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.     

Analysis of compound postsynaptic potentials in the central nervous system of the surf clam

Compound postsynaptic potentials, comprising graded excitatory-inhibitory sequences, are the characteristic mode of response to afferent input exhibited by a population of cells in the visceroparietal ganglion of Spisula. Experimentally induced interaction between the phases of the response indicates that the observed sequential invasion represents differences in individual component latencies, rather than the physiological resultant of two separate processes having simultaneous onset but different rates of decay. Excitation is depressed by changes in membrane conductance throughout the duration of the inhibitory phase; moreover, since similar pathways from the periphery initiate both phases, excitatory events are limited to a duration roughly equal in length to the latency for the inhibition. Within this interval repetitive volleys can evoke summation of excitatory events. The inhibitory mechanism is temporally stable, however, and dominates the membrane during repetitive trains of volleys at 1 to 100 per sec. Artificially generated increases in the membrane potential decrease the IPSP while increasing the amplitude of the EPSP. Thus, both phases of the compound response appear to result from events occurring at chemically transmitting synaptic loci. Evidence is presented that these events are driven via collaterals of the same afferent fibers. The behavioral role of these response sequences is uncertain. Analogies, in terms of some observed reflex activity in these clams, appear to exist but presently lack experimental verification.     

The initiation of bursts in thalamic neurons and the cortical control of thalamic sensitivity

Thalamic neurons generate high-frequency bursts of action potentials when a low-threshold (T-type) calcium current, located in soma and dendrites, becomes activated. Computational models were used to investigate the bursting properties of thalamic relay and reticular neurons. These two types of thalamic cells differ fundamentally in their ability to generate bursts following either excitatory or inhibitory events. Bursts generated with excitatory inputs in relay cells required a high degree of convergence from excitatory inputs, whereas moderate excitation drove burst discharges in reticular neurons from hyperpolarized levels. The opposite holds for inhibitory rebound bursts, which are more difficult to evoke in reticular neurons than in relay cells. The differences between the reticular neurons and thalamocortical neurons were due to different kinetics of the T-current, different electrotonic properties and different distribution patterns of the T-current in the two cell types. These properties enable the cortex to control the sensitivity of the thalamus to inputs and are also important for understanding states such as absence seizures.     

Control of computational dynamics of coupled integrate-and-fire neurons

 Generation and control of different dynamical modes of computational processes in a net of interconnected integrate-and-fire neurons are demonstrated. A net architecture resembling a generic cortical structure is formed from pairs of excitatory and inhibitory units with excitatory connections between and inhibitory connections within pairs. Integrate-and-fire model neurons derived from detailed conductance-based models of neocortical pyramidal cells and fast-spiking interneurons are employed for the excitatory and inhibitory units, respectively. Firing-rate adaptation is incorporated into the excitatory units based on the regulation of the slow afterhyperpolarization phase of action potentials by intracellular calcium ions. Saturation of synaptic conductances is implemented for the interconnections between units. It is shown that neuronal adaptation of the excitatory units can generate richer net dynamics than relaxation to fixed-point attractors in a pattern space. At strong adaptivity, i.e. when the neuronal excitability is strongly influenced by the preceding activity, complex dynamics of either aperiodic or limit-cycle character are generated in both the pattern space and the phase space of all dynamical variables. This regime corresponds to an exploratory mode of the system, in which the pattern space can be searched. At weak adaptivity, the dynamics are governed by fixed-point attractors in the pattern space, and this corresponds to a mode for retrieval of a particular pattern. In the brain, neuronal adaptivity can be regulated by various neuromodulators. The results are in accordance with those recently obtained by means of more abstract models formulated in terms of mean firing rates. The increased realism makes the present model reveal more detailed mechanisms and strengthens the relevance of the conclusions to biological systems. The simplicity and realism of the coupled integrate-and-fire neurons make the present model useful for studies of systems in which the temporal aspects of neural coding are important. Received: 8 December 1995 / Accepted in revised form: 23 January 1997     

A neuron model with learning capability and its relation to mechanisms of association

A neuron model with the ability of learning has been examined by means of mathematical and statistical methods. By use of the established anatomical concepts the main features of the model can be described as follows.The synapses are randomly distributed on the dendrites in a way that can be described by poisson processes. The afferent connections to the synapses are also random.The input signals are divided into excitatory, inhibitory and unspecified signals. The latter, whose detailed action is not specified, may involve excitatory as well as inhibitory action on the cell. Signals are described in terms of impulse frequencies.Learning takes place through facilitation of excitatory synapses. The condition for facilitation is the occurrence of simultaneous presynaptic and postsynaptic activity. The synaptical changes occurring during repeated learning are superimposed. Inhibitory synapses are capable of influencing learning by blocking the dendritic transmission.It is shown that, under certain conditions, a collection of model cells is able to work as an associative memory. This means that a pattern of output signals that once occurred through the combined action of the excitatory, the inhibitory, and the unspecified signals may later be recalled by applying just the two former signal patterns. It is shown that excitatory and inhibitory signals are similar in their ability to evoke associations.However there is also a difference between excitation and inhibition due to the fact that the pattern of inhibitory signals is subject to a non-linear transformation. This implies that great similarity is required between the inhibitory pattern once present during learning and the inhibitory pattern that is fed in later in order to obtain an associative recall. This phenomenon is called pattern separation and is supposed to be of importance when discriminating between patterns.     

Stochastic automaton models for interaction of excitatory and inhibitory impulse sequences in neurons

The mechanisms by which excitatory and inhibitory input impulse sequences interact in changing the spike probability in neurons are examined in the two mathematical neuron models; one is a real-time neuron model which is close to physiological reality, and the other a stochastic automaton model for the temporal pattern discrimination proposed in the previous paper (Tsukada et al., 1976), which is developed in this paper as neuron models for interaction of excitatory and inhibitory input impulse sequences. The interval distributions of the output spike train from these models tend to be multimodal and are compared with those used for experimental data, reported by Bishop et al. (1964) for geniculate neuron activity and Poisson process deleting model analyzed by Ten Hoopen et al. (1966). Special attention, moreover, should be paid to how different forms of inhibitory input are transformed into the output interval distributions through these neuron models. These results exhibit a clear correlation between inhibitory input form and output interval distribution. More detailed information on this mechanism is obtained from the computations of recurrence-time under the stationary condition to go from active state to itself for the first time, each of which is influenced by the inhibitory input forms. In addition to these facts, some resultant characteristics on interval histogram and serial correlation are discussed in relation to physiological data from the literature.     

A feedforward model of suppressive and facilitatory habituation effects

 Simple exposure to repeatitive stimulation is known to induce short-term learning effects across a wide range of species. These effects can be both suppressive and facilitatory depending on stimulus conditions: repeatitive presentation of a weak stimulus decreases the strength of the response (habituation), whereas presentation of a tonic stimulus following a series of weak stimuli transiently increases the response strength (dishabituation). Although these phenomena have been comprehensively characterized at both behavioral and cellular levels, most existing models of nonassociative learning focus exclusively on the suppressive or facilitatory changes in response, and do not attempt to relate cellular events to behavior. I propose here a feedforward model of habituation effects that explains both suppressive and facilitatory changes in response relying on the interaction between excitatory and inhibitory processes that develop in parallel on two different timescales. The model's properties are used to explain the rate sensitivity property of habituation and recovery and stimulus dishabituation. Received: 1 June 2001 / Accepted in revised form: 4 December 2001     

When inhibition not excitation synchronizes neural firing

Excitatory and inhibitory synaptic coupling can have counter-intuitive effects on the synchronization of neuronal firing. While it might appear that excitatory coupling would lead to synchronization, we show that frequently inhibition rather than excitation synchronizes firing. We study two identical neurons described by integrate-and-fire models, general phase-coupled models or the Hodgkin-Huxley model with mutual, non-instantaneous excitatory or inhibitory synapses between them. We find that if the rise time of the synapse is longer than the duration of an action potential, inhibition not excitation leads to synchronized firing.     

Spiking neural network model for memorizing sequences with forward and backward recall

We present an oscillatory network of conductance based spiking neurons of Hodgkin–Huxley type as a model of memory storage and retrieval of sequences of events (or objects). The model is inspired by psychological and neurobiological evidence on sequential memories. The building block of the model is an oscillatory module which contains excitatory and inhibitory neurons with all-to-all connections. The connection architecture comprises two layers. A lower layer represents consecutive events during their storage and recall. This layer is composed of oscillatory modules. Plastic excitatory connections between the modules are implemented using an STDP type learning rule for sequential storage. Excitatory neurons in the upper layer project star-like modifiable connections toward the excitatory lower layer neurons. These neurons in the upper layer are used to tag sequences of events represented in the lower layer. Computer simulations demonstrate good performance of the model including difficult cases when different sequences contain overlapping events. We show that the model with STDP type or anti-STDP type learning rules can be applied for the simulation of forward and backward replay of neural spikes respectively.     

Balanced Excitatory and Inhibitory Synaptic Currents Promote Efficient Coding and Metabolic Efficiency

A balance between excitatory and inhibitory synaptic currents is thought to be important for several aspects of information processing in cortical neurons in vivo, including gain control, bandwidth and receptive field structure. These factors will affect the firing rate of cortical neurons and their reliability, with consequences for their information coding and energy consumption. Yet how balanced synaptic currents contribute to the coding efficiency and energy efficiency of cortical neurons remains unclear. We used single compartment computational models with stochastic voltage-gated ion channels to determine whether synaptic regimes that produce balanced excitatory and inhibitory currents have specific advantages over other input regimes. Specifically, we compared models with only excitatory synaptic inputs to those with equal excitatory and inhibitory conductances, and stronger inhibitory than excitatory conductances (i.e. approximately balanced synaptic currents). Using these models, we show that balanced synaptic currents evoke fewer spikes per second than excitatory inputs alone or equal excitatory and inhibitory conductances. However, spikes evoked by balanced synaptic inputs are more informative (bits/spike), so that spike trains evoked by all three regimes have similar information rates (bits/s). Consequently, because spikes dominate the energy consumption of our computational models, approximately balanced synaptic currents are also more energy efficient than other synaptic regimes. Thus, by producing fewer, more informative spikes approximately balanced synaptic currents in cortical neurons can promote both coding efficiency and energy efficiency.     

Does inhibition balance excitation in neocortex?

The distribution of inhibitory and excitatory synapses on neocortical neurons is at odds with a simple view that cortical functioning can persist by maintaining a balance between inhibitory and excitatory drives. Pyramidal cells can potentially be shut down by very powerful proximal inhibitory synapses, despite these accounting for perhaps less than 1% of their total number of synaptic inputs. Interneurons in contrast are dominated by excitatory inputs. These may be powerful enough to effect an apparent depolarizing block at the soma. In this extreme case though, models suggest that action potentials are generated down the axon, and the cells behave like integrate-and-fire neurons. We discuss possible network implications of these modelling studies.     

The suprachiasmatic nucleus exhibits diurnal variations in spontaneous excitatory postsynaptic activity

A most prominent feature of neurons in the suprachiasmatic nucleus (SCN) is the circadian rhythm in spontaneous firing frequency. To disclose synaptic mechanisms associated with the rhythmic activity, the spontaneous postsynaptic activity was studied using whole-cell, patch clamp recordings in the ventral region of the SCN in slice preparations from rats. The synaptic events were compared between two time intervals corresponding to the highest and lowest electrical activity within the SCN during subjective daytime and nighttime, respectively. The gamma-aminobutyric acid (GABA)-mediated spontaneous inhibitory activity showed no diurnal variations, but the excitatory activity was markedly higher in frequency, without differences in amplitude, during the subjective day compared to the subjective night. Spontaneous and evoked inhibitory synaptic events were blocked by the GABA(A) receptor antagonist bicuculline. The alpha-amino-hydroxy-5-methylisoxazole-4-propionic acid (AMPA/kainate) receptor antagonist 6-cyano-7-nitroquinoxaline-2, 3-dione (CNQX) blocked most of the excitatory activity. In addition, CNQX reduced the spontaneous inhibitory activity. The N-methyl-D-aspartate antagonist D-2-amino-5-phosphonopentanoic acid reduced the inhibitory activity to a lesser degree, and there was no significant difference in amplitude or frequency of synaptic events in control and Mg2+-free solutions, indicating that the AMPA receptor plays an important role in regulating the inhibitory release of GABA within the SCN. Ipsi- and contralateral stimulation of the SCN consistently evoked excitatory synaptic responses. Inhibitory synaptic responses occurred in some neurons upon increasing stimulus strength. In conclusion, this study shows that there is a substantial influence from spontaneous glutamatergic synapses on the ventral part of the SCN and that these exhibit daily variations in activity. Diurnal fluctuations in spontaneous excitatory postsynaptic activity within this network may contribute to the mechanisms for synchronization of rhythms between individual SCN neurons and may underlie the daily variations in the spontaneous firing frequency of SCN neurons.     

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.     

Coupled Van der Pol oscillators — A model of excitatory and inhibitory neural interactions

A system of mutually coupled Van der Pol equations is derived from an extended version of the Wilson and Cowan model for the dynamics of a number of excitatory and inhibitory neural subsets. In the lowest order of approximation, interactions between excitatory and inhibitory subsets appear as linear elastic coupling, while those within and between excitatory and excitatory subsets appear as nonlinear frictional coupling. The case of two coupled oscillators is investigated by the method of averaging and the stability conditions for two mode oscillations are obtained. Internal resonance is also discussed briefly in the case of identical oscillators.     

老化和精神疾病引起的皮层抑制功能变化

脑神经网络信息加工的实现方式主要依赖于兴奋性和抑制性突触连接.脑内抑制性神经元数量较少,但在信息加工和神经可塑性等方面作用极其重要,而且抑制系统失常与多种脑功能障碍有关联.脑内抑制性神经环路可粗略分为皮层内和皮层间(包括前馈和反馈)两种,分别介导同一脑区内和不同脑区间的抑制作用.本文先围绕中心-外周抑制和运动方向互斥介绍了皮层间、皮层内抑制的行为表现和作用机制,然后以老化和精神疾病为例综述了脑功能障碍与视觉系统皮层抑制功能变化间的联系,希望能对相关研究工作有所助益.     

Inferring network activity from synaptic noise

During intense network activity in vivo, cortical neurons are in a high-conductance state, in which the membrane potential (V(m)) is subject to a tremendous fluctuating activity. Clearly, this "synaptic noise" contains information about the activity of the network, but there are presently no methods available to extract this information. We focus here on this problem from a computational neuroscience perspective, with the aim of drawing methods to analyze experimental data. We start from models of cortical neurons, in which high-conductance states stem from the random release of thousands of excitatory and inhibitory synapses. This highly complex system can be simplified by using global synaptic conductances described by effective stochastic processes. The advantage of this approach is that one can derive analytically a number of properties from the statistics of resulting V(m) fluctuations. For example, the global excitatory and inhibitory conductances can be extracted from synaptic noise, and can be related to the mean activity of presynaptic neurons. We show here that extracting the variances of excitatory and inhibitory synaptic conductances can provide estimates of the mean temporal correlation-or level of synchrony-among thousands of neurons in the network. Thus, "probing the network" through intracellular V(m) activity is possible and constitutes a promising approach, but it will require a continuous effort combining theory, computational models and intracellular physiology.     

Emergent dynamics in a model of visual cortex

This paper proposes that the network dynamics of the mammalian visual cortex are highly structured and strongly shaped by temporally localized barrages of excitatory and inhibitory firing we call ‘multiple-firing events’ (MFEs). Our proposal is based on careful study of a network of spiking neurons built to reflect the coarse physiology of a small patch of layer 2/3 of V1. When appropriately benchmarked this network is capable of reproducing the qualitative features of a range of phenomena observed in the real visual cortex, including spontaneous background patterns, orientation-specific responses, surround suppression and gamma-band oscillations. Detailed investigation into the relevant regimes reveals causal relationships among dynamical events driven by a strong competition between the excitatory and inhibitory populations. It suggests that along with firing rates, MFE characteristics can be a powerful signature of a regime. Testable predictions based on model observations and dynamical analysis are proposed.     

Population density models of integrate-and-fire neurons with jumps: well-posedness

In this paper we study the well-posedness of different models of population of leaky integrate-and-fire neurons with a population density approach. The synaptic interaction between neurons is modeled by a potential jump at the reception of a spike. We study populations that are self excitatory or self inhibitory. We distinguish the cases where this interaction is instantaneous from the one where there is a repartition of conduction delays. In the case of a bounded density of delays both excitatory and inhibitory population models are shown to be well-posed. But without conduction delay the solution of the model of self excitatory neurons may blow up. We analyze the different behaviours of the model with jumps compared to its diffusion approximation.     

Different extrinsic trophic factors regulate neurite outgrowth and synapse formation between identified Lymnaea neurons

The requirement for trophic factors in neurite outgrowth is well established, though their role in synapse formation is yet to be determined. Moreover, the issue of whether the trophic factors mediating neurite outgrowth are also responsible for synapse specification has not yet been resolved. To test whether trophic factors mediating neurite outgrowth and synapse formation between identified neurons are conserved in two molluscan species and whether these developmental processes are differentially regulated by different trophic factors, we used soma-soma and neurite-neurite synapses between identified Lymnaea neurons. We demonstrate here that the trophic factors present in Aplysia hemolymph, although sufficient to induce neurite outgrowth from Lymnaea neurons, do not promote specific synapse formation between excitatory partners. Specifically, the identified presynaptic neuron visceral dorsal 4 (VD4) and postsynaptic neuron left pedal dorsal 1 (LPeD1) were either paired in a soma-soma configuration or plated individually to allow neuritic contacts. Cells were cultured in either Lymnaea brain-conditioned medium (CM) or on poly-L-lysine dishes that were pretreated with Aplysia hemolymph (ApHM), but contained only Lymnaea defined medium (DM; does not promote neurite outgrowth). In ApHM-coated dishes containing DM, Lymnaea neurons exhibited extensive neurite outgrowth, but appropriate excitatory synapses failed to develop between the cells. Instead, inappropriate reciprocal inhibitory synapses formed between VD4 and LPeD1. Similar inappropriate inhibitory synapses were observed in Aplysia hemolymph-pretreated dishes that contained dialyzed Aplysia hemolymph. These inhibitory synapses were novel and inappropriate, because they do not exist in vivo. A receptor tyrosine kinase inhibitor (Lavendustin A) blocked neurite outgrowth induced by both Lymnaea CM and ApHM. However, it did not affect inappropriate inhibitory synapse formation between the neurons. These data demonstrate that neurite outgrowth but not inappropriate inhibitory synapse formation involves receptor tyrosine kinases. Together, our data provide direct evidence that trophic factors required for neurite outgrowth are conserved among two different molluscan species, and that neurite extension and synapse specification between excitatory partners are likely mediated by different trophic factors.