Global bifurcations of a periodically forced nonlinear oscillator

The effects of periodic pulsatile stimulation on a simple mathematical model of biological oscillations, called the radial isochron clock (RIC), are investigated as a function of stimulus frequency and amplitude. This system can be reduced to a two parameter, one-dimensional circle map. Numerical and topological methods are used to give a very detailed picture of the observed bifurcations over the complete range of parameters. The bifurcations are generic for a class of models which generalize the RIC.     

Holling's “hungry mantid” model for the invertebrate functional response considered as a Markov process. III. Stable satiation distribution

In this paper, we study an analytical model describing predatory behaviour. It is assumed that the parameter describing the predator's behaviour is its satiation. Using semigroup methods and compactness arguments we prove that a stable satiation distribution is reached if t. Furthermore, using a Trotter-Kato theorem we justify the transition to the much simpler problem that is obtained if the prey biomass tends to zero.     

Distribution of myosin and the glial fibrillary acidic protein (GFA Protein) in rat spinal cord and in the human frontal cortex as revealed by immunofluorescence microscopy

Summary The glial fibrillary acidic (GFA) protein and myosin were localized in rat spinal cord and human frontal cortex using specific antibodies against GFA protein from human spinal cord and highly purified smooth myosin from chicken gizzard by means of an indirect immunofluorescence microscopical approach. A strong GFA protein and myosin immunoreactivity was found in astrocytes of the white and grey matter and in the external glial limitans membrane. The very fine branches of astrocytic processes stained with antiGFA protein, but not with anti-myosin. Similar results were obtained with the human frontal cortex, where myosin antibodies failed to reveal the very fine branches of protoplasmic astrocytes.As a whole, staining with the GFA protein antiserum was more crisp than with the myosin antibody.Thanks are due to Professor J.R. Wolff, Max-Planck Institute for Biophysical Chemistry, Göttingen, for stimulating discussions, to Ursula König, Christa Mahlmeister and Renate Steffens for skilful technical assistance, and to Heidi Waluk for the photographic workSupported by grants from Deutsche Forschungsgemeinschaft (Br 634/1, Dr 91/1, Un 34/4, Ste 105/19)Dedicated to Prof. Dr. med. H. Leonhardt on the occasion of his 60. birthday     

Correlation between temperature range of growth and structural transitions in membranes and lipids of Escherichia coli K12

Purified cytoplasmic and outer membranes isolated from cells of wild-type Escherichia coli grown at different temperatures were labelled with 1,6-diphenyl-1,3,5-hexatriene and anlyzed using fluorescence polarization techniques. Lipids extracted from the membranes were similarly analyzed using fluorescence polarization. The thermotropic structural transition in outer membranes changed as a function of growth temperature. The structural transition in cytoplasmic membranes and lipids extracted from either cytoplasmic or outer membranes did not change with growth temperature. These data suggest that adaptive changes which occur in the outer membrane determine the temperature range of growth of E. coli. These changes apparently require alterations in outer membrane components other than phospholipids.     

Rate of polymer formation and entropy production during competitive replication

Summary The rate of increase in the mean polymer formation rate constant during competitive replication byQ RNA variants (Kramer et al., 1974) has been shown to agree statistically with the variance in their formation rate constants. This result demonstrates that Fisher's fundamental theorem of natural selection (Fisher, 1930) can define time variations in the mean rate of synthesis for a heterogeneous population of replicating polymers. It was also revealed that RNA replication, far from equilibrium, accompanied a progressive decrease in the order of the entropy production derivative, with respect to time, that reached a maximum (with the next higher order being zero). Maximization of entropy at equilibrium, in compliance with the second law of thermodynamics, therefore appears as a natural extension of the earlier non-equilibrium pattern of entropy production within the system. The order of the zero-valued entropy production derivative was shown to be determined by the chemical affinity, and its rate of decrease was specified by the mean polymer formation rate constant.     

Effects of water conductivity on electrocommunication in the weak-electric fish Brienomyrus niger (Mormyriformes)

A characteristic electric organ discharge display in social encounters between mormyrid fish is a temporary discharge cessation. Using this response, we have investigated the useful range of electrocommunication under different water conductivity conditions in the mormyrid Brienomyrus niger. An individual fish was confined to a porous ceramic shelter tube and moved from a starting distance of 380 cm toward a similarly confined conspecific until discharge, cessation occurred. The moved fish was subsequently returned to its original, position. Water conductivity affects the peak-to-peak source voltage of the electric organ and the sensitivity of the fish's electroreceptors. Within a range of 10 to 36 000 μS/cm, the peak-to-peak amplitude of the electric organ discharge declined as a power function. At 120 μS/cm, the amplitude was 50%, and at 300μS/cm, 30% of the 10 μS/cm value. The interfish distance at which discharge cessation occurred and the associated electric field gradients were dependent on water conductivity and upon the spatial orientation of the two fish (end-to-end or parallel orientations of their shelter tubes). The respective ranges were from 135 cm and 0.02 mV/cm at 52 μS/cm (parallel orientation) to 22 cm and 0.36 mV/cm at 678 μS/cm (end-to-end orientation). When the data for both tube orientations were combined, the relationship between water conductivity (x) and the distance at which discharge cessation occurred (y) could be expressed by a power function, y=K·x^a (with K=10^2.97 and a=?0.56). When an electrically ‘silent’ fish was moved away from its conspecific, a discharge resumption in the form of a high-frequency rebound occasionally effected changes in the other fish's discharge activity at distances up to 157 cm (with an associated electric, field gradient of 0.01 mV/cm under the lowest conductivity condition).     

Acute abdominal vagotomy reduces drinking to peripheral but not central angiotensin II

Rats were tested two or three days after bilateral abdominal vagotomy or a laparotomy control procedure for their drinking responses to subcutaneous (1 mg-kg-1) or intracerebroventricular (100 ng) injections of angiotensin II. Vagotomy delayed the initiation of drinking and decreased 60-min water intake after subcutaneous, but not after intracerebroventricular, angiotensin II. This is the shortest postoperative interval in which the decrease in drinking after systemic injection of angiotensin II by abdominal vagotomy has been observed. The failure of vagotomy to decrease the response to intracerebroventricular angiotensin II demonstrates that the deficit after subcutaneous injection was not a nonspecific effect of recent vagotomy. These results, therefore, suggest that the abdominal vagus is necessary for normal drinking in response to circulating angiotensin II. Furthermore, the selective and acute onset of the deficit is consistent with the loss of a specific, rather than tonic facilitatory, vagal mechanism for drinking after elevation of circulating angiotensin II levels. Finally, the results imply that the physiological mechanisms which mediate the drinking responses to central and peripheral angiotensin are not identical.     

Co-localization of ecdysteroid receptors and c-fos-like protein in the brain of Manduca sexta larvae

Summary The presence of c-fos, a marker for cell activation, was investigated in cerebral neurons actively expressing ecdysteroid receptors during larval-pupal development in the tobacco hornworm, Manduca sexta. Colocalization was accomplished by ecdysteroid autoradiography using the tritiated high affinity 20-hydroxyecdysone agonist ponasterone A and immunocytochemistry with an antibody to a peptide sequence which is highly conserved in both human and murine c-fos. Immunoreactivity to a c-fos-like protein(s) was present in nuclei of many neurons of all the developmental stages examined. However, with the exception of the optic lobe, cells expressing nuclear ecdysteroid receptors were more immunoreactive than non-ecdysteroid-binding neurons. These data suggest that ecdysteroid-induced gene activation and translation may involve c-fos expression. Offprint requests to: H.-J. Bidmon