Central adaptation models of the vestibulo-ocular and optokinetic systems

A theoretical analysis of two models of the vestibulo-ocular and optokinetic systems was performed. Each model contains a filter element in the vestibular periphery to account for peripheral adaptation, and a filter element in the central vestibulooptokinetic circuit to account for central adaptation. Both models account for1 adaptation, i.e. a response decay to a constant angular acceleration input, in both peripheral vestibular afferent and vestibulo-ocular reflex (VOR) responses and2 the reversal phases of optokinetic after-nystagmus (OKAN) and the VOR and3 oscillatory behavior such as periodic alternating nystagmus. The two models differ regarding the order of their VOR transfer function. Also, they predict different OKAN patterns following a prolonged optokinetic stimulus. These models have behavioral implications and suggest future experiments.     

Behaviour of dictyostelium discoideum amoebae and Escherichia coli grown together in chemostat culture

When Dictyostelium discoideum amoebae and Escherichia coli were grown together in chemostat culture damped oscillations in the popullation densities of the organisms occurred followed by a sudden increase in bacterial numbers and a concommitant decrease in the number of amoebae. After the system had come to equilibrium altering the dilution rate resulted in a monotonic change in the experimental variables to new steady state levels. A square wave increase in the concentration of limiting nutrient in the feed medium during the oscillatory phase of culture produced a sinusoidal response indistinguishable from that prior to the perturbation. The results are more complicated than those predicted by simple models of microbial predator-prey dynamics although they correspond most nearly to models which incorporate saturation kinetics.     

A computational model of how an interaction between the thalamocortical and thalamic reticular neurons transforms the low-frequency oscillations of the globus pallidus

In Parkinson’s disease, neurons of the internal segment of the globus pallidus (GPi) display the low-frequency tremor-related oscillations. These oscillatory activities are transmitted to the thalamic relay nuclei. Computer models of the interacting thalamocortical (TC) and thalamic reticular (RE) neurons were used to explore how the TC-RE network processes the low-frequency oscillations of the GPi neurons. The simulation results show that, by an interaction between the TC and RE neurons, the TC-RE network transforms a low-frequency oscillatory activity of the GPi neurons to a higher frequency of oscillatory activity of the TC neurons (the superharmonic frequency transformation). In addition to the interaction between the TC and RE neurons, the low-threshold calcium current in the RE and TC neurons and the hyperpolarization-activated cation current (I _h) in the TC neurons have significant roles in the superharmonic frequency transformation property of the TC-RE network. The external globus pallidus (GPe) oscillatory activity, which is directly transmitted to the RE nucleus also displays a significant modulatory effect on the superharmonic frequency transformation property of the TC-RE network. Action Editor: John Rinzel     

Generating oscillatory bursts from a network of regular spiking neurons without inhibition

Avian nucleus isthmi pars parvocellularis (Ipc) neurons are reciprocally connected with the layer 10 (L10) neurons in the optic tectum and respond with oscillatory bursts to visual stimulation. Our in vitro experiments show that both neuron types respond with regular spiking to somatic current injection and that the feedforward and feedback synaptic connections are excitatory, but of different strength and time course. To elucidate mechanisms of oscillatory bursting in this network of regularly spiking neurons, we investigated an experimentally constrained model of coupled leaky integrate-and-fire neurons with spike-rate adaptation. The model reproduces the observed Ipc oscillatory bursting in response to simulated visual stimulation. A scan through the model parameter volume reveals that Ipc oscillatory burst generation can be caused by strong and brief feedforward synaptic conductance changes. The mechanism is sensitive to the parameter values of spike-rate adaptation. In conclusion, we show that a network of regular-spiking neurons with feedforward excitation and spike-rate adaptation can generate oscillatory bursting in response to a constant input.     

Neural mechanisms of target ranging in FM bats: physiological evidence from bats and frogs

Echolocating bats assess target range by the delay in echo relative to the emitted sonar pulse. Earlier studies in FM bats showed that a population of neurons in auditory centers above the inferior colliculus (IC) is tuned to echo delay, with different neurons tuned to different echo delays. A building block for delay-tuned responses is paradoxical latency shift (PLS), featuring longer response latencies to more intense sounds. PLS is first created in the IC, where neurons exhibit unit-specific quantum increase in response latency with increasing sound level. Other IC neurons display oscillatory discharges whose period is unit-specific and level tolerant, indicating that this is attributable to cell’s intrinsic properties. High-threshold inhibition of oscillatory discharge produces PLS, indicating that oscillatory discharge is a building block for PLS. To investigate the cellular basis of oscillatory discharges, we performed whole-cell patch-clamp recordings from IC neurons in leopard frogs (which also exhibit oscillatory discharges and PLS). These recordings show that IC neurons are heterogeneous displaying diverse biophysical phenotypes; each phenotype (and cell) has its own membrane time constant, input resistance, and strengths of I _h, I _kir, I _kv—these intrinsic properties give rise to cell-specific resonance which can be observed through current and afferent stimulations.     

Transient oscillations induced by delayed growth response in the chemostat

In this paper, in order to try to account for the transient oscillations observed in chemostat experiments, we consider a model of single species growth in a chemostat that involves delayed growth response. The time delay models the lag involved in the nutrient conversion process. Both monotone response functions and nonmonotone response functions are considered. The nonmonotone response function models the inhibitory effects of growth response of certain nutrients when concentrations are too high. By applying local and global Hopf bifurcation theorems, we prove that the model has unstable periodic solutions that bifurcate from unstable nonnegative equilibria as the parameter measuring the delay passes through certain critical values and that these local periodic solutions can persist, even if the delay parameter moves far from the critical (local) bifurcation values.When there are two positive equilibria, then positive periodic solutions can exist. When there is a unique positive equilibrium, the model does not have positive periodic oscillations and the unique positive equilibrium is globally asymptotically stable. However, the model can have periodic solutions that change sign. Although these solutions are not biologically meaningful, provided the initial data starts close enough to the unstable manifold of one of these periodic solutions they may still help to account for the transient oscillations that have been frequently observed in chemostat experiments. Numerical simulations are provided to illustrate that the model has varying degrees of transient oscillatory behaviour that can be controlled by the choice of the initial data.Mathematics Subject Classification: 34D20, 34K20, 92D25Research was partially supported by NSERC of Canada.This work was partly done while this author was a postdoc at McMaster.     

Bounds for generalized Dreitlein-Smoes models

The analysis of a previous paper obtaining bounds on the total population number of species (chemical or biological) described by the recently proposed Dreitlein-Smoes model of oscillatory kinetic systems, including diffusion, is extended to generalized models of the Dreitlein-Smoes type, describing a system ofS components withS>2. The results for such generalized models are analogous to those of the previous case. It is found that the effects of diffusion serve to restrict the region in the concentration space available to limitcycle type oscillations.     

Glucose‐dependent Insulin Modulation of Oscillatory Lipolysis in Perifused Rat Adipocytes

Objective: We showed glucose‐dependent lipolytic oscillations in adipocytes that are modulated by free fatty acids (FFAs). We hypothesized that the oscillations are driven by oscillatory glucose metabolism that leads to oscillatory formation of α‐glycerophosphate (α‐GP), oscillatory removal of long‐chain coenzyme A (LC‐CoA) by α‐GP to form triglycerides, and oscillatory relief of LC‐CoA inhibition of triglyceride lipases. This study examined the effect of insulin on this hypothesis. Research Methods and Procedures: Samples were collected every minute from perifused rat adipocytes during the basal state followed by insulin (±glucose) or isoproterenol (±insulin; n = 4 each). Results: Insulin caused a significant increase in glycerol release (18%), with a concomitant significant decrease in FFA release (38%). Without glucose, insulin had no effect on glycerol release while still decreasing FFA release (35%). Insulin (5 μU/mL) attenuated the response of lipolysis to isoproterenol (～3‐fold increase with isoproterenol vs. 2‐fold increase with insulin + isoproterenol). However, 1 mU/mL insulin amplified the lipolytic response (～5‐fold increase in glycerol release with insulin + isoproterenol), with a concomitant increase in FFA reesterification (no increase in FFA release compared with isoproterenol alone). Discussion: We interpret these results to be due to insulin's ability to increase glucose uptake and conversion to α‐GP, thus removing LC‐CoA inhibition of triglyceride lipases. While the physiological importance of lipolytic oscillations remains to be determined, we hypothesize that such an oscillation may play an important role in the delivery of FFAs to the liver, β cells, and other tissues.     

Sound-evoked oscillation and paradoxical latency shift in the inferior colliculus neurons of the big fruit-eating bat, <Emphasis Type="Italic">Artibeus jamaicensis</Emphasis>

Frequency tuning, temporal response pattern and latency properties of inferior colliculus neurons were investigated in the big fruit-eating bat, Artibeus jamaicensis. Neurons having best frequencies between 48–72 kHz and between 24–32 kHz are overrepresented. The inferior colliculus neurons had either phasic (consisting in only one response cycle at all stimulus intensities) or long-lasting oscillatory responses (consisting of multiple response cycles). Seventeen percent of neurons displayed paradoxical latency shift, i.e. their response latency increased with increasing sound level. Three types of paradoxical latency shift were found: (1) stable, that does not depend on sound duration, (2) duration-dependent, that grows with increasing sound duration, and (3) progressive, whose magnitude increases with increasing sound level. The temporal properties of paradoxical latency shift neurons compare well with those of neurons having long-lasting oscillatory responses, i.e. median inter-spike intervals and paradoxical latency shift below 6 ms are overrepresented. In addition, oscillatory and paradoxical latency shift neurons behave similarly when tested with tones of different durations. Temporal properties of oscillation and PLS found in the IC of fruit-eating bats are similar to those found in the IC of insectivorous bats using downward frequency-modulated echolocation calls.     

In vitro DNA-based predator-prey system with oscillatory kinetics

A coupled system of two isothermal in vitro DNA/RNA amplification reactions using different primers is modeled kinetically with realistic rate parameters and shown to exhibit oscillatory behavior in a flow reactor. One of the two isothermal amplification reactions acts as a predator of the other, the prey. The mechanism of the oscillatory behavior is analyzed in terms of a hierarchy of kinetic models. The work provides an insight into the choice of parameters for experiments. The latter are important in providing detailed insight into the complex processes of ecological interactions and their evolution.     

Model evaluation for glycolytic oscillations in yeast biotransformations of xenobiotics

Anaerobic glycolysis in yeast perturbed by the reduction of xenobiotic ketones is studied numerically in two models which possess the same topology but different levels of complexity. By comparing both models' predictions for concentrations and fluxes as well as steady or oscillatory temporal behavior we answer the question what phenomena require what kind of minimum model abstraction. While mean concentrations and fluxes are predicted in agreement by both models we observe different domains of oscillatory behavior in parameter space. Generic properties of the glycolytic response to ketones are discussed.     

Seasonal differences in the effects of oscillatory and uni‐directional flow on the growth and nitrate‐uptake rates of juvenile Laminaria digitata (Phaeophyceae)

The influence of oscillatory versus unidirectional flow on the growth and nitrate‐uptake rates of juvenile kelp, Laminaria digitata, was determined seasonally in experimental treatments that simulated as closely as possible natural environmental conditions. In winter, regardless of flow condition (oscillatory and unidirectional) or water velocity, no influence of water motion was observed on the growth rate of L. digitata. In summer, when ambient nitrate concentrations were low, increased water motion enhanced macroalgal growth, which is assumed to be related to an increase in the rate of supply of nutrients to the blade surface. Nitrate‐uptake rates were significantly influenced by water motion and season. Lowest nitrate‐uptake rates were observed for velocities <5 cm · s^?1 and nitrate‐uptake rates increased by 20%–50% under oscillatory motion compared to unidirectional flow at the same average speed. These data further suggested that the diffusion boundary layer played a significant role in influencing nitrate‐uptake rates. However, while increased nitrate‐uptake in oscillatory flow was clear, this was not reflected in growth rates and further work is required to understand the disconnection of nitrate‐uptake and growth by L. digitata in oscillatory flow. The data obtained support those from related field‐based studies, which suggest that in summer, when insufficient nitrogen is available in the water to saturate metabolic demand, the growth rate of kelps will be influenced by water motion restricting mass transfer of nitrogen.     

Neural organization of the locomotive oscillator

We study the relation of neural development, organization, and activity to behavior. We provide a model of the locomotive oscillator, a neural system supplying alternating stimulation to extensor and flexor muscles creating an oscillatory motion. We propose a protocol by which this neural system starting from unstructured, unconnected neural populations develops structure and function. The protocol is studied by both computer simulation and mathematical analysis. Our main results are 1 The locomotive oscillator self-organizes and maintains its organization, assuming certain properties of the neural populations. 2 Imperfections disturbing the functional adequacy of the neural populations may lead to the deterioration and disappearance of the oscillatory behavior. 3 The locomotive oscillator may fail to organize if the development is not staged in time.     

Locally oscillatory motion of RNA helix derived from linear relationships of backbone torsion angles

A linear relationship in each of the torsion angle pairs, α-β, β-?, ?-ζ, and α-γ, has been found by applying a statistical method based on the concept of circular variates to backbone torsion angle data of helical in yeast tTNA^Phe. A series of helical dimer models generated with these relationships have been found to be stereochemically acceptable, and the models also indicate that the backbone unit in the RNA helix is geometrically capable of an oscillatory motion with the distance of about 3.4 Å between adjacent bases. The motion of the backbone unit is analogous to that of a helical spring. The adjacent bases, because of being attached to the backbone, oscillate in a manner similar to the oscillatory dimer model proposed by Davis and Tinoco [Davis, R. C. & Tinoco, I., Jr. (1968) Biopolymers 6 , 223–242]. Here, the oscillation of the backbone unit in the RNA helix is discussed in terms of two geometrical quantities: the torsion (τ) and curvature (κ) of the helix. On these lines, a stereochemical model of RNA strand separation is proposed.     

Conditions for periodic solutions of volterra differential systems

As a contribution to the discussion of oscillatory models for interacting species it is shown that two-species Volterra models can never have limit cycles, and a complete enumeration is given of conditions which the parameters of these models must satisfy in order that a part of the phase space be filled with a family of closed curves; sketches of phase portraits are also given. These results complement and correct older results by Bautin and by Coppel on quadratic differential systems. The paper opens with a brief discussion of some more practical aspects of the ecological application of oscillatory models.     

Evaluation of the Oscillatory Interference Model of Grid Cell Firing through Analysis and Measured Period Variance of Some Biological Oscillators

Models of the hexagonally arrayed spatial activity pattern of grid cell firing in the literature generally fall into two main categories: continuous attractor models or oscillatory interference models. Burak and Fiete (2009, PLoS Comput Biol) recently examined noise in two continuous attractor models, but did not consider oscillatory interference models in detail. Here we analyze an oscillatory interference model to examine the effects of noise on its stability and spatial firing properties. We show analytically that the square of the drift in encoded position due to noise is proportional to time and inversely proportional to the number of oscillators. We also show there is a relatively fixed breakdown point, independent of many parameters of the model, past which noise overwhelms the spatial signal. Based on this result, we show that a pair of oscillators are expected to maintain a stable grid for approximately t = 5µ ³ /(4πσ) ² seconds where µ is the mean period of an oscillator in seconds and σ² its variance in seconds². We apply this criterion to recordings of individual persistent spiking neurons in postsubiculum (dorsal presubiculum) and layers III and V of entorhinal cortex, to subthreshold membrane potential oscillation recordings in layer II stellate cells of medial entorhinal cortex and to values from the literature regarding medial septum theta bursting cells. All oscillators examined have expected stability times far below those seen in experimental recordings of grid cells, suggesting the examined biological oscillators are unfit as a substrate for current implementations of oscillatory interference models. However, oscillatory interference models can tolerate small amounts of noise, suggesting the utility of circuit level effects which might reduce oscillator variability. Further implications for grid cell models are discussed.     

On the synchrony of steady state visual evoked potentials and oscillatory burst events

In this paper, we investigate the large-scale synchrony of EEG oscillatory bursts, during stimulation by a flickering square of light. Whereas most studies focus on averaged raw EEG responses, this study considers oscillatory events within EEG of single trials, which leads to various new insights. We recorded EEG signals before, during and after stimulation by a flickering square of light in medium (16 Hz) and high frequency (32 Hz) ranges. Similar oscillatory bursts, to those observed in spontaneous EEG, can be found in single-trial synchrony of steady state visual evoked potentials (SSVEP). These bursts are extracted from the EEG of single trials using bump modeling. Stochastic event synchrony method is applied to those events, which quantifies synchronies of oscillatory bursts on a large-scale basis. Those oscillatory patterns have a significantly higher degree of co-occurrence during SSVEP, uncorrelated with ongoing signal synchrony. It means that EEG oscillatory patterns are presumably an outcome of brain activity, rather than a mere side effect of ongoing EEG. They undergo a consistent reorganization during visual stimulation, preferentially along the visual pathway, depending on magno or parvo stimulations. Flickering stimuli may induce some cognitive side-effects depending on the stimulation frequency.

On the dynamics of a simple biochemical control circuit

The quantitative dynamics of a biochemical control circuit that regulates enzyme or protein synthesis by end-product feedback is analyzed. We first study a simplified repressible system, which is known to exhibit either a steady state or an oscillatory solution. By showing the analogy of thisn-dimensional system with a time-delay equation for a single variable the mechanism of the self-sustained oscillations becomes transparent. In a more sophisticated system we will find as well either steady state or oscillatory solutions. We determine the role of the parameters with respect to stability and frequency. The most general case will be treated by means of the concept of Lyapunov exponents.