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PubMed2000

Carbon nanotube-based nonvolatile random access memory for molecular computing

A concept for molecular electronics exploiting carbon nanotubes as both molecular device elements and molecular wires for reading and writing information was developed. Each device element is based on a suspended, crossed nanotube geometry that leads to bistable, electrostatically switchable ON/OFF states. The device elements are naturally addressable in large arrays by the carbon nanotube molecular wires making up the devices. These reversible, bistable device elements could be used to construct nonvolatile random access memory and logic function tables at an integration level approaching 10(12) elements per square centimeter and an element operation frequency in excess of 100 gigahertz. The viability of this concept is demonstrated by detailed calculations and by the experimental realization of a reversible, bistable nanotube-based bit.

Journal Article↗
PubMed2006

Noisy inputs and the induction of on-off switching behavior in a neuronal pacemaker.

Neuronal oscillators can function as bistable toggle switches, flipping between quiescence and rhythmic firing in response to an input stimulus. In theory, such switching should be sensitive to small noisy inputs if the bistable states are in close proximity, which we test here using a perfused squid axon preparation. We find that small noisy stimulus currents induce a multitude of paths between two nearby stable states: repetitive firing and quiescence. The pattern of on-off switching of the pacemaker depends on the intensity, spectral properties, and phase angle of stimulus current fluctuations. Analysis by spike-triggered averaging of the stimulus currents near the transitions reveals that sinusoidal stimuli timed antiphase or in phase with repetitive firing correlates with switching of the pacemaker off or on, respectively. Our results reveal a distinct form of bistability in which noise can either silence pacemaker activity, trigger repetitive firing, or induce sporadic burst patterns similar to those recorded in a variety of normal and pathological neurons.

Algorithms↗
PubMed2002

A biophysical model of nonlinear dynamics underlying plateau potentials and calcium spikes in purkinje cell dendrites.

Computational capabilities of Purkinje cells (PCs) are central to the cerebellum function. Information originating from the whole nervous system converges on their dendrites, and their axon is the sole output of the cerebellar cortex. PC dendrites respond to weak synaptic activation with long-lasting, low-amplitude plateau potentials, but stronger synaptic activation can generate fast, large amplitude calcium spikes. Pharmacological data have suggested the involvement of only the P-type of Ca channels in both of these electric responses. However, the mechanism allowing this Ca current to underlie responses with such different dynamics is still unclear. This mechanism was explored by constraining a biophysical model with electrophysiological, Ca-imaging, and single ion channel data. A model is presented here incorporating a simplified description of [Ca](i) regulation and three ionic currents: 1) the P-type Ca current, 2) a delayed-rectifier K current, and 3) a generic class of K channels activating sharply in the sub-threshold voltage range. This model sustains fast spikes and long-lasting plateaus terminating spontaneously with recovery of the resting potential. Small depolarizing, tonic inputs turn plateaus into a stable membrane state and endow the dendrite with bistability properties. With larger tonic inputs, the plateau remains the unique equilibrium state, showing long traces of transient inhibitory inputs that are called "valley potentials" because their dynamics mirrors that of inverted, finite-duration plateaus. Analyzing the slow subsystem obtained by assuming instantaneous activation of the delayed-rectifier reveals that the time course of plateaus and valleys is controlled by the slow [Ca](i) dynamics, which arises from the high Ca-buffering capacity of PCs. A bifurcation analysis shows that tonic currents modulate sub-threshold dynamics by displacing the resting state along a hysteresis region edged by two saddle-node bifurcations; these bifurcations mark transitions from finite-duration plateaus to bistability and from bistability to valley potentials, respectively. This low-dimensionality model may be introduced into large-scale models to explore the role of PC dendrite computations in the functional capabilities of the cerebellum.

Algorithms↗
PubMed2005

Nature of the transition between two modes of external space perception in tilted subjects.

A striking feature of visual verticality estimates in the dark is undercompensation for lateral body tilt. Earlier studies and models suggest that this so-called Aubert (A) effect increases gradually to around 130 degrees tilt and then decays smoothly on approaching the inverted position. By contrast, we recently found an abrupt transition toward errors of opposite sign (E effect) when body tilt exceeded 135 degrees . The present study was undertaken to clarify the nature of this transition. We tested the subjective visual vertical in stationary roll-tilted human subjects using various rotation paradigms and testing methods. Cluster analysis identified two clearly separate response modes (A or E effect), present in all conditions, which dominated in different but overlapping tilt ranges. Within the overlap zone, the subjective vertical appeared bistable on repeated testing with responses in both categories. The tilt range where bistability occurred depended on the direction of the preceding rotation (hysteresis). The overlap zone shifted to a smaller tilt angle when testing was preceded by a rotation through the inverted position, compared with short opposite rotations from upright. We discuss the possibility that the A-E transition reflects a reference shift from compensating line settings for the head deviation from upright to basing them on the tilt deviation of the feet from upright. In this scenario, both the A and the E effect reflect tilt undercompensation. To explain the hysteresis and the bistability, we propose that the transition is triggered when perceived body tilt, a signal with known noise and hysteresis properties, crosses a fixed threshold.

Adaptation, Physiological↗
PubMed1999

Ca(2+)-activated nonselective cationic current (I(CAN)) in turtle motoneurons.

The presence of a calcium-activated nonspecific cationic (CAN) current in turtle motoneurons and its involvement in plateau potentials, bistability, and wind-up was investigated by intracellular recordings in a spinal cord slice preparation. In the presence of tetraethylammonium (TEA) and tetrodotoxin (TTX), calcium action potentials evoked by depolarizing current pulses were always followed by an afterdepolarization associated with a decrease in input resistance. The presence of the afterdepolarization depended on the calcium spike and not on membrane potential. Replacement of extracellular sodium by choline or N-methyl-D-glucamine (NMDG) reduced the afterdepolarization, confirming that it was mediated by a CAN current. Plateau potentials and wind-up were evoked in response to intracellular current pulses in the presence of agonist for different metabotropic receptors. Replacement of extracellular sodium by choline or NMDG did not abolish the generation of plateau potentials, bistability, or wind-up, showing that Na(+) was not the principal charge carrier. It is concluded that plateau potentials, bistability and wind-up in turtle motoneurons do not depend on a CAN current even though its presence can be detected.

Action Potentials↗
PubMedDate not supplied

Categorical and prolonged potentials are evoked when brief, intermediate-intensity flashes stimulate horseshoe crab lateral eye photoreceptors during octopamine neuromodulation.

Octopamine, a major efferent neurotransmitter in the lateral eye of the horseshoe crab (Limulus polyphemus), has previously been shown to modulate photoreceptor responses evoked by long flashes. Quantification of these data indicates that this modulation produced a genuine increase in sensitivity to light which cannot be entirely due to an increase in optical efficiency consequent on an anatomical alteration. Other previous studies demonstrated that extrinsic current can modulate Limulus lateral eye photoreceptor cells by inducing a bistable membrane potential with two distinct states. The present study was therefore undertaken to find out if octopamine could modulate visual responses by inducing prolonged and bistable polarization shifts similar to those demonstrated in several other neural systems. Intracellular microelectrodes were used to execute an electrophysiological study of the receptor potentials evoked in the lateral eye of Limulus when brief (20-ms) flashes were delivered while 50 microM octopamine perfused dark-adapted photoreceptors. The combined chemical and optical stimuli prolonged photoreceptor responses to light to the degree that they often exceeded the duration of the brief stimulus by hundreds of milliseconds. Moreover, these prolonged potentials were clearly bistable because they were categorical--either a prolongation was perceptually clear-cut and present or it was not, with no intermediate patterns being observed. During seawater control perfusions, such prolongations were absent. This appears to be the first demonstration of such categorical and prolonged potentials in a photoreceptor neuron. This finding particularly suggests that efferent-driven neuromodulation can enable the development of a persisting short-term representation of a brief stimulus, with this representation being retained at the most distal possible neural site.

Animals↗
PubMed2003

Dynamics of deterministic and stochastic paired excitatory-inhibitory delayed feedback.

We examine the effects of paired delayed excitatory and inhibitory feedback on a single integrate-and-fire neuron with reversal potentials embedded within a feedback network. These effects are studied using bifurcation theory and numerical analysis. The feedback occurs through modulation of the excitatory and inhibitory conductances by the previous firing history of the neuron; as a consequence, the feedback also modifies the membrane time constant. Such paired feedback is ubiquitous in the nervous system. We assume that the feedback dynamics are slower than the membrane time constant, which leads to a rate model formulation. Our article provides an extensive analysis of the possible dynamical behaviors of such simple yet realistic neural loops as a function of the balance between positive and negative feedback, with and without noise, and offers insight into the potential behaviors such loops can exhibit in response to time-varying external inputs. With excitatory feedback, the system can be quiescent, can be periodically firing, or can exhibit bistability between these two states. With inhibitory feedback, quiescence, oscillatory firing rates, and bistability between constant and oscillatory firing-rate solutions are possible. The general case of paired feedback exhibits a blend of the behaviors seen in the extreme cases and can produce chaotic firing. We further derive a condition for a dynamically balanced paired feedback in which there is neither bistability nor oscillations. We also show how a biophysically plausible smoothing of the firing function by noise can modify the existence and stability of fixed points and oscillations of the system. We take advantage in our mathematical analysis of the existence of an invariant manifold, which reduces the dimensionality of the dynamics, and prove the stability of this manifold. The novel computational challenges involved in analyzing such dynamics with and without noise are also described. Our results demonstrate that a paired delayed feedback loop can act as a sophisticated computational unit, capable of switching between a variety of behaviors depending on the input current, the relative strengths and asymmetry of the two parallel feedback pathways, and the delay distributions and noise level.

Action Potentials↗
PubMed2004

Topology and robustness in the Drosophila segment polarity network.

A complex hierarchy of genetic interactions converts a single-celled Drosophila melanogaster egg into a multicellular embryo with 14 segments. Previously, von Dassow et al. reported that a mathematical model of the genetic interactions that defined the polarity of segments (the segment polarity network) was robust (von Dassow et al. 2000). As quantitative information about the system was unavailable, parameters were sampled randomly. A surprisingly large fraction of these parameter sets allowed the model to maintain and elaborate on the segment polarity pattern. This robustness is due to the positive feedback of gene products on their own expression, which induces individual cells in a model segment to adopt different stable expression states (bistability) corresponding to different cell types in the segment polarity pattern. A positive feedback loop will only yield multiple stable states when the parameters that describe it satisfy a particular inequality. By testing which random parameter sets satisfy these inequalities, I show that bistability is necessary to form the segment polarity pattern and serves as a strong predictor of which parameter sets will succeed in forming the pattern. Although the original model was robust to parameter variation, it could not reproduce the observed effects of cell division on the pattern of gene expression. I present a modified version that incorporates recent experimental evidence and does successfully mimic the consequences of cell division. The behavior of this modified model can also be understood in terms of bistability in positive feedback of gene expression. I discuss how this topological property of networks provides robust pattern formation and how large changes in parameters can change the specific pattern produced by a network.

Animals↗
PubMed2004

Multisite phosphorylation and network dynamics of cyclin-dependent kinase signaling in the eukaryotic cell cycle.

Multisite phosphorylation of regulatory proteins has been proposed to underlie ultrasensitive responses required to generate nontrivial dynamics in complex biological signaling networks. We used a random search strategy to analyze the role of multisite phosphorylation of key proteins regulating cyclin-dependent kinase (CDK) activity in a model of the eukaryotic cell cycle. We show that multisite phosphorylation of either CDK, CDC25, wee1, or CDK-activating kinase is sufficient to generate dynamical behaviors including bistability and limit cycles. Moreover, combining multiple feedback loops based on multisite phosphorylation do not destabilize the cell cycle network by inducing complex behavior, but rather increase the overall robustness of the network. In this model we find that bistability is the major dynamical behavior of the CDK signaling network, and that negative feedback converts bistability into limit cycle behavior. We also compare the dynamical behavior of several simplified models of CDK regulation to the fully detailed model. In summary, our findings suggest that multisite phosphorylation of proteins is a critical biological mechanism in generating the essential dynamics and ensuring robust behavior of the cell cycle.

Cell Cycle↗
PubMed2004

Signaling in small subcellular volumes. II. Stochastic and diffusion effects on synaptic network properties.

The synaptic signaling network is capable of sophisticated cellular computations. These include the ability to respond selectively to different patterns of input, and to sustain changes in response over long periods. The small volume of the synapse complicates the analysis of signaling because the chemical environment is strongly affected by diffusion and stochasticity. This study is based on an updated version of a previously proposed synaptic signaling circuit (Bhalla and Iyengar, 1999) and analyzes three network computation properties in small volumes: bistability, thresholding, and pattern selectivity. Simulations show that although there are diffusive regimes in which bistability may persist, chemical noise at small volumes overwhelms bistability. In the deterministic situation, the network exhibits a sharp threshold for transition between lower and upper stable states. This transition is broadened and individual runs partition between lower and upper states, when stochasticity is considered. The third network property, pattern selectivity, is severely degraded at synaptic volumes. However, there are regimes in which a process similar to stochastic resonance operates and amplifies pattern selectivity. These results imply that simple scaling of signaling conditions to femtoliter volumes is unlikely, and microenvironments, such as reaction complex formation, may be essential for reliable small-volume signaling.

Calcium↗
PubMed1999

Human gamma band activity and perception of a gestalt.

Neuronal oscillations in the gamma band (above 30 Hz) have been proposed to be a possible mechanism for the visual representation of objects. The present study examined the topography of gamma band spectral power and event-related potentials in human EEG associated with perceptual switching effected by rotating ambiguous (bistable) figures. Eleven healthy human subjects were presented two rotating bistable figures: first, a face figure that allowed perception of a sad or happy face depending on orientation and therefore caused a perceptual switch at defined points in time when rotated, and, second, a modified version of the Rubin vase, allowing perception as a vase or two faces whereby the switch was orientation-independent. Nonrotating figures served as further control stimuli. EEG was recorded using a high-density array with 128 electrodes. We found a negative event-related potential associated with the switching of the sad-happy figure, which was most pronounced at central prefrontal sites. Gamma band activity (GBA) was enhanced at occipital electrode sites in the rotating bistable figures compared with the standing stimuli, being maximal at vertical stimulus orientations that allowed an easy recognition of the sad and happy face or the vase-faces, respectively. At anterior electrodes, GBA showed a complementary pattern, being maximal when stimuli were oriented horizontally. The findings support the notion that formation of a visual percept may involve oscillations in a distributed neuronal assembly.

Adult↗
PubMed2001

Functional modules in biological signalling networks.

Signalling pathways carry information from the outside of the cell to cellular machinery capable of producing biochemical or physiological responses. Although linear signalling plays an important role in biological regulation, signalling pathways are often interconnected to form networks. We have used computational analysis to study emergent properties of simple networks that consist of up to four pathways, We find that when one pathway gates signal flow through other pathways which produce physiological responses, gating results in signal prolongation such that the signal may be consolidated into a physiological response. When two pathways combine to form a feedback loop such feedback loops can exhibit bistability. Negative regulators of the loop can serve as the locus for flexibility whereby the system has the capability of switching states or functioning as a proportional read-out system. Networks where bistable feedback loops are connected to gates can lead to persistent signal activation at distal locations. These emergent properties indicate system analysis of signalling networks may be useful in understanding higher-order biological functions.

Animals↗
PubMed2004

Controllable donor-acceptor neutral [2]rotaxanes.

In pursuit of a neutral bistable [2]rotaxane made up of two tetraarylmethane stoppers--both carrying one isopropyl and two tert-butyl groups located at the para positions on each of three of the four aryl rings--known to permit the slippage of the pi-electron-donating 1,5-dinaphtho[38]crown-10 (1/5DNP38C10) at the thermodynamic instigation of pi-electron-accepting recognition sites, in this case, pyromellitic diimide (PmI) and 1,4,5,8-naphthalenetetracarboxylate diimide (NpI) units separated from each other along the rod section of the rotaxane's dumbbell component, and from the para positions of the fourth aryl group of the two stoppers by pentamethylene chains, a modular approach was employed in the synthesis of the dumbbell-shaped compound NpPmD, as well as of its two degenerate counterparts, one (PmPmD) which contains two PmI units and the other (NpNpD) which contains two NpI units. The bistable [2]rotaxane NpPmR, as well as its two degenerate analogues PmPmR and NpNpR, were obtained from the corresponding dumbbell-shaped compounds NpPmD, PmPmD, and NpNpD and 1/5DNP38C10 by slippage. Dynamic 1H NMR spectroscopy in CD2Cl2 revealed that shuttling of the 1/5DNP38C10 ring occurs in NpNpR and PmPmR, with activation barriers of 277 K of 14.0 and 10.9 kcal mol(-1), respectively, reflecting a much more pronounced donor-acceptor stabilizing interaction involving the NpI units over the PmI ones. The photophysical and electrochemical properties of the three neutral [2]rotaxanes and their dumbbell-shaped precursors have also been investigated in CH2Cl2. Interactions between 1/5DNP38C10 and PmI and NpI units located within the rod section of the dumbbell components of the [2]rotaxane give rise to the appearance of charge-transfer bands, the energies of which correlate with the electron-accepting properties of the two diimide moieties. Comparison between the positions of the visible absorption bands in the three [2]rotaxanes shows that, in NpPmR, the major translational isomer is the one in which 1/5DNP38C10 encircles the NpI unit. Correlations of the reduction potentials for all the compounds studied confirm that, in this non-degenerate [2]rotaxane, one of the translational isomers predominates. Furthermore, after deactivation of the NpI unit by one-electron reduction, the 1/5DNP38C10 macrocycle moves to the PmI unit. Li+ ions have been found to strengthen the interaction between the electron-donating crown ether and the electron-accepting diimide units, particularly the PmI one. Titration experiments show that two Li+ ions are involved in the strengthening of the donor-acceptor interaction. Addition of Li+ ions to NpPmR induces the 1/5DNP38C10 macrocycle to move from the NpI to the PmI unit. The Li+-ion-promoted switching of NpPmR in a 4:1 mixture of CD2Cl2 and CD3COCD3 has also been shown by 1H NMR spectroscopy to involve the mechanical movement of the 1/5DNP38C10 macrocycle from the NpI to the PmI unit, a process that can be reversed by adding an excess of [12]crown-4 to sequester the Li+ ions.

Journal Article↗
PubMed1976

Normal upper abdominal vasculature: a study correlating contact B scanning with arteriography and gross anatomy.

Visualization of the normal upper abdominal vessels has been reported using gray scale ultrasound contact scanners. In this report we will demonstrate that the same vessels can also be seen on scans made with bistable equipment. The vessels on serial sagittal and transverse ultrasound scans will be compared with arteriograms, anatomic drawings, and cadaver photographs to provide the anatomic justification for identifying the vessels seen on the ultrasound images. Modifications in scanning technique and equipment setting to obtain the bistable images of vessels are discussed.

Abdomen↗
PubMed1977

Gray scale measurement of biparietal diameter.

Fetal biparietal diameter measurements were obtained simultaneously by gray scale and bistable ultrasonography. The bistable presentation was measured from leading edge to leading edge, while the gray scale presentation was measured from leading point to leading point and middle to middle of the band of echoes defining the fetal head. Statistical analysis of 50 patients demonstrated good reproducibility of the biparietal diameter measurement by each method and intraobserver variation fell well within the acceptable range. In all but one patient differences in measurements between observers and measurement methods were trivial and of no clinical significance. In the patients in whom there was a statistically significant difference, the variability was from 1 to 2 mm with the exception of one patient in whom the variability was about 4 mm.

Cephalometry↗
PubMed1993

Sequence-dependent DNA structure. The role of base stacking interactions.

The sequence-dependent structure of DNA is analysed on the basis of the energetics of the base stacking (pi-pi) interactions. The conformational preferences of the ten possible base-pair steps in double-helical DNA have been calculated and compared with experimental data from X-ray fibre diffraction, X-ray crystal structures and gel-running experiments. The calculations account for many features of sequence-dependent DNA structure, including polymorphism in DNA, the lack of polymorphism in RNA, the structure of Z-DNA, bistability in pyrimidine-purine (YR) steps, the origin of propeller twist and buckle and the role of TATA sequences at the sites of origin of replication. The computational model used specifically allows for the charge distribution associated with the out-of-plane pi-electron density of the bases. The results obtained are rationalized on the basis of the shapes and charge distributions of the bases. Calladine's cross-strand steric clashes at pyrimidine-purine (YR) and CX/XG steps are reproduced. In AX/XT steps, same-strand steric clashes occur between the thymine methyl group and the 5'-neighbouring sugar. They are the cause of the large negative propeller twist observed in A.T base-pairs. Steric clashes between the thymine methyl group and the 5'-neighbouring base block A-DNA conformations in AX/XT steps. Electrostatic interactions between partial atomic charges are most important for C.G base-pairs which are highly polarized. They lead to strong preferences for positive slide and negative slide conformations in CG and GC steps, respectively. This combination can be accommodated in poly(CG) by left-handed Z-DNA. Many of the more subtle sequence-dependent effects are caused by electrostatic interactions between the partial atomic charges on one base-pair and the out-of-plane pi-electron density on another. The effect is most important in CX-XG steps and leads to bistability. In general, electrostatic interactions cause non-zero slide. This is opposed by the hydrophobic effect which favours the zero slide B-type conformation. Thus, B-DNA is observed at high water content in fibres and electrostatic interactions force high or low slide A or C-DNA conformations at low water content. If two juxtaposed steps have very different conformational preferences, this incompatibility can lead to unusual structures such as Z-DNA or strain such as in TATA sequences.

Base Sequence↗
PubMed1998

Contact activation of blood coagulation: trigger properties and hysteresis. Kinetic recognition of foreign surfaces upon contact activation of blood coagulation: a hypothesis.

A mathematical model of contact activation of blood coagulation was developed and analysed. The model variables are concentrations of factor XIIa, kallikrein and activated high-molecular-weight kininogen. Concentrations of active factors were shown to depend on the activating signal value in a hysteretic manner. Within a range of relatively small signals, two (activated and non-activated) stable states coexist (bistability). Signals of the natural environment (surfaces of endothelial and blood cells) seem to be in the range of bistability; therefore, contact activation that persists for a short time can induce a transition of the system to the activated state, and, correspondingly, the formation of a clot. The system cannot return to the initial state, which is characterized by low activation levels, until the activating signals decrease significantly below those present in the circulation.

Blood Coagulation↗
PubMed2002

Recurrent inhibitory dynamics: the role of state-dependent distributions of conduction delay times.

We have formulated and analysed a dynamic model for recurrent inhibition that takes into account the state dependence of the delayed feedback signal (due to the variation in threshold of fibres with their size) and the distribution of these delays (due to the distribution of fibre diameters in the feedback pathway). Using a combination of analytic and numerical tools, we have analysed the behaviour of this model. Depending on the parameter values chosen, as well as the initial preparation of the system, there may be a spectrum of post-synaptic firing dynamics ranging from stable constant values through periodic bursting (limit cycle) behaviour and chaotic firing as well as bistable behaviours. Using detailed parameter estimation for a physiologically motivated example (the CA3-basket cell-mossy fibre system in the hippocampus), we present some of these numerical behaviours. The numerical results corroborate the results of the analytic characterization of the solutions. Namely, for some parameter values the model has a single stable steady state while for the others there is a bistability in which the eventual behaviour depends on the magnitude of stimulation (the initial function).

Animals↗