Multielement analysis of biological samples by inductively coupled plasma-mass spectrometry

Interest in the biological behavior of a growing number of elements, along with increasing recognition of the importance of interactions among them, demands a versatile and reliable technique for multielement analysis of biological samples. Significant improvements over the sensitivity achieved with conventional inductively coupled plasma (ICP) optical emission spectrometries have been realized with the introduction of quadrupole mass spectrometry (MS) for detection of ions in the plasma. The hybrid technique of ICP-MS promises to be a method of rapid multielement analysis, at detection limits that approach or surpass those of other technologies. However, the application of ICP-MS to analyses of biological interest is truly in its infancy. Here we report the use of ICP-MS for the determination of more than 30 elements of biological interest in a tissue and a biological fluid (rat liver and serum, respectively). Experimental values of the elements serve as a basis for discussion of analytical protocols, performance criteria, and certain problems peculiar to ICP-MS.     

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.     

Models for contact-mediated pattern formation: cells that form parallel arrays

Kinetic continuum models are derived for cells that crawl over a 2D substrate, undergo random reorientation, and turn in response to contact with a neighbor. The integro-partial differential equations account for changes in the distribution of orientations in the population. It is found that behavior depends on parameters such as total mass, random motility, adherence, and sloughing rates, as well as on broad aspects of the contact response. Linear stability analysis, and numerical, and cellular automata simulations reveal that as parameters are varied, a bifurcation leads to loss of stability of a uniform (isotropic) steady state, in favor of an (anisotropic) patterned state in which cells are aligned in parallel arrays.     

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     

Sex determination and differentiation in organisms other than higher plants

The understanding of sex determination in general, but in particular in mammals, has been a subject of scientific speculation for a long time. It has been shown that in many vertebrate and invertebrate species, the sex of an individual is determined by the individual's chromosomal constitution. Initial studies of classical genetic searching for sex-transforming mutations and the scrupulous analyses of modified phenotypes have shed light on the mechanism(s) of sex-determination. They paved the road to successful studies at molecular level. After a brief review on sex determination in chosen model species, the “Drosophila system” is presented to exemplify a possible general principle for sex determinism.     

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     

Differential winter mortality and seasonal selection in the polymorphic ladybird Adalia bipunctata (L) in the Netherlands

Seasonal selection acting on the melanic polymorphism in the two-spot ladybird Adalia bipunctata was investigated in The Netherlands. An increase in melanic frequency over the spring-summer reproductive period was quantified. The selective advantage gained by melanics averaged 9%, but significant heterogeneity occurred between populations. Adult hibernation behaviour is described. The beetles when outdoors show a highly clumped distribution both between and within trees. The distribution of the morph classes between aggregations is random. Survivorship in a hibernating cohort (initial n= 1898) on a grid of 70 lime trees near Utrecht was monitored by making three counts over the winter of 1981–1982. Intense selection favouring each melanic morph occurred during December and January. The relative fitness of non-melanics was 0.55 (melanics =1). The discovery of dead beetles in late January (about 5% of total losses) and the absence of spatially density-dependent mortality were consistent with a climatic stress rather than selective predation. The period of selection was associated with very cold temperatures averaging up to 4°C below normal and an overall mortality of nearly 75%. There was no change in morph frequency, near normal temperatures and a lower mortality from February to early April. Examination of groups of nearby trees in late January strongly suggested that similar differential mortality had occurred except on some willows. This difference was probably due to the more protected hibernation sites available on these trees. Samples of hibernating cohorts at three other sites showed no evidence of differential mortality. Laboratory experiments with hibernating beetles found no difference in survivorship or rate of weight loss between starved non-melanics and melanics in temperature regimes with and without periods of adult activity. It is concluded that the intense winter selection on the study limes is probably exceptional. Examination of changes in morph frequency through the annual cycle suggests that at some sites the selection favouring melanics during reproduction is counterbalanced by selection against melanics in late summer or early autumn. The results are discussed in relation to mathematical models of cyclical selection and to other field studies including that of Timoféeff-Ressovsky (1940), who found large decreases in melanic frequency during hibernation in Berlin.