Further results on the survival of a gene represented in a founder population

This paper is concerned with gene survival in a population which may increase without density dependence according to a generalization of the Moran model for haploid individuals. A selective advantage to one allele and the possibility of differential reproductive rates are allowed. Simple conditions are given for ultimate homozygosity to be certain and for the possibility of ultimate polymorphism. The results complement and extend those of Heyde (1981, 1982).     

Gene expression changes associated with cytotoxicity identified using cDNA arrays

In order to investigate gene expression changes associated with cytotoxicity, we used cDNA arrays to monitor the expression of over 5,000 genes in response to toxic stress in the HepG2 liver cell line. Cells were treated with cytotoxic doses of acetaminophen, caffeine or thioacetamide for nine time points ranging from 1 to 24 h. Samples of mRNA from each time point were used to prepare radiolabeled cDNA, which was hybridized to nylon-membrane-based cDNA arrays. High-stringency washes were applied to reduce cross-hybridization. Analysis of spot intensities revealed that each compound led to approximately 150-250 gene expression changes that were sustained over at least three adjacent time points. The affected genes could be classified into clusters based on their temporal patterns of differential expression. A common set of 44 genes showed similar expression changes in response to all three compounds. Of these changes, 90% could be confirmed by quantitative RT-PCR analysis. The results indicate that detailed array-based time-course studies, coupled with a sensitive and highly specific confirmation assay, provide a powerful means of identifying cytotoxicity-associated gene expression changes. Electronic Publication     

Cycles in cannibalistic egg-larval interactions

A model of a cannibalistic larval-egg interaction such as occurs in Tribolium is developed which leads to a system of nonlinear Volterra integral equations. I determine the local stability properties of the unique equilibrium point of the model. A Hopf bifurcation analysis shows that the model always undergoes a subcritical bifurcation when stability is lost. Numerical solutions confirm the presence of multiple attractors over a range of parameter values. The form of the cycles observed in the numerical solutions is analogous to that observed in laboratory populations of Tribolium.     

Convergence to equilibrium in a genetic model with differential viability between the sexes

A single locus, diallelic selection model with female and male viability differences is studied. If the variables are ratios of allele frequencies in each sex, a 2-dimensional difference equation describes the model. Because of the strong monotonicity of the resulting map, every initial genotypic structure converges to an equilibrium structure assuming that no equilibrium has eigenvalues on the unit circle.Partially supported by funds provided by a Science and Education Grant to the USDA-Forest Service, Southeastern Forest Experiment Station, Population Genetics of Forest Trees Research Unit, Raleigh, USASupported by a grant from the Max Kade Foundation, New York, USA     

The singularly perturbed Hodgkin-Huxley equations as a tool for the analysis of repetitive nerve activity

A qualitative analysis of the Hodgkin-Huxley model (Hodgkin and Huxley 1952), which closely mimics the ionic processes at a real nerve membrane, is performed by means of a singular perturbation theory. This was achieved by introducing a perturbation parameter that, if decreased, speeds up the fast variables of the Hodgkin-Huxley equations (membrane potential and sodium activation), whereas it does not affect the slow variables (sodium inactivation and potassium activation). In the most extreme case, if the perturbation parameter is set to zero, the original four-dimensional system degenerates to a system with only two differential equations. This degenerate system is easier to analyze and much more intuitive than the original Hodgkin-Huxley equations. It shows, like the original model, an infinite train of action potentials if stimulated by an input current in a suitable range. Additionally, explanations for the increased sensitivity to depolarizing current steps that precedes an action potential can be found by analysis of the degenerate system. Using the theory of Mishchenko and Rozov (1980) it is shown that the degenerate system does not only represent a simplification of the original Hodgkin-Huxley equations but also gives a valid approximation of the original model at least for stimulating currents that are constant within a suitable range.     

Statistical methods for model comparison in parameter estimation problems for distributed systems

In this note we outline some recent results on the development of a statistical testing methodology for inverse problems involving partial differential equation models. Applications to several problems from biology are presented. The statistical tests, which are in the spirit of analysis of variance (ANOVA), are based on asymptotic distributional results for estimators and residuals in a least squares approach.Research supported in part under grants NSF MCS 8504316, NASA NAG-1-517, and AFOSRF-49620-86-C-0111. Part of this research was carried out while the first author was a visiting scientist at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA, which is operated under NASA contracts NASI-18107 and NASI-18605     

A gastric trichobezoar in a chimpanzee

A firm, mobile, oblong mass was discovered as an incidental finding in the stomach of a chimpanzee (Pan troglodytes) during routine surgery. It was removed and determined to be a trichobezoar.     

Numerical simulation of thermal bone necrosis during cementation of femoral prostheses

The implant of a femoral prosthesis is a critical process because of the relatively high temperature values reached at the bone/cement interface during the cementation of the infibulum. In fact, the cement is actually a polymer that polymerizes in situ generating heat. Moreover, the conversion of monomer into polymer is never 100%; this is dangerous because of the toxicity of the monomer. In this paper, we present a 3-D axisymmetric mathematical model capable of taking into account both the geometry of the implant and the chemical/physical properties of the cement. This model, together with its numerical simulation, thus represents a useful tool to set up the optimal conditions for the new materials developed in this orthopaedic field. The real complex geometry is assumed to be a bone/cement/metallic system having cylindrical symmetry, thus allowing the model to be reduced to two space variables. The cementation process is described by the Fourier heat equation coupled with a suitable polymerization kinetics. The numerical approximation is accomplished by semi-implicit finite differences in time and finite elements in space with numerical quadrature. The full discrete scheme amounts to solve linear positive definite symmetric systems preceded by an elementwise algebraic computation. We present various numerical simulations which confirm some critical aspects of this orthopaedic fixing technique such as thermal bone necrosis and the presence of unreacted residual monomer.This work was partially supported by MURST (Fondi per la Ricerca Scientifica 40%) and CNR (IAN, Contract 880032601, and Progetto Finalizzato Sistemi Informatici e Calcolo Parallelo, Sottoprogetto Calcolo Scientifico per Grandi Sistemi) of Italy     

Models for age structured populations with distributed maturation rates

In the use of age structured population models for agricultural applications such as the modeling of crop-pest interactions it is often essential that the model take into account the distribution in maturation rates present in some or all of the populations. The traditional method for incorporating distributed maturation rates into crop and pest models has been the so-called distributed delay method. In this paper we review the application of the distributed delay formalism to the McKendrick equation of an age structured population. We discuss the mathematical properties of the system of ordinary differential equations arising out of the distributed delay formalism. We then discuss an alternative method involving modification of the Leslie matrix.     

Absence of subtransition in racemic dipalmitoylphosphatidylcholine vesicles

dl-Dipalmitoylphosphatidylcholine multilamellar vesicle suspensions were examined by the method of differential scanning calorimetry. A lack of the subtransition at 18°C was established. Such a subtransition is characteristic for l-dipalmitoylphosphatidylcholine suspensions. This lack is supposed to be the result of the impossibility of the racemic phospholipid mixture to form the low-temperature crystal structure L_c.