Numerical solution of a nonlinear advance-delay-differential equation from nerve conduction theory

A functional differential equation which is nonlinear and involves forward and backward deviating arguments is solved numerically. The equation models conduction in a myelinated nerve axon in which the myelin completely insulates the membrane, so that the potential change jumps from node to node. The equation is of first order with boundary values given at t=±. The problem is approximated via a difference scheme which solves the problem on a finite interval by utilizing an asymptotic representation at the endpoints, cubic interpolation and iterative techniques to approximate the delays, and a continuation method to start the procedure. The procedure is tested on a class of problems which are solvable analytically to access the scheme's accuracy and stability, then applied to the problem that models propagation in a myelinated axon. The solution's dependence on various model parameters of physical interest is studied. This is the first numerical study of myelinated nerve conduction in which the advance and delay terms are treated explicitly.Supported in part by NSF Grant MCS8301724 and by a Biomedical Research Support Grant 2SO7RR0706618 from NIH     

Growth Regulation In Multilayered Cultures of Human Diploid Fibroblasts: the Roles of Contact, Movement and Matrix Production

Abstract. Early subcultures of human embryonic lung fibroblasts are exceptional, as they grow far beyond confluence before growth ceases: the stationary dish may well contain 3-10 monolayer equivalents. Maximal growth rates, however, occur at about one-sixth confluence when doubling times are 15-20 hr; a density at which cell contacts begin to become frequent. the fact that a slowing down of growth is first apparent at such low densities argues against this regulation being due to diffusion effects. Confirmation of the role of short-range or contact interactions in growth regulation comes from an experiment using mixed cultures of fibroblasts: this shows that growth inhibition is not carried by medium-borne influences but depends on short-range (<1 mm) interactions. Evidence that cells can escape the effects of such contact interactions and so divide comes from time-lapse studies of dense cultures: there is a burst of motility soon after a fresh-medium change, which is followed by a burst of mitosis × 20 hr later. A medium change to conditioned medium supplemented with 10% foetal calf serum leads to neither the burst of motility nor the subsequent burst of mitosis, although this medium is better able to support the growth of sparse cells than is fresh medium. Data are also presented to show that the amount of collagen deposited in superconfluent cultures affects their growth: the stimulation of collagen production with ascorbic acid leads to an unexpectedly low stationary cell density and rather less movement in the culture. This result suggests that the collagen stabilizes cell contacts that are responsible for growth inhibition. the question of why these cells grow more slowly as density increases cannot be answered directly by these experiments; nevertheless, the results suggest that cell contact affects the permeability of the cell membrane to medium.     

The origin of lift forces in fluttering flight

A two-dimensional nonlinear integro-differential equation with time-varying coefficients describing the behavior of the fluttering wing-body systems typical of natural flight mechanisms has been deduced from the Navier-Stokes equation which generalizes local pressure and velocity distributions in the externally oscillating air field. The resulting equation for the wing forces is combined with an analogous expression for the forces of gravitation and acceleration associated with the body. The air acceleration force, not previously considered in bio-physical models of insect and bird flight, is shown to arise from a formal analysis of unsteady or time-varying contributions to the velocity field, while the square form of the conventional steady state aerodynamic forces is derived from the intertial terms in the Navier-Stokes equation with the aid of the approximations of Newtonian impact theory. Previous calculations (Houghton, 1964) have indicated that the contribution to gravitational stability of air acceleration and aerodynamic life are roughly in the ratio of 3:1.     

DETERMINATION OF GUSTATORY SUCROSE THRESHOLD IN WATER BY USE OF A LINEAR SUCROSE GRADIENT

A novel experimental method was developed which allows the determination of the threshold concentration of sucrose by use of a linear sucrose gradient in water. With this method a continuous tasting of the test-liquid is possible. A panel of 15 persons experienced in taste-testing was used. Three gradients of different steepness were applied: 0 to 1.5% (w/w) sucrose in 2 min (I), 3 min (II) and 4 min (III). The results of the new method were compared with those of the standard method (DIN). With gradients I and II we found values which were significantly higher than those of the standard method (I: 0.49% (w/w); II: 0.46% (w/w); DIN: 0.31% (w/w)), whereas with gradient III the same threshold value was found as with the DIN-Method (III: 0.32% (w/w)).     

A phase I trial of recombinant tumor necrosis factor (rTNF) administered by continuous intravenous infusion in patients with disseminated malignancy

rTNF was administered to 28 patients with advanced metastatic cancers by continuous intra venous infusion for 5 consecutive days every 2 weeks. The dose levels were 30, 40, 70, 110, 180 and 290 µg/M²/day. Groups of 3 patients were started at each successive dose level and then on subsequent courses treated with the next dose level through 4 escalations as tolerated. Tumor types were: colon cancer 14; adenocarcinoma of unknown primary, 2; renal cancer, 2; leiomyosarcoma, 2; lung cancer, 1; prostate cancer, 1; thymona, 1; bladder cancer; 1; parotid, 1; Kaposi's sarcoma 2; ovarian 1. Toxicities included fever and chills (usually within the first 8 hours of infusion), fatigue, headache, decreased performance status, hypotension and CNS. All patients experienced leukopenia and thrombocytopenia within 24 hours or less after start of infusion with return of baseline by 72 hours after rTNF was stopped. The fall in these counts averaged 50% and was not dose related. No major changes in liver or renal function, coagulation or blood lipids were seen. Major dose limiting toxicities were fatigue, confusion, thrombocytopenia, seizures, hypotension and decreased performance status. NK cell activity measured against K562 target cells was augmented from about 30% target cell lysis to about 70% target cell lysis over the first 7 days of treatment. Two patients, both with metastatic colon cancer showed transient, objective tumor regression which did not qualify as a partial response. One patient with ovarian cancer had a stable partial response but progressed after 13 courses of treatment. Continuous infusion of TNF can be safely administered to patients with a maximum tolerated dose of only between 30 and 40 µg/M²/day. In addition, the MTD with continuous infusion seems to be highly variable and unpredictable from patient to patient. These data suggest that continuous infusion will not be an optimal way to administer TNF.     

Molecular evolution of enzyme structure: Construction of a hybrid hamster/Escherichia coli aspartate transcarbamoylase

Summary Aspartate transcarbamoylase (ATCase, EC 2.1.3.2) is the first unique enzyme common to de novo pyrimidine biosynthesis and is involved in a variety of structural patterns in different organisms. InEscherichia coli, ATCase is a functionally independent, oligomeric enzyme; in hamster, it is part of a trifunctional protein complex, designated CAD, that includes the preceding and subsequent enzymes of the biosynthetic pathway (carbamoyl phosphate synthetase and dihydroorotase). The complete complementary DNA (cDNA) nucleotide sequence of the ATCase-encoding portion of the hamster CAD gene is reported here. A comparison of the deduced amino acid sequences of the hamster andE. coli catalytic peptides revealed an overall 44% amino acid similarity, substantial conservation of predicted secondary structure, and complete conservation of all the amino acids implicated in the active site of theE. coli enzyme. These observations led to the construction of a functional hybrid ATCase formed by intragenic fusion based on the known tertiary structure of the bacterial enzyme. In this fusion, the amino terminal half (the “polar domain”) of the fusion protein was provided by a hamster ATCase cDNA subclone, and the carboxyl terminal portion (the “equatorial domain”) was derived from a clonedpyrBI operon ofE. coli K-12. The recombinant plasmid bearing the hybrid ATCase was shown to satisfy growth requirements of transformedE. coli pyrB ⁻ cells. The functionality of thisE. coli-hamster hybrid enzyme confirms conservation of essential structure-function relationships between evolutionarily distant and structurally divergent ATCases.     

Amplification of small signals by voltage-gated sodium channels in drone photoreceptors

Summary Photoreceptor cells of the drone,Apismellifera , have a voltage-gated Na⁺ membrane conductance that can be blocked by tetrodotoxin (TTX) and generates an action potential on abrupt depolarization: an action potential is triggered by the rising phase of a receptor potential evoked by an intense light flash (Autrum and von Zwehl 1964; Baumann 1968). We measured the intracellular voltage response to a small (9%), brief (30 ms) decrease in light intensity from a background, and found that its amplitude was decreased by 1M TTX. The response amplitude was maximal when the background intensity depolarized the cell to –38 mV. With intensities depolarizing the cell membrane to –45 to –33 mV the average response amplitude was decreased by TTX from 1.2mV to 0.5mV. TTX is also known to decrease the voltage noise during steady illumination (Ferraro et al. 1983) but, despite this, the ratio of peak-to-peak signal to noise was, on average, decreased by TTX. The results suggest that drone photoreceptors use voltage-gated Na⁺ channels for graded amplification of responses to small, rapid changes in light intensity.Abbreviations TTX tetrodotoxin - V _i intracellular potential with respect to the bath - V _o extracellular potential - V _m,V _i-V _o approximate transmembrane potential - S amplitude of the voltage response to an 8.9% decrease in light intensity - N voltage noise, usually measured as root mean square voltage deviation as described in Methods     

Influence of ammonium and extracellular pH on the amino and organic acid contents of suspension culture cells of Acer pseudoplatanus

The effects of supplied ammonium and nitrate on the amino and organic acid contents and enzyme activities of cell suspension cultures of Acer pseudoplatanus L. were examined. Regardless of nitrogen source the pH of the culture medium strongly affected the malate and citrate contents of the cells; these organic acid pools declined at pH 5, but increased at pH 7 and 8. Over a period of two days, ammonium had little effect on the responses of the organic acid pool sizes to the pH of the medium. In contrast, ammonium had a strong influence on amino acid pool sizes, and this effect was dependent on the pH of the medium. At pH 5 there was no increase in cell ammonium or amino acid contents, but at higher pH values cellular ammonium content rose, accompanied by accumulation of glutamine, glutamate and asparagine. Over several days, supplied ammonium led to an increase in activity of glutamate dehydrogenase irrespective of any changes in internal ammonium and amino acid contents. If the pH of the medium was allowed to fall below pH 4 in the presence of ammonium, phosphoenolpyruvate (PEP) carboxylase activity declined to a very low value over several days; at higher pH, the activity of this enzyme, and that of NAD malic enzyme and NAD malate dehydrogenase, remained substantial irrespective of whether the nitrogen source was NH⁺₄ or NO-₃.