Distribution Of Refractory Periods Research Articles

Analytical refractory period distribution for a class of time-variant biochemical systems with second-order reactions.

Refractory period (RP), the waiting time between signals, can induce complex signaling dynamics, such as acceleration, adaptation, and oscillation, within many cellular biochemical networks. However, its underlying molecular mechanisms are still unclear. Rigorously estimating the RP distribution may be essential to identify its causal regulatory mechanisms. Traditional methods of estimating the RP distribution depend on solving the underlying Chemical Master Equations (CMEs), the dominant modeling formalism of biochemical systems. However, exact solutions of the CME are only known for simple reaction systems with zero- and first-order reactions or specific systems with second-order reactions. General solutions still need to be derived for systems with bimolecular reactions. It is even more challenging if large state-space and nonconstant reaction rates are involved. Here, we developed a direct method to gain the analytical RP distribution for a class of second-order reaction systems with nonconstant reaction rates and large state space. Instead of using the CME, we used an equivalent path-wise representation, which is the solution to a transformed martingale problem of the CME. This allowed us to bypass solving a CME. We then applied the method to derive the analytical RP distribution of a real complex biochemical network with second-order reactions, the Drosophila phototransduction cascade. Our approach provides an alternative to the CMEs in deriving the analytical RP distributions of a class of second-order reaction systems. Since the bimolecular reactions are common in biological systems, our approach could enhance understanding real-world biochemical processes.

A biomimetic fly photoreceptor model elucidates how stochastic adaptive quantal sampling provides a large dynamic range.

Light intensities (photons s–1 μm–2) in a natural scene vary over several orders of magnitude from shady woods to direct sunlight. A major challenge facing the visual system is how to map such a large dynamic input range into its limited output range, so that a signal is neither buried in noise in darkness nor saturated in brightness. A fly photoreceptor has achieved such a large dynamic range; it can encode intensity changes from single to billions of photons, outperforming man‐made light sensors. This performance requires powerful light adaptation, the neural implementation of which has only become clear recently. A computational fly photoreceptor model, which mimics the real phototransduction processes, has elucidated how light adaptation happens dynamically through stochastic adaptive quantal information sampling. A Drosophila R1–R6 photoreceptor's light sensor, the rhabdomere, has 30,000 microvilli, each of which stochastically samples incoming photons. Each microvillus employs a full G‐protein‐coupled receptor signalling pathway to adaptively transduce photons into quantum bumps (QBs, or samples). QBs then sum the macroscopic photoreceptor responses, governed by four quantal sampling factors (limitations): (i) the number of photon sampling units in the cell structure (microvilli), (ii) sample size (QB waveform), (iii) latency distribution (time delay between photon arrival and emergence of a QB), and (iv) refractory period distribution (time for a microvillus to recover after a QB). Here, we review how these factors jointly orchestrate light adaptation over a large dynamic range.

Refractoriness enhances temporal coding by auditory nerve fibers.

A universal property of spiking neurons is refractoriness, a transient decrease in discharge probability immediately following an action potential (spike). The refractory period lasts only one to a few milliseconds, but has the potential to affect temporal coding of acoustic stimuli by auditory neurons, which are capable of submillisecond spike-time precision. Here this possibility was investigated systematically by recording spike times from chicken auditory nerve fibers in vivo while stimulating with repeated pure tones at characteristic frequency. Refractory periods were tightly distributed, with a mean of 1.58 ms. A statistical model was developed to recapitulate each fiber's responses and then used to predict the effect of removing the refractory period on a cell-by-cell basis for two largely independent facets of temporal coding: faithful entrainment of interspike intervals to the stimulus frequency and precise synchronization of spike times to the stimulus phase. The ratio of the refractory period to the stimulus period predicted the impact of refractoriness on entrainment and synchronization. For ratios less than ∼0.9, refractoriness enhanced entrainment and this enhancement was often accompanied by an increase in spike-time precision. At higher ratios, little or no change in entrainment or synchronization was observed. Given the tight distribution of refractory periods, the ability of refractoriness to improve temporal coding is restricted to neurons responding to low-frequency stimuli. Enhanced encoding of low frequencies likely affects sound localization and pitch perception in the auditory system, as well as perception in nonauditory sensory modalities, because all spiking neurons exhibit refractoriness.

Letter to the Editor

To the Editor: In their Letter to the Editor, Drs Berenfeld, Pertsov, and Jalife1 suggest that our recent article entitled “The Distribution of Refractory Periods Influences the Dynamics of Ventricular Fibrillation”2 characterized the nature of wave organization during fibrillation. They also state that our study “provides important and useful information, particularly in regard to the existence of action potential duration gradients during VF.” With respect to these comments, we should clarify that we did not focus on the nature of wave organization in ventricular fibrillation (VF), nor did we show the existence of action potential duration (APD) gradients during VF. We correlated APD gradients measured in hearts with a normal rhythm (either paced or sinus rhythm) with the distributions of mean activation intervals and fast Fourier transform (FFT) spectra around the epicardium from the same hearts in VF. The main conclusion is stated in the title of the article.2 Berenfeld et al1 criticized the study claiming that we did not address technical issues and overinterpreted our data. Surprisingly, the issues that they raised and their concerns over the …

Decrease in nerve temperature: a model for increased temporal dispersion

A decrease in nerve temperature causes a proportional decrease in conduction velocity which, in percentage terms, is equal for all nerve fibers. The absolute decrease in conduction velocity is larger for faster conducting nerve fibers. This results in a compression and a shift to lower values of the conduction velocity distribution and an increase in temporal dispersion. The purpose of this study was to determine if these effects could be detected by a combination of two collision techniques designed to obtain the motor conduction velocity distribution and refractory period distribution. In 12 healthy volunteers we measured the conduction velocity distribution in the median nerve at nerve temperatures of 25 and 40°C. The results showed that our method could detect the predicted changes in conduction velocity distribution and temporal dispersion. We conclude that temperature change is a model that can be used to study temporal dispersion. This may be a first step towards distinguishing between the effects of conduction block and (abnormal) temporal dispersion in demyelinated nerve fibers.

Comparison of two techniques to measure the motor nerve refractory period distribution

The techniques introduced by Ingram et al. and by Kimura to assess the motor nerve refractory period distribution were compared in the peroneal nerve of 28 healthy subjects. Twenty of these subjects were examined twice with an interval of 6–20 days. Results obtained with Ingram's technique yielded a narrower refractory period distribution, displayed less inter-individual variability, and were more reproducible than those obtained with Kimura's technique. The mean refractory period for the 5% slowest recovering fibres (MRP 95 ) was 1.51 msec (S.D. 0.14) for Ingram's technique and 2.15 msec (S.D. 0.72) for Kimura's technique. The coefficient of variation of the MRP 95 was 8% for Ingram's technique, and 22% for Kimura's technique. The present data do not allow a definite conclusion concerning the association of refractory period with age, gender and height. Ingram's technique would be favoured for practical application over Kimura's technique on the basis of this study.

Comparison of two techniques to measure the motor nerve refractory period distribution

The techniques introduced by Ingram et al. and by Kimura to assess the motor nerve refractory period distribution were compared in the peroneal nerve of 28 healthy subjects. Twenty of these subjects were examined twice with an interval of 6–20 days. Results obtained with Ingram's technique yielded a narrower refractory period distribution, displayed less inter-individual variability, and were more reproducible than those obtained with Kimura's technique. The mean refractory period for the 5% slowest recovering fibres (MRP 95) was 1.51 msec (S.D. 0.14) for Ingram's technique and 2.15 msec (S.D. 0.72) for Kimura's technique. The coefficient of variation of the MRP 95 was 8% for Ingram's technique, and 22% for Kimura's technique. The present data do not allow a definite conclusion concerning the association of refractory period with age, gender and height. Ingram's technique would be favoured for practical application over Kimura's technique on the basis of this study.

Motor nerve refractory period distribution assessed by two techniques in diabetic polyneuropathy

The techniques introduced by Kimura and Ingram et al. were applied to assess the distribution of motor refractory periods (DMRPs) in peroneal fibres of 28 diabetics with symptoms indicating polyneuropathy and in 28 controls. Results were compared with conventional motor nerve conduction velocity (MNCV) and compound muscle action potential (CMAP) measurements. MRP95 and MRP90 (the 5% and 10% slowest recovering fibres) obtained with Ingram's technique were prolonged in the diabetic patients. In the 26 patients with a value of MRP95 and MNCV, a prolonged MRP95 and a decreased MNCV were found in 12 patients. Thus conventional MNCV had a sensitivity of 46% to detect neuropathy; addition of MRP95 obtained with Ingram's technique raised the sensitivity to 73%. Specificity was 100% in both cases. With Kimura's technique or with the fast recovering fibres in Ingram's technique, it was not possible to discriminate the patients from the controls. This study indicates that measurement of the DMRP with the technique introduced by Ingram et al. improves the electrophysiological diagnosis of diabetic polyneuropathy.

Motor nerve refractory period distribution assessed by two techniques in diabetic polyneuropathy

The techniques introduced by Kimura and Ingram et al. were applied to assess the distribution of motor refractory periods (DMRPs) in peroneal fibres of 28 diabetics with symptoms indicating polyneuropathy and in 28 controls. Results were compared with conventional motor nerve conduction velocity (MNCV) and compound muscle action potential (CMAP) measurements. MRP 95 and MRP 90 (the 5% and 10% slowest recovering fibres) obtained with Ingram's technique were prolonged in the diabetic patients. In the 26 patients with a value of MRP 95 and MNCV, a prolonged MRP 95 and a decreased MNCV were found in 12 patients. Thus conventional MNCV had a sensitivity of 46% to detect neuropathy; addition of MRP 95 obtained with Ingram's technique raised the sensitivity to 73%. Specificity was 100% in both cases. With Kimura's technique or with the fast recovering fibres in Ingram's technique, it was not possible to discriminate the patients from the controls. This study indicates that measurement of the DMRP with the technique introduced by Ingram et al. improves the electrophysiological diagnosis of diabetic polyneuropathy.

Three-dimensional computer model of the entire human heart for simulation of reentry and tachycardia: Gap phenomenon and Wolff-Parkinson-White syndrome

A computer model of the entire human heart has been developed for simulation of the excitation and repolarization process. Spatial distribution of refractory periods and conduction velocities in the different cardiac tissues, the anisotropy of conduction in the ventricles, and the cycle length dependence of refractory periods and conduction velocities are taken into account. The algorithm calculating the activation process is based on a modified version of Huygen's principle for constructing wavefronts. This study presents simulations concerning the gap phenomenon of the conduction system and the initiation of tachycardias in a heart with Wolff-Parkinson-White syndrome. Results are compared for different basic cycle lengths and for normal and prolonged refractory periods in the His-Purkinje system. The gap phenomenon was found to be present only when using the prolonged refractory periods in the His-Purkinje-system at a cycle length of 700 ms. Induction of tachycardia by a single extrastimulus in the high right atrium in a heart with a bidirectionally conducting accessory pathway is possible by properly timed extrastimuli. The coupling interval of the stimulus for initiating a reentrant tachycardia depends on the cycle length, the conduction velocities and the set of refractory periods used. The same parameters determine whether or not a gap phenomenon in atrioventricular conduction occurs. The model may be useful for investigating similar questions concerning the reentry phenomena of tachycardia.

The Mechanism of Simulated Torsade de Pointes in a Computer Model of Propagated Excitation

Mechanism of Torsade de Pointes. A computer model that simulated propagation, nonuniform cycle length dependent recovery of excitability, and slow propagation during incomplete recovery in cardiac muscle has been shown to exhibit behavior similar to torsade de pointes. The conditions required in the model resembled those in long QT syndromes with regionally prolonged ventricular repolarization. In the model, premature excitation of a path with relatively short refractory periods resulted in sequential reentry of that path from a region with longer refractory periods. Sites of reentry become progressively more distal to the site of initiation. The episodes terminated spontaneously when reentrant excitation reached the end of unclosed paths or collided in closed paths. Each reentry site moved away from its initial position in the short recovery path because the distance traversed by propagation in that path exceeded the distance at which reentry occurred via the longer recovery region. The migrating sites of reentry resulted in changing QRS waveform in calculated electrocardiograms including changing QRS polarity when calculated from appropriate sites. Variations of the basic behavior occurred with nonuniform distribution of refractory periods within relatively short and long refractory period regions and included unidirectional progression of reentry sites and multiple circuits of reentry in closed paths. Termination of serial reentry at times other than those when activation reached the end of unclosed paths or collided in closed paths also occurred with nonuniform distribution of refractory periods. Findings provide a plausible explanation for the changing QRS waveform, spontaneous termination, and association of torsade de pointes with long QT syndromes but do not elucidate the mechanism of initiation of the tachyarrhythmia.

Enhancement of acoustic startle by electrical stimulation of the amygdala.

The present study demonstrated that electrical stimulation of the amygdala enhanced the acoustic startle response. A 25-ms train of 0.1-ms pulses initiated 5 ms before the onset of a 20-ms noise burst significantly increased startle at currents from 40 to 400 microA. Electrode placements just medial to the amygdala (in the pathway connecting the amygdala to the brain stem) increased startle with the lowest currents. Startle was also increased in all animals with stimulation in the central, medial, and intercalated nuclei of the amygdala. Stimulation in areas surrounding the amygdaloid complex was ineffective. In a second experiment, paired pulses with interpulse intervals between 0.1 and 20.0 ms delivered to the amygdala demonstrated that the stimulated axons had a distribution of refractory periods between 0.6 and 1.0 ms. This suggests that the population of neurons which subserves the enhancement of acoustic startle is fairly homogeneous and has small, myelinated axons.

The double collision technique: a new method for measurement of the motor nerve refractory period distribution in man

A new, double collision, technique is described for non-invasive measurement of the motor nerve refractory period distribution for human peripheral nerves. In contrast to previous collision techniques, this method is independent of the transient changes in nerve and muscle fibre conduction which can distort test muscle responses. The end-point of the distribution is determined by a null response; this permits accurate identification of those nerve fibres with the longest refractory periods. We have used the double collision technique to measure the refractory period distributions for the median nerve at the wrist in 20 normal subjects aged between 22 and 58 (mean 35) years. 150% maximal stimuli were used with a controlled limb temperature of 35°C. Following a conditioning stimulus, the mean latencies for recovery of 5%, 50%, 95% and 99% of motor nerve fibres were 0.94, 1.03, 1.12 and 1.23 msec respectively. Data are also presented for the ulnar and peroneal nerves. The results show that the human motor nerve refractory period distribution is much less dispersed than has been previously supposed.

Use of the double collision technique for determination of the normal motor nerve refractory period distribution

Use of the double collision technique for determination of the normal motor nerve refractory period distribution

Axonal physiology of chronic spinal cord injury in the cat: Intracellular recording in vitro

The properties of action potential conduction in single axons of the cat thoracic spinal cord were examined with microelectrode recording and electrical stimulation in vitro. The study included normal animals, animals chronically paralyzed by contusion of the cord, and animals showing some degree of locomotory recovery following a similar injury and several weeks of transient paralysis. The control studies were designed to compare the results of microelectrode sampling in vitro with morphological and in vivo physiological data. The pathophysiological studies were intended to investigate the continuity and function of axons identified morphologically in paralyzing lesions, and to examine the hypothesis that functional loss is associated with chronic axonal dysfunction, as well as direct axonal loss. Most of the recordings were made from dorsal columns and ventral tracts at 23–25°C. The conduction velocities recorded in the normal cord were consistent with morphological data on caliber spectra, given the selectivity of the microelectrodes for larger axons. The refractory period of transmission was approximately 2–4 ms at 23–25°C and 0.7–2 ms at 37°C. Prolonged depolarizing after-potentials were recorded, following action potentials greater than 70 mV amplitude. Axons outside the lesion in injured cord showed only slight reductions from control in the mean and range of conduction velocity and refractory period distributions. The number of axons impaled per electrode track was reduced by up to one half. Relatively few impaled axons conducted through the lesion site in the injured cords: 16% in recovering animals and 7% in chronically paralyzed, as compared with 61% in uninjured controls. The mean conduction velocity of these through-conducting axons was significantly less than that of the normal population, particularly in paralyzed animals, and refractory period was significantly prolonged for conduction through the lesion in the paralyzed group. When axons conducting through the middle of the isolated spinal tract were challenged by raising the temperature, conduction block occurred below physiological temperature (37°C) for 7% of axons in controls, 14% in recovering and 73% in paralyzed cats. The mean temperature of heat block in normal axons was 41°C. Some axons appear to survive in paralyzing contusion trauma of this type. Those axons that remain in the lesion site project through it but their conduction properties are abnormal, particularly in animals that remain chronically paralyzed. Action potentials in many axons may be effectively blocked at the chronic lesion site, contributing to the overall functional deficits.

Natural and evoked atrial flutter due to circus movement in dogs: Role of abnormal atrial pathways, slow conduction, nonuniform refractory period distribution and premature beats

Natural atrial flutter was discovered In a dog. Two forms of the arrhythmia resembling the human counterparts of typical and atypical atrial flutter were noted. The Observations in this dog led to studies in a series of normal dogs in which the extrastimulus technique was used to evoke runs of repetitive activity simulating but unlike true atrial flutter. Epicardial atrial activation maps were made from 72 to 96 bipolar complexes recorded during the arrhythmias. Multiple effective refractory periods were determined and these values were used to construct maps of the refractory period distribution. Dog 1, with true atrial flutter, demonstrated a complex form of circus motion characterized by unidirectional block and one-way conduction. Abnormal slowing of the unblocked circus wave stabilized and maintained the repetition by permitting more time for recovery of a uniform state of excitability ahead of the wave. The slow conduction in this dog was associated with right atrial hypoplasia and discontinuity in the preferential atrial conduction pathways. The circus activation patterns in the dogs with evoked flutter were similar to those in true flutter; however, the cycle lengths were shorter and the circus wave conducted faster. In evoked flutter the regional differences in refractory period duration determined the one-way block and circus conduction patterns. The circus pattern was caused by a nonuniform bimodal refractory state of the atrium that simultaneously exerted a blocking effect while permitting conduction and complex shaping of the unblocked wave, which was routed back to its site of origin. Thus atrial flutter was the result of three Interacting factors: (1) an atrial premature beat, (2) nonuniform distribution of atrial refractory periods, and (3) slow conduction of the circus wave initiated by factors 1 and 2.

Nerve fibre velocity and refractory period distributions in nerve trunks.

With the use of a double stimulus technique, nerve fibre velocity range measurements were performed over a single conduction distance in 13 normal subjects and over two conduction distances in another 12 normal subjects. The velocity ranges were found to be dependent upon the conduction distance, owing to unknown refractory period delays. Refractory period values were calculated for the 12 subjects and also direct refractory period distribution measurements were made on 15 normal subjects using a twin stimulus and automatic subtraction technique. Corrections to the velocity range measurements were made upon differing assumptions as to the correlation between refractory period and fibre conduction velocity. It was concluded that a single median value refractory period obtained from the distribution was the best correction to use, based upon the hypothesis that for group A fibres the random scatter of refractory period values is far greater than any variation due to a correlation between refractory period and fibre conduction velocity. It was found important to recognize that calculated values of velocity range are a function not only of the spread of fibre conduction velocities but also of refractory periods.

Quantitative measurement of neural post-stimulation excitability with behavioral methods

Previous paired-pulse techniques for estimating neural refractory periods of neurons mediating behaviors elicited by electrical stimulation of the brain are shown to be inadequate for characterizing the distribution of refractory periods. A new method is proposed which makes possible quantitative analysis of neural excitability cycle changes. Excitability increases for fibers mediating bar pressing for rewarding brain stimulation are found at all C-T intervals from 0.4 to 1.2 msec. The results are discussed in terms of local potential summation, relative and absolute refractory periods.

Contribution to the probabilistic theory of neural nets: I. Randomization of refractory periods and of stimulus intervals

Aggregates of neurons are considered in which the frequency of occurrence of neurons with a specified value of the refractory period follows certain probability distributions. Input-output functions are derived for such aggregates. In particular, if input and output intensities are defined in terms of stimulus frequencies and firing frequencies per neuron respectively, it is shown that a rectangular distribution of refractory periods leads to a logarithmic input-output curve. If input and output are defined in terms of the total number of stimuli and firings in the aggregate, it is shown how the “mobilization” picture leads to the logarithmic input-output curve.