A theoretical explanation of the Piper-Steenbjerg effect

The relation between plant yield and plant nutrient concentration is sometimes found to be negative, a phenomenon called the Piper-Steenbjerg (PS) effect. A model was used to examine the underlying causes of the PS effect, and the conditions under which it is most likely to occur. The model uses the nutrient productivity concept for plant growth and a nutrient uptake equation in which root growth rate and external nutrient concentration determine the uptake rate. The study suggests that the PS effect occurs when the fast growth of plants grown in an initially higher nutrient medium eventually leads to a more rapid depletion of external nutrients than the slow growth of plants grown in an initially lower nutrient medium. The fast growth of plants combined with a rapid decrease of nutrient uptake leads to a fall in plant nutrient concentration. When these large plants with very low nutrient concentrations are compared with the smaller, slow-growing plants, a PS effect may be found depending on the time at which the plants are harvested, and on the range of initial values of the external nutrient content. When it occurs, the effect is greatest when the depletion volume per unit new root (V_d) is lowest, and when the mobility of nutrients in the medium is highest (α=1). The results are sufficiently general to apply to a variety of nutrients, plant species and growth media.     

A theoretical explanation of “Concomitant resistance”

Concomitant resistance is a tumor growth dynamic which results when the growth of a second tumor implant is inhibited by the presence of the first. Recently, we modeled tumor growth in the presence of a regenerating liver after partial hepatectomy (Michelson and Leith,Bull. Math. Biol. 57, 345–366, 1995), with an interlocking pair of growth control triads to account for the accelerated growth observed in both tissues. We also modeled tumor dormancy and recurrence as a dynamic equilibrium achieved between proliferating and quiescent subpopulations. In this paper those studies are extended to initially model the concomitant resistance case. Two interlocking model systems are proposed. In one an interactive competition between the tumor implants is described, while in the other purely proportional growth inhibition is described. The equilibria and dynamics of each system when the coefficients are held constant are presented for three subcases of model parameters. We show that the dynamic called concomitant resistance can be real or apparent, and that if the model coefficients are held constant, the only way to truly achieve concomitant resistance is by forcing one of the tumors into total quiescence. If this is the true state of the inhibited implant, then a non-constant recruitment signal is required to insure regrowth when the inhibitor mass is excised. We compare these theoretical results to a potential explanation of the phenomenon provided by Prehn (Cancer Res. 53, 3266–3269, 1993).     

Innovative biomechanics for directional hearing in small flies

In humans and animals alike, the localization of sound constitutes a fundamental processing task of the auditory system. Directional hearing relies on acoustic cues such as the interaural amplitude and time differences and also, sometimes, the signal spectral composition. In small animals, such as insects, the auditory receptors are forcibly set close together, a design constraint imposing very short interaural distances. Due to the physics of sound propagation, the close proximity of the sound receivers results in vanishingly small amplitude and time cues. Yet, because of their directionality, small auditory systems embed original and innovative solutions that can be of inspirational value to some acute problems of technological miniaturization. Such ears are found in a parasitoid fly that acoustically locates its singing cricket host. Anatomically rather unconventional, the fly's auditory system is endowed with a directional sensitivity that is based on the mechanical coupling between its two hemilateral tympanal membranes. The functional principle permitting this directionality may be of particular relevance for technological applications necessitating sensors that are low cost, low weight, and low energy. Based on silicon-etching technology, early prototypes of sub-millimeter acoustic sensors provide evidence for directional mechanical responses. Further developments hold the promise of applications in hearing aid technology, vibration sensors, and miniature video-acoustic surveillance systems.     

Physics of directional hearing in the cricket Gryllus bimaculatus

In the cricket ear, sound acts on the external surface of the tympanum and also reaches the inner surface after travelling in at least three pathways in the tracheal system. We have determined the transmission gain of the three internal sound pathways; that is, the change of amplitude and phase angle from the entrances of the tracheal system to the inner surface of the tympanum. In addition, we have measured the diffraction and time of arrival of sound at the ear and at the three entrances at various directions of sound incidence. By combining these data we have calculated how the total driving force at the tympanum depends on the direction of sound. The results are in reasonable agreement with the directionality of the tympanal vibrations as determined with laser vibrometry.At the frequency of the calling song (4.7 kHz), the direction of the sound has little effect on the amplitudes of the sounds acting on the tympanum, but large effects on their phase angles, especially of the sound waves entering the tracheal system at the contralateral side of the body. The master parameter for causing the directionality of the ear in the forward direction is the sound wave entering the contralateral thoracic spiracle. The phase of this sound component may change by 130–140° with sound direction. The transmission of sound from the contralateral inputs is dominated by a very selective high-pass filter, and large changes in amplitude and phase are seen in the transmitted sounds when the sound frequency changes from 4 to 5 kHz. The directionality is therefore very dependent on sound frequency.The transmission gains vary considerably in different individuals, and much variation was also found in the directional patterns of the ears, especially in the effects of sounds from contralateral directions. However, the directional pattern in the frontal direction is quite robust (at least 5 dB difference between the 330° and 30° directions), so these variations have only little effect on how well the individual animals can approach singing conspecifics.Abbreviations CS contralateral spiracle - CT contralateral tympanum - IS ipsilateral spiracle - IT ipsilateral tympanum - P the vectorial sum of the sounds acting on the tympanum     

A theoretical explanation for some effects of calcium on the facilitation of neurotransmitter release

A quantal model developed earlier by the authors is recast in terms of common macroscopic variables and applied to the well-documented T, P, N/L, AE neuron network of a leech ganglion. The electrical potential of a neuron (φ) and the ion potentials (φ_a) for Na⁺, K⁺, Cl^? and Ca²⁺ are featured, though it proves possible to reduce the resulting set of coupled non-linear diffusion equations to a single pair whose admissible solutions are defined by a simple algebraic dispersion relation. Less than 30 s is required to solve the system for a functional interval of 2·25 s on a CYBER 175 computer using a modified Runge-Kutta algorithm, the program for which is given. Irreversible effects are included but reversibility is stressed, since the neurons are seen to exchange energy with their environment only in the immediate neighborhood of firing peaks. Plasma oscillations, resulting from a disruption of the Debye layer, offer a sound physical mechanism whereby transient currents and ion exchanges of the observed magnitudes may be generated.The total energy H and information rate Γ_I transferred across the neural membrane are also calculated in terms of φ and φ_a. It is shown that while φ is determined primarily by the K⁺ potential, Γ_I depends mainly on the Ca²⁺ potential together with its time derivatives, and H depends on both the K⁺ and Ca²⁺ potentials. This also makes it possible, not only to compare φ (t) solutions for each of the neurons in the incrementally-loaded network to experimental measurements of φ(t) made for similar stimulus levels, but also to trace the correlated flows of energy and information through the system. Nearly all of the distinctive features of the experimental curves are reproduced, despite the presence of such complexities as wide variations in pulse frequencies and amplitudes, sudden suppression of firing in one neuron when another begins to fire, refractory phases of different durations, and facilitation building to plateau values only slightly less than peak amplitudes for the sensory neurons.While both the energy and information curves possess sharp maxima which coincide with the firing pulses of the potential curves, those for Γ_I (t) are bimodal with rounded maxima that must represent transmissions associated with ion motions instead of polarization effects. In the case of the L and AE neurons, these curves exhibit a series of discrete energy/information packets that could easily produce the proportional increases in muscle tension actually observed.     

Chromosome banding in amphibia

In the chromosomes of 12 frog species of the suborder Diplasiocoela (Amphibia, Anura), the constitutive heterochromatin and the nucleolus organizer regions (NORs) have been specifically stained. On most of the chromosomes, aside from the centric heterochromatin, telomeric and interstitial C-bands were also found. The various C-bands display a very variable reaction to alkaline pretreatment; this indicates heterogeneity in the constitutive heterochromatin. Sex chromosomes could not be identified in any of the species studied. The number and chromosomal positions of the NORs vary quite strongly between species and between families. In 4 species of the genus Rana, there were, aside from the standard-NORs in chromosome pair 10, between 4 and 14 extra, small NORs detectable in the smaller chromosome pairs. As possible causal mechanism of these additional small NORs the reintegration of amplified rDNA during amphibian oogenesis is suggested. Q- or G-bands could only be recognized in mitotic prophase chromosomes. The strong spiralization of metaphase chromosomes prevents the differential demonstration of Q- or G-bands in the euchromatic regions.     

Chromosome banding in amphibia

A modified BrdU-Hoechst-Giemsa technique permitted the demonstration of easily reproducible replication patterns in the somatic chromosomes of Amphibia. These banding patterns allow for the first time a precise identification of all chromosomes and the analysis of the patterns of replication in the various stages of S-phase in Amphibia. Several possibilities for the use of this technique were demonstrated on three frog species of the family Ranidae, all differing greatly in their DNA-content. With this method, the homomorphic chromosome pair No. 4 in Rana esculenta could be identified as sex-specific chromosomes of the XX/XY-type. All male animals exhibit an extremely late replicating region in the Y-chromosome, which is lacking in the X-chromosome; in the female animals, both X-chromosomes replicate synchronously. These sex-specific chromosomes cannot be distinguished by other banding techniques. In the highly heteromorphic ZZ/ZW-sex chromosome system of Pyxicephalus adspersus a synchronous replication of the two Z-chromosomes of male animals and a very late replication of the short arm of the W-chromosome of female animals was demonstrated. These results support the assumption that there is no dosage compensation for Z-linked or X-linked genes by the sex chromosome inactivation mechanism in the sex chromosomes of Amphibia.     

A Golgi study on the hypothalamus of amphibia

Summary The neuronal typology in the hypothalamus of the frog and the crested newt was studied by the Golgi technique. In the newt, piriform, multipolar or cerebrospinal fluid (CSF)-contacting neurons of relatively primitive type, according to the classification of Ramón-Moliner, are encountered in the preoptic area. Moreover, magnocellular neurons are impregnated. In the frog the preoptic area shows a more varied typology. The posterior hypothalami of the frog and the newt exhibit mainly bipolar CSF-contacting and piriform neurons. These latter are generally tufted, but some bipolar of multipolar cells are encountered, especially in the frog. The simple anatomical organization of the amphibian hypothalamus corresponds well with the pattern of a generalized integrative area where multimodal sensory inputs converge — including visceral information from cerebrospinal fluid by means of hypothalamic CSF-contacting sensors — to regulate the neuroendocrine outflow.Work performed under CNR project Biology of reproduction     

Sound transmission and directional hearing in field crickets: neurophysiological studies outdoors

Many studies provide detailed behavioural and neurophysiological information on the ability of crickets to localize a sound source under ideal acoustic conditions, but very little is known about how they perform in real habitats. We investigated directional hearing of crickets in the field using a neurophysiological approach, by recording the activity of the two prominent, bilaterally homologous AN1 neurons simultaneously in a cricket’s habitat. The discharge and latency differences of the pair of neurons in response to conspecific chirps presented at different distances and directions were taken as a measure of directional information. The maximum hearing distance differed between individuals and weather conditions from 1 to 15 m (mean 9.2 m). Although the AN1 activity generally decreased with increasing distance, large fluctuations in the magnitude of responses occurred with distance, indicating that the intensity gradient over distance is often irregular. The directional information provided in the discharge differences of the two neurons also varied with distance. Again, there was no simple directional gradient on the transmission channel; rather, with decreasing distance to the source there were receiver locations providing suprathreshold responses, but no directional information. The consequences for the ability of field crickets to communicate acoustically close to the ground are discussed.     

Chromosome banding in amphibia

The chromosomes of 26 species of Anura from variously highly evolved groups were analysed with the fluorescent GC-specific antibiotics mithramycin and chromomycin A₃ as well as with the AT-specific quinacrine. The mithramycin- and chromomycin A₃-stainings generally resulted in a pattern of the constitutive heterochromatin opposite to the one obtained with quinacrine stain. The weaker a heterochromatic region fluoresces with quinacrine, the stronger is the intensity of the fluorescence achieved with mithramycin and chromomycin A₃. Some of the telomeric and interstitial heterochromatic regions, however, exhibit no enhanced fluorescence with any of the fluorochromes. The nucleolar constrictions of the nucleolus organizer regions (NORs) displayed the brightest mithramycin- and chromomycin A₃-fluorescence in the karyotypes and interphase nuclei of all species examined. The contrast of the brightly fluorescing GC-rich heterochromatin and of the NORs is considerably enhanced, when the non-fluorescent AT-specific oligopeptide distamycin A is employed as a counterstain. No banding patterns were observed with the fluorochromes in the euchromatic regions of the metaphase chromosomes; this is attributed to the strong spiralization of the anuran chromosomes. A cytochemical classification of the various chromatin types in the anuran chromosomes is discussed on the basis of the differential labelings found on the constitutive heterochromatin by means of the fluorochromes.This paper is dedicated to Professor Dr. Hans Bauer on the occasion of his 75th birthday