Decreased Response to Acetylcholine during Aging of Aplysia Neuron R15

How aging affects the communication between neurons is poorly understood. To address this question, we have studied the electrophysiological properties of identified neuron R15 of the marine mollusk Aplysia californica. R15 is a bursting neuron in the abdominal ganglia of the central nervous system and is implicated in reproduction, water balance, and heart function. Exposure to acetylcholine (ACh) causes an increase in R15 burst firing. Whole-cell recordings of R15 in the intact ganglia dissected from mature and old Aplysia showed specific changes in burst firing and properties of action potentials induced by ACh. We found that while there were no significant changes in resting membrane potential and latency in response to ACh, the burst number and burst duration is altered during aging. The action potential waveform analysis showed that unlike mature neurons, the duration of depolarization and the repolarization amplitude and duration did not change in old neurons in response to ACh. Furthermore, single neuron quantitative analysis of acetylcholine receptors (AChRs) suggested alteration of expression of specific AChRs in R15 neurons during aging. These results suggest a defect in cholinergic transmission during aging of the R15 neuron.     

Leader neurons in leaky integrate and fire neural network simulations

In this paper, we highlight the topological properties of leader neurons whose existence is an experimental fact. Several experimental studies show the existence of leader neurons in population bursts of activity in 2D living neural networks (Eytan and Marom, J Neurosci 26(33):8465–8476, 2006; Eckmann et al., New J Phys 10(015011), 2008). A leader neuron is defined as a neuron which fires at the beginning of a burst (respectively network spike) more often than we expect by chance considering its mean firing rate. This means that leader neurons have some burst triggering power beyond a chance-level statistical effect. In this study, we characterize these leader neuron properties. This naturally leads us to simulate neural 2D networks. To build our simulations, we choose the leaky integrate and fire (lIF) neuron model (Gerstner and Kistler 2002; Cessac, J Math Biol 56(3):311–345, 2008), which allows fast simulations (Izhikevich, IEEE Trans Neural Netw 15(5):1063–1070, 2004; Gerstner and Naud, Science 326:379–380, 2009). The dynamics of our lIF model has got stable leader neurons in the burst population that we simulate. These leader neurons are excitatory neurons and have a low membrane potential firing threshold. Except for these two first properties, the conditions required for a neuron to be a leader neuron are difficult to identify and seem to depend on several parameters involved in the simulations themselves. However, a detailed linear analysis shows a trend of the properties required for a neuron to be a leader neuron. Our main finding is: A leader neuron sends signals to many excitatory neurons as well as to few inhibitory neurons and a leader neuron receives only signals from few other excitatory neurons. Our linear analysis exhibits five essential properties of leader neurons each with different relative importance. This means that considering a given neural network with a fixed mean number of connections per neuron, our analysis gives us a way of predicting which neuron is a good leader neuron and which is not. Our prediction formula correctly assesses leadership for at least ninety percent of neurons.     

GABAA- and AMPA-like receptors modulate the activity of an identified neuron within the central pattern generator of the pond snail Lymnaea stagnalis

To examine the neurochemistry underlying the firing of the RPeD1 neuron in the respiratory central pattern generator of the pond snail, Lymnaea stagnalis, we examined electrophysiologically and pharmacologically either “active” or “silent” preparations by intracellular recording and pharmacology. GABA inhibited electrical firing by hyperpolarizing RPeD1, while picrotoxin, an antagonist of GABA_A receptors, excited silent cells and reversed GABA-induced inhibition. Action potential activity was terminated by 1 mM glutamate (Glu) while silent cells were depolarized by the GluR agonists, AMPA, and NMDA. Kainate exerted a complex triphasic effect on membrane potential. However, only bath application of AMPA desensitized the firing. These data indicate that GABA inhibits RPeD1 via activation of GABA_A receptors, while Glu stimulates the neuron by activating AMPA-sensitive GluRs.     

Seizure-like afterdischarges simulated in a model neuron

To explore non-synaptic mechanisms in paroxysmal discharges, we used a computer model of a simplified hippocampal pyramidal cell, surrounded by interstitial space and a “glial-endothelial” buffer system. Ion channels for Na⁺, K⁺, Ca²⁺ and Cl⁻ _, ion antiport 3Na/Ca, and “active” ion pumps were represented in the neuron membrane. The glia had “leak” conductances and an ion pump. Fluxes, concentration changes and cell swelling were computed. The neuron was stimulated by injecting current. Afterdischarge (AD) followed stimulation if depolarization due to rising interstitial K⁺ concentration ([K⁺]_o) activated persistent Na⁺ current (I _Na,P). AD was either simple or self-regenerating; either regular (tonic) or burst-type (clonic); and always self-limiting. Self-regenerating AD required sufficient I _Na,P to ensure re-excitation. Burst firing depended on activation of dendritic Ca²⁺ currents and Ca-dependent K⁺ current. Varying glial buffer function influenced [K⁺]_o accumulation and afterdischarge duration. Variations in Na⁺ and K⁺ currents influenced the threshold and the duration of AD. The data show that high [K⁺]_o and intrinsic membrane currents can produce the feedback of self-regenerating afterdischarges without synaptic input. The simulated discharge resembles neuron behavior during paroxysmal firing in living brain tissue. Action Editor: David Terman     

Time-Dependent Molecular Memory in Single Voltage-Gated Sodium Channel

Excitability in neurons is associated with firing of action potentials and requires the opening of voltage-gated sodium channels with membrane depolarization. Sustained membrane depolarization, as seen in pathophysiological conditions like epilepsy, can have profound implications on the biophysical properties of voltage-gated ion channels. Therefore, we sought to characterize the effect of sustained membrane depolarization on single voltage-gated Na⁺ channels. Single-channel activity was recorded in the cell-attached patch-clamp mode from the rNa_v1.2α channels expressed in CHO cells. Classical statistical analysis revealed complex nonlinear changes in channel dwell times and unitary conductance of single Na⁺ channels as a function of conditioning membrane depolarization. Signal processing tools like weighted wavelet Z (WWZ) and discrete Fourier transform analyses attributed a “pseudo-oscillatory” nature to the observed nonlinear variation in the kinetic parameters. Modeling studies using the hidden Markov model (HMM) illustrated significant changes in kinetic states and underlying state transition rate constants upon conditioning depolarization. Our results suggest that sustained membrane depolarization induces novel nonlinear properties in voltage-gated Na⁺ channels. Prolonged membrane depolarization also induced a “molecular memory” phenomenon, characterized by clusters of dwell time events and strong autocorrelation in the dwell time series similar to that reported recently for single enzyme molecules. The persistence of such molecular memory was found to be dependent on the duration of depolarization. Voltage-gated Na⁺ channel with the observed time-dependent nonlinear properties and the molecular memory phenomenon may determine the functional state of the channel and, in turn, the excitability of a neuron.     

Rapid Estradiol-17β Modulation of Opioid Actions on the Electrical and Secretory Activity of Rat Oxytocin Neurons In vivo

During pregnancy, emergence of endogenous opioid inhibition of oxytocin neurons is revealed by increased oxytocin secretion after administration of the opioid receptor antagonist, naloxone. Here we show that prolonged estradiol-17β and progesterone treatment (mimicking pregnancy levels) potentiates naloxone-induced oxytocin secretion in urethane-anesthetized virgin female rats. We further show that estradiol-17β alone rapidly modifies opioid interactions with oxytocin neurons, by recording their firing rate in anesthetized rats sensitized to naloxone by morphine dependence. Naloxone-induced morphine withdrawal strongly increased the firing rate of oxytocin neurons in morphine dependent rats. Estradiol-17β did not alter basal oxytocin neuron firing rate over 30 min, but amplified naloxone-induced increases in firing rate. Firing pattern analysis indicated that acute estradiol-17β increased oxytocin secretion in dependent rats by increasing action potential clustering without an overall increase in firing rate. Hence, rapid estradiol-17β actions might underpin enhanced oxytocin neuron responses to naloxone in pregnancy. Special issue article in honor of George Fink.     

The enzymatic neuron as a reaction-diffusion network of cyclic nucleotides

Recent evidence suggests that the cyclic nucleotides play a central role in the intracellular processing of neural signals. The dynamics of this system may be seen as a realization of the enzymatic neuron model. Enzymatic neurons are formal neurons which map binary afferent signals into patterns of excitation across an abstract membrane. The distribution of enzyme-like elements called excitases enables a set of local threshold functions to determine the firing activity of the neuron. This paper analyzes the basic properties of enzymatic neurons in a simple continuous-time framework, and shows how they may be presented as reaction-diffusion networks which model the cyclic nucleotide system. We present the results of computer simulations of this neuron and discuss its implications for selectional learning and its relation to conventional two-factor systems. One fundamental property of the reaction-diffusion neuron is its so-called “double-dynamics” property; examination of this property and its contribution to the computing power of the neuron provides some insight into the obscure relation between microscopic and macroscopic models of computation.     

Electrophysiological and Morphological Properties of Neurons Acutely Isolated from the Rostral Gustatory Zone of the Rat Nucleus of the Solitary Tract

The biophysical and morphological characteristics of acutelyisolated neurons from the rostral nucleus of the solitary tract(rNST) were investigated under current clamp conditions andcompared with the results obtained from neurons recorded inbrain slices. The passive membrane properties of the isolatedneurons were similar to rNST neurons in brain slices and theneurons maintained their morphological characteristics althoughtheir dendritic tree was truncated. The isolated neurons alsoretained their characteristic repetitive firing properties.In addition we also noted developmental changes in the intrinsicmembrane properties of the isolated neurons, such as a shorteningin action potential duration, decrease in membrane time constantand input resistance, that occurred when these parameters werecompared in neurons isolated from young (5–10 days) andolder animals. These enzymatically dispersed neurons thereforeretained both the membrane properties and morphology observedin the intact brainstem and in vitro brain slice preparation.The use of this isolated neuron preparation provides a basisfor further study of rNST neurobiology. Chem. Senses 21: 729–737,1996     

Amphetamine elicited potential changes in vertebrate and invertebrate central neurons

The effects of amphetamine on potential changes in both vertebrate and invertebrate central neurons and factors affecting the potential changes were tested. The animals studied included mice, newborn rat and African snail. Seizure was elicited after lethal doses of d-amphetamine (75 mg/kg, i.p.) administration in mice. Repetitive firing of the action potentials were elicited after d-amphetamine (1-30 microM) administration in thin thalamic brain slices of newborn rat. Bursting firing of action potentials in the giant African central RP4 neuron were also elicited after d-amphetamine or l-amphetamine (0.27 mM) administration. The amphetamine elicited bursting firing of action potentials was not blocked even after high concentrations of d-tubocurarine, atropine, haloperidol, hexamethonium administration. Therefore, the amphetamine elicited potential changes may not be directly related to the activation of the receptors of the neuron. The bursting firing of action potentials elicited by amphetamine occurred 20-30 min after amphetamine administration extracellularly, even after high concentrations of d-amphetamine administration (0.27, 1 mM). However, the bursting firing of potentials occurred immediately if amphetamine was administrated intracellularly at lower concentration. Extracellular application of ruthenium red, the calcium antagonist, abolished the amphetamine elicited bursting firing of action potentials. If intracellular injection of EGTA, a calcium ion chelator, or injection with high concentrations of magnesium, the bursting firing of potentials were immediately abolished. These results suggested that the active site of amphetamine may be inside of the neuron and the calcium ion in the neuron played an important role on the bursting of potentials. In two-electrode voltage clamped RP4 neuron, amphetamine, at 0.27 mM, decreased the total inward and steady outward currents of the RP4 neuron. d-Amphetamine also decreased the calcium, Ia and the steady-state outward currents of the RP4 neuron. Besides, amphetamine elicited a negative slope resistance (NSR) if membrane potential was in the range of -50 to -10 mV. The NSR was decreased in cobalt substituted calcium free and sodium free solution. The effects of secondary messengers on the amphetamine elicited potential changes were tested. The bursting firing of action potentials elicited by amphetamine in central snail neurons decreased following extracellular application of H8 (N-(2-methyl-amino) ethyl-3-isoquinoline sulphonamide dihydrochloride), a specific protein kinase A inhibitor and anisomycin, a protein synthesis inhibitor. However, the bursting firing of action potentials were not affected after extracellular application of H7 (1,(5-isoquinolinesulphonyl)-2-methylpiperasine dihydrochloride), a specific protein kinase C (PKC) inhibitor, or intracellular application of GDPbetaS, a G protein inhibitor. The oscillation of membrane potential of the bursting activity was blocked after intracellular injection of 3'-deoxyadenosine, an adenylyl-cyclase inhibitor. These results suggested that the bursting firing of action potentials elicited by d-amphetamine in snail neuron may be associated with the cyclic AMP second messenger system; on the other hand, it may not be associated with the G protein and protein kinase C activity. It is concluded that amphetamine elicited potential changes in both vertebrate and invertebrate central neurons. The changes are closely related to the ionic currents and second messengers of the neurons.     

White-noise stimulation of the Hodgkin–Huxley model

 We studied the combined influence of noise and constant current stimulations on the Hodgkin–Huxley neuron model through time and frequency analysis of the membrane-potential dynamics. We observed that, in agreement with experimental data (Guttman et al. 1974), at low noise and low constant current stimulation the behavior of the model is well approximated by that of the linearized Hodgkin–Huxley system. Conversely, nonlinearities due to firing dominate at large noise or current stimulations. The transition between the two regimes is abrupt, and takes place in the same range of noise and current intensities as the noise-induced transition characterized by the qualitative change in the stationary distribution of the membrane potential (Tanabe and Pakdaman 2001a). The implications of these results are discussed. Received: 27 July 2001 / Accepted in revised form: 18 December 2001     

Dynamical features of higher-order correlation events: impact on cortical cells

Cortical neurons receive signals from thousands of other neurons. The statistical properties of the input spike trains substantially shape the output response properties of each neuron. Experimental and theoretical investigations have mostly focused on the second order statistical features of the input spike trains (mean firing rates and pairwise correlations). Little is known of how higher order correlations affect the integration and firing behavior of a cell independently of the second order statistics. To address this issue, we simulated the dynamics of a population of 5000 neurons, controlling both their second order and higher-order correlation properties to reflect physiological data. We then used these ensemble dynamics as the input stage to morphologically reconstructed cortical cells (layer 5 pyramidal, layer 4 spiny stellate cell), and to an integrate and fire neuron. Our results show that changes done solely to the higher-order correlation properties of the network’s dynamics significantly affect the response properties of a target neuron, both in terms of output rate and spike timing. Moreover, the neuronal morphology and voltage dependent mechanisms of the target neuron considerably modulate the quantitative aspects of these effects. Finally, we show how these results affect sparseness of neuronal representations, tuning properties, and feature selectivity of cortical cells. An erratum to this article can be found at     

Postinhibitory unit response of crustacean stretch receptors after direct and recurrent inhibition

The postinhibitory response of a slowly adapting neuron was investigated in experiments on an isolated preparation of crustacean stretch receptor and abdominal nerve chain. The structural features of this preparation are such that this response can be regarded as the response of the postsynaptic membrane to synaptic inhibition and not the action of synaptic excitation. IPSPs arise in the slowly adapting neuron in response to stimulation of the abdominal nerve chain (direct inhibition) or to excitation of the neuron itself (recurrent inhibition). The postinhibitory response consists of the development of action potentials or an increase in their amplitude and frequency. The magnitude of the response is determined by the duration of the inhibition and the state of the neuron membrane. The postinhibitory response was strongest when IPSPs were superposed on cathodal depression. IPSPs and an intracellular hyperpolarizing current evoke similar postinhibitory responses. Repetitive excitation of an inhibitory neuron may result in the appearance of a regular spike discharge from a previously inactive neuron through the mechanism of the postinhibitory response. Activation of a chain of recurrent inhibition increases the duration of the postinhibitory response evoked by direct inhibition or by a hyperpolarizing current. The existence of a chain of recurrent inhibition prevents the cessation of firing by a neuron during increasing cathodal depression. A mechanism of postinhibitory rebound lies at the basis of this phenomenon.     

Motoneuron membrane potentials follow a time inhomogeneous jump diffusion process

Stochastic leaky integrate-and-fire models are popular due to their simplicity and statistical tractability. They have been widely applied to gain understanding of the underlying mechanisms for spike timing in neurons, and have served as building blocks for more elaborate models. Especially the Ornstein–Uhlenbeck process is popular to describe the stochastic fluctuations in the membrane potential of a neuron, but also other models like the square-root model or models with a non-linear drift are sometimes applied. Data that can be described by such models have to be stationary and thus, the simple models can only be applied over short time windows. However, experimental data show varying time constants, state dependent noise, a graded firing threshold and time-inhomogeneous input. In the present study we build a jump diffusion model that incorporates these features, and introduce a firing mechanism with a state dependent intensity. In addition, we suggest statistical methods to estimate all unknown quantities and apply these to analyze turtle motoneuron membrane potentials. Finally, simulated and real data are compared and discussed. We find that a square-root diffusion describes the data much better than an Ornstein–Uhlenbeck process with constant diffusion coefficient. Further, the membrane time constant decreases with increasing depolarization, as expected from the increase in synaptic conductance. The network activity, which the neuron is exposed to, can be reasonably estimated to be a threshold version of the nerve output from the network. Moreover, the spiking characteristics are well described by a Poisson spike train with an intensity depending exponentially on the membrane potential.     

A cross-interval spike train analysis: the correlation between spike generation and temporal integration of doublets

A stochastic spike train analysis technique is introduced to reveal the correlation between the firing of the next spike and the temporal integration period of two consecutive spikes (i.e., a doublet). Statistics of spike firing times between neurons are established to obtain the conditional probability of spike firing in relation to the integration period. The existence of a temporal integration period is deduced from the time interval between two consecutive spikes fired in a reference neuron as a precondition to the generation of the next spike in a compared neuron. This analysis can show whether the coupled spike firing in the compared neuron is correlated with the last or the second-to-last spike in the reference neuron. Analysis of simulated and experimentally recorded biological spike trains shows that the effects of excitatory and inhibitory temporal integration are extracted by this method without relying on any subthreshold potential recordings. The analysis also shows that, with temporal integration, a neuron driven by random firing patterns can produce fairly regular firing patterns under appropriate conditions. This regularity in firing can be enhanced by temporal integration of spikes in a chain of polysynaptically connected neurons. The bandpass filtering of spike firings by temporal integration is discussed. The results also reveal that signal transmission delays may be attributed not just to conduction and synaptic delays, but also to the delay time needed for temporal integration. Received: 3 March 1997 / Accepted in revised form: 6 November 1997     

Effect of different glucose supply conditions on neuronal energy metabolism

The glucose-excited neurons in brain can sense blood glucose levels and reflect different firing states, which are mainly associated with regulation of blood glucose and energy demand in the brain. In this paper, a new model of glucose-excited neuron in hypothalamus is proposed. The firing properties and energy consumption of this type of neuron under conditions of different glucose levels are simulated and analyzed. The results show that the firing rate and firing duration of the neuron both increase with increasing extracellular glucose levels, but the maximum energy power for an AP is reduced. Further study suggests that the neuron firstly absorbs energy substrates (e.g. glucose) from the blood to prepare for the high energy demand of high-frequency spikes.     

Relating ion channel expression, bifurcation structure, and diverse firing patterns in a model of an identified motor neuron

Neurons show diverse firing patterns. Even neurons belonging to a single chemical or morphological class, or the same identified neuron, can display different types of electrical activity. For example, motor neuron MN5, which innervates a flight muscle of adult Drosophila, can show distinct firing patterns under the same recording conditions. We developed a two-dimensional biophysical model and show that a core complement of just two voltage-gated channels is sufficient to generate firing pattern diversity. We propose Shab and DmNa _v to be two candidate genes that could encode these core currents, and find that changes in Shab channel expression in the model can reproduce activity resembling the main firing patterns observed in MN5 recordings. We use bifurcation analysis to describe the different transitions between rest and spiking states that result from variations in Shab channel expression, exposing a connection between ion channel expression, bifurcation structure, and firing patterns in models of membrane potential dynamics.     

Library-based numerical reduction of the Hodgkin–Huxley neuron for network simulation

We present an efficient library-based numerical method for simulating the Hodgkin–Huxley (HH) neuronal networks. The key components in our numerical method involve (i) a pre-computed high resolution data library which contains typical neuronal trajectories (i.e., the time-courses of membrane potential and gating variables) during the interval of an action potential (spike), thus allowing us to avoid resolving the spikes in detail and to use large numerical time steps for evolving the HH neuron equations; (ii) an algorithm of spike-spike corrections within the groups of strongly coupled neurons to account for spike-spike interactions in a single large time step. By using the library method, we can evolve the HH networks using time steps one order of magnitude larger than the typical time steps used for resolving the trajectories without the library, while achieving comparable resolution in statistical quantifications of the network activity, such as average firing rate, interspike interval distribution, power spectra of voltage traces. Moreover, our large time steps using the library method can break the stability requirement of standard methods (such as Runge–Kutta (RK) methods) for the original dynamics. We compare our library-based method with RK methods, and find that our method can capture very well phase-locked, synchronous, and chaotic dynamics of HH neuronal networks. It is important to point out that, in essence, our library-based HH neuron solver can be viewed as a numerical reduction of the HH neuron to an integrate-and-fire (I&F) neuronal representation that does not sacrifice the gating dynamics (as normally done in the analytical reduction to an I&F neuron).     

Frequency switching in a two-compartmental model of the dopaminergic neuron

Mid-brain dopaminergic (DA) neurons display two functionally distinct modes of electrical activity: low- and high-frequency firing. The high-frequency firing is linked to important behavioral events in vivo. However, it cannot be elicited by standard manipulations in vitro. We had suggested a two-compartmental model of the DA cell that united data on firing frequencies under different experimental conditions. We now analyze dynamics of this model. The analysis was possible due to introduction of timescale separation among variables. We formulate the requirements for low and high frequencies. We found that the modulation of the SK current gating controls the frequency rise under applied depolarization. This provides a new mechanism that limits the frequency in the control conditions and allows high-frequency responses to depolarization if the SK current gating is downregulated. The mechanism is based on changing Ca^2 + balance and can also be achieved by direct modulation of the balance. Interestingly, such changes do not affect the high-frequency oscillations under NMDA. Therefore, altering Ca^2 + balance allows combining the high-frequency response to NMDA activation with the inability of other treatments to effectively elevate the frequency. We conclude that manipulations affecting Ca^2 + balance are most effective in controlling the frequency range. This modeling prediction gives a clue to the mechanism of the high-frequency firing in the DA neuron in vivo and in vitro.     

Spikes annihilation in the Hodgkin-Huxley neuron

The Hodgkin–Huxley (HH) neuron is a nonlinear system with two stable states: A fixed point and a limit cycle. Both of them co-exist. The behavior of this neuron can be switched between these two equilibria, namely spiking and resting respectively, by using a perturbation method. The change from spiking to resting is named Spike Annihilation, and the transition from resting to spiking is named Spike Generation. Our intention is to determine if the HH neuron in 2D is controllable (i.e., if it can be driven from a quiescent state to a spiking state and vice versa). It turns out that the general system is unsolvable.¹ In this paper, first of all,² we analytically prove the existence of a brief current pulse, which, when delivered to the HH neuron during its repetitively firing state, annihilates its spikes. We also formally derive the characteristics of this brief current pulse. We then proceed to explore experimentally, by using numerical simulations, the properties of this pulse, namely the range of time when it can be inserted (the minimum phase and the maximum phase), its magnitude, and its duration. In addition, we study the solution of annihilating the spikes by using two successive stimuli, when the first is, of its own, unable to annihilate the neuron. Finally, we investigate the inverse problem of annihilation, namely the spike generation problem, when the neuron switches from resting to firing. ¹ This conclusion is a consequence of three well-known fundamental results, namely Hilbert 16th Problem, the Poincare–Bendixon Theorem and the Hopf Bifurcation Theorem. ² We are extremely grateful to the feedback we received from the anonymous Referees to the initial version of the paper. Their comments significantly improved the quality of the current version. Thanks a lot!     

A study and model of the role of the Renshaw cell in regulating the transient firing rate of the motoneuron

 This study sought to investigate the role of the Renshaw cell with respect to transient motoneuron firing. By studying the cat motoneuron and Renshaw cell, several low-order lumped parameter models were developed that simulate the known characteristics of the injected input current vs. firing rate. The neuron models in the Renshaw cell inhibition configuration were tuned to fit experimental data from cat motoneurons. Models included both linear versions and those with sigmoidal nonlinearities. Results of the simulation indicate that the motoneuron itself provides the adaptation seen in its firing rate and that the Renshaw cell’s role is primarily to fine-tune the motoneuron’s adaptation process. Received: 23 July 1993/Accepted in revised form: 9 February 1994