Membrane Potential Dependent Duration of Action Potentials in Cultured Rat Hippocampal Neurons

(1) Fluctuations of the membrane potential states are essential for the brain functions from the response of individual neurons to the cognitive function of the brain. It has been reported in slice preparations that the action potential duration is dependent on the membrane potential states. (2) In order to examine whether dependence of action potential duration on the membrane potential could happen in isolated individual neurons that have no network connections, we studied the membrane potential dependence of the action potential duration by artificially setting the membrane potentials to different states in individual cultured rat hippocampal neurons using patch-clamp technique. (3) We showed that the action potential of individual neurons generated from depolarized membrane potentials had broader durations than those generated from hyperpolarized membrane potentials. (4) Furthermore, the membrane potential dependence of the action potential duration was significantly reduced in the presence of voltage-gated K⁺ channel blockers, TEA, and 4-AP, suggesting involvement of both delayed rectifier I _K and transient I _A current in the membrane potential dependence of the action potential duration. (5) These results indicated that the dependence of action potential duration on the membrane potential states could be an intrinsic property of individual neurons. Bo Gong and Mingna Liu contributed equally to this work.     

A model of oscillation generation by molluscan neurons

A model describing slow oscillations of membrane potential in molluscan neurons is suggested. It is based on the view that the depolarization phase is due to the slow calcium current, whereas the hyperpolarization phase is due to the potassium current activated by intracellular Ca ions. It is shown that depending on values of the parameters of the model there are three possible types of electrical activity of the neurons: stable membrane hyperpolarization up to the resting potential which is between ?49 and ?53 mV; slow oscillations of membrane potential from ?30 to ?60 mV, with a period of 12–17 sec, and stable membrane depolarization to between ?40 and ?30 mV, which may lead to the onset of stable rhythmic activity of these neurons. Dependence of the amplitude of the oscillations of potential on the extracellular concentration of Ca, K, and Na ions was calculated and agrees qualitatively with the experimental data of Barker and Gainer [4].     

Rhythmic bioelectrical activity of the cerebral cortex analyzed with allowance for the nonlinear voltage dependence of excitatory postsynaptic potentials induced by neocortical neurons

A nonlinear voltage dependence between the membrane and excitatory postsynaptic potentials coming via corticocortical connections was derived based on literature data. The existence of a region of stability of oscillations with increasing mean value of nonspecific afferent input was shown. As the afferent input strongly increases, a high-frequency component of oscillations (40-60 Hz), appeas which may result in the instability of oscillations and initiation of abnormal brain activity.     

Rhythmical processes in the cerebral cortex bioelectrical activity in arousal reaction: qualitative nonlinear analysis involving refractoriness

An integral equation that takes into account the absolute and relative refractory periods of cortical cells was added to the earlier obtained integral equations describing the cooperation of excitatory and inhibitory neurons of the cerebral cortex, and its substantiation was suggested. The steady states and the stable region of oscillations of the mean membrane potential of excitatory neurons were investigated depending on the mean afferent influx value on the assumption of the normal threshold distribution of cells. The existence of a parameter multitude in the region of stability was shown when a suppression of the delta-rhythm and an enhancement of the theta-rhythm up to its dominance take place increasing nonspecific afferent influx, which shows up a white noise, and decrease of the theta-rhythm during further increase in nonspecific activation. Simultaneously the frequencies of the major cerebral rhythms increase. The conformity of the theoretically calculated dependences of changes of the spectrum upon increasing nonspecific afferent influx to the experimental data obtained during the electrical stimulation of the rabbit midbrain reticular formation was demonstrated.     

Long-term potentiation in rat hippocampal neurons is accompanied by spatially widespread changes in intrinsic oscillatory dynamics and excitability

Oscillations in neural activity are a prominent feature of many brain states. Individual hippocampal neurons exhibit intrinsic membrane potential oscillations and intrinsic resonance in the theta frequency range. We found that the subthreshold resonance frequency of CA1 pyramidal neurons was location dependent, varying more than 3-fold between the soma and the distal dendrites. Furthermore, activity- and NMDA-receptor-dependent long-term plasticity increased this resonance frequency through changes in h channel properties. The increase in resonance frequency and an associated reduction in excitability were nearly identical in the soma and the first 300 mum of the apical dendrites. These spatially widespread changes accompanying long-term synaptic potentiation also reduced the neuron's ability to elicit spikes evoked through a nonpotentiated synaptic pathway. Our results suggest that the frequency response of these neurons depends on the dendritic location of their inputs and that activity can regulate their response dynamics within an oscillating neural network.     

Integration and segregation of activity in entorhinal-hippocampal subregions by neocortical slow oscillations

Brain systems communicate by means of neuronal oscillations at multiple temporal and spatial scales. In anesthetized rats, we find that neocortical "slow" oscillation engages neurons in prefrontal, somatosensory, entorhinal, and subicular cortices into synchronous transitions between UP and DOWN states, with a corresponding bimodal distribution of their membrane potential. The membrane potential of hippocampal granule cells and CA3 and CA1 pyramidal cells lacked bimodality, yet it was influenced by the slow oscillation in a region-specific manner. Furthermore, in both anesthetized and naturally sleeping rats, the cortical UP states resulted in increased activity of dentate and most CA1 neurons, as well as the highest probability of ripple events. Yet, the CA3-CA1 network could self-organize into gamma bursts and occasional ripples during the DOWN state. Thus, neo/paleocortical and hippocampal networks periodically reset, self-organize, and temporally coordinate their cell assemblies via the slow oscillation.     

Membrane Potential Fluctuations Determine the Precision of Spike Timing and Synchronous Activity: A Model Study

It is much debated on what time scale information is encoded by neuronal spike activity. With a phenomenological model that transforms time-dependent membrane potential fluctuations into spike trains, we investigate constraints for the timing of spikes and for synchronous activity of neurons with common input. The model of spike generation has a variable threshold that depends on the time elapsed since the previous action potential and on the preceding membrane potential changes. To ensure that the model operates in a biologically meaningful range, the model was adjusted to fit the responses of a fly visual interneuron to motion stimuli. The dependence of spike timing on the membrane potential dynamics was analyzed. Fast membrane potential fluctuations are needed to trigger spikes with a high temporal precision. Slow fluctuations lead to spike activity with a rate about proportional to the membrane potential. Thus, for a given level of stochastic input, the frequency range of membrane potential fluctuations induced by a stimulus determines whether a neuron can use a rate code or a temporal code. The relationship between the steepness of membrane potential fluctuations and the timing of spikes has also implications for synchronous activity in neurons with common input. Fast membrane potential changes must be shared by the neurons to produce synchronous activity.     

Active hippocampal networks undergo spontaneous synaptic modification

The brain is self-writable; as the brain voluntarily adapts itself to a changing environment, the neural circuitry rearranges its functional connectivity by referring to its own activity. How the internal activity modifies synaptic weights is largely unknown, however. Here we report that spontaneous activity causes complex reorganization of synaptic connectivity without any external (or artificial) stimuli. Under physiologically relevant ionic conditions, CA3 pyramidal cells in hippocampal slices displayed spontaneous spikes with bistable slow oscillations of membrane potential, alternating between the so-called UP and DOWN states. The generation of slow oscillations did not require fast synaptic transmission, but their patterns were coordinated by local circuit activity. In the course of generating spontaneous activity, individual neurons acquired bidirectional long-lasting synaptic modification. The spontaneous synaptic plasticity depended on a rise in intracellular calcium concentrations of postsynaptic cells, but not on NMDA receptor activity. The direction and amount of the plasticity varied depending on slow oscillation patterns and synapse locations, and thus, they were diverse in a network. Once this global synaptic refinement occurred, the same neurons now displayed different patterns of spontaneous activity, which in turn exhibited different levels of synaptic plasticity. Thus, active networks continuously update their internal states through ongoing synaptic plasticity. With computational simulations, we suggest that with this slow oscillation-induced plasticity, a recurrent network converges on a more specific state, compared to that with spike timing-dependent plasticity alone.     

Functional states of an excitable membrane and their dependence on its parameter values

The property of an excitable membrane of a nerve cell to change the type of electrical activity has been examined with the change of the value of applied current (I). The dependence of this property on the values of the membrane parameters is determined. Two different functional states depending on the values of the membrane parameters are considered. For one of the states a change in the value of I is accompanied by a change in the type of activity (damped periodic oscillations jump to undamped periodic oscillations or vice versa). For the other state the type of activity remains phasic (damped periodic oscillations) for each value of I. For the mathematical model of a membrane we have considered the problem of obtaining the boundary, partitioning the parameter space into the regions to which these functional states correspond. We suggest a mathematical set of this problem and give its algorithm. These boundaries have been constructed for two different variable parameters of the model. A good agreement between the boundaries and the experimental values of sodium and potassium conductances for different excitable membranes has been obtained.     

Sleepy dialogues between cortex and hippocampus: who talks to whom?

During NREM sleep, neocortical neurons undergo near-synchronous transitions, every second or so, between UP states, during which they are depolarized and fire actively, and DOWN states, during which they are hyperpolarized and completely silent. In this issue of Neuron, Isomura et al. report that slow oscillations of membrane potential occur near-synchronously not only in neocortex but also in entorhinal cortex and subiculum. Within the hippocampus proper, pyramidal neurons lack the bistability of UP and DOWN states, but their firing is strongly modulated by cortical activity during the UP state. Intriguingly, many hippocampal neurons fire during the cortical DOWN state. Thus, during sleep UP states, the cortex can talk to the hippocampus, but it is unclear whether the hippocampus talks back.     

Neuronal oscillations enhance stimulus discrimination by ensuring action potential precision

Although oscillations in membrane potential are a prominent feature of sensory, motor, and cognitive function, their precise role in signal processing remains elusive. Here we show, using a combination of in vivo, in vitro, and theoretical approaches, that both synaptically and intrinsically generated membrane potential oscillations dramatically improve action potential (AP) precision by removing the membrane potential variance associated with jitter-accumulating trains of APs. This increased AP precision occurred irrespective of cell type and—at oscillation frequencies ranging from 3 to 65 Hz—permitted accurate discernment of up to 1,000 different stimuli. At low oscillation frequencies, stimulus discrimination showed a clear phase dependence whereby inputs arriving during the trough and the early rising phase of an oscillation cycle were most robustly discriminated. Thus, by ensuring AP precision, membrane potential oscillations dramatically enhance the discriminatory capabilities of individual neurons and networks of cells and provide one attractive explanation for their abundance in neurophysiological systems.     

How the nonlinear voltage dependence of the amplitude of excitatory postsynaptic potentials induced by cerebral cortical neurons affects cortical rhythmic activity

A nonlinear dependence of the amplitude of excitatory postsynaptic potentials on the membrane potentials was derived. The existence of a region of oscillation stability with an increase in the mean value of nonspecific afferent inflow was demonstrated. A high-frequency oscillation component (40–60 Hz) appears with a pronounced increase in the afferent inflow; this can cause instability in oscillations and abnormal brain activity.     

Dynamics of Sparsely Connected Networks of Excitatory and Inhibitory Spiking Neurons

The dynamics of networks of sparsely connected excitatory and inhibitory integrate-and-fire neurons are studied analytically. The analysis reveals a rich repertoire of states, including synchronous states in which neurons fire regularly; asynchronous states with stationary global activity and very irregular individual cell activity; and states in which the global activity oscillates but individual cells fire irregularly, typically at rates lower than the global oscillation frequency. The network can switch between these states, provided the external frequency, or the balance between excitation and inhibition, is varied. Two types of network oscillations are observed. In the fast oscillatory state, the network frequency is almost fully controlled by the synaptic time scale. In the slow oscillatory state, the network frequency depends mostly on the membrane time constant. Finite size effects in the asynchronous state are also discussed.     

Emergent oscillations in a realistic network: the role of inhibition and the effect of the spatiotemporal distribution of the input.

We have simulated a network of 10,000 two-compartment cells, spatially distributed on a two-dimensional sheet; 15% of the cells were inhibitory. The input to the network was spatially delimited. Global oscillations frequently were achieved with a simple set of connectivity rules. The inhibitory neurons paced the network, whereas the excitatory neurons amplified the input, permitting oscillations at low-input intensities. Inhibitory neurons were active over a greater area than excitatory ones, forming a ring of inhibition. The oscillation frequency was modulated to some extent by the input intensity, as has been shown experimentally in the striate cortex, but predominantly by the properties of the inhibitory neurons and their connections: the membrane and synaptic time constants and the distribution of delays. In networks that showed oscillations and in those that did not, widely distributed inputs could lead to the specific recruitment of the inhibitory neurons and to near zero activity of the excitatory cells. Hence the spatial distribution of excitatory inputs could provide a means of selectively exciting or inhibiting a target network. Finally, neither the presence of oscillations nor the global spike activity provided any reliable indication of the level of excitatory output from the network.     

Emergent Oscillations in a Realistic Network: The Role of Inhibition and the Effect of the Spatiotemporal Distribution of the Input

We have simulated a network of 10,000 two-compartment cells, spatially distributed on a two-dimensional sheet; 15% of the cells were inhibitory. The input to the network was spatially delimited. Global oscillations frequently were achieved with a simple set of connectivity rules. The inhibitory neurons paced the network, whereas the excitatory neurons amplified the input, permitting oscillations at low-input intensities. Inhibitory neurons were active over a greater area than excitatory ones, forming a ring of inhibition. The oscillation frequency was modulated to some extent by the input intensity, as has been shown experimentally in the striate cortex, but predominantly by the properties of the inhibitory neurons and their connections: the membrane and synaptic time constants and the distribution of delays.In networks that showed oscillations and in those that did not, widely distributed inputs could lead to the specific recruitment of the inhibitory neurons and to near zero activity of the excitatory cells. Hence the spatial distribution of excitatory inputs could provide a means of selectively exciting or inhibiting a target network. Finally, neither the presence of oscillations nor the global spike activity provided any reliable indication of the level of excitatory output from the network.     

Neural organization of the ventilatory activity in the frog,Rana catesbeiana. II

The paralyzed, decerebrate frog, Rana catesbeiana, displays “fictive” oropharyngeal and pulmonary ventilations. In order to evaluate the neuronal correlates of these two centrally programmed ventilatory bursting patterns, we have performed intra-and extracellular recordings of bulbar respiratory neurons in this fictively breathing preparation. A total of 123 respiratory neurons were recorded from the caudal medulla. Of 51 antidromically activated neurons, 20 were vagal motoneurons and 31 were hypoglossal motoneurons. Respiratory neurons that depolarized during the lung (L) or non-lung (N) ventilatory phases were classified as L or N neurons, respectively. Phase spanning neurons (S) were active during both L and N phases. Some neurons showed oscillations of membrane potential synchronous with oropharyngeal ventilation. Those active during the buccal elevation phase were exclusively L neurons whereas those having buccal depressor activity were exclusively N neurons. Synaptic drive potentials were observed in all neurons recorded intracellularly. In some neurons, hyperpolarization was caused by inhibitory postsynaptic potentials, as demonstrated by reversal of membrane potential trajectory after intracellular chloride iontophoresis. Some individual motoneurons and interneurons exhibited both pulmonary and buccal ventilatory activity, indicating that both pattern generators project to a common motor control system. 1994 John Wiley & Sons, Inc.     

Energy features in spontaneous up and down oscillations

Spontaneous brain activities consume most of the brain’s energy. So if we want to understand how the brain operates, we must take into account these spontaneous activities. Up and down transitions of membrane potentials are considered to be one of significant spontaneous activities. This kind of oscillation always shows bistable and bimodal distribution of membrane potentials. Our previous theoretical studies on up and down oscillations mainly looked at the ion channel dynamics. In this paper, we focus on energy feature of spontaneous up and down transitions based on a network model and its simulation. The simulated results indicate that the energy is a robust index and distinguishable of excitatory and inhibitory neurons. Meanwhile, one the whole, energy consumption of neurons shows bistable feature and bimodal distribution as well as the membrane potential, which turns out that the indicator of energy consumption encodes up and down states in this spontaneous activity. In detail, energy consumption mainly occurs during up states temporally, and mostly concentrates inside neurons rather than synapses spatially. The stimulation related energy is small, indicating that energy consumption is not driven by external stimulus, but internal spontaneous activity. This point of view is also consistent with brain imaging results. Through the observation and analysis of the findings, we prove the validity of the model again, and we can further explore the energy mechanism of more spontaneous activities.     

K(+)-dependent composite gating of the yeast K(+) channel, Tok1

TOK1 encodes an outwardly rectifying K(+) channel in the plasma membrane of the budding yeast Saccharomyces cerevisiae. It is capable of dwelling in two kinetically distinct impermeable states, a near-instantaneously activating R state and a set of related delayed activating C states (formerly called C(2) and C(1), respectively). Dwell in the R state is dependent on membrane potential and both internal and external K(+) in a manner consistent with the K(+) electrochemical potential being its determinant, where dwell in the C states is dependent on voltage and only external K(+). Whereas activation from the C states showed high temperature dependencies, typical of gating transitions in other Shaker-like channels, activation from the R state had a temperature dependence nearly as low as that of simple ionic diffusion. These findings lead us to conclude that although the C states reflect the activity of an internally oriented channel gate, the R state results from an intrinsic gating property of the channel filter region.     

TTX-Resistant NMDA Receptor-Mediated Membrane Potential Oscillations in Neonatal Mouse Hb9 Interneurons

Conditional neuronal membrane potential oscillations have been identified as a potential mechanism to help support or generate rhythmogenesis in neural circuits. A genetically identified population of ventromedial interneurons, called Hb9, in the mouse spinal cord has been shown to generate TTX-resistant membrane potential oscillations in the presence of NMDA, serotonin and dopamine, but these oscillatory properties are not well characterized. Hb9 interneurons are rhythmically active during fictive locomotor-like behavior. In this study, we report that exogenous N-Methyl-D-Aspartic acid (NMDA) application is sufficient to produce membrane potential oscillations in Hb9 interneurons. In contrast, exogenous serotonin and dopamine application, alone or in combination, are not sufficient. The properties of NMDA-induced oscillations vary among the Hb9 interneuron population; their frequency and amplitude increase with increasing NMDA concentration. NMDA does not modulate the T-type calcium current (I_Ca(T)), which is thought to be important in generating locomotor-like activity, in Hb9 neurons. These results suggest that NMDA receptor activation is sufficient for the generation of TTX-resistant NMDA-induced membrane potential oscillations in Hb9 interneurons.