Noise-induced burst and spike synchronizations in an inhibitory small-world network of subthreshold bursting neurons

We are interested in noise-induced firings of subthreshold neurons which may be used for encoding environmental stimuli. Noise-induced population synchronization was previously studied only for the case of global coupling, unlike the case of subthreshold spiking neurons. Hence, we investigate the effect of complex network architecture on noise-induced synchronization in an inhibitory population of subthreshold bursting Hindmarsh–Rose neurons. For modeling complex synaptic connectivity, we consider the Watts–Strogatz small-world network which interpolates between regular lattice and random network via rewiring, and investigate the effect of small-world connectivity on emergence of noise-induced population synchronization. Thus, noise-induced burst synchronization (synchrony on the slow bursting time scale) and spike synchronization (synchrony on the fast spike time scale) are found to appear in a synchronized region of the J–D plane (J: synaptic inhibition strength and D: noise intensity). As the rewiring probability p is decreased from 1 (random network) to 0 (regular lattice), the region of spike synchronization shrinks rapidly in the J–D plane, while the region of the burst synchronization decreases slowly. We separate the slow bursting and the fast spiking time scales via frequency filtering, and characterize the noise-induced burst and spike synchronizations by employing realistic order parameters and statistical-mechanical measures introduced in our recent work. Thus, the bursting and spiking thresholds for the burst and spike synchronization transitions are determined in terms of the bursting and spiking order parameters, respectively. Furthermore, we also measure the degrees of burst and spike synchronizations in terms of the statistical-mechanical bursting and spiking measures, respectively.     

Neural rate equations for bursting dynamics derived from conductance-based equations

A method of obtaining rate equations from conductance-based equations is developed and applied to fast-spiking and bursting neocortical neurons. It involves splitting systems of conductance-based equations into fast and slow subsystems, and averaging the effects of fast terms that drive the slowly varying quantities by showing that their average is closely proportional to the firing rate. The dependence of the firing rate on the injected current is then approximated in the analysis. The resulting behavior of the slow variables is then substituted back into the fast equations, with the further approximation of replacing the fast voltages in these terms by effective values. For bursting neurons the method yields two coupled limit-cycle oscillators: a self-exciting oscillator for the slow variables that commences limit-cycle oscillations at a critical current and modulates a fast spike-generating oscillator, thereby leading to slowly modulated bursts with a group of spikes in each burst. The dynamics of these coupled oscillators are then verified against those of the conductance-based equations. Finally, it is shown how to place the results in a form suitable for use in mean-field equations for neural population dynamics.     

Effects of Salicylic Acid and Its Salts on Electrical Activity of Neurons of <Emphasis Type="Italic">Helix albescens</Emphasis>

We studied changes in the parameters of electrical activity of identified neurons of the parietal ganglion, PPa1 and PPa2, and of non-identified cells of the visceral ganglion (VG) of the snail Helix albescens; these changes were caused by application of salicylic acid and its salts (cobalt and zinc salicylates, CS and ZS, respectively). The above substances began to modify significantly the functional state of the neurons under study when applied in concentrations of 10⁻⁴ to 10⁻³ M. Salicylic acid suppressed the activity of all studied neurons. Application of salicylic acid in the concentration of 10⁻³ M led to a decrease in the impulsation frequency of VG neurons by factors of 1.2 to 1.5 and to an increase in the duration of AP (on average, by 2.8 ± ± 0.6 msec). In PPa1 and PPa2 cells, we observed increases in both the AP duration (by 2.4 ± 0.8 and 3.6 ± ± 1.3 msec, respectively) and that of postactivation hyperpolarization (by 29.8 ± 11 0 and 39.6 ± 9.4 msec). In the concentration of 10⁻² M, salicylic acid completely but relatively reversibly suppressed the impulse activity of all the neurons under study, causing deep hyperpolarization of their membranes. Salts of this acid, CS and ZS, demonstrated significant modulatory effects on the activity of the studied neurons; these substances initiated or enhanced the grouping of APs in bursts and also increased the AP duration. Application of 10⁻³ M CS resulted in an increase in the AP duration by, on average, 2.75 ± 0.4 msec (only in the PPa2 neuron), whereas 10⁻³ M ZS exerted analogous effects on both above neurons (in PPa1, by 2.7 ± 0.4, while in PPa2, by 3.1 ± 0.6 msec). In the case where the tested salicylates were applied in the concentration of 10⁻² M, the AP duration increased in all the cells under study (on average, by 11.8 ± 2.46 msec in VG neurons, and by 7.0 ± ± 0.4 and 7.8 ± 1.2 msec in PPa1 and PPa2 cells, respectively). With application of CS, analogous values determined by application of ZS were 14.6 ± 4.6, 6.8 ± 0.54, and 9.0 ± 0.89 msec. We assume that the modulatory effects of salicylates are mediated by their influence on the intracellular system of cyclic nucleotides. Neirofiziologiya/Neurophysiology, Vol. 37, No. 2, pp. 142–150, March–April, 2005.     

Effect of a honey and arginine-glutamine-hydroxymethylbutyrate mixture on the healing of colon anastomosis in rats immunosuppressed with tacrolimus

ABSTRACT

We compared the effect of honey and a mixture of arginine-glutamine-hydroxymethylbutyrate (AGHMB) on healing of a descending colon anastomosis in rats that were immunosuppressed with tacrolimus (Tac). Sprague-Dawley rats were divided into four groups: untreated control, Tac, Tac + honey and Tac + AGHMB. Colon resection and anastomosis were performed on day 14 and re-laparotomy was performed on the day 21 of the study. Anastomotic bursting pressure, macroscopic adhesion score, weekly body weight changes, histopathological features and immunohistochemical staining of TGF-β1 were determined for all groups. We found no significant difference in anastomotic bursting pressure among the experimental groups. We found significant weekly increases in body weight for the Tac + honey group. We found no significant difference in the weekly body weight measurements for the Tac + AGHMB group. We found significant increases in TGF-β1 expression in the Tac + honey group compared to the control and Tac groups. No significant differences in inflammatory cell infiltration, fibroblast proliferation or collagen deposition were found between the Tac + honey and Tac + AGHMB groups; however, a significant difference in neovascularization between these groups was found. Neovascularization in the Tac + honey group was significantly greater than for the Tac + AGHMB group. We found that both honey and the AGHMB mixture were beneficial for anastomotic wound healing in rats that were immunosuppressed using Tac.     

峰峰间期逐渐增大的动力学机制

在3或4个轻度结扎受损的大鼠坐骨神经上加入5mmol／L EGTA的无钙灌流液的神经生理实验中,可以观察到一种在活动相峰峰间期逐渐增大的周期阵发放电现象。从非线性动力学角度分析该现象产生的动力学机制对于理解神经元复杂的放电行为具有重要意义。通过Hindmarsh-Rose神经元模型的分析,对该现象产生的一种可能的机制进行了揭示,即鞍结分岔和鞍点同宿分岔支配着这种阵发放电形式,而且后者对峰峰阃期逐渐的增大起着更重要的作用。     

Ghostbursting: A Novel Neuronal Burst Mechanism

Pyramidal cells in the electrosensory lateral line lobe (ELL) of weakly electric fish have been observed to produce high-frequency burst discharge with constant depolarizing current (Turner et al., 1994). We present a two-compartment model of an ELL pyramidal cell that produces burst discharges similar to those seen in experiments. The burst mechanism involves a slowly changing interaction between the somatic and dendritic action potentials. Burst termination occurs when the trajectory of the system is reinjected in phase space near the ghost of a saddle-node bifurcation of fixed points. The burst trajectory reinjection is studied using quasi-static bifurcation theory, that shows a period doubling transition in the fast subsystem as the cause of burst termination. As the applied depolarization is increased, the model exhibits first resting, then tonic firing, and finally chaotic bursting behavior, in contrast with many other burst models. The transition between tonic firing and burst firing is due to a saddle-node bifurcation of limit cycles. Analysis of this bifurcation shows that the route to chaos in these neurons is type I intermittency, and we present experimental analysis of ELL pyramidal cell burst trains that support this model prediction. By varying parameters in a way that changes the positions of both saddle-node bifurcations in parameter space, we produce a wide gallery of burst patterns, which span a significant range of burst time scales.     

State-Dependent Effects of Na Channel Noise on Neuronal Burst Generation

We explore the effects of stochastic sodium (Na) channel activation on the variability and dynamics of spiking and bursting in a model neuron. The complete model segregates Hodgin-Huxley-type currents into two compartments, and undergoes applied current-dependent bifurcations between regimes of periodic bursting, chaotic bursting, and tonic spiking. Noise is added to simulate variable, finite sizes of the population of Na channels in the fast spiking compartment.During tonic firing, Na channel noise causes variability in interspike intervals (ISIs). The variance, as well as the sensitivity to noise, depend on the model's biophysical complexity. They are smallest in an isolated spiking compartment; increase significantly upon coupling to a passive compartment; and increase again when the second compartment also includes slow-acting currents. In this full model, sufficient noise can convert tonic firing into bursting.During bursting, the actions of Na channel noise are state-dependent. The higher the noise level, the greater the jitter in spike timing within bursts. The noise makes the burst durations of periodic regimes variable, while decreasing burst length duration and variance in a chaotic regime. Na channel noise blurs the sharp transitions of spike time and burst length seen at the bifurcations of the noise-free model. Close to such a bifurcation, the burst behaviors of previously periodic and chaotic regimes become essentially indistinguishable.We discuss biophysical mechanisms, dynamical interpretations and physiological implications. We suggest that noise associated with finite populations of Na channels could evoke very different effects on the intrinsic variability of spiking and bursting discharges, depending on a biological neuron's complexity and applied current-dependent state. We find that simulated channel noise in the model neuron qualitatively replicates the observed variability in burst length and interburst interval in an isolated biological bursting neuron.