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PubMed2005

Bistability explains threshold phenomena in protein aggregation both in vitro and in vivo.

Neurodegenerative disease can originate from the misfolding and aggregation of proteins, such as Amyloid-beta, SOD1, or Huntingtin. Fortunately, all cells possess protein quality control machinery that sequesters misfolded proteins, either refolding or degrading them, before they can self-associate into proteotoxic oligomers and aggregates. This activity is largely performed by the stress response chaperones (i.e., Hsp70). However, the expression level of molecular chaperones varies widely among cell types. To understand the potential consequence of this variation, we studied the process of protein aggregation in the presence of molecular chaperones using mathematical modeling. We demonstrate that protein aggregation, in the presence of molecular chaperones, is a bistable process. Bistability in protein aggregation offers an explanation for threshold transitions to high aggregate concentration, which are observed both in vitro and in vivo. Additionally, we show that slight variations in chaperone concentration, due to natural fluctuations, have important consequences in a bistable system for the onset of protein aggregation. Therefore, our results offer a possible theoretical explanation for neuronal vulnerability observed in vivo and the onset of neurodegenerative phenotypes in neurons lacking an effective heat-shock response.

Animals↗

PubMedDate not supplied

[The branching structure of the bistable dendrite].

A branching structure consisting of three bistable cylindrical branches was considered. Both stable and unstable solutions for the voltage distribution in such a structure, were obtained using the method developed in our laboratory. This made it possible to calculate the input current-voltage characteristic of the bistable branching structure, including unstable segments of this characteristic. Possible stable states of the structure when its proximal end is loaded by a resistance were determined. It is shown that the binary exclusive-OR could be accomplished by the elementary branching structure of a bistable dendrite. A model with overexcitation carried out by Ca-dependent K channels was developed. It is shown that the model parameters do not fall outside the physiological range of values.

Calcium Channels↗

PubMed1978

A comparison of the "phrygian cap" deformity with bistable and gray scale ultrasound.

Sixteen patients with a "phrygian cap" deformity of the gall bladder seen with oral cholecystography were further evaluated with both bistable and gray scale ultrasound. The bistable technique produced internal echoes that were suspicious of gall stones. When this same area was reevaluated with the more accurate gray scale technique, the folded-fundus deformity was clearly visualized.

Cholelithiasis↗

PubMed1977

[Bistability of pyruvate production by E. coli ML30 in continuous culture].

The pyruvate production of E. coli ML30 in continuous cultures was investigated. In a glucose mineralsalt medium with ammonium as the limiting substrate two stable stationary states (bistability) of pyruvate concentration were obtained. The bistability was limited to dilution rates lower than 0.3 h-1 and connected with a decrease of the yield coefficient (Y Glc) from approximately 0.45 to approximately 0.1.

Culture Media↗

PubMed1977

[Bistability in the activity of glutamine synthetase in ammonium-limiting chemostat cultures of Escherichia coli ML 30].

The approximative estimation of the function micron([NH+4]) in cultures of E. coli ML 30 had shown that bistability of the ammonium concentration in ammonium limited continuous cultures could be possible (BERGTER et al. 1977). This phenomenon suggested a bistability in the regulation of ammonia assimilation. Therefore, the activity of one key enzyme of the two ammonia assimilation systems was measured. The distribution of the activity of glutamine synthetase in ammonia limited continuous cultures after different transition states confirmed this suggestion.

Ammonia↗

PubMed1993

Bistability, switches and working memory in a two-neuron inhibitory-feedback model.

It was reported earlier that an inhibitory-feedback network inspired by neostriatal circuitry may exhibit a bistable character and spontaneous switching phenomenon within the neuronal activity. In the presence of noise and external excitation, a few local neurons switch "on" and generate streams of impulses while other neurons remain quiescent. In time, the existing "on" neurons spontaneously switch "off" and other neurons switch "on". In this paper we examine the nature of the bistability and switching phenomenon using a simple model consisting of two mutually inhibitory neurons. For nonspiking neuron model, described by a system of nonlinear differential equations, we present a simple bifurcation analysis, which follows the birth and annihilation of two stable fixed points when model parameters are varied. We show that both nonspiking and spiking models may have two stable states, but only spiking neurons exhibit switching. The mechanism of switching for model spiking neurons, described by an equivalent RC circuit with a number of currents, is analyzed using computer simulations. It is shown that switching can be described by a two-state Markov chain with one parameter, which depends on the set of model physiological parameters, such as duration of afterhyperpolarization (AHP), maximum and the time duration of inhibitory post-synaptic potentials (IPSP's) and amplitude of the neuron noise input. "On" and "off" states of the model can be rapidly changed by localized excitatory input and the network then sustains the pattern of "on" and "off" states. That is, such a network can be used as a programmable memory device.(ABSTRACT TRUNCATED AT 250 WORDS)

Action Potentials↗

PubMed2002

Temperature dependence of bistability in squid giant axons with alkaline intracellular pH.

Raising the intracellular pH (pHi) above 7.7 in intracellularly perfused squid giant axons causes spontaneous firing of action potentials. The firing frequency ranged from 20 Hz at 0 degrees C to 200 Hz at 23 degrees C. Above 23 degrees C, the axons were quiescent. They were bistable for 13 <T <23 degrees C. That is, they were either quiescent or spontaneously firing. Below 13 degrees C, spontaneous firing was the only stable element. The primary effects of changes in temperature on the underlying ionic currents were on gating of the delayed rectifier potassium channel IK, and the sodium ion channel INa. The kinetics of IK had a Q10 of 3.63. The effect of T on INa was more complicated in that the peak INa amplitude increased with T, as demonstrated in earlier reports. This effect, as well as the changes in INa kinetics produced by changes in T, were mimicked in the context of a model of INa gating in which activation and inactivations are coupled. Electrical activity was simulated in a model of the action potential with appropriate temperature-dependent modifications for INa and IK. The model predicts a change from monostability (spontaneous firing) at relatively low temperatures to bistability (quiescence and spontaneous firing) as the temperature is raised, followed by change back to monostability (quiescence) as the temperature is further increased, which is consistent with the experimental results.

Action Potentials↗

PubMed2004

Quantum Zeno features of bistable perception.

A generalized quantum theoretical framework, not restricted to the validity domain of standard quantum physics, is used to model the dynamics of the bistable perception of ambiguous visual stimuli such as the Necker cube. The central idea is to treat the perception process in terms of the evolution of an unstable two-state system. This gives rise to a "Necker-Zeno" effect, in analogy to the quantum Zeno effect. A quantitative relation between the involved time scales is theoretically derived. This relation is found to be satisfied by empirically obtained cognitive time scales relevant for bistable perception.

Cognition↗

PubMed2005

Background-activity-dependent properties of a network model for working memory that incorporates cellular bistability.

In models of working memory, transient stimuli are encoded by feature-selective persistent neural activity. Network models of working memory are also implicitly bistable. In the absence of a brief stimulus, only spontaneous, low-level, and presumably nonpatterned neural activity is seen. In many working-memory models, local recurrent excitation combined with long-range inhibition (Mexican hat coupling) can result in a network-induced, spatially localized persistent activity or "bump state" that coexists with a stable uniform state. There is now renewed interest in the concept that individual neurons might have some intrinsic ability to sustain persistent activity without recurrent network interactions. A recent visuospatial working-memory model (Camperi and Wang 1998) incorporates both intrinsic bistability of individual neurons within a firing rate network model and a single population of neurons on a ring with lateral inhibitory coupling. We have explored this model in more detail and have characterized the response properties with changes in background synaptic input I(o) and stimulus width. We find that only a small range of I(o) yields a working-memory-like coexistence of bump and uniform solutions that are both stable. There is a rather larger range where only the bump solution is stable that might correspond instead to a feature-selective long-term memory. Such a network therefore requires careful tuning to exhibit working-memory-like function. Interestingly, where bumps and uniform stable states coexist, we find a continuous family of stable bumps representing stimulus width. Thus, in the range of parameters corresponding to working memory, the model is capable of capturing a two-parameter family of stimulus features including both orientation and width.

Action Potentials↗

PubMed1996

A model for a bistable biochemical trigger of mitosis.

The activation of maturation promoting factor (MPF, cyclin B/Cdc2), which starts mitosis, is modeled as a bistable biochemical switch or trigger. A small, slow parameter change can cause an abrupt transition by a saddle-node bifurcation from a stable steady state of low activity to one of high activity. The switch is not reversed if the parameter change is reversed (hysteresis). The dynamical features necessary for this triggering action are the presence of two stable steady states (low-activity and high-activity), and one unstable steady state. The key biochemical kinetic features of the model are (1) mutual activation by MPF and Cdc25, which makes the activation of MPF effectively autocatalytic, and (2) binding of MPF by Suc1, which inhibits MPF autocatalysis and stabilizes the low-activity steady state until the amount of MPF begins to approach or exceed stoichiometrically the amount of Suc1, then allows strong autocatalysis and full activation. The special virtues of bistable triggering, and the general types of biochemical mechanism which can produce it, are discussed.

CDC2 Protein Kinase↗

PubMed2004

Bistability and switching in the lysis/lysogeny genetic regulatory network of bacteriophage lambda.

Bistability and switching are two important aspects of the genetic regulatory network of lambda phage. Positive and negative feedbacks are key regulatory mechanisms in this network. By the introduction of threshold values, the developmental pathway of lambda phage is divided into different stages. If the protein level reaches a threshold value, positive or negative feedback will be effective and regulate the process of development. Using this regulatory mechanism, we present a quantitative model to realize bistability and switching of lambda phage based on experimental data. This model gives descriptions of decisive mechanisms for different pathways in induction. A stochastic model is also introduced for describing statistical properties of switching in induction. A stochastic degradation rate is used to represent intrinsic noise in induction for switching the system from the lysogenic pathway to the lysis pathway. The approach in this paper represents an attempt to describe the regulatory mechanism in genetic regulatory network under the influence of intrinsic noise in the framework of continuous models.

Bacteriolysis↗

PubMed2005

Bistability and an Allee effect as emergent consequences of stage-specific predation.

The Allee effect, a reduction of individual fitness at low population density that can lead to sudden and unannounced extinctions, has been shown to come about through a number of mechanisms, usually associated with group behavior or mate search. Recent papers show that it may arise through size-selective predation, without explicit assumptions relating individual fitness to population density. It arises from the shift that a predator induces in the population stage distribution of its prey. We study the parameter conditions that lead to such an emergent Allee effect. The emergent Allee effect occurs under fairly broad conditions. We show that stage-specific predation can also induce bistability between alternative states where both prey and predator are present. A perturbation analysis on the equilibria shows that all equilibria are highly robust to changes in predator density. Our work shows that when size-specific interactions are taken into account, bistabilities and catastrophic collapses are possible even in purely exploitative food webs, which has substantial implications for questions related to food web theory and conservation issues.

Animals↗

PubMed2004

Dynamics of non-convulsive epileptic phenomena modeled by a bistable neuronal network.

It is currently believed that the mechanisms underlying spindle oscillations are related to those that generate spike and wave (SW) discharges. The mechanisms of transition between these two types of activity, however, are not well understood. In order to provide more insight into the dynamics of the neuronal networks leading to seizure generation in a rat experimental model of absence epilepsy we developed a computational model of thalamo-cortical circuits based on relevant (patho)physiological data. The model is constructed at the macroscopic level since this approach allows to investigate dynamical properties of the system and the role played by different mechanisms in the process of seizure generation, both at short and long time scales. The main results are the following: (i) SW discharges represent dynamical bifurcations that occur in a bistable neuronal network; (ii) the durations of paroxysmal and normal epochs have exponential distributions, indicating that transitions between these two stable states occur randomly over time with constant probabilities; (iii) the probabilistic nature of the onset of paroxysmal activity implies that it is not possible to predict its occurrence; (iv) the bistable nature of the dynamical system allows that an ictal state may be aborted by a single counter-stimulus.

Animals↗

PubMed2004

A laminar cortical model for 3D perception of slanted and curved surfaces and of 2D images: development, attention, and bistability.

A model of laminar visual cortical dynamics proposes how 3D boundary and surface representations arise from viewing slanted and curved 3D objects and 2D images. The 3D boundary representations emerge from non-classical receptive field interactions within intracortical and intercortical feedback circuits. Such non-classical interactions within cortical areas V1 and V2 contextually disambiguate classical receptive field responses to ambiguous visual cues using cells that are sensitive to colinear contours, angles, and disparity gradients. Remarkably, these cell types can all be explained as variants of a unified perceptual grouping circuit whose most familiar example is a 2D colinear bipole cell. Model simulations show how this circuit can develop cell selectivity to colinear contours and angles, how slanted surfaces can activate 3D boundary representations that are sensitive to angles and disparity gradients, how 3D filling-in occurs across slanted surfaces, how a 2D Necker cube image can be represented in 3D, and how bistable 3D Necker cube percepts occur. The model also explains data about slant aftereffects and 3D neon color spreading. It shows how chemical transmitters that habituate, or depress, in an activity-dependent way can help to control development and also to trigger bistable 3D percepts and slant aftereffects. Attention can influence which of these percepts is perceived by propagating selectively along object boundaries.

Attention↗

PubMed2000

Bistability in the Ca(2+)/calmodulin-dependent protein kinase-phosphatase system.

A mathematical model is presented of autophosphorylation of Ca(2+)/calmodulin-dependent protein kinase (CaMKII) and its dephosphorylation by a phosphatase. If the total concentration of CaMKII subunits is significantly higher than the phosphatase Michaelis constant, two stable steady states of the CaMKII autophosphorylation can exist in a Ca(2+) concentration range from below the resting value of the intracellular [Ca(2+)] to the threshold concentration for induction of long-term potentiation (LTP). Bistability is a robust phenomenon, it occurs over a wide range of parameters of the model. Ca(2+) transients that switch CaMKII from the low-phosphorylated state to the high-phosphorylated one are in the same range of amplitudes and frequencies as the Ca(2+) transients that induce LTP. These results show that the CaMKII-phosphatase bistability may play an important role in long-term synaptic modifications. They also suggest a plausible explanation for the very high concentrations of CaMKII found in postsynaptic densities of cerebral neurons.

Animals↗

PubMed2001

Prion diseases: dynamics of the infection and properties of the bistable transition.

Prion diseases are thought to result from a pathogenic, conformational change in a cellular protein, the prion protein. The pathogenic isoform seems to convert the normal isoform in an autocatalytic process. In contrast to the conditions used for in vitro studies of enzyme kinetics, the concentration of the catalyst is not much lower than that of the substrate in the course of infection. This feature may endow the system with a time-hierarchy allowing the pathogenic isoform to relax very slowly in the course of infection. This may contribute to the long incubation periods observed in prion diseases. The dynamic process of prion propagation, including turnover of the cellular prion protein, displays bistable properties. Sporadic prion diseases may result from a change in one of the parameters associated with metabolism of the prion protein. The bistable transition observed in sporadic disease is reversible, whereas that observed in cases of exogenous contamination is irreversible. This model is consistent with the occurrence of rare, sporadic forms of prion diseases. It may also explain why only some individuals of a cohort develop a prion disease following transient food contamination.

Animals↗

PubMed2003

Bistable secondary structures of small RNAs and their structural probing by comparative imino proton NMR spectroscopy.

We investigate 25-34 nucleotide RNA sequences, that have been rationally designed to adopt two different secondary structures that are in thermodynamic equilibrium. Experimental evidence for the co-existence of the two conformers results from the NH...N 1H NMR spectra. When compared to the NH...N 1H NMR spectra of appropriate reference sequences the equilibrium position is easily quantifiable even without the assignment of the individual NH resonances. The reference sequences represent several Watson-Crick base-paired double helical segments, each encountered in either of the two conformers of the bistable target sequence. In addition, we rationalize the influence of nucleotide mutations on the equilibrium position of one of the bistable RNA sequences. The approach further allows a detailed thermodynamic analysis and the evaluation of secondary structure predictions for multistable RNAs obtained by computational methods.

Base Composition↗

PubMed1990

Usefulness of information in bistable system and Dyson model for the origin of metabolism.

Useful or meaningful information for the transition between disordered and ordered states occurring in a chemical system, which organizes itself out of molecular chaos, is stochastically discussed from the viewpoint of dynamical system theory. To make the discussion perspicuous it is helpful to assume that the time evolution of the chemical system proceeds by a univariate, bistable one-step process of birth-and-death type. The model for the evolution of primordial metabolism proposed by Dyson is a bistable system, and hence this model answers the purpose of illustrating the usefulness of information.

Biological Evolution↗