G = C were highly correlated between third codon positions and intergenic regions, with a lower degree of deviation in intergenic regions, and were not correlated with overall genomic G+C content.

Conclusions

During the course of bacterial chromosome evolution, the effects of asymmetric directional mutation pressures are commonly observed in weakly selected positions. The degree of deviation from equality is highly variable among species, and within species is higher in third codon positions than in intergenic regions. The orientation of these effects is almost universal and is compatible in most cases with the hypothesis of an excess of cytosine deamination in the single-stranded state during DNA replication. However, the variation in G+C content between species is influenced by factors other than asymmetric mutation pressure.

     

The two-locus ancestral graph in a subdivided population: convergence as the number of demes grows in the island model

We study the ancestral recombination graph for a pair of sites in a geographically structured population. In particular, we consider the limiting behavior of the graph, under Wrights island model, as the number of subpopulations, or demes, goes to infinity. After an instantaneous sample-size adjustment, the graph becomes identical to the two-locus graph in an unstructured population, but with a time scale that depends on the migration rate and the deme size. Interestingly, when migration is gametic, this rescaling of time increases the population mutation rate but does not affect the population recombination rate. We compare this to the case of a partially-selfing population, in which both mutation and recombination depend on the selfing rate. Our result for gametic migration holds both for finite-sized demes, and in the limit as the deme size goes to infinity. However, when migration occurs during the diploid phase of the life cycle and demes are finite in size, the population recombination rate does depend on the migration rate, in a way that is reminiscent of partial selfing. Simulations imply that convergence to a rescaled panmictic ancestral recombination graph occurs for any number of sites as the number of demes approaches infinity.Send offprint request to: Sabin LessardS. Lessard was supported by grants from the Natural Sciences and Research Council of Canada, the Fonds Québécois de la Recherche sur la Nature et les Technologies, and the Université de Montréal.J. Wakeley was supported by a Career Award (DEB-0133760) and by a grant (DEB-9815367) from the National Science Foundation.     

Mechanisms of DNA expansion

Unstable transmission of repeating segments in genes is now recognized as a new class of mutations causing human disease. Genetic instability observed in disease is termed an expansion mutation when the mutation is an increase in the copy number of a repeated unit, commonly a di-or trinucleotide. While the expansion mutation is well characterized in disease, the mechanism by which expansion occurs is not clear. This article focuses on physical properties of expansion at repeating nucleotides that may provide clues to the mechanism. Both biochemical and genetic data indicate that DNA structure is part of the mechanism and the underlying cause for expansion.     

Dinucleotide repeat expansion catalyzed by bacteriophage T4 DNA polymerase in vitro

DNA replication normally occurs with high fidelity, but certain "slippery" regions of DNA with tracts of mono-, di-, and trinucleotide repeats are frequently mutation hot spots. We have developed an in vitro assay to study the mechanism of dinucleotide repeat expansion. The primer-template resembles a base excision repair substrate with a single nucleotide gap centered opposite a tract of nine CA repeats; nonrepeat sequences flank the dinucleotide repeats. DNA polymerases are expected to repair the gap, but further extension is possible if the DNA polymerase can displace the downstream oligonucleotide. We report here that the wild type bacteriophage T4 DNA polymerase carries out gap and strand displacement replication and also catalyzes a dinucleotide expansion reaction. Repeat expansion was not detected for an exonuclease-deficient T4 DNA polymerase or for Escherichia coli DNA polymerase I. The dinucleotide repeat expansion reaction catalyzed by wild type T4 DNA polymerase required a downstream oligonucleotide to "stall" replication and 3' --> 5' exonuclease activity to remove the 3'-nonrepeat sequence adjacent to the repeat tract in the template strand. These results suggest that dinucleotide repeat expansion may be stimulated in vivo during DNA repair or during processing of Okazaki fragments.     

Unblocked statistical-coil tetrapeptides in aqueous solution: quantum-chemical computation of the carbon-13 NMR chemical shifts

We recently reported a theoretical characterization of representative ensembles of statistical-coil conformations for tetrapeptides with unblocked termini in aqueous solution, at pH 7. The results showed good agreement between the computed Boltzmann-averaged and experimentally-determined values for both the vicinal coupling constants ³J_NH and the -proton chemical shifts. Here, we carry out a cluster analysis of the ensembles of conformations generated in that study, and use them to compute the Boltzmann-averaged values of the quantum-chemical ¹³C chemical shifts for different amino acids in the unblocked tetrapeptides GGXA (where X stands for Phe, Arg, His, Glu, Ile, Lys, Gln, Tyr, Leu, Thr, Ala, Gly and Val). The values of the ¹³C chemical shifts in these thirteen amino acids (for which experimental data are available) were computed by using Density Functional Theory with a 6–311+G(2d,p) basis set. Good agreement is found in terms of both the correlation coefficient (R) and standard deviations of the difference between the computed Bolztmann-averaged and the NMR-determined values for the ¹³C chemical shifts. These results suggest that it may be possible to build a reliable theoretically-derived database of chemical shifts for statistical-coil residues. The results of the current study contribute to our understanding of the relations between chemical shifts, dihedral angles and vicinal coupling constants, ³J_NH. In addition, they can shed light as to how the statistical-coilconformation is related to the conformational preference of more structured states, such as the -helical conformation.     

Identifying dramatic selection shifts in phylogenetic trees

Background

The rate of evolution varies spatially along genomes and temporally in time. The presence of evolutionary rate variation is an informative signal that often marks functional regions of genomes and historical selection events. There exist many tests for temporal rate variation, or heterotachy, that start by partitioning sampled sequences into two or more groups and testing rate homogeneity among the groups. I develop a Bayesian method to infer phylogenetic trees with a divergence point, or dramatic temporal shifts in selection pressure that affect many nucleotide sites simultaneously, located at an unknown position in the tree.

Results

Simulation demonstrates that the method is most able to detect divergence points when rate variation and the number of affected sites is high, but not beyond biologically relevant values. The method is applied to two viral data sets. A divergence point is identified separating the B and C subtypes, two genetically distinct variants of HIV that have spread into different human populations with the AIDS epidemic. In contrast, no strong signal of temporal rate variation is found in a sample of F and H genotypes, two genetic variants of HBV that have likely evolved with humans during their immigration and expansion into the Americas.

Conclusion

Temporal shifts in evolutionary rate of sufficient magnitude are detectable in the history of sampled sequences. The ability to detect such divergence points without the need to specify a prior hypothesis about the location or timing of the divergence point should help scientists identify historically important selection events and decipher mechanisms of evolution.

     

The chromoplasts of Or mutants of cauliflower (Brassica oleracea L. var. botrytis)

Summary. The Or mutation in cauliflower (Brassica oleracea L. var. botrytis) leads to abnormal accumulations of -carotene in orange chromoplasts, in tissues in which leucoplasts are characteristic of wild-type plants. Or chromoplasts were investigated by light microscopy of fresh materials and electron microscopy of glutaraldehyde- and potassium permanganate-fixed materials. Carotenoid inclusions in Or chromoplasts resemble those found in carrot root chromoplasts in their optical activity and angular shape. Electron microscopy revealed that the inclusions are made up of parallel, membrane-bound compartments. These stacks of membranes are variously rolled and folded into three-dimensional objects. We classify Or chromoplasts as membranous chromoplasts. The Or mutation also limits plastid replication so that a single chromoplast constitutes the plastidome in most of the affected cells. There are one to two chromoplasts in each cell of a shoot apex. The ability of differentiated chromoplasts to divide in the apical meristems of Or mutant plants resembles the ability of proplastids to maintain plastid continuity from cell to cell in meristems of Arabidopsis thaliana mutants in which plastid replication is drastically limited. The findings are used to discuss the number of levels of regulation involved in plastid replication.     

Asymmetric replication of an oriC plasmid in Escherichia coli

Summary Plasmid pTSO118 containing the Escherichia coli origin of replication, oriC, initiated replication simultaneously with the chromosome when temperature-sensitive host cells were synchronized by temperature shifts. Replicating intermediates of the plasmid as well as of the chromosome were isolated from the outer membrane fraction of the cell. Plasmid DNA with eye structures was enriched when cytosine-1--arabinofuranoside was introduced into the culture during replication. Electron microscopy of the replicating molecules, after digestion with restriction endonucleases, showed that the replication fork proceeds exclusively counter-clockwise towards the unc operon. We conclude that the replication of the oriC plasmid is unidirectional or, if bidirectional, is highly asymmetric.     

Distributed Shared Arrays: Portable Shared-Memory Programming Interface for Multiple Computer Systems

This paper describes the design and implementation of a parallel programming environment called Distributed Shared Array (DSA), which provides a shared global array abstract across different machines connected by a network. In DSA, users can define and use global arrays that can be accessed uniformly from any machines in the network. Explicit management of array area allocation, replication, and migration is achieved by explicit calls for array manipulation: defining array regions, reading and writing array regions, synchronization, and control of replication and migration. The DSA is integrated with Grid (Globus) services. This paper also describes the use of our model for gene cluster analysis, multiple alignment and molecular dynamics simulation. In these applications, global arrays are used for storing the distance matrix, alignment matrix and atom coordinates, respectively. Large array areas, which cannot be stored in the memory of individual machines, are made available by the DSA. Scalable performance of DSA was obtained compared to that of conventional parallel programs written in MPI.     

Kinetics of rapid RNA evolution in vitro

Summary A rapidly acquired partial resistance to the replicase antagonist, ethidium bromide (EB), seen by Spiegelman and coresearchers in Q RNA variants competitively replicating under defined conditions in vitro, reflected existence of a pool of mutant RNA molecules, preadapted to EB, and their cross-propagation from the pre-EB optimum species, MDV-1, and from other kindred variants, some of which remained undetected, according to this quantitative analysis of midivariant RNA replication kinetics. DNAlike features of their evolution, such as the cloning of variants from an MDV-1 subtype and a complicance with the fundamental theorem of natural selection, resulted from the suppression, both real and apparent, of intrinsic RNA heterogeneity through sampling and detection methods, and also by the ascendency of self-propagation over cross-propagation with advancement of a superior variant. The deficit in mean polymer fitness, compared with optimum levels, determines the lower limit of this heterogeneity. Stability conditions for frequency equilibrium and strategies for counteracting viral drug resistance have been considered.