Information encoded in gene-frequency trajectories.

In this work we present a systematic mathematical approximation scheme that exposes the way that information, about the evolutionary forces of selection and random genetic drift, is encoded within gene-frequency trajectories. We determine approximate, time-dependent, gene-frequency trajectory statistics, assuming additive selection. We use the probability of fixation to test and illustrate the approximation scheme introduced. For the case where the strength of selection and the effective population size have constant values, we show how a standard diffusion approximation result, for the probability of fixation, systematically emerges when increasing numbers of approximate trajectory statistics are taken into account. We then provide examples of how time-dependent parameters influence gene-frequency statistics.

Loss and fixation of strongly favoured new variants: Understanding and extending Haldane's result via the Wright-Fisher model.

The implications of Haldane's analysis for the fixation of beneficial alleles lies at the heart of much of 'population genetic thinking' and underlies many approaches that have been tailored to the detection of positive selection. Within the framework of a branching process, Haldane gave an approximation for the probability that fixation ultimately occurs when the selective advantage of a beneficial allele is small (≪1). Here, we make no use of branching processes. Rather, we work solely within a finite-population Wright-Fisher framework. We use this framework to analyse where Haldane's result applies, and extend Haldane's analysis. In particular, we present results for: (i) the domain of applicability of Haldane's analysis; (ii) the probability that loss occurs up to a given time; (iii) the probabilities that loss and fixation ultimately occur; (iv) an analytic approximation associated with the probability of loss and fixation ultimately occurring; (v) quantification of the crossover from weak to strong selection; (vi) determination of the number of invasive alleles that have a significant probability (>0.95) of invading a novel population. We note that the results obtained for (ii), (iii) and (iv) hold for an arbitrary initial number of mutations, and for selection that can be arbitrarily strong. Our results have fundamental implications for population and conservation genetics, and open up new avenues to identify traces of historically beneficial alleles through comparative genomics.

Lethal mutations with fluctuating heterozygous effect: the lethal force of effective dominance.

The theory of population genetics leads to the expectation that in very large populations the frequencies of recessive lethal mutations are close to the square root of the mutation rate, corresponding to mutation-selection balance. There are numerous examples where the frequencies of such alleles are orders of magnitude larger than this result. In this work we theoretically investigate the role of temporal fluctuations in the heterozygous effect (h) for lethal mutations in very large populations. For fluctuations of h, around a mean value of [Formula: see text], we find a biased outcome that is described by an effective dominance coefficient, heff, that is generally less than the mean dominance coefficient, i.e., [Formula: see text]. In the case where the mean dominance coefficient is zero, the effective dominance coefficient is negative: heff < 0, corresponding to the lethal allele behaving as though overdominant and having an elevated mean frequency. This case plausibly explains mean allele frequencies that are an order of magnitude larger than the equilibrium frequency of a recessive allele with a constant dominance coefficient. Our analysis may be relevant to explaining lethal disorders with anomalously high frequencies, such as cystic fibrosis and Tay-Sachs, and may open the door to further investigations into the statistics of fluctuations of the heterozygous effect.

Safe prognostication following cardiac arrest: The role of the pharmacokinetics of fentanyl in patients treated with targeted temperature management.

BACKGROUND: Neurological prognostication following cardiac arrest (CA) is complex and sedative agents may significantly impair responses to clinical examination. This study investigates the elimination of fentanyl in patients treated with targeted temperature management (TTM). METHODS: We measured the blood concentration of fentanyl in 23 post-cardiac arrest patients treated with TTM following discontinuation of continuous infusion. Fentanyl was discontinued when the patients were rewarmed to a temperature of 36-36.5 °C and a blood sample taken 12 h later. Measured concentrations were compared with predicted concentrations using population pharmacokinetic parameters. Variables likely to prolong half-life were analysed using a multivariate regression model. RESULTS: We found a statistically significant difference between median measured and predicted concentrations (measured 0.93 µg/L [range 0.11-8.29 µg/L] vs. predicted 0.30 µg/L [range 0.16-0.59 µg/L]; p < 0.05). Univariate analysis identified a significant relationship between estimated fentanyl half-life and serum lactate concentrations (r = 0.45, p < 0.05). Multivariate linear regression identified two variables (SAPS score and genotype), which together were able to explain approximately 30 % of the variation in the population (adjusted R2 = 0.3177, p = 0.0194). No significant relationships were found between fentanyl half-life and patients' clinical or biochemical variables or co-administration of drugs metabolized by cytochrome p450. CONCLUSIONS: There is marked variation in the clearance of fentanyl following continuous infusion during TTM after CA which correlates with illness severity, lactate concentration and genetic polymorphisms of the cytochrome p450 liver enzymes. Sustained presence of fentanyl may influence response to neurological examination at 12 h post discontinuation in patients receiving the drug as an infusion as part of TTM.

The increase of the functional entropy of the human brain with age.

We use entropy to characterize intrinsic ageing properties of the human brain. Analysis of fMRI data from a large dataset of individuals, using resting state BOLD signals, demonstrated that a functional entropy associated with brain activity increases with age. During an average lifespan, the entropy, which was calculated from a population of individuals, increased by approximately 0.1 bits, due to correlations in BOLD activity becoming more widely distributed. We attribute this to the number of excitatory neurons and the excitatory conductance decreasing with age. Incorporating these properties into a computational model leads to quantitatively similar results to the fMRI data. Our dataset involved males and females and we found significant differences between them. The entropy of males at birth was lower than that of females. However, the entropies of the two sexes increase at different rates, and intersect at approximately 50 years; after this age, males have a larger entropy.

Population growth enhances the mean fixation time of neutral mutations and the persistence of neutral variation.

A fundamental result of population genetics states that a new mutation, at an unlinked neutral locus in a randomly mating diploid population, has a mean time of fixation of ∼4N(e) generations, where N(e) is the effective population size. This result is based on an assumption of fixed population size, which does not universally hold in natural populations. Here, we analyze such neutral fixations in populations of changing size within the framework of the diffusion approximation. General expressions are derived for the mean and variance of the fixation time in changing populations. Some explicit results are given for two cases: (i) the effective population size undergoes a sudden change, representing a sudden population expansion or a sudden bottleneck; (ii) the effective population changes linearly for a limited period of time and then remains constant. Additionally, a lower bound for the mean time of fixation is obtained for an effective population size that increases with time, and this is applied to exponentially growing populations. The results obtained in this work show, among other things, that for populations that increase in size, the mean time of fixation can be enhanced, sometimes substantially so, over 4N(e,0) generations, where N(e,0) is the effective population size at the time the mutation arises. Such an enhancement is associated with (i) an increased probability of neutral polymorphism in a population and (ii) an enhanced persistence of high-frequency neutral variation, which is the variation most likely to be observed.

A unified treatment of the probability of fixation when population size and the strength of selection change over time.

The fixation probability is determined when population size and selection change over time and differs from Kimura's result, with long-term implications for a population. It is found that changes in population size are not equivalent to the corresponding changes in selection and can result in less drift than anticipated.

Testing the level of ant activity associated with quorum sensing: an empirical approach leading to the establishment and test of a null-model (response to the comment of Richardson et al.).

In a paper in this journal (Nouvellet et al., 2010), we presented results from experiments on the behaviour of the Pharaoh's ant, Monomorium pharaonis, along with a substantial statistical and theoretical analysis of the results. In a minor part of our paper, we compared our results with the related work of Richardson et al. (2010a). These authors have subsequently commented on our interpretation of their work (Richardson et al., 2011). In this Letter we respond to the comments of Richardson et al. (2011), and give detailed arguments why we stand by our original conclusions.

A compact result for the time-dependent probability of fixation at a neutral locus.

A result is derived, in the form of a sum, for the time-dependent probability of fixation of an unlinked neutral locus. The result captures many of the key features of the probability of fixation in a highly compact form. For 'small' times (t ≲ 4N(e)) a single term of the sum accurately determines the time-dependent probability of fixation. This is in contrast to the well-known result of Kimura, which requires the contribution of many terms in a different sum, for 'small' times. Going beyond small times, an approximation is derived for the time-dependent probability of fixation which applies for all times when the initial relative allele frequency is small.

Dual E1A oncolytic adenovirus: targeting tumor heterogeneity with two independent cancer-specific promoter elements, DF3/MUC1 and hTERT.

The therapeutic utility of oncolytic adenoviruses controlled by a single, tumor-specific regulatory element may be limited by the intra- and inter-tumoral heterogeneity that characterizes many cancers. To address this issue, we constructed an oncolytic adenovirus that uses two distinct tumor-specific promoters (DF3/Muc1 and hTERT) to drive separate E1A expression cassettes, in combination with deletion of the viral E1B region, which confers additional tumor selectivity and increased oncolytic activity. The resultant virus, Adeno-DF3-E1A/hTERT-E1A, induced higher levels of E1A oncoprotein, enhanced oncolysis and an earlier and higher apoptotic index in infected tumor cells than following infection with Adeno-hTERT-E1A, which harbors a single hTERT promoter-driven E1A cassette. In isolated U251 human gliosarcoma cell holoclones (putative cancer stem cells), where DF3/Muc1 expression is substantially enriched and hTERT expression is decreased compared with the parental U251 cell population, E1A production and oncolysis were strongly decreased following infection with Adeno-hTERT-E1A, but not Adeno-DF3-E1A/hTERT-E1A. The strong oncolytic activity of Adeno-DF3-E1A/hTERT-E1A translated into superior anti-tumor activity over Adeno-hTERT-E1A in vivo in a U251 solid tumor xenograft model, where hTERT levels were >90% suppressed and the DF3/Muc1 to hTERT expression ratio was substantially increased compared with cultured U251 cells. The enhanced anti-tumor activity of the dual-targeted Adeno-DF3-E1A/hTERT-E1A was achieved despite premature viral host cell death and decreased production of functional viral progeny, which limited tumor cell spread of the viral infection. These findings highlight the therapeutic benefit of targeting oncolytic viruses to heterogeneous tumor cell populations.

Comparison and content of the Wright-Fisher model of random genetic drift, the diffusion approximation, and an intermediate model.

We investigate the detailed connection between the Wright-Fisher model of random genetic drift and the diffusion approximation, under the assumption that selection and drift are weak and so cause small changes over a single generation. A representation of the mathematics underlying the Wright-Fisher model is introduced which allows the connection to be made with the corresponding mathematics underlying the diffusion approximation. Two 'hybrid' models are also introduced which lie 'between' the Wright-Fisher model and the diffusion approximation. In model 1 the relative allele frequency takes discrete values while time is continuous; in model 2 time is discrete and relative allele frequency is continuous. While both hybrid models appear to have a similar status and the same level of plausibility, the different nature of time and frequency in the two models leads to significant mathematical differences. Model 2 is mathematically inconsistent and has to be ruled out as being meaningful. Model 1 is used to clarify the content of Kimura's solution of the diffusion equation, which is shown to have the natural interpretation as describing only those populations where alleles are segregating. By contrast the Wright-Fisher model and the solution of the diffusion equation of McKane and Waxman cover populations of all categories, namely populations where alleles segregate, are lost, or fix.

Child health, developmental plasticity, and epigenetic programming.

Plasticity in developmental programming has evolved in order to provide the best chances of survival and reproductive success to the organism under changing environments. Environmental conditions that are experienced in early life can profoundly influence human biology and long-term health. Developmental origins of health and disease and life-history transitions are purported to use placental, nutritional, and endocrine cues for setting long-term biological, mental, and behavioral strategies in response to local ecological and/or social conditions. The window of developmental plasticity extends from preconception to early childhood and involves epigenetic responses to environmental changes, which exert their effects during life-history phase transitions. These epigenetic responses influence development, cell- and tissue-specific gene expression, and sexual dimorphism, and, in exceptional cases, could be transmitted transgenerationally. Translational epigenetic research in child health is a reiterative process that ranges from research in the basic sciences, preclinical research, and pediatric clinical research. Identifying the epigenetic consequences of fetal programming creates potential applications in clinical practice: the development of epigenetic biomarkers for early diagnosis of disease, the ability to identify susceptible individuals at risk for adult diseases, and the development of novel preventive and curative measures that are based on diet and/or novel epigenetic drugs.

Testing the level of ant activity associated with quorum sensing: An empirical approach leading to the establishment and test of a null-model.

On the basis of experimental observations, this paper develops two well-defined mathematical models for the level of activity of Pharaoh's ants within their nesting area, with the aim of providing a more general understanding of animal activity. Under specific conditions, we observe that the activity of ants within their nesting area appears to show no dependence on their density. Making the assumption that all ants move independently of one another, this behaviour can be mathematically modelled as a random process based on the binomial distribution. Developing the model on this basis allows an exponential distribution to be exposed that underlies the time-intervals between ants leaving the nesting area. Such a distribution is present, irrespective of whether the ant population in the nesting area remains constant or steadily depletes, and suggests that ant-ant interactions do not play any significant role in determining ant activity under the experimental conditions adopted. The mathematical framework presented plays the role of a null model that will have a wide range of applications for detecting other determinants of activity-level (not addressed in this study) including environmental and social factors such as food availability, temperature, humidity, presence of pheromone trails, along with intraspecific and interspecific interactions outside the nest and, indeed, more generally. The null model should have applications to a range of organisms. Lastly, we discuss our data in relation to a recent study of ants leaving their nest (Richardson et al., 2010) in which the null model was rejected in favour of record dynamics, where ant-ant interactions were conjectured to play a role.

A stochastic model for a single click of Muller's ratchet.

This work presents a new approach to Muller's ratchet, where Haigh's model is approximately mapped into a simpler model that describes the behaviour of a population after a click of the ratchet, i.e., after loss of what was the fittest class. This new model predicts the distribution of times to the next click of the ratchet and is equivalent to a Wright-Fisher model for a population of haploid asexual individuals with one locus and two alleles. Within this model, the fittest members of a population correspond to carriers of one allele, while all other individuals have suboptimal fitness and are represented as carriers of the other allele. In this way, all suboptimal fitness individuals are amalgamated into a single "mutant" class. The approach presented here has some limitations and the potential for improvement. However, it does lead to results for the rate of the ratchet that, over a wide range of parameters, are accurate within one order of magnitude of simulation results. This contrasts with existing approaches, which are designed for only one or other of the two different parameter regimes known for the ratchet and are more accurate only in the parameter regime they were designed for. Numerical results are presented for the mean time between clicks of the ratchet for (i) the Wright-Fisher model, (ii) a diffusion approximation of this model and (iii) individually based simulations of a full model. The diffusion approximation is validated over a wide range of parameters by its close agreement with the Wright-Fisher model. The present work predicts that: (a) the time between clicks of the ratchet is insensitive to the value of the selection coefficient when the genomic mutation rate is large compared with the selection coefficient against a deleterious mutation, (b) the time interval between clicks of the ratchet has, approximately, an exponential distribution (or its discrete analogue). It is thus possible to determine the variance in times between clicks, given the expected time between clicks. Evidence for both (a) and (b) is seen in simulations.

Scaling and fractal behaviour underlying meiotic recombination.

In this paper we investigate some of the mathematical properties of meiotic recombination. Working within the framework of a genetic model with n loci, where alpha alleles are possible at each locus, we find that the proportion of all possible diploid parental genotypes that can produce a particular haploid gamete is exp[-n log(alpha(2)/[2alpha-1])]. We show that this proportion connects recombination with a fractal geometry of dimension log(2alpha-1)/log(alpha). The fractal dimension of a geometric object manifests itself when it is measured at increasingly smaller length scales. Decreasing the length scale of a geometric object is found to be directly analogous, in a genetics problem, to specifying a multilocus haplotype at a larger number of loci, and it is here that the fractal dimension reveals itself.

Fundamental insights into the random movement of animals from a single distance-related statistic.

Statistical theories of animal movement have often been based on models of random walks, where movements take place in discrete steps and occur at discrete times. The multiplicity of distributions required in these approaches to describe animal movement (i.e., the distributions of angles, discrete steps, and times) have effects that cannot be simply disentangled, and hence they cannot be unambiguously determined. Here we present a mathematical formulation of continuous animal movements. In this new framework, it is shown that a single time-dependent distance statistic, the mean square displacement, which may be directly measured or mathematically modeled, is a central determinant of such random walks and encapsulates key information about the statistical properties of animal movements. The model and methodology presented here not only allow the determination of what were previously viewed as independent aspects of animal movements, such as the distribution of angular changes in direction, but also, because of the new emphasis on the mean square displacement, they may open up a new set of questions concerning animal movement and related phenomena. The results established in this work are directly applied to the foraging behavior of Pharaoh's ants, and very close agreement is found between observation and theory.

Overexpression of an activated REL mutant enhances the transformed state of the human B-lymphoma BJAB cell line and alters its gene expression profile.

The human REL proto-oncogene encodes a transcription factor in the nuclear factor (NF)-kappaB family. Overexpression of REL is acutely transforming in chicken lymphoid cells, but has not been shown to transform any mammalian lymphoid cell type. In this report, we show that overexpression of a highly transforming mutant of REL (RELDeltaTAD1) increases the oncogenic properties of the human B-cell lymphoma BJAB cell line, as shown by increased colony formation in soft agar, tumor formation in SCID (severe combined immunodeficient) mice, and adhesion. BJAB-RELDeltaTAD1 cells also show decreased activation of caspase in response to doxorubicin. BJAB-RELDeltaTAD1 cells have increased levels of active nuclear REL protein as determined by immunofluorescence, subcellular fractionation and electrophoretic mobility shift assay. Overexpression of RELDeltaTAD1 in BJAB cells has transformed the gene expression profile of BJAB cells from that of a germinal center B-cell subtype of diffuse large B-cell lymphoma (DLBCL) (GCB-DLBCL) to that of an activated B-cell subtype (ABC-DLBCL), as evidenced by increased expression of many ABC-defining mRNAs. Upregulated genes in BJAB-RELDeltaTAD1 cells include several NF-kappaB targets that encode proteins previously implicated in B-cell development or oncogenesis, including BCL2, IRF4, CD40 and VCAM1. The cell system we describe here may be valuable for further characterizing the molecular details of REL-induced lymphoma in humans.

Fixation at a locus with multiple alleles: Structure and solution of the Wright Fisher model.

We consider the Wright Fisher model for a finite population of diploid sexual organisms where selection acts at a locus with multiple alleles. The mathematical description of a such a model requires vectors and matrices of a multidimensional nature, and hence has a considerable level of complexity. In the present work we avoid this complexity by introducing a simple mathematical transformation. This yields a description of the model in terms of ordinary vectors and ordinary matrices, thereby allowing standard linear algebra techniques to be directly employed. The new description yields a common mathematical representation of the Wright Fisher model that applies for arbitrary numbers of alleles. Within this framework, it is shown how the dynamics decomposes into component parts that are responsible for the different possible transitions of segregating and fixed populations, thereby allowing a clearer understanding of the population dynamics. This decomposition allows expressions to be directly derived for the mean time of fixation, the mean time of segregation (i.e., the sojourn time) and the probability of fixation. Numerical methods are discussed for the evaluation of these quantities.

Potentiation of methoxymorpholinyl doxorubicin antitumor activity by P450 3A4 gene transfer.

Preclinical and clinical studies of CYP gene-directed enzyme prodrug therapy have been focused on anticancer prodrugs activated by CYP2B enzymes, which have low endogenous expression in human liver; however, the gene therapeutic potential of CYP3A enzymes, which are highly expressed in human liver, remains unknown. This study investigated methoxymorpholinyl doxorubicin (MMDX; nemorubicin), a novel CYP3A-activated anticancer prodrug. Retroviral transfer of CYP3A4 increased 9L gliosarcoma cell chemosensitivity to MMDX 120-fold (IC(50)=0.2 nM in 9L/3A4 cells). In CHO cells, overexpression of P450 reductase in combination with CYP3A4 enhanced chemosensitivity to MMDX, and to ifosfamide, another CYP3A4 prodrug, 11- to 23-fold compared with CYP3A4 expression alone. CYP3A4 expression and MMDX chemosensitivity were increased in human lung (A549) and brain (U251) tumor cells infected with replication-defective adenovirus encoding CYP3A4. Coinfection with Onyx-017, a replication-conditional adenovirus that coamplifies and coreplicates the Adeno-3A4 virus, led to large increases in CYP3A4 RNA but only modest increases in CYP3A4 protein and activity. MMDX induced remarkable growth delay of 9L/3A4 tumors, but not the P450-deficient parental 9L tumors, in immunodeficient mice administered low-dose MMDX either intravenous or by direct intratumoral (i.t.) injection (60 microg kg(-1), every 7 days x 3). Notably, the i.t. route was substantially less toxic to the mouse host. No antitumor activity was observed with intraperitoneal MMDX treatment, suggesting a substantial hepatic first pass effect, with activated MMDX metabolites formed in the liver having poor access to the tumor site. These studies demonstrate that human CYP3A4 has strong potential for MMDX prodrug-activation therapy and suggest that endogenous tumor cell expression of CYP3A4, and not hepatic CYP3A4 activity, is a key determinant of responsiveness to MMDX therapy in cancer patients in vivo.

Adaptation to slow environmental change, with apparent anticipation of selection.

We investigate a genetic model of a large population of sexual organisms in a changing environment. The organisms are subject to stabilising selection on a quantitative trait, with environmental change causing the fitness optimum to move. When the fitness optimum moves slowly, adaptation to the changing environment occurs by means of reasonably well-separated substitutions at the loci controlling the trait. In this way, the trait generally tracks the moving optimum, but in such a case, the population may exhibit periods of time where the mean trait value overshoots the moving optimal trait value, thereby exhibiting an apparent anticipation of selection. The mechanism underlying this phenomenon is determined from consideration of a simpler model that correctly captures the observed dynamical behaviour. We note that very slow rates of changes of traits are seen in the fossil record and the present work may be relevant to this topic.