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PubMed2004

Hysteresis vs. graded responses: the connections make all the difference.

Biological regulatory systems have the potential to provide graded responses to stimuli or may demonstrate switch-like properties. Our understanding of the system design principles controlling these responses is still at a rudimentary stage, and here we consider several recent experimental and theoretical studies that focus on these system design principles. Overt positive feedback loops, or double-negative feedback loops, can produce bistable or multistable systems under the appropriate conditions and can produce graded responses under other conditions. Several design features favor bistability in negatively controlled genetic systems, including a high kinetic order for repression and a large difference in the rates of gene expression in the "on" and "off" states. In positive feedback, a high kinetic order for the activation of gene expression favors bistability. Multistability can result from the combined effects of positive and negative regulators, or from the combined effects of regulators that each demonstrate bistability. Finally, bistability can result in enzymatic systems in which multiple reversible covalent modifications occur, even when no overt feedback loops are present.

Feedback, Physiological↗
PubMed1997

Prolonged firing in motor units: evidence of plateau potentials in human motoneurons?

Serotonin (5-HT) and norepinephrine-dependent plateau potentials are found in spinal motoneurons in reduced turtle and cat preparations. Triggering the plateau potential by short-lasting synaptic excitation causes a prolonged self-sustained firing, which can be terminated by short-lasting synaptic inhibition. The presence of plateau potentials can also allow neurons to fire in a bistable manner, i.e., shifting between stable low and high firing frequencies. Such a bistable firing behavior has been found in soleus motor units in unrestrained rats. In the present study single motor-unit activity was recorded from low-threshold units in human soleus and tibialis anterior muscles to evaluate whether a bistable firing behavior and/or prolonged firing could be evoked. Vibration of the homonymous muscle tendon (30-100 Hz, 2-10 s) was used as excitatory input to the motoneuron pool. Brief excitation while the muscle was electrically silent induced firing during the vibration and sometimes recruited units into prolonged stable firing outlasting the vibratory stimulus. However, a bistable firing behavior, i.e., vibration-induced maintained shifts between two stable levels of firing, could not be convincingly demonstrated. The reason for this was twofold. First, low-threshold human motor units tended to jump to a "preferred firing range" shortly after voluntary recruitment. This firing range was the same as when units were recruited from silence into prolonged firing by vibration. Below the preferred firing range, maintained firing was unstable and usually only possible when subjects were listening to the spike potentials or had visual force-feedback. Second, vibration when units were firing in the preferred firing range caused a transient increase in firing frequency but no maintained frequency shifts. Recordings from pairs of motor units showed that short-lasting vibration could recruit one unit into prolonged firing, while a second unit, which already fired in its preferred firing range, only transiently increased its firing rate during the vibration. This suggests that the prolonged firing was not the result of an increase in the common synaptic drive to the motoneuron pool. We conclude that a bistable firing behavior as seen in intact rats is probably absent in human low-threshold motor units, but that prolonged firing could be seen in response to short-lasting excitation. This latter phenomenon is compatible with the existence of plateau potentials, which have to have a threshold close to the threshold for sodium spike generation.

Adult↗
PubMed2006

Multistable and multistep dynamics in neutrophil differentiation.

BACKGROUND: Cell differentiation has long been theorized to represent a switch in a bistable system, and recent experimental work in micro-organisms has revealed bistable dynamics in small gene regulatory circuits. However, the dynamics of mammalian cell differentiation has not been analyzed with respect to bistability. RESULTS: Here we studied how HL60 promyelocytic precursor cells transition to the neutrophil cell lineage after stimulation with the differentiation inducer, dimethyl sulfoxide (DMSO). Single cell analysis of the expression kinetics of the differentiation marker CD11b (Mac-1) revealed all-or-none switch-like behavior, in contrast to the seemingly graduated change of expression when measured as a population average. Progression from the precursor to the differentiated state was detected as a discrete transition between low (CD11bLow) and high (CD11bHigh) expressor subpopulations distinguishable in a bimodal distribution. Hysteresis in the dependence of CD11b expression on DMSO dose suggests that this bimodality may reflect a bistable dynamic. But when an "unswitched" (CD11bLow) subpopulation of cells in the bistable/bimodal regime was isolated and cultured, these cells were found to differ from undifferentiated precursor cells in that they were "primed" to differentiate. CONCLUSION: These findings indicate that differentiation of human HL60 cells into neutrophils does not result from a simple state transition of a bistable switch as traditionally modeled. Instead, mammalian differentiation appears to be a multi-step process in a high-dimensional system, a result which is consistent with the high connectivity of the cells' complex underlying gene regulatory network.

CD11b Antigen↗
PubMed2026

Kinetic model of E-P condensates dynamics reveals transcriptional speed, noise, and energy trade-offs.

Gene regulation emerges from the interplay between chromatin architecture and the molecular interactions that connect enhancers to promoters. To study how these interactions shape transcriptional dynamics, we developed a kinetic model that incorporates multivalent enhancer-promoter binding, transcription factor competition, steric constraints, and chromatin accessibility. The model shows that competition among regulatory factors can generate bistable promoter states at the expense of increased transcriptional noise, revealing a direct relationship between bistability and noise levels. It further predicts that promoter response times are fastest in parameter regimes where bistability appears, suggesting that regulatory dynamics supporting two promoter states may intrinsically enable rapid activation. Extending this analysis, we find that intermediate chromatin accessibility and competition between activators and repressors both promote bistable enhancer-bound promoter clusters and fast switching at the cost of higher noise, whereas very high or low accessibility and noncompetitive transcription factors result in monostable expression states. The model also offers a quantitative framework to compare the energetic costs of different regulatory strategies, indicating that, under energy constraints, cells may favor adjusting transcription factor concentrations rather than altering chromatin accessibility, thereby linking energy expenditure to regulatory flexibility and robustness.

Kinetics↗
PubMed1990

Circuits constructed from identified Aplysia neurons exhibit multiple patterns of persistent activity.

We have used identified neurons from the abdominal ganglion of the mollusc Aplysia to construct and analyze two circuits in vitro. Each of these circuits was capable of producing two patterns of persistent activity; that is, they had bistable output states. The output could be switched between the stable states by a brief, external input. One circuit consisted of cocultured L10 and left upper quadrant (LUQ) neurons that formed reciprocal, inhibitory connections. In one stable state L10 was active and the LUQ was quiescent, whereas in the other stable state L10 was quiescent and the LUQ was active. A second circuit consisted of co-cultured L7 and L12 neurons that formed reciprocal, excitatory connections. In this circuit, both cells were quiescent in one stable state and both cells fired continuously in the other state. Bistable output in both circuits resulted from the nonlinear firing characteristics of each neuron and the feedback between the two neurons. We explored how the stability of the neuronal output could be controlled by the background currents injected into each neuron. We observed a relatively well-defined range of currents for which bistability occurred, consistent with the values expected from the measured strengths of the connections and a simple model. Outside of the range, the output was stable in only a single state. These results suggest how stable patterns of output are produced by some in vivo circuits and how command neurons from higher neural centers may control the activity of these circuits. The criteria that guided us in forming our circuits in culture were derived from theoretical studies on the properties of certain neuronal network models (e.g., Hopfield, J. J. 1984. Proc. Natl. Acad. Sci. USA. 81:3088-3092). Our results show that circuits consisting of only two co-cultured neurons can exhibit bistable output states of the form hypothesized to occur in populations of neurons.

Animals↗
PubMed2002

Structure and dynamics of ferroelectric liquid crystal cells exhibiting thresholdless switching.

Surface-stabilized ferroelectric liquid crystal cells are usually bistable, with the spontaneous polarization either up or down, perpendicular to the plane of the cell. In materials with high spontaneous polarization the polarization charge self-interaction leads to a monostable structure that exhibits a thresholdless, "V-shaped" switching of the optical response to an applied voltage. With a model that includes the electrostatic self-energy of the spontaneous polarization, we examine the transition from bistablity to monostability as a function of the polar and nonpolar anchoring energies, the liquid crystal elasticity, and the thickness of the alignment layers. Two bistable and one monostable structures are possible. The bistable state is only obtained when the thickness of the insulating alignment layer and the polar anchoring energy are small, or when the spontaneous polarization is small. From linear stability analysis we get analytical expressions for the limits of stability of the structures. Numerical calculations show that in some ranges of the parameters two structures can coexist. We also present the calculation of the polarization fluctuation modes. The lowest one becomes soft at the continuous transitions among the structures and at the limits of stability.

Journal Article↗
PubMed2003

Sensitivity of explosion to departure from partial equilibrium.

We study a thermochemical gaseous system in the vicinity of the bifurcation related to the emergence of bistability. Corrections to the standard deterministic dynamics induced by the perturbation of the particle velocity distribution are obtained from the solution of the Boltzmann equation. Using these results, analytical expressions including the nonequilibrium effects are derived for the ignition time in the explosive regime and mean first passage time in the bistable regime. It is demonstrated that a departure from partial equilibrium can shift the bifurcation point. The system which was bistable according to the standard deterministic approach, can become monostable and explosive in the presence of nonequilibrium effects. Even when the system remains in the bistable regime, the mean first passage time can be changed by several orders of magnitude. In the monostable domain, the ignition time can be about ten times smaller than the unperturbed value. These analytical predictions agree well with the results of the microscopic simulations of the dilute gas system.

Journal Article↗
PubMed2004

External noise imposed on the reaction-diffusion system CO+O2-->CO2 on Ir(111) surfaces: experiment and theory.

We study experimentally and theoretically the influence of noise on the fractions of CO and oxygen in the constant gas flow directed at an Ir(111) surface during CO oxidation. Depending on the noise strength and the fraction Y of CO we observe in the deterministically bistable region a large variety of different types of behavior. These include bistable behavior for small noise intensities, transitions from the upper to the lower branch of the bistable loop and vice versa, island nucleation and growth and noise-induced switching. Near the boundary of the bistable region and in the presence of noise the transition between the two branches takes place via very slow domain wall motion with time scales of the order of 10(4)-10(5) s. The experiments were carried out in an UHV system for which the mass flow could be controlled very precisely. The modeling was using the reaction-diffusion system underlying the reaction studied for which all the kinetic coefficients are known rather precisely. Our numerical analysis was performed for one and two spatial dimensions showing qualitatively similar behavior. The comparison between the experimental results and the modeling shows semiquantitative to quantitative agreement.

Journal Article↗
PubMed2005

Differential modulation of anterior cingulate cortical activity by afferents from ventral tegmental area and mediodorsal thalamus.

A distinct increase in cell firing activity is reported in prefrontal cortex during working memory tasks. The afferents that modulate this activity are not yet identified. Using in vivo intracellular recording and labelling of prefrontal cortical pyramidal neurons in anaesthetized rats, we systematically evaluated the influences of afferent projections arising from the ventral tegmental area (VTA) and mediodorsal thalamus (MD) by phasic electrical stimulation with a range of stimulus frequencies. Both VTA- and MD-responsive pyramidal neurons exhibited extensive intracortical axon arborization. Neither single shocks to the VTA at 0.2 Hz, nor low frequency trains of stimuli at 1-4 Hz (< 5 Hz) interrupted the periodicity of membrane bistability in bistable pyramidal neurons. However, high-frequency VTA-train stimulation (10-50 Hz) interrupted the bistability, and produced sustained membrane depolarizations accompanied by intense tonic firing in a frequency-dependent manner. Electrical stimulation of MD (10-50 Hz) did not produce sustained activity in the same PFC neurons. Thus, the sustained activity induced by high-frequency VTA trains is input selective. This effect of VTA-train stimulation was attenuated by systemic injection of the D1 receptor antagonist, SCH 23390, and blocked by acute dopamine (DA) depletion produced via alpha-methyl-para-tyrosine pre-treatment, suggesting that sustained cortical activity is mediated by DA. Chemical stimulation of VTA via intra-VTA infusion of NMDA induced sustained activity similar to VTA-train stimulation. Thus, while both VTA- and MD-responsive pyramidal neurons exhibited extensive intracortical axon arborization, VTA synapses (as opposed to MD synapses) may be critically positioned in the dendritic arborizations of anterior cingulate cortical pyramidal neurons, which may allow their modulation of sustained activity in prefrontal bistable neurons.

Action Potentials↗
PubMed2006

New perspectives on the mechanical basis for airway hyperreactivity and airway hypersensitivity in asthma.

We revisit the airway wall model of Lambert et. al. (Lambert RK, Wiggs BR, Kuwano K, Hogg JC, and Pare PD. J Appl Physiol 74: 2771-2781, 1993). We examine in detail the notion of a general airway bistability such that the airway lumen can suddenly decrease from a relatively open to a relatively closed condition without needing additional increase in active airway smooth muscle (ASM) tension during the stimulation. The onset of this bistability is an emergent consequence of the balance of forces associated with airway wall properties, parenchymal tissue properties, maximum lung elastic recoil, and the maximum stress that the ASM can generate. In healthy lungs, we find that all these properties reside in conditions that largely prevent the emergence of the bistability even during maximum ASM stimulation. In asthmatic airways, however, the airway wall and ASM remodeling conditions can tip the balance so as to promote the onset of the bistability at a lower dose of ASM stimulation (enhanced sensitivity) and then work to amplify the maximum constriction reached by each airway (enhanced reactivity). Hence, a larger fraction of asthmatic airways can display overall airway hyperreactivity. Simulations studies examine the role of increasing ASM maximum tension, airway wall stiffening, reduced lung volume, and decreased parenchymal tethering. Results predict that the single most important factor causing this airway hyperreactivity is amplified maximum ASM tension and not a thickening of the airway wall per se.

Asthma↗
PubMed1983

Control of intercellular communication by voltage dependence of gap junctional conductance.

The junctional conductance between coupled amphibian blastomeres exhibits a high degree of voltage dependence, as previously described in voltage clamp studies (Spray, D.C., A.L. Harris, and M.V.L. Bennett (1981) J. Gen. Physiol. 77: 77-95; Harris, A.L., D.C. Spray, and M.V.L. Bennett (1981) J. Gen. Physiol. 77: 95-117). The present study examines the properties which this voltage dependence confers on electrotonic coupling between cells. The effects of applied pulses and ramps of current are studied experimentally and are modeled by calculation. During sufficiently large current pulses applied to one cell of a pair, the cells uncouple and then recouple after termination of the pulses. Ramps of current applied to one of the cells can give voltage-current (V-I) relations with a region of hysteresis within which the cells are stably coupled or stably uncoupled depending on previous history. Intrinsically generated currents are able to cause bistability of coupling in the absence of externally applied current. Calculations from the parameters of junctional conductance defined under voltage clamp fully account for these findings and illustrate how junctional and nonjunctional conductances affect the V-I relations in the region of bistability. Recordings from several cells within a small group show that boundaries of intercellular communication can be altered by applied current, a finding that also can be accounted for by voltage dependence of junctional conductance. The "Appendix" examines quantitatively the criteria required for bistability of coupling and the relevance of bistability for intercellular signaling. The plasticity of coupling which the voltage dependence of junctional conductance confers on cells offers an intriguing mechanism by which patterns of intercellular communication could be determined and changed in developing tissues.

Ambystoma↗
PubMed1995

Synaptic interactions among excitatory afferents to nucleus accumbens neurons: hippocampal gating of prefrontal cortical input.

The interactions among excitatory inputs arising from the prefrontal cortex, amygdala, and hippocampus, and innervating nucleus accumbens neurons were studied using in vivo intracellular recording techniques. Neurons recorded in the accumbens displayed one of three activity states: (1) silent, (2) spontaneously firing at low, constant rates, or (3) a bistable membrane potential, characterized by alternating periods of activity and silence occurring in concert with spontaneous transitions between two steady-state membrane potentials (average, -77.3 +/- 7.1 mV base, -63.0 +/- 7.4 mV plateau). These neurons also exhibited a high degree of convergence of responses elicited by stimulation of each of the three excitatory inputs tested. Activation of hippocampal afferents, but not cortical, amygdaloid, or thalamic afferents, induced bistable cells to switch to the depolarized (active) state. In contrast, no bistable cells were encountered in the nucleus accumbens following an acute transection of the fornix. Furthermore, microinjection of lidocaine in the vicinity of the hippocampal afferents at the level of the fornix caused a reversible elimination of the plateau phase in bistable cells. These data suggest that hippocampal input is necessary for accumbens neurons to enter a depolarized, active state. Furthermore, activation of prefrontal cortical inputs fail to evoke spike firing in accumbens neurons unless they are in this active state. Consequently, the hippocampus appears to be capable of gating prefrontal corticoaccumbens throughput.

Action Potentials↗
PubMed2004

Redox-controllable amphiphilic [2]rotaxanes.

With the fabrication of molecular electronic devices (MEDs) and the construction of nanoelectromechanical systems (NEMSs) as incentives, two constitutionally isomeric, redox-controllable [2]rotaxanes have been synthesized and characterized in solution. Therein, they both behave as near-perfect molecular switches, that is, to all intents and purposes, these two rotaxanes can be switched precisely by applying appropriate redox stimuli between two distinct chemomechanical states. Their dumbbell-shaped components are composed of polyether chains interrupted along their lengths by i) two pi-electron rich recognition sites-a tetrathiafulvalene (TTF) unit and a 1,5-dioxynaphthalene (DNP) moiety-with ii) a rigid terphenylene spacer placed between the two recognition sites, and then terminated by iii) a hydrophobic tetraarylmethane stopper at one end and a hydrophilic dendritic stopper at the other end of the dumbbells, thus conferring amphiphilicity upon these molecules. A template-directed protocol produces a means to introduce the tetracationic cyclophane, cyclobis(paraquat-p-phenylene) (CBPQT(4+)), which contains two pi-electron accepting bipyridinium units, mechanically interlocked around the dumbbell-shaped components. Both the TTF unit and the DNP moiety are potential stations for CBPQT(4+), since they can establish charge-transfer and hydrogen bonding interactions with the bipyridinium units of the cyclophane, thereby introducing bistability into the [2]rotaxanes. In both constitutional isomers, (1)H NMR and absorption spectroscopies, together with electrochemical investigations, reveal that the CBPQT(4+) ring is predominantly located on the TTF unit, leading to the existence of a single translational isomer (co-conformation) in both cases. In addition, a model [2]rotaxane, incorporating hydrophobic tetraarylmethane stoppers at both ends of its dumbbell-shaped component, has also been synthesized as a point of reference. Molecular synthetic approaches were used to construct convergently the dumbbell-shaped compounds by assembling progressively smaller building blocks in the shape of the rigid spacer, the TTF unit and the DNP moiety, and the hydrophobic and hydrophilic stoppers. The two amphiphilic bistable [2]rotaxanes are constitutional isomers in the sense that, in one constitution, the TTF unit is adjacent to the hydrophobic stopper, whereas in the other, it is next to the hydrophilic stopper. All three bistable [2]rotaxanes have been isolated as green solids. Electrospray and fast atom bombardment mass spectra support the gross structural assignments given to all three of these mechanically interlocked compounds. Their photophysical and electrochemical properties have been investigated in acetonitrile. The results obtained from these investigations confirm that, in all three [2]rotaxanes, i) the CBPQT(4+) cyclophane encircles the TTF unit, ii) the CBPQT(4+) cyclophane shuttles between the TTF and DNP stations upon electrochemical or chemical oxidation/reduction of the TTF unit, and iii) folded conformations are present in which the CBPQT(4+) cyclophane, while encircling the TTF unit, interacts through its pi-accepting bipyridinium exteriors with other pi-donating components of the dumbbells, especially those located within the stoppers.

Journal Article↗
PubMed1977

[Dependence of the specific growth rate of Escherichia coli MI 30 on the ammonia concentration].

The transient behaviour of ammonium limited continuous cultures of E. coli ML 30 led to the hypothesis that the bistability of pyruvate formation primarily is caused by a bistability of the ammonia metabolism. Therefore, a function of mu([NH+4]) should be expected different from that of Monod type. Measurements of the specific growth rate during washout of continuous cultures at different ammonium concentrations and at such low cell concentrations that the changes in the ammonium concentration of the medium could be neglected, showed a complex function with a relative minimum near 2 mg/1NH+4. This function allows bistability of the ammonium concentration in an ammonium limited continuous culture. The results are discussed on the basis of the two systems of ammonia assimilation found in prokaryotic cells.

Ammonia↗
PubMed1993

Different ionic conductances are modulated during the late receptor potential and the prolonged depolarizing afterpotential in Hermissenda type A photoreceptors.

Wavelength-dependent, bistable phenomena were found in the receptor potential of Hermissenda crassicornis type A photoreceptors. Short exposure to blue light induced a prolonged depolarizing afterpotential (PDA) following the cessation of the light stimulus. Stronger adaptation to blue light, as caused by prolonged exposure and/or high intensity stimulation, effected a reduction in the early depolarizing transient of the late receptor potential (LRP) as elicited by subsequent stimuli. Vast separation of LRP emergence and PDA emergence could be obtained in photoreceptors in which a strong cancellation of the LRP was accomplished but a PDA still emerged after cessation of the light stimulus. Short exposure to yellow light cancelled the PDA, and stronger adaptation restored the LRP (opposite effect to blue light). The initial depolarizing part of the LRP had earlier been demonstrated to be mediated by the light-dependent increase of an inward conductance. In contrast, in this study the PDA was found to be accompanied by the reduction of an outward conductance, most likely a K+ conductance. A bistable photopigment system is thought to control the bistable receptor potential phenomenology by regulating the different membrane conductances during the LRP and the PDA.

Animals↗
PubMed2001

Chaos and population disappearances in simple ecological models.

A class of truncated unimodal discrete-time single species models for which low or high densities result in extinction in the following generation are considered. A classification of the dynamics of these maps into five types is proven: (i) extinction in finite time for all initial densities, (ii) semistability in which all orbits tend toward the origin or a semistable fixed point, (iii) bistability for which the origin and an interval bounded away from the origin are attracting, (iv) chaotic semistability in which there is an interval of chaotic dynamics whose compliment lies in the origin's basin of attraction and (v) essential extinction in which almost every (but not every) initial population density leads to extinction in finite time. Applying these results to the Logistic, Ricker and generalized Beverton-Holt maps with constant harvesting rates, two birfurcations are shown to lead to sudden population disappearances: a saddle node bifurcation corresponding to a transition from bistability to extinction and a chaotic blue sky catastrophe corresponding to a transition from bistability to essential extinction.

Animals↗
PubMed1996

Fructose 2,6-bisphosphate induces irreversible transitions in cell-free extracts of rat liver.

The effect of fructose 2,6-bisphosphate on the dynamics of the 6-phosphofructo-1-kinase/fructose-1,6-bisphosphatase cycle is investigated in a cell-free extract of rat liver under steady-state conditions. Bistability emerges on the basis of the reciprocal allosteric modulation of 6-phosphofructo-1-kinase and fructose-1,6-bisphosphatase. Under conditions of bistability fructose 2,6-bisphosphate may cause transitions between alternative steady states. However, in contrast to what is frequently observed in bistable systems, within a broad range of experimental conditions these transitions proceed irreversibly from states with high ATP to states characterized by low ATP.

Adenosine Triphosphate↗
PubMed1984

A base-centred explanation of the B-to-A transition in DNA.

In the traditional view, the bistable feature responsible for the switch between the B and A forms of DNA was the sugar-phosphate backbone. Several recent assays of the sequence-dependent structure of DNA are not compatible with that hypothesis. Here we show that certain kinds of base-pair step, mainly those of the pyrimidine-purine variety, can stack in a "bistable" fashion so as to produce one of two overall helix shapes A or B. Further, we suggest that the passive, elastic stiffness of the backbone is responsible for communicating the stacking configuration from bistable steps to their "neutral" neighbours. The role of water molecules, in stabilizing the B form of DNA over the A, may simply be to form hydrogen-bonded bridges with the minor-groove edges of neutral steps in the B configuration.

Base Sequence↗