The frequency-dependent Wright-Fisher model: diffusive and non-diffusive approximations

We study a class of processes that are akin to the Wright-Fisher model, with transition probabilities weighted in terms of the frequency-dependent fitness of the population types. By considering an approximate weak formulation of the discrete problem, we are able to derive a corresponding continuous weak formulation for the probability density. Therefore, we obtain a family of partial differential equations (PDE) for the evolution of the probability density, and which will be an approximation of the discrete process in the joint large population, small time-steps and weak selection limit. If the fitness functions are sufficiently regular, we can recast the weak formulation in a more standard formulation, without any boundary conditions, but supplemented by a number of conservation laws. The equations in this family can be purely diffusive, purely hyperbolic or of convection-diffusion type, with frequency dependent convection. The particular outcome will depend on the assumed scalings. The diffusive equations are of the degenerate type; using a duality approach, we also obtain a frequency dependent version of the Kimura equation without any further assumptions. We also show that the convective approximation is related to the replicator dynamics and provide some estimate of how accurate is the convective approximation, with respect to the convective-diffusion approximation. In particular, we show that the mode, but not the expected value, of the probability distribution is modelled by the replicator dynamics. Some numerical simulations that illustrate the results are also presented

Somatic sex-specific transcriptome differences in Drosophila revealed by whole transcriptome sequencing

<p>Abstract</p> <p>Background</p> <p>Understanding animal development and physiology at a molecular-biological level has been advanced by the ability to determine at high resolution the repertoire of mRNA molecules by whole transcriptome resequencing. This includes the ability to detect and quantify rare abundance transcripts and isoform-specific mRNA variants produced from a gene.</p> <p>The sex hierarchy consists of a pre-mRNA splicing cascade that directs the production of sex-specific transcription factors that specify nearly all sexual dimorphism. We have used deep RNA sequencing to gain insight into how the Drosophila sex hierarchy generates somatic sex differences, by examining gene and transcript isoform expression differences between the sexes in adult head tissues.</p> <p>Results</p> <p>Here we find 1,381 genes that differ in overall expression levels and 1,370 isoform-specific transcripts that differ between males and females. Additionally, we find 512 genes not regulated downstream of <it>transformer </it>that are significantly more highly expressed in males than females. These 512 genes are enriched on the × chromosome and reside adjacent to dosage compensation complex entry sites, which taken together suggests that their residence on the × chromosome might be sufficient to confer male-biased expression. There are no transcription unit structural features, from a set of features, that are robustly significantly different in the genes with significant sex differences in the ratio of isoform-specific transcripts, as compared to random isoform-specific transcripts, suggesting that there is no single molecular mechanism that generates isoform-specific transcript differences between the sexes, even though the sex hierarchy is known to include three pre-mRNA splicing factors.</p> <p>Conclusions</p> <p>We identify thousands of genes that show sex-specific differences in overall gene expression levels, and identify hundreds of additional genes that have differences in the abundance of isoform-specific transcripts. No transcription unit structural feature was robustly enriched in the sex-differentially expressed transcript isoforms. Additionally, we found that many genes with male-biased expression were enriched on the × chromosome and reside adjacent to dosage compensation entry sites, suggesting that differences in sex chromosome composition contributes to dimorphism in gene expression. Taken together, this study provides new insight into the molecular underpinnings of sexual differentiation.</p

GABAergic Neuron Deficit As An Idiopathic Generalized Epilepsy Mechanism: The Role Of BRD2 Haploinsufficiency In Juvenile Myoclonic Epilepsy

Idiopathic generalized epilepsy (IGE) syndromes represent about 30% of all epilepsies. They have strong, but elusive, genetic components and sex-specific seizure expression. Multiple linkage and population association studies have connected the bromodomain-containing gene BRD2 to forms of IGE. In mice, a null mutation at the homologous Brd2 locus results in embryonic lethality while heterozygous Brd2+/− mice are viable and overtly normal. However, using the flurothyl model, we now show, that compared to the Brd2+/+ littermates, Brd2+/− males have a decreased clonic, and females a decreased tonic-clonic, seizure threshold. Additionally, long-term EEG/video recordings captured spontaneous seizures in three out of five recorded Brd2+/− female mice. Anatomical analysis of specific regions of the brain further revealed significant differences in Brd2+/− vs +/+ mice. Specifically, there were decreases in the numbers of GABAergic (parvalbumin- or GAD67-immunopositive) neurons along the basal ganglia pathway, i.e., in the neocortex and striatum of Brd2+/− mice, compared to Brd2+/+ mice. There were also fewer GABAergic neurons in the substantia nigra reticulata (SNR), yet there was a minor, possibly compensatory increase in the GABA producing enzyme GAD67 in these SNR cells. Further, GAD67 expression in the superior colliculus and ventral medial thalamic nucleus, the main SNR outputs, was significantly decreased in Brd2+/− mice, further supporting GABA downregulation. Our data show that the non-channel-encoding, developmentally critical Brd2 gene is associated with i) sex-specific increases in seizure susceptibility, ii) the development of spontaneous seizures, and iii) seizure-related anatomical changes in the GABA system, supporting BRD2's involvement in human IGE

Mating alters gene expression patterns in Drosophila melanogaster male heads

<p>Abstract</p> <p>Background</p> <p>Behavior is a complex process resulting from the integration of genetic and environmental information. <it>Drosophila melanogaster </it>rely on multiple sensory modalities for reproductive success, and mating causes physiological changes in both sexes that affect reproductive output or behavior. Some of these effects are likely mediated by changes in gene expression. Courtship and mating alter female transcript profiles, but it is not known how mating affects male gene expression.</p> <p>Results</p> <p>We used <it>Drosophila </it>genome arrays to identify changes in gene expression profiles that occur in mated male heads. Forty-seven genes differed between mated and control heads 2 hrs post mating. Many mating-responsive genes are highly expressed in non-neural head tissues, including an adipose tissue called the fat body. One fat body-enriched gene, <it>female-specific independent of transformer </it>(<it>fit</it>), is a downstream target of the somatic sex-determination hierarchy, a genetic pathway that regulates <it>Drosophila</it> reproductive behaviors as well as expression of some fat-expressed genes; three other mating-responsive loci are also downstream components of this pathway. Another mating-responsive gene expressed in fat, <it>Juvenile hormone esterase </it>(<it>Jhe</it>), is necessary for robust male courtship behavior and mating success.</p> <p>Conclusions</p> <p>Our study demonstrates that mating causes changes in male head gene expression profiles and supports an increasing body of work implicating adipose signaling in behavior modulation. Since several mating-induced genes are sex-determination hierarchy target genes, additional mating-responsive loci may be downstream components of this pathway as well.</p

Failure of the Patellar Tendon with the Patella Everted versus Noneverted in a Matched-Pair Cadaver Model

Avoidance of patellar eversion during total knee arthroplasty may help to prevent injury to the patellar tendon. The purpose of this study was to compare the load-to-failure of the everted versus the noneverted patella in a cadaveric model. Fourteen cadaver knees (seven pairs) were loaded to failure with the patella everted in one knee and not everted in the other. Mean load-at-ultimate failure in the patella-everted group was 1,111 ± 572 N, and in the patella-noneverted group was 1,621 ± 683 N (p = 0.01). Additionally, loads-at-initial-partial failure were lower (p = 0.04) in the patella-everted compared to the patella-noneverted group, 573 ± 302 N versus 1,115 ± 358 N, respectively. A partial failure of the patellar tendon occurred in 100% of the everted specimens, whereas only 57% of the noneverted specimens had partial failure. These findings suggest patella eversion may lead to failure of the patellar insertion at lower loads than when the patella is not everted