Membrane Potential Bistability 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.

Conditions for Kir-induced bistability of membrane potential in capillary endothelial cells

A simplified model for electrophysiology of endothelial cells is used to examine the conditions that can lead to bistability of membrane resting potential. The model includes the effects of inward-rectifying potassium (Kir) ion channels, whose current–voltage relationship shows an interval of negative slope and whose maximum conductance is dependent on the extracellular potassium concentration. The background current resulting from other types of channels is assumed to be linearly related to membrane potential. A method is presented for identifying the boundaries in the parameter space for the background currents of the regions of bistability. It is shown that these regions are relatively narrow and depend on extracellular potassium concentration. The results are used to define conditions leading to transitions between depolarized and hyperpolarized membrane states. These behaviors can influence the properties of conducted responses, in which changes in membrane potential are propagated along blood vessel walls. Conducted responses are important in the local regulation of blood flow in the brain and other tissues.

Dynamic Analysis of the Conditional Oscillator Underlying Slow Waves in Thalamocortical Neurons.

During non-REM sleep the EEG shows characteristics waves that are generated by the dynamic interactions between cortical and thalamic oscillators. In thalamic neurons, low-threshold T-type Ca2+ channels play a pivotal role in almost every type of neuronal oscillations, including slow (< 1 Hz) waves, sleep spindles and delta waves. The transient opening of T channels gives rise to the low threshold spikes (LTSs), and associated high frequency bursts of action potentials, that are characteristically present during sleep spindles and delta waves, whereas the persistent opening of a small fraction of T channels, (i.e., ITwindow) is responsible for the membrane potential bistability underlying sleep slow oscillations. Surprisingly thalamocortical (TC) neurons express a very high density of T channels that largely exceed the amount required to generate LTSs and therefore, to support certain, if not all, sleep oscillations. Here, to clarify the relationship between T current density and sleep oscillations, we systematically investigated the impact of the T conductance level on the intrinsic rhythmic activities generated in TC neurons, combining in vitro experiments and TC neuron simulation. Using bifurcation analysis, we provide insights into the dynamical processes taking place at the transition between slow and delta oscillations. Our results show that although stable delta oscillations can be evoked with minimal T conductance, the full range of slow oscillation patterns, including groups of delta oscillations separated by Up states (“grouped-delta slow waves”) requires a high density of T channels. Moreover, high levels of T conductance ensure the robustness of different types of slow oscillations.

Nonlinear conductance and heterogeneity of voltage-gated ion channels allow defining electrical surface domains in cell membranes

The membrane potential of a cell measured by typical electrophysiological methods is only an average magnitude and experimental techniques allowing a more detailed mapping of the cell surface have shown the existence of spatial domains with locally different electric potentials and currents. Electrical potentials in non-neural cells are regulated by the nonlinear conductance of membrane ion channels. Voltage-gated potassium channels participate in cell hyperpolarization/depolarization processes and control the electrical signals over the cell surface, constituting good candidates to study basic biological questions on a more simplified scale than the complex cell membrane. These channels show also a high heterogeneity, making it possible to analyze the effects of diversity in the electrical responses of channels localized on spatial domains. We use a phenomenological approach of voltage gating that reproduces the observed rectification characteristics of inward rectifying potassium channels and relate the threshold voltage heterogeneity of the channels to the establishment of spatial domains with different electrical sensitivities. Although our model is only a limited picture of the whole cell membrane, it shows that domains with different ion channels may permit or suppress steady state bioelectrical signals over the cell surface according to their particular voltage sensitivity. Also, the nonlinear electrical coupling of channels with different threshold potentials can lead to a rich variety of bioelectrical phenomena, including regions of membrane potential bi-stability.

Adult spinal V2a interneurons show increased excitability and serotonin-dependent bistability.

In mice, most studies of the organization of the spinal central pattern generator (CPG) for locomotion, and its component neuron classes, have been performed on neonatal [postnatal day (P)2-P4] animals. While the neonatal spinal cord can generate a basic locomotor pattern, it is often argued that the CPG network is in an immature form whose detailed properties mature with postnatal development. Here, we compare intrinsic properties and serotonergic modulation of the V2a class of excitatory spinal interneurons in behaviorally mature (older than P43) mice to those in neonatal mice. Using perforated patch recordings from genetically tagged V2a interneurons, we revealed an age-dependent increase in excitability. The input resistance increased, the rheobase values decreased, and the relation between injected current and firing frequency (F/I plot) showed higher excitability in the adult neurons, with almost all neurons firing tonically during a current step. The adult action potential (AP) properties became narrower and taller, and the AP threshold hyperpolarized. While in neonates the AP afterhyperpolarization was monophasic, most adult V2a interneurons showed a biphasic afterhyperpolarization. Serotonin increased excitability and depolarized most neonatal and adult V2a interneurons. However, in ∼30% of adult V2a interneurons, serotonin additionally elicited spontaneous intrinsic membrane potential bistability, resulting in alternations between hyperpolarized and depolarized states with a dramatically decreased membrane input resistance and facilitation of evoked plateau potentials. This was never seen in younger animals. Our findings indicate a significant postnatal development of the properties of locomotor-related V2a interneurons, which could alter their interpretation of synaptic inputs in the locomotor CPG.

Membrane Potential Bistability in Nonexcitable Cells as Described by Inward and Outward Voltage-Gated Ion Channels

The membrane potential of nonexcitable cells, defined as the electrical potential difference between the cell cytoplasm and the extracellular environment when the current is zero, is controlled by the individual electrical conductance of different ion channels. In particular, inward- and outward-rectifying voltage-gated channels are crucial for cell hyperpolarization/depolarization processes, being amenable to direct physical study. High (in absolute value) negative membrane potentials are characteristic of terminally differentiated cells, while low membrane potentials are found in relatively depolarized, more plastic cells (e.g., stem, embryonic, and cancer cells). We study theoretically the hyperpolarized and depolarized values of the membrane potential, as well as the possibility to obtain a bistability behavior, using simplified models for the ion channels that regulate this potential. The bistability regions, which are defined in the multidimensional state space determining the cell state, can be relevant for the understanding of the different model cell states and the transitions between them, which are triggered by changes in the external environment.

A non-inactivating high-voltage-activated two-pore Na⁺ channel that supports ultra-long action potentials and membrane bistability.

Action potentials (APs) are fundamental cellular electrical signals. The genesis of short APs lasting milliseconds is well understood. Ultra-long APs (ulAPs) lasting seconds to minutes also occur in eukaryotic organisms, but their biological functions and mechanisms of generation are largely unknown. Here, we identify TPC3, a previously uncharacterized member of the two-pore channel protein family, as a new voltage-gated Na+ channel (NaV) that generates ulAPs, and that establishes membrane potential bistability. Unlike the rapidly inactivating NaVs that generate short APs in neurons, TPC3 has a high activation threshold, activates slowly, and does not inactivate—three properties that help generate long-lasting APs and guard the membrane against unintended perturbation. In amphibian oocytes, TPC3 forms a channel similar to channels induced by depolarization and sperm entry into eggs. TPC3 homologs are present in plants and animals, and they may be important for cellular processes and behaviors associated with prolonged membrane depolarization.

A defined heteromeric KV1 channel stabilizes the intrinsic pacemaking and regulates the output of deep cerebellar nuclear neurons to thalamic targets

The output of the cerebellum to the motor axis of the central nervous system is orchestrated mainly by synaptic inputs and intrinsic pacemaker activity of deep cerebellar nuclear (DCN) projection neurons. Herein, we demonstrate that the soma of these cells is enriched with K(V)1 channels produced by mandatory multi-merization of K(V)1.1, 1.2 α and KV β2 subunits. Being constitutively active, the K(+) current (IK(V)1) mediated by these channels stabilizes the rate and regulates the temporal precision of self-sustained firing of these neurons. Placed strategically, IK(V)1 provides a powerful counter-balance to prolonged depolarizing inputs, attenuates the rebound excitation, and dampens the membrane potential bi-stability. Somatic location with low activation threshold render IK(V)1 instrumental in voltage-dependent de-coupling of the axon initial segment from the cell body of projection neurons, impeding invasion of back-propagating action potentials into the somato-dendritic compartment. The latter is also demonstrated to secure the dominance of clock-like somatic pacemaking in driving the regenerative firing activity of these neurons, to encode time variant inputs with high fidelity. Through the use of multi-compartmental modelling and retro-axonal labelling, the physiological significance of the described functions for processing and communication of information from the lateral DCN to thalamic relay nuclei is established.

“Apneas” in Purkinje cell activity: evidence for the bistability of membrane potential in the awake cat cerebellum

Sustained neural activity can be the result of either the dynamics of recurrent neural networks or the intrinsic properties of individual cells. In the later case, it has been shown in different brain areas that neurons can present a bistable behavior where brief inputs produce a prolonged increase in discharge rate due to a depolarized membrane potential. Neurons in this active condition, the “up-state”, can switch to a hyperpolarized/down-state where they do not fire (O'Donnell and Grace, 1995). In vitro studies in different species have shown that Purkinje cells (PCs) of the cerebellum posses the intrinsic machinery to be considered bistable (Williams et al., 2002). The bistability of membrane potential is manifested in two firing profiles, namely, tonic firing of simple spikes (SSs) in the up-state and pausing periods in the down-state (Loewenstein et al., 2005; Schonewille et al., 2006). These neurons can toggle between both states spontaneously or after brief but significant stimulation in in vitro as well as in anesthetized in vivo preparations using intra and extracellular recordings. However, a recent discrepancy has emerged regarding whether or not PCs in awake animals can toggle from a preponderant up-state to the hyperpolarized condition (Schonewille et al., 2006). Yartsev et al. (2009) confronted these issues using extracellular recordings in the awake, behaving cat. They demonstrated that half of the PCs show long pauses in SSs activity that switched back and forth with periods of continuous firing. These cells, called pausing PCs (PPs), were clearly distinguished from continuous firing PCs using the following quantitative methods: (i) the coefficient of variation in the inter-spike interval (ISI); (ii) the dip test for unimodal instantaneous firing rate; and (iii) a bi-exponential fit to the ISI histogram – only in PPCs two distinct exponentials could be obtained (see Figures 1A (IV), B (IV)). The “apneas” in PCs activity seem to be independent of inhibitory inputs, and they show a duration that is similar to the periods of hyperpolarization observed in intracellular recordings. Hence, bistability inferred indirectly by extracellular recordings may be present in a large portion of PCs in the awake cat.

Pausing Purkinje cells in the cerebellum of the awake cat

A recent controversy has emerged concerning the existence of long pauses, presumably reflecting bistability of membrane potential, in the cerebellar Purkinje cells (PC) of awake animals. It is generally agreed that in the anesthetized animals and in vitro, these cells switch between two stable membrane potential states: a depolarized state (the ‘up-state’) characterized by continuous firing of simple spikes (SS) and a hyperpolarized state (the ‘down-state’) characterized by long pauses in the SS activity. To address the existence of long pauses in the neural activity of cerebellar PCs in the awake and behaving animal we used extracellular recordings in cats and find that approximately half of the recorded PCs exhibit such long pauses in the SS activity and transition between activity – periods with uninterrupted SS lasting an average of 1300 ms – and pauses up to several seconds. We called these cells pausing Purkinje cells (PPC) and they can easily be distinguished from continuous firing Purkinje cells. In most PPCs, state transitions in both directions were often associated (25% of state transitions) with complex spikes (CSs). This is consistent with intracellular findings of CS-driven state transitions. In sum, we present proof for the existence of long pauses in the PC SS activity that probably reflect underlying bistability, provide the first in-depth analysis of these pauses and show for the first time that transitions in and out of these pauses are related to CS firing in the awake and behaving animal.

Bistability of cerebellar Purkinje cells modulated by sensory stimulation

A persistent change in neuronal activity after brief stimuli is a common feature of many neuronal microcircuits. This persistent activity can be sustained by ongoing reverberant network activity or by the intrinsic biophysical properties of individual cells. Here we demonstrate that rat and guinea pig cerebellar Purkinje cells in vivo show bistability of membrane potential and spike output on the time scale of seconds. The transition between membrane potential states can be bidirectionally triggered by the same brief current pulses. We also show that sensory activation of the climbing fiber input can switch Purkinje cells between the two states. The intrinsic nature of Purkinje cell bistability and its control by sensory input can be explained by a simple biophysical model. Purkinje cell bistability may have a key role in the short-term processing and storage of sensory information in the cerebellar cortex.

Recruitment of motor neuronal persistent inward currents shapes withdrawal reflexes in the frog

The details of behaviour are determined by the interplay of synaptic connectivity within neuronal circuitry and the intrinsic membrane properties of individual neurones. One particularly dramatic intrinsic property displayed by neurones in many regions of the nervous system is membrane potential bistability, in which transient excitation of a neurone results in a persistent depolarization outlasting the initial excitation. Here we characterize the contribution of such intrinsic bistability, also referred to as plateau properties and mediated by persistent inward currents (PICs), in spinal motor neurones to the production of withdrawal behaviours in the frog. We performed experiments on the isolated frog spinal cord with attached hindlimb. This preparation allowed the simultaneous monitoring of muscle activations during motor behaviour and intracellular neuronal recordings. We found that PICs, following their potentiation by serotonin (5-HT), are recruited and contribute to the production of withdrawal behaviours. These properties conferred a voltage-dependent prolongation to the duration of motor neuronal activity. Consistent with this potentiation of motor neuronal PICs, 5-HT also increased the duration of evoked muscle activations. This behavioural potentiation, as well as the expression of PICs in individual neurones, was reduced following antagonism of L-type Ca(2+) channels. These results demonstrate that PICs in motor neurones can be recruited during the production of behaviour and play a role in specifying the temporal details of motor output.

Regulation of main olfactory bulb mitral cell excitability by metabotropic glutamate receptor mGluR1.

In the rodent main olfactory bulb (MOB), mitral cells (MCs) express high levels of the group I metabotropic glutamate receptor (mGluR) subtype, mGluR1. The significance of this receptor in modulating MC excitability is unknown. We investigated the physiological role of mGluR1 in regulating MC activity in rat and mouse MOB slices. The selective group I agonist (RS)-3,5-dihydroxyphenylglycine (DHPG), but not group II or III agonists, induced potent, dose-dependent, and reversible depolarization and increased firing of MCs. These effects persisted in the presence of blockers of fast synaptic transmission, indicating that they are due to direct activation of mGluRs on MCs. Voltage-clamp recordings showed that DHPG elicited a voltage-dependent inward current consisting of multiple components sensitive to potassium and calcium channel blockade and intracellular calcium chelation. MC excitatory responses to DHPG were absent in mGluR1 knockout mice but persisted in mGluR5 knockout mice. Broad-spectrum LY341495, MCPG, as well as preferential mGluR1 LY367385 antagonists blocked the excitatory effects of DHPG and also potently modulated MC spontaneous and olfactory nerve-evoked excitability. mGluR antagonists altered spontaneous membrane potential bistability, increasing the duration of the up and down states. mGluR antagonists also substantially attenuated MC responses to sensory input, decreasing the probability and increasing the latency of olfactory nerve-evoked spikes. These findings suggest that endogenous glutamate tonically modulates MC excitability and responsiveness to olfactory nerve input, and hence the operation of the MOB circuitry, via activation of mGluR1.

Propagation of quasi-stable activation in a chain of recurrent neural networks

We consider a chain of feed-forward connected recurrent networks of leaky-integrate-and-fire neurons with membrane potential bistability. It is shown that lump neural activation, lasting for several seconds at each recurrent network, is gradually relayed along the chain. The time scale of the lump activation and its propagation along the chain agrees with that characterizing mental process. These results suggest that our model will provide possible neural mechanisms underlying mental representation of episodes.

Membrane potential bistability is controlled by the hyperpolarization-activated current I(H) in rat cerebellar Purkinje neurons in vitro.

We investigated the role of the hyperpolarization-activated mixed cation current, I(H), in the control of spontaneous action potential firing of rat cerebellar Purkinje neurons in brain slices. Extracellular recordings revealed that the continual action potential firing of Purkinje neurons was disrupted by the pharmacological blockade of I(H). Blockade of I(H) revealed spontaneous transitions between periods of tonic action potential firing and quiescence, without effects on the frequency or variance of action potential generation. Whole-cell recordings revealed that blockade of I(H) unmasked a form of membrane potential bistability, where transitions between tonic firing and quiescent states (separated by approximately 20 mV) were evoked by excitatory and inhibitory postsynaptic potentials, or by the delivery of brief (20 ms) somatic or dendritic positive and negative current pulses. The stable upper state of tonic action potential firing was maintained by the recruitment of axo-somatic voltage-activated sodium, but not calcium, channels. Negative modulation of I(H) by serotonin unmasked bistability, indicating that bistability of Purkinje neurons is likely to occur under physiological conditions. These data indicate that I(H) acts as a 'safety net', maintaining the membrane potential of Purkinje neurons within the range necessary for the generation of tonic action potential firing. Following the downregulation of I(H), synaptic inhibition can generate long periods (seconds) of quiescence, the duration of which can be controlled by climbing fibre activation and by the underlying 'tone' of parallel fibre activity.

Osmolality influences bistability of membrane potential under hypokalemic conditions in mouse skeletal muscle: an experimental and theoretical study

The membrane potential in mouse skeletal muscle depends on both extracellular osmolality and potassium concentration. These dependencies have been related to two membrane transporters, Na +/K +/2Cl − co-transporter and the inward potassium rectifier channel. To investigate the relation of the Na +/K +/2Cl − co-transporter and the inward potassium rectifier channel in a qualitative way, a combined electrophysiological and modelling approach was used. The experimental results show that the bistability of the membrane potential, which is related to the conductive state of the inward potassium rectifier channel, is shifted to higher extracellular potassium values when medium osmolality is increased. These results are confirmed by the computer simulation calculations for increased co-transporter flux. The combined results indicate that the co-transporter is capable of modulating the conductive state of the inward potassium rectifier channel.

All thalamocortical neurones possess a T-type Ca2+ 'window' current that enables the expression of bistability-mediated activities.

1. The existence of a non-negligible steady-state ('window') component of the low threshold, T-type Ca2+current (IT) and an appropriately large ratio of IT to ILeak conductance (i.e. gT/gLeak) have been shown to underlie a novel form of intrinsic bistability that is present in about 15 % of thalamocortical (TC) neurones. 2. In the present experiments, the dynamic clamp technique was used to introduce into mammalian TC neurones in vitro either an artificial, i.e. computer-generated, IT in order to enhance endogenous IT, or an artificial inward ILeak to decrease endogenous ILeak. Using this method, we were able to investigate directly whether the majority of TC neurones appear non-bistable because their intrinsic ionic membrane properties are essentially different (i.e. presence of a negligible IT 'window' component), or simply because they possess a gT or gLeak conductance that is insufficiently large or small, respectively. 3. The validity of the dynamic clamp arrangement and the accuracy of artificial IT were confirmed by (i) recreating the low threshold calcium potential (LTCP) with artificial IT following its block by Ni2+ (0.5-1 mM), and (ii) blocking endogenous LTCPs with an artificial outward IT. 4. Augmentation of endogenous IT by an artificial analog or introduction of an artificial inward ILeak transformed all non-bistable TC neurones to bistable cells that expressed the full array of bistability-mediated behaviours, i.e. input signal amplification, slow oscillatory activity and membrane potential bistability. 5. These results demonstrate the existence of a non-negligible IT 'window' component in all TC neurones and suggest that rather than being a novel group of neurones, bistable cells are merely representative of an interesting region of dynamical modes in the (gT, gLeak) parameter space that may be expressed under certain physiological or pathological conditions by all TC neurones and other types of excitable cells that possess an IT 'window' component with similar biophysical properties.

2324 A method to estimate the real [Ca 2+] i from signals of fluorescentcalcium dyes

1.1. Neuron LP1 of Hermissenda crassicornis shows pronounced anomalous rectification at a membrane potential of −65 mV, or more negative, indicated by a 3- to 4-fold reduction in input resistance, producing an S-shaped current-voltage relationship.2.2. Axotomized LPls show membrane potential bistability since shifts in membrane potential between stable levels at ca −45 and −65 mV accompanied by a change in input resistance occur spontaneously or are induced by current pulses.3.3. Stability at −65 mV appears to be due to activation of the anomalous rectifier.

N-methyl-D-aspartate receptor-induced, inherent oscillatory activity in neurons active during fictive locomotion in the lamprey

Bath application of N-methyl-aspartate induces fictive locomotor activity in the isolated spinal cord preparation of the lamprey, as well as TTX-resistant membrane potential oscillations in many individual neurons. This inherent oscillatory activity is shown to depend on a specific activation of N-methyl-D-aspartate (NMDA) receptors. This activation initiates voltage-dependent, magnesium-requiring membrane potential bistability, presumably due to a development of a region of negative slope conductance in the current-voltage relation of the neuron. When sodium ions were removed from the bathing solution, oscillations disappeared, and the membrane potential was maintained at a hyperpolarized level, suggesting that the depolarizing current during the oscillatory cycle is mainly carried by sodium ions. Replacing Ca2+ with Ba2+ also leads to a cessation of oscillatory activity, with the membrane potential remaining at the more depolarized level. This indicates an involvement of a Ca2+-dependent K+ current during the repolarization phase. These findings, together with the voltage dependence, can account for the main characteristics of the NMDA receptor-induced, TTX-resistant membrane potential oscillations. This oscillatory behavior has been demonstrated in motoneurons and in several interneurons including CC interneurons but has not been found in edge cells, dorsal cells, or lateral interneurons. The possibility that inherent oscillatory membrane properties may contribute to the activity pattern during fictive locomotion was investigated in experiments with intracellular current injection in the absence of TTX. The stimulation effects obtained required the presence of magnesium ions and were analogous to the stimulation effects seen during oscillations after TTX blockade. Together with similarities in, for instance, frequency and amplitude between the locomotor oscillatory activity and the TTX-resistant oscillations, the results are compatible with an involvement of inherent, oscillatory membrane properties during fictive locomotion in the lamprey spinal cord.

Bistability of membrane potential and anomalous rectification in neuron LP1 of Hermissenda

1. 1. Neuron LP1 of Hermissenda crassicornis shows pronounced anomalous rectification at a membrane potential of −65 mV, or more negative, indicated by a 3- to 4-fold reduction in input resistance, producing an S-shaped current-voltage relationship. 2. 2. Axotomized LPls show membrane potential bistability since shifts in membrane potential between stable levels at ca −45 and −65 mV accompanied by a change in input resistance occur spontaneously or are induced by current pulses. 3. 3. Stability at −65 mV appears to be due to activation of the anomalous rectifier.