Slow oscillations in blood pressure via a nonlinear feedback model

Blood pressure is well established to contain a potential oscillation between 0.1 and 0.4 Hz, which is proposed to reflect resonant feedback in the baroreflex loop. A linear feedback model, comprising delay and lag terms for the vasculature, and a linear proportional derivative controller have been proposed to account for the 0.4-Hz oscillation in blood pressure in rats. However, although this model can produce oscillations at the required frequency, some strict relationships between the controller and vasculature parameters must be true for the oscillations to be stable. We developed a nonlinear model, containing an amplitude-limiting nonlinearity that allows for similar oscillations under a very mild set of assumptions. Models constructed from arterial pressure and sympathetic nerve activity recordings obtained from conscious rabbits under resting conditions suggest that the nonlinearity in the feedback loop is not contained within the vasculature, but rather is confined to the central nervous system. The advantage of the model is that it provides for sustained stable oscillations under a wide variety of situations even where gain at various points along the feedback loop may be altered, a situation that is not possible with a linear feedback model. Our model shows how variations in some of the nonlinearity characteristics can account for growth or decay in the oscillations and situations where the oscillations can disappear altogether. Such variations are shown to accord well with observed experimental data. Additionally, using a nonlinear feedback model, it is straightforward to show that the variation in frequency of the oscillations in blood pressure in rats (0.4 Hz), rabbits (0.3 Hz), and humans (0.1 Hz) is primarily due to scaling effects of conduction times between species.     

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.     

Breaking of nonlinear cylindrical plasma oscillations

Nonlinear axisymmetric cylindrical plasma oscillations are investigated analytically and numerically. It is shown that the breaking of strongly nonlinear oscillations is attributed to a singularity in the electron density and occurs several periods after the onset of an off-axis density maximum. For weakly nonlinear conditions, an analytic dependence of the breaking time of the oscillations on their amplitude is obtained based on the effect of intersection of electron trajectories and is shown to agree with numerical results.     

Properties and performance of microorganisms in chemostat culture

In the design of new processes for large-scale production of microbial cells and their products, fermentation technologists may well be led to consider the utility of continuous-flow culture systems, with their inherent high productivity potential. However, the properties and performance of microorganisms in chemostat culture are markedly different from those in batch culture and this must be taken into account. This review illustrates, with selected examples, the range of properties that are expressed differently (sometimes uniquely) in chemostat culture and points to the possible ways in which these chemostatinduced changes in microbial behaviour may be exploited.     

Intercellular communication via intracellular calcium oscillations

In this letter, we present the results of a simple model for intercellular communication via calcium oscillations, motivated in part by a recent experimental study. The model describes two cells (a "donor" and "sensor") whose intracellular dynamics involve a calcium-induced, calcium release process. The cells are coupled by assuming that the input of the sensor cell is proportional to the output of the donor cell. As one varies the frequency of calcium oscillations of the donor cell, the sensor cell passes through a sequence of N : M phase-locked regimes and exhibits a "Devil's staircase" behavior. Such a phase-locked response has been seen experimentally in pulsatile stimulation of single cells. We also study a stochastic version of the coupled two-cell model. We find that phase locking holds for realistic choices for the cell volume.     

Sustained oscillations via coherence resonance in SIR

Sustained oscillations in a stochastic SIR model are studied using a new multiple scale analysis. It captures the interaction of the deterministic and stochastic elements together with the separation of time scales inherent in the appearance of these dynamics. The nearly regular fluctuations in the infected and susceptible populations are described via an explicit construction of a stochastic amplitude equation. The agreement between the power spectral densities of the full model and the approximation verifies that coherence resonance is driving the behavior. The validity criteria for this asymptotic approximation give explicit expressions for the parameter ranges in which one expects to observe this phenomenon.     

Competition of plasmid-bearing Pseudomonas putida strains catabolizing naphthalene via various pathways in chemostat culture

Plasmid-carrying Pseudomonas putida strains degrade naphthalene through different biochemical pathways. The influence of various combinations of host bacteria and plasmids on growth characteristics and competitiveness of P. putida strains was studied in chemostat culture at a low dilution rate (D=0.05 h⁻¹) with naphthalene as the sole source of carbon and energy. Under naphthalene limitation, the plasmid-bearing strains degrading naphthalene that use catechol 1,2-dioxygenase for catechol oxidation (ortho pathway), were the most competitive. The strains bearing plasmids that control naphthalene catabolism via catechol 2,3-dioxygenase (meta pathway), were less competitive. Under these conditions the strain carrying plasmid pBS4, which encodes for naphthalene catabolism via gentisic acid, was the least competitive. Received: 24 February 1997 / Received revision: 22 May 1997 / Accepted: 25 May 1997     

Bulbocortical interplay in olfactory information processing via synchronous oscillations

Emergence of synchronous oscillatory activity is an inherent feature of the olfactory systems of insects, mollusks and mammals. A class of simple computational models of the mammalian olfactory system consisting of olfactory bulb and olfactory cortex is constructed to explore possible roles of the related neural circuitry in olfactory information processing via synchronous oscillations. In the models, the bulbar neural circuitry is represented by a chain of oscillators and that of cortex is analogous to an associative memory network with horizontal synaptic connections. The models incorporate the backprojection from cortical units to the bulbar oscillators in particular ways. They exhibit rapid and robust synchronous oscillations in the presence of odorant stimuli, while they show either nonoscillatory states or propagating waves in the absence of stimuli, depending on the values of model parameters. In both models, the backprojection is shown to enhance the establishment of large-scale synchrony. The results suggest that the modulation of neural activity through centrifugal inputs may play an important role at the early stage of cortical information processing.     

RANKL-induced TRPV2 expression regulates osteoclastogenesis via calcium oscillations

The receptor activator of NFκB ligand (RANKL) induces Ca(2+) oscillations and activates the Nuclear Factor of Activated T cells 1 (NFATc1) during osteoclast differentiation (osteoclastogenesis). Ca(2+) oscillations are an important trigger signal for osteoclastogenesis, however the molecular basis of Ca(2+) permeable influx pathways serving Ca(2+) oscillations has not yet been identified. Using a DNA microarray, we found that Transient Receptor Potential Vanilloid channels 2 (TRPV2) are expressed significantly in RANKL-treated RAW264.7 cells (preosteoclasts) compared to untreated cells. Therefore, we further investigated the expression and functional role of TRPV2 on Ca(2+) oscillations and osteoclastogenesis. We found that RANKL dominantly up-regulates TRPV2 expression in preosteoclasts, and evokes spontaneous Ca(2+) oscillations and a transient inward cation current in a time-dependent manner. TRPV inhibitor ruthenium red and tetracycline-induced TRPV2 silencing significantly decreased both the frequency of Ca(2+) oscillations and the transient inward currents in RANKL-treated preosteoclasts. Silencing of store-operated Ca(2+) entry (SOCE) proteins similarly suppressed both RANKL-induced oscillations and currents in preosteoclasts. Furthermore, suppression of TRPV2 also reduced RANKL-induced NAFTc1 expression, its nuclear translocation, and osteoclastogenesis. In summary, Ca(2+) oscillations in preosteoclasts are triggered by RANKL-dependent TRPV2 and SOCE activation and intracellular Ca(2+) release. Subsequent activation of NFATc1 promotes osteoclastogenesis.     

Dimensional analysis of nonlinear oscillations in brain, heart, and muscle

We present some numerical studies on the dimensional analysis of temporal oscillations observed in human electroencephalograms (EEG), heart rates, and muscle tremors. We show that it is insufficient to characterize the individual system by a single dimension value alone. We also present some detailed numerical analysis of the scaling structure of the attractors reconstructed from the time signal. Our methods are based on the concept of local gauge functions, which we derive from the raw signals and from transformed signals obtained through singular value decomposition. We are able to confirm and improve earlier results on the change of dimensionality of EEG signals. For heart rates we observe an increase of the dimensional complexity during sleep, and for muscle tremor data we find significant changes in the dimensionality depending on the isometrical contraction of the muscle. We attempt to indicate which factors are important in determining dimension estimates and where specific problems lie in each of the examples.     

Hippocampal-prefrontal connectivity predicts midfrontal oscillations and long-term memory performance

The hippocampus and prefrontal cortex interact to support working memory (WM) and long-term memory [1-3]. Neurophysiologically, WM is thought to be subserved by reverberatory activity of distributed networks within the prefrontal cortex (PFC) [2, 4-8], which become synchronized with reverberatory activity in the hippocampus [1, 4]. This electrophysiological synchronization is difficult to study in humans because noninvasive electroencephalography (EEG) cannot measure hippocampus activity. Here, using a novel integration of EEG and diffusion-weighted imaging, it is shown that individuals with relatively stronger anatomical connectivity linking the hippocampus to the right ventrolateral PFC (ventral Brodmann area 46) exhibited slower frequency neuronal oscillations during a WM task. Furthermore, subjects with stronger hippocampus-PFC connectivity were better able to encode the complex pictures used in the WM task into long-term memory. These findings are consistent with models suggesting that electrophysiological oscillations provide a mechanism of long-range interactions [9] and link hippocampus-PFC structural connectivity to PFC rhythmic electrical dynamics and memory performance. More generally, these results highlight the importance of incorporating individual differences when linking structure and function to cognition.     

Time-dependent regimes of a Bursian diode II: Characteristic features of nonlinear oscillations

A study is made of the physical phenomena characteristic of nonlinear oscillations in a Bursian diode in the regime with a virtual cathode. The question of how the shape of the oscillations varies as the beam current density increases is investigated for the first time. Sharp jumps in the time evolution of the convective current are revealed, and their causes are explained. The reason is found for the onset of long-lived electrons, and their properties are analyzed.     

Equality of average and steady-state levels in some nonlinear models of biological oscillations

Nonlinear oscillatory systems, playing a major role in biology, do not exhibit harmonic oscillations. Therefore, one might assume that the average value of any of their oscillating variables is unequal to the steady-state value. For a number of mathematical models of calcium oscillations (e.g. the Somogyi–Stucki model and several models developed by Goldbeter and co-workers), the average value of the cytosolic calcium concentration (not, however, of the concentration in the intracellular store) does equal its value at the corresponding unstable steady state at the same parameter values. The average value for parameter values in the unstable region is even equal to the level at the stable steady state for other parameter values, which allow stability. This holds for all parameters except those involved in the net flux across the cell membrane. We compare these properties with a similar property of the Higgins–Selkov model of glycolytic oscillations and two-dimensional Lotka–Volterra equations. Here, we show that this equality property is critically dependent on the following conditions: There must exist a net flux across the model boundaries that is linearly dependent on the concentration variable for which the equality property holds plus an additive constant, while being independent of all others. A number of models satisfy these conditions or can be transformed such that they do so. We discuss our results in view of the question which advantages oscillations may have in biology. For example, the implications of the findings for the decoding of calcium oscillations are outlined. Moreover, we elucidate interrelations with metabolic control analysis. This paper is dedicated to the memory of the late Reinhart Heinrich, who was the academic teacher of S.S. and, to a great extent, also of M.M.     

A nonlinear model for studying oscillations in the blood pressure control system

The idea that physiological systems sometimes include oscillations as part of their control function is a relatively new idea; the paper discusses the role of such oscillations in the regulation of arterial blood pressure and how they can be studied by modelling techniques. A nonlinear model is proposed which can be related directly to the physiology. This is seen as an important step because mainly previous studies of biological oscillations have used lumped equations, e.g. the Van der Pol equation, which do not possess this property. On the basis of the model, the oscillatory behaviour of the blood pressure control system is analysed by the application of the dual input describing function technique, a powerful analytical method which has wide application to the study of nonlinear oscillatory phenomena in physiology.The final section of the paper considers the digital simulation of the model by Z transform techniques and how the simulation can be used to study the interaction of respiratory and blood pressure control systems.     

Observation of nonlinear coupling between drift and ion-acoustic oscillations in low-frequency plasma turbulence

It is shown experimentally that the characteristics of structural ion-acoustic turbulence in a plasma are governed primarily by the development of density gradient-driven drift oscillations. The cyclicity of appearance and disappearance of drift wave packets and ensembles of ion-acoustic solitons in a steady-state turbulent plasma, as well as the correlation between them, is determined.