Electrical Inexcitability of the Frog Neuromuscular Synapse

Frog muscle endplates were explored with an extracellular microelectrode. An intracellular microelectrode nearby simultaneously monitored invasion of the endplate by a spike directly evoked by a third microelectrode placed away from the endplate in the same fiber. External positivities were seen only at sites generating miniature endplate potentials. The external positivity reached a maximum prior to the internally recorded potential and was followed by a small late negativity. Small movements away from active synaptic sites resulted in positive-negative-positive potential sequences characteristic of activity and propagation. Since the external potential is a function of membrane current, the absence of negativity associated with the rising phase of the spike indicates the absence of inward current at synaptic sites. Thus, the synaptic membrane appears not to be excited by a depolarization of the magnitude of an action potential. In an Appendix it is shown that the late negativity and earlier maximum of the external potential can be accounted for by capacitative current through passive membrane.     

The velocity of conduction in nerve fiber and its electric characteristics

The theory developed in this paper shows that the propagation of spike potential along a nerve fiber and the conduction of an electric wave along an inert inorganic conductor follow a common quantitative relationship. This result gives further support to the belief that propagation of excitation is an electrical process. The basic idea of the theory is derived from the consideration that velocity has, by its mathematical definition, a local meaning; conduction in a nerve is completely determined by the local characteristics of the latter, as well as those of the wave. The final formula derived does not make use of any other field of science beyond the fundamental principles of electricity. It gives the conduction velocity in terms of the electric characteristics of the fiber and of the duration of the spike potential. The formula is in agreement with the known dependence of the conduction velocity on various parameters characterizing the axon. The computed velocity agrees with the measured ones on the squid giant axon, crab nerve axon, frog muscle fiber and Nitella cell. The membrane inductance appears as a velocity controling agent which prevents also a possible distortion of the spike potential during conduction. The structural meaning of the electric characteristics of the axon membrane is discussed from the viewpoint of the diffusion theory. A formula for the velocity of spread of the electrotonus is also derived.     

Reliability of spike and burst firing in thalamocortical relay cells

The reliability and precision of the timing of spikes in a spike train is an important aspect of neuronal coding. We investigated reliability in thalamocortical relay (TCR) cells in the acute slice and also in a Morris-Lecar model with several extensions. A frozen Gaussian noise current, superimposed on a DC current, was injected into the TCR cell soma. The neuron responded with spike trains that showed trial-to-trial variability, due to amongst others slow changes in its internal state and the experimental setup. The DC current allowed to bring the neuron in different states, characterized by a well defined membrane voltage (between ?80 and ?50 mV) and by a specific firing regime that on depolarization gradually shifted from a predominantly bursting regime to a tonic spiking regime. The filtered frozen white noise generated a spike pattern output with a broad spike interval distribution. The coincidence factor and the Hunter and Milton measure were used as reliability measures of the output spike train. In the experimental TCR cell as well as the Morris-Lecar model cell the reliability depends on the shape (steepness) of the current input versus spike frequency output curve. The model also allowed to study the contribution of three relevant ionic membrane currents to reliability: a T-type calcium current, a cation selective h-current and a calcium dependent potassium current in order to allow bursting, investigate the consequences of a more complex current-frequency relation and produce realistic firing rates. The reliability of the output of the TCR cell increases with depolarization. In hyperpolarized states bursts are more reliable than single spikes. The analytically derived relations were capable to predict several of the experimentally recorded spike features.     

Coherence resonance for neuronal bursting with spike undershoot

Although the bursting patterns with spike undershoot are involved with the achievement of physiological or cognitive functions of brain with synaptic noise, noise induced-coherence resonance (CR) from resting state or subthreshold oscillations instead of bursting has been widely identified to play positive roles in information process. Instead, in the present paper, CR characterized by the increase firstly and then decease of peak value of power spectrum of spike trains is evoked from a bursting pattern with spike undershoot, which means that the minimal membrane potential within burst is lower than that of the subthreshold oscillations between bursts, while CR cannot be evoked from the bursting pattern without spike undershoot. With bifurcations and fast-slow variable dissection method, the bursting patterns with and without spike undershoot are classified into “Sub-Hopf/Fold” bursting and “Fold/Homoclinic” bursting, respectively. For the bursting with spike undershoot, the trajectory of the subthreshold oscillations is very close to that of the spikes within burst. Therefore, noise can induce more spikes from the subthreshold oscillations and modulate the bursting regularity, which leads to the appearance of CR. For the bursting pattern without spike undershoot, the trajectory of the quiescent state is not close to that of the spikes within burst, and noise cannot induce spikes from the quiescent state between bursts, which is cause for non-CR. The result provides a novel case of CR phenomenon and extends the scopes of CR concept, presents that noise can enhance rather than suppress information of the bursting patterns with spike undershoot, which are helpful for understanding the dynamics and the potential physiological or cognitive functions of the nerve fiber or brain neurons with such bursting patterns.     

Model of spike propagation reliability along the myelinated axon corrupted by axonal intrinsic noise sources

We investigated how selected electromorphological parameters of myelinated axons influence the preservation of interspike intervals when the propagation of action potentials is corrupted by axonal intrinsic noise. Hereby we tried to determine how the intrinsic axonal noise influences the performance of axons serving as carriers for temporal coding. The strategy of this coding supposes that interspike intervals presented to higher order neurons would minimally be deprived of information included in interspike intervals at the axonal initial segment. Our experiments were conducted using a computer model of the myelinated axon constructed in a software environment GENESIS (GEneral NEural SImulation System). We varied the axonal diameter, myelin sheath thickness, axonal length, stimulation current and channel distribution to determine how these parameters influence the role of noise in spike propagation and hence in preserving the interspike intervals. Our results, expressed as the standard deviation of spike travel times, showed that by stimulating the axons with regular rectangular pulses the interspike intervals were preserved with a microsecond accuracy. Stimulating the axons with pulses imitating postsynaptic currents, greater changes of interspike intervals were found, but the influence of implemented noise on the jitter of interspike intervals was approximately the same.     

Model of spike propagation reliability along the myelinated axon corrupted by axonal intrinsic noise sources

We investigated how selected electromorphological parameters of myelinated axons influence the preservation of interspike intervals when the propagation of action potentials is corrupted by axonal intrinsic noise. Hereby we tried to determine how the intrinsic axonal noise influences the performance of axons serving as carriers for temporal coding. The strategy of this coding supposes that interspike intervals presented to higher order neurons would minimally be deprived of information included in interspike intervals at the axonal initial segment. Our experiments were conducted using a computer model of the myelinated axon constructed in a software environment GENESIS (GEneral NEural SImulation System). We varied the axonal diameter, myelin sheath thickness, axonal length, stimulation current and channel distribution to determine how these parameters influence the role of noise in spike propagation and hence in preserving the interspike intervals. Our results, expressed as the standard deviation of spike travel times, showed that by stimulating the axons with regular rectangular pulses the interspike intervals were preserved with a microsecond accuracy. Stimulation with pulses imitating postsynaptic currents, greater changes of interspike intervals were found, but the influence of implemented noise on the jitter of interspike intervals was approximately the same.     

Variability of bursting patterns in a neuron model in the presence of noise

Spiking and bursting patterns of neurons are characterized by a high degree of variability. A single neuron can demonstrate endogenously various bursting patterns, changing in response to external disturbances due to synapses, or to intrinsic factors such as channel noise. We argue that in a model of the leech heart interneuron existing variations of bursting patterns are significantly enhanced by a small noise. In the absence of noise this model shows periodic bursting with fixed numbers of interspikes for most parameter values. As the parameter of activation kinetics of a slow potassium current is shifted to more hyperpolarized values of the membrane potential, the model undergoes a sequence of incremental spike adding transitions accumulating towards a periodic tonic spiking activity. Within a narrow parameter window around every spike adding transition, spike alteration of bursting is deterministically chaotic due to homoclinic bifurcations of a saddle periodic orbit. We have found that near these transitions the interneuron model becomes extremely sensitive to small random perturbations that cause a wide expansion and overlapping of the chaotic windows. The chaotic behavior is characterized by positive values of the largest Lyapunov exponent, and of the Shannon entropy of probability distribution of spike numbers per burst. The windows of chaotic dynamics resemble the Arnold tongues being plotted in the parameter plane, where the noise intensity serves as a second control parameter. We determine the critical noise intensities above which the interneuron model generates only irregular bursting within the overlapped windows.     

Dynamic relationship between the slow potential and spikes in cockroach ocellar neurons

The relationship between the slow potential and spikes of second-order ocellar neurons of the cockroach, Periplaneta americana, was studied. The stimulus was a sinusoidally modulated light with various mean illuminances. A solitary spike was generated at the depolarizing phase of the modulation response. Analysis of the relationship between the amplitude/frequency of voltage modulation and the rate of spike generation showed that (a) the spike initiation process was bandpass at approximately 0.5-5 Hz, (b) the process contained a dynamic linearity and a static nonlinearity, and (c) the spike threshold at optimal frequencies (0.5-5 Hz) remained unchanged over a mean illuminance range of 3.6 log units, whereas (d) the spike threshold at frequencies of less than 0.5 Hz was lower at a dimmer mean illuminance. The voltage noise in the response was larger and the mean membrane potential level was more positive at a dimmer mean illuminance. Steady or noise current injection during sinusoidal light stimulation showed that (a) the decrease in the spike threshold at a dimmer mean illuminance was due to the increase in the noise variance: the noise had facilitatory effects on the spike initiation; and (b) the change in the mean potential level had little effect on the spike threshold. We conclude that fundamental signal modifications occur during the spike initiation in the cockroach ocellar neuron, a finding that differs from the spike initiation process in other visual systems, including Limulus eye and vertebrate retina, in which it is presumed that little signal modification occurs at the analog-to-digital conversion process.     

Spike latency and jitter of neuronal membrane patches with stochastic Hodgkin-Huxley channels

Ion channel stochasticity can influence the voltage dynamics of neuronal membrane, with stronger effects for smaller patches of membrane because of the correspondingly smaller number of channels. We examine this question with respect to first spike statistics in response to a periodic input of membrane patches including stochastic Hodgkin-Huxley channels, comparing these responses to spontaneous firing. Without noise, firing threshold of the model depends on frequency—a sinusoidal stimulus is subthreshold for low and high frequencies and suprathreshold for intermediate frequencies. When channel noise is added, a stimulus in the lower range of subthreshold frequencies can influence spike output, while high subthreshold frequencies remain subthreshold. Both input frequency and channel noise strength influence spike timing. Specifically, spike latency and jitter have distinct minima as a function of input frequency, showing a resonance like behavior. With either no input, or low frequency subthreshold input, or input in the low or high suprathreshold frequency range, channel noise reduces latency and jitter, with the strongest impact for the lowest input frequencies. In contrast, for an intermediate range of suprathreshold frequencies, where an optimal input gives a minimum latency, the noise effect reverses, and spike latency and jitter increase with channel noise. Thus, a resonant minimum of the spike response as a function of frequency becomes more pronounced with less noise. Spike latency and jitter also depend on the initial phase of the input, resulting in minimal latencies at an optimal phase, and depend on the membrane time constant, with a longer time constant broadening frequency tuning for minimal latency and jitter. Taken together, these results suggest how stochasticity of ion channels may influence spike timing and thus coding for neurons with functionally localized concentrations of channels, such as in “hot spots” of dendrites, spines or axons.     

Stochastic processes in neurophysiology: Transformation from point to continuous processes

The spike train activity of neurones is considered as a point process, and methods of analysing and interpreting recorded spike trains are considered. The generation of a continuous process (membrane noise) from interacting point processes is described.     

Information transmission in cercal giant interneurons is unaffected by axonal conduction noise

What are the fundamental constraints on the precision and accuracy with which nervous systems can process information? One constraint must reflect the intrinsic “noisiness” of the mechanisms that transmit information between nerve cells. Most neurons transmit information through the probabilistic generation and propagation of spikes along axons, and recent modeling studies suggest that noise from spike propagation might pose a significant constraint on the rate at which information could be transmitted between neurons. However, the magnitude and functional significance of this noise source in actual cells remains poorly understood. We measured variability in conduction time along the axons of identified neurons in the cercal sensory system of the cricket Acheta domesticus, and used information theory to calculate the effects of this variability on sensory coding. We found that the variability in spike propagation speed is not large enough to constrain the accuracy of neural encoding in this system.     

Synchronization of pacemaker cell firing by weak ELF fields: Simulation by a circuit model

Entrainment of output action potentials from repetitively firing pacemaker cells, brought about by regularly spaced excitatory or inhibitory postsynaptic inputs, is a well-known phenomenon. Synchronization of neural firing patterns by extremely low frequency (ELF) external electric fields has also been observed. Whereas current densities of ≈10 A-m⁻² are required for direct excitation of otherwise quiescent neural tissue, much lower peak current densities (≈10⁻² A-m²) have been reported to entrain spontaneously firing molluscan pacemaker cells. We have developed a neural spike generator circuit model that simulates repetitive spike generation by a space clamped patch (area ≈ 10⁻⁷ m²) of excitable membrane subjected to depolarizing current. Picoampere (pA) range variation of DC depolarizing current causes a corresponding smooth variation of neural spike frequency, producing a physiologically realistic stimulus-response (S-R) characteristic. When lower pA range 60 Hz AC current is superposed upon the DC depolarizing current, smooth variation of the S-R characteristic is distorted by subharmonic locking of the spike generator at 30, 20, 15, 12, 10 Hz, and higher order subharmonic frequencies. Although the additional superposition of a physiologically realistic level of “white” current noise, covering the bandwidth 4–200 Hz, suffices to obscure higher order subharmonic locking, locking at 30, 20, and 15 Hz is still clearly evident in the presence of noise. Subharmonic locking is observed at a root mean square AC simulated tissue current density of ≈10⁻⁵ A-m⁻². Bioelectromagnetics 19:92–97, 1998. © 1998 Wiley-Liss, Inc.     

The Initiation of Spike Potential in Barnacle Muscle Fibers under Low Intracellular Ca++

Electrical properties of the muscle fiber membrane were studied in the barnacle, Balanus nubilus Darw. by using intracellular electrode techniques. A depolarization of the membrane does not usually produce an all-or-none spike potential in the normal muscle fiber even though a mechanical response is elicited. The intracellular injection of Ca⁺⁺-binding agents (K₂SO₄ and K salt of EDTA solution, K₃ citrate solution, etc.) renders the fiber capable of initiating all-or-none spikes. The overshoot of such a spike potential increases with increasing external Ca concentration, the increment for a tenfold increase in Ca concentration being about 29 mv. The threshold membrane potential for the spike and also for the K conductance increase shifts to more positive membrane potentials with increasing [Ca⁺⁺]_out. The removal of Na ions from the external medium does not change the configuration of the spike potential. In the absence of Ca⁺⁺ in the external medium, the spike potential is restored by Ba⁺⁺ and Sr⁺⁺ but not by Mg⁺⁺. The overshoot of the spike potential increases with increasing [Ba⁺⁺]_out or [Sr⁺⁺]_out. The Ca influx through the membrane of the fiber treated with K₂SO₄ and EDTA was examined with Ca⁴⁵. The influx was 14 pmol per sec. per cm² for the resting membrane and 35 to 85 pmol per cm² for one spike. From these results it is concluded that the spike potential of the barnacle muscle fiber results from the permeability increase of the membrane to Ca⁺⁺ (Ba⁺⁺ or Sr⁺⁺).     

Chemically Mediated Transmission at a Giant Fiber Synapse in the Central Nervous System of a Vertebrate

The hatchetfish, Gasteropelecus, possesses large pectoral fin adductor muscles whose simultaneous contraction enables the fish to dart upwards at the approach of a predator. These muscles can be excited by either Mauthner fiber. In the medulla, each Mauthner fiber forms axo-axonic synapses on four "giant fibers," two on each side of the midline. Each pair of giant fibers innervates ipsilateral motoneurons controlling the pectoral fin adductor muscles. Mauthner fibers and giant fibers can be penetrated simultaneously by microelectrodes close to the synapses between them. Electrophysiological evidence indicates that transmission from Mauthner to giant fiber is chemically mediated. Under some conditions miniature postsynaptic potentials (PSP's) are observed, suggesting quantal release of transmitter. However, relatively high frequency stimulation reduces PSP amplitude below that of the miniature potentials, but causes no complete failures of PSP's. Thus quantum size is reduced or postsynaptic membrane is desensitized. Ramp currents in Mauthner fibers that rise too slowly to initiate spikes can evoke responses in giant fibers that appear to be asynchronous PSP's. Probably both spikes and ramp currents act on the same secretory mechanism. A single Mauthner fiber spike is followed by prolonged depression of transmission; also PSP amplitude is little affected by current pulses that markedly alter presynaptic spike height. These findings suggest that even a small spike releases most of an immediately available store of transmitter. If so, the probability of release by a single spike is high for any quantum of transmitter within this store.     

Properties of synaptic noise in tonically active human motoneurons

The objective of these experiments was to determine the amount of synaptic noise on the cell membrane at various intervals after an action potential in a motoneuron firing at a specified frequency. Sources of noise such as variations in the level of voluntary drive were minimized by selecting only segments of the spike train in which the unit was running within prescribed frequency limits. The level of the membrane potential of the motoneuron during these intervals was determined using two test “pulses” (compound Ia excitatory postsynaptic potentials) of known amplitude. This enabled the probability of the membrane potential falling within a voltage “window” of known size at known times after the preceding spike to be determined. The probability density histograms showed that the fluctuations of membrane potential about a target interspike trajectory (i.e., the membrane noise) increased with time after the preceding spike. These fluctuations in the membrane potential can be accounted for by a one-dimensional “random walk” model of membrane noise. This model explains the salient features of the interval histograms, such as positive skewness at low target frequencies. A quantitative test of the model demonstrated its applicability to the motor pools of tibialis and masseter.     

The influence of an unmyelinated terminal on repetitive firing of a mammalian receptor afferent fiber

The distal end of a myelinated receptor afferent fiber consists of an unmyelinated terminal membrane which is assumed to be the site of sensory transduction, whereas the action potential encoding appears at a distal node of Ranvier. In the present paper a model of a mammalian myelinated nerve fiber was augmented by an unmyelinated terminal segment into which stimulating current was injected thus modelling the situation at a myelinated receptor afferent fiber. It was found that the introduction of the unmyelinated terminal reduces the repetitive firing rate shown by the model. However, also the amplitude of the spikes at the site of action potential generation diminishes through the large electrical load which the unmyelinated terminal imposes onto the active parts of the nerve fiber model. This "loss" of spike amplitude can abolish the ability of the model to show repetitive activity, if the unmyelinated terminal increases in size. On the other hand, the incorporation of sodium channels into the terminal membrane compensates the spike amplitude reduction introduced by the electrical load of that membrane. This allows repetitive firing at a lower frequency than would be possible for a model with an equivalent sodium-channel-free terminal. The results show that the unmyelinated terminal present at the distal end of myelinated receptor afferent fibers has not only the ability to provide sensory transduction but evokes also a reduction in the discharge rate of the encoding membrane.     

Quantitative investigations of amperometric spike feet suggest different controlling factors of the fusion pore in exocytosis at chromaffin cells

Around 30% of exocytosis events recorded by amperometry at carbon fiber microelectrodes exhibit a pre-spike feature (PSF) termed a “foot”. This wave is associated with the release of the neurotransmitters via a transitory fusion pore, whilst the large, main exocytotic spike is due to complete release. The amperometric data reported herein were obtained using bovine chromaffin cells stimulated with either potassium or barium ions, two commonly-employed elicitors of exocytosis. Identical trends are observed with both activators: (i) they induce the same ratio (close to 30%) of events with a foot in the population of amperometric spikes, and (ii) spikes with a foot can be divided into two primary categories, depending on the temporal variation of the current wave (viz. as a ramp, or a ramp followed by a plateau). Correlations between the characteristics of the whole current spike, and of its observed foot, have been sought; such analyses demonstrate that the maximum current of both foot and spike signals are highly correlated, but, in contrast, the integrated charges of both are poorly correlated. Moreover, the temporal duration of the PSF is fully uncorrelated with any parameter pertaining to the main current spike. On the basis of these reproducible observations, it is hypothesized that the characteristics (dimensions and topology, at least) of each secretory vesicle determine the probability of formation of the fusion pore and its maximum size, whilst molecular factors of the cell membrane control its duration, and, consequently, the amount delivered prior to the massive exocytosis of catecholamines observed as a spike in amperometry.     

Integrative Synaptic Mechanisms in the Caudal Ganglion of the Crayfish

A study of activity recorded with intracellular micropipettes was undertaken in the caudal abdominal ganglion of the crayfish in order to gain information about central fiber to fiber synaptic mechanisms. This synaptic system has well developed integrative properties. Excitatory post-synaptic potentials can be graded, and synaptic potentials from different inputs can sum to initiate spike discharge. In most impaled units, the spike discharge fails to destroy the synaptic potential, thereby allowing sustained depolarization and multiple spike discharge following single pulse stimulation to an afferent input. Some units had characteristics which suggest a graded threshold for spike generation along the post-synaptic fiber membrane. Other impaled units responded to afferent stimulation with spike discharges of two distinct amplitudes. The smaller or "abortive" spikes in such units may represent non-invading activity in branches of the post-synaptic axon. On a few occasions one afferent input was shown to inhibit the spike discharge initiated by another presynaptic input.     

Neural Coding with Graded Membrane Potential Changes and Spikes

The neural encoding of sensory stimuli is usually investigated for spike responses, although many neurons are known to convey information by graded membrane potential changes. We compare by model simulations how well different dynamical stimuli can be discriminated on the basis of spiking or graded responses. Although a continuously varying membrane potential contains more information than binary spike trains, we find situations where different stimuli can be better discriminated on the basis of spike responses than on the basis of graded responses. Spikes can be superior to graded membrane potential fluctuations if spikes sharpen the temporal structure of neuronal responses by amplifying fast transients of the membrane potential. Such fast membrane potential changes can be induced deterministically by the stimulus or can be due to membrane potential noise that is influenced in its statistical properties by the stimulus. The graded response mode is superior for discrimination between stimuli on a fine time scale.