On phase locking of pulse encoders

Several models have been proposed to underststand the patterns of nerve impulses produced by periodic stimuli. This paper shows that for a very large class of such models there exists a pattern of phases that repeats periodically after a finite number of pulses; the actual pulses produced by the model depend on its initial condition, but in all cases they either follow such a pattern or approach it asymptotically. This paper is dedicated to the memory of M. G. F. Fuortes, neurophysiologist, who honored me with his friendship     

Adaptation in the Visual Cortex: Influence of Membrane Trajectory and Neuronal Firing Pattern on Slow Afterpotentials

The input/output relationship in primary visual cortex neurons is influenced by the history of the preceding activity. To understand the impact that membrane potential trajectory and firing pattern has on the activation of slow conductances in cortical neurons we compared the afterpotentials that followed responses to different stimuli evoking similar numbers of action potentials. In particular, we compared afterpotentials following the intracellular injection of either square or sinusoidal currents lasting 20 seconds. Both stimuli were intracellular surrogates of different neuronal responses to prolonged visual stimulation. Recordings from 99 neurons in slices of visual cortex revealed that for stimuli evoking an equivalent number of spikes, sinusoidal current injection activated a slow afterhyperpolarization of significantly larger amplitude (8.5±3.3 mV) and duration (33±17 s) than that evoked by a square pulse (6.4±3.7 mV, 28±17 s; p<0.05). Spike frequency adaptation had a faster time course and was larger during plateau (square pulse) than during intermittent (sinusoidal) depolarizations. Similar results were obtained in 17 neurons intracellularly recorded from the visual cortex in vivo. The differences in the afterpotentials evoked with both protocols were abolished by removing calcium from the extracellular medium or by application of the L-type calcium channel blocker nifedipine, suggesting that the activation of a calcium-dependent current is at the base of this afterpotential difference. These findings suggest that not only the spikes, but the membrane potential values and firing patterns evoked by a particular stimulation protocol determine the responses to any subsequent incoming input in a time window that spans for tens of seconds to even minutes.     

Studies on the excitability of the central program generator in the spinal cord of the terrapin Pseudemys scripta elegans

We present observations on the multicyclic scratch reflex in spinal terrapins as produced by electrical stimuli applied to the shell at the specific regions at which a mechanical stimulus produces the reflex. EMGs and hip and knee movements are recorded. The responses to the electrical stimuli are similar to the responses to mechanical stimuli. There is a three phase EMG pattern (Stein and Grossman, 1980), to which the movement pattern is related (Bakker and Crowe, 1982). A response may consist of a series of up to 25 movement cycles with a total time course of up to about 30 sec. The initial cycles of a response are relatively fast (less than 1 sec), but the cycles at the expiration of the response may have a duration of 2-3 sec. A single electrical stimulus pulse is often insufficient to trigger a series response. Instead, a weak EMG burst of a few tenths of a second duration, together with a slight movement, is often seen. However, a second pulse can set the cycle series in motion even after an interval of 40 sec between the pulses. A further booster stimulus pulse given while a reflex response is taking place can increase the speed of the movement. If the booster pulse is given just after cessation of reflex activity it can restart the activity, but this second cycle series is often shorter than the first one. The results indicate that the excitability of the central program generator is not constant. Long duration changes in the excitability are produced within the spinal cord.     

Walking in Fourier’s space: algorithms for the computation of periodicities in song patterns by the cricket Gryllus bimaculatus

Is discrimination of the envelope of an acoustic signal based on spectral or temporal computations? To investigate this question for the cricket Gryllus bimaculatus, pattern envelopes were constructed by the addition of several sine waves and modified by systematic phase changes. The phonotactic response of female crickets towards such sinusoidal but also rectangular pulse patterns was quantified on a locomotion compensator. Envelope patterns that exhibited a modulation frequency of 25 Hz as the dominant frequency were attractive and although changes of phase modified the temporal pattern, the values of attractiveness remained unaffected. Removal of the 25-Hz component reduced the phonotactic scores. Patterns in which other frequency components exhibited a larger amplitude than the 25-Hz component were less attractive. However, the combination of an unattractive pulse period with the attractive modulation frequency of 25 Hz in a pattern revealed that such stimuli were unattractive despite the presence of the 25-Hz component. A comparison of the attractiveness of all patterns revealed that female crickets evaluated the duration of pulse period over a wide range of duty cycles. The combined evidence showed that pattern envelopes were processed in the time- and not in the spectral domain.     

Saccadic eye movements and the detection of fast-moving gratings

Experiments are presented in which the effect of saccadic eye movements on the visibility of sinusoidal gratings drifting with velocities between 2 deg/s and 400 deg/s is investigated. The results demonstrate that saccades are highly useful for detecting this class of stimuli. Due to a saccade, otherwise subthreshold stimuli become visible as short, distinct flashes of the seemingly statinoary pattern. The paper analyzes in detail the dependence of the amount of facilitation on saccade size and relative direction and isolates the additional effect of saccadic suppression. A simple model is proposed which predicts the experimental findings.     

Photobehavior of Halobacterium halobium: sinusoidal stimulation and a suppression effect of responses to flashes

Sequences of reversals recorded by single-cell observation of Halobacterium halobium are analyzed. Autocorrelation functions of spontaneous and stimulated reversals are computed; the results show that the only periodicity present in our data is that of the stimulus. Several different patterns of light stimuli were used. Responses to repetitive linear ramps of different slopes and to sinusoidal lights with different mean values and/or modulation depths are reported, showing that the modulation depth is the stimulus parameter most effective in eliciting photoresponses. Responses to more complex stimuli obtained by superimposing flashes to sinusoidal stimuli are also reported; a suppression effect depending on the phase of the sinusoidal stimulation is shown in responses to complex stimuli. A model which accounts for this effect is proposed.     

Excitation properties of the squid axon membrane and model systems with current stimulation. Statistical evaluation and comparison.

The space-clamped squid axon membrane and two versions of the Hodgkin-Huxley model (the original, and a strongly adapting version) are subjected to a first order dynamic analysis. Stable, repetitive firing is induced by phase-locking nerve impulses to sinusoidal currents. The entrained impulses are then pulse position modulated by additional, small amplitude perturbation sinusoidal currents with respect to which the frequencies response of impulse density functions are measured. (Impulse density is defined as the number of impulses per unit time of an ensemble of membranes with each membrane subject to the same stimulus). Two categories of dynamic response are observed: one shows clear indications of a corner frequency, the other has the corner frequency obscured by dynamics associated with first order conductance perturbations in the interspike interval. The axon membrane responds with first order perturbations whereas the unmodified Hodgkin-Huxley model does not. Quantitative dynamic signatures suggest that the relaxation times of axonal recovery excitation variables are twice as long as those of the corresponding model variables. A number of other quantitative differences between axon and models, including the values of threshold stimuli are also observed.     

Modulation of motoneuronal firing behavior after spinal cord injury using intraspinal microstimulation current pulses: a modeling study.

We simulated the effects of delivering focal electrical stimuli to the central nervous system to modulate the firing rate of neurons and alleviate motor disorders. Application of these stimuli to the spinal cord to reduce the increased excitability of motoneurons and resulting spasticity after spinal cord injury (SCI) was examined by means of a morphologically detailed computer model of a spinal motoneuron. High-frequency sinusoidal and rectangular pulses as well as biphasic charge-balanced and charge-imbalanced pulses were examined. Our results suggest that suprathreshold high-frequency sinusoidal or rectangular current pulses could inactivate the Na+ channels in the soma and initial segment, and block action potentials from propagating through the axon. Subthreshold biphasic charge-imbalanced pulses reduced the motoneuronal firing rate significantly (up to approximately 25% reduction). The reduction in firing rate was achieved through stimulation-induced hyperpolarization generated in the first node of Ranvier. Because of their low net DC current, these pulses could be tolerated safely by the tissue. To deliver charge-imbalanced pulses with the lowest net DC current and induce the largest reduction in motoneuronal firing rate, we studied the effect of various charge-imbalanced pulse parameters. Short pulse durations were found to induce the largest reduction in firing rate for the same net DC level. Subthreshold high-frequency sinusoidal and rectangular current pulses and low-frequency biphasic charge-balanced pulses, on the other hand, were ineffective in reducing the motoneuronal firing rate. In conclusion, the proposed electrical stimulation paradigms could provide potential rehabilitation interventions for suppressing the excitability of neurons to reduce the severity of motor disorders after injury to the central nervous system.     

果蝇nasuta亚群求爱歌的种间识别与进化遗传学研究

果蝇ｎａｓｕｔａ亚群由１４个种、亚种和分类群组成,广泛分布于印度－太平洋区域。本文首次记录了ｎａｓｕｔａ亚群种的求爱歌,测量了脉冲歌时域模式的参数：脉冲串间隔（ＩＢＩ）、脉冲间隔（ＩＰＩ）、脉冲串时间长度（ＰＴＬ）、每个脉冲串的脉冲数（ＰＮ）、脉冲时间长度（ＰＬ）、波动周期时间长度（ＣＬ）。采用计算机声谱分析技术,作出求爱歌信号的三维数字功率谱图,进行频率分析。发现Ｄ．ｐｕｌａｕｎａ和Ｔａｘｏｎ－Ｆ不发出求爱歌声信号,视觉在交配中可能起重要作用。对其余种、亚种和分类群的求爱歌分析表明,ｎａｓｕｔａ亚群种的求爱歌分为脉冲歌和正弦歌。对部分种的正反交Ｆ１求爱歌分析表明,脉冲歌时域参数,如ＩＰＩ平均值为Ｘ染色体连锁或常染色体多基因控制,正弦歌频率偏向母方。根据不同种、亚种和分类群脉冲歌的时域模式构建ｎａｓｕｔａ亚群的系统树,对亚群中不同种、亚种和分类群的亲缘关系进行讨论。     

Pulse-rate recognition in an insect: evidence of a role for oscillatory neurons

Various mechanisms have been proposed as the neural basis for pulse-rate recognition in insects and anurans, including models employing high- and low-pass filters, autocorrelation, and neural resonance. We used the katydid Tettigonia cantans to test these models by measuring female responsiveness on a walking compensator to stimuli varying in temporal pattern. Each model predicts secondary responses to certain stimuli other than the standard conspecific pulse rate. Females responded strongly to stimuli with a pulse-rate equal to half the standard rate, but not to stimuli with double the standard rate. When every second pulse or interval was varied in length, females responded only when the resulting stimuli were rhythmic with respect to the period of the standard signal. These results provide evidence rejecting the use of either high-/low-pass filter networks or autocorrelation mechanisms. We suggest that rate recognition in this species relies on the resonant properties of neurons involved in signal recognition. According to this model, signals with a pulse rate equal to the resonant frequency of the neurons stimulate the female to respond. The results are discussed with regard to both neural and evolutionary implications of resonance as a mechanism for signal recognition. In memory of Dagmar von Helversen (1944–2003)     

Fading memory model for airway smooth muscle dynamic response

This work presents the application of a fading memory model to describe the behavior of contracted airway smooth muscle (ASM) for two biophysical cases: finite duration length steps and longitudinal sinusoidal oscillations. The model parameters were initially determined from literature data on transient step length change response and subsequently the model was applied to the two cases. Results were compared with previously published experimental data on ASM oscillations. The model confirms a trend observed in the experimental data which shows that: (i) the value of tissue length change is the most important factor to determine the degree of cross-bridge detachment and (ii) a strong correlation exists between increasing frequency and declining stiffness until a certain frequency (∼25 Hz) beyond which frequency dependence is negligible. Although the model was not intended to simulate biophysical events individually, the data could be explained by cross-bridge cycling rates. As the frequency increases, cross-bridge reattachment becomes less likely, until no further cross-bridge attachment is possible.     

Intracellular recording from a spider vibration receptor

The present study introduces a new preparation of a spider vibration receptor that allows intracellular recording of responses to natural mechanical or electrical stimulation of the associated mechanoreceptor cells. The spider vibration receptor is a lyriform slit sense organ made up of 21 cuticular slits located on the distal end of the metatarsus of each walking leg. The organ is stimulated when the tarsus receives substrate vibrations, which it transmits to the organ’s cuticular structures, reducing the displacement to about one tenth due to geometrical reasons. Current clamp recording was used to record action potentials generated by electrical or mechanical stimuli. Square pulse stimulation identified two groups of sensory cells, the first being single-spike cells which generated only one or two action potentials and the second being multi-spike cells which produced bursts of action potentials. When the more natural mechanical sinusoidal stimulation was applied, differences in adaptation rate between the two cell types remained. In agreement with prior extracellular recordings, both cell types showed a decrease in the threshold tarsus deflection with increasing stimulus frequency. Off-responses to mechanical stimuli have also been seen in the metatarsal organ for the first time.     

Level dependent signal flow in the light pupil reflex

Latency of pupillary responses to light stimuli are smaller for larger steps of light, and larger for smaller steps of light (Alpern 1954; Lowenstein et al. 1964; Lee et al. 1969; Terdiman et al. 1969; Cibis et al. 1977; and many others). Miller and Thompson (1978), however, reported negligible change in pupil cycle time (period of high gain instability oscillations) with increased mean brightness. Sandberg and Stark (1968) reportd a negligible reduction in phase lag of pupillary responses to sinusoidal light stimuli as the modulation coefficient (m) increased. To resolve the inconsistency between the well-documented dependence of latency upon brightness, and the apparent absence of level dependence in the phase characteristics (as reflected directly in the responses to sinusoidal stimuli and indirectly in pupil cycle time experiments) we measured: 1. Latency to step stimuli of light, 2. Phase of responses to sinusoidal light stimuli and 3. Period (pupil cycle time) of high gain instability oscillations. The dependence of pupillary latency upon stimulus level (both light and accommodation) and the interaction between accommodation and light responses were investigated. We show that most of the level dependence of light-pupil latency resides in the afferent path. In the companion papers, we demonstrate that: 1. Phase of pupillary response to sinusoidal light stimuli is reduced by increased mean light level, but is independent of pupil size and accommodative stimulus level; and 2. The period of high gain oscillations is shown to decrease with increased mean light level. Taken together, these results imply the existence of a Level Dependent Signal Flow (LDSF) operator that resides in the light-pupil pathway, but not in the accommodation-pupil pathway. We propose a systems model of this operator in which the neural signals controlling pupil size are treated as waves whose phase velocity increases in response to brighter stimuli, and decreases in response to dimmer stimuli. When parameters of the model are adjusted to fit measured pupillary latency over a range of light levels, the model exhibits reduced phase lag in response to increased mean light level in the sinusoidal paradigm, and it exhibits reduced pupil cycle time in the high-gain oscillation paradigm. The model exhibits saturation of the LDSF effect in all paradigms at high light levels, as do experimental results. It simulates directional asymmetry of pupillary response to positive and negative steps of light, with constriction more rapid than dilatation. Finally, it simulates tonic pupillary constriction in response to modulation of a light simulus without changing average light level (Varju 1964; Troelstra 1968). All of these stimulated results are in accord with experimental observation.     

Mismatch negativity (MMN) for sequences of auditory and visual stimuli: evidence for a mechanism specific to the auditory modality

ERPs to sequences of standard and deviant sinusoidal 100 msec tone pips, high-contrast sinusoidal gratings and to their simultaneously presented combinations were recorded. Mismatch negativity (MMN), an ERP component elicited by deviant stimuli, was estimated for the different stimulus sequences in order to find out whether it reflects modality-specific processes or non-specific attentive phenomena. In addition to the auditory modality, we studied whether the mismatch response could be evoked by a deviant visual stimulus in a visual sequence or by a deviant stimulus in either modality. The results show that only auditory stimuli produced the mismatch response, suggesting that MMN is not a manifestation of a general attentional mechanism but is probably specific to the auditory modality.     

On the Modelling of Biological Patterns with Mechanochemical Models: Insights from Analysis and Computation

The diversity of biological form is generated by a relatively small number of underlying mechanisms. Consequently, mathematical and computational modelling can, and does, provide insight into how cellular level interactions ultimately give rise to higher level structure. Given cells respond to mechanical stimuli, it is therefore important to consider the effects of these responses within biological self-organisation models. Here, we consider the self-organisation properties of a mechanochemical model previously developed by three of the authors in Acta Biomater. 4, 613–621 (2008), which is capable of reproducing the behaviour of a population of cells cultured on an elastic substrate in response to a variety of stimuli. In particular, we examine the conditions under which stable spatial patterns can emerge with this model, focusing on the influence of mechanical stimuli and the interplay of non-local phenomena. To this end, we have performed a linear stability analysis and numerical simulations based on a mixed finite element formulation, which have allowed us to study the dynamical behaviour of the system in terms of the qualitative shape of the dispersion relation. We show that the consideration of mechanotaxis, namely changes in migration speeds and directions in response to mechanical stimuli alters the conditions for pattern formation in a singular manner. Furthermore without non-local effects, responses to mechanical stimuli are observed to result in dispersion relations with positive growth rates at arbitrarily large wavenumbers, in turn yielding heterogeneity at the cellular level in model predictions. This highlights the sensitivity and necessity of non-local effects in mechanically influenced biological pattern formation models and the ultimate failure of the continuum approximation in their absence.     

Pattern formation in one- and two-dimensional shape-space models of the immune system.

A large-scale model of the immune network is analyzed, using the shape-space formalism. In this formalism, it is assumed that the immunoglobulin receptors on B cells can be characterized by their unique portions, or idiotypes, that have shapes that can be represented in a space of a small finite dimension. Two receptors are assumed to interact to the extent that the shapes of their idiotypes are complementary. This is modeled by assuming that shapes interact maximally whenever their coordinates in the space-space are equal and opposite, and that the strength of interaction falls off for less complementary shapes in a manner described by a Gaussian function of the Euclidean "distance" between the pair of interacting shapes. The degree of stimulation of a cell when confronted with complementary idiotypes is modeled using a log bell-shaped interaction function. This leads to three possible equilibrium states for each clone: a virgin, an immune, and a suppressed state. The stability properties of the three possible homogeneous steady states of the network are examined. For the parameters chosen, the homogeneous virgin state is stable to both uniform and sinusoidal perturbations of small amplitude. A sufficiently large perturbation will, however, destabilize the virgin state and lead to an immune reaction. Thus, the virgin system is both stable and responsive to perturbations. The homogeneous immune state is unstable to both uniform and sinusoidal perturbations, whereas the homogeneous suppressed state is stable to uniform, but unstable to sinusoidal, perturbations. The non-uniform patterns that arise from perturbations of the homogeneous states are examined numerically. These patterns represent the actual immune repertoire of an animal, according to the present model. The effect of varying the standard deviation sigma of the Gaussian is numerically analyzed in a one-dimensional model. If sigma is large compared to the size of the shape-space, the system attains a fixed non-uniform equilibrium. Conversely if sigma is small, the system attains one out of many possible non-uniform equilibria, with the final pattern depending on the initial conditions. This demonstrates the plasticity of the immune repertoire in this shape-space model. We describe how the repertoire organizes itself into large clusters of clones having similar behavior. These results are extended by analyzing pattern formation in a two-dimensional (2-D) shape-space.(ABSTRACT TRUNCATED AT 400 WORDS)     

Phonotaxis in flying crickets

The steering responses of three species of field crickets, Teleogryllus oceanicus, T. commodus, and Gryllus bimaculatus, were characterized during tethered flight using single tone-pulses (rather than model calling song) presented at carrier frequencies from 3-100 kHz. This range of frequencies encompasses the natural songs of crickets (4-20 kHz, Fig. 1) as well as the echolocation cries of insectivorous bats (12-100 kHz). The single-pulse stimulus paradigm was necessary to assess the aversive nature of high carrier frequencies without introducing complications due to the attractive properties of repeated pulse stimuli such as model calling songs. Unlike the natural calling song, single tone-pulses were not attractive and did not elicit positive phonotactic steering even when presented at the calling song carrier frequency (Figs. 2, 3, and 9). In addition to temporal pattern, phonotactic steering was sensitive to carrier frequency as well as sound intensity. Three discrete flight steering behaviors positive phonotaxis, negative phonotaxis and evasion, were elicited by appropriate combinations of frequency, temporal pattern and sound intensity (Fig. 12). Positive phonotactic steering required a model calling song temporal pattern, was tuned to 5 kHz and was restricted to frequencies below 9 kHz. Negative phonotactic steering, similar to the 'early warning' bat-avoidance behavior of moths, was produced by low intensity (55 dB SPL) tone-pulses at frequencies between 12 and 100 kHz (Figs. 2, 3, and 9). In contrast to model calling song, single tone-pulses of high intensity 5-10 kHz elicited negative phonotactic steering; low intensity ultrasound (20-100 kHz) produced only negative phonotactic steering, regardless of pulse repetition pattern. 'Evasive', side-to-side steering, similar to the 'last-chance' bat-evasion behavior of moths was produced in response to high intensity (greater than 90 dB) ultrasound (20-100 kHz). Since the demonstration of negative phonotactic steering did not require the use of a calling song temporal pattern, avoidance of ultrasound cannot be the result of systematic errors in localizing an inherently attractive stimulus when presented at high carrier frequencies. Unlike attraction to model calling song, the ultrasound-mediated steering responses were of short latency (25-35 ms) and were produced in an open loop manner (Fig. 4), both properties of escape behaviors.(ABSTRACT TRUNCATED AT 400 WORDS)     

Pulsed pheromone stimuli affect the temporal response of antennal receptor neurones of the adult cabbage looper moth

Abstract. Male cabbage looper moths, Trichoplusia ni (Hiibner) (Lepidoptera: Noctuidae), fly upwind in response to pheromone blends produced and released by calling conspecific females. Specialized sensilla on the male antenna contain sensitive, highly specific olfactory receptor neurones which respond to constant olfactory signals, with a phasic-tonic pattern of action potential discharge. Olfactory stimuli in nature are not uniform. They are thought to consist of pulses of odours whose distribution is shaped by wind and local environmental features. We begin to evaluate this natural situation by stimulating pheromone-sensitive sensilla with short (200 ms) paired pulses of the major component of the female's pheromone blend, (Z)-7-dodecen-l-ol acetate (Z-7,12:AC). Different stimulus protocols in which the pulses were separated from each other by varying intervals were evaluated. The interval between pulses had a large effect on the phasic component of the response. Intervals between pulses as short as 30 ms reduced the response to a second pulse by > 50%. When the intervals between pulses were longer than 3 s, significant differences were not seen between the responses to the first and second pulse. Implications for male orientation in natural, female-produced, pheromone plumes are discussed.     

Effects of transient receptor potential-like current on the firing pattern of action potentials in the Hodgkin-Huxley neuron during exposure to sinusoidal external voltage

Transient receptor potential vanilloid-1 (TRPV1) channels play a role in several inflammatory and nociceptive processes. Previous work showed that magnetic electrical field-induced antinociceptive [corrected] action is mediated by activation of capsaicin-sensitive sensory afferents. In this study, a modified Hodgkin-Huxley model, in which TRP-like current (ITRP) was incorporated, was implemented to predict the firing behavior of action potentials (APs), as the model neuron was exposed to sinusoidal changes in externally-applied voltage. When model neuron is exposed to low-frequency sinusoidal voltage, increased maximal conductance of ITRP can enhance repetitive bursts of APs accompanied by a shortening of inter-spike interval (ISI) in AP firing. The change in ISIs with number of interval is periodic with the phase-locking. In addition, increased maximal conductance of ITRP can abolish chaotic pattern of AP firing in model neuron during exposure to high-frequency voltage. The ISI pattern is converted from irregular to constant, as maximal conductance of ITRP is increased under such high-frequency voltage. Our simulation results suggest that modulation of TRP-like channels functionally expressed in small-diameter peripheral sensory neurons should be an important mechanism through which it can contribute to the firing pattern of APs.