A Wiener-type neuronal model in the presence of exponential refractoriness

An instantaneous return process in the presence of random refractoriness for Wiener model of single neuron activity is considered. The case of exponential distributed refractoriness is analyzed and expressions for output distributions and interspike intervals density are obtained in closed form. A computational study is performed to elucidate the role played by the model parameters in affecting the firing probabilities and the interspike distribution.     

A neuronal modeling paradigm in the presence of refractoriness

A mathematical characterization of the membrane potential as an instantaneous return process in the presence of refractoriness is investigated for diffusion models of single neuron's activity, assuming that the firing threshold acts as an elastic barrier. Steady-state probability densities and asymptotic moments of the neuronal membrane potential are explicitly obtained in a form that is suitable for quantitative evaluations. For the Ornstein-Uhlenbeck (OU) and Feller neuronal models, closed form expression are obtained for asymptotic mean and variance of the neuronal membrane potential and an analysis of the different features exhibited by the above mentioned models is performed.     

Superposition of impulse activity in a rapidly-adapting afferent unit model

Mechanosensory afferent units consist of a parent axon, the peripheral axonal arborization, and the branch terminal mechanoreceptors. The present work uses a mathematical model to describe the contribution of a given number of rapidly-adapting mechanoreceptors to the impulse pattern of their parent axon. In the model impulses initiated by any driven mechanoreceptor instantaneously propagate orthodromically and antidromically. The model also incorporates the axonal absolute refractory period as well as ortho-and antidromically elicited recovery cycles. In separate computations, periodic or random (Poisson process) trains of short-duration stimuli at constant amplitude are delivered to a given number (N=2–30) of co-innervated mechanoreceptors. The superposition of component impulse trains always departs from the theoretical ideal (Poisson process). Such departures are attributable to: (i) the number of driven mechanoreceptors, when N is small, (ii) axonal absolute refractory period, during maximal amplitude stimulation, and (iii) antidromic recovery cycles as well as absolute refractoriness, during submaximal-amplitude stimulation. Computations reveal that this instantaneous reset model results in the elimination of information extracted by driven mechanoreceptors. Model predictions with Poisson stimulation at varied amplitudes are compared to G-hair afferent unit responses to analogous stimulation. Qualitatively opposite results with respect to parent axonal impulse patterns imply that the axonal arborization is not simply a substrate for impulse propagation from branch terminals to parent axon.     

A neural net model for the α-rhythm

Pulse-interval distributions are obtained for a counting system in which there is a gradual, rather than abrupt, increase in excitability following the registration of a pulse (relative refractoriness). The results are applicable to systems in which Poisson counting would be observed in the absence of such effects, and in which the memory reaches back at most one pulse. Choosing a particular functional form for the recovery function, the theory fits the experimentally measured distribution for the maintained discharge in the cat's retinal ganglion cell. It is also consistent with the notion that Weber's Law emerges from refractoriness in the visual system, as first proposed by van der Velden.This work was supported in part by the National Science Foundation     

Vulnerable window for conduction block in a one-dimensional cable of cardiac cells, 2: multiple extrasystoles

Unidirectional conduction block of premature extrasystoles can lead to initiation of cardiac reentry, causing lethal arrhythmias including ventricular fibrillation. Multiple extrasystoles are often more effective at inducing unidirectional conduction block and reentry than a single extrasystole. Since the substrate for conduction block is spatial dispersion of refractoriness, in this study we investigate how the first extrasystole modulates this dispersion to influence the "vulnerable window" for conduction block by subsequent extrasystoles, particularly in relation to action potential duration restitution and conduction velocity restitution properties. Using a kinematic model to represent wavefront-waveback interactions and simulations with the Luo-Rudy model in a one-dimensional cable of cardiac cells, we show that in homogeneous tissue, a premature extrasystole can create a large dispersion of refractoriness leading to conduction block of a subsequent extrasystole. In heterogeneous tissue, however, a premature extrasystole can either reduce or enhance the dispersion of refractoriness depending on its propagation direction with respect to the previous beat. With multiple extrasystoles at random coupling intervals, vulnerability to conduction block is proportional to their number. In general, steep action potential duration restitution and broad conduction velocity restitution promote dispersion of refractoriness in response to multiple extrasystoles, and thus enhance vulnerability to conduction block. These restitution properties also promote spatially discordant alternans, a setting which is particularly prone to conduction block. The equivalent dispersion of refractoriness created dynamically in homogeneous tissue by spatially discordant alternans is more likely to cause conduction block than a comparable degree of preexisting dispersion in heterogeneous tissue.     

Poisson process stimulation of an excitable membrane cable model.

The convergence of multiple inputs within a single-neuronal substrate is a common design feature of both peripheral and central nervous systems. Typically, the result of such convergence impinges upon an intracellularly contiguous axon, where it is encoded into a train of action potentials. The simplest representation of the result of convergence of multiple inputs is a Poisson process; a general representation of axonal excitability is the Hodgkin-Huxley/cable theory formalism. The present work addressed multiple input convergence upon an axon by applying Poisson process stimulation to the Hodgkin-Huxley axonal cable. The results showed that both absolute and relative refractory periods yielded in the axonal output a random but non-Poisson process. While smaller amplitude stimuli elicited a type of short-interval conditioning, larger amplitude stimuli elicited impulse trains approaching Poisson criteria except for the effects of refractoriness. These results were obtained for stimulus trains consisting of pulses of constant amplitude and constant or variable durations. By contrast, with or without stimulus pulse shape variability, the post-impulse conditional probability for impulse initiation in the steady-state was a Poisson-like process. For stimulus variability consisting of randomly smaller amplitudes or randomly longer durations, mean impulse frequency was attenuated or potentiated, respectively. Limitations and implications of these computations are discussed.     

Statistical study on reverberation between two mutually excitatory neuron groups

The reverberation that occurs between two neuron groups, which have excitatory mono-synaptic random connections with each other can be studied theoretically by employing a model neuron, which expresses well the characters of a real neuron. In this model we consider three effects, which are; the effect of the summation of the excitatory post-synaptic potential (EPSP) of neurons; the effect of the spontaneous firing of neurons as a noise in groups and the effect of the relative refractory period of neurons. As a result, it is shown that under the effect of the summation of the EPSP of neurons and the effect of the noise, the systematic threshold p theta takes the same value as is observed in practice. The effect of the relative refractory period has been considered in order to explain the low speed of the increase in firing activity, as observed in the reverberating system. It suppresses slightly the speed of the increase in firing activity (pi) in the system. Moreover, the speed can be suppressed by making the refractory effect strong according to the increase of pi. However, the initial increase of pi at a high speed that was observed in the experiment cannot be explained simply by the effect of the refractoriness, even if it were the absolute refractoriness.     

The impact of rate heterogeneity on inference of phylogenetic models of trait evolution

Rates of trait evolution are known to vary across phylogenies; however, standard evolutionary models assume a homogeneous process of trait change. These simple methods are widely applied in small‐scale phylogenetic studies, whereas models of rate heterogeneity are not, so the prevalence and patterns of potential rate variation in groups up to hundreds of species remain unclear. The extent to which trait evolution is modelled accurately on a given phylogeny is also largely unknown because studies typically lack absolute model fit tests. We investigated these issues by applying both rate‐static and variable‐rates methods on (i) body mass data for 88 avian clades of 10–318 species, and (ii) data simulated under a range of rate‐heterogeneity scenarios. Our results show that rate heterogeneity is present across small‐scaled avian clades, and consequently applying only standard single‐process models prompts inaccurate inferences about the generating evolutionary process. Specifically, these approaches underestimate rate variation, and systematically mislabel temporal trends in trait evolution. Conversely, variable‐rates approaches have superior relative fit (they are the best model) and absolute fit (they describe the data well). We show that rate changes such as single internal branch variations, rate decreases and early bursts are hard to detect, even by variable‐rates models. We also use recently developed absolute adequacy tests to highlight misleading conclusions based on relative fit alone (e.g. a consistent preference for constrained evolution when isolated terminal branch rate increases are present). This work highlights the potential for robust inferences about trait evolution when fitting flexible models in conjunction with tests for absolute model fit.     

Accession of sweet stimuli to receptors. I. Absolute dominance of one molecular species in binary mixtures

Intensity/time studies of sweetness response in pure solutions of each of nine different sweet stimuli have been carried out. Both variables exhibit simple power functions of the form Intensity (S) = kscns and Persistence (P) = kpcnp. In binary mixtures of these nine stimuli a depression (or negative synergism) of both sweetness intensity and persistence is observed which is predictable from the low exponents of the power functions. Combination of both power functions allows the "effective concentration" of each stimulus in a binary mixture to be calculated from its observed intensity/time characteristics. All "effective concentrations" calculable in this way show absolute dominance of one stimulus in mixtures of two irrespective of the relative proportions of the two stimuli. It is suggested that the "effective concentrations" may reflect real concentrations of a single molecular species in the microenvironment of the receptor. Thus the accession of sweet molecules to ordered, localized concentrations at the receptor is ultimately dependent on chemical structure.     

Audio-Visual Speech Cue Combination

Background

Different sources of sensory information can interact, often shaping what we think we have seen or heard. This can enhance the precision of perceptual decisions relative to those made on the basis of a single source of information. From a computational perspective, there are multiple reasons why this might happen, and each predicts a different degree of enhanced precision. Relatively slight improvements can arise when perceptual decisions are made on the basis of multiple independent sensory estimates, as opposed to just one. These improvements can arise as a consequence of probability summation. Greater improvements can occur if two initially independent estimates are summated to form a single integrated code, especially if the summation is weighted in accordance with the variance associated with each independent estimate. This form of combination is often described as a Bayesian maximum likelihood estimate. Still greater improvements are possible if the two sources of information are encoded via a common physiological process.

Principal Findings

Here we show that the provision of simultaneous audio and visual speech cues can result in substantial sensitivity improvements, relative to single sensory modality based decisions. The magnitude of the improvements is greater than can be predicted on the basis of either a Bayesian maximum likelihood estimate or a probability summation.

Conclusion

Our data suggest that primary estimates of speech content are determined by a physiological process that takes input from both visual and auditory processing, resulting in greater sensitivity than would be possible if initially independent audio and visual estimates were formed and then subsequently combined.     

Photoperiodic control of the termination of reproduction in Japanese quail (Coturnix coturnix japonica)

Typically, birds come into breeding in the spring as a response to long days, and end reproduction some weeks later by becoming refractory to those long days. The refractory state is subsequently dissipated by the short days of autumn and winter, so producing once again a bird that can respond to long days. Bird species differ in the extent to which refractoriness is developed; the present experiments took advantage of the relative, rather than the absolute, refractoriness in quail to measure quantitatively the dissipation process. Quail were made refractory by exposure to long days, then transferred to short days and at various times thereafter photostimulated with longer daylengths, the degree of photoresponsiveness being assessed by measuring changes in luteinizing hormone (LH) secretion or cloacal gland size or both. The most clearcut results came from using 13L:11D as the test stimulus to measure photoresponsiveness, and this indicated, in both intact and castrated quail, no response to 13L:11D after one week of short days, a minor response after two weeks, a strong response after three weeks and a full response after five weeks. Thus refractoriness appears to be dissipated gradually under short days, and not in an all-or-none fashion. Confirmation of this conclusion came from experiments in which refractory quail were moved to short days and after one or two weeks transferred to a range of long daylengths. After one week of short days no responses were obtained to 13L:11D or 14L:10D and moderate responses only to 16L:8D, but after two weeks of short days the magnitudes of all the responses were increased.(ABSTRACT TRUNCATED AT 250 WORDS)     

Copper-catalyzed divergent kinetic resolution of racemic allylic substrates

When a racemic mixture is fully consumed the products may still be enantiomerically enriched. In particular, the regiodivergent kinetic resolution is a process in which a single chiral catalyst or reagent reacts with a racemic substrate to form regioisomers possessing an opposite configuration on the newly-formed stereogenic centers. This review reports the major advances in the field of the copper-catalyzed regiodivergent and stereodivergent kinetic resolution of allylic substrates with organometallic reagents. The chiral recognition matching phenomena found with particular allylic substrates with the absolute configuration of the chiral catalyst allows in some cases an excellent control of the regio- and stereoselectivity, sheding some light on the so-called "black-box" mechanism of a copper-catalyzed asymmetric allylic alkylation.     

Evaluation of Postspike Changes in Neuronal Excitability by Comparing Ordinary and Shuffled Autocorrelation Functions

Responses of single neurons to tonal signals amplitude-modulated by repeating segments of lowfrequency noise were studied in the dorsal (cochlear) medullary nucleus and midbrain auditory center (torus semicircularis) of the grass frog Rana temporaria. An autocorrelation function of the response to a total presentation and a shuffled autocorrelation function were derived. The latter was obtained by correlating the impulse response to each segment of the modulated signal with responses to all other segments with the exception of the initial one. After the necessary normalization, the function differed from the initial autocorrelation only in lacking postspike changes in excitability. A delay dependence of the ratio of the two functions directly demonstrated the time course of the postspike change in excitability of the studied cell. The majority of second-order neurons, which are in the dorsal nucleus of the medulla oblongata, were characterized only by brief intervals of absolute and relative refractoriness. However, cells with excitability that was markedly facilitated immediately after the refractory period were observed even in this nucleus. Neurons with a complex pattern of postspike changes in excitability were detected in the torus semicircularis. In these cells, a comparatively long postspike decrease in excitability was usually interrupted by intervals in which the neuron sensitivity was significantly higher than normal. The results demonstrate that spike generation has a marked effect on subsequent activity in brainstem auditory units. The effects may play an important role in the formation of the temporal pattern of neuronal responses to auditory signals.     

Synchronization of Early Afterdepolarizations and Arrhythmogenesis in Heterogeneous Cardiac Tissue Models

Early afterdepolarizations (EADs) are linked to both triggered arrhythmias and reentrant arrhythmias by causing premature ventricular complexes (PVCs), focal excitations, or heterogeneous tissue substrates for reentry formation. However, a critical number of cells that synchronously exhibit EADs are needed to result in arrhythmia triggers and substrates in tissue. In this study, we use mathematical modeling and computer simulations to investigate EAD synchronization and arrhythmia induction in tissue models with random cell-to-cell variations. Our major observations are as follows. Random cell-to-cell variations in action potential duration without EAD presence do not cause large dispersion of refractoriness in well-coupled tissue. In the presence of phase-2 EADs, the cells may synchronously exhibit the same number of EADs or no EADs with a very small dispersion of refractoriness, or synchronize regionally to result in large dispersion of refractoriness. In the presence of phase-3 EADs, regional synchronization leads to propagating EADs, forming PVCs in tissue. Interestingly, even though the uncoupled cells exhibit either no EAD or only a single EAD, when these cells are coupled to form a tissue, more than one PVC can occur. When the PVCs occur at different locations and time, multifocal arrhythmias are triggered, with the foci shifting in space and time in an irregular manner. The focal arrhythmias either spontaneously terminate or degenerate into reentrant arrhythmias due to heterogeneities and spatiotemporal chaotic dynamics of the foci.     

Stability analysis of a mathematical neuron model

The “second method” of Liapunov is used to perform a stability analysis of a mathematical model of the neuron. This analysis is based on the hypothesis that the firing of the neuron coincides with a temporary state of instability of the system, and that the initiation of all-or-none process depends on the magnitude of membrane depolarization and its first time derivative. It is found that the stability (and hence the possibility of a second firing) is restored approximately when the rate of membrane repolarization is at a maximum. This result predicts that the duration of the period of absolute refractoriness in neurons would be about 75 per cent of the spike duration, and thus shorter than the value usually obtained from experimental measurements.     

Analysis of single unit activity evoked by tones amplitude-modulated with low-frequency noise in frog medulla

A method of constructing shuffled autocorrelation functions (SACF) was used to characterize single units in the dorsal medullar nucleus of the common frog (Rana temporaria). A continuous characteristic frequency tone modulated by repeating pieces of low-frequency noise was used as a stimulus. SACF was calculated as the correlation between the firing discharges evoked by different repeating pieces of the low-frequency noise. This approach obviates the influence of refractoriness and also considerably increases the sample representativity. Comparison of the SACF with the conventional ACF permits estimating the temporal dynamics of changes in the postspike excitability of the neuron. Analysis of several examples demonstrates the possibility of facilitation just after the period of absolute refractoriness in some tonic units. Neurons exhibiting only a phasic response to the onset of nonmodulated voice-frequency pieces were able to selectively respond to special moments of noise amplitude modulation. These cells demonstrate extremely high synchronism of reaction. We also describe a neuron characterized by an intrinsic periodicity of firing not connected with the dynamics of arriving stimuli.     

Electrical properties of Paramecium caudatum: all-or-none electrogenesis

Summary Specimens of Paramecium immersed in solutions of CaCl₂ show graded electrogenesis in response to imposed transmembrane current. However, when BaCl₂ in a final concentration of 0.25 mM is added to a 1 mM CaCl₂ solution, an outward current pulse of 10^-10 amp or greater elicits an all-or-none transient reversal in membrane potential having a duration of about 40 msec. An increase of [Ba⁺⁺] results in (a) lower resting potential, (b) positive shift in critical firing level, (c) increased overshoot of the action potential, (d) decreased hyperpolarizing afterpotential, and (e) increased duration of the action potential (a.p.). If [Ca⁺⁺] is increased along with [Ba⁺⁺] so as to keep the ratio [Ba⁺⁺]/[Ca⁺⁺] constant, the same results are obtained except that the duration of the a. p. remains unaltered. Thus, effects a-d appear to be related to [Ba⁺⁺] and not to [Ca⁺⁺] or [Cl^-]. The degree of overshoot in 1 mM Ca is linearly related to log [Ba⁺⁺] with a slope of approximately 22 mv. With the ratio [Ba⁺⁺]/[Ca⁺⁺] constant, the slope closely approaches the ideal value of 29 mv. The evidence indicates that prolongation of the action potential is due to a delayed onset of Ba inactivation, and that this in turn is a function of surface-bound Ba. Other features of the action potential are absolute refractoriness during its rising and plateau phases, relative refractoriness lasting several seconds, and repetitive firing in response to steady current depolarization. The response is unaffected by TTX and TEA. Mn prolongs the action potential. Sr has an action similar to Ba, whereas the addition of K, Na, Rb, or Mg to the basic calcium medium is unaccompanied by all-or-none electrogenesis.On leave of absence from the Zoological Institute, Faculty of Science, University of Tokyo.Support came from National Science Foundation grant GB-5752x, U.S.P.H.S. grant NB-03664, and in part from Office of Naval Research grant Nonr 4785(00) administered by the Marine Biological Laboratory, Woods Hole.