An asymptotic maximum principle for essentially linear evolution models

Recent work on mutation-selection models has revealed that, under specific assumptions on the fitness function and the mutation rates, asymptotic estimates for the leading eigenvalue of the mutation-reproduction matrix may be obtained through a low-dimensional maximum principle in the limit N-->infinity (where N, or N(d) with d> or =1, is proportional to the number of types). In order to extend this variational principle to a larger class of models, we consider here a family of reversible matrices of asymptotic dimension N(d) and identify conditions under which the high-dimensional Rayleigh-Ritz variational problem may be reduced to a low-dimensional one that yields the leading eigenvalue up to an error term of order 1/N. For a large class of mutation-selection models, this implies estimates for the mean fitness, as well as a concentration result for the ancestral distribution of types.     

A quasispecies approach to the evolution of sexual replication in unicellular organisms

This study develops a simplified model describing the evolutionary dynamics of a population composed of obligate sexually and asexually reproducing, unicellular organisms. The model assumes that the organisms have diploid genomes consisting of two chromosomes, and that the sexual organisms replicate by first dividing into haploid intermediates, which then combine with other haploids, followed by the normal mitotic division of the resulting diploid into two new daughter cells. We assume that the fitness landscape of the diploids is analogous to the single-fitness-peak approach often used in single-chromosome studies. That is, we assume a master chromosome that becomes defective with just one point mutation. The diploid fitness then depends on whether the genome has zero, one, or two copies of the master chromosome. We also assume that only pairs of haploids with a master chromosome are capable of combining so as to produce sexual diploid cells, and that this process is described by second-order kinetics. We find that, in a range of intermediate values of the replication fidelity, sexually reproducing cells can outcompete asexual ones, provided the initial abundance of sexual cells is above some threshold value. The range of values where sexual reproduction outcompetes asexual reproduction increases with decreasing replication rate and increasing population density. We critically evaluate a common approach, based on a group selection perspective, used to study the competition between populations and show its flaws in addressing the evolution of sex problem.     

On the evolution of epistasis III: the haploid case with mutation

Whether interaction between genes is better represented by synergistic or antagonistic epistasis has been a focus of experimental research in bacterial population genetics. Our previous research on evolution of modifiers of epistasis in diploid systems has indicated that the strength of positive or negative epistasis should increase provided linkage disequilibrium is maintained. Here we study a modifier of epistasis in fitness between two loci in a haploid system. Epistasis is modified in the neighborhood of a mutation-selection balance. We show that when linkage in the three-locus system is tight, an increase in the frequency of a modifier allele that induces either more negative or more positive epistasis is possible. Epistasis here can be measured on either an additive or multiplicative scale.     

A quasispecies approach to viral evolution in the context of an adaptive immune system

A deeper understanding of the mechanisms that determine viral evolution in the context of an adaptive immune system is vital for the development of efficient strategies to defeat viral infections. The problem of describing these mechanisms is discussed using the concept of quasispecies. Conditions for both an optimal immune response and for highest viral viability are derived from theoretical models and are supported by empirical data.     

Maintenance of polygenic variation through mutation-selection balance: bifurcation analysis of a biallelic model

Biallelic models which ignore linkage disequilibrium have been used to study variability maintained by mutation in the presence of Gaussian stabilizing selection. Recent work of Barton (1986) showed that these models have stable equilibria at which the mean phenotype differed from the optimum, and that the variability maintained at such equilibria would be higher than at the symmetric equilibria calculated by Bulmer (1980) and others. Here I determine the bifurcation structure of this model, and confirm and extend Barton's results. The form of the bifurcations gives information about the domains of attraction of various equilibria, and shows why the nonsymmetric equilibria may not be observed. The techniques may prove useful in the analysis of other population genetic models.     

Spectral properties of perselenosulfide

The riductive scission of a diselenide (selenocystamine) produced by disulfide gives the perselenosulfide, a new compound. Its formation kinetics, carried out a several pH values, were recorded spectrophotometrically at 375 nm. The lability of perselenosulfide bond by cianolysis has been demonstrated.     

Pattern generation in molecular evolution: Exploitation of the variation in RNA landscapes

Evolution of RNA secondary structure is studied using simulation techniques and statistical analysis of fitness landscapes. The transition from RNA sequence to RNA secondary structure leads to fitness landscapes that have local variations in their ruggedness. Evolution exploits these variations. In stable environments it moves the quasispecies toward relatively flat peaks, where not only the master sequence but also its mutants have a high fitness. In a rapidly changing environment, the situation is reversed; evolution moves the quasispecies to a region where the correlation between secondary structures of neighboring RNA sequences is relatively low. In selection for simple secondary structures the movement toward flat peaks leads to pattern generation in the RNA sequences. Patterns are generated at the level of polynucleotide frequencies and the distribution of purines and pyrimidines. The patterns increase the modularity of the sequence. They thereby prevent the formation of alternative secondary structures after mutations. The movement of the quasispecies toward relatively rugged parts of the landscape results in pattern generation at the level of the RNA secondary structure. The base-pairing frequency of the sequences increases. The patterns that are generated in the RNA sequences and the RNA secondary structures are not directly selected for and can be regarded as a side effect of the evolutionary dynamics of the system. Correspondence to: M.A. Huynen     

Asymptotic properties of infinite Leslie matrices

The stable population theory is classically applicable to populations in which there is a maximum age after which individuals die. Demetrius [1972. On an infinite population matrix. Math. Biosci. 13, 133-137] extended this theory to infinite Leslie matrices, in which the longevity of individuals is potentially infinite. However, Demetrius had to assume that the survival probability per time step tends to 0 with age. We generalise here the conditions of application of the stable population theory to infinite Leslie matrix models and apply these results to two examples, including or not senescence.     

Spectral tuning and evolution of primate short-wavelength-sensitive visual pigments

The peak sensitivities (λ(max)) of the short-wavelength-sensitive-1 (SWS1) pigments in mammals range from the ultraviolet (UV) (360-400 nm) to the violet (400-450 nm) regions of the spectrum. In most cases, a UV or violet peak is determined by the residue present at site 86, with Phe conferring UV sensitivity (UVS) and either Ser, Tyr or Val causing a shift to violet wavelengths. In primates, however, the tuning mechanism of violet-sensitive (VS) pigments would appear to differ. In this study, we examine the tuning mechanisms of prosimian SWS1 pigments. One species, the aye-aye, possesses a pigment with Phe86 but in vitro spectral analysis reveals a VS rather than a UVS pigment. Other residues (Cys, Ser and Val) at site 86 in prosimians also gave VS pigments. Substitution at site 86 is not, therefore, the primary mechanism for the tuning of VS pigments in primates, and phylogenetic analysis indicates that substitutions at site 86 have occurred at least five times in primate evolution. The sole potential tuning site that is conserved in all primate VS pigments is Pro93, which when substituted by Thr (as found in mammalian UVS pigments) in the aye-aye pigment shifted the peak absorbance into the UV region with a λ(max) value at 371 nm. We, therefore, conclude that the tuning of VS pigments in primates depends on Pro93, not Tyr86 as in other mammals. However, it remains uncertain whether the initial event that gave rise to the VS pigment in the ancestral primate was achieved by a Thr93Pro or a Phe86Tyr substitution.     

The evolution of payoff matrices: providing incentives to cooperate

Most of the work in evolutionary game theory starts with a model of a social situation that gives rise to a particular payoff matrix and analyses how behaviour evolves through natural selection. Here, we invert this approach and ask, given a model of how individuals behave, how the payoff matrix will evolve through natural selection. In particular, we ask whether a prisoner's dilemma game is stable against invasions by mutant genotypes that alter the payoffs. To answer this question, we develop a two-tiered framework with goal-oriented dynamics at the behavioural time scale and a diploid population genetic model at the evolutionary time scale. Our results are two-fold: first, we show that the prisoner's dilemma is subject to invasions by mutants that provide incentives for cooperation to their partners, and that the resulting game is a coordination game similar to the hawk-dove game. Second, we find that for a large class of mutants and symmetric games, a stable genetic polymorphism will exist in the locus determining the payoff matrix, resulting in a complex pattern of behavioural diversity in the population. Our results highlight the importance of considering the evolution of payoff matrices to understand the evolution of animal social systems.     

Analytical solution of the evolution dynamics on a multiplicative-fitness landscape

In an infinite population the frequency distribution of individuals carrying a given number of mutations obeys a set of recursion equations, the equilibrium solution of which describes the mutation-selection balance. Although this solution is well-known in the case of a multiplicative-fitness landscape, where it is assumed that all mutations are deleterious and that each new mutation reduces the fitness of the individual by the same fraction, we are not aware of the existence of an analytical solution for the full dynamics. Using the generating function approach, we present here an explicit analytical solution for the frequency distribution recursion equations valid for all generations and initial conditions.This research was supported by Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), Proj. No. 99/09644-9. The work of J.F.F. was supported in part by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq).     

Spectral properties of conformational motion in proteins

The conformational dynamics of large fragments of protein structure within the framework of a generalized model of bounded diffusion (GMBD) have been considered. This model is a development of the known ordinary model of bounded diffusion (MBD). The latter model assumes that the driving force of motion, which is at the same time a source of friction, has negligibly small correlation time (white noise). In contrast to the MBD, the GMBD takes into account the finite character of friction correlation time, i.e. memory friction effects. Two different mechanisms of friction for the fragment are considered: (1) friction by rapid density fluctuations due to the harmonic vibrational motion of atoms and (2) friction by slow encounters with surrounding fragments of protein structure. The present theory shows that at high frequencies the power decay of the spectrum which takes place in the MBD is replaced by an exponential one. In the narrow intermediate frequency range the results of the GMBD coincide with those of the MBD. At low frequencies the results of the two models differ quantitatively, though their qualitative behaviour is similar.     

Spectral and electrochemical properties of vanadyl hexadecafluorophthalocyanine

A vanadyl complex with perfluorinate phthalocyanine, VOPcF₁₆, was prepared. The monomer-dimer solvent dependence was confirmed based on the solvent effect for the Q-band position-that is, VOPcF₁₆ exists as a monomer in a nonpolar solvent such as benzene, but dimerizes in a polar solvent such as acetone. Electron spin resonance data also supported the solvent dependence found. In addition, the substituent effect of fluorine atoms on the redox properties was investigated by measuring the cyclic voltammograms in dichloromethane. On the reduction side, three redox couples were observed, the first two of which were assigned as being due to the reduction of the phthalocyanine ring (to LUMO), whose potentials are 0.4–0.5 V higher than those of the tetra-t-butyl and octabutoxy derivatives, VOPc(t-Bu)₄ and VOPc(O-n-Bu)₈.     

A stochastic model for the mutation-selection balance in an infinite asexual population with a genome of fixed size

A stochastic model is presented which describes the evolution of a genome of a haploid species in an infinite population. The genome is a finite set of elements. The elements are divided into different classes according to their effect on the fitness of the organism. Repeated mutations of the genome elements are permitted, in particular positive mutations are introduced. The distribution of the deleterious elements in the genome with respect to the impact on the fitness is given after the replication step. The steady state is fully described including the distribution and the fitness.     

Spectral properties of adrenaline in micellar environment

An absorption and fluorescence spectral and temporal studies on the solubilzation properties of adrenaline in micellar environment in sodium dodecyl sulfate (SDS) and in tetradodecyltrimethyl ammonium bromide (TTABr) has been carried out. Observed Stokes shifts have been correlated with polarity parameters which allowed an estimate of the dielectric constant of the adrenaline environment in SDS and TTABr micelles at 44 and 58, respectively. Experiments with methanol-water mixtures indicate that the hydrogen bonding formation with solvent and the hydrophilic nature of adrenaline influence its solubilization in micelles. Fluorescence and anisotropy decay analysis has shown that neutral adrenaline in SDS micelle is partitioned between aqueous phase (70%) and less polar, micellar phase (30%) and the interactions are limited to the Guy-Chapman layer without deeper penetration into micellar hydrophobic core.     

Spectral properties of cytochromes from Staphylococcus aureus

Two cytochrome b with peaks at 554 and 558 nm and cytochrome a with alpha-peak at 603 nm were found in intact cells and membranes of Staphylococcus aureus using low-temperature spectrophotometry and registration of second- and fourth-order finite difference spectra of cytochromes. Analysis of the cytochrome functioning in membranes isolated from the cells at the exponential and stationary growth phases revealed no difference in the set of these carriers. Analysis of cytochrome reduction with different substrates demonstrated identity of the cytochrome composition in the respiratory chain, reduced with NADH, lactate, alpha-glycerophosphate, malate and succinate. Cytochrome omicron with gamma-peak at 416 nm in the CO-spectra was found to be involved in oxidation of all the substrates tested both in intact cells and membranes of Staphylococcus aureus.