Immunochemical and electrophysiological analyses of magnetically responsive neurons in the mollusc Tritonia diomedea

Tritonia diomedea uses the Earth’s magnetic field as an orientation cue, but little is known about the neural mechanisms that underlie magnetic orientation behavior in this or other animals. Six large, individually identifiable neurons in the brain of Tritonia (left and right Pd5, Pd6, Pd7) are known to respond with altered electrical activity to changes in earth-strength magnetic fields. In this study we used immunochemical, electrophysiological, and neuroanatomical techniques to investigate the function of the Pd5 neurons, the largest magnetically responsive cells. Immunocytochemical studies localized TPeps, neuropeptides isolated from Pd5, to dense-cored vesicles within the Pd5 somata and within neurites adjacent to ciliated foot epithelial cells. Anatomical analyses revealed that neurites from Pd5 are located within nerves innervating the ipsilateral foot and body wall. These results imply that Pd5 project to the foot and regulate ciliary beating through paracrine release. Electrophysiological recordings indicated that, although both LPd5 and RPd5 responded to the same magnetic stimuli, the pattern of spiking in the two cells differed. Given that TPeps increase ciliary beating and Tritonia locomotes using pedal cilia, our results are consistent with the hypothesis that Pd5 neurons control or modulate the ciliary activity involved in crawling during orientation behavior.     

Magnetic field perception in the Rainbow Trout, <Emphasis Type="Italic">Oncorhynchus</Emphasis> <Emphasis Type="Italic">mykiss</Emphasis>

In this study, we present evidence for the perception of different magnetic field parameters in a facultative anadromous fish species of the family Salmonidae. Magnetic field perception of the rainbow trout, Oncorhynchus mykiss, was demonstrated with a heartbeat conditioning test. The electrocardiogram was measured with subcutaneously inserted silver wire electrodes in freely swimming fish. We demonstrate a conditioned response (i.e. a significant longer interval between two heartbeats) to an intensity/inclination shift for three adult and two juvenile rainbow trouts. Moreover, a conditioned response to a 90° direction shift was demonstrated for three adult and two juvenile trouts. These findings support the hypothesis that the rainbow trout is able to perceive different magnetic field parameters. Furthermore, the study demonstrates magnetosensation in different developmental stages in the rainbow trout, i.e. juvenile and adult fish.     

A comparison of three different stochastic population models with regard to persistence time

Results are summarized from the literature on three commonly used stochastic population models with regard to persistence time. In addition, several new results are introduced to clearly illustrate similarities between the models. Specifically, the relations between the mean persistence time and higher-order moments for discrete-time Markov chain models, continuous-time Markov chain models, and stochastic differential equation models are compared for populations experiencing demographic variability. Similarities between the models are demonstrated analytically, and computational results are provided to show that estimated persistence times for the three stochastic models are generally in good agreement when the models are consistently formulated. As an example, the three stochastic models are applied to a population satisfying logistic growth. Logistic growth is interesting as different birth and death rates can yield the same logistic differential equation. However, the persistence behavior of the population is strongly dependent on the explicit forms for the birth and death rates. Computational results demonstrate how dramatically the mean persistence time can vary for different populations that experience the same logistic growth.     

A model for the interaction of two chemicals

We describe a method for studying the interaction of two anesthetic agents, Morphine and Midazolam, acting simultaneously in the same individual. Representing the levels of the two chemicals by diffusion processes, we assume their interaction is governed by a linear combination of the separate components. Pharmacological data is used to estimate the model parameters and, in particular, to determine the coefficient in the linear combination. This leads to the conclusion that the two chemicals have a counteractive effect.     

Extracellular noise-induced stochastic synchronization in heterogeneous quorum sensing network

Quorum sensing is a bacterial mechanism used to synchronize the coordinated response of a microbial population. Because quorum sensing in Gram-negative bacteria depends on release and detection of a diffusible signaling molecule (autoinducer) among a multicellular group, it is considered a simple form of cell-cell communication for the purposes of mathematical analysis. Stochastic equation systems have provided a common approach to model biochemical or biophysical processes. Recently, the effect of noise to synchronize a specific homogeneous quorum sensing network was successfully modeled using a stochastic equation system with fixed parameters. The question remains of how to model quorum sensing networks in a general setting. To address this question, we first set a stochastic equation system as a general model for a heterogeneous quorum sensing network. Then, using two relevant biophysical characteristics of Gram-negative bacteria (the permeability of the cell membrane to the autoinducer and the symmetry of autoinducer diffusion) we construct the solution of the stochastic equation system at an abstract level. The solution indicates that stable synchronization of a quorum sensing network is robustly induced by an environment with a heterogenous distribution of extracellular and intracellular noise. The synchronization is independent of the initial state of the system and is solely the result of the connectivity of the cell network established through the effects of extracellular noise.     

Pedal neuron 3 serves a significant role in effecting turning during crawling by the marine slug <Emphasis Type="Italic">Tritonia diomedea</Emphasis> (Bergh)

The marine nudibranch Tritonia diomedea crawls using its ciliated foot surface as the sole means of propulsion. Turning while crawling involves raising a small portion of the lateral foot margin on the side of the turn. The cilia in the lifted area no longer contribute to propulsion, and this asymmetry in thrust turns the animal towards the lifted side. Neurons located in the pedal ganglia of the brain contribute to these foot margin contractions. T. diomedea has a natural tendency to turn upstream (rheotaxis), and pedal flexion neuron Pedal 3 elicits foot margin lift and receives modulatory input from flow receptors. To assess the contribution of this single cell in turning behavior, two fine wires were glued to the surface of the brain over left and right Pedal 3. We determined that Pedal 3 activity is correlated with subsequent ipsilateral turns, preceding the lift of the foot margin and the change in orientation by a consistent interval. Both Pedal 3 cells show synchronous bursts of activity, and the firing frequency of the ipsilateral Pedal 3 increased before turns were observed to that side. Stimulation of the electrode over Pedal 3 proved sufficient to elicit an ipsilateral turn in Tritonia.     

Use of a magnetic compass for Y-axis orientation in premetamorphic newts (Triturus boscai)

Experiments were carried out to investigate whether premetamorphic larvae of Boscas newt (Triturus boscai) are capable of using the geomagnetic field for Y-axis orientation (i.e., orientation toward and away from shore). Larvae were trained outdoor in two different training configurations, using one training tank aligned along the magnetic north–south axis, with shore facing north, and another training tank positioned with its length along the east–west axis, with shore located west. After training, premetamorphic newts were tested in an outdoor circular arena surrounded by a pair of orthogonally aligned cube-surface coils used to alter the alignment of the Earths magnetic field. Each newt was tested only once, in one of four magnetic field alignments: ambient magnetic field (i.e., magnetic north at North), and three altered fields (magnetic north rotated to East, West, South). Distributions of magnetic bearings from tested larvae indicated that they oriented bimodally along the magnetic direction of the trained Y-axis. These findings demonstrate that T. boscai larvae are sensitive to the geomagnetic field and can use it for orienting along a learned Y-axis. This study is the first to provide evidence of Y-axis orientation, accomplished by a magnetic compass, in larval urodeles.     

A comparison of persistence-time estimation for discrete and continuous stochastic population models that include demographic and environmental variability

A discrete-time Markov chain model, a continuous-time Markov chain model, and a stochastic differential equation model are compared for a population experiencing demographic and environmental variability. It is assumed that the environment produces random changes in the per capita birth and death rates, which are independent from the inherent random (demographic) variations in the number of births and deaths for any time interval. An existence and uniqueness result is proved for the stochastic differential equation system. Similarities between the models are demonstrated analytically and computational results are provided to show that estimated persistence times for the three stochastic models are generally in good agreement when the models satisfy certain consistency conditions.     

A model for the oscillatory motion of single dynein molecules

Axonemal dynein is the molecular motor responsible for the rhythmic beating of eukaryotic cilia and flagella. An individual axonemal dynein molecule is capable of both unidirectional and oscillatory motion along a microtubule (Nature 393 (1998) 711). We propose a model which links the physical motion of a two-headed dynein molecule to its ATP hydrolysis cycle, and which exhibits both processive and oscillatory behaviors. A mathematical analysis of the model is used to make experimentally testable predictions.     

Bringing consistency to simulation of population models--Poisson simulation as a bridge between micro and macro simulation

Population models concern collections of discrete entities such as atoms, cells, humans, animals, etc., where the focus is on the number of entities in a population. Because of the complexity of such models, simulation is usually needed to reproduce their complete dynamic and stochastic behaviour. Two main types of simulation models are used for different purposes, namely micro-simulation models, where each individual is described with its particular attributes and behaviour, and macro-simulation models based on stochastic differential equations, where the population is described in aggregated terms by the number of individuals in different states. Consistency between micro- and macro-models is a crucial but often neglected aspect. This paper demonstrates how the Poisson Simulation technique can be used to produce a population macro-model consistent with the corresponding micro-model. This is accomplished by defining Poisson Simulation in strictly mathematical terms as a series of Poisson processes that generate sequences of Poisson distributions with dynamically varying parameters. The method can be applied to any population model. It provides the unique stochastic and dynamic macro-model consistent with a correct micro-model. The paper also presents a general macro form for stochastic and dynamic population models. In an appendix Poisson Simulation is compared with Markov Simulation showing a number of advantages. Especially aggregation into state variables and aggregation of many events per time-step makes Poisson Simulation orders of magnitude faster than Markov Simulation. Furthermore, you can build and execute much larger and more complicated models with Poisson Simulation than is possible with the Markov approach.     

A geometric model for initial orientation errors in pigeon navigation

All mobile animals respond to gradients in signals in their environment, such as light, sound, odours and magnetic and electric fields, but it remains controversial how they might use these signals to navigate over long distances. The Earth's surface is essentially two-dimensional, so two stimuli are needed to act as coordinates for navigation. However, no environmental fields are known to be simple enough to act as perpendicular coordinates on a two-dimensional grid. Here, we propose a model for navigation in which we assume that an animal has a simplified ‘cognitive map’ in which environmental stimuli act as perpendicular coordinates. We then investigate how systematic deviation of the contour lines of the environmental signals from a simple orthogonal arrangement can cause errors in position determination and lead to systematic patterns of directional errors in initial homing directions taken by pigeons. The model reproduces patterns of initial orientation errors seen in previously collected data from homing pigeons, predicts that errors should increase with distance from the loft, and provides a basis for efforts to identify further sources of orientation errors made by homing pigeons.     

随机Lotka-Volterra系统的稳定性

利用Lyapunov方法与K．lto公式及鞅的理论,研究了随机Lotka-Volterra系统正平衡点的全局渐近稳定性．得到了随机全局渐近稳定的主要定理,并以确定性系统的全局稳定性作为定理的推论．     

Dynamic models for animal orientation

The orientation of an animal moving in a plane towards a point-like mark is investigated. The control exerted by the optomotor (tracking) response on the motion of the animal is interpreted as an external force acting on the animal itself, which is modeled as a dipole or as a single point.The optomotor response is assumed as a rather general function of distance and angle. Differential equations governing the motion are derived and analyzed qualitatively and numerically. The role of distance-dependence and of the width of the visual field is investigated in detail and related to some typical kinds of paths in the plane, such as hitting the mark, coming close to the mark within a short distance, circular or undulating motion around the mark.A first version of this paper has been read at the Oberwolfach Conference on Mathematical Biology, June 1978     

Three-dimensional movements and swimming activity of a northern elephant seal

We attached a video system and data recorder to a northern elephant seal to track its three-dimensional movements and observe propulsive strokes of the hind flippers. During 6 h of recording, the seal made 20 dives and spent 90% of the time submerged. Average dive duration, maximum depth and swimming speed were 14.9 min+/-6.1 S.D., 289 m+/-117 S.D. and 1.1 m s(-1)+/-0.12 S.D., respectively. The distance swum during a dive averaged 925 m+/-339 S.D., and the average descent and ascent angles were 41 degrees +/-18 S.D. and 50 degrees +/-21 S.D., respectively. Dive paths were remarkably straight suggesting that the seal was navigating while submerged. We identified three modes of swimming based on the interval between propulsive strokes: continuous stroking; stroke-and-glide swimming; and prolonged gliding. The seal used continuous stroking from the surface to a mean depth of 20 m followed by stroke-and-glide swimming. Prolonged gliding started at a mean depth of 60 m and continued to the bottom of dives. For dives to depths of 300 m or more, 75% of the descent time was spent in prolonged gliding and 10% in stroke-and-glide swimming, amounting to 5.9-9.6 min of passive descent per dive. Average swimming speed varied little with swimming mode and was not a good indicator of propulsive effort. It appears that the seal can use prolonged gliding to reduce the cost of transport and increase dive duration. Energetically efficient locomotion may help explain the long and deep dives that routinely exceed the theoretical aerobic dive limit in this species.     

Stochastic aggregative responses and spatial patterns of parasitism in patchy host-parasitoid interactions

Summary Assuming random search by parasitoids within host-containing patches, and a constant search rate, current host-parasitoid models suggest that positive searching time aggregation by parasitoids in patches of high host density should tend to produce spatially density dependent parasitism at the patch level. However, these models view the aggregative response as a deterministic process, ignoring variability in searching time (T _s) allocation among patches of equal host density, and it is not clear that stochastic analogues of these deterministic models would predict the same result.This question is examined by adding a stochastic aggregative response to the well-known random parasitoid equation, the deterministic equation on which most existing models have been based. Simulations, based on data collected in an earlier laboratory study, indicate that this stochastic model generates very different relationships between parasitoid searching behavior and spatial patterns of parasitism than are predicted using the deterministic approach. The stochastic model suggests that positive aggregative responses, in which patches of high host density receive larger allocations of searching time (on the average) than patches containing lower densities, may fail to produce spatially density dependent parasitism at the patch level if searching time allocation is also more variable at the higher densities. Similarly, a flat response, in which mean searching times do not vary among patches of different host density, may lead to density dependent, density independent, or inversely density dependent parasitism, depending on the variance of the searching time values among patches at different density levels. The different predictions generated by the deterministic and stochastic models can be explained on purely mathematical grounds.When models are written in units of total foraging time (T _TOT), different equations are usually required to describe the spatial features of host-parasitoid and predator-prey interactions. Because the model considered here is written in units of active searching time (T _s) it should, in cases in which the underlying assumptions hold, be capable of describing these different interactions in the framework of a single (unified) equation. This equation may also apply to some plant-herbivore systems and, to indicate its potential generality, might be referred to as a random forager equation.     

Parameter estimation for the distribution of single cell lag times

In Quantitative Microbial Risk Assessment, it is vital to understand how lag times of individual cells are distributed over a bacterial population. Such identified distributions can be used to predict the time by which, in a growth-supporting environment, a few pathogenic cells can multiply to a poisoning concentration level.We model the lag time of a single cell, inoculated into a new environment, by the delay of the growth function characterizing the generated subpopulation. We introduce an easy-to-implement procedure, based on the method of moments, to estimate the parameters of the distribution of single cell lag times. The advantage of the method is especially apparent for cases where the initial number of cells is small and random, and the culture is detectable only in the exponential growth phase.     

Analysis of the migration behaviour of single microtubules in electric fields

By video contrast microscopy, individual microtubules formed from pure tubulin in the presence of taxol were studied in constant electric fields. At nearly physiological conditions, i.e., in a buffer at pH 6.8 and 120 mM ionic strength, suspended microtubules moved towards the anode with an electrophoretic mobility of approximately 2.6 x 10(-4) cm(2)/V s, corresponding to an unbalanced negative charge of 0.19 electron charges per tubulin dimer. Strikingly, this value is lower by a factor of at least 50 than that calculated from crystallographic data for the non-assembled tubulin dimer. Moreover, the taxol-stabilized microtubules had an isoelectric point of about pH 4.2 which is significantly lower than that known for the tubulin monomers. This indicates that microtubule formation is accompanied by substantial changes of charge distribution within the tubulin subunits. Constant electric fields were shown to affect also the orientation of microtubules gliding across a kinesin-coated surface at pH 6.8.