The effects of needle-sharing and opioid substitution therapy on incidence of hepatitis C virus infection and reinfection in people who inject drugs.

Although high hepatitis C virus (HCV) prevalence has been observed in people who inject drugs (PWID) for decades, research suggests incidence is falling. We examined whether PWIDs' use of opioid substitution therapy (OST) and their needle-and-syringe sharing behaviour explained HCV incidence. We assessed HCV incidence in 235 PWID in Melbourne, Australia, and performed discrete-time survival with needle-sharing and OST status as independent variables. HCV infection, reinfection and combined infection/reinfection incidences were 7·6 [95% confidence interval (CI) 4·8-11·9], 12·4 (95% CI 9·1-17·0) and 9·7 (95% CI 7·4-12·6) per 100 person-years, respectively. Needle-sharing was significantly associated with higher incidence of naive HCV infection [hazard ratio (HR) 4·9, 95% CI 1·3-17·7] but not reinfection (HR 1·85, 95% CI 0·79-4·32); however, a cross-model test suggested this difference was sample specific. Past month use of OST had non-significant protective effects against naive HCV infection and reinfection. Our data confirm previous evidence of greatly reduced HCV incidence in PWID, but not the significant protective effect of OST on HCV incidence detected in recent studies. Our findings reinforce the need for greater access to HCV testing and prevention services to accelerate the decline in incidence, and HCV treatment, management and support to limit reinfection.

Factors affecting the errors in the estimation of evolutionary distances between sequences.

Phylogenetic methods that use matrices of pairwise distances between sequences (e.g., neighbor joining) will only give accurate results when the initial estimates of the pairwise distances are accurate. For many different models of sequence evolution, analytical formulae are known that give estimates of the distance between two sequences as a function of the observed numbers of substitutions of various classes. These are often of a form that we call "log transform formulae". Errors in these distance estimates become larger as the time t since divergence of the two sequences increases. For long times, the log transform formulae can sometimes give divergent distance estimates when applied to finite sequences. We show that these errors become significant when t approximately 1/2 |lambda(max)|(-1) logN, where lambda(max) is the eigenvalue of the substitution rate matrix with the largest absolute value and N is the sequence length. Various likelihood-based methods have been proposed to estimate the values of parameters in rate matrices. If rate matrix parameters are known with reasonable accuracy, it is possible to use the maximum likelihood method to estimate evolutionary distances while keeping the rate parameters fixed. We show that errors in distances estimated in this way only become significant when t approximately 1/2 |lambda(1)|(-1) logN, where lambda(1) is the eigenvalue of the substitution rate matrix with the smallest nonzero absolute value. The accuracy of likelihood-based distance estimates is therefore much higher than those based on log transform formulae, particularly in cases where there is a large range of timescales involved in the rate matrix (e.g., when the ratio of transition to transversion rates is large). We discuss several practical ways of estimating the rate matrix parameters before distance calculation and hence of increasing the accuracy of distance estimates.

Bayesian phylogenetics using an RNA substitution model applied to early mammalian evolution.

We study the phylogeny of the placental mammals using molecular data from all mitochondrial tRNAs and rRNAs of 54 species. We use probabilistic substitution models specific to evolution in base paired regions of RNA. A number of these models have been implemented in a new phylogenetic inference software package for carrying out maximum likelihood and Bayesian phylogenetic inferences. We describe our Bayesian phylogenetic method which uses a Markov chain Monte Carlo algorithm to provide samples from the posterior distribution of tree topologies. Our results show support for four primary mammalian clades, in agreement with recent studies of much larger data sets mainly comprising nuclear DNA. We discuss some issues arising when using Bayesian techniques on RNA sequence data.

Limitation of Trypanosoma brucei parasitaemia results from density-dependent parasite differentiation and parasite killing by the host immune response.

In the bloodstream of its mammalian host, the "slender" form of Trypanosoma brucei replicates extracellularly, producing a parasitaemia. At high density, the level of parasitaemia is limited at a sublethal level by differentiation to the non-replicative "stumpy" form and by the host immune response. Here, we derive continuous time equations to model the time-course, cell types and level of trypanosome parasitaemia, and compare the best fits with experimental data. The best fits that were obtained favour a model in which both density-dependent trypanosome differentiation and host immune response have a role in limiting the increase of parasites, much poorer fits being obtained when differentiation and immune response are considered independently of one another. Best fits also favour a model in which the slender-to-stumpy differentiation progresses in a manner that is essentially independent of the cell cycle. Finally, these models also make the prediction that the density-dependent trypanosome differentiation mechanism can give rise to oscillations in parasitaemia level. These oscillations are independent of the immune system and are not due to antigenic variation.

The influence of predator--prey population dynamics on the long-term evolution of food web structure.

We develop a set of equations to describe the population dynamics of many interacting species in food webs. Predator-prey interactions are nonlinear, and are based on ratio-dependent functional responses. The equations account for competition for resources between members of the same species, and between members of different species. Predators divide their total hunting/foraging effort between the available prey species according to an evolutionarily stable strategy (ESS). The ESS foraging behaviour does not correspond to the predictions of optimal foraging theory. We use the population dynamics equations in simulations of the Webworld model of evolving ecosystems. New species are added to an existing food web due to speciation events, whilst species become extinct due to coevolution and competition. We study the dynamics of species-diversity in Webworld on a macro-evolutionary time-scale. Coevolutionary interactions are strong enough to cause continuous overturn of species, in contrast to our previous Webworld simulations with simpler population dynamics. Although there are significant fluctuations in species diversity because of speciation and extinction, very large-scale extinction avalanches appear to be absent from the dynamics, and we find no evidence for self-organized criticality.

RNA sequence evolution with secondary structure constraints: comparison of substitution rate models using maximum-likelihood methods.

We test models for the evolution of helical regions of RNA sequences, where the base pairing constraint leads to correlated compensatory substitutions occurring on either side of the pair. These models are of three types: 6-state models include only the four Watson-Crick pairs plus GU and UG; 7-state models include a single mismatch state that combines all of the 10 possible mismatches; 16-state models treat all mismatch states separately. We analyzed a set of eubacterial ribosomal RNA sequences with a well-established phylogenetic tree structure. For each model, the maximum-likelihood values of the parameters were obtained. The models were compared using the Akaike information criterion, the likelihood-ratio test, and Cox's test. With a high significance level, models that permit a nonzero rate of double substitutions performed better than those that assume zero double substitution rate. Some models assume symmetry between GC and CG, between AU and UA, and between GU and UG. Models that relaxed this symmetry assumption performed slightly better, but the tests did not all agree on the significance level. The most general time-reversible model significantly outperformed any of the simplifications. We consider the relative merits of all these models for molecular phylogenetics.

Dilution wave and negative-order crystallization kinetics of chain molecules.

We show that the crystal growth rate of a very long-chain n-alkane C C(198)H(398) from solution can decrease with increasing supersaturation and follow strongly negative order kinetics. The experimental behavior can be well represented by a theoretical model which allows the molecule to attach and detach as either extended or folded in two. The obstruction of extended-chain growth by unstable folded depositions increases disproportionately with increasing concentration. As a consequence of this abnormal kinetics, a "dilution wave" can propagate and trigger a folded-to-extended-chain transformation on its way.

Redundant and non-functional guide RNA genes in Trypanosoma brucei are a consequence of multiple genes per minicircle.

The mitochondrial mRNA of the parasitic protozoa Trypanosoma brucei is extensively edited by the insertion, and occasional deletion, of uridine residues. The editing is mediated by over 200 guide RNAs (gRNAs) that are encoded in circular DNA molecules called minicircles. There are some 250 different types of minicircle, called classes, with each encoding several gRNAs. Sequencing of gRNAs and minicircles has revealed a surprising amount of both redundancy, where gRNAs from different minicircle classes edit exactly the same part of an mRNA, and non-functionality, where partial or no complementarity is found between gRNA and mRNA. How does this redundancy and non-functionality arise and persist? We propose the following. Minicircle classes that contain several functional gRNA genes can be lost from the population via drift and replaced by more minicircle classes that contain fewer functional gRNA genes, on the condition that the cells keep a full complement of functional gRNAs. We demonstrate this hypothesis in a computer simulation of a model of minicircle evolution. We show that this process leads to an increasing number of minicircle classes and inevitably to only one functional gRNA per minicircle. Moreover, we show that the genome contains more minicircle classes than is actually necessary for cell survival. We also analyse the available minicircle sequence data and conclude that T. brucei is at a transient stage in this process. In addition, ten new putative gRNAs have been discovered.

The mimetic transition: a simulation study of the evolution of learning by imitation.

Culturally transmitted ideas or memes must have had a large effect on the survival and fecundity of early humans. Those with better techniques of obtaining food and making tools, clothing and shelters would have had a substantial advantage. It has been proposed that memes can explain why our species has an unusually large brain and high cognitive ability: the brain evolved because of selection for the ability to imitate. This article presents an evolutionary model of a population in which culturally transmitted memes can have both positive and negative effects on the fitness of individuals. It is found that genes for increased imitative ability are selectively favoured. The model predicts that imitative ability increases slowly until a mimetic transition occurs where memes become able to spread like an epidemic. At this point there is a dramatic increase in the imitative ability, the number of memes known per individual and the mean fitness of the population. Selection for increased imitative ability is able to overcome substantial selection against increased brain size in some cases.

A population genetics model for multiple quantitative traits exhibiting pleiotropy and epistasis.

We study a population genetics model of an organism with a genome of L(tot)loci that determine the values of T quantitative traits. Each trait is controlled by a subset of L loci assigned randomly from the genome. There is an optimum value for each trait, and stabilizing selection acts on the phenotype as a whole to maintain actual trait values close to their optima. The model contains pleiotropic effects (loci can affect more than one trait) and epistasis in fitness. We use adaptive walk simulations to find high-fitness genotypes and to study the way these genotypes are distributed in sequence space. We then simulate the evolution of haploid and diploid populations on these fitness landscapes and show that the genotypes of populations are able to drift through sequence space despite stabilizing selection on the phenotype. We study the way the rate of drift and the extent of the accessible region of sequence space is affected by mutation rate, selection strength, population size, recombination rate, and the parameters L and T that control the landscape shape. There are three regimes of the model. If LT<>L(tot), there are many small peaks that can be spread over a wide region of sequence space. Compensatory neutral mutations are important in the population dynamics in this case.

A theoretical study of random segregation of minicircles in trypanosomatids.

The kinetoplast (k) DNA network of trypanosomatids is made up of approximately 50 maxicircles and the order of 10(4) minicircles. It has been proposed, based on various observations and experiments, that the minicircles are randomly segregated between daughter cells when the parent cell divides. In this paper, this random segregation hypothesis is theoretically tested in a population dynamics model to see if it can account for the observed phenomena. The hypothesis is shown to successfully explain, in Leishmania tarentolae, the observation that there are a few major and many minor minicircle classes, the fluctuations of minicircle class copy numbers over time, the loss of non-essential minicircle classes, the long survival times of a few of these classes and that these classes are likely to be the major classes within the population. Implications of the model are examined for trypanosomatids in general, leading to several predictions. The model predicts variation in network size within a population, variation in the average network size and large-scale changes in class copy number over long time-scales, an evolutionary pressure towards larger network sizes, the selective advantage of non-random over random segregation, very strong selection for the amplified class in Crithidia fasciculata if its minicircles undergo random segregation and that Trypanosoma brucei may use sexual reproduction to maintain its viability.

Compensatory neutral mutations and the evolution of RNA.

There are many examples of RNA molecules in which the secondary structure has been strongly conserved during evolution, but the base sequence is much less conserved, e.g., transfer RNA, ribosomal RNA, and ribonuclease P. A model of compensatory neutral mutations is used here to describe the evolution of the base sequence in RNA helices. There are two loci (i.e., the two sides of the pair) with four alleles at each locus (corresponding to A, C, G, U). Watson-Crick base pairs (AU, CG, GC, and UA) are each assigned a fitness 1, whilst all other pairs are treated as mismatches and assigned fitness 1-s. A population of N diploid individuals is considered with a mutation rate of u per base. For biologically reasonable parameter values, the frequency of mismatches is always small but the frequency of the four matching pairs can vary over a wide range. Using a diffusion model, the stationary distribution for the frequency x of any of the four matching pairs is calculated. The shape depends on the combination of variables beta = 8Nu2/9s. For small beta, the distribution diverges at the two extremes, x = 0 and x = 1-z, where z is the mean frequency of mismatches. The population typically consists almost entirely of one of the four types of matching pairs, but occasionally makes shifts between the four possible states. The mean rate at which these shifts occur is calculated here. The effect of recombination between the two loci is to decrease the probability density at intermediate x, and to increase the weight at the extremes. The rate of transition between the four states is slowed by recombination (as originally shown by Kimura in a two-allele model with irreversible mutation). A very small recombination rate r approximately u2/s is sufficient to increase the mean time between transitions dramatically. In addition to its application to RNA, this model is also relevant to the 'shifting balance' theory describing the drift of populations between alternative equilibria separated by low fitness valleys. Equilibrium values for the frequencies of the different allele combinations in an infinite population are also calculated. It is shown that for low recombination rates the equilibrium is symmetric, but there is a critical recombination rate above which alternative asymmetric equilibria become stable.

Population evolution on a multiplicative single-peak fitness landscape.

A theory for evolution of either gene sequences or molecular sequences must take into account that a population consists of a finite number of individuals with related sequences. Such a population will not behave in the deterministic way expected for an infinite population, nor will it behave as in adaptive walk models, where the whole of the population is represented by a single sequence. Here we study a model for evolution of population in a fitness landscape with a single fitness peak. This landscape is simple enough for finite size population effects to be studied in detail. Each of the N individuals in the population is represented by a sequence of L genes which may either be advantageous or disadvantageous. The fitness of an individual with k disadvantageous genes is Wk = (1-s)k, where s determines the strength of selection. In the limit L-->infinity, the model reduces to the problem of Muller's Ratchet: the population moves away from the fitness peak at a constant rate due to the accumulation of disadvantageous mutations. For finite length sequences, a population placed initially at the fitness peak will evolve away from the peak until a balance is reached between mutation and selection. From then on the population will wander through a spherical shell in sequence space at a constant mean Hamming distance from the optimum sequence. We give an approximate theory for the way depends on N, L, s, and the mutation rate u. This is found to agree well with numerical simulation. Selection is less effective on small populations, so increases as N decreases. Our simulations also show that the mean overlap between gene sequences separated by a time of t generations is of the form Q(t) = Q infinity + (Q0-Q infinity)exp(-2ut), which means that the rate of evolution within the spherical shell is independent of the selection strength. We give a simplified model which can be solved exactly for which Q(t) has precisely this form. We then consider the limit L-->infinity keeping U = uL constant. We suppose that each mutation may be favourable with probability p, or unfavourable with probability 1-p. We show that for p less than a critical value pc, the population decreases in fitness for all values of U, whereas for pc < p < 1/2, the population increases in fitness for small U and decreases in fitness for large U. In this case there is an optimum non-zero value of U at which the fitness increases most rapidly, and natural selection will favour species with non-zero mutation rates.

Genetic distance and species formation in evolving populations.

We compare the behavior of the genetic distance between individuals in evolving populations for three stochastic models. In the first model reproduction is asexual and the distribution of genetic distances reflects the genealogical tree of the population. This distribution fluctuates greatly in time, even for very large populations. In the second model reproduction is sexual with random mating allowed between any pair of individuals. In this case, the population becomes homogeneous and the genetic distance between pairs of individuals has small fluctuations which vanish in the limit of an infinitely large population. In the third model reproduction is still sexual but instead of random mating, mating only occurs between individuals which are genetically similar to each other. In that case, the population splits spontaneously into species which are in reproductive isolation from one another and one observes a steady state with a continual appearance and extinction of species in the population. We discuss this model in relation to the biological theory of speciation and isolating mechanisms. We also point out similarities between these three models of evolving populations and the theory of disordered systems in physics.

Creep measurements on gelatin gels.

The present work describes creep measurements on a series of concentrations of gelatin gels well above the critical gel concentration C0, using a high precision constant stress rheometer. Results for the concentration dependence of compliance are close to those expected both from theory and from dynamic oscillatory measurements of gel modulus. The concentration dependence of viscosity follows an approximate power law behaviour, with eta proportional C1.1. This exponent is consistent with relaxation in the sol fraction, and in regions of dangling chain attached to the gel. At concentrations closer to C0 we predict that a higher power law regime will prevail.