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.     

Local mutagenesis of Rous sarcoma virus: The major sites of tyrosine and serine phosphorylation of p60src are dispensable for transformation

We have constructed mutants of Rous sarcoma virus expressing p60^src that are underphosphorylated on serine or tyrosine, by linker insertion or insertion/ deletion into cloned Rous sarcoma virus DNA, and recovery of mutant virus by transfection of chicken embryo fibroblasts. Cells infected with mutants whose p60^src lack the major site of either serine or tyrosine phosphorylation were morphologically transformed and formed colonies in soft agar. The tyrosine kinase activities of the mutant p60^src measured in vivo and in vitro were close to the wild type activity. Peptide mapping showed that phosphorylation on tyrosine and serine of p60^src is independent: the major phosphorylated tyrosine and the major phosphorylated serine can each be phosphorylated in the absence of phosphorylation of the other.     

Rates of mutant structural chromosome rearrangements in human fetuses: data from prenatal cytogenetic studies and associations with maternal age and parental mutagen exposure.

In 27,225 prenatal cytogenetic studies of amniotic fluid reported to the New York State Chromosome Registry and the United States Interregional Chromosome Register System, there were 61 cases with a structural chromosomal abnormality not known inherited, a rate per 1,000 of 2.24. Of these 33, 1.21 per 1,000 were known de novo and nonmosaic; consequently, the rate of events resulting from germinal mutation is highly likely to be between these two limits. The rates per 1,000 of unbalanced abnormalities were 0.59-1.29; of balanced abnormalities, 0.62-0.96; of balanced Robertsonian translocations, 0.22-0.29; and of unbalanced Robertsonian translocations, 0.07-0.11. The rates of fetuses with supernumerary markers and fragments were unexpectedly high: 0.26-0.70 per 1,000. These abnormalities were associated with increased maternal age (38.0 +/- 5.4 to 38.4 +/- 3.6 compared to 35.6 +/- 4.3 in controls), but even after adjustment for the bias to preferential study of older women, the observed rates of these supernumerary abnormalities were greater than would be expected from live-birth studies or rates estimated in all recognized conceptuses. There were trends to elevated maternal age for the group of all balanced rearrangements, and to diminished maternal age for the nonsupernumerary, non-Robertsonian unbalanced rearrangements. In 136 women studied primarily because of exposure to a putative mutagen, a de novo deletion and an inversion not known inherited were detected. The rate of abnormality in these 136, 1.47%, was significantly greater than the rate of abnormality in the remainder: 0.14%-0.22%.     

Interaction of F1-ATPase, from ox heart mitochondria with its naturally occurring inhibitor protein. Studies using radio-iodinated inhibitor protein

The ox heart mitochondrial inhibitor protein may be iodinated with up to 0.8 mol 125I per mol inhibitor with no loss of inhibitory activity, with no change in binding affinity to submitochondrial particles, and without alteration in the response of membrane-bound inhibitor to energisation. Tryptic peptide maps reveal a single labelled peptide, consistent with modification of the single tyrosine residue of the protein. A single type of high-affinity binding site (Kd=96 . 10 (-9)M) for the inhibitor protein has been measured in submitochondrial particles. The concentration of this site is proportional to the amount of membrane-bound F1, and there appears to be one such site per F1 molecule. The ATp hydrolytic activity of submitochondrial particles is inversely proportional to the occupancy of the high-affinity binding site for the inhibitor protein. No evidence is found for a non-inhibitory binding site on the membrane or on other mitochondrial proteins. In intact mitochondria from bovine heart, the inhibitor protein is present in an approx. 1:1 ratio with F1. Submitochondrial particles prepared by sonication of these mitochondria with MgATP contain about 0.75 mol inhibitor protein per mol F1, and show about 25% of the ATPase activity of inhibitor-free submitochondrial particles. Additional inhibitor protein can be bound to these particles to a level of 0.2 mol/mol F1, with consequent loss of ATPase activity. If MgATP is omitted from the medium, or inhibitors of ATP hydrolysis are present, the rate of combination between F1 and its inhibitor protein is very much reduced. The equilibrium level of binding is, however, unaltered. These results suggest the presence of a single, high-affinity, inhibitory binding site for inhibitor protein on membrane-bound F1. The energisation of coupled submitochondrial particles by succinate oxidation or by ATP hydrolysis results in both the dissociation of inhibitor protein into solution, and the activation of ATP hydrolysis. At least 80% of the membrane-bound F1-inhibitor complex responds to this energisation by participating in a new equilibrium between bound and free inhibitor protein. This finding suggests that a delocalised energy pool is important in promoting inhibitor protein release from F1. Dissipation of the electrochemical gradient by uncouplers, or the binding of oligomycin or efrapetin effectively blocks energised release of the inhibitor protein. Conversely, the addition of aurovertin or adenosine 5'--[beta, lambda--imido]triphosphate enhances energy-driven release. The mode of action of various inhibitors on binding and energised release of the protein inhibitor is discussed.     

Determination of the molecular conformation of beta-D-O2,2'-cyclouridine in aqueous solution by proton magnetic resonance spectroscopy

The solution conformation of β-D -O²,2′-cyclouridine has been determined at 27 and 88°C in D₂O by proton magnetic resonance spectroscopy. The conformation is described in terms of a fixed syn-like sugar-base torsional angle, a type S furanose ring conformation (similar to 2′-endo), and a temperature-dependent exocyclic C(4)′–C(5′) rotamer population containing approximately 50% of the gauche-gauche form at 27°C. β-D -O²,2′-Cyclouridine 5′-phosphate likewise possesses a type S furanose ring conformation.