Detection of deterministic behavior within the tissue injury-induced persistent firing of nociceptive neurons in the dorsal horn of the rat spinal cord

To unravel the temporal features of the peripheral tissue injury induced persistent nociceptive discharge, single wide dynamic range (WDR) unit activity was recorded extracellularly in lumbar dorsal horn of anesthetized rats and interspike interval (ISI) series were obtained. Subcutaneous (s.c.) bee venom (BV) injection induced persistent discharge of spinal WDR neurons and has been well established to be a good model in evaluation of tissue injury induced pain. By applying a more novel approach, i.e., the unstable periodic orbit (UPO) identification method, we detected a family of significant separate UPOs (period-1, 2 and 3 orbits) within the ISI series of BV-induced nociceptive discharge, but not spontaneous background activity of spinal WDR neuron. Furthermore, temporally dynamic changes of UPOs at lower period-1, 2 and 3 for 4 successive time segments within 1 h time course of WDR unit firing showed temporally dynamic changes, i.e., new orbits with longer ISIs emerged and those with shorter ISIs vanished with time change. By using this method we suggest that BV-induced nociceptive discharge of spinal WDR neuron be a kind of deterministic activity and various UPOs may play some role in temporal coding of sensory information.     

健康人心率变异性中的不稳定周期轨道

为刻划心脏节律存在的确定性动力学特征,运用不稳定周期轨道分析方法对健康青年人的RR间期时间序列数据进行分析。研究结果揭示健康人心脏节律中存在显著的不稳定周期轨道及不稳定周期轨道分级（周期1、周期2,周期3,周期4）现象,表明健康青年人心脏节律的动力学特性中包含着显著的确定性行为。通过跟踪不周期轨道随时间的演变,迹表明心脏节律的变化中存在着因有的非平稳性。     

Lidocaine suppresses subthreshold oscillations by inhibiting persistent Na(+) current in injured dorsal root ganglion neurons

The aim of this study was to determine the effect and mechanism of low concentration of lidocaine on subthreshold membrane potential oscillations (SMPO) and burst discharges in chronically compressed dorsal root ganglion (DRG) neurons. DRG neurons were isolated by enzymatic dissociation method. SMPO, burst discharges and single spike were elicited by whole cell patch-clamp technique in current clamp mode. Persistent Na(+) current (I(NaP)) and transient Na(+) current (I(NaT)) were elicited in voltage clamp mode. The results showed that SMPO was suppressed and burst discharges were eliminated by tetrodotoxin (TTX, 0.2 micromol/l) in current clamp mode, I(NaP) was blocked by 0.2 micromol/l TTX in voltage clamp mode. SMPO, burst discharges and I(NaP) were also suppressed by low concentration of lidocaine (10 micromol/l) respectively. However, single spike and I(NaT) could only be blocked by high concentration of lidocaine (5 mmol/l). From these results, it is suggested that I(NaP) mediates the generation of SMPO in injured DRG neurons. Low concentration of lidocaine (10 micromol/l) suppresses SMPO by selectively inhibiting I(NaP), but not I(NaT), in chronically compressed DRG neurons.     

Specific subunits of voltage-gated sodium channel underlying the subthreshold membrane potential oscillations: Potential therapeutic targets for neuropathic pain

The treatment of neuropathic pain remains a major challenge to pain clinicians. Certain nociceptive and non-nociceptive dorsal root ganglion (DRG) neurons may develop abnormal spontaneous activities following peripheral nerve injury, which is believed to be a major contributor to chronic pain. Subthreshold membrane potential oscillation (SMPO) observed in injured DRG neurons was reported to be involved in the generation of abnormal spontaneous activity. Tetrodotoxin-sensitive sodium (Na⁺) channels were testified to be involved in the generation of SMPO, but their specific subunits have not been clarified. We hypothesize that the subunits of voltage-gated sodium channel, Na_v1.3 and Na_v1.6, are involved in the generation of SMPO. An attempt to test this hypothesis may lead to a new therapeutic strategy for neuropathic pain.     

混沌放电的可兴奋性细胞对外界刺激反应敏感的动力学机制

在大鼠损伤背根节神经元受到去甲肾上腺(NE)、四乙基胺(TEA)和高浓度钙等剌激的实验中,观察到非周期放电的神经元明显地比周期放电的神经元对外界刺激的反应敏感程度高。现有的结果表明许多非周期放电的神经元实际上表现为确定性的混沌运动,比如混沌尖峰放电、混沌簇放电以及整数倍放电等。以修正的胰腺B细胞Chay模型为例,通过对其分岔结构的分析和对构成混沌吸引子的基本骨架的不稳定周期轨道的计算,揭示了分岔、激变和混沌运动对参数敏感依赖性是该现象产生的动力学机制。同时指出以往使用平均发放率来刻划可兴奋性细胞放电活动存在的缺陷,提出了一种新的利用周期轨道信息的刻划方法。     

神经元的确定性与随机性整数倍放电

在大鼠损伤背根节神经元的自发放电中发现了整数倍放电, 为了阐明这种放电所产生的原因, 首先研究神经元模型中确定性混沌所引起的整数倍放电与噪声所诱发的整数倍放电的峰峰间期（ＩＳＩ） 序列,通过分析得到前者的ＩＳＩ序列是非线性可预报的,具有确定的非线性特性,但由噪声所诱发的整数倍放电的ＩＳＩ序列是不可预报的, 这表明这两种机制所产生的整数倍放电具有不同的特点,存在着定性的差别,并且混沌运动所产生的整数倍放电是由混沌中各阶不稳定周期轨道决定的。从这种差别出发,分析了实验中整数倍放电的ＩＳＩ 序列,得到该ＩＳＩ 序列是可非线性预报的,这表明大鼠损伤背根节神经元自发放电中的整数倍放电更可能是由确定性机制所产生的     

Dynamics of period-doubling bifurcation to chaos in the spontaneous neural firing patterns

Period-doubling bifurcation to chaos were discovered in spontaneous firings of Onchidium pacemaker neurons. In this paper, we provide three cases of bifurcation processes related to period-doubling bifurcation cascades to chaos observed in the spontaneous firing patterns recorded from an injured site of rat sciatic nerve as a pacemaker. Period-doubling bifurcation cascades to period-4 (π(2,2)) firstly, and then to chaos, at last to a periodicity, which can be period-5, period-4 (π(4)) and period-3, respectively, in different pacemakers. The three bifurcation processes are labeled as case I, II and III, respectively, manifesting procedures different to those of period-adding bifurcation. Higher-dimensional unstable periodic orbits (UPOs) can be detected in the chaos, built close relationships to the periodic firing patterns. Case III bifurcation process is similar to that discovered in the Onchidium pacemaker neurons and simulated in theoretical model-Chay model. The extra-large Feigenbaum constant manifesting in the period-doubling bifurcation process, induced by quasi-discontinuous characteristics exhibited in the first return maps of both ISI series and slow variable of Chay model, shows that higher-dimensional periodic behaviors appeared difficult within the period-doubling bifurcation cascades. The results not only provide examples of period-doubling bifurcation to chaos and chaos with higher-dimensional UPOs, but also reveal the dynamical features of the period-doubling bifurcation cascades to chaos.     

Periodic orbits: a new language for neuronal dynamics.

A new nonlinear dynamical analysis is applied to complex behavior from neuronal systems. The conceptual foundation of this analysis is the abstraction of observed neuronal activities into a dynamical landscape characterized by a hierarchy of "unstable periodic orbits" (UPOs). UPOs are rigorously identified in data sets representative of three different levels of organization in mammalian brain. An analysis based on UPOs affords a novel alternative method of decoding, predicting, and controlling these neuronal systems.     

Possible mechanism of bursting suppression in nociceptive neurons

The use of the mathematical model of rat nociceptive neuron membrane allowed us to predict a new mechanism of suppression of ectopic bursting discharges, which arise in neurons of dorsal root ganglia and are one of the causes of neuropathic pain. The treatment with comenic acid leads to switching off the ectopic bursting discharges due to a decrease in the effective charge transferring via the activation gating structure of the slow sodium channels (Na _V1.8a). Comenic acid is a drug substance of a new non-opioid analgesic [1] Thus, this analgesic not only reduces the frequency of rhythmic discharges of nociceptive neuron membrane [2] but also it suppresses its ectopic bursting discharges.     

A tale of two cycles – distinguishing quasi-cycles and limit cycles in finite predator–prey populations

Periodic predator – prey dynamics in constant environments are usually taken as indicative of deterministic limit cycles. It is known, however, that demographic stochasticity in finite populations can also give rise to regular population cycles, even when the corresponding deterministic models predict a stable equilibrium. Specifically, such quasi-cycles are expected in stochastic versions of deterministic models exhibiting equilibrium dynamics with weakly damped oscillations. The existence of quasi-cycles substantially expands the scope for natural patterns of periodic population oscillations caused by ecological interactions, thereby complicating the conclusive interpretation of such patterns. Here we show how to distinguish between quasi-cycles and noisy limit cycles based on observing changing population sizes in predator – prey populations. We start by confirming that both types of cycle can occur in the individual-based version of a widely used class of deterministic predator – prey model. We then show that it is feasible and straightforward to accurately distinguish between the two types of cycle through the combined analysis of autocorrelations and marginal distributions of population sizes. Finally, by confronting these results with real ecological time series, we demonstrate that by using our methods even short and imperfect time series allow quasi-cycles and limit cycles to be distinguished reliably.     

Actions of calcitonin gene-related peptide on rat sensory ganglion neurones

The membrane actions of calcitonin gene-related peptide (CGRP) and the effect of CGRP on the Ca-dependent action potential of rat dorsal root ganglion (DRG) neurons have been studied by means of an intracellular recording technique in isolated DRG of 2-3-week-old rats in vitro. Bath application of CGRP (10(-8)-10(-6) M for 1-5 min) elicited a slow reversible hyperpolarization and this hyperpolarizing effect was still observed in the medium containing TTX and TEA. However, about half of the large cells, classified by duration of action potential, were depolarized by CGRP. These membrane effects of CGRP were associated with an increase in membrane input resistance (about 20%). In addition, CGRP increased the duration of Ca-dependent action potentials. Our results are consistent with the role of CGRP as an excitatory neurotransmitter or neuromodulator in DRG-spinal cord.     

Modulation of neuronal excitability by intracellular calcium buffering: from spiking to bursting

We have investigated the detailed regulation of neuronal firing pattern by the cytosolic calcium buffering capacity using a combination of mathematical modeling and patch-clamp recording in acute slice. Theoretical results show that a high calcium buffer concentration alters the characteristic regular firing of cerebellar granule cells and that a transition to various modes of oscillations occurs, including bursting. Using bifurcation analysis, we show that this transition from spiking to bursting is a consequence of the major slowdown of calcium dynamics. Patch-clamp recordings on cerebellar granule cells loaded with a high concentration of the fast calcium buffer BAPTA (15 mM) reveal dramatic alterations in their excitability as compared to cells loaded with 0.15 mM BAPTA. In high calcium buffering conditions, granule cells exhibit all bursting behaviors predicted by the model whereas bursting is never observed in low buffering. These results suggest that cytosolic calcium buffering capacity can tightly modulate neuronal firing patterns leading to generation of complex patterns and therefore that calcium-binding proteins may play a critical role in the non-synaptic plasticity and information processing in the central nervous system.     

Electrical connection between two bursting neurons inHelix pomatia

In some preparations of the CNS ofHelix pomatia, two neurons with bursting activity may be present in the right parietal ganglion, where usually there is only one bursting neuron RPal. If electrical activity of these neurons is recorded simultaneously, fluctuations of membrane potential are almost completely synchronized. Artificial depolarization and hyperpolarization of the membrane of one neuron caused depolarization or hyperpolarization of the other neuron. During long-term recording of the activity of both neurons synchronous modulation of their bursting activity was observed. Modulating factor (a peptide fraction obtained from the water-soluble part of snail brain homogenate) led to potentiation of the bursting activity of both neurons. It is concluded from the results of these experiments that two bursting RPal neurons, connected electrically with one another, may exist in the snail nervous system. In cases when the parameters of pacemaker activity of these two neurons are closely similar, electrical connection guarantees synchronization of their bursting activity and ensures a common frequency of changes in their membrane potential.     

离体运动神经元对腹外侧索刺激的突触反应特征

应用新片大鼠脊髓薄片运动神经元细胞内记录技术,对电刺激腹外侧索诱发的突触反应进行了电生理特性分析。结果在２８个测试的ＭＮ中,２２人有兴奋性突触后电位反应,其中２个跟随在抑制性突触反应这后,６个还对单或串刺激产生慢ＥＰＳＰ反应;ＶＬＦ－ＥＰＳＰ的潜伏期频数分布呈峰坡性偏态;同－ＭＮ的ＶＬＦ－ＥＰＳＰ与腹根ＥＰＳＰ间有典型的空间总和。     

Background sodium current stabilizes bursting in respiratory pacemaker neurons

Endogenous pacemaker properties have been proposed to generate rhythmic activity underlying many behaviors including respiration. For pacemakers to generate regenerative bursting, background currents maintain their membrane potential (Vm) within a range where bi-stable properties are expressed, thereby stabilizing rhythmogenesis. We previously found that the baseline Vm of respiratory pacemakers is stabilized against hyperpolarizing shifts in their Vm. In response to prolonged hyperpolarizing current injection synaptically isolated respiratory pacemakers steadily depolarize and resume bursting, suggesting a stabilizing background current is involved. What is the ionic basis of this background current in respiratory pacemakers? Here we demonstrate that in low-[Na(+)](o) ACSF, synaptically isolated respiratory pacemakers hyperpolarized and remained outside the bursting window, but could burst upon depolarizing current injection. These data suggest that pacemakers possess a background sodium current that is necessary to bring their Vm into a bursting range. Low-[Na(+)](o) ACSF also abolished the depolarizing shift evoked during prolonged hyperpolarizing current injection, and bursting did not resume. This depolarizing shift persisted in the presence of I(h)-current blockers, but was abolished in tetrodotoxin. Although, under control conditions, the Vm of synaptically isolated respiratory pacemaker neurons was not significantly affected when [K(+)](o) was changed from 3 to 8 mM, the Vm is altered when [K(+)](o) was raised in low-[Na(+)](o) ACSF. Thus, current-clamp studies suggest that respiratory pacemaker neurons possess a background sodium current that maintains their membrane potential within a range where they express bursting, thereby stabilizing rhythmogenesis.     

大鼠视上核神经元自发放电节律的确定性机制

利用非线性动力学的方法,在多种生物数据中找到了确定性机制。大鼠下丘脑视上核（ｓｕｐｒａｏｐｔｉｃ ｎｕｃｌｅｕｓ,ＳＯＮ）神经元自发产生不规则的放电。为了研究这些不规则放电是否含有确定性机制,用电流钳对大鼠ＳＯＮ神经元进行全细胞纪录,取动作电位峰峰间期序列（ｉｎｔｅｒｓｐｉｋｅ ｉｎｔｅｒｖａｌ,ＩＳＩ）作为研究对象。采用一种新的检测时间序列非稳定周期轨道的方法分析ＩＳＩ序列,发现ＩＳＩ含有非稳定     

大鼠视上核神经元自发放电节律的确定性机制

利用非线性动力学的方法 ,在多种生物数据中找到了确定性机制。大鼠下丘脑视上核(supraopticnucleus,SON)神经元自发产生不规则的放电。为了研究这些不规则放电是否含有确定性机制 ,用电流钳对大鼠SON神经元进行全细胞纪录,取动作电位峰峰间期序列(interspikeinterval,ISI)作为研究对象。采用一种新的检测时间序列非稳定周期轨道的方法分析ISI序列 ,发现ISI含有非稳定周期轨道族 ,即周期1 ,周期2 ,和周期3存在。结果表明 ,SON神经元的自发放电序列存在确定性的动力学机制。     

Single transient K channels in mammalian sensory neurons.

A single-channel recording of the transient outward current (A-current) was obtained from dorsal root ganglion cells in culture using patch-clamp techniques. Depolarization of the membrane patch elicited pulse like current of a uniform amplitude in an outward direction, of which the unitary conductance was 20 pS. Alteration of extracellular ionic compositions indicated that the charge carriers were K ions. A systematic study was made on the voltage-dependence of the ensemble average current; (a) the activation started at a potential around -60 mV; (b) the time course of the activation was relatively rapid; (c) the channel was completely inactivated at a potential positive to -40 mV. Two time constants (tau f = 100 ms and tau s = 4,000 ms) were detected in the decay of the current indicating that the channels had two different states of inactivation. A convulsant, 4-aminopyridine (4-AP), acted on the channel only from the intracellular side of the membrane. 4-AP (5 mM) reduced not only mean open time (by 50%) but also the single-channel conductance (by 20%). The properties of the channel were independent of Ca ions in the intracellular space.     

血管升压素对大鼠背根神经节神经元膜的作用

为研究血管升压素(arginine vasopressin,AVP)对大鼠背根神经节(dorsal root ganglion,DRG)神经元的作用及其机制,用细胞内微电极记录技术记录离体灌流DRG神经元的膜电位。结果如下:(1)在受检的120个细胞中,大多数(81.67％)在滴加AVP后产生明显的超极化反应。(2)滴加AVP(10μmol/L)后膜电导增加约19.34％(P<0.05)。(3)灌流平衡液巾的NaCl以氯化胆碱(CH-Cl)置代和用Cd2+阻断Ca2+通道后,AVP引起超极化反应的幅值均无明显变化(P>0.05),而加入K+通道阻断剂四乙铵(TEA)后,AVP引起的超极化反应幅值明显减小(P<0.05)。(4)AVP引起的超极化反应可被AVP V.受体拈抗剂阻断。结果捉示,AVP可使DRG大多数神经元膜产生超极化,DRG神经元膜上存在AVP V,受体,且AVP引起的超极化反应是通过神经元膜上AVP V.受体介导的K+外流所致.AVP可能参与了初级感觉信息传入的调制。