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PubMedDate not supplied

Liver system. V. Activation-extinction line of cyclic hepatocyte activities.

The excitation-extintion line of hepatocytes from an inert state towards the stabilization of a given activity is described. Within the cell, the switching on of any given activity is a competitive process among different activities. The process is driven by the influence field created in the environment of the Rappaport acinus by sinusoidal blood which changes its characteristics during its passage from the portal zone to the central vein. Every step of the excitation-extintion pathway follows the so-called law of autoisodiasostasis (AIS), i.e. it is characterized by an oscillatory motion between restoring (homopoiesis or HP) and working (homeorhesis or HR) states. Since the cyclical bistable equilibrium of AIS characterizes all conditions of hepatocyte activities, the AIS cycle can be defined a limit cycle.

Humans↗
PubMed2000

Switching characteristics of a model for biochemical-reaction networks describing autophosphorylation versus dephosphorylation of Ca2+/calmodulin-dependent protein kinase II.

Ca2+/calmodulin-dependent protein kinase II (CaMKII) has been suggested to participate in various cellular phenomena triggered by Ca2+ signalling. In the present study, we addressed the functional role of CaMKII in molecular-signal transduction in cells by mathematical modelling of putative biochemical-reaction networks thought to represent an essential part of molecular events responsible for CaMKII-related cellular phenomena. These networks include Ca2+/calmodulin-dependent threonine-286/287 (Thr286/287) autophosphorylation of CaMKII versus dephosphorylation of the enzyme. Computer simulation of the model was performed to examine the relation between the Ca2+-signalling pattern as an input and the resulting degree of Thr286/287 autophosphorylation (m) as an output. Under the simplified condition that the Ca2+ concentration during Ca2+ signalling was set to remain constant with time, the biochemical-reaction networks were shown to function as a switch. There is a threshold for gamma, a parameter representing the probability that the Thr286/287-dephosphorylated CaMKII subunit binds with the Ca2+/calmodulin complex; if gamma is above this threshold, m increases with time to a large degree (switch-on); otherwise, it remains near zero (switch-off). Mathematically, this sharp onset of m at the threshold can be accounted for by a change in the structure of the dynamic system describing the model, from bistability to monostability; this is analogous to the first-order phase transition in statistical physics. For the oscillatory time course of [Ca2+], switching characteristics were also shown with respect to the frequency and the maximum amplitude of the oscillation. These results suggest that graded information mediated by Ca2+ signalling is digitized into all-or-non information mediated by Thr286/287 autophosphorylation of CaMKII.

Animals↗
PubMed2002

Visual processing in the ketamine-anesthetized monkey. Optokinetic and blood oxygenation level-dependent responses.

We used optokinetic responses and functional magnetic resonance imaging (fMRI) to examine visual processing in monkeys whose conscious state was modulated by low doses (1-2 mg/kg) of the dissociative anesthetic ketamine. We found that, despite the animal's dissociated state and despite specific influences of ketamine on the oculomotor system, optokinetic nystagmus (OKN) could be reliably elicited with large, moving visual patterns. Responses were horizontally bidirectional for monocular stimulation, indicating that ketamine did not eliminate cortical processing of the motion stimulus. Also, results from fMRI directly demonstrated that the cortical blood oxygenation level-dependent (BOLD) response to visual patterns was preserved at the same ketamine doses used to elicit OKN. Finally, in the ketamine-anesthetized state, perceptually bistable motion stimuli produced patterns of spontaneously alternating OKN that normally would be tightly coupled to perceptual changes. These results, taken together, demonstrate that after ketamine administration cortical circuits continue to processes visual patterns in a dose-dependent manner despite the animal's behavioral dissociation. While perceptual experience is difficult to evaluate under these conditions, oculomotor patterns revealed that the brain not only registers but also acts upon its sensory input, employing it to drive a sensorimotor loop and even responding to a sensory conflict by engaging in spontaneous perception-related state changes. The ketamine-anesthetized monkey preparation thereby offers a safe and viable paradigm for the behavioral and electrophysiological investigation of issues related to conscious perception and anesthesia, as well as neural mechanisms of basic sensory processing.

Anesthetics, Dissociative↗
PubMed2006

Coexistence in the chemostat as a result of metabolic by-products.

Classical chemostat models assume that competition is purely exploitative and mediated via a common, limiting and single resource. However, in laboratory experiments with pathogens related to the genetic disease Cystic Fibrosis, species specific properties of production, inhibition and consumption of a metabolic by-product, acetate, were found. These assumptions were implemented into a mathematical chemostat model which consists of four nonlinear ordinary differential equations describing two species competing for one limiting nutrient in an open system. We derive classical chemostat results and find that our basic model supports the competitive exclusion principle, the bistability of the system as well as stable coexistence. The analytical results are illustrated by numerical simulations performed with experimentally measured parameter values. As a variant of our basic model, mimicking testing of antibiotics for therapeutic treatments in mixed cultures instead of pure ones, we consider the introduction of a lethal inhibitor, which cannot be eliminated by one of the species and is selective for the stronger competitor. We discuss our theoretical results in relation to our experimental model system and find that simulations coincide with the qualitative behavior of the experimental result in the case where the metabolic by-product serves as a second carbon source for one of the species, but not the producer.

Acetic Acid↗
PubMed2006

Cell-cell communication by quorum sensing and dimension-reduction.

Several bacterial taxa change their behavior if the population density exceeds a certain threshold. This phenomenon is the consequence of a communication system between the bacteria and is called quorum sensing (QS). Up to now, this phenomenon is mostly modeled at population level. However, new experimental techniques allow for single cell analysis. We introduce a modeling approach for the description of this QS system, including a discussion of the regulatory network and its bistable behavior. Based on this single-cell model we develop and analyze a spatially structured model for a cell population. Special attention is given to the scaling behavior w.r.t. the cell size (leading to an approximation theorem for stationary solutions) and its consequences for the interpretation of cell communication (QS versus diffusion sensing). Concluding, we apply the modeling approach to spatially structured experimental data.

4-Butyrolactone↗
PubMed2006

Modelling of predator-prey trophic interactions. Part II: three trophic levels.

A general class of lumped parameter models describing the local dynamics of a tri-trophic chain in a controlled environment is analyzed in detail. The trophic functions characterizing the interactions are defined only by some properties and allow us to treat both prey-dependent and ratio-dependent models in a unified manner. Conditions for existence and stability of extinction and coexistence equilibrium states are determined. Some peculiar aspects of the dynamics of the system depending on the bioecological parameters are presented, with particular attention to bistability situations, limit cycles and chaotic behaviours.

Animals↗
PubMed2003

Time representing cortical activities: two models inspired by prefrontal persistent activity.

Timing information in the range of seconds is significantly correlated with our behavior. There is growing interest in the cognitive behaviors that rely on perception, comparison, or generation of timing. However, little is known about the neural mechanisms underlying such behaviors. Here we model two different neural mechanisms to represent timing information in the range of seconds. In one model, a recurrent network of bistable spiking neurons shows a quasistable state that is initiated by a brief input and typically lasts for a few to several seconds. The duration of this quasistable activity may be regarded as the neural representation of internal time obeying a psychophysical law of time recognition. Another model uses synfire chains to provide the timing information necessary for predicting the times of anticipated events. In this model, the neurons projected to by multiple synfire chains are conditioned to fire synchronously at the times when an external event (GO signal) is expected. The conditioning is accomplished by spike-timing-dependent plasticity. The two models are inspired by the prefrontal activities of the monkeys engaging in different timing-information-related tasks. Thus, this cortical region may provide the timing information required for organizing various behaviors.

Action Potentials↗
PubMed2005

Dynamics of multifrequency coordination using parametric driving: theory and experiment.

The coupling of movement behavior and environmental signals has been extensively studied within the domain of rhythmic coordination tasks. However, in contrast to most traditional coordination studies, here we drive the coupled sensorimotor system far beyond the frequency regime in which these signals may be synchronized. Our goal is to identify the properties of the coupling between the human subject and the environment. Earlier studies have shown that the environmental signal may be parametrically coupled to the effectors. A necessary feature of parametrically driven oscillators is the existence of stable 1:1 and 1:2 coordination modes. Here, we test this prediction experimentally using a coordination paradigm in which subjects were asked to coincide peak finger flexion with an auditory metronome beat. The rate of the metronome was increased in steps of 0.5 Hz from 2.5 Hz to 12 Hz. It was observed that the subjects shifted involuntarily from a 1:1 to a 1:2 coordination mode at high driving frequencies, as predicted. These results are examined in the context of an extended form of the Haken-Kelso-Bunz (Haken et al. 1985) model (HKB) for bimanual coordination, which includes a parametric driving term (Jirsa et al. 2000). Unimanual coordination is treated as a special case of this extended model. An important feature of the HKB model is bistability and the presence of a phase transition from an anti-phase mode to in-phase mode of coordination. Our description of unimanual coordination leads to a mechanism for phase transitions that is distinct from that seen in the HKB model. The transition is mediated by the dynamics of both the amplitude and the phase of the oscillator. More generally, we propose the existence of two types of transitions in our extended theory, that is, phase-mediated and amplitude-mediated transitions. Both have characteristic features; in particular, their transients are mutually orthogonal in the plane spanned by the amplitude and phase of the oscillator. The analytical and numerical results of our theoretical model are demonstrated to compare favorably with our experimental results.

Adult↗
PubMed2000

Relative phase dynamics in perturbed interlimb coordination: stability and stochasticity.

Various stability features of bimanual rhythmic coordination, including phase transitions, have been modeled successfully by means of a one-dimensional equation of motion for relative phase obeying a gradient dynamics, the Haken-Kelso-Bunz model. The present study aimed at assessing pattern stability for stationary performance and estimating the model parameters (a, b, and Q) for the stochastic extension of this model. Estimates of a and b allowed for reconstruction of the potential defining the gradient dynamics. Two coordination patterns between the forearms (in-phase, antiphase) were performed at seven different frequencies. Model parameters were estimated on the basis of an exponential decay parameter describing the relaxation behavior of continuous relative phase following a mechanical perturbation. Variability of relative phase and relaxation time provided measures of pattern stability. Although the predicted inverse relation between pattern stability and movement frequency was observed for the lower tempo conditions, it was absent for the higher tempos, reflecting the influence of task constraints. No statistically significant differences in stability were observed between the two coordination modes, indicating the influence of intention. The reconstructed potential reflected the observed stability features, underscoring the adequacy of the parameter estimations. The relaxation process could not be captured adequately by means of a simple exponential decay function but required an additional oscillatory term. In accordance with previous assumptions, noise strength Q did not vary as a function of movement frequency. However, systematic differences in Q were observed between the two coordination modes. The advantages and (potential) pitfalls of using stationary performance of single patterns to examine the stability features of a bistable potential were discussed.

Computer Simulation↗
PubMed2001

Circular stationary solutions in two-dimensional neural fields.

Stationary solutions are studied in two-dimensional homogeneous neural fields of the lateral-inhibition type. It is shown that in extending the one-dimensional theory to two dimensions, new phenomena arise. We discuss the conditions for the existence of localized solutions analogous to the one-dimensional theory and show that they are no longer sufficient in two dimensions. We give indications for the existence of mono- and bistable dynamics as known from the one-dimensional theory and, additionally, a tri-stable type of dynamic in two-dimensional neural fields, where, depending on the input, excitation dies out, spreads without limit, or causes a stable localized excitation.

Brain↗
PubMed2000

Hopf bifurcations in multiple-parameter space of the hodgkin-huxley equations II. Singularity theoretic approach and highly degenerate bifurcations.

In the Hodgkin-Huxley equations (HH), we have identified the parameter regions in which either two stable periodic solutions with different amplitudes and periods and an equilibrium point or two stable periodic solutions coexist. The global structure of bifurcations in the multiple-parameter space in the HH suggested that the bistabilities of the periodic solutions are associated with the degenerate Hopf bifurcation points by which several qualitatively different behaviors are organized. In this paper, we clarify this by analyzing the details of the degenerate Hopf bifurcations using the singularity theory approach which deals with local bifurcations near a highly degenerate fixed point.

Axons↗
PubMed2000

Mode dynamics of interacting neural populations by bi-orthogonal spectral decomposition.

A system of coupled bistable Hopf oscillators with an external periodic input source was used to model the ability of interacting neural populations to synchronize and desynchronize in response to variations of the input signal. We propose that, in biological systems, the settings of internal and external coupling strengths will affect the behaviour of the system to a greater degree than the input frequency. While input frequency and coupling strength were varied, the spatio-temporal dynamics of the network was examined by the bi-orthogonal decomposition technique. Within this method, effects of variation of input frequency and coupling strength were analyzed in terms of global, spatial and temporal mode entropy and energy, using the spatio-temporal data of the system. We observed a discontinuous evolution of spatio-temporal patterns depending sensitively on both the input frequency and the internal and external coupling strengths of the network.

Animals↗
PubMed1997

Phase response characteristics of model neurons determine which patterns are expressed in a ring circuit model of gait generation.

In order to assess the relative contributions to pattern-generation of the intrinsic properties of individual neurons and of their connectivity, we examined a ring circuit composed of four complex physiologically based oscillators. This circuit produced patterns that correspond to several quadrupedal gaits, including the walk, the bound, and the gallop. An analysis using the phase response curve (PRC) of an uncoupled oscillator accurately predicted all modes exhibited by this circuit and their phasic relationships--with the caveat that in certain parameter ranges, bistability in the individual oscillators added nongait patterns that were not amenable to PRC analysis, but further enriched the pattern-generating repertoire of the circuit. The key insights in the PRC analysis were that in a gait pattern, since all oscillators are entrained at the same frequency, the phase advance or delay caused by the action of each oscillator on its postsynaptic oscillator must be the same, and the sum of the normalized phase differences around the ring must equal to an integer. As suggested by several previous studies, our analysis showed that the capacity to exhibit a large number of patterns is inherent in the ring circuit configuration. In addition, our analysis revealed that the shape of the PRC for the individual oscillators determines which of the theoretically possible modes can be generated using these oscillators as circuit elements. PRCs that have a complex shape enable a circuit to produce a wider variety of patterns, and since complex neurons tend to have complex PRCs, enriching the repertoire of patterns exhibited by a circuit may be the function of some intrinsic neuronal complexity. Our analysis showed that gait transitions, or more generally, pattern transitions, in a ring circuit do not require rewiring the circuit or any changes in the strength of the connections. Instead, transitions can be achieved by using a control parameter, such as stimulus intensity, to sculpt the PRC so that it has the appropriate shape for the desired pattern(s). A transition can then be achieved simply by changing the value of the control parameter so that the first pattern either ceases to exist or loses stability, while a second pattern either comes into existence or gains stability. Our analysis illustrates the predictive value of PRCs in circuit analysis and can be extended to provide a design method for pattern-generating circuits.

Animals↗
PubMed2007

Heterogeneity in expression of the Escherichia coli colicin K activity gene cka is controlled by the SOS system and stochastic factors.

Phenotypic diversity provides populations of prokaryotic and eukaryotic organisms with the flexibility required to adapt to and/or survive environmental perturbations. Consequently, there is much interest in unraveling the molecular mechanisms of heterogeneity. A classical example of heterogeneity in Escherichia coli is the subset (3%) of the population that expresses the colicin K activity gene (cka) upon nutrient starvation. Here, we report on the mechanism underlying this variable response. As colicin synthesis is regulated by the LexA protein, the central regulator of the SOS response, we focused on the role of LexA and the SOS system in the variable cka expression. Real-time RT-PCR showed that the SOS system, without exogenous DNA damage, induces moderate levels of cka expression. The use of cka-gfp fusions demonstrated that modification of the conserved LexA boxes in the cka promoter region affected LexA binding affinity and the percentage of cka-gfp expressing cells in the population. A lexA-gfp fusion showed that the lexA gene is highly expressed in a subset of bacteria. Furthermore, cka-gfp fusions cloned into higher copy plasmid vectors increased the percentage of cka-gfp positive bacteria. Together, these results indicate that the bistability in cka expression in the bacterial population is determined by (1) basal SOS activity, (2) stochastic factors and possibly (3) the interplay of LexA dimers at cka operator. Other LexA regulated processes could exhibit similar regulation.

Bacterial Proteins↗
PubMed2002

Static and dynamic behavior of a class of unstructured models of continuous bioreactors with growth associated product.

The static and dynamic behavior of a class of unstructured models of continuous bioprocesses, for which the product is growth associated, are analyzed using elementary concepts of singularity theory and continuation techniques. The class consists of models for which both the rates of utilization of limiting substrate and product formation are linearly proportional to the specific cell growth rate. The kinetic expressions are allowed to assume general forms of substrate and nonbiomass product. The steady-state analysis allows the derivation of analytical results and the construction of a useful picture in the models' parameter space delineating the different static behavior these models can predict, including unique steady states and bistability. The analysis of the dynamic behavior allows the derivation of general analytical conditions for the occurrence of periodic behavior in the models. It is also shown that the subclass of these models for which the specific cell growth rate expression is monotonic with respect to the nonbiomass product is unable to predict a stable oscillatory behavior regardless of the expression of the growth rate. These results illustrate the fundamental weakness of this class of unstructured models in predicting transient behavior in continuous cultures. The effect of kinetic and operating parameters on the stability characteristics of these models is also investigated.

Journal Article↗
PubMed2006

Differential control of active and silent phases in relaxation models of neuronal rhythms.

Rhythmic bursting activity, found in many biological systems, serves a variety of important functions. Such activity is composed of episodes, or bursts (the active phase, AP) that are separated by quiescent periods (the silent phase, SP). Here, we use mean field, firing rate models of excitatory neural network activity to study how AP and SP durations depend on two critical network parameters that control network connectivity and cellular excitability. In these models, the AP and SP correspond to the network's underlying bistability on a fast time scale due to rapid recurrent excitatory connectivity. Activity switches between the AP and SP because of two types of slow negative feedback: synaptic depression-which has a divisive effect on the network input/output function, or cellular adaptation-a subtractive effect on the input/output function. We show that if a model incorporates the divisive process (regardless of the presence of the subtractive process), then increasing cellular excitability will speed up the activity, mostly by decreasing the silent phase. Reciprocally, if the subtractive process is present, increasing the excitatory connectivity will slow down the activity, mostly by lengthening the active phase. We also show that the model incorporating both slow processes is less sensitive to parameter variations than the models with only one process. Finally, we note that these network models are formally analogous to a type of cellular pacemaker and thus similar results apply to these cellular pacemakers.

Action Potentials↗
PubMed2006

The impact of the allee effect in dispersal and patch-occupancy age on the dynamics of metapopulations.

In this paper, we introduce a Levins-type metapopulation model with empty and occupied patches, and dispersing population. We structure the proportion of occupied patches according to the patch-occupancy age. We observe that patch-occupancy age may destabilize the metapopulation, leading to persistent oscillations. We also allow for the dispersal rate to vary with the proportion of empty patches in a monotone or unimodal way. The unimodal dependence leads to multiple non-trivial equilibria and bistability when the reproduction number of the metapopulation R < 1 but greater than a lower critical value R(*). We show that the metapopulation will persist independently of its initial status if R > 1.

Animals↗
PubMed1989

The return of elastomer valves.

This paper concerns the heart valves to be used mainly in artificial hearts. Most of our tricusp semilunar valves are made of polyurethane. These valves have functioned in artificial hearts for up to 62 days, and have been implanted in sheep for 1 year without evidence of thromboembolism. Our valves have a wide opening, using redundant leaflets that are "bistable." Accelerated testing by air jet provides 1,000 closures per second. Regurgitation is measured in an apparatus with the help of a competent valve. All polyurethanes change with age, but Silastic does not.

Animals↗