On the role of subthreshold dynamics in neuronal signaling

The role of subthreshold dynamics in neuronal signaling is examined using periodic pulse train stimulation of the Fitzhugh-Nagumo (FN) model of nerve membrane excitability and results from the squid giant axon as an experimental data base. For a broad range of stimulus conditions the first pulse in a pulse train elicited an action potential, whereas all subsequent pulses elicited subthreshold responses, both in the axon and in the FN model. These results are not well described by the Hodgkin and Huxley 1952 model. Various different patterns of subthreshold responses, including chaotic dynamics, can be observed in both systems-the FN model and the axon-depending upon stimulus conditions. For some conditions action potentials are occasionally interspersed among the subthreshold events with randomly occurring interspike intervals. The randomness is directly attributable to the underlying subthreshold chaos-deterministic chaos-rather than to a stochastic noise source. We conclude that this mechanism may contribute to multimodal interspike interval histograms which have been observed from individual neurons throughout the nervous system.     

Resolution of pheromone pulses in receptor cells of Antheraea polyphemus at different temperatures

The ability of pheromone receptor cells of male Antheraea polyphemus (Saturniidae) to resolve stimulus pulses was determined at different temperatures (8°, 18°, 28°C). The cells were stimulated by repeated 20-ms puffs of the pheromone components (E, Z)-6, 11-hexadecadienyl acetate and (E, Z)-6,11-hexadecadienal. At higher temperatures, higher frequencies of stimulus pulses were resolved by the nerve-impulse response: about 1.25 pulses per second at 8°C, 2.5 pulses/s at 18°C and 5 pulses/s at 28°C. The decreased ability of receptor cells to resolve stimulus pulses at low temperatures may reduce the male moth's chance of reaching the pheromone source. The peak nerve-impulse frequency increased whereas the duration of nerve-impulse responses to single stimulus pulses decreased at higher temperatures. At a given temperature and stimulus intensity the peak nerveimpulse frequency decreased with shorter intervals between the stimulus pulses, but the duration of the responses remained almost constant. The time needed for recovery from adaptation caused by a single stimulus pulse was longer at lower temperatures. The aldehyde receptor cell recovered more quickly than the acetate cell. At low stimulus concentration, the resolution ability of the acetate cell was strongly decreased, whereas in the aldehyde cell it was only slightly impaired.     

A New Approach for Determining Phase Response Curves Reveals that Purkinje Cells Can Act as Perfect Integrators

Cerebellar Purkinje cells display complex intrinsic dynamics. They fire spontaneously, exhibit bistability, and via mutual network interactions are involved in the generation of high frequency oscillations and travelling waves of activity. To probe the dynamical properties of Purkinje cells we measured their phase response curves (PRCs). PRCs quantify the change in spike phase caused by a stimulus as a function of its temporal position within the interspike interval, and are widely used to predict neuronal responses to more complex stimulus patterns. Significant variability in the interspike interval during spontaneous firing can lead to PRCs with a low signal-to-noise ratio, requiring averaging over thousands of trials. We show using electrophysiological experiments and simulations that the PRC calculated in the traditional way by sampling the interspike interval with brief current pulses is biased. We introduce a corrected approach for calculating PRCs which eliminates this bias. Using our new approach, we show that Purkinje cell PRCs change qualitatively depending on the firing frequency of the cell. At high firing rates, Purkinje cells exhibit single-peaked, or monophasic PRCs. Surprisingly, at low firing rates, Purkinje cell PRCs are largely independent of phase, resembling PRCs of ideal non-leaky integrate-and-fire neurons. These results indicate that Purkinje cells can act as perfect integrators at low firing rates, and that the integration mode of Purkinje cells depends on their firing rate.     

No neural evidence for dynamic auditory tuning of the A1 receptor in the ear of the noctuid moth, <Emphasis Type="Italic">Noctua pronuba</Emphasis>

By examining the mechanical properties of the tympanum of the noctuid moth, Noctua pronuba, Windmill et al. (2006) suggested that this insect increases (up-tunes) the frequencies of its best hearing when exposed to high intensity sounds (HIS) resembling the echolocation calls of attacking bats. We tested whether this biophysical phenomenon was encoded in the neural responses of this moth’s most sensitive auditory receptor (A1 cell) before and after exposure to HIS. We measured: (1) the number of A1 action potentials (spikes) per stimulus pulse; (2) the proportion of A1 spike periods below that determined to elicit evasive flight maneuvers and, (3) the change in A1 cell firing (spike number, interspike interval, stimulus/spike latency) over a duration of time similar to that in which up-tuning lasts. We observed no significant spiking response changes in the predicted direction to any of the frequencies tested following exposure to HIS and we observed only two of the 24 predicted time-dependent changes to A1 firing. These results indicate that tympanal up-tuning does not result in a change to this moth’s auditory frequency sensitivity and we suggest either sensillar resonances or increases in thoracic muscle tension following exposure to HIS as alternative explanations.     

Repetitive stimulation of olfactory receptor cells in female silkmoths Bombyx mori L

The pheromone-sensitive receptor cells of male moth antennae are capable of detecting the rapid changes in stimulus intensity encountered in natural pheromone odour plumes. We investigated temporal response characteristics of the two receptor cell types of the sensillum trichodeum of female Bombyx mori, which are most sensitive to benzoic acid and 2,6-dimethyl-5-heptene-2-ol (DMH), respectively. The cells were repetitively stimulated with 50-ms pulses of benzoic acid and (±)-linalool, an effective mimic of DMH, at various pulse rates and different stimulus intensities. By recording receptor potentials and nerve impulses we demonstrated that both receptor cell types were able to follow stimulus pulses at least up to eight pulses per sec, with a more pronounced modulation of the responses in the DMH cell. The resolution capability of the two cell types showed little dependence on stimulus intensity. In their ability to resolve pulsed odour stimuli, the receptor cells for benzoic acid and DMH were as good as pheromone receptor cells.     

Stimulation pulse characteristics and electrode configuration determine site of excitation in isolated mammalian skeletal muscle: implications for fatigue.

We examined whether electrical field stimulation with varying characteristics could excite isolated mammalian skeletal muscle through different sites. Supramaximal (20-V, 0.1-ms) pulse stimulation with transverse wire or parallel plate electrodes evoked similar forces in nonfatigued slow-twitch soleus and fast-twitch extensor digitorum longus (EDL) muscles from mice. d-tubocurarine shifted the twitch force-stimulation strength relationship toward higher pulse strengths with both electrode configurations in soleus muscle, suggesting that weaker pulses excite muscle via neuromuscular transmission. With wire stimulation, movement of the recording electrode along the muscle caused a delay between the stimulus artifact and the peak of the action potential, consistent with action potential propagation along the sarcolemma. TTX abolished all contractions evoked with 20-V, 0.1-ms pulses, suggesting that excitation occurred via voltage-dependent Na+ channels and, hence, muscle action potentials. TTX did not prevent force development with > or = 0.4-ms pulses in soleus or 1-ms pulses in EDL muscle. Furthermore, myoplasmic Ca2+ (i.e., the fura 2 ratio) and sarcomere shortening were greater during tetanic stimulation with 2.0-ms than with 0.5-ms pulses in flexor digitorum brevis fibers from rats. TTX prevented all shortening and Ca2+ release with 0.5-ms, but not 2.0-ms, pulses, indicating that longer pulses can directly trigger Ca2+ release. Hence, proper interpretation of mechanistic studies requires precise understanding of how muscles are excited; otherwise, incorrect conclusions can be made. Using this new understanding, we showed that disrupted propagation of action potentials along the surface membrane is a major cause of fatigue in soleus muscle that is focally and continuously stimulated at 125 Hz.     

Long rise times of sound pulses in grasshopper songs improve the directionality cues received by the CNS from the auditory receptors

Auditory receptors of the locust (Locusta migratoria) were investigated with respect to the directionality cues which are present in their spiking responses, with special emphasis on how directional cues are influenced by the rise time of sound signals. Intensity differences between the ears influence two possible cues in the receptor responses, spike count and response latency. Variation in rise time of sound pulses had little effect on the overall spike count; however, it had a substantial effect on the temporal distribution of the receptor's spiking response, especially on the latencies of first spikes. In particular, with ramplike stimuli the slope of the latency vs. intensity curves was steeper as compared to stimuli with steep onsets (Fig. 3). Stimuli with flat ramplike onsets lead to an increase of the latency differences of discharges between left and right tympanic receptors. This type of ramplike stimulus could thus facilitate directional hearing. This hypothesis was corroborated by a Monte Carlo simulation in which the probability of incorrect directional decisions was determined on the basis of the receptor latencies and spike counts. Slowly rising ramps significantly improved the decisions based on response latency, as compared to stimuli with sudden onsets (Fig. 4). These results are compared to behavioural results obtained with the grasshopper Ch. biguttulus. The stridulation signals of the females of this species consist of ramplike pulses, which could be an adaptation to facilitate directional hearing of phonotactically approaching males.Abbreviations HFR high frequency receptor - ILD interaural level difference - LFR low frequency receptor - SPL sound pressure level - WN white noise     

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.     

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.     

Contractile Activation in Frog Skeletal Muscle

Contractile activation was studied in frog single muscle fibers treated with tetrodotoxin to block action potentials. The membrane potential in a short segment of the fiber was controlled with a two-electrode voltage clamp, and the contractile response of superficial myofibrils in this segment was observed microscopically. The strength-duration relation for contractile activation was similar to that reported by Adrian, Chandler, and Hodgkin (1969); at 3.9°C, the contraction threshold was –44 mV for long depolarizing pulses (100-ms) and increased to +64 mV for 2-ms depolarizations. Hyperpolarizing postpulses shifted the threshold for 2-ms pulses to more positive values, and a similar, but smaller, effect was produced by hyperpolarizing prepulses. The decay of excitability following subthreshold pulses showed two apparently distinct components; at 3.9°C, excitability fell to 50% of its initial value within 4 ms, while the subsequent decline of excitability proceeded with a half-time of about 20 ms.     

Apparent absence of a redox requirement for blue light activation of pump current in broad bean guard cells

In guard cells, membrane hyperpolarization in response to a blue light (BL) stimulus is achieved by the activation of a plasma membrane H(+)-ATPase. Using the patch clamp technique on broad bean (Vicia faba) guard cells we demonstrate that both steady-state- and BL-induced pump currents require ATP and are blocked by vanadate perfused into the guard cell during patch clamp recording. Background-pump current and BL-activated currents are voltage independent over a wide range of membrane potentials. During BL-activated responses significant hyperpolarization is achieved that is sufficient to promote K(+) uptake. BL activation of pump current becomes desensitized by three or four pulses of 30 s x 100 micromol m(-2) s(-1) BL. This desensitization is not a result of pump inhibition as maximal responses to fusicoccin are observed after full BL desensitization. BL treatments prior to whole cell recording show that BL desensitization is not due to washout of a secondary messenger by whole cell perfusion, but appears to be an important feature of the BL-stimulated pump response. We found no evidence for an electrogenic BL-stimulated redox chain in the plasma membrane of guard cells as no steady-state- or BL-activated currents are detected with NADH or NADPH added to the cytosol in the absence of ATP. Steady-state- nor BL-activated currents are affected by the inclusion along with ATP of 1 mM NADH in the pipette under saturating red light or by including NADPH in the pipette under darkness or saturating red light. These data suggest that reduced products of photosynthesis do not significantly modulate plasma membrane pump currents and are unlikely to be critical regulators in BL-stimulation of the plasma membrane H(+)-ATPase in guard cells.     

Regression analysis of non-stationary discharges in neurons; Adaptation in the electrosensory afferent of dogfish

Interspike interval histograms, as usually regarded for the estimation of statistical variabilities in neuronal spike trains, were applied to non-stationary dynamic responses of a PD receptor. Sliding mean values were introduced describing the average receptor response on defined, recurrent stimuli; mean spike frequencies and interspike intervals were computed a) for fixed sequential analysis periods (of e.g. 500 ms), b) for analysis periods shifted by every consecutive interspike interval (thus the number of spikes being constant), and c) by fitting the dynamic responses for suitable analytic functions (e.g. exponential functions). With these methods variabilities in the non-stationary neuronal impulse patterns were investigated for electrosensory PD afferents in Lorenzinian ampulla of dogfish (Scyliorhinus canicula) with electric stimuli up to 50 nA and defined temperatures between 7° C and 25° C. In this temperature range all investigated ampullae were spontaneously active, the irregularities in neuronal discharges and averaged spike frequencies depended strongly on temperature, the latter showing maxima between 13° C and 19° C. In preparations with small disturbances we generally found static interspike interval histograms following approximatively a Gaussian distribution. The same was true for the momentary spike frequency and its deviation during the dynamic response to given electrical stimuli. A suprathreshold rectangular current (e.g.-0.5 nA) led to a marked but transient synchronisation in spike generation; the higher the stimulus strength, the smaller the standard deviation (s.d.) from mean spike frequency in the beginning of the dynamic response; during adaptation the s.d. increased up to that of the static response frequency. Relating, however, s.d. for different currents, times, and temperatures to the corresponding mean spike frequency led to fairly constant coefficients of variation; s.d. was approximatively a linear function of the sliding mean value even in the dynamic response of the electroreceptor (scaling).Supported by the Deutsche Forschungsgemeinschaft (Br 310/11)     

Different effects of blocked potassium channels on action potentials, accommodation, adaptation and anode break excitation in human motor and sensory myelinated nerve fibres: computer simulations

 Action potentials and electrotonic responses to 300-ms depolarizing and hyperpolarizing currents for human motor and sensory myelinated nerve fibres have been simulated on the basis of double cable models. The effects of blocked nodal or internodal potassium (fast or slow) channels on the fibre action potentials, early and late adaptations to 30-ms suprathreshold slowly increasing depolarizing stimuli have been examined. The effects of the same channels on accommodation after the termination of a prolonged (100 ms) hyperpolarizing current pulse have also been investigated. By removing the nodal fast potassium conductance the action potentials of the sensory fibres are considerably broader than those of the motor neurons. For both types of fibres, the blocked nodal slow potassium channels have a substantially smaller effect on the action potential repolarization. When the suprathreshold depolarizing current intensity is increased, the onset of the spike burst occurs sooner, which is common in the behaviour of the fibres. The most striking differences in the burst activity during early adaptation have been found between the fibres when the nodal fast potassium channels are blocked. The results obtained confirm the fact that the motor fibres adapt more quickly to sustained depolarizing current pulses than the sensory ones. The results also show that normal human motor and sensory fibres cannot be excited by a 100-ms hyperpolarizing current pulse, even at the threshold level. When removing the potassium channels in the nodal or internodal axolemma, the posthyperpolarization increase in excitability is small, which is common in the behaviour of the fibres. However, anode break excitation can be simulated in the fibres with simultaneous removal of the potassium channels under the myelin sheath, and this is more pronounced in the human sensory fibres than in motor fibres. This phenomenon can also be found when the internodal and some of the nodal (fast or slow) potassium channels are simultaneously blocked. Received: 8 November 1999 / Accepted in revised form: 29 February 2000     

Mechanism of inhibition following reflex discharge in spinal cord interneurons

Using the method of microelectrode (intracellular and extracellular) recording, the mechanism of inhibition following reflex discharge in interneurons of the lumbosacral section of the spinal cord of cats on activation of cutaneous and high-threshold muscle afferents was studied. It was shown that the postdischarge depression of the reflex responses 10–20 msec after the moment of activation of the neuron is due to afterprocesses in the same neuron and presynaptic pathways. The depression of spike potentials from the 20th to the 100th msec is produced by inhibitory postsynaptic potentials (IPSP). During the development of IPSP the inhibition of spike potentials can be due to both a decrease of the depolarization of the postsynaptic membrane below the critical threshold and a decrease of sensitivity of the cell membrane to the depolarizing action of the excitatory postsynaptic potential (EPSP). At intervals between the stimuli of 30–100 msec the duration of EPSP after the first stimulus does not differ from that after the second stimulus. Hence, it is suggested that the presynaptic mechanisms do not play an essential part in this type of inhibition of interneurons. The inhibition following the excitation favors the formation of a discrete message to the neurons of higher orders.I. P. Pavlov Institute of Physiology, Academy of Sciences of the USSR, Leningrad. Translated from Neirofiziologiya, Vol. 2, No. 1, pp. 3–9, January–February, 1970.     

Enhanced specificity of information in axons with negatively correlated adjacent interspike intervals

A model is formulated for the conversion of a motoneuron's spike train to tension in a muscle. This model demonstrates that a spike train whose adjacent interspike intervals are negatively correlated results in a steady-state tension which fluctuates less about its mean value than if the interspike intervals are randomly arranged. The ability of a spike train to develop more distinguishable levels of tension by negative correlation between adjacent interspike intervals is more significant for interspike interval distributions with greater dispersion. The number of distinguishable tension levels increases by about 33 percent when a typical set of neuromuscular parameters are used. These results may be generalized to the smoothing of postsynaptic potentials and the regulation of blood pressure.     

Optimal stimulus shapes for neuronal excitation

An important problem in neuronal computation is to discern how features of stimuli control the timing of action potentials. One aspect of this problem is to determine how an action potential, or spike, can be elicited with the least energy cost, e.g., a minimal amount of applied current. Here we show in the Hodgkin & Huxley model of the action potential and in experiments on squid giant axons that: 1) spike generation in a neuron can be highly discriminatory for stimulus shape and 2) the optimal stimulus shape is dependent upon inputs to the neuron. We show how polarity and time course of post-synaptic currents determine which of these optimal stimulus shapes best excites the neuron. These results are obtained mathematically using the calculus of variations and experimentally using a stochastic search methodology. Our findings reveal a surprising complexity of computation at the single cell level that may be relevant for understanding optimization of signaling in neurons and neuronal networks.     

Cell responses to acoustic stimuli in the pterothoracic ganglion of two noctuoid moths

Summary The spike activity of various types of cell responses in the pterothoracic ganglion ofAscalapha odorata (Noctuidae) andEmpyreuma pugione (Arctiidae) was studied. Pure tones (16 kHz forA. odorata and 20 kHz forE. pugione, 45 ms pulses) were presented at a 1 Hz rate over 9 s and at intensities ranging from 25 to 95 dB SPL. The values of the latency period and the interspike intervals allowed us to describe the intensity-latency and intensity-response functions as well as the spike distribution during the responses, the latter being given by the instantaneous frequency, i.e., as the inverse value of the mean of the nine measurements of each interspike interval during the response time. Repeater (RA₁ and RA₂) is a type of cell response that shows a phasic-tonic spike distribution similar to that of the receptor cells (A₁ and A₂) (Fig. 3), but that differs from the latter in a longer (ca. 1.0 ms) latency period, a lower number of spikes per pulse, and a lower instantaneous frequency during the response time (Tables 1 and 2). Another repeater type of cell response (RA) differs from the receptors and the other two repeaters in the form of its intensity-latency function, having the widest dynamic range (from 40 to 50 dB), and exhibiting the highest maximal number of spikes per pulse of all the response types recorded (Fig. 2, Table 1). We recorded also strictly phasic responses (1 or 2 spikes per pulse), which are considered as pulse markers. Of these, one (PM₁ has a shorter latency period (ca. 10 ms) and higher sensitivity than the other (PM₂) (Fig. 4). Two other types of cell responses showed significant differences in their latency period and the number of spikes per pulse under binaural and monoaural stimulation and are assumed to be the consequence of binaural summation, one by inhibition (BSI) and the other by excitation (BSE) (Fig. 5); they also differ in the spike distribution during the response. For the other types of cell responses recorded we used names that reflect the form of their spike distribution: chopper, build, On-S, tonic, and suppression (Figs. 8–12). The spike distributions during the response time recorded in the pterothoracic ganglion of these two noctuoid moths are compared with the temporal patterns of discharge described in the auditory neurons of the first relay stations of birds and mammals. Our results suggest that in the auditory pathway of the two moth species there is divergence, which could facilitate the parallel processing of the sensory information, and convergence, that could play a role in the directional localization of the acoustic signals. The complexity of this central auditory processing in animals with only 2 receptors in each peripheral organ is considerable, and we discuss its possible biological meaning.     

Correspondence between evoked vocal responses and auditory thresholds in Pleurodema thaul (Amphibia; Leptodactylidae)

Thresholds for evoked vocal responses and thresholds of multiunit midbrain auditory responses to pure tones and synthetic calls were investigated in males of Pleurodema thaul, as behavioral thresholds well above auditory sensitivity have been reported for other anurans. Thresholds for evoked vocal responses to synthetic advertisement calls played back at increasing intensity averaged 43 dB RMS SPL (range 31–52 dB RMS SPL), measured at the subjects’ position. Number of pulses increased with stimulus intensities, reaching a plateau at about 18–39 dB above threshold and decreased at higher intensities. Latency to call followed inverse trends relative to number of pulses. Neural audiograms yielded an average best threshold in the high frequency range of 46.6 dB RMS SPL (range 41–51 dB RMS SPL) and a center frequency of 1.9 kHz (range 1.7–2.6 kHz). Auditory thresholds for a synthetic call having a carrier frequency of 2.1 kHz averaged 44 dB RMS SPL (range 39–47 dB RMS SPL). The similarity between thresholds for advertisement calling and auditory thresholds for the advertisement call indicates that male P. thaul use the full extent of their auditory sensitivity in acoustic interactions, likely an evolutionary adaptation allowing chorusing activity in low-density aggregations.