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PubMed2004

Two-state membrane potential fluctuations driven by weak pairwise correlations.

Physiological experiments demonstrate the existence of weak pairwise correlations of neuronal activity in mammalian cortex (Singer, 1993). The functional implications of this correlated activity are hotly debated (Roskies et al., 1999). Nevertheless, it is generally considered a widespread feature of cortical dynamics. In recent years, another line of research has attracted great interest: the observation of a bimodal distribution of the membrane potential defining up states and down states at the single cell level (Wilson & Kawaguchi, 1996; Steriade, Contreras, & Amzica, 1994; Contreras & Steriade, 1995; Steriade, 2001). Here we use a theoretical approach to demonstrate that the latter phenomenon is a natural consequence of the former. In particular, we show that weak pairwise correlations of the inputs to a compartmental model of a layer V pyramidal cell can induce bimodality in its membrane potential. We show how this relationship can account for the observed increase of the power in the gamma-frequency band during up states, as well as the increase in the standard deviation and fraction of time spent in the depolarized state (Anderson, Lampl, Reichova, Carandini, & Ferster, 2000). In order to quantify the relationship between the correlation properties of a cortical network and the bistable dynamics of single neurons, we introduce a number of new indices. Subsequently, we demonstrate that a quantitative agreement with the experimental data can be achieved, introducing voltage-dependent mechanisms in our neuronal model such as Ca(2+)- and Ca(2+)-dependent K(+) channels. In addition, we show that the up states and down states of the membrane potential are dependent on the dendritic morphology of cortical neurons. Furthermore, bringing together network and single cell dynamics under a unified view allows the direct transfer of results obtained in one context to the other and suggests a new experimental paradigm: the use of specific intracellular analysis as a powerful tool to reveal the properties of the correlation structure present in the network dynamics.

Algorithms↗
PubMed1998

Ion channel stochasticity may be critical in determining the reliability and precision of spike timing.

The firing reliability and precision of an isopotential membrane patch consisting of a realistically large number of ion channels is investigated using a stochastic Hodgkin-Huxley (HH) model. In sharp contrast to the deterministic HH model, the biophysically inspired stochastic model reproduces qualitatively the different reliability and precision characteristics of spike firing in response to DC and fluctuating current input in neocortical neurons, as reported by Mainen & Sejnowski (1995). For DC inputs, spike timing is highly unreliable; the reliability and precision are significantly increased for fluctuating current input. This behavior is critically determined by the relatively small number of excitable channels that are opened near threshold for spike firing rather than by the total number of channels that exist in the membrane patch. Channel fluctuations, together with the inherent bistability in the HH equations, give rise to three additional experimentally observed phenomena: subthreshold oscillations in the membrane voltage for DC input, "spontaneous" spikes for subthreshold inputs, and "missing" spikes for suprathreshold inputs. We suggest that the noise inherent in the operation of ion channels enables neurons to act as "smart" encoders. Slowly varying, uncorrelated inputs are coded with low reliability and accuracy and, hence, the information about such inputs is encoded almost exclusively by the spike rate. On the other hand, correlated presynaptic activity produces sharp fluctuations in the input to the postsynaptic cell, which are then encoded with high reliability and accuracy. In this case, information about the input exists in the exact timing of the spikes. We conclude that channel stochasticity should be considered in realistic models of neurons.

Action Potentials↗
PubMed1998

A hierarchical model of binocular rivalry.

Binocular rivalry is the alternating percept that can result when the two eyes see different scenes. Recent psychophysical evidence supports the notion that some aspects of binocular rivalry bear functional similarities to other bistable percepts. We build a model based on the hypothesis (Logothetis & Schall, 1989; Leopold & Logothetis, 1996; Logothetis, Leopold & Sheinberg, 1996) that alternation can be generated by competition between top-down cortical explanations for the inputs, rather than by direct competition between the inputs. Recent neurophysiological evidence shows that some binocular neurons are modulated with the changing percept; others are not, even if they are selective between the stimuli presented to the eyes. We extend our model to a hierarchy to address these effects.

Algorithms↗
PubMed1997

An analog memory circuit for spiking silicon neurons.

A simple circuit is described that functions as an analog memory whose state and dynamics are directly controlled by pulsatile inputs. The circuit has been incorporated into a silicon neuron with a spatially extensive dendritic tree as a means of controlling the spike firing threshold of an integrate-and-fire soma. Spiking activity generated by the neuron itself and by other units in a network can thereby regulate the neuron's excitability over time periods ranging from milliseconds to many minutes. Experimental results are presented showing applications to temporal edge sharpening, bistable behavior, and a network that learns in the manner of classical conditioning.

Action Potentials↗
PubMed2007

Mean-driven and fluctuation-driven persistent activity in recurrent networks.

Spike trains from cortical neurons show a high degree of irregularity, with coefficients of variation (CV) of their interspike interval (ISI) distribution close to or higher than one. It has been suggested that this irregularity might be a reflection of a particular dynamical state of the local cortical circuit in which excitation and inhibition balance each other. In this "balanced" state, the mean current to the neurons is below threshold, and firing is driven by current fluctuations, resulting in irregular Poisson-like spike trains. Recent data show that the degree of irregularity in neuronal spike trains recorded during the delay period of working memory experiments is the same for both low-activity states of a few Hz and for elevated, persistent activity states of a few tens of Hz. Since the difference between these persistent activity states cannot be due to external factors coming from sensory inputs, this suggests that the underlying network dynamics might support coexisting balanced states at different firing rates. We use mean field techniques to study the possible existence of multiple balanced steady states in recurrent networks of current-based leaky integrate-and-fire (LIF) neurons. To assess the degree of balance of a steady state, we extend existing mean-field theories so that not only the firing rate, but also the coefficient of variation of the interspike interval distribution of the neurons, are determined self-consistently. Depending on the connectivity parameters of the network, we find bistable solutions of different types. If the local recurrent connectivity is mainly excitatory, the two stable steady states differ mainly in the mean current to the neurons. In this case, the mean drive in the elevated persistent activity state is suprathreshold and typically characterized by low spiking irregularity. If the local recurrent excitatory and inhibitory drives are both large and nearly balanced, or even dominated by inhibition, two stable states coexist, both with subthreshold current drive. In this case, the spiking variability in both the resting state and the mnemonic persistent state is large, but the balance condition implies parameter fine-tuning. Since the degree of required fine-tuning increases with network size and, on the other hand, the size of the fluctuations in the afferent current to the cells increases for small networks, overall we find that fluctuation-driven persistent activity in the very simplified type of models we analyze is not a robust phenomenon. Possible implications of considering more realistic models are discussed.

Action Potentials↗
PubMed2004

When motion is not perceived: evidence from adaptation and dynamical stability.

Adaptation was used to probe the perceiver's activation state when either motion or nonmotion percepts are formed for bistable, single-element apparent motion stimuli. Although adaptation was not observed in every instance, when it was observed its effect was to increase the probability of both motion-to-nonmotion and nonmotion-to-motion switches, the time scale of adaptation corresponding to neurophysiological observations for directionally selective cortical cells (Giaschi et al. 1993). This susceptibility to de-stabilizing adaptation effects indicated that the nonmotion percept was not the result of inadequate stimulation producing subthreshold levels of motion detector activation; if that were the case, activation-dependent adaptation would have decreased the nonmotion-to-motion switching rate by reducing activation further below threshold. Above-threshold activation levels are therefore associated with both nonmotion and motion perceptual states, and the failure to perceive motion despite the presence of adequate motion detector stimulation can be attributed to inhibitory competition between detectors activated by motion-specifying stimulus information and detectors activated to similar levels by motion-independent stimulus information, consistent with the dynamical quality of single-element apparent motion.

Adaptation, Ocular↗
PubMed2005

Dynamical vs. judgmental comparison: hysteresis effects in motion perception.

Perceptual comparison was investigated by gradually varying the relative length of two apparent motion paths, and independently determining when an initial percept was lost during the course of attribute change and when an alternative percept emerged. Dynamical comparison was indicated by a range of attribute values for which perception was bistable. Within this range, a percept that lost stability was immediately replaced by an alternative percept. Judgmental comparison was indicated by a range of attribute values for which perception was uncertain. When an initial percept was lost, an alternative percept did not immediately emerge because the alternatives being compared could not be distinguished. Differences in the effects of random noise on dynamical vs. judgmental comparison were demonstrated with computational simulations, and implications are discussed for motion energy models and solutions to the motion correspondence problem.

Attention↗
PubMed1994

The interaction of depth parameters in motion integration with polar plaids.

Many parameters have been investigated as to their effect on the way in which the visual system is able to integrate different motion directions at the same visual location. Of special interest have been parameters that determine the depth relationship between surfaces, such as disparity, relative contrast, and occlusion versus transparency. The preferred stimulus for this research has been the 'plaid', usually constructed from two linear gratings. The present study concentrated not on these Cartesian plaids, but on polar plaids, made from a combination of concentric circles and radial gratings. These kinds of plaids also have a special theoretical significance: within the Lie Transformation Group approach to visual pattern processing, Cartesian and polar stimuli represent different invariances in the visual world. This study compared Cartesian, polar and hybrid plaids as to their propensity to be perceived as coherently moving stimuli. Cartesian and polar plaids were similar in terms of the effects of intersection luminance and relative contrast on coherence, polar plaids being consistently less coherent. Hybrid plaids did not usually cohere at all. Adaptation to an unambiguously coherent plaid decreased perceived coherence when tested with a bistable plaid from the same, and not from the other Lie group, i.e. there was within-group adaptation but no between-group adaptation. Polar plaids also offer the possibility of studying the influence of another depth parameter on motion integration: expansion or contraction of circular gratings, which represent motion-in-depth toward or away from the observer. This motion-in-depth was tested for interaction with disparity or relative contrast in the determination of motion integration. The results were negative under the present conditions. Thus not all depth parameters contribute equally to the determination of the stimulus depth relations affecting the motion integration process.

Depth Perception↗
PubMed1975

Neural regulation of respiration.

The main respiratory muscles are under both voluntary and involuntary (automatic) control. These two control systems come from separate sites in the CNS and have separate descending pathways; the final integration of these outputs occurs at segmental levels in the cord. Voluntary control arises from the motor and premotor cortex and descends in the cord in the corticospinal tract. Involuntary control is mediated by both rhythmic and nonrhythmic systems located in the brainstem. Recent studies have associated the classic respiratory centers with specific nuclei in the brainstem. The pneumotaxic center is located in the nucleus parabrachialis, and the medullary respiratory centers are located in the vicinity of the nucleus of the solitary tract (dorsal respiratory group) and the nuclei ambiguus and retroambigualis (ventral respiratory group). Most axons from the medullary nuclei cross in the medulla and descend in the ventral and lateral columns to segmental levels. The classic medullary respiratory centers described by Pitts have been shown to be the site of origin of tonically firing long reticulospinal axons that descend in the ventral and lateral columns. This system is thought to provide a nonrhythmic involuntary biasing of the membrane potential of respiratory motoneurons in the cord. The site of generation of eupnic breathing and the mechanism of rhythm generation remain unknown. However, recent studies indicate that reciprocal inhibition between populations of inspiratory and expiratory cells (bistable oscillator model) does not occur in the medulla; rather we suggest that inhibitory phasing of inspiratory cells generates inspiratory rhythm, and periodic inhibition of tonically active expiratory neurons results in respiratory rhythm. We suggest that the inhibitory phasing occurs in the dorsal respiratory group, which is also the site of integration of respiratory afferents. The main site of integration of the voluntary and involuntary control systems is the cord where the respiratory motoneuron output is determined by descending information from these systems, as well as with intrasegmental and intersegmental reflexes. Separation of the voluntary and involuntary control systems also occurs in man and discrete lesions may interrupt one system without significant alteration of the other.

Animals↗
PubMed2003

Attention-biased multi-stable surface perception in three-dimensional structure-from-motion.

Retinal velocity distributions can lead to a percept of three-dimensional (3D) structure (structure-from-motion [SFM]). SFM stimuli are intrinsically ambiguous with regard to depth ordering. A classic example is the orthographic projection of a revolving transparent cylinder, which can be perceived as a 3D cylinder that rotates clockwise and counterclockwise alternately. Prevailing models attribute such bistable percepts to inhibitory connections between neurons that are tuned to opposite motion directions at equal binocular disparities. Cylinder stimuli can yield not only two but as many as four different percepts. Besides the well-documented clockwise and counterclockwise spinning transparent cylinders, observers can also perceive two transparent half-cylinders, either convex or concave, one in front of the other. Observers are able to bias the time during which a percept is present by attending to one or the other percept. We examined this phenomenon quantitatively and found that in standard SFM stimuli, the percept of two convex transparent half-cylinders can occur just as often as the percept of (counter-) clockwise spinning cylinders. So far, however, all interpretations of experimental (neurophysiological) data and all proposed mechanisms for SFM perception have focused solely on the two classical cylinder percepts. Prevailing models cannot explain the existence of the other two percepts. We suggest an alternative model to explain attention-biased multi-stable perception.

Attention↗
PubMed2006

Retinal image shifts, but not eye movements per se, cause alternations in awareness during binocular rivalry.

Particularly promising studies on visual awareness exploit a generally used perceptual bistability phenomenon, "binocular rivalry"--in which the two eyes' images alternately dominate--because it can dissociate the visual input from the perceptual output. To successfully study awareness, it is crucial to know the extent to which eye movements alter the input. Although there is convincing evidence that perceptual alternations can occur without eye movements, the literature on their exact role is mixed. Moreover, recent work has demonstrated that eye movements, first, correlate positively with perceptual alternations in binocular rivalry, and second, often accompany covert attention shifts (that were previously thought to be purely mental). Here, we asked whether eye movements cause perceptual alternations, and if so, whether it is either the execution of the eye movement or the resulting retinal image change that causes the alternation. Subjects viewed repetitive line patterns, enabling a distinction of saccades that did produce foveal image changes from those that did not. Subjects reported binocular rivalry alternations. We found that, although a saccade is not essential to initiate percept changes, the foveal image change resulting from a (micro)saccade is a deciding factor for percept dominance. We conclude that the foveal image must change to have a saccade cause a change in awareness. This sheds new light on the interaction between spatial attention shifts and perceptual alternations.

Awareness↗
PubMed2006

Unraveling adaptation and mutual inhibition in perceptual rivalry.

When the visual system is confronted with incompatible images in the same part of the visual field, the conscious percept switches back and forth between the rivaling stimuli. Such spontaneous flips provide important clues to the neuronal basis for visual awareness. The general idea is that two representations compete for dominance in a process of mutual inhibition, in which adaptation shifts the balance to and fro. The inherent nonlinear nature of the rivalrous flip-flop and its stochastic behavior, however, made it impossible to disentangle inhibition and adaptation. Here we report a general method to measure the time course, and asymmetries, of mechanisms involved in perceptual rivalry. Supported by model simulations, we show the dynamics of opponent interactions between mutual inhibition and adaptation. The findings not only provide new insight into the mechanism underlying rivalry but also offer new opportunities to study and compare a wide range of bistable processes in the brain and their relation to visual awareness.

Adaptation, Physiological↗
PubMed1994

Different phase responses of the two circadian oscillators in Gonyaulax.

Two circadian oscillators have been previously shown to exist in the unicellular alga Gonyaulax polyedra by virtue of different periods for two different rhythms, which occur under certain experimental conditions. Here we show that phase shifts in response to light pulses also differ for these two rhythms. The phase response curves (PRCs) for white or blue light pulses are similar in shape and amplitude, but are somewhat displaced in time and have a slightly larger delay portion for the aggregation rhythm, corresponding to the A oscillator. In contrast, the aggregation rhythm PRC for dark pulses in a red light background has a much larger amplitude than that for the bioluminescence rhythm (B oscillator). These results suggest that the light input mechanism of the B oscillator is mainly blue-sensitive, whereas that of the A oscillator is sensitive to both red and blue light. This is supported by entrainment experiments: Dark pulses given as a skeleton 24-hr scotoperiod in a blue light background act as a strong zeitgeber for both oscillators. But if red light is used as background, there is bistability in the entrainment of the B oscillator, whereas the A oscillator is entrained to a definitive phase angle, regardless of the cells' prior phase of entrainment. Finally, the two oscillators can be differentially entrained with 22-hr T cycles using 3-hr dark pulses interrupting red light (19 hr), whereas both oscillators are entrained when the dark pulses interrupt blue light.

Circadian Rhythm↗
PubMed2006

Multiscale Hy3S: hybrid stochastic simulation for supercomputers.

BACKGROUND: Stochastic simulation has become a useful tool to both study natural biological systems and design new synthetic ones. By capturing the intrinsic molecular fluctuations of "small" systems, these simulations produce a more accurate picture of single cell dynamics, including interesting phenomena missed by deterministic methods, such as noise-induced oscillations and transitions between stable states. However, the computational cost of the original stochastic simulation algorithm can be high, motivating the use of hybrid stochastic methods. Hybrid stochastic methods partition the system into multiple subsets and describe each subset as a different representation, such as a jump Markov, Poisson, continuous Markov, or deterministic process. By applying valid approximations and self-consistently merging disparate descriptions, a method can be considerably faster, while retaining accuracy. In this paper, we describe Hy3S, a collection of multiscale simulation programs. RESULTS: Building on our previous work on developing novel hybrid stochastic algorithms, we have created the Hy3S software package to enable scientists and engineers to both study and design extremely large well-mixed biological systems with many thousands of reactions and chemical species. We have added adaptive stochastic numerical integrators to permit the robust simulation of dynamically stiff biological systems. In addition, Hy3S has many useful features, including embarrassingly parallelized simulations with MPI; special discrete events, such as transcriptional and translation elongation and cell division; mid-simulation perturbations in both the number of molecules of species and reaction kinetic parameters; combinatorial variation of both initial conditions and kinetic parameters to enable sensitivity analysis; use of NetCDF optimized binary format to quickly read and write large datasets; and a simple graphical user interface, written in Matlab, to help users create biological systems and analyze data. We demonstrate the accuracy and efficiency of Hy3S with examples, including a large-scale system benchmark and a complex bistable biochemical network with positive feedback. The software itself is open-sourced under the GPL license and is modular, allowing users to modify it for their own purposes. CONCLUSION: Hy3S is a powerful suite of simulation programs for simulating the stochastic dynamics of networks of biochemical reactions. Its first public version enables computational biologists to more efficiently investigate the dynamics of realistic biological systems.

Cell Physiological Phenomena↗
PubMed2006

Inverse bifurcation analysis: application to simple gene systems.

BACKGROUND: Bifurcation analysis has proven to be a powerful method for understanding the qualitative behavior of gene regulatory networks. In addition to the more traditional forward problem of determining the mapping from parameter space to the space of model behavior, the inverse problem of determining model parameters to result in certain desired properties of the bifurcation diagram provides an attractive methodology for addressing important biological problems. These include understanding how the robustness of qualitative behavior arises from system design as well as providing a way to engineer biological networks with qualitative properties. RESULTS: We demonstrate that certain inverse bifurcation problems of biological interest may be cast as optimization problems involving minimal distances of reference parameter sets to bifurcation manifolds. This formulation allows for an iterative solution procedure based on performing a sequence of eigen-system computations and one-parameter continuations of solutions, the latter being a standard capability in existing numerical bifurcation software. As applications of the proposed method, we show that the problem of maximizing regions of a given qualitative behavior as well as the reverse engineering of bistable gene switches can be modelled and efficiently solved.

Journal Article↗
PubMed2003

Optical switching in chiropticenes.

Chiropticenes are a novel class of predesigned chiral molecular switches that are triggered and controlled by a combination of both light and electric field. Chiropticenes contain an optically active (chiral) center and, as a consequence, provide two accessible equal energy bistable states resembling the molecular elements of binary logic. Structural engineering of the basic switch design is investigated to modulate the thermal and optical switching behavior of the resulting compounds. A simple screening methodology is presented to detect switching behavior in the solid state employing standard NMR and FT-IR spectroscopy. Validation of this method is demonstrated by the switching properties of newly synthesized anthraquinone dye based Chiropticenes. Functioning as a chiroptical dipole switch, Chiropticenes promise broad applications in emerging optoelectronic and molecular electronic technologies.

Computers, Molecular↗
PubMed2003

Single-molecule designs for electric switches and rectifiers.

A design for molecular rectifiers is proposed. Current rectification is based on the spatial asymmetry of a molecule and requires only one resonant conducting molecular orbital. Rectification is caused by asymmetric coupling of the orbital to the electrodes, which results in asymmetric movement of the two Fermi levels with respect to the orbital under external bias. Results from numerical studies of the family of suggested molecular rectifiers, HS-(CH(2))(n)-C(6)H(4)(CH(2))(m)SH, are presented. Current rectification ratios in excess of 100 are achievable for n = 2 and m > 6. A class of bistable stator-rotor molecules is proposed. The stationary part connects the two electrodes and facilitates electron transport between them. The rotary part, which has a large dipole moment, is attached to an atom of the stator via a single sigma bond. Electrostatic bonds formed between the oxygen atom of the rotor and hydrogen atoms of the stator make the symmetric orientation of the dipole unstable. The rotor has two potential minima with equal energy for rotation about the sigma bond. The dipole can be flipped between the two states by an external electric field. Both rotor-orientation states have asymmetric current-voltage characteristics that are the reverse of each other, so they are distinguishable electrically. Theoretical results on conformation, energy barriers, retention times, switching voltages, and current-voltage characteristics are presented for a particular stator-rotor molecule. Such molecules could be the base for single-molecule switches, reversible diodes, and other molecular electronic devices.

Computer Simulation↗
PubMed2004

A longitudinal SEM approach to STAI data:two comprehensive multitrait-multistate models.

I investigated psychometric properties of data gathered with the State-Trait Anxiety Inventory (STAI; Spielberger, Gorsuch, Lushene, Vagg, & Jacobs, 1983, 1993) using structural equation modeling. Two features were integrated into the modeling: Bistability refers to the duality that is raised once the wording effect is recognized, and second-order, state-residual/trait decomposition refers to the basic bidimensionality of the data, which is revealed in a longitudinal perspective. I tested the approach on 2 samples of French adults (total N = 888) borrowed from Vautier and Jmel (2003). The models provided acceptable goodness of fit and supported the empirical need for hypothesizing 2 trait factors and 4 transient sources of true variance. I assessed the multidimensional composition of the composites using reliability analyses. I discuss theoretical consequences of the approach.

Adult↗