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PubMed1998

Acidic deposition, plant pests, and the fate of forest ecosystems.

We present and analyze a nonlinear dynamical system modelling forest-pests interactions and the way they are affected by acidic deposition. The model includes mechanisms of carbon and nitrogen exchange between soil and vegetation, biomass decomposition and microbial mineralization, and defoliation by pest grazers, which are partially controlled by avian or mammalian predators. Acidic deposition is assumed to directly damage vegetation, to decrease soil pH, which in turn damages roots and inhibits microbial activity, and to predispose trees to increased pest attack. All the model parameters are set to realistic values except the inflow of protons to soil and the predation mortality inflicted to the pest which are allowed to vary inside reasonable ranges. A numerical bifurcation analysis with respect to these two parameters is carried out. Five functioning modes are uncovered: (i) pest-free equilibrium; (ii) pest persisting at endemic equilibrium; (iii) forest-pest permanent oscillations; (iv) bistable behavior with the system converging either to pest-free equilibrium or endemic pest presence in accordance with initial conditions; (v) bistable behavior with convergence to endemic pest presence or permanent oscillations depending on initial conditions. Catastrophic bifurcations between the different behavior modes are possible, provided the abundance of predators is not too small. Numerical simulation shows that increasing acidic load can lead the forest to collapse in a short time period without important warning signals.

Acid Rain↗
PubMed1997

A mathematical model for intracellular effects of toxins on DNA adduction and repair.

The process by which certain classes of toxins compounds or their metabolites may react with DNA to alter the genetic information contained in subsequent generations of cells or organisms are a major component of hazard associated with exposure to chemicals in the environment. Many classes of chemicals may form DNA adducts and there may or may not be a defined mechanism to remove a particular adduct from DNA independent of replication. Many compounds and metabolites that bind DNA also readily bind existing proteins; some classes of toxins and DNA adducts have the capacity to inactivate a repair enzyme and divert the repair process competitively. This paper formulates an intracellular dynamic model for one aspect of the action of toxins that form DNA adducts, recognizing a capacity for removal of those adducts by a repair enzyme combined with reaction of the toxin and/or the DNA adduct to inactivate the repair enzyme. This paper model illustrates the possible saturation of repair enzyme capacity by the toxin dosage and shows that bistable behavior can occur, with the potential to induce abrupt shifts away from steady state equilibria. The model suggests that bistable behavior, dose and variation between individuals or tissues may combine under certain conditions to amplify the biological effect of dose observed as DNA adduction and its consequences as mutation. A model recognizing stochastic phenomena also indicates that variation in within-cell toxin concentration may promote jumps between stable equilibria.

DNA Adducts↗
PubMed1999

Subharmonic resonance and chaos in forced excitable systems.

Forced excitable systems arise in a number of biological and physiological applications and have been studied analytically and computationally by numerous authors. Existence and stability of harmonic and subharmonic solutions of a forced piecewise-linear Fitzhugh-Nagumo-like system were studied in Othmer ad Watanabe (1994) and in Xie et al. (1996). The results of those papers were for small and moderate amplitude forcing. In this paper we study the existence of subharmonic solutions of this system under large-amplitude forcing. As in the case of intermediate-amplitude forcing, bistability between 1 : 1 and 2 : 1 solutions is possible for some parameters. In the case of large-amplitude forcing, bistability between 2 : 2 and 2 : 1 solutions, which does not occur in the case of intermediate-amplitude forcing, is also possible for some parameters. We identify several new canonical return maps for a singular system, and we show that chaotic dynamics can occur in some regions of parameter space. We also prove that there is a direct transition from 2 : 2 phase-locking to chaos after the first period-doubling bifurcation, rather than via the infinite sequence of period doublings seen in a smooth quadratic interval map. Coexistence of chaotic dynamics and stable phase-locking can also occur.

Cardiovascular Physiological Phenomena↗
PubMedDate not supplied

A cellular mechanism for graded persistent activity in a model neuron and its implications in working memory.

Working memory represents the ability of the brain to hold information for relatively short periods of time. Working memory is believed mediated by persistent neuronal firing. A broadly accepted hypothesis is that persistent activity is generated by reverberating synaptic input. However, single cortical neurons capable of showing persistent firing were recently reported. In this modeling study, we propose a cellular mechanism to generate persistent firing of multiple firing rates in single neurons. In the proposed mechanism, bistable concentrations of inositol 1,4,5-trisphosphate (IP3) and Ca2+ is achieved by IP3 formation and IP3-induced Ca2+ release from stores in multiple subcellular domains. A postsynaptic firing rate-dependent switching of these bistable elements can demonstrate graded persistent firing of the rat entorhinal neurons. Such a firing rate-dependent switching may be extended to a variety of intracellular Ca2+ signaling cascades.

Animals↗
PubMed1996

Experimental evidence of a temperature-related conformational change of the hydrophilic portion of gangliosides.

The present paper reports the experimental observation of an interesting thermodynamic process which could be biologically important: such behaviour, shown by some gangliosides, is likely to be peculiar of these glycosidic compounds as it has never been observed for other membrane-type amphiphilic molecules. In water solution, gangliosides have been found to present a bistable behaviour between two stable states (called A and B) which does not involve any change in the primary structure of the molecule. The interconversion between state A and state B, and vice versa, does not occur spontaneously, but has to be triggered by some external agent, which makes this system a potentially regulated process with important biological correlations. In the present experiments, state B is reached from state A with a temperature rise in the range 30-55 degrees C. The new state is stable regardless of any possible temperature cycle. The initial state A is then regained when the ganglioside solution is dried and the solute is redissolved. The two states are believed to correspond to two different conformations of the hydrophilic portion of the molecule. The bistable behaviour is shown by the gangliosides GM2, GM1, GD1a, GD1b and Fuc-GD1b, GT1b, however, does not show such an effect.

Animals↗
PubMed1984

Metrics of saccade responses to visual double stimuli: two different modes.

Earlier studies using visual double stimuli along the horizontal axis have revealed a strong averaging tendency in the saccadic system. This study shows averaging also for equally eccentric double stimuli with a modest difference in direction (delta phi = 30 deg). When the difference is enlarged (delta phi = 90 deg) the response pattern becomes bistable; i.e. the eye jumps near either one or the other stimulus. This bistable response mode is reflected also in saccade amplitude when double stimuli along the horizontal axis have a large difference in eccentricity. It is concluded that the saccadic system response mode to double stimuli depends on interstimulus spacing. Furthermore, both types of response can be shown to exist with double stimuli confined to one visual half-field.

Eye Movements↗
PubMed1991

The cyclopean ternus display and the perception of element versus group movement.

This study investigated the perception of bistable stroboscopic motion (Ternus display) with cyclopean stimuli created from retinal disparity embedded in dynamic random-element stereograms, the responses to which arise at binocular-integration levels of the visual system. To provide comparison data, observers were also tested with luminance-domain stimuli matched as closely as possible to their cyclopean counterparts. The results showed that the perception of element vs group movement was similar for both stimulus domains: element movement predominated at short interstimulus intervals (ISIs) while group movement predominated at long ISIs, and there was a tendency for a greater percentage of group movement to occur with a longer frame duration. These results cast suspicion on the interpretation of bistable motion that assumes element movement is a signature of a lower-level, short-range motion system whereas group movement is a signature of a higher-level, long-range system; both percepts are engendered at binocular-integration levels of vision.

Depth Perception↗
PubMed2005

Biological significance of autoregulation through steady state analysis of genetic networks.

Autoregulation of regulatory proteins is a recurring theme in genetic networks. Autoregulation is an important component of a genetic regulatory network besides protein-protein and protein-DNA interactions, stoichiometry, multiple binding sites and cooperativity. Although the biological significance of autoregulation has been studied before, its significance in presence of other mechanisms is not clearly enumerated. We have analyzed at steady state the significance of autoregulation in presence of other molecular mechanisms by considering hypothetical genetic networks. We demonstrate that autoregulation of a regulatory protein can impart amplification to the response. Further, autoregulation of an activator binding to the DNA as a dimer can introduce bistability, thus forcing the system to reside in two distinct steady states. In combination with autoregulation, cooperative binding can further increase the sensitivity and can yield a highly ultrasensitive response. We conclude that autoregulation with the help of other molecular mechanisms can impart distinct system level properties such as amplification, sensitivity and bistability. The results are further discussed in relation to various examples of genetic networks that exist in biological systems.

DNA↗
PubMed2005

Near-infrared laser illumination transforms the fluorescence absorbing X-Gal reaction product BCI into a transparent, yet brightly fluorescent substance.

The beta-galactosidase protein generated by the bacterial LacZ gene is widely used to map gene expression patterns. The ease of its use is only rivaled by green fluorescent protein, which can be used in combination with various other procedures such as immunocytochemistry, flow cytometry, or tract tracing. The beta-galactosidase enzymatic reaction potentially provides a more sensitive assay of gene expression than green fluorescent protein. However, the virtual impermeability and tendency to absorb light over a wide range limit the use of the most frequently used beta-galactosidase substrate, X-Gal, in combination with other fluorescent labeling procedures. Here, we provide details on a simple photoactivation procedure that transforms the light-absorbing X-Gal product, 5-bromo-4-chloro-3-indolyl (BCI) precipitate, into an intensely fluorescent product excited by 488 and 633 nm light. Photoactivation is achieved through exposure to 730 nm near-infrared light emitted from a femtosecond titanium-doped Sapphire laser. Photoactivation of BCI occurs in tissue sections suspended in buffered saline, glycerol, or even embedded in epoxy resin. A protocol for the use of BCI photoactivation is here provided. Importantly, the BCI photoactivated product is photoswitchable, displaying bistable photochromism. This permits the use of the fluorescent product in a variety of co-localization studies in conjunction with other imaging modalities. As with other bistable and photoswitchable products, the BCI reaction product shows concentration quenching at high density and can be degraded by continuous exposure to intense 730 nm illumination. Therefore, care must be taken in developing imaging strategies. Our findings have implications for the use of X-Gal in gene and protein detection and provide a novel substrate for high density digital information storage.

Animals↗
PubMed2004

Bio-switches: what makes them robust?

Ideas of how a system of interacting enzymes can act as a switch are based on the concept of bistability of a biochemical network. This means that, because of the very structure of a signaling pathway, the system can be in one of two stable steady states: active or inactive. Switching from one state to another may then occur in response to external stimuli or as a result of internal development. However, the bistability of a biochemical network might not be robust enough to be the sole mechanism behind bio-switching. On the basis of recent experimental data on the cell-cycle G2/M transition during starfish oocyte meiotic maturation, it is shown that cooperative phenomena--such as phase changes associated with clustering, dissolution of aggregates and so on--may play central roles in providing a decisive and irreversible transition.

Animals↗
PubMed2006

Theory of the normal waking EEG: from single neurones to waveforms in the alpha, beta and gamma frequency ranges.

The classic alpha rhythm, recorded intracortically, consists of alternating surface-negative troughs and briefer surface-positive peaks. The troughs are associated with neuronal hyperpolarization, the peaks with brief depolarization and burst firing. Each hyperpolarization is mainly a potassium potential, lasting approximately 100 ms. Depolarization and burst firing arise when this inactivates. In the desynchronized state, membrane potential is poised just below threshold. Firing in vivo is somewhat irregular and non-bursting. It is suggested that EEG bistability (classic alpha vs desynchronization) corresponds to bistability of single pyramidal cells. In vitro, paired pulses lead to depression of synaptic transmission in synapses linking two pyramidal cells, but to facilitation in synapses linking pyramidal cells to inhibitory neurones. These effects should be recruited by burst firing in vivo. Thus, enhancement of inhibitory and excitatory transmission occur respectively during the classic alpha rhythm, and the desynchronized state. As a result both states tend to be self-sustaining. In the desynchronized state high frequency (gamma or beta) activity predominates. In simulations, gamma activity has been modeled as the behaviour of cortical networks where populations of excitatory and inhibitory neurones interact. These simulations assume conduction times between neurones to be negligible. However, this is not true for long-distance interactions. Introduction into the models of plausible conduction delays should slow the oscillation frequency. The activated cortex can then produce not only gamma activity but also beta, and sometimes alpha activity. Thus, alpha frequencies can arise both in the "idling" cortex (classic alpha), and in the activated cortex, although the respective mechanisms are quite different.

Alpha Rhythm↗
PubMed2005

Ion excitation in a linear quadrupole ion trap with an added octopole field.

Modeling of ion motion and experimental investigations of ion excitation in a linear quadrupole trap with a 4% added octopole field are described. The results are compared with those obtained with a conventional round rod set. Motion in the effective potential of the rod set can explain many of the observed phenomena. The frequencies of ion oscillation in the x and y directions shift with amplitude in opposite directions as the amplitudes of oscillation increase. Excitation profiles for ion fragmentation become asymmetric and in some cases show bistable behavior where the amplitude of oscillation suddenly jumps between high and low values with very small changes in excitation frequency. Experiments show these effects. Ions are injected into a linear trap, stored, isolated, excited for MS/MS, and then mass analyzed in a time-of-flight mass analyzer. Frequency shifts between the x and y motions are observed, and in some cases asymmetric excitation profiles and bistable behavior are observed. Higher MS/MS efficiencies are expected when an octopole field is added. MS/MS efficiencies (N(2) collision gas) have been measured for a conventional quadrupole rod set and a linear ion trap with a 4% added octopole field. Efficiencies are chemical compound dependent, but when an octopole field is added, efficiencies can be substantially higher than with a conventional rod set, particularly at pressures of 1.4 x 10(-4) torr or less.

Ions↗
PubMed2003

Kinetic simulation of signal transduction system in hippocampal long-term potentiation with dynamic modeling of protein phosphatase 2A.

We modeled and analyzed a signal transduction system of long-term potentiation (LTP) in hippocampal post-synapse. Bhalla and Iyengar [Science 283(1999) 381] have developed a hippocampal LTP model. In the conventional model, the concentration of protein phosphatase 2A (PP2A) was fixed. However, it was reported that dynamic inactivation of PP2A was essential for LTP [J. Neurochem. 74 (2000) 807]. We introduced a dynamic modeling of PP2A; inactivation (phosphorylation) of PP2A by calcium/calmodulin-dependent protein kinase II (CaMKII) in the presence of calcium/calmodulin, self-activation (autodephosphorylation) of PP2A, and inactivation (dephosphorylation) of CaMKII by PP2A. This model includes complex feedback loops; both CaMKII and PP2A are autoactivated, while they inactivate each other. Moreover, we proposed an analysis strategy for model validation by applying the results of sensitivity analysis. In our system, calcineurin (CaN) played an essential role, rather than the activation of protein kinase C (PKC) as documented in the conventional model. From results of the analysis of our model, we found the following robustness as characteristics of bistability in our model: (1). PP2A reactions against calcium ion (Ca(2+)) perturbation; (2). PP2A inactivation against PP2A increase; (3). protein phosphatase 1 (PP1) activation against PF2A increase; and (4). PP2A reactions against PP2A initial concentration. These properties facilitated LTP induction in our system. We showed that another mechanism could introduce bistable behavior by adding dynamic reactions of PP2A.

Animals↗
PubMed2003

Dynamics of the cell cycle: checkpoints, sizers, and timers.

We have developed a generic mathematical model of a cell cycle signaling network in higher eukaryotes that can be used to simulate both the G1/S and G2/M transitions. In our model, the positive feedback facilitated by CDC25 and wee1 causes bistability in cyclin-dependent kinase activity, whereas the negative feedback facilitated by SKP2 or anaphase-promoting-complex turns this bistable behavior into limit cycle behavior. The cell cycle checkpoint is a Hopf bifurcation point. These behaviors are coordinated by growth and division to maintain normal cell cycle and size homeostasis. This model successfully reproduces sizer, timer, and the restriction point features of the eukaryotic cell cycle, in addition to other experimental findings.

Animals↗
PubMed1998

Simulation of the fertilization Ca2+ wave in Xenopus laevis eggs.

In the preceding paper Fontanilla and Nuccitelli (Biophysical Journal 75:2079-2087 (1998)) present detailed measurements of the shape and speed of the fertilization Ca2+ wave in Xenopus laevis eggs. In order to help interpret their results, we develop here a computational technique based on the finite element method that allows us to carry out realistic simulations of the fertilization wave. Our simulations support the hypothesis that the physiological state of the mature egg is bistable, i.e., that its cytoplasm can accommodate two alternative physiological Ca2+ concentrations: a low concentration characteristic of the prefertilization state and a greatly elevated concentration characteristic of the state following the passage of the wave. We explore this hypothesis by assuming that the bistability is due to the release and re-uptake properties of the endoplasmic reticulum (ER) as determined by inositol trisphosphate (IP3) receptor/Ca2+ channels and sarcoendoplasmic reticulum calcium ATPase (SERCA) pumps. When combined with buffered diffusion of Ca2+ in the cytoplasm, our simulations show that inhomogeneities in the Ca2+ release properties near the plasma membrane are required to explain the temporal and spatial dependences of the shape and speed of these waves. Our results are consistent with an elevated IP3 concentration near the plasma membrane in the unfertilized egg that is augmented significantly near the site of fertilization. These gradients are essential in determining the concave shape of the Ca2+ fertilization wave front.

Animals↗
PubMed2000

L-type calcium channels modulate glutamate-driven bursting activity in the nucleus accumbens in vivo.

The majority of adult nucleus accumbens medium spiny neurons exhibit a bistable membrane potential that fluctuates between a relatively hyperpolarized (Down) state (average=-76 mV) and a less hyperpolarized (Up) state (average=-60 mV) near firing threshold. During in vivo extracellular recordings from nucleus accumbens neurons, we used microiontophoresis to apply glutamate and selected neurons that fired in bursting patterns reflecting a subthreshold bistable membrane potential. The average frequency of bursts events was 0.85 Hz. The average burst duration was 392+/-3.5 ms, with an average of 13.4 spikes and an average spike frequency of 30.6+/-3.1 Hz per burst. To determine the involvement of the L-type calcium channel in the bursting pattern, we applied the benzothiazepine L-type calcium channel blocker, diltiazem. Diltiazem rapidly (<2 min) and reversibly decreased the burst duration by 29% and the frequency of spikes within a burst by 30% without changing the overall burst event frequency. The results provide the first in vivo electrophysiological evidence implicating an L-type calcium channel that modulates glutamate-induced burst firing of nucleus accumbens neurons.

Animals↗
PubMed2002

Critical switch of the metabolic fluxes by phosphofructo-2-kinase:fructose-2,6-bisphosphatase. A kinetic model.

A kinetic model for the bifunctional enzyme, phosphofructo-2-kinase:fructose-2,6-bisphosphatase, is analysed by application of the graph-theoretical method, considering comparable levels for all participants. Certain elementary reactions, distributed on the enzyme surface, are considered to be co-ordinated in a single conformational transition (a model of parallel molecular operations). The method allows us to identify in the kinetic scheme its destabilising sub-scheme as a branched cycle of elementary reactions. Under certain conditions this sub-scheme induces critical phenomena (bistability or oscillations). The computer calculations for the estimated parameter values fit well the experimental observations for this system. The model explains the periodic or bistable counterphase changes of the two opposing activities of this enzyme, observed after glucose perfusion of rat hepatic enzyme samples, and predicts drastic critical changes in kinetic behaviour induced by small external signals. The model also shows the necessity of the phosphoryl intermediate in the mechanism of the bisphosphatase for the critical kind of kinetic behaviour.

Adenosine Triphosphate↗
PubMed1992

Studies on re-entrant arrhythmias and ectopic beats in excitable tissues by bifurcation analyses.

A phase-plane bifurcation analysis is a useful way to theoretically understand how various types of arrhythmias may arise from excitable tissues. In this paper, we have performed phase-plane bifurcation analysis to characterize arrhythmogenic states in excitable tissues. To achieve this, we have first formulated a model which is simple enough to be mathematically tractable, yet captures the non-linear features of cardiac excitation and conduction. In this model, single cells are connected in a circular fashion by gap conductances. Each cell carries the following two types of currents: a passive outward current and an inward "excitable" current which contains an activation and an inactivation gate. The activation gate is responsible for the upstroke of action potential and inactivation gate is responsible for the termination of the plateau potential. With this model, we have constructed bifurcation diagrams as a function of a bifurcation parameter. The parameter chosen as the bifurcation parameter has the property of raising maximum diastolic potential while shorting the refractory period. Our analysis revealed the existence of three distinct multi-stable phases in certain ranges of the bifurcation parameter: (1) bistability between a rotor and a quiescent state, (2) bistability between rotor and ectopic beats, and (3) three stable states co-existing among quiescent state, rotor, and ectopic beats. In these three regions, external impulses exert very distinct effects: In region 1, a brief current pulse can annihilate a re-entrant arrhythmia to quiescence. To initiate re-entry from a quiescent tissue, however, it takes two pulses (a primary pulse followed by a premature pulse at a site different from the "primary" site). In region 2, a brief pulse can convert a re-entrant arrhythmia to ectopic beats. To convert the ectopic beats back to circus movement, these beats have to be suppressed by a few brief current pulses to initiate one-way propagation. Depending on the frequency and strength of impulses in region 3, the tissue can switch back and forth among quiescence, circus movement, and ectopic beats. For comparison, we have also included a more complete Beeler-Reuter cardiac cell model in our analysis and obtained essentially the same results. From the behavioral similarities of these models, we conclude that re-entrant and ectopic arrhythmias must be intrinsic properties of excitable tissues and external stimuli can convert one mode of arrhythmia to another in the multistability regions.(ABSTRACT TRUNCATED AT 400 WORDS)

Action Potentials↗