Solving Non-homogeneous Nested Recursions Using Trees

The solutions to certain nested recursions, such as Conolly's C(n) = C(n-C(n-1))+C(n-1-C(n-2)), with initial conditions C(1)=1, C(2)=2, have a well-established combinatorial interpretation in terms of counting leaves in an infinite binary tree. This tree-based interpretation, which has a natural generalization to a k-term nested recursion of this type, only applies to homogeneous recursions, and only solves each recursion for one set of initial conditions determined by the tree. In this paper, we extend the tree-based interpretation to solve a non-homogeneous version of the k-term recursion that includes a constant term. To do so we introduce a tree-grafting methodology that inserts copies of a finite tree into the infinite k-ary tree associated with the solution of the corresponding homogeneous k-term recursion. This technique can also be used to solve the given non-homogeneous recursion with various sets of initial conditions.Comment: 14 page

Natural variation in a glucuronosyltransferase modulates propionate sensitivity in a C. elegans propionic acidemia model

Mutations in human metabolic genes can lead to rare diseases known as inborn errors of human metabolism. For instance, patients with loss-of-function mutations in either subunit of propionyl-CoA carboxylase suffer from propionic acidemia because they cannot catabolize propionate, leading to its harmful accumulation. Both the penetrance and expressivity of metabolic disorders can be modulated by genetic background. However, modifiers of these diseases are difficult to identify because of the lack of statistical power for rare diseases in human genetics. Here, we use a model of propionic acidemia in the nematode Caenorhabditis elegans to identify genetic modifiers of propionate sensitivity. Using genome-wide association (GWA) mapping across wild strains, we identify several genomic regions correlated with reduced propionate sensitivity. We find that natural variation in the putative glucuronosyltransferase GLCT-3, a homolog of human B3GAT, partly explains differences in propionate sensitivity in one of these genomic intervals. We demonstrate that loss-of-function alleles in glct-3 render the animals less sensitive to propionate. Additionally, we find that C. elegans has an expansion of the glct gene family, suggesting that the number of members of this family could influence sensitivity to excess propionate. Our findings demonstrate that natural variation in genes that are not directly associated with propionate breakdown can modulate propionate sensitivity. Our study provides a framework for using C. elegans to characterize the contributions of genetic background in models of human inborn errors in metabolism

Cdk9 and H2Bub1 signal to Clr6-CII/Rpd3S to suppress aberrant antisense transcription

Mono-ubiquitylation of histone H2B (H2Bub1) and phosphorylation of elongation factor Spt5 by cyclin-dependent kinase 9 (Cdk9) occur during transcription by RNA polymerase II (RNAPII), and are mutually dependent in fission yeast. It remained unclear whether Cdk9 and H2Bub1 cooperate to regulate the expression of individual genes. Here, we show that Cdk9 inhibition or H2Bub1 loss induces intragenic antisense transcription of ∼10% of fission yeast genes, with each perturbation affecting largely distinct subsets; ablation of both pathways de-represses antisense transcription of over half the genome. H2Bub1 and phospho-Spt5 have similar genome-wide distributions; both modifications are enriched, and directly proportional to each other, in coding regions, and decrease abruptly around the cleavage and polyadenylation signal (CPS). Cdk9-dependence of antisense suppression at specific genes correlates with high H2Bub1 occupancy, and with promoter-proximal RNAPII pausing. Genetic interactions link Cdk9, H2Bub1 and the histone deacetylase Clr6-CII, while combined Cdk9 inhibition and H2Bub1 loss impair Clr6-CII recruitment to chromatin and lead to decreased occupancy and increased acetylation of histones within gene coding regions. These results uncover novel interactions between co-transcriptional histone modification pathways, which link regulation of RNAPII transcription elongation to suppression of aberrant initiation

Candida albicans repetitive elements display epigenetic diversity and plasticity

Transcriptionally silent heterochromatin is associated with repetitive DNA. It is poorly understood whether and how heterochromatin differs between different organisms and whether its structure can be remodelled in response to environmental signals. Here, we address this question by analysing the chromatin state associated with DNA repeats in the human fungal pathogen Candida albicans. Our analyses indicate that, contrary to model systems, each type of repetitive element is assembled into a distinct chromatin state. Classical Sir2-dependent hypoacetylated and hypomethylated chromatin is associated with the rDNA locus while telomeric regions are assembled into a weak heterochromatin that is only mildly hypoacetylated and hypomethylated. Major Repeat Sequences, a class of tandem repeats, are assembled into an intermediate chromatin state bearing features of both euchromatin and heterochromatin. Marker gene silencing assays and genome-wide RNA sequencing reveals that C. albicans heterochromatin represses expression of repeat-associated coding and non-coding RNAs. We find that telomeric heterochromatin is dynamic and remodelled upon an environmental change. Weak heterochromatin is associated with telomeres at 30?°C, while robust heterochromatin is assembled over these regions at 39?°C, a temperature mimicking moderate fever in the host. Thus in C. albicans, differential chromatin states controls gene expression and epigenetic plasticity is linked to adaptation

Evaporation from three water bodies of different sizes and climates: Measurements and scaling analysis

Evaporation from small reservoirs, wetlands, and lakes continues to be a theoretical and practical problem in surface hydrology and micrometeorology because atmospheric flows above such systems can rarely be approximated as stationary and planar-homogeneous with no mean subsidence (hereafter referred to as idealized flow state). Here, the turbulence statistics of temperature(T)and water vapor (q)most pertinent to lake evaporation measurementsover three water bodies differing in climate, thermal inertia and degree of advective conditions are explored. The three systems included Lac Le´man in Switzerland (high thermal inertia, near homogeneous conditions with no appreciable advection due to long upwind fetch), Eshkol reservoir in Israel (intermediate thermal inertia, frequent strong advective conditions) and Tilopozo wetland in Chile (low thermal inertia, frequent but moderate advection). The data analysis focused on how similarity constants for the flux-variance approach, CT/Cq, and relative transport efficiencies RwT/Rwq, are perturbed from unity with increased advection or the active role of temperature. When advection is small and thermal inertia is large, CT/Cq 1)primarily due to the active role of temperature, which is consistent with a large number of studies conducted over bare soil and vegetated surfaces. However, when advection is significantly large, then CT/Cq >1 (orRwT/Rwq < 1). When advection is moderate and thermal inertia is low, then CT/Cq �1. This latter equality, while consistent with Monin–Obukhov similarity theory (MOST), is due to the fact that advection tends to increase CT/Cq above unity while the active role of temperature tends to decrease CT/Cq below unity. A simplified scaling analysis derived from the scalar variance budget equation, explained qualitatively how advection could per¬turb MOST scaling (assumed to represent the idealized flow state)

Evaporation from a small water reservoir: Direct measurements and estimates

Summary Knowing the rate of evaporation from surface water resources such as chan¬nels and reservoirs is essential for precise management of the water balance. However, evaporation is difficult to measure experimentally over water surfaces and several tech¬niques and models have been suggested and used in the past for its determination. In this research, evaporation from a small water reservoir in northern Israel was measured and estimated using several experimental techniques and models during the rainless summer. Evaporation was measured with an eddy covariance (EC) system consisting of a three-dimensional sonic anemometer and a Krypton hygrometer. Measurements of net radia¬tion, air temperature and humidity, and water temperature enabled estimation of other energy balance components. Several models and energy balance closure were evaluated. In addition, evaporation from a class-A pan was measured at the site. EC evaporation measurements for 21 days averaged 5.48 mm day�1. Best model predictions were obtained with two combined flux-gradient and energy balance models (Penman–Mon¬teith–Unsworth and Penman–Brutsaert), which with the water heat flux term, gave sim¬ilar daily average evaporation rates, that were up to 3% smaller than the corresponding EC values. The ratio between daily pan and EC evaporation varied from 0.96 to 1.94. The bulk mass transfer coefficient was estimated using a model based on measurements of water surface temperature, evaporation rate and absolute humidity at 0.9 and 2.9 m above the water surface, and using two theoretical approaches. The bulk transfer coefficient

The Value of Information for Populations in Varying Environments

The notion of information pervades informal descriptions of biological systems, but formal treatments face the problem of defining a quantitative measure of information rooted in a concept of fitness, which is itself an elusive notion. Here, we present a model of population dynamics where this problem is amenable to a mathematical analysis. In the limit where any information about future environmental variations is common to the members of the population, our model is equivalent to known models of financial investment. In this case, the population can be interpreted as a portfolio of financial assets and previous analyses have shown that a key quantity of Shannon's communication theory, the mutual information, sets a fundamental limit on the value of information. We show that this bound can be violated when accounting for features that are irrelevant in finance but inherent to biological systems, such as the stochasticity present at the individual level. This leads us to generalize the measures of uncertainty and information usually encountered in information theory

The genetic basis of natural variation in C. elegans telomere length [preprint]

Telomeres are involved in the maintenance of chromosomes and the prevention of genome instability. Despite this central importance, significant variation in telomere length has been observed in a variety of organisms. The genetic determinants of telomere-length variation and their effects on organismal fitness are largely unexplored. Here, we describe natural variation in telomere length across the Caenorhabditis elegans species. We identify a large-effect variant that contributes to differences in telomere length. The variant alters the conserved oligosaccharide/oligonucleotide-binding fold of POT-2, a homolog of a human telomere-capping shelterin complex subunit. Mutations within this domain likely reduce the ability of POT-2 to bind telomeric DNA, thereby increasing telomere length. We find that telomere-length variation does not correlate with offspring production or longevity in C. elegans wild isolates, suggesting that naturally long telomeres play a limited role in modifying fitness phenotypes in C. elegans

The Genetic Basis of Natural Variation in Caenorhabditis elegans Telomere Length

Telomeres are involved in the maintenance of chromosomes and the prevention of genome instability. Despite this central importance, significant variation in telomere length has been observed in a variety of organisms. The genetic determinants of telomere-length variation and their effects on organismal fitness are largely unexplored. Here, we describe natural variation in telomere length across the Caenorhabditis elegans species. We identify a large-effect variant that contributes to differences in telomere length. The variant alters the conserved oligonucleotide/oligosaccharide-binding fold of protection of telomeres 2 (POT-2), a homolog of a human telomere-capping shelterin complex subunit. Mutations within this domain likely reduce the ability of POT-2 to bind telomeric DNA, thereby increasing telomere length. We find that telomere-length variation does not correlate with offspring production or longevity in C. elegans wild isolates, suggesting that naturally long telomeres play a limited role in modifying fitness phenotypes in C. elegans

A nucleosome turnover map reveals that the stability of histone H4 Lys20 methylation depends on histone recycling in transcribed chromatin

Nucleosome composition actively contributes to chromatin structure and accessibility. Cells have developed mechanisms to remove or recycle histones, generating a landscape of differentially aged nucleosomes. This study aimed to create a high-resolution, genome-wide map of nucleosome turnover in Schizosaccharomyces pombe. The recombination-induced tag exchange (RITE) method was used to study replication-independent nucleosome turnover through the appearance of new histone H3 and the disappearance or preservation of old histone H3. The genome-wide location of histones was determined by chromatin immunoprecipitation–exonuclease methodology (ChIP-exo). The findings were compared with diverse chromatin marks, including histone variant H2A.Z, post-translational histone modifications, and Pol II binding. Finally, genome-wide mapping of the methylation states of H4K20 was performed to determine the relationship between methylation (mono, di, and tri) of this residue and nucleosome turnover. Our analysis showed that histone recycling resulted in low nucleosome turnover in the coding regions of active genes, stably expressed at intermediate levels. High levels of transcription resulted in the incorporation of new histones primarily at the end of transcribed units. H4K20 was methylated in low-turnover nucleosomes in euchromatic regions, notably in the coding regions of long genes that were expressed at low levels. This transcription-dependent accumulation of histone methylation was dependent on the histone chaperone complex FACT. Our data showed that nucleosome turnover is highly dynamic in the genome and that several mechanisms are at play to either maintain or suppress stability. In particular, we found that FACT-associated transcription conserves histones by recycling them and is required for progressive H4K20 methylation