Bistable Neurons Research Articles

A machine-learning tool to identify bistable states from calcium imaging data.

Mapping neuronal activation using calcium imaging in vivo during behavioural tasks has advanced our understanding of nervous system function. In almost all of these studies, calcium imaging is used to infer spike probabilities because action potentials activate voltage-gated calcium channels and increase intracellular calcium levels. However, neurons not only fire action potentials, but also convey information via intrinsic dynamics such as by generating bistable membrane potential states. Although a number of tools for spike inference have been developed and are currently being used, no tool exists for converting calcium imaging signals to maps of cellular state in bistable neurons. Purkinje neurons in the larval zebrafish cerebellum exhibit membrane potential bistability, firing either tonically or in bursts. Several studies have implicated the role of a population code in cerebellar function, with bistability adding an extra layer of complexity to this code. In the present study, we develop a tool, CaMLSort, which uses convolutional recurrent neural networks to classify calcium imaging traces as arising from either tonic or bursting cells. We validate this classifier using a number of different methods and find that it performs well on simulated event rasters as well as real biological data that it had not previously seen. Moreover, we find that CaMLsort generalizes to other bistable neurons, such as dopaminergic neurons in the ventral tegmental area of mice. Thus, this tool offers a new way of analysing calcium imaging data from bistable neurons to understand how they participate in network computation and natural behaviours. KEY POINTS: Calcium imaging, compriising the gold standard of inferring neuronal activity, does not report cellular state in neurons that are bistable, such as Purkinje neurons in the cerebellum of larval zebrafish. We model the relationship between Purkinje neuron electrical activity and its corresponding calcium signal to compile a dataset of state-labelled simulated calcium signals. We apply machine-learning methods to this dataset to develop a tool that can classify the state of a Purkinje neuron using only its calcium signal, which works well on real data even though it was trained only on simulated data. CaMLsort (Calcium imaging and Machine Learning based tool to sort intracellular state) also generalizes well to bistable neurons in a different brain region (ventral tegmental area) in a different model organism (mouse). This tool can facilitate our understanding of how these neurons carry out their functions in a circuit.

BSNN: Towards faster and better conversion of artificial neural networks to spiking neural networks with bistable neurons.

The spiking neural network (SNN) computes and communicates information through discrete binary events. Recent work has achieved essential progress on an excellent performance by converting ANN to SNN. Due to the difference in information processing, the converted deep SNN usually suffers serious performance loss and large time delay. In this paper, we analyze the reasons for the performance loss and propose a novel bistable spiking neural network (BSNN) that addresses the problem of the phase lead and phase lag. Also, we design synchronous neurons (SN) to help efficiently improve performance when ResNet structure-based ANNs are converted. BSNN significantly improves the performance of the converted SNN by enabling more accurate delivery of information to the next layer after one cycle. Experimental results show that the proposed method only needs 1/4–1/10 of the time steps compared to previous work to achieve nearly lossless conversion. We demonstrate better ANN-SNN conversion for VGG16, ResNet20, and ResNet34 on challenging datasets including CIFAR-10 (95.16% top-1), CIFAR-100 (78.12% top-1), and ImageNet (72.64% top-1).

Dynamic responses of neurons in different states under magnetic field stimulation.

Transcranial magnetic stimulation (TMS) is an effective method to treat neurophysiological disorders by modulating the electrical activities of neurons. Neurons can exhibit complex nonlinear behaviors underlying the external stimuli. Currently, we do not know how stimulation interacts with endogenous neural activity. In this paper, the effects of magnetic field on spiking neuron, bursting neuron and bistable neuron are studied based on the Hodgkin-Huxley (HH) neuron model. The results show that the neurons in three different states can exhibit different dynamic responses under magnetic field stimulation. The magnetic field stimulation could increase or decrease the firing frequencies of spiking neuron, bursting neuron and bistable neuron. The transitions between different firing patterns of neurons can be promoted by changing the parameters of the magnetic field. Magnetic field stimulation has a minimal impact on the firing temporal sequence sequences in bursting neuron than that in spiking neuron and bistable neuron. These results provided an insight into the impact of neuronal states on neuronal dynamic responses under brain stimulation and show that subtle changes in external conditions and stimuli can cause complex neuronal responses. This study can help us understand the state-dependent coding mechanism of neurons under electromagnetic stimulation.

Firing dynamics in hybrid coupled populations of bistable neurons

We study the firing behavior of bistable neurons that are coupled by both electrical and chemical synapses, constituting a hybrid coupled population. We use stochastic Hodgkin–Huxley model neurons for the dynamics of individual bistable units within the population and the connectivity is implemented with a scale-free network topology which is a widely used network paradigm in theoretical studies of neural circuits. By analyzing the electrical activity of both whole population and individual neurons, it is shown that population mean firing rate exhibits a non-monotonic behavior in the space of electrical and chemical coupling strengths. We identify dynamical mechanisms that shape such non-monotonic spiking behavior and show that different types of population spiking patterns can emerge by fine-tuning the coupling strengths of electrical and chemical synapses. Furthermore, we map the transitions between observed dynamical states in the parameter space of interest depending on the level of individual neuron bistability, existence probability of a synapse type and intrinsic ion channel noise.

Synchronization-induced spike termination in networks of bistable neurons

We observe and study a self-organized phenomenon whereby the activity in a network of spiking neurons spontaneously terminates. We consider different types of populations, consisting of bistable model neurons connected electrically by gap junctions, or by either excitatory or inhibitory synapses, in a scale-free connection topology. We find that strongly synchronized population spiking events lead to complete cessation of activity in excitatory networks, but not in gap junction or inhibitory networks. We identify the underlying mechanism responsible for this phenomenon by examining the particular shape of the excitatory postsynaptic currents that arise in the neurons. We also examine the effects of the synaptic time constant, coupling strength, and channel noise on the occurrence of the phenomenon.

Efficient Coding and Energy Efficiency Are Promoted by Balanced Excitatory and Inhibitory Synaptic Currents in Neuronal Network.

Selective pressure may drive neural systems to process as much information as possible with the lowest energy cost. Recent experiment evidence revealed that the ratio between synaptic excitation and inhibition (E/I) in local cortex is generally maintained at a certain value which may influence the efficiency of energy consumption and information transmission of neural networks. To understand this issue deeply, we constructed a typical recurrent Hodgkin-Huxley network model and studied the general principles that governs the relationship among the E/I synaptic current ratio, the energy cost and total amount of information transmission. We observed in such a network that there exists an optimal E/I synaptic current ratio in the network by which the information transmission achieves the maximum with relatively low energy cost. The coding energy efficiency which is defined as the mutual information divided by the energy cost, achieved the maximum with the balanced synaptic current. Although background noise degrades information transmission and imposes an additional energy cost, we find an optimal noise intensity that yields the largest information transmission and energy efficiency at this optimal E/I synaptic transmission ratio. The maximization of energy efficiency also requires a certain part of energy cost associated with spontaneous spiking and synaptic activities. We further proved this finding with analytical solution based on the response function of bistable neurons, and demonstrated that optimal net synaptic currents are capable of maximizing both the mutual information and energy efficiency. These results revealed that the development of E/I synaptic current balance could lead a cortical network to operate at a highly efficient information transmission rate at a relatively low energy cost. The generality of neuronal models and the recurrent network configuration used here suggest that the existence of an optimal E/I cell ratio for highly efficient energy costs and information maximization is a potential principle for cortical circuit networks.SummaryWe conducted numerical simulations and mathematical analysis to examine the energy efficiency of neural information transmission in a recurrent network as a function of the ratio of excitatory and inhibitory synaptic connections. We obtained a general solution showing that there exists an optimal E/I synaptic ratio in a recurrent network at which the information transmission as well as the energy efficiency of this network achieves a global maximum. These results reflect general mechanisms for sensory coding processes, which may give insight into the energy efficiency of neural communication and coding.

Impact of membrane bistability on dynamical response of neuronal populations.

Neurons in many brain areas can develop a pronounced depolarized state of membrane potential (up state) in addition to the normal hyperpolarized state near the resting potential. The influence of the up state on signal encoding, however, is not well investigated. Here we construct a one-dimensional bistable neuron model and calculate the linear dynamical response to noisy oscillatory inputs analytically. We find that with the appearance of an up state, the transmission function is enhanced by the emergence of a local maximum at some optimal frequency and the phase lag relative to the input signal is reduced. We characterize the dependence of the enhancement of frequency response on intrinsic dynamics and on the occupancy of the up state.

Dynamics and reliability of bistable neurons driven with time-dependent stimuli.

The reliability of a spiking neuron depends on the frequency content of the driving input signal. Previous studies have shown that well above threshold, regularly firing neurons generate reliable responses when the input signal resonates with the firing frequency of the cell. Instead, well below threshold, reliable responses are obtained when the input frequency resonates with the subthreshold oscillations of the neuron. Previous theories, however, provide no clear prediction for the input frequency giving rise to maximally reliable spiking at threshold, which is probably the most relevant firing regime in mammalian cortex under physiological conditions. In particular, when the firing onset is governed by a subcritical Hopf bifurcation, the frequency of subthreshold oscillations often differs from the firing rate at threshold. The predictions of previous studies, hence, cannot be smoothly merged at threshold. Here we explore the behavior of reliability in bistable neurons near threshold using three types of driving stimuli: constant, periodic, and stochastic. We find that the two natural frequencies of the system, associated with the two coexisting attractors, provide a rich variety of possible locking modes with the external signal. Reliability is determined by the sensitivity to noise of each locking mode and by the transition probabilities between modes. Noise increases the amount of spike time jitter, and minimal jitter is obtained for input frequencies coinciding with the suprathreshold firing rate of the cell. In addition, noise may either enhance or inhibit transitions between the two attractors, depending on the input frequency. The dual role played by noise in bistable systems implies that reliability is determined by a delicate balance between spike time jitter and the rate of transitions between attractors.

Optimal size of stochastic Hodgkin-Huxley neuronal systems for maximal energy efficiency in coding pulse signals.

The generation and conduction of action potentials (APs) represents a fundamental means of communication in the nervous system and is a metabolically expensive process. In this paper, we investigate the energy efficiency of neural systems in transferring pulse signals with APs. By analytically solving a bistable neuron model that mimics the AP generation with a particle crossing the barrier of a double well, we find the optimal number of ion channels that maximizes the energy efficiency of a neuron. We also investigate the energy efficiency of a neuron population in which the input pulse signals are represented with synchronized spikes and read out with a downstream coincidence detector neuron. We find an optimal number of neurons in neuron population, as well as the number of ion channels in each neuron that maximizes the energy efficiency. The energy efficiency also depends on the characters of the input signals, e.g., the pulse strength and the interpulse intervals. These results are confirmed by computer simulation of the stochastic Hodgkin-Huxley model with a detailed description of the ion channel random gating. We argue that the tradeoff between signal transmission reliability and energy cost may influence the size of the neural systems when energy use is constrained.

Gating-signal propagation by a feed-forward neural motif

We study the signal propagation in a feed-forward motif consisting of three bistable neurons: Two input neurons receive input signals and the third output neuron generates the output. We find that a weak input signal can be propagated from the input neurons to the output neuron without amplitude attenuation. We further reveal that the initial states of the input neurons and the coupling strength act as signal gates and determine whether the propagation is enhanced or not. We also investigate the effect of the input signal frequency on enhanced signal propagation.

Neural networks including microRNAs

Numerous experimental studies performed during the past decade indicate that the synaptic plasticity, observed in neurons on the time scale comparable or longer than a few minutes, may be related to changes in the expression of genes transcribed into mRNAs and microRNAs (miRNAs). To illustrate what may happen in this case, the author presents a generic coarse-grained kinetic model describing the interplay of the membrane voltage pulses and gene expression with emphasis on miRNAs. The analysis is based on temporal differential equations. Under steady-state conditions, the kinetics under consideration are predicted to exhibit a unique steady state or bistability. The miRNA diffusion via gap junctions is shown to be able to synchronize and stabilize the kinetics in an array of bistable neurons. Such arrays are expected to serve as memory chips in brain.

Mechanisms Gating the Flow of Information in the Cortex: What They Might Look Like and What Their Uses may be

The notion of gating as a mechanism capable of controlling the flow of information from one set of neurons to another, has been studied in many regions of the central nervous system. In the nucleus accumbens, where evidence is especially clear, gating seems to rely on the action of bistable neurons, i.e., of neurons that oscillate between a quiescent “down” state and a firing “up” state, and that act as AND-gates relative to their entries. Independently from these observations, a growing body of evidence now indicates that bistable neurons are also quite abundant in the cortex, although their exact functions in the dynamics of the brain remain to be determined. Here, we propose that at least some of these bistable cortical neurons are part of circuits devoted to gating information flow within the cortex. We also suggest that currently available structural, electrophysiological, and imaging data support the existence of at least three different types of gating architectures. The first architecture involves gating directly by the cortex itself. The second architecture features circuits spanning the cortex and the thalamus. The third architecture extends itself through the cortex, the basal ganglia, and the thalamus. These propositions highlight the variety of mechanisms that could regulate the passage of action potentials between cortical neurons sets. They also suggest that gating mechanisms require larger-scale neural circuitry to control the state of the gates themselves, in order to fit in the overall wiring of the brain and complement its dynamics.

The Neuronal Replicator Hypothesis

We propose that replication (with mutation) of patterns of neuronal activity can occur within the brain using known neurophysiological processes. Thereby evolutionary algorithms implemented by neuro- nal circuits can play a role in cognition. Replication of structured neuronal representations is assumed in several cognitive architectures. Replicators overcome some limitations of selectionist models of neuronal search. Hebbian learning is combined with replication to structure exploration on the basis of associations learned in the past. Neuromodulatory gating of sets of bistable neurons allows patterns of activation to be copied with mutation. If the probability of copying a set is related to the utility of that set, then an evolutionary algorithm can be implemented at rapid timescales in the brain. Populations of neuronal replicators can undertake a more rapid and stable search than can be achieved by serial modification of a single solution. Hebbian learning added to neuronal replication allows a powerful structuring of variability capable of learning the location of a global optimum from multiple previously visited local optima. Replication of solutions can solve the problem of catastrophic forgetting in the stability-plasticity dilemma. In short, neuronal replication is essential to explain several features of flexible cognition. Predictions are made for the experimental validation of the neuronal replicator hypothesis.

Graded information extraction by neural-network dynamics with multihysteretic neurons

A major goal in the study of neural networks is to create novel information-processing algorithms inferred from the real brain. Recent neurophysiological evidence of graded persistent activity suggests that the brain possesses neural mechanisms for retrieval of graded information, which could be described by the neural-network dynamics with attractors that are continuously dependent on the initial state. Theoretical studies have also demonstrated that model neurons with a multihysteretic response property can generate robust continuous attractors. Inspired by these lines of evidence, we proposed an algorithm given by the multihysteretic neuron-network dynamics, devised to retrieve graded information specific to a given topic (i.e., context, represented by the initial state). To demonstrate the validity of the proposed algorithm, we examined keyword extraction from documents, which is best fitted for evaluating the appropriateness of retrieval of graded information. The performance of keyword extraction by using our algorithm was significantly high (measured by the average precision of document retrieval, for which the appropriateness of keyword extraction is crucial) compared with standard document-retrieval methods. Moreover, our algorithm exhibited much higher performance than the neural-network dynamics with bistable neurons, which can also produce robust continuous attractors but only represent dichotomous information at the single-cell level. These findings indicate that the capability to manage graded information at the single-cell level was essential for obtaining a high performing algorithm.

Context-dependent retrieval of information by neural-network dynamics with continuous attractors

Memory retrieval in neural networks has traditionally been described by dynamic systems with discrete attractors. However, recent neurophysiological findings of graded persistent activity suggest that memory retrieval in the brain is more likely to be described by dynamic systems with continuous attractors. To explore what sort of information processing is achieved by continuous-attractor dynamics, keyword extraction from documents by a network of bistable neurons, which gives robust continuous attractors, is examined. Given an associative network of terms, a continuous attractor led by propagation of neuronal activation in this network appears to represent keywords that express underlying meaning of a document encoded in the initial state of the network-activation pattern. A dominant hypothesis in cognitive psychology is that long-term memory is archived in the network structure, which resembles associative networks of terms. Our results suggest that keyword extraction by the neural-network dynamics with continuous attractors might symbolically represent context-dependent retrieval of short-term memory from long-term memory in the brain.

Robust persistent activity in neural fields with asymmetric connectivity

Modeling studies have shown that recurrent interactions within neural networks are capable of self-sustaining non-uniform activity profiles. These patterns are thought to be the neural basis of working memory. However, the lack of robustness challenge this view as already small deviations from the assumed interaction symmetry destroy the attractor state. Here we analyze attractor states of a neural field model composed of bistable neurons. We show the existence of self-stabilized patterns that robustly represent the cue position in the presence of a substantial asymmetry in the connection profile. Using approximation techniques we derive an explicit expression for a threshold value describing the transition to a traveling activity wave.

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.

Bistable neuromodules

We study bistable neurons and neuromodules and show that the dynamics are dependent upon the history of the system. A feedback mechanism is incorporated to generate bifurcation diagrams. The results from a linear stability analysis can be shown to match with the iterative techniques. Synaptic weights, biases and gradients of transfer functions are varied. The work can be applied to artificial neural networks and developing brains.

The Modulation of Corticoaccumbens Transmission by Limbic Afferents and Dopamine: A Model for the Pathophysiology of Schizophrenia

The prefrontal cortex (PFC) throughput in the accumbens is dependent on two systems: it is gated by depolarizations arising from the hippocampal input, and it is attenuated by dopamine (DA) acting presynaptically on PFC terminals and on accumbens neurons by decreasing excitability. Systemic administration of DA agonists also appears to interfere with PFC transmission in another manner-by affecting the transitions to the depolarized state. The chapter shows that systemic administration of D1 and D2 DA agonists causes a decrease in the frequency of transitions to the depolarized state in bistable neurons. Furthermore, systemic administration of the psychotomimetic phenycyclidine (PCP) also causes a potent suppression of the bistable state. As the primary action of these drugs is a slowing of the frequency of the bistable state rather than a decrease in its amplitude, these drugs are most likely acting directly or indirectly on the hippocampus. Therefore, administration of DA agonists and PCP or damage to the hippocampus has a similar impact in the accumbens. The ability of the hippocampus to gate the PFC has implications of relevance to schizophrenia. It has been suggested that a deficit in hippocampal function may be involved in the etiology of schizophrenia. In addition, afferents from the amygdala to the nucleus accumbens also appear to exert a unique modulatory influence over the PFC inputs. During in vivo intracellular recording, stimulation of the amygdala evoked a long-latency depolarization of the membrane of accumbens neurons. Therefore, the amygdala appears to exert a narrow, time-locked facilitation that may be selective for specific stimuli. These systems are likely to exert both a context-dependent (hippocampal) and affect-selective (amygdalar) gating of PFC throughput in the accumbens.