Further contributions to a probabilistic interpretation of the mathematical biophysics of the central nervous system

Following a previous paper, equations are derived for the most probable time of firing of an efferent neuron in terms of the intensityE of excitation of the afferent pathway, whenE is either constant or any given function of time. The equations are not differential equations, but in integral form. It is suggested that ε, correspondinglyj, represent the number of excitatory, correspondingly inhibitory, terminal bulbs excited within the period of latent addition at a given most probable time. The relation between the suggested theory and the old one, based on differential equations for ε andj is discussed.     

A reinterpretation of the mathematical biophysics of the central nervous system in the light of neurophysiological findings

The fundamental equations for the interaction between neurons used in mathematical biophysics seem at first incompatible with the actual neurophysiological findings on the synaptic transmission. It is shown, however, that those equations may be readily interpreted in terms of accepted neurophysiological views. What has been termed “synapse” in mathematical biophysics must be regarded as a complicated network of internuncial neurons. It is shown that, under rather conditions, the number of those interneurons willstatistically vary with time according to the differential equation postulated for the excitatory and inhibitory factors. The latter are thus interpreted as the number of excitatory and inhibitory interneurons.     

On a stochastic model for the firing sequence of a neuron

A stochastic model of a neuron with excitatories and inhibitories incident on it is studied. The excitatory and the inhibitory sequences are independent renewal processes. The effect of an excitatory is to increase the membrane potential by random amounts that are independently and identically distributed, while an inhibitory causes a reset of the potential to the rest level so that the accumulation must start anew. When the potential crosses a threshold level K, the neuron fires. Immediately after this, the membrane potential returns to the rest level. An expression for the probability density function of the interval between two successive firings is derived, and special cases worked out. Graphs of the mean and the mean − √variance versus the threshold level are presented and discussed.     

Effects of phase on homeostatic spike rates

Recent experimental results by Talathi et al. (Neurosci Lett 455:145–149, 2009) showed a divergence in the spike rates of two types of population spike events, representing the putative activity of the excitatory and inhibitory neurons in the CA1 area of an animal model for temporal lobe epilepsy. The divergence in the spike rate was accompanied by a shift in the phase of oscillations between these spike rates leading to a spontaneous epileptic seizure. In this study, we propose a model of homeostatic synaptic plasticity which assumes that the target spike rate of populations of excitatory and inhibitory neurons in the brain is a function of the phase difference between the excitatory and inhibitory spike rates. With this model of homeostatic synaptic plasticity, we are able to simulate the spike rate dynamics seen experimentally by Talathi et al. in a large network of interacting excitatory and inhibitory neurons using two different spiking neuron models. A drift analysis of the spike rates resulting from the homeostatic synaptic plasticity update rule allowed us to determine the type of synapse that may be primarily involved in the spike rate imbalance in the experimental observation by Talathi et al. We find excitatory neurons, particularly those in which the excitatory neuron is presynaptic, have the most influence in producing the diverging spike rates and causing the spike rates to be anti-phase. Our analysis suggests that the excitatory neuronal population, more specifically the excitatory to excitatory synaptic connections, could be implicated in a methodology designed to control epileptic seizures.     

Inhibitory innervation of a lobster muscle

Summary Inhibitory neuromuscular synapses formed by the common inhibitor (CI) neuron on the distal accessory flexor muscle (DAFM) in the lobster, Homarus americanus, were studied with electrophysiological and electron-microscopic (thin-section and freeze-fracture) techniques. Postsynaptic inhibition as indicated by inhibitory junctional potentials was several-fold stronger on distal compared to proximal muscle fibers. This difference correlated with the results of serial thin-section studies, which showed more inhibitory synapses on distal fibers than on their proximal counterparts. Effects of postsynaptic inhibition on excitatory junctional potentials via current shunting had a morphological correlate in the spatial relationship between inhibitory and excitatory synapses on the distal fibers. Inhibitory synapses were larger than their excitatory counterparts and had fewer glial processes. In freeze-fracture views, inhibitory synapses did not appear as raised plateaus in the P-face as do excitatory synapses, and their active zones were more widely scattered. The intramembrane particles in the inhibitory postsynaptic membrane-representing neurotransmitter receptors-are arranged in parallel rows in the sarcolemmal P-face and have complementary furrows in the sarcolemmal E-face. Altogether, our findings help to describe a population of inhibitory neuromuscular synapses formed by the CI neuron in lobster muscle.     

Mandibular premotor interneurons of larval Manduca sexta

Simultaneous intracellular recordings were made from interneurons and from closer or opener mandibular motor neurons in the isolated suboesophageal ganglion of the larva of Manduca sexta. This article describes various morphologically and physiologically distinguishable premotor spiking interneurons which make direct excitatory connections with the motor neurons. In addition, two presumptive non-spiking interneurons make excitatory and inhibitory connections respectively with opener motor neurons. Both classes of interneurons receive excitatory and inhibitory sensory inputs from the mouthparts. Their circuitry and functions are discussed.Abbreviations A anterior - AP action potential - CEC circumoesophageal connective - Cl-MN closer motor neuron - EPSP excitatory postsynaptic potential - IN interneuron - IPSP inhibitory postsynaptic potential - MdN mandibular nerve - MN motor neuron - MxN maxillary nerve - O-MN opener motor neuron - PSP postsynaptic potential     

Anisotropic connectivity and cooperative phenomena as a basis for orientation sensitivity in the visual cortex

A computer simulation model of the neural circuitry underlying orientation sensitivity in cortical neurons is examined. The model consists of a network of 3000 neurons divided into two functionally distinct cell types: excitatory (E-cells) and inhibitory (I-cells). We demonstrate that both orientation sensitivity and shape selectivity can be accounted for by making the following assumptions: 1) thalamic afferents to a sheet of cortical neurons are retionotopically organized; 2) thalamic afferents come from a single neuron, or at most a few neurons, in the lateral geniculate nucleus; 3) cortical activity is cooperative, i.e. largely dependent on intracortical connections, some of which have anisotropies along directions parallel to the pial surface. Anisotropies are specified only by the distribution of cells which are postsynaptic to a particular neuron, without specifying the axonal or dendritic contributions. In this paper, orientation sensitivity arises through cooperative interactions among neurons having anisotropic excitatory, and isotropic inhibitory connections.     

Physiological characteristics and reflex activation of DUM (octopaminergic) neurons of locust metathoracic ganglion

Intracellular recordings were made from single or pairs of somata of the dorsal unpaired median (DUM) neurons of the metathoracic ganglion of the locust Schistocerca gregaria and the grasshopper Romalea microptera, during reflex actions, direct electric excitation and orthodromic and antidromic neural stimulation. Some, possibly all, of these neurons are unique, identifiable individuals in regard to their targets, which are specific peripheral muscles. Their physiological properties and the ways they are activated synaptically are, however, similar. Large, overshooting action potentials, comprising three components, occur. The first component in time is small and represents an excitatory synaptic potential for orthodromic stimulation or an axon spike (AS) for antidromic stimulation, electrotonically conducted into the soma. The second component is larger, being an electrotonically conducted integrating segment spike (ISS). The final component is the soma spike (SS). Neither AS nor ISS have a late positive phase, but there is a large, prolonged one for SS. The latter, combined with rapid accommodation, determine a low maximum firing rate for the neurons. Most nerves entering the ganglion make excitatory inputs onto each DUM neuron, which is readily driven to spike by electric excitation of either connective. There is a great deal of spontaneous excitatory synaptic input to each DUM neuron and a high proportion of it is common. Although there is no detectable electrical coupling between the cells, there is about 30% synchronous firing, apparently due to the common inputs; independent excitation and inhibition also occur. All sensory modalities tested have inputs to the neurons, which tend to fire constantly at a low rate (1 per 3–4 sec). In reflex actions, DUM neurons tend to fire before motor output occurs. It is suggested that the cells will be found to have many functions serving a general role comparable to that achieved by the release of adrenaline in vertebrates.     

Differences in synaptic output between excitatory and inhibitory motoneurons in a crayfish muscle

A pair of antagonistic motoneurons, one excitatory and one inhibitory, innervates the distal accessory flexor muscle in the walking limb of the crayfish Procambarus clarkii. The number and size of synapses formed by these two axons on the muscle fibers (neuromuscular synapses) and on each other (axo-axonal synapses) were estimated using thin-section electron microscopy. Although profiles of nerve terminals of the two axons occur in roughly equal proportions, the frequency of occurrence of neuromuscular synapses differed markedly: 73% were excitatory and 27% were inhibitory. However, inhibitory synapses were 4–5 times larger than excitatory ones, and consequently, the total contact areas devoted to neuromuscular synapses were similar for both axons. Axo-axonal synapses were predominantly from the inhibitory axon to the excitatory axon (86%), and a few were from the excitatory axon to the inhibitory axon (14%). The role of the inhibitory axo-axonal synapse is presynaptic inhibition, but that of the excitatory axo-axonal synapse is not known. The differences in size of neuromuscular synapses between the two axons may reflect intrinsic determinants of the neuron, while the similarity in total synaptic area may reflect retrograde influences from the muscle for regulating synapse number.     

蛙下丘听觉神经元对双耳强度差检测功能的建模和仿真

建立了蛙下丘听觉神经元对双耳刺激强度差检测功能的一个数学模型。按此模型所作的计算机仿真和相应实验结果比较的一致性支持了下列假设 :下丘中的EO神经元对同侧刺激不产生反应可能是由于接受了来自同侧的强烈抑制性输入 ,从而掩盖了它同时接受到的来自同侧耳的兴奋性输入。而来自同侧的抑制性输入 ,与来自对侧的兴奋性输入可能通过突触前抑制的相互作用 ,则导致了EE神经元的双耳抑制现象。     

Drosophila mutant with a transducer defect

The trp is a conditional phototransduction mutant of Drosophila. Direct electrical measurements and shot noise analysis suggest that a prolonged intense light causes in the mutant a reduction in the quantum efficiency for quantum bump production that does not arise from bleaching of the visual pigment. This effect depends on the duration of the light and only weakly on its intensity. In the normal fly, an intense blue light that shifts the visual pigment from rhodopsin to metarhodopsin, induces an excitatory process manifested by a prolonged depolarizing after potential (PDA). In the mutant, the PDA has a small amplitude and bump noise is superimposed on the response. It can thus be shown that the excitatory process underlying the PDA is also present in those trp mutants where the PDA voltage response is small or absent. It is suggested that the absence of the PDA voltage response in the mutant is probably due to a defect in an intermediate process, which links the excitatory process to the membrane conductance change.Presented at the EMBO-Workshop on Transduction Mechanism of Photoreceptors, Jülich, Germany, October 4–8, 1976     

Synchronization and sensitivity enhancement of the Hodgkin-Huxley neurons due to inhibitory inputs

Recent experimental results imply that inhibitory postsynaptic potentials can play a functional role in realizing synchronization of neuronal firing in the brain. In order to examine the relation between inhibition and synchronous firing of neurons theoretically, we analyze possible effects of synchronization and sensitivity enhancement caused by inhibitory inputs to neurons with a biologically realistic model of the Hodgkin-Huxley equations. The result shows that, after an inhibitory spike, the firing probability of a single postsynaptic neuron exposed to random excitatory background activity oscillates with time. The oscillation of the firing probability can be related to synchronous firing of neurons receiving an inhibitory spike simultaneously. Further, we show that when an inhibitory spike input precedes an excitatory spike input, the presence of such preceding inhibition raises the firing probability peak of the neuron after the excitatory input. The result indicates that an inhibitory spike input can enhance the sensitivity of the postsynaptic neuron to the following excitatory spike input. Two neural network models based on these effects on postsynaptic neurons caused by inhibitory inputs are proposed to demonstrate possible mechanisms of detecting particular spatiotemporal spike patterns. Received: 15 April 1999 /Accepted in revised form: 25 November 1999     

The epileptic neuron: II

Conditions under which a neuron can maintain repetitive discharges are studied with the view that some light may be shed on the problem of epilepsy. It is shown that if there are excitatory and inhibitory substances as well as binding substances in volved, then for repetitive discharges to occur, the formation of the substances must be intracellular. The geometric physical characteristics of the system are also determining factors. The role of a fatigue factor is considered in an attempt to understand the frequency and duration of mild and severe epileptic attacks.     

Vibrational resonance in a randomly connected neural network

A randomly connected network is constructed with similar characteristics (e.g., the ratio of excitatory and inhibitory neurons, the connection probability between neurons, and the axonal conduction delays) as that in the mammalian neocortex and the effects of high-frequency electrical field on the response of the network to a subthreshold low-frequency electrical field are studied in detail. It is found that both the amplitude and frequency of the high-frequency electrical field can modulate the response of the network to the low-frequency electric field. Moreover, vibrational resonance (VR) phenomenon induced by the two types of electrical fields can also be influenced by the network parameters, such as the neuron population, the connection probability between neurons and the synaptic strength. It is interesting that VR is found to be related with the ratio of excitatory neurons that are under high-frequency electrical stimuli. In summary, it is suggested that the interaction of excitatory and inhibitory currents is also an important factor that can influence the performance of VR in neural networks.     

Probabilistic Firing of Neurons Considered as a First Passage Problem

A formalized neuron receiving unitary excitatory impulses at random is considered. Each impulse provokes an effect of equal magnitude and of a duration not constant for each impulse, but which varies according to an exponential distribution. The effects sum until a threshold is reached when a response occurs. The distribution of intervals between successive responses is computed and compared with those obtained from a model in which the effects decay exponentially with time. Upon introducing inhibitory impulses also, the theory is applied to data on discharge characteristics of driven and spontaneously active thalamic neurons reported in the literature.     

Excitatory and inhibitory receptive fields of tectal cells are differentially modified by magnocellular and parvocellular divisions of the pigeon nucleus isthmi

It has been known that magnocellular and parvocellular divisions of the pigeon nucleus isthmi exert excitatory and inhibitory actions on tectal cells, respectively. The present study shows that injection of N-methyl-D-aspartate into the parvocellular division results in an increase in responsive strength and extent of the inhibitory receptive fields, which expand into the excitatory receptive fields of tectal cells. This injection concurrently leads to a decrease in responsiveness and extent of the excitatory fields. On the other hand, injection of acetylcholine into the magnocellular division enhances visual responsiveness, although the excitatory field is not obviously changed in extent. Meanwhile, strength and extent of the inhibitory fields are decreased by acetylcholine. The excitatory and inhibitory fields are reduced in both strength and extent by magnocellular and parvocellular injection of lidocaine, respectively. It suggests that isthmic inputs from both parvocellular and magnocellular divisions converge onto the same tectal cells, and the magnocellular and parvocellular subnuclei can modulate excitatory and inhibitory receptive fields of tectal cells, respectively, with some interactions between both fields. Accepted: 1 March 2000     

Information processing in the femur-tibia control loop of stick insects

The complicated response characteristics of the identified nonspiking interneuron type E4 upon elongation stimuli to the femoral chordotonal organ (fCO) can be obtained by a computer simulation using the neuronal network simulator BioSim, if the following assumptions were introduced: (1) The interneurons receive direct excitatory input from position- and velocity-sensitive fCO afferents but also, in parallel delayed inhibition from the same velocity-sensitive afferents. (2) Position-sensitive afferents in part show adaptation with a rather long time-constant. A subsequent experimental analysis demonstrated that all these assumptions fit the reality: (1) Interneurons of type E4 receive direct excitatory input from fCO afferents. (2) Interneurons of type E4 are affected by velocity dependent delayed inhibitory inputs from the fCO. (3) The fCO does contain adapting position-sensitive sensory neurons, which have not been described before. The described principle of the information processing is also able to generate the response in interneurons of type E6 with less steep amplitude-velocity characteristic due to a different weighting of the direct excitation and delayed inhibition.Abbreviations EPSP excitatory postsynaptic potential - FETi fast extensor tibiae motor neuron - fCO femoral chordotonal organ - FT-control loop femur-tibia control loop - IPSP inhibitory postsynaptic potential - SETi slow extensor tibiae motor neuron     

Odour sensitivity of antennal olfactory cells underlying grooved pegs of Anopheles gambiae s.s. and An. quadriannulatus

In female mosquitoes of the anthropophilic species Anopheles gambiae Giles s.s. and the zoophilic An. quadriannulatus Theobald single sensillum recordings from grooved pegs were made. In both species, the majority of these sensilla responded to ammonium hydroxide, butylamine and propanoic acid, whereas a smaller part responded to acetone. Lactic acid, butanone, 3-methyl phenol and 1-octen-3-ol evoked responses in a minority of grooved pegs only. In An. gambiae these four substances evoked either excitatory or inhibitory responses. In An. quadriannulatus excitatory and inhibitory responses were only found on stimulation with lactic acid; butanone, 3-methyl phenol and 1-octen-3-ol only evoked inhibition in the pegs of this species. More than half of the grooved pegs responded to water vapour with an increase in spike frequency. As opposed to this, in some pegs inhibitory responses were found upon stimulation with vapour of low humidity. This suggests that grooved pegs may play a role in humidity perception in Anopheles. Dose-response relations were investigated for cells excited by ammonium hydroxide, butylamine and propanoic acid. Excitatory responses to these three substances were dose-dependent. No significant differences were found between the dose-response curves of the two species. It is concluded that in both species the host odours tested are not perceived by specialist cells. Combined information from generalist cells may provide a detailed `odour profile' of the host.     

The common inhibitory neuron innervates every leg muscle in crabs

Summary The muscles proximal to the autotomy plane in the walking legs of two crab species,Eriphia spinifrons andCarcinus maenas, are innervated by the common inhibitory neuron (CI). Thus, CI is truly common to all 11 leg muscles. It is suggested that CI has the essential function in all leg muscles of preventing the tonic muscle fibers from participating in rapid contraction and relaxation cycles during walking.Abbreviation CI common inhibitory neuron On leave of absence from: Laboratoire de Neurobiologie Comparée, C.N.R.S. Université de Bordeaux I, Place du Docteur Bertrand Peyneau, F-33120 Arcachon, France