A model of a thalamic neuron

We modify our recent three equilibrium-point model of neuronal bursting by a means of a small deformation of the nullclines in the x-y phase plane to give a model that can have as many as five equilibrium points. In this model the middle stable equilibrium point (e.p.) is separated from the outer stable and unstable e.ps by two saddle points. If the system is started at rest at the middle stable e.p. it has the following complex properties: A short suprathreshold current pulse switches the model from a silent state to a bursting state, or to give a single burst, depending on the choice of parameters. A subthreshold depolarizing current step gives a passive response at rest, but if the model is either constantly hyperpolarized or constantly depolarized, then the same current step gives different active responses. At a hyperpolarized level this consists of a burst response that shows refractoriness. At a depolarized level it consists of tonic firing with a linear frequency--current relationship. Hyperpolarization from rest is followed by post-inhibitory rebound. The model responds in a unique and characteristic way to an applied current ramp. These properties are very similar to those that have been recently recorded intracellularly from neurons in the mammalian thalamus. In the x-y phase plane our models of the repetitively firing neuron, the bursting neuron and the thalamic neuron form a progression of models in which the y nullcline in the subthreshold region is deformed once to give the burst neuron model, and a second time to give the thalamic neuron model. Each deformation can be interpreted as corresponding to the inclusion of a slow inward current in the model. As these currents are included so the associated firing properties increase in complexity.     

Analysis of bursting in a thalamic neuron model

We extend a quantitative model for low-voltage, slow-wave excitability based on the T-type calcium current (Wang et al. 1991) by juxtaposing it with a Hodgkin-Huxley-like model for fast sodium spiking in the high voltage regime to account for the distinct firing modes of thalamic neurons. We employ bifurcation analysis to illustrate the stimulus-response behavior of the full model under both voltage regimes. The model neuron shows continuous sodium spiking when depolarized sufficiently from rest. Depending on the parameters of calcium current inactivation, there are two types of low-voltage responses to a hyperpolarizing current step: a single rebound low threshold spike (LTS) upon release of the step and periodic LTSs. Bursting is seen as sodium spikes ride the LTS crest. In both cases, we analyze the LTS burst response by projecting its trajectory into a fast/slow phase plane. We also use phase plane methods to show that a potassium A-current shifts the threshold for sodium spikes, reducing the number of fast sodium spikes in an LTS burst. It can also annihilate periodic bursting. We extend the previous work of Rose and Hindmarsh (1989a–c) for a thalamic neuron and propose a simpler model for thalamic activity. We consider burst modulation by using a neuromodulator-dependent potassium leakage conductance as a control parameter. These results correspond with experiments showing that the application of certain neurotransmitters can switch firing modes. Received: 18 July 1993/Accepted in revised form: 22 January 1994     

Microwave-induced and pharmacological suppression of somatic pain under conditions of the formalin test in mice

We examined pain-related behavioral reactions and non-pain behavioral manifestations in mice under conditions of the formalin test. Levels of analgesia induced by i.p. injections of analgin, microwave irradiation of an antinociceptive acupuncture point (AP), E-36, or combined application of the above factors were measured. The duration of the pain behavioral reaction (licking of the injured limb) decreased due to irradiation of the AP with microwaves and to injection of 8.3 mg/kg analgin by 24.3% and 53.8%, on average, respectively. Combination of injection of analgin in a smaller dose (4.2 mg/kg) and microwave irradiation of the AP suppressed manifestations of the pain behavioral reaction by 43.4%. Thus, combination of pharmacologically induced analgesia with the action of microwaves on the antinociceptive AP allows one to significantly decrease the doses of analgesic preparations necessary to provide a full-level analgesic effect; in such a way, side effects of the respective drugs can be weakened. Neirofiziologiya/Neurophysiology, Vol. 38, No. 1, pp. 46–51, January–February, 2006.     

Mechanism of long lasting synaptic inhibition of a silent neuron of Helix pomatia

• 1.1. Long lasting synaptic inhibitions (LLI) were recorded in the silent cells LPL1 and RPL1 of Helix pomatia.
• 2.2. During LLI the excitability of the cell was strongly reduced.
• 3.3. The membrane conductance changes during LLI were characterized using the voltage-clamp technique.
• 4.4. LLI in the silent cell LPL1 is mediated by a synaptically induced inhibition of the voltage-dependent inward Ca²⁺ -current.

     

Unit responses of the thalamic and ventral anterior thalamic nuclei to electrical stimulation of thalamic relay nuclei in cats

Responses of 92 neurons of the reticular (R) and 105 neurons of the ventral anterior (VA) thalamic nuclei to stimulation of the ventrobasal complex (VB) and the lateral (GL) and medial (GM) geniculate bodies were investigated in cats immobilized with D-tobocurarine. Altogether 72.2% of R neurons and 76.2% of VA neurons responded to stimulation of VB whereas only 15.0% of R neurons and 27.1% of VA neurons responded to stimulation of GM and 10.2% of R neurons and 19.6% of VA neurons responded to stimulation of GL. The response of the R and VA neurons to stimulation of the relay nuclei as a rule was expressed as excitation. A primary inhibitory response was observed for only two R and three VA neurons. Two types of excitable neurons were distinguished: The first respond to afferent stimulation by a discharge consisting of 5–15 spikes with a frequency of 250–300/sec; the second respond by single action potentials. Neurons of the first type closely resemble inhibitory interneurons in the character of the response. Antidromic responses were recorded from 2.2% of R neurons and 7.8% of VA neurons during stimulation of the relay nuclei. Among the R and VA neurons there are some which respond to stimulation not only of one, but of two or even three relay nuclei. If stimulation of one relay nucleus is accompanied by a response of a R or VA neuron, preceding stimulation of another nucleus leads to inhibition of the response to the testing stimulus if the interval between conditioning and testing stimuli is less than 30–50 msec.A. A. Bogomolets Institute of Physiology, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Neirofiziologiya, Vol. 8, No. 6, pp. 597–605, November–December, 1976.     

Mathematical properties of responses of a neuron model

Recently, Nagumo and Sato proposed a mathematical neuron model in the form of a nonlinear difference equation and investigated its response characteristic. The result showed that the input-output relationship of the neuron model is quite complicated and takes the form of an extended Cantor's function. It also explained the unusual and unsuspected phenomenon found by Harmon in experimental studies with his transistor neuron model. — In this paper, a fraction representation of a sequence of pulses is proposed. A mathematical treatment of the same neuron model based on the representation gives the same result as in the previous paper. Moreover, many mathematical properties, including the one where the ratio of the number of 1's contained in a cycle of a sequence to the length of the cycle gives any rational number between 0 and 1, were obtained by investigating sequences generated by the model.     

NOS抑制剂对甲醛炎性痛诱导的大鼠痛反应及脊髓神经元凋亡的影响

目的：观察甲醛炎性痛是否可诱导脊髓神经元凋亡以及一氧化氮（NO）对甲醛炎性痛诱导的大鼠痛反应以及脊髓神经元凋亡的影响。方法：采用行为学方法观察大鼠自发痛反应,流式细胞术检测脊髓神经元凋亡率。结果：与正常大鼠比较,甲醛炎性痛可诱导大鼠脊髓神经元凋亡率明显增加,于注射甲醛后3d时最为明显。预先鞘内注射NOS抑制剂L-NAME可剂量依赖性抑制足底注射甲醛诱导的大鼠第一相和第二相痛反应,并可剂量依赖性抑制足底注射甲醛诱导的脊髓神经元凋亡过程;正常大鼠鞘内注射L-Arg也可诱发出伤害性反应和脊髓神经元凋亡。结论：甲醛炎性痛可诱导脊髓神经元发生凋亡,于注射甲醛后3d神经元凋亡最为明显;炎性痛诱导的NO产生增多促进了脊髓伤害性信息传递过程,并在炎性痛诱导的脊髓神经元凋亡过程中发挥促进作用。     

On periodic responses of a mathematical neuron model

The periodic responses of a mathematical neuron model, when periodically varying input stimuli are applied to the model, are investigated. An explicit representation of periodic responses is obtained. It is shown that a periodic response as a 0–1 string is a uniform string. That is, the 1's of the 0–1 string are distributed uniformly in the string.     

Spatiotemporal dynamics of cortical sensorimotor integration in behaving mice

Tactile information is actively acquired and processed in the brain through concerted interactions between movement and sensation. Somatosensory input is often the result of self-generated movement during the active touch of objects, and conversely, sensory information is used to refine motor control. There must therefore be important interactions between sensory and motor pathways, which we chose to investigate in the mouse whisker sensorimotor system. Voltage-sensitive dye was applied to the neocortex of mice to directly image the membrane potential dynamics of sensorimotor cortex with subcolumnar spatial resolution and millisecond temporal precision. Single brief whisker deflections evoked highly distributed depolarizing cortical sensory responses, which began in the primary somatosensory barrel cortex and subsequently excited the whisker motor cortex. The spread of sensory information to motor cortex was dynamically regulated by behavior and correlated with the generation of sensory-evoked whisker movement. Sensory processing in motor cortex may therefore contribute significantly to active tactile sensory perception.     

The assembly of ionic currents in a thalamic neuron. III. The seven-dimensional model

We replace our earlier three-dimensional ha-model of a thalamic neuron (Rose & Hindmarsh, Proc. R. Soc. Lond. B 237, 289-312 (1989b)) by a seven-dimensional ha-model. The stability and state diagrams for this seven-dimensional model are shown to be similar to those of the three-dimensional system with which it is compared. Two examples that illustrate how the seven-dimensional model can be related to experimental recordings are then discussed in detail. In each case we show the state and stability diagrams and the time courses of the different ionic currents during the burst response. We discuss how the various components of the state diagram could be determined experimentally. These experiments are illustrated by using our model to simulate the results of actual experiments. Finally the state and stability diagrams are transferred to a current-voltage diagram. This shows the advantage of the state diagram compared with the current-voltage diagram for representing the dynamics of the firing of a thalamic neuron.     

The assembly of ionic currents in a thalamic neuron. I. The three-dimensional model

We have previously discussed qualitative models for bursting and thalamic neurons that were obtained by modifying a simple two-dimensional model for repetitive firing. In this paper we report the results of making a similar sequence of modifications to a more elaborate six-dimensional model of repetitive firing which is based on the Hodgkin-Huxley equations. To do this we first reduce the six-dimensional model to a two-dimensional model that resembles our original two-dimensional qualitative model. This is achieved by defining a new variable, which we call q. We then add a subthreshold inward current and a subthreshold outward current having a variable, z, that changes slowly. This gives a three-dimensional (v,q,z) model of the Hodgkin-Huxley type, which we refer to as the z-model. Depending on the choice of parameter values this model resembles our previous models of bursting and thalamic neurons. At each stage in the development of these models we return to the corresponding seven-dimensional model to confirm that we can obtain similar solutions by using the complete system of equations. The analysis of the three-dimensional model involves a state diagram and a stability diagram. The state diagram shows the projection of the phase path from v,q,z space into the v,z plane, together with the projections of the curves z = 0 and v = q = 0. The stability of the points on the curve v = q = 0, which we call the v, q nullcurve, is determined by the stability diagram. Taken together the state and stability diagrams show how to assemble the ionic currents to produce a given firing pattern.     

Effect of electrical stimulation of the inferior central raphe nucleus on spontaneous and induced thalamic neuron activity in awake cats

Using microelectrode technique in chronic experiments it was shown that electrical stimulation of the inferior raphe nucleus inhibited spontaneous activity of the thalamic neurons and that evoked by stimulation of radial nerves. Changes in the activity of the same neurons were absent in case of stimulation of the bulbar reticular formation.     

Timing of secondary vestibular neuron responses to a range of rotational head movements

Secondary vestibular neurons exhibit a wide variety of responses to a head movement, with the response of each secondary neuron depending upon the particular primary afferents converging onto it. A single head movement is thereby registered in a distributed manner. This paper focuses on implications of afferent convergence to the relative timing of secondary neuron response modulation during rotational movements about a combination of horizontal axes. In particular, the neurons of interest are those that receive input from afferents innervating the vertical semicircular canals, and the movements of interest are those that have a sinusoidal component about one vertical canal axis and a sinusoidal component about another, approximately orthogonal, vertical canal axis. Under these conditions, the present research shows that it is possible for two or more secondary neurons to have a different relative timing of response (i.e., different relative phase of the periodic modulation in firing rate) for different head movements, and for the neurons to switch their order of response for different movements. For particular head movements, those same neurons will respond in phase. From the point of view of the nervous system, the relative timing of neuron responses may tell which movement is taking place, but with certain restrictions as discussed in the present paper. Shown here is that, among those head movements for which the two components of rotation may be at any phase relative to one another and have any relative amplitude, an in-phase response of just two neurons cannot identify a single motion. Two neurons that respond in phase for one motion must respond in phase for an entire range of motions; all motions in that range are thus response-equivalent, in the sense that the pair of neurons cannot distinguish between the two motions. On the other hand, an in-phase response of three neurons can identify a single motion, for certain patterns of primary afferent convergence. Received: 16 December 1996 / Accepted in revised form: 3 April 1998     

Macrophages behaving badly: infected cells and subversion of immune responses to Theileria annulata

The protozoan parasite Theileria annulata is the causative agent of the tick-borne disease tropical theileriosis, responsible for morbidity and mortality of cattle in many developing countries. Here, John Campbell and Roger Spooner discuss how the parasite might evade immune destruction during an acute primary infection. Theileria annulata macroschizont-infected macrophages act as over-efficient antigen-presenting cells within the infected draining lymph node. Infected cells activate CD4+ and CD8+ T cells abnormally, giving rise to a cascade of cytokine production. This altered immune response does not reject the parasitized cells, and might actively participate in the growth of the developing parasite.     

Spinal NTS1 receptors regulate nociceptive signaling in a rat formalin tonic pain model

Central administration of the neuropeptide neurotensin (NT) was shown to induce antinociceptive responses both spinally and supraspinally. Although NTS2 receptors play an important role in modulating the activity of spinal neurons, we have recently implicated NTS1 receptors in NT's analgesic effects in acute spinal pain paradigms. The current experiments were thus designed to examine the antinociceptive effects of intrathecal administration of NTS1 agonists in formalin-induced tonic pain in rats. We first established, using immunoblotting and immunohistochemical approaches, that NTS1 receptors were present in small- and medium-sized dorsal root ganglion cells and localized in the superficial layers of the dorsal horn of the spinal cord. We then examined the effects of intrathecal injection of NT (1–15 μg/kg) or NTS1 preferring agonists on the nocifensive response to intraplantar formalin. Both NTS1-agonists, PD149163 (10–120 μg/kg) and NT69L (1–100 μg/kg), dose-dependently attenuated the formalin-induced behaviors. Accordingly, NTS1 agonists markedly suppressed pain-evoked c- fos expression in the superficial, nucleus proprius and neck regions of the spinal dorsal horn. The concomitant administration of PD149163 with the NTS1 antagonist SR48692 (3 μg/kg) significantly reversed PD149163-induced antinociception, confirming the implication of NTS1 in tonic pain. In contrast, NT69L's analgesic effects were partly abolished by co-administration of SR48692, indicating that NT69L-induced effects may also be exerted through interaction with NTS2. These results demonstrate that NTS1 receptors play a key role in the mediation of the analgesic effects of NT in persistent pain and suggest that NTS1-selective agonists may represent a new line of analgesic compounds.     

Naloxone reversal of morphine analgesia but failure to alter reactivity to pain in the formalin test.

Rats treated with naloxone in doses sufficient (10 mg/kg) to completely antagonize morphine analgesia showed no decrease in their thresholds of reactivity to formalin-induced chronic pain. These findings fail to support the hypothesis that tonic release of endogenous opioids acting at naloxone-sensitive receptors decreases sensitivity or reactivity to pain stimuli.     

The assembly of ionic currents in a thalamic neuron. II. The stability and state diagrams

In the previous model of a thalamic neuron (R.M. Rose & J.L. Hindmarsh, Proc. R. Soc. Lond. B237, 267-288 (1989], which we referred to as the z-model, the burst response was terminated by the slow activation of a subthreshold outward current. In this paper we show that similar results can be obtained if the burst response is terminated by slow inactivation of the subthreshold inward current, Isa. We illustrate the use of this new model, which we refer to as the ha-model, by using it to explain the response of a thalamic neuron to a double ramp current. The main aim of the paper is to show how the stability and state diagrams introduced previously can be used to explain various types of firing pattern of thalamic and other neurons. We show that increasing the threshold for the fast action potentials leads to low threshold spikes of increased amplitude. Also, addition of a second subthreshold inward current adds a new stability region, which enables us to explain the origin of plateau potentials. In addition, various types of subthreshold oscillation are produced by relocating a previously stable equilibrium point in an unstable region. Finally, we predict a sequence of responses to current steps from different levels of background current that extends the burst, rest, tonic sequence of thalamic neurons. The stability and state diagrams therefore provide us with a useful way of explaining further properties of thalamic neurons and appear to have further applications to other mammalian neurons.