Minghao Yang

Integer multiple spiking in neuronal pacemakers without external periodic stimulation

Abstract An integer multiple spiking, whose interspike intervals (ISIs) were mostly located at the integer multiples of a basic ISI, was observed in the experiment on a neuronal pacemaker without external periodic stimulation. It was observed between the period 1 spiking and the subthreshold oscillation when extra-cellular calcium concentration ([Ca ++ ] o ) was changed as a control parameter. A Hopf bifurcation point across which the period 1 spiking changed into the subthreshold oscillation directly was observed in the corresponding parameter region in the deterministic Chay model. In the stochastic Chay model, if the parameter v c (corresponding to [Ca ++ ] o in the experiment) was changed across the Hopf bifurcation point, the integer multiple spiking, appeared between the period 1 spiking and the subthreshold oscillation, was simulated. It exhibited similar characters to those in the experiment and was verified to be caused by autonomous stochastic resonance (ASR). The result revealed the sequence of firing patterns near the Hopf bifurcation point and indicated that ASR was probably the cause of the generation of the integer multiple spiking in the experiment.

Experimental observation of the stochastic bursting caused by coherence resonance in a neural pacemaker

The inter-burst intervals (IBIs) of the stochastic bursting caused by the effect of coherence resonance (CR) in Hindmarsh-Rose model exhibited multiple mode and were approximately integer multiples of a basic IBI. A similar bursting pattern was found in the experiment on an experimental neural pacemaker perfused with solution whose extracellular calcium concentration ([Ca2+]o) was lower than the normal level in which the firing pattern was period 1 spiking. The results verified the existence of the stochastic bursting and implied its CR mechanism. In addition, the distinction between the integer multiple bursting and the integer multiple spiking, another classical firing pattern caused by CR, was identified. The integer multiple bursting was generated in the parameter region where [Ca2+]o was lower than normal.

A SERIES OF BIFURCATION SCENARIOS IN THE FIRING PATTERN TRANSITIONS IN AN EXPERIMENTAL NEURAL PACEMAKER

Various bifurcation scenarios from period-1 bursting to period-1 spiking via a complex procedure were simulated in previous theoretical studies on neuronal models. The results revealed a general principle of neuronal firing pattern transitions. In this letter, three types of bifurcation scenarios with respect to extracellar calcium concentration ([Ca++]o) were discovered in experiments on neural pacemakers. Such a series of bifurcation scenarios implied complex structure of bifurcations in the firing pattern transitions of neurons. In the two-dimensional parameter space of Chay model, three classical kinds of bifurcation scenarios with respect to the bifurcation parameter vc (the reverse potential of calcium concentration) were simulated. By the variation of the conditional parameter, λn, the relationship among the three bifurcation scenarios was revealed. The results not only verified the existence of different bifurcation scenarios in real neuronal system, but also indicated that the differences among t...

IDENTIFYING DISTINCT STOCHASTIC DYNAMICS FROM CHAOS: A STUDY ON MULTIMODAL NEURAL FIRING PATTERNS

Some chaotic and a series of stochastic neural firings are multimodal. Stochastic multimodal firing patterns are of special importance because they indicate a possible utility of noise. A number of previous studies confused the dynamics of chaotic and stochastic multimodal firing patterns. The confusion resulted partly from inappropriate interpretations of estimations of nonlinear time series measures. With deliberately chosen examples the present paper introduces strategies and methods of identification of stochastic firing patterns from chaotic ones. Aided by theoretical simulation we show that the stochastic multimodal firing patterns result from the effects of noise on neuronal systems near to a bifurcation between two simpler attractors, such as a point attractor and a limit cycle attractor or two limit cycle attractors. In contrast, the multimodal chaotic firing trains are generated by the dynamics of a specific strange attractor. Three systems were carefully chosen to elucidate these two mechanisms. An experimental neural pacemaker model and the Chay mathematical model were used to show the stochastic dynamics, while the deterministic Wang model was used to show the deterministic dynamics. The usage and interpretation of nonlinear time series measures were systematically tested by applying them to firing trains generated by the three systems. We successfully identified the distinct differences between stochastic and chaotic multimodal firing patterns and showed the dynamics underlying two categories of stochastic firing patterns. The first category results from the effects of noise on the neuronal system near a Hopf bifurcation. The second category results from the effects of noise on the period-adding bifurcation between two limit cycles. Although direct application of nonlinear measures to interspike interval series of these firing trains misleadingly implies chaotic properties, definition of eigen events based on more appropriate judgments of the underlying dynamics leads to accurate identifications of the stochastic properties.

Potentiation of synaptic strength and intrinsic excitability in the nucleus accumbens after 10 days of morphine withdrawal.

Neuroadaptations in the nucleus accumbens (NAc) are associated with the development of drug addiction. Plasticity in synaptic strength and intrinsic excitability of NAc medium spiny neurons (MSNs) play critical roles in addiction induced by different classes of abused drugs. However, it is unknown whether morphine exposure influences synaptic strength, intrinsic excitability or both in NAc. Here we show that chronic withdrawal (10 days after the last injection) from repeated morphine exposure elicited potentiation in both glutamatergic synaptic strength and intrinsic excitability of MSNs in NAc shell (NAcSh). The potentiation of synaptic strength was demonstrated by an increase in the frequency of miniature excitatory postsynaptic currents (mEPSCs), a decrease in the paired‐pulse ratio (PPR), and an increase in the ratio of α‐amino‐3‐hydroxy‐5‐methyl‐isoxazole propionic acid receptors (AMPAR)‐ to N‐methyl‐D‐aspartate receptors (NMDAR)‐mediated currents. The potentiation of intrinsic excitability was mediated by inhibition of the sustained potassium currents via extrasynaptic NMDAR activation. The function of the presynaptic group II metabotropic glutamate receptors (mGluR2/3) was downregulated, enhancing the probability of glutamate release on synaptic terminals during chronic morphine withdrawal. Pretreatment with the mGluR2/3 agonist LY379268 completely blocked potentiation of both synaptic strength and intrinsic excitability. These results suggest that chronic morphine withdrawal downregulates mGluR2/3 to induce potentiation of MSN glutamatergic synapse via increased glutamate release, leading to potentiation of intrinsic excitability. Such potentiation of both synaptic strength and intrinsic excitability might contribute to neuroadaptations induced by morphine application.

Different classifications of UPOs in the parametrically different chaotic ISI series of a neural pacemaker

Various interspike intervals (ISIs) in a series of spontaneous discharges of experimental neural pacemakers were identified as chaotic and as lying between stable period 2 and stable period 3. The method of So et al. for detection of unstable periodic orbits (UPOs) was applied to analyze two chaotic ISI series generated under the action of [Ca2+]o in different concentrations. In the chaotic ISI series near the stable period 2, an unstable period 2 orbit was detected. In the chaotic ISI series near the stable period 3, both an unstable period 2 orbit and an unstable period 3 orbit were detected. The location of the unstable period 2 orbit was close to that of the stable period 2 in the return map, while the location of the unstable period 3 orbit was close to that of the stable period 3. The results not only revealed the structures of various chaotic ISI series, but also indicated that the classification of UPOs could reflect the experimental control parameters at which the chaotic ISI series were generated. The previously discovered period adding bifurcation in the ISI series generated by experimental neural pacemakers [12] was further described in terms of the evolution of the period orbits.

COHERENCE RESONANCE–INDUCED STOCHASTIC NEURAL FIRING AT A SADDLE-NODE BIFURCATION

Coherence resonance at a saddle-node bifurcation point and the corresponding stochastic firing patterns are simulated in a theoretical neuronal model. The characteristics of noise-induced neural firing pattern, such as exponential decay in histogram of interspike interval (ISI) series, independence and stochasticity within ISI series are identified. Firing pattern similar to the simulated results was discovered in biological experiment on a neural pacemaker. The difference between this firing and integer multiple firing generated at a Hopf bifurcation point is also given. The results not only revealed the stochastic dynamics near a saddle-node bifurcation, but also gave practical approaches to identify the saddle-node bifurcation and to distinguish it from the Hopf bifurcation in neuronal system. In addition, many previously observed firing patterns can be attribute to stochastic firing pattern near such a saddle-node bifurcation.

Noise Induced Multi-Mode Neural Firings in a Period Adding Bifurcation Scenario

A series of new firing patterns lying between two kinds of periodic bursting patterns and randomly alternating on the two kinds of periodic bursts, were discovered in the experiment on neural pacemaker and induced by noise in Chay model near each bifurcation point in a period adding bifurcation scenario without chaos, exhibiting multi-mode characteristics that was the signature of autonomous stochastic resonance in neuronal firing. Two endogenous characteristics near each bifurcation point that made noise induce the new firing patterns were identified. One was that there existed critical phase between the trajectories of the two kinds of bursting patterns. The other was that the periods of the two kinds of bursting patterns near each bifurcation point were small.

Effects of NR2A and NR2B-containing N-methyl-D-aspartate receptors on neuronal-firing properties.

The N-methyl-D-aspartate receptors (NMDARs) play a key role in synaptic plasticity, but it remains unclear whether the intrinsic-firing properties, another major determinant of the functional output of neurons, are regulated by activation of NMDARs. Here, we examine the effects of NMDAR activation on the intrinsic-firing properties of medium spiny neurons in nucleus accumbens in vitro. NMDAR activation by bath application of NMDA increased both the intrinsic excitability and the spike adaptation of these neurons. Furthermore, selective activation of NR2A-containing NMDARs mediated the enhancement of spike adaptation, whereas selective activation of NR2B-containing NMDARs increased the intrinsic excitability, suggesting that NR2A-containing and NR2B-containing NMDARs play different roles in mediating the intrinsic-firing properties of neurons.

Individual aortic baroreceptors are sensitive to different ranges of blood pressures

Many receptors, including thermal receptors and mechanical receptors, are only activated by stimuli within a clearly defined range of intensities. Differences in the receptive ranges enable individual receptors and their sensory centers to precisely detect the intensity of the stimulus and changes in intensity. Baroreceptors are the sensory terminals of the baroreflex. It is well understood that an increasing number of baroreceptors are recruited to produce afferent action potentials as the blood pressure increases, indicating that individual baroreceptors have different pressure thresholds. The present study revealed that individual baroreceptors could stop their afferent signals when the blood pressure exceeds a certain level, indicating that individual baroreceptors are sensitive to a specific range of blood pressure. The receptive ranges of individual baroreceptors differ in terms of the total range, the lower threshold, and the upper threshold. Of 85 baroreceptors examined in this study, the upper thresholds for about half were within the physiological blood pressure range. These results indicate that supraphysiological blood pressure is unlikely to be encoded by the recruitment of more baroreceptors. Instead, supraphysiological blood pressure levels might be signaled by an increase in the frequency of action potentials or by other mechanisms. In conclusion, our results indicate that rabbit baroreceptors are activated by blood pressure levels within specific receptive ranges. These findings should encourage further studies to examine the role of population coding of blood pressure by baroreceptors in the baroreflex.