Kinetic theory of age-structured stochastic birth-death processes

Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but are unable to describe stochastic fluctuations or population-size-dependent birth and death rates. Stochastic theories that treat semi-Markov age-dependent processes using, e.g., the Bellman-Harris equation do not resolve a population's age structure and are unable to quantify population-size dependencies. Conversely, current theories that include size-dependent population dynamics (e.g., mathematical models that include carrying capacity such as the logistic equation) cannot be easily extended to take into account age-dependent birth and death rates. In this paper, we present a systematic derivation of a new, fully stochastic kinetic theory for interacting age-structured populations. By defining multiparticle probability density functions, we derive a hierarchy of kinetic equations for the stochastic evolution of an aging population undergoing birth and death. We show that the fully stochastic age-dependent birth-death process precludes factorization of the corresponding probability densities, which then must be solved by using a Bogoliubov-–Born–-Green–-Kirkwood-–Yvon-like hierarchy. Explicit solutions are derived in three limits: no birth, no death, and steady state. These are then compared with their corresponding mean-field results. Our results generalize both deterministic models and existing master equation approaches by providing an intuitive and efficient way to simultaneously model age- and population-dependent stochastic dynamics applicable to the study of demography, stem cell dynamics, and disease evolution

Isolated bilateral simplex ureteric ectopia: Bladder capacity as an indicator of continence outcome

INTRODUCTION: Isolated bilateral simplex ectopic ureters (BSEUs) are rare but pose a therapeutic challenge: ureteric reimplantation alone does not accomplish continence in all. Identifying the patients needing additional procedures for continence early could prevent multiple operations. OBJECTIVE: Potential preoperative indicators for postoperative continence are explored in eight BSEU girls without cloacal, anorectal, or spinal anomalies. STUDY DESIGN: With institutional approval, all patients with BSEU between 1985 and 2012 were retrospectively reviewed. Cystoscopy determined the site of ureteric ectopia (6 of 16 at the bladder neck [BN], 5 of 16 below the BN, and 5 of 16 in the distal urethra). Bladders were assessed by a combination of ultrasound, urodynamics, micturating cystourethrogram, cystoscopic, and intraoperative observations. Expected bladder capacity for age (EBCA) was calculated by 30 ml + (30 ml × age in years) or 38 ml + (2.5 ml × age in months) for children greater or less than 2 years, respectively. Continence outcomes were appraised at a minimum of 4 years. The small number of patients precludes credible statistical analysis and therefore raw data are presented. RESULTS: Patients underwent cross-trigonal ureteric reimplantation at 1–5.5 years, in five without BN surgery and in three with a Young–Dees–Leadbetter BN tightening. Of those without BN surgery at reimplantation, four achieved satisfactory continence for their age, but one has had multiple procedures culminating in BN closure, ileocystoplasty, and Mitrofanoff. Among the BN-tightening group, one was in nappies at 4 years, one had residual stress incontinence after two further BN injections, and one proceeded to artificial urinary sphincter after two BN injections. Five patients had significant renal impairment. DISCUSSION: Patients with satisfactory continence after reimplantation alone and those needing further procedures tended to differ in their preoperative observations of bladder capacity and apparent BN competence. This study suggests preoperative observations of an empty bladder on serial ultrasound and/or a wide-open BN with small or even moderate bladder capacity at cystoscopy to indicate the need for BN surgery. In contrast, children with bladder filling to at least 30% of expected bladder capacity for age on preoperative ultrasound or apposition of the BN at cystoscopy may achieve satisfactory continence after ureteric reimplantation alone. Bladder capacity as an indicator of BN competence can also be correlated to continence outcomes in previously published series. Polyuria associated with renal impairment can exacerbate the challenge for continence. CONCLUSION: Preoperative bladder capacity appears to be an indicator of inherent BN function and a thorough assessment of the urinary tract by cystoscopy, ultrasound, micturating cystourethrogram, and functional imaging may guide the surgeon on the need for BN surgery at the time of ureteric reimplantation. Where continence remains elusive, patients should be counselled that a further BN injection is occasionally of value although more significant BN procedures are required for most

Nonlocal density functionals and the linear response of the homogeneous electron gas

The known and usable truly nonlocal functionals for exchange-correlation energy of the inhomogeneous electron gas are the ADA (average density approximation) and the WDA (weighted density approximation). ADA, by design, yields the correct linear response function of the uniform electron gas. WDA is constructed so that it is exact in the limit of one-electron systems. We derive an expression for the linear response of the uniform gas in the WDA, and calculate it for several flavors of WDA. We then compare the results with the Monte-Carlo data on the exchange-correlation local field correction, and identify the weak points of conventional WDA in the homogeneous limit. We suggest how the WDA can be modified to improve the response function. The resulting approximation is a good one in both opposite limits, and should be useful for practical nonlocal density functional calculations.Comment: 4 pages, two eps figures embedde

An Evolutionary Reduction Principle for Mutation Rates at Multiple Loci

A model of mutation rate evolution for multiple loci under arbitrary selection is analyzed. Results are obtained using techniques from Karlin (1982) that overcome the weak selection constraints needed for tractability in prior studies of multilocus event models. A multivariate form of the reduction principle is found: reduction results at individual loci combine topologically to produce a surface of mutation rate alterations that are neutral for a new modifier allele. New mutation rates survive if and only if they fall below this surface - a generalization of the hyperplane found by Zhivotovsky et al. (1994) for a multilocus recombination modifier. Increases in mutation rates at some loci may evolve if compensated for by decreases at other loci. The strength of selection on the modifier scales in proportion to the number of germline cell divisions, and increases with the number of loci affected. Loci that do not make a difference to marginal fitnesses at equilibrium are not subject to the reduction principle, and under fine tuning of mutation rates would be expected to have higher mutation rates than loci in mutation-selection balance. Other results include the nonexistence of 'viability analogous, Hardy-Weinberg' modifier polymorphisms under multiplicative mutation, and the sufficiency of average transmission rates to encapsulate the effect of modifier polymorphisms on the transmission of loci under selection. A conjecture is offered regarding situations, like recombination in the presence of mutation, that exhibit departures from the reduction principle. Constraints for tractability are: tight linkage of all loci, initial fixation at the modifier locus, and mutation distributions comprising transition probabilities of reversible Markov chains.Comment: v3: Final corrections. v2: Revised title, reworked and expanded introductory and discussion sections, added corollaries, new results on modifier polymorphisms, minor corrections. 49 pages, 64 reference

Strong polarization-induced reduction of addition energies in single-molecule nanojunctions

We address polarization-induced renormalization of molecular levels in solid-state based single-molecule transistors and focus on an organic conjugate molecule where a surprisingly large reduction of the addition energy has been observed. We have developed a scheme that combines a self-consistent solution of a quantum chemical calculation with a realistic description of the screening environment. Our results indeed show a large reduction, and we explain this to be a consequence of both (a) a reduction of the electrostatic molecular charging energy and (b) polarization induced level shifts of the HOMO and LUMO levels. Finally, we calculate the charge stability diagram and explain at a qualitative level general features observed experimentally.Comment: 9 pages, 5 figure

Wound healing and hyper-hydration - a counter intuitive model

Winters seminal work in the 1960s relating to providing an optimal level of moisture to aid wound healing (granulation and re-epithelialisation) has been the single most effective advance in wound care over many decades. As such the development of advanced wound dressings that manage the fluidic wound environment have provided significant benefits in terms of healing to both patient and clinician. Although moist wound healing provides the guiding management principle confusion may arise between what is deemed to be an adequate level of tissue hydration and the risk of developing maceration. In addition, the counter-intuitive model ‘hyper-hydration’ of tissue appears to frustrate the moist wound healing approach and advocate a course of intervention whereby tissue is hydrated beyond what is a normally acceptable therapeutic level. This paper discusses tissue hydration, the cause and effect of maceration and distinguishes these from hyper-hydration of tissue. The rationale is to provide the clinician with a knowledge base that allows optimisation of treatment and outcomes and explains the reasoning behind wound healing using hyper-hydration

Adaptive walks on time-dependent fitness landscapes

The idea of adaptive walks on fitness landscapes as a means of studying evolutionary processes on large time scales is extended to fitness landscapes that are slowly changing over time. The influence of ruggedness and of the amount of static fitness contributions are investigated for model landscapes derived from Kauffman's $NK$ landscapes. Depending on the amount of static fitness contributions in the landscape, the evolutionary dynamics can be divided into a percolating and a non-percolating phase. In the percolating phase, the walker performs a random walk over the regions of the landscape with high fitness.Comment: 7 pages, 6 eps-figures, RevTeX, submitted to Phys. Rev.

Study of the genetic variability in a Parkinson's Disease gene: EIF4G1

Chartier-Harlin and colleagues [2] recently reported mutations in the eukaryotic translation initiation factor 4-gamma (EIF4G1) gene in families with parkinsonism. Large-scale screening found two mutations (p.R1205H and p.A502V) only in affected individuals, although their relative frequency was very low. The aim of this study was to investigate EIF4G1 parkinsonism-related variants in two separate cohorts and study coding variability across the gene. We first screened a series of familial Parkinson's Disease (PD) patients in an attempt to confirm previous results by showing segregation. Then, to determine the extent of coding variation in the gene, we first screened a cohort of sub-Saharan African individuals from the Centre d'Etude du Polymorphisme Humain - Human Genome Diversity Cell Line Panel (HGDP) [1] and then analyzed data from 5350 individuals National Heart, Lung, and Blood Institute (NHLBI) exome sequencing project. We failed to identify any PD-related mutations in the familial samples. Conversely we found the p.A502V variant in the NHLBI population. We observed a high number of coding polymorphism in the exons where the two PD variants have been previously reported. We conclude that either EIF4G1 variants are an extremely rare cause of familial PD in Caucasian cohorts, or that A502V is in fact a rare benign variant not involved in PD aetiology. Our data also suggests that the protein can tolerate some extent of variability particularly at this point of the gene

Footprints of Inversions at Present and Past Pseudoautosomal Boundaries in Human Sex Chromosomes

The human sex chromosomes have stopped recombining gradually, which has left five evolutionary strata on the X chromosome. Y inversions are thought to have suppressed X–Y recombination but clear evidence is missing. Here, we looked for such evidence by focusing on a region—the X-added region (XAR)—that includes the pseudoautosomal region and the most recent strata 3 to 5. We estimated and analyzed the whole set of parsimonious scenarios of Y inversions given the gene order in XAR and its Y homolog. Comparing these to scenarios for simulated sequences suggests that the strata 4 and 5 were formed by Y inversions. By comparing the X and Y DNA sequences, we found clear evidence of two Y inversions associated with duplications that coincide with the boundaries of strata 4 and 5. Divergence between duplicates is in agreement with the timing of strata 4 and 5 formation. These duplicates show a complex pattern of gene conversion that resembles the pattern previously found for AMELXY, a stratum 3 locus. This suggests that this locus—despite AMELY being unbroken—was possibly involved in a Y inversion that formed stratum 3. However, no clear evidence supporting the formation of stratum 3 by a Y inversion was found, probably because this stratum is too old for such an inversion to be detectable. Our results strongly support the view that the most recent human strata have arisen by Y inversions and suggest that inversions have played a major role in the differentiation of our sex chromosomes

Expression and trans-specific polymorphism of self-incompatibility RNases in Coffea (Rubiaceae)

Self-incompatibility (SI) is widespread in the angiosperms, but identifying the biochemical components of SI mechanisms has proven to be difficult in most lineages. Coffea (coffee; Rubiaceae) is a genus of old-world tropical understory trees in which the vast majority of diploid species utilize a mechanism of gametophytic self-incompatibility (GSI). The S-RNase GSI system was one of the first SI mechanisms to be biochemically characterized, and likely represents the ancestral Eudicot condition as evidenced by its functional characterization in both asterid (Solanaceae, Plantaginaceae) and rosid (Rosaceae) lineages. The S-RNase GSI mechanism employs the activity of class III RNase T2 proteins to terminate the growth of "self" pollen tubes. Here, we investigate the mechanism of Coffea GSI and specifically examine the potential for homology to S-RNase GSI by sequencing class III RNase T2 genes in populations of 14 African and Madagascan Coffea species and the closely related self-compatible species Psilanthus ebracteolatus. Phylogenetic analyses of these sequences aligned to a diverse sample of plant RNase T2 genes show that the Coffea genome contains at least three class III RNase T2 genes. Patterns of tissue-specific gene expression identify one of these RNase T2 genes as the putative Coffea S-RNase gene. We show that populations of SI Coffea are remarkably polymorphic for putative S-RNase alleles, and exhibit a persistent pattern of trans-specific polymorphism characteristic of all S-RNase genes previously isolated from GSI Eudicot lineages. We thus conclude that Coffea GSI is most likely homologous to the classic Eudicot S-RNase system, which was retained since the divergence of the Rubiaceae lineage from an ancient SI Eudicot ancestor, nearly 90 million years ago.United States National Science Foundation [0849186]; Society of Systematic Biologists; American Society of Plant Taxonomists; Duke University Graduate Schoolinfo:eu-repo/semantics/publishedVersio