Dysregulation of murine long noncoding single-cell transcriptome in nonalcoholic steatohepatitis and liver fibrosis.

LncRNAs comprise a heterogeneous class of RNA-encoding genes typified by low expression, nuclear enrichment, high tissue-specificity, and functional diversity, but the vast majority remain uncharacterized. Here, we assembled the mouse liver noncoding transcriptome from >2000 bulk RNA-seq samples and discovered 48,261 liver-expressed lncRNAs, a majority novel. Using these lncRNAs as a single-cell transcriptomic reference set, we elucidated lncRNA dysregulation in mouse models of high fat diet-induced nonalcoholic steatohepatitis and carbon tetrachloride-induced liver fibrosis. Trajectory inference analysis revealed lncRNA zonation patterns across the liver lobule in each major liver cell population. Perturbations in lncRNA expression and zonation were common in several disease-associated liver cell types, including nonalcoholic steatohepatitis-associated macrophages, a hallmark of fatty liver disease progression, and collagen-producing myofibroblasts, a central feature of liver fibrosis. Single-cell-based gene regulatory network analysis using bigSCale2 linked individual lncRNAs to specific biological pathways, and network-essential regulatory lncRNAs with disease-associated functions were identified by their high network centrality metrics. For a subset of these lncRNAs, promoter sequences of the network-defined lncRNA target genes were significantly enriched for lncRNA triplex formation, providing independent mechanistic support for the lncRNA-target gene linkages predicted by the gene regulatory networks. These findings elucidate liver lncRNA cell-type specificities, spatial zonation patterns, associated regulatory networks, and temporal patterns of dysregulation during hepatic disease progression. A subset of the liver disease-associated regulatory lncRNAs identified have human orthologs and are promising candidates for biomarkers and therapeutic targets.

MAnorm2 for quantitatively comparing groups of ChIP-seq samples.

Eukaryotic gene transcription is regulated by a large cohort of chromatin-associated proteins, and inferring their differential binding sites between cellular contexts requires a rigorous comparison of the corresponding ChIP-seq data. We present MAnorm2, a new computational tool for quantitatively comparing groups of ChIP-seq samples. MAnorm2 uses a hierarchical strategy for normalization of ChIP-seq data and assesses within-group variability of ChIP-seq signals based on an empirical Bayes framework. In this framework, MAnorm2 allows for abundant differential ChIP-seq signals between groups of samples as well as very different global within-group variability between groups. Using a number of real ChIP-seq data sets, we observed that MAnorm2 clearly outperformed existing tools for differential ChIP-seq analysis, especially when the groups of samples being compared had distinct global within-group variability.

Harnessing natural variation to identify cis regulators of sex-biased gene expression in a multi-strain mouse liver model.

Sex differences in gene expression are widespread in the liver, where many autosomal factors act in tandem with growth hormone signaling to regulate individual variability of sex differences in liver metabolism and disease. Here, we compare hepatic transcriptomic and epigenetic profiles of mouse strains C57BL/6J and CAST/EiJ, representing two subspecies separated by 0.5-1 million years of evolution, to elucidate the actions of genetic factors regulating liver sex differences. We identify 144 protein coding genes and 78 lncRNAs showing strain-conserved sex bias; many have gene ontologies relevant to liver function, are more highly liver-specific and show greater sex bias, and are more proximally regulated than genes whose sex bias is strain-dependent. The strain-conserved genes include key growth hormone-dependent transcriptional regulators of liver sex bias; however, three other transcription factors, Trim24, Tox, and Zfp809, lose their sex-biased expression in CAST/EiJ mouse liver. To elucidate the observed strain specificities in expression, we characterized the strain-dependence of sex-biased chromatin opening and enhancer marks at cis regulatory elements (CREs) within expression quantitative trait loci (eQTL) regulating liver sex-biased genes. Strikingly, 208 of 286 eQTLs with strain-specific, sex-differential effects on expression were associated with a complete gain, loss, or reversal of the sex differences in expression between strains. Moreover, 166 of the 286 eQTLs were linked to the strain-dependent gain or loss of localized sex-biased CREs. Remarkably, a subset of these CREs apparently lacked strain-specific genetic variants yet showed coordinated, strain-dependent sex-biased epigenetic regulation. Thus, we directly link hundreds of strain-specific genetic variants to the high variability in CRE activity and expression of sex-biased genes and uncover underlying genetically-determined epigenetic states controlling liver sex bias in genetically diverse mouse populations.

TCDD dysregulation of lncRNA expression, liver zonation and intercellular communication across the liver lobule.

The persistent environmental aryl hydrocarbon receptor agonist and hepatotoxin TCDD (2,3,7,8-tetrachlorodibenzo-p-dioxin) induces hepatic lipid accumulation (steatosis), inflammation (steatohepatitis) and fibrosis. Thousands of liver-expressed, nuclear-localized lncRNAs with regulatory potential have been identified; however, their roles in TCDD-induced hepatoxicity and liver disease are unknown. We analyzed single nucleus (sn)RNA-seq data from control and subchronic (4 wk) TCDD-exposed mouse liver to determine liver cell-type specificity, zonation and differential expression profiles for thousands of lncRNAs. TCDD dysregulated >4000 of these lncRNAs in one or more liver cell types, including 684 lncRNAs specifically dysregulated in liver non-parenchymal cells. Trajectory inference analysis revealed major disruption by TCDD of hepatocyte zonation, affecting >800 genes, including 121 lncRNAs, with strong enrichment for lipid metabolism genes. TCDD also dysregulated expression of >200 transcription factors, including 19 Nuclear Receptors, most notably in hepatocytes and Kupffer cells. TCDD-induced changes in cell-cell communication patterns included marked decreases in EGF signaling from hepatocytes to non-parenchymal cells and increases in extracellular matrix-receptor interactions central to liver fibrosis. Gene regulatory networks constructed from the snRNA-seq data identified TCDD-exposed liver network-essential lncRNA regulators linked to functions such as fatty acid metabolic process, peroxisome and xenobiotic metabolism. Networks were validated by the striking enrichments that predicted regulatory lncRNAs showed for specific biological pathways. These findings highlight the power of snRNA-seq to discover functional roles for many xenobiotic-responsive lncRNAs in both hepatocytes and liver non-parenchymal cells and to elucidate novel aspects of foreign chemical-induced hepatotoxicity and liver disease, including dysregulation of intercellular communication within the liver lobule.

Increased brain volume from higher cereal and lower coffee intake: shared genetic determinants and impacts on cognition and metabolism.

It is unclear how different diets may affect human brain development and if genetic and environmental factors play a part. We investigated diet effects in the UK Biobank data from 18,879 healthy adults and discovered anticorrelated brain-wide gray matter volume (GMV)-association patterns between coffee and cereal intake, coincidence with their anticorrelated genetic constructs. The Mendelian randomization approach further indicated a causal effect of higher coffee intake on reduced total GMV, which is likely through regulating the expression of genes responsible for synaptic development in the brain. The identified genetic factors may further affect people's lifestyle habits and body/blood fat levels through the mediation of cereal/coffee intake, and the brain-wide expression pattern of gene CPLX3, a dedicated marker of subplate neurons that regulate cortical development and plasticity, may underlie the shared GMV-association patterns among the coffee/cereal intake and cognitive functions. All the main findings were successfully replicated. Our findings thus revealed that high-cereal and low-coffee diets shared similar brain and genetic constructs, leading to long-term beneficial associations regarding cognitive, body mass index (BMI), and other metabolic measures. This study has important implications for public health, especially during the pandemic, given the poorer outcomes of COVID-19 patients with greater BMIs.

Sex-biased genetic programs in liver metabolism and liver fibrosis are controlled by EZH1 and EZH2.

Sex differences in the incidence and progression of many liver diseases, including liver fibrosis and hepatocellular carcinoma, are associated with sex-biased hepatic expression of hundreds of genes. This sexual dimorphism is largely determined by the sex-specific pattern of pituitary growth hormone secretion, which controls a transcriptional regulatory network operative in the context of sex-biased and growth hormone-regulated chromatin states. Histone H3K27-trimethylation yields a major sex-biased repressive chromatin mark deposited at many strongly female-biased genes in male mouse liver, but not at male-biased genes in female liver, and is catalyzed by polycomb repressive complex-2 through its homologous catalytic subunits, Ezh1 and Ezh2. Here, we used Ezh1-knockout mice with a hepatocyte-specific knockout of Ezh2 to investigate the sex bias of liver H3K27-trimethylation and its functional role in regulating sex-differences in the liver. Combined hepatic Ezh1/Ezh2 deficiency led to a significant loss of sex-biased gene expression, particularly in male liver, where many female-biased genes were increased in expression while male-biased genes showed decreased expression. The associated loss of H3K27me3 marks, and increases in the active enhancer marks H3K27ac and H3K4me1, were also more pronounced in male liver. Further, Ezh1/Ezh2 deficiency in male liver, and to a lesser extent in female liver, led to up regulation of many genes linked to liver fibrosis and liver cancer, which may contribute to the observed liver pathologies and the increased sensitivity of these mice to hepatotoxin exposure. Thus, Ezh1/Ezh2-catalyzed H3K27-trimethyation regulates sex-dependent genetic programs in liver metabolism and liver fibrosis through its sex-dependent effects on the epigenome, and may thereby determine the sex-bias in liver disease susceptibility.

Global analysis of expression, maturation and subcellular localization of mouse liver transcriptome identifies novel sex-biased and TCPOBOP-responsive long non-coding RNAs.

BACKGROUND: While nuclear transcription and RNA processing and localization are well established for protein coding genes (PCGs), these processes are poorly understood for long non-coding (lnc)RNAs. Here, we characterize global patterns of transcript expression, maturation and localization for mouse liver RNA, including more than 15,000 lncRNAs. PolyA-selected liver RNA was isolated and sequenced from four subcellular fractions (chromatin, nucleoplasm, total nucleus, and cytoplasm), and from the chromatin-bound fraction without polyA selection. RESULTS: Transcript processing, determined from normalized intronic to exonic sequence read density ratios, progressively increased for PCG transcripts in going from the chromatin-bound fraction to the nucleoplasm and then on to the cytoplasm. Transcript maturation was similar for lncRNAs in the chromatin fraction, but was significantly lower in the nucleoplasm and cytoplasm. LncRNA transcripts were 11-fold more likely to be significantly enriched in the nucleus than cytoplasm, and 100-fold more likely to be significantly chromatin-bound than nucleoplasmic. Sequencing chromatin-bound RNA greatly increased the sensitivity for detecting lowly expressed lncRNAs and enabled us to discover and localize hundreds of novel regulated liver lncRNAs, including lncRNAs showing sex-biased expression or responsiveness to TCPOBOP a xenobiotic agonist ligand of constitutive androstane receptor (Nr1i3). CONCLUSIONS: Integration of our findings with prior studies and lncRNA annotations identified candidate regulatory lncRNAs for a variety of hepatic functions based on gene co-localization within topologically associating domains or transcription divergent or antisense to PCGs associated with pathways linked to hepatic physiology and disease.

Improved estimates of mean pharmacokinetic parameters for increased accuracy in dosing and reduced risk to patients.

AIMS: Pharmacokinetic equations, which relate different parameters of a single individual, are often applied to reported mean parameter-values, with the aim of estimating the mean value of an unreported parameter. Due to population heterogeneity this approach generally leads to errors in their estimation. We provide details of this source of error. Our aim is to take into account the effects of population heterogeneity in commonly used pharmacokinetic models. This provides improved estimates and knowledge of the concentration of a drug in the plasma over time. METHODS: Inequalities and approximations for corrected mean estimates are derived. These results are then applied to published clinical-trial data to illustrate their accuracy in practical situations. RESULTS: By using mean values within the pharmacokinetic equations for a single individual, we show that estimates of mean parameter values, for a variety of dosing regimens, generally have errors. Using published clinical trial data, we show that such estimates can systematically deviate from the exact mean value by up to 19%. We provide analytical results, which amount to inequalities when there are systematic deviations from exact results, along with approximate results that improve the accuracy of estimates. CONCLUSIONS: Medical, pharmacy and nursing students should be educated about errors and inequalities that can arise when transforming reported mean values of pharmacokinetic parameters into the mean values of parameters that are required, but not reported. Using approximate results, that correct estimates of mean parameter values so that they more accurately reflect actual average values, may provide a practical solution.

Loss of growth hormone-mediated signal transducer and activator of transcription 5 (STAT5) signaling in mice results in insulin sensitivity with obesity.

Growth hormone (GH) has an important function as an insulin antagonist with elevated insulin sensitivity evident in humans and mice lacking a functional GH receptor (GHR). We sought the molecular basis for this sensitivity by utilizing a panel of mice possessing specific deletions of GHR signaling pathways. Metabolic clamps and glucose homeostasis tests were undertaken in these obese adult C57BL/6 male mice, which indicated impaired hepatic gluconeogenesis. Insulin sensitivity and glucose disappearance rate were enhanced in muscle and adipose of mice lacking the ability to activate the signal transducer and activator of transcription (STAT)5 via the GHR (Ghr-391-/-) as for GHR-null (GHR-/-) mice. These changes were associated with a striking inhibition of hepatic glucose output associated with altered glycogen metabolism and elevated hepatic glycogen content during unfed state. The enhanced hepatic insulin sensitivity was associated with increased insulin receptor ß and insulin receptor substrate 1 activation along with activated downstream protein kinase B signaling cascades. Although phosphoenolpyruvate carboxykinase (Pck)-1 expression was unchanged, its inhibitory acetylation was elevated because of decreased sirtuin-2 expression, thereby promoting loss of PCK1. Loss of STAT5 signaling to defined chromatin immunoprecipitation targets would further increase lipogenesis, supporting hepatosteatosis while lowering glucose output. Finally, up-regulation of IL-15 expression in muscle, with increased secretion of adiponectin and fibroblast growth factor 1 from adipose tissue, is expected to promote insulin sensitivity.-Chhabra, Y., Nelson, C. N., Plescher, M., Barclay, J. L., Smith, A. G., Andrikopoulos, S., Mangiafico, S., Waxman, D. J., Brooks, A. J., Waters, M. J. Loss of growth hormone-mediated signal transducer and activator of transcription 5 (STAT5) signaling in mice results in insulin sensitivity with obesity.

Sub- or supercritical transmissibilities in a finite disease outbreak: Symmetry in outbreak properties of a disease conditioned on extinction.

This work is concerned with the transmissibility of a disease, on observation of an outbreak of limited size. When such an outbreak occurs, an accurate estimate of the transmissibility of the responsible pathogen is essential for an appropriate response to future outbreaks. Transmissibility is usually characterised in terms of the reproduction number, R, which is the mean number of new cases of infection produced by a single infectious individual. A subcritical reproduction number (R < 1) guarantees that an outbreak will eventually die out of its own accord. By contrast, a supercritical reproduction number (R > 1) does not guarantee spread of the disease, since even with appreciable transmissibility, an outbreak may become extinct due to stochastic effects associated with a small number of infected individuals. Once the number of infectious individuals is conditioned on extinction, we show that an exact symmetry of the underlying theory ensures two distinct values of R, one larger than unity, the other smaller than unity, for which all outbreak properties are identical, with no signature of difference. Therefore a disease with a subcritical R, or its supercritical counterpart, when conditioned on extinction, have, for a given outbreak, identical individual likelihoods. In the full likelihood, this symmetry is lost, since the individual likelihood for a subcritical R is weighted by an extinction probability of unity, but the individual likelihood of a supercritical R is weighted by a sub-unity extinction probability. However, the inference can still benefit from the underlying symmetry, since it yields a mapping of all supercritical reproduction numbers onto the subcritical domain (R < 1), thereby speeding up evaluation of the likelihood profile. The symmetry holds in the standard situation, where the distribution of secondary cases is Poisson, as well as where this distribution has a negative binomial form and super-spreading can occur.

Effects of dynamical and structural modifications on synchronization.

Synchronization is a phenomenon of the collective behavior of coupled oscillators and involves the detailed interplay of the intrinsic frequencies of the oscillators, the underlying topological features of their interaction network, and external perturbations. In this work we investigate, in the strong coupling regime, the response of a system to external perturbations of its natural frequencies and network modifications. Our investigation relies on two performance measures (one for phases and the other for frequencies) and a spectral perturbation analysis. Given strongly localized perturbations in time, corresponding to the dominant eigenmode of the weighted Laplacian matrix of the network, we present a sufficient condition for the maximization of the system's stability, along with analytical results for the effects of structural perturbations on the system's response. A number of simulations are conducted to illustrate the theory presented.

Predicting drug-disease associations with heterogeneous network embedding.

The prediction of drug-disease associations holds great potential for precision medicine in the era of big data and is important for the identification of new indications for existing drugs. The associations between drugs and diseases can be regarded as a complex heterogeneous network with multiple types of nodes and links. In this paper, we propose a method, namely HED (Heterogeneous network Embedding for Drug-disease association), to predict potential associations between drugs and diseases based on a drug-disease heterogeneous network. Specifically, with the heterogeneous network constructed from known drug-disease associations, HED employs network embedding to characterize drug-disease associations and then trains a classifier to predict novel potential drug-disease associations. The results on two real datasets show that HED outperforms existing popular approaches. Furthermore, some of our predictions have been verified by evidence from literature. For instance, carvedilol, a drug that was originally used for heart failure, left ventricular dysfunction, and hypertension, is predicted to be useful for atrial fibrillation by HED, which is supported by clinical trials.

What is adaptation and how should it be measured?

Adaptation is a defining property of living systems. It occurs when organisms become better suited to their environment. The phenomena that people find most fascinating about biological systems are, in general, the result of adaptive processes. Examples include the mammalian central nervous system, the flight of birds and insects, photosynthesis, and the human hand. However, despite the centrality of adaptation for biology, there is no generally agreed quantitative way to describe the degree to which an organism is adapted. Here, we address this situation by proposing a quantitative measure of adaptation. We also present results of computer simulations which demonstrate that some changes in parameter values cause mean adaptedness and mean relative fitness to change in opposite directions. This indicates that adaptedness and relative fitness are distinct concepts. We suggest that the measure of adaptedness proposed in this work may help to resolve questions about 'units of selection' and 'major transitions in evolution'.

Exact results for the probability and stochastic dynamics of fixation in the Wright-Fisher model.

In this work we consider fixation of an allele in a population. Fixation is key to understanding the way long-term evolutionary change occurs at the gene and molecular levels. Two basic aspects of fixation are: (i) the chance it occurs and (ii) the way the gene frequency progresses to fixation. We present exact results for both aspects of fixation for the Wright-Fisher model. We give the exact fixation probability for some different schemes of frequency-dependent selection. We also give the corresponding exact stochastic difference equation that generates frequency trajectories which ultimately fix. Exactness of the results means selection need not be weak. There are possible applications of this work to data analysis, modelling, and tests of approximations. The methodology employed illustrates that knowledge of the fixation probability, for all initial frequencies, fully characterises the dynamics of the Wright-Fisher model. The stochastic equations for fixing trajectories allow insight into the way fixation occurs. They provide the alternative picture that fixation is driven by the injection of one carrier of the fixing allele into the population each generation. The stochastic equations allow explicit calculation of some properties of fixing trajectories and their efficient simulation. The results are illustrated and tested with simulations.

Evolutionary control: Targeted change of allele frequencies in natural populations using externally directed evolution.

Random processes in biology, in particular random genetic drift, often make it difficult to predict the fate of a particular mutation in a population. Using principles of theoretical population genetics, we present a form of biological control that ensures a focal allele's frequency, at a given locus, achieves a prescribed probability distribution at a given time. This control is in the form of an additional evolutionary force that acts on a population. We provide the mathematical framework that determines the additional force. Our analysis indicates that generally the additional force depends on the frequency of the focal allele, and it may also depend on the time. We argue that translating this additional force into an externally controlled process, which has the possibility of being implemented in a number of different ways corresponding to selection, migration, mutation, or a combination of these, may provide a flexible instrument for targeted change of traits of interest in natural populations. This framework may be applied, or used as an informed form of guidance, in a variety of different biological scenarios including: yield and pesticide optimisation in crop production, biofermentation, the local regulation of human-associated natural populations, such as parasitic animals, or bacterial communities in hospitals.

Metronomic cyclophosphamide activation of anti-tumor immunity: tumor model, mouse host, and drug schedule dependence of gene responses and their upstream regulators.

BACKGROUND: Cyclophosphamide (CPA) can activate immunogenic tumor cell death, which induces immune-based tumor ablation and long-term anti-tumor immunity in a syngeneic C57BL/6 (B6) mouse GL261 glioma model when CPA is given on a 6-day repeating metronomic schedule (CPA/6d). In contrast, we find that two other syngeneic B6 mouse tumors, LLC lung carcinoma and B16F10 melanoma, do not exhibit these drug-induced immune responses despite their intrinsic sensitivity to CPA cytotoxicity. METHODS: To elucidate underlying mechanisms, we investigated gene expression and molecular pathway changes associated with the disparate immune responsiveness of these tumors to CPA/6d treatment. RESULTS: Global transcriptome analysis indicated substantial elevation of basal GL261 immune infiltration and strong CPA/6d activation of GL261 immune stimulatory pathways and their upstream regulators, but without preferential depletion of negative immune regulators compared to LLC and B16F10 tumors. In LLC tumors, where CPA/6d treatment is shown to be anti-angiogenic, CPA/6d suppressed VEGFA target genes and down regulated cell adhesion and leukocyte transendothelial migration genes. In GL261 tumors implanted in adaptive immune-deficient scid mice, where CPA/6d-induced GL261 regression is incomplete and late tumor growth rebound can occur, T cell receptor signaling and certain cytokine-cytokine receptor responses seen in B6 mice were deficient. Extending the CPA treatment interval from 6 to 9 days (CPA/9d) - which results in a strong but transient natural killer cell response followed by early tumor growth rebound - induced fewer cytokines and increased expression of drug metabolism genes. CONCLUSIONS: These findings elucidate molecular response pathways activated by intermittent metronomic CPA treatment and identify deficiencies that characterize immune-unresponsive tumor models and drug schedules.

The influence of genetic drift on the formation and stability of polymorphisms arising from negative frequency-dependent selection.

We consider the simplest form of negative frequency-dependent selection in a biallelic haploid population, where the selection coefficient of a mutant allele is a linear function of the allele's frequency, and changes from positive to negative as the frequency is increased. In an effectively infinite population this behaviour leads to a stable polymorphism. We present a theoretical investigation of what occurs in a finite population, where a long-lived polymorphism may be formed, but which fluctuates and ultimately disappears due to random genetic drift. We model the dynamics as a branching process and explicitly take into account differences between the census population size and the effective population size, which play different roles in the dynamics. We characterise the behaviour of the population in terms of three distinct timescales associated with: (i) early loss of mutant alleles, (ii) achievement of the long-lived polymorphism, (iii) disappearance of the polymorphism. Timescales (i) and (iii) depend on the effective population size and are, as a consequence, affected by random genetic drift, while timescale (ii) depends primarily on the census size and is relatively insensitive to genetic drift. Analysis and simulations of the branching process clarify the different influences of the census and effective population sizes. One substantial quantitative difference, between populations where the effective and census population sizes coincide and where they differ, lies in the number of mutant alleles in the long-lived polymorphism. This number is approximately proportional to the census size. Thus assuming the census size equals a much smaller effective population size predicts a much smaller number of mutants in the long-lived polymorphism.

An informational transition in conditioned Markov chains: Applied to genetics and evolution.

In this work we assume that we have some knowledge about the state of a population at two known times, when the dynamics is governed by a Markov chain such as a Wright-Fisher model. Such knowledge could be obtained, for example, from observations made on ancient and contemporary DNA, or during laboratory experiments involving long term evolution. A natural assumption is that the behaviour of the population, between observations, is related to (or constrained by) what was actually observed. The present work shows that this assumption has limited validity. When the time interval between observations is larger than a characteristic value, which is a property of the population under consideration, there is a range of intermediate times where the behaviour of the population has reduced or no dependence on what was observed and an equilibrium-like distribution applies. Thus, for example, if the frequency of an allele is observed at two different times, then for a large enough time interval between observations, the population has reduced or no dependence on the two observed frequencies for a range of intermediate times. Given observations of a population at two times, we provide a general theoretical analysis of the behaviour of the population at all intermediate times, and determine an expression for the characteristic time interval, beyond which the observations do not constrain the population's behaviour over a range of intermediate times. The findings of this work relate to what can be meaningfully inferred about a population at intermediate times, given knowledge of terminal states.

A modified Wright-Fisher model that incorporates Ne: A variant of the standard model with increased biological realism and reduced computational complexity.

The Wright-Fisher model is an important model in evolutionary biology and population genetics. It has been applied in numerous analyses of finite populations with discrete generations. It is recognised that real populations can behave, in some key aspects, as though their size that is not the census size, N, but rather a smaller size, namely the effective population size, Ne. However, in the Wright-Fisher model, there is no distinction between the effective and census population sizes. Equivalently, we can say that in this model, Ne coincides with N. The Wright-Fisher model therefore lacks an important aspect of biological realism. Here, we present a method that allows Ne to be directly incorporated into the Wright-Fisher model. The modified model involves matrices whose size is determined by Ne. Thus apart from increased biological realism, the modified model also has reduced computational complexity, particularly so when Ne⪡N. For complex problems, it may be hard or impossible to numerically analyse the most commonly-used approximation of the Wright-Fisher model that incorporates Ne, namely the diffusion approximation. An alternative approach is simulation. However, the simulations need to be sufficiently detailed that they yield an effective size that is different to the census size. Simulations may also be time consuming and have attendant statistical errors. The method presented in this work may then be the only alternative to simulations, when Ne differs from N. We illustrate the straightforward application of the method to some problems involving allele fixation and the determination of the equilibrium site frequency spectrum. We then apply the method to the problem of fixation when three alleles are segregating in a population. This latter problem is significantly more complex than a two allele problem and since the diffusion equation cannot be numerically solved, the only other way Ne can be incorporated into the analysis is by simulation. We have achieved good accuracy in all cases considered. In summary, the present work extends the realism and tractability of an important model of evolutionary biology and population genetics.

Cognitive training can reduce the rate of cognitive aging: a neuroimaging cohort study.

BACKGROUND: The neural mechanisms underlying the restorative effects of cognitive training on aging brains remain unclear. To address this issue, we examined the relationship between changes in spontaneous brain activity and cognitive performance that occur after cognitive training. METHODS: Participants were older adults who were part of a randomized control trial within a larger longitudinal cognitive training study. We conducted single-domain and multi-domain cognitive training in two respective intervention groups. Participants were trained for 1 h, twice a week, for 12 weeks. Cognition was assessed in all participants and magnetic resonance images were obtained at baseline and 1 year after training. To assess spontaneous fluctuations in brain activity, we acquired resting-state fMRI data. Two indices-functional entropy and time-domain entropy-were used to measure the effects of training. Functional entropy increases with aging, and indicates disruptions in functional conectivity. Time-domain entropy decreases with aging, and indicates structural alterations in the brain and blood-flow reduction. RESULTS: Seventy participants completed the study: 26 in the multi-domain cognitive training group (70.38 ± 3.30 yrs), 27 in single-domain group (70.48 ± 3.93 yrs), and 17 in a control group (68.59 ± 3.24 yrs). Functional entropy increased significantly less in the multi-domain (p = 0.047) and single-domain groups (p = 9.51 × 10(-4)) compared with the control group. In the multi-domain group, this was true in the paracentral lobule (p = 0.004, Bonferroni corrected p < 0.05). Time-domain entropy also improved with training. Compared with controls, time-domain entropy in the multi-domain group decreased less in the inferior frontal gyrus pars opercularis (p = 3.59 × 10(-4)), the medial part of superior frontal gyrus (p = 1.17 × 10(-5)), and the thalamus (p = 4.72 × 10(-5)), while that in the single-domain group decreased less in the cuneus (p = 2.58 × 10(-4), Bonferroni corrected p < 0.05). Additionally, changes in regional entropy for some regions such as hippocampus significantly correlated with improvements in cognitive performance. CONCLUSIONS: Cognitive training can induce plastic changes in neural functional connectivity of healthy older people, and these changes may underlie the positive effect of cognitive training. TRIAL REGISTRATION: ChiCTR-TRC-08000732 (Date of registration: 5th November, 2008).