Inhibitory Coupling Research Articles

Influence of inhibition on sequence replay - A mean field model

Event Abstract Back to Event Influence of inhibition on sequence replay - A mean field model Alvaro Tejero Cantero1, Axel Kammerer1* and Christian Leibold1 1 LMU Munich, Department of Biology II, Germany Memory sequences can be stored using networks of binary neurons with binary synapses. We investigate different forms of inhibition and their effect on storage, extending on a mean field approach by Leibold and Kempter (2006) 1. There, it was shown that capacity increases as the code becomes more sparse (less neurons per memory), but that the network cannot replay if the code is too sparse.Here, we show that the introduction of global inhibitory feedback allows successful replay of sequences with sparser representations, thereby increasing the memory capacity of the network. At the same time,the range of firing thresholds compatible with replay becomes broader, suggesting a more robust replay.Further extending the analysis, we look at transient replay. The system shows a graceful degradation of memory replay when departing from the optimal replay conditions, producing correct, but transient, memory replay before falling into a state of silence or non memory-related activity.We discuss the precise requirements for an inhibitory coupling to enhance memory capacity and robustness and the possible biological implications of our findings. Figure: Region of stable replay predicted by the mean field model without inhibition (upper wedge) and with inhibition (lower brown area). Shown is the number of iterations before the memory replay fails, depending on the threshold and the number of active neurons in a memory pattern. Brown areas show stable replay over all 100 iterations. Inhibition allows stable replay of sparser patterns, increasing the capacity. Both cases show transient replay over about 10 iterations. With inhibition, this means even sparser patterns can be stored, but no sequence will exceed the length of 10. Figure 1 References 1C. Leibold, R. Kempter, Neural Computation, 2006, 18, 904-941 Keywords: computational neuroscience Conference: Bernstein Conference on Computational Neuroscience, Berlin, Germany, 27 Sep - 1 Oct, 2010. Presentation Type: Presentation Topic: Bernstein Conference on Computational Neuroscience Citation: Tejero Cantero A, Kammerer A and Leibold C (2010). Influence of inhibition on sequence replay - A mean field model. Front. Comput. Neurosci. Conference Abstract: Bernstein Conference on Computational Neuroscience. doi: 10.3389/conf.fncom.2010.51.00085 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 14 Sep 2010; Published Online: 23 Sep 2010. * Correspondence: Dr. Axel Kammerer, LMU Munich, Department of Biology II, Munich, Germany, kammerer@bio.lmu.de Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Alvaro Tejero Cantero Axel Kammerer Christian Leibold Google Alvaro Tejero Cantero Axel Kammerer Christian Leibold Google Scholar Alvaro Tejero Cantero Axel Kammerer Christian Leibold PubMed Alvaro Tejero Cantero Axel Kammerer Christian Leibold Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

Analysis of stability of neural network with inhibitory neurons

Phase coding in a neural network composed of neural oscillators with inhibitory neurons was studied based on the theory of stochastic phase dynamics. We found that with increasing the coupling coefficients of inhibitory neural oscillators, the firing density in excitatory population transits to a critical state. In this case, when we increase the inhibitory coupling, the firing density will come into dynamic balance again and tend to a fixed value gradually. According to the phenomenon, in the paper we found parameter regions to exhibit those different population states, called dividing zones including flat fading zone, rapid fading zone and critical zone. Based on the dividing zones we can choose the number ratio between inhibitory neurons and excitatory neurons in the neural network, and estimate the coupling action of inhibitory population and excitatory population. Our research also shows that the balance value, enabling the firing density to reach the dynamic balance, does not depend on initial conditions. In addition, the critical value in critical state is only related to the number ratio between inhibitory neurons and excitatory neurons, but is independent of inhibitory coupling and excitatory coupling.

Inhibitory network of spiking neurons may express a sharp peak of synchrony at low frequency band

Spike synchronization remains an important issue in neuroscience, and inhibitory networks are the best candidates to provide such synchrony. Increasing evidence indicates that in many brain area inhibitory interneurons of similar properties make reciprocal connections. We found that a hybrid, as well as model network, consisting of two reciprocally inhibitory spiking neurons may express a peak of synchronization in a narrow range of low spiking frequencies in addition to classically described plateau of synchrony at a wide range of high frequencies. Occurrence of the low frequency peak of synchrony requires a moderate-to-strong inhibitory coupling and relatively fast synapses. This novel possibility of synchronization in a narrow range of network parameters may have an important implication in discrimination and encoding of signals of precise intensity, as well as in altering network ability to process information.

Excitatory effects of gap junction blockers on cerebral cortex seizure‐like activity in rats and mice

The role of gap junctions in seizures is an area of intense research. Many groups have reported anticonvulsant effects of gap junction blockade, strengthening the case for a role for gap junctions in ictogenesis. The cerebral cortex is underrepresented in this body of research. We have investigated the effect of gap junction blockade on seizure-like activity in rat and mouse cerebral cortex slices. Seizure-like activity was induced by perfusing with low-magnesium artificial cerebrospinal fluid. The effect of three gap junction blockers was investigated in rat cortical slices; quinine (200 and 400 microm), quinidine (100 and 200 microm), and carbenoxolone (100 and 200 microm). In addition, the effect of mefloquine was investigated in wild-type mice and connexin36 knockout mice. The data were analyzed for the effect on frequency and amplitude of seizure-like events. Paradoxical excitatory effects on seizure-like activity were observed for all three agents in rat cortical slices. Quinine (200 microm) and carbenoxolone (100 microm) increased both the frequency and amplitude of seizure-like events. Quinidine (100 microm) increased the frequency of events. Higher doses of quinine (400 microm) and carbenoxolone (200 microm) had biphasic excitatory-inhibitory effects. Similar excitatory effects were observed in adult wild-type mouse cortical slices perfused with mefloquine (5 microm or 10 microm), but were absent in slices from connexin36-deficient mice. In conclusion, we have shown a paradoxical proseizure effect of pharmacologic gap junction blockade in a cortical model of seizure-like activity. We suggest that this effect is probably due to a disruption of inhibitory interneuron coupling secondary to connexin36 blockade.

Control of bursting activity by modulation of ionic currents

Our study is focused on modulation of dynamics of single leech heart interneurons (HNs). We consider two models of HNs representing these neurons under two different pharmacological treatments: (1) blocking of Ca2+ currents and inhibitory coupling with the Ca2+-containing saline and partial blocking of K+ currents; (2) decoupling HNs with bicuculline. In (1), an HN demonstrates slow plateau-like oscillations [1,2]. In (2), an HN demonstrates endogenously bursting activity [3]. We analyze how the interburst interval and burst duration could be controlled by manipulating hyperpolarization-activated current, Ih, and persistent Na+ current, IP, namely by variation of their conductances and the half-activation voltages, V1/2. For example, burst duration increases greatly from 1.7 s to 8.9 s as Vh,1/2 increased from -30 mV to 4 mV. The interburst interval grows from 0.6 s to 125 s as the Vh,1/2 decreases from 4 [mV] to -56 [mV] in accordance with a saddlenode bifurcation. In (2), we similarly show that the variation of Vh,1/2 could be a target for modulation of the bursting. In both cases, we show co-existence of bursting and silence. Interestingly, the co-existence is sensitive to gh (and to maximal conductance of fast Ca2+ current, gCaF too in (2)) and is not sensitive to the maximal conductances of other currents. In (1), if gh is increased from 4 nS to 8 nS, the bistability is then observed in an almost five-fold larger range of the leak conductance values, gleak. In (2), if either gh is changed from 4 nS to 8 nS or gCaF is changed from 5 nS to 0 nS, the bistability is observed in an almost two-fold larger range of gleak. If the bistability is an indication of a dysfunctional dynamics, this observation describes a new, potentially pathological role of overexpression of Ih and ICaF.

Bifurcation in neuronal networks with hub structure

We investigate bifurcations in neuronal networks with a hub structure. It is known that hubs play a leading role in characterizing the network dynamical behavior. However, the dynamics of hubs or star-coupled systems is not well understood. Here, we study rather subnetworks with a star-like configuration. This coupled system is an important motif in complex networks. Thus, our study is a basic step for understanding structure formation in large networks. We use the Morris–Lecar neuron with class I and class II excitabilities as a node. Homogeneous (coupling the same class neurons) and heterogeneous (coupling different class neurons) cases are considered for both excitatory and inhibitory coupling. For the homogeneous system class II neurons are suitable for achieving both complete and cluster synchronization in excitatory and inhibitory coupling, respectively. For the heterogeneous system with inhibitory coupling, the class I hub neuron has a wider parameter region of synchronous firings than the class II hub. Moreover, the class I hub neuron with the excitatory synapse gives rise to bifurcations of synchronized states and multi-stability (coexistence of a few different states) is observed.

Different roles of cytoarchitectonic BA 44 and BA 45 in phonological and semantic verbal fluency as revealed by dynamic causal modelling

The interactions of left cytoarchitectonic BA 44 and BA 45 during semantic and phonological verbal fluency tasks were investigated using dynamic causal modelling (DCM). Three different models were tested, all of which featured BA 44 and BA 45 as top-down driven interconnected nodes projecting to the motor cortex as the final output region. Model #1 represents the hypothesis that BA 45 is involved in lexical retrieval including both semantic and phonological processes, while BA 44 supports other phonological processes. Model #2 reflects the notion of a clear-cut segregation of computational processes sustained by BA 44 (phonological processing) and BA 45 (semantic processing). Model #3 was based on the hypothesis that both BA 44 and BA 45 support semantic and phonological processing. When these models were compared against each other by Bayesian model selection, evidence emerged in favour of the first model, implying that BA 45 supports word retrieval processes whereas BA 44 is involved in processing phonological information during word generation. In a subsequent analysis of the derived model parameters for model #1, all connection strengths were significantly positive except for the inhibitory coupling between BA 44 and BA 45. This inhibition may reflect how the phonological analysis in BA 44 during word generation constrains lexical word retrieval in BA 45. To conclude, DCM provided additional insights into the roles of BA 44 and BA 45 during verbal fluency revealing the involvement of BA 45 in lexical retrieval and the relevance of BA 44 for phonological processing during word generation.

Asymmetry in pulse-coupled oscillators with delay

We studied the dynamics of synchronization in asymmetrically coupled neural oscillators with time delay. Stability analysis revealed that symmetric excitatory coupling results in synchrony at multiple phase relations. Asymmetry yields two saddle-node bifurcations of the stable states when coupling is asymmetric. By contrast, with inhibitory coupling only in phase or antiphase is stable as long as coupling is symmetric. Otherwise, these stable states shift or even vanish. The reduced bistability range suggests the beneficial role of asymmetric coupling for reliable neural information transfer.

Inverse synchronizations in coupled time-delay systems with inhibitory coupling

Transitions between inverse anticipatory, inverse complete, and inverse lag synchronizations are shown to occur as a function of the coupling delay in unidirectionally coupled time-delay systems with inhibitory coupling. We have also shown that the same general asymptotic stability condition obtained using the Krasovskii-Lyapunov functional theory can be valid for the cases where (i) both the coefficients of the Delta(t) (error variable) and Delta(tau)=Delta(t-tau) (error variable with delay) terms in the error equation corresponding to the synchronization manifold are time independent and (ii) the coefficient of the Delta term is time independent, while that of the Delta(tau) term is time dependent. The existence of different kinds of synchronization is corroborated using similarity function, probability of synchronization, and also from changes in the spectrum of Lyapunov exponents of the coupled time-delay systems.

Stationary pattern formation in a discrete excitable system with strong inhibitory coupling

We study a discrete model described by coupled excitable elements following the monostable FitzHugh-Nagumo equations. Our model has a weakly coupled activator and a strongly coupled inhibitor. For two-coupled excitable elements, we show that the trivial state always exists stably, while nontrivial stable states appear depending on the coupling strengths. In a one-dimensional array, only the elements near the initial condition step remain at nontrivial states. We discuss stationary pattern formation in a one-dimensional array and a two-dimensional lattice using the analytical results of a two-coupled system.

δ Receptors Are Required for Full Inhibitory Coupling of μ Receptors to Voltage-Dependent Ca2+ Channels in Dorsal Root Ganglion Neurons

Recombinant micro and delta opioid receptors expressed in cell lines can form heterodimers with distinctive properties and trafficking. However, a role for opioid receptor heterodimerization in neurons has yet to be identified. The inhibitory coupling of opioid receptors to voltage-dependent Ca(2+) channels (VDCCs) is a relatively inefficient process and therefore provides a sensitive assay of altered opioid receptor function and expression. We examined micro-receptor coupling to VDCCs in dorsal root ganglion neurons of delta(+/+), delta(+/-), and delta(-/-) mice. Neurons deficient in delta receptors exhibited reduced inhibition of VDCCs by morphine and [D-Ala(2),Phe(4),Gly(5)-ol]-enkephalin (DAMGO). An absence of delta receptors caused reduced efficacy of DAMGO without affecting potency. An absence of delta receptors reduced neither the density of VDCCs nor their inhibition by either the GABA(B) receptor agonist baclofen or intracellular guanosine 5'-O-(3-thio)triphosphate. Flow cytometry revealed a reduction in micro-receptor surface expression in delta(-/-) neurons without altered DAMGO-induced internalization. There was no change in micro-receptor mRNA levels. D-Phe-Cys-Tyr-D-Trp-Arg-Thr-Pen-Thr-NH(2)-sensitive mu-receptor-coupling efficacy was fully restored to delta(+/+) levels in delta(-/-) neurons by expression of recombinant delta receptors. However, the dimerization-deficient delta-15 construct expressed in delta(-/-) neurons failed to fully restore the inhibitory coupling of micro-receptors compared with that seen in delta(+/+) neurons, suggesting that, although not essential for micro-receptor function, micro-delta receptor dimerization contributes to full micro-agonist efficacy. Because DAMGO exhibited a similar potency in delta(+/+) and delta(-/-) neurons and caused similar levels of internalization, the role for heterodimerization is probably at the level of receptor biosynthesis.

Predictions of Phase-Locking in Excitatory Hybrid Networks: Excitation Does Not Promote Phase-Locking in Pattern-Generating Networks as Reliably as Inhibition

Phase-locked activity is thought to underlie many high-level functions of the nervous system, the simplest of which are produced by central pattern generators (CPGs). It is not known whether we can define a theoretical framework that is sufficiently general to predict phase-locking in actual biological CPGs, nor is it known why the CPGs that have been characterized are dominated by inhibition. Previously, we applied a method based on phase response curves measured using inputs of biologically realistic amplitude and duration to predict the existence and stability of 1:1 phase-locked modes in hybrid networks of one biological and one model bursting neuron reciprocally connected with artificial inhibitory synapses. Here we extend this analysis to excitatory coupling. Using the pyloric dilator neuron from the stomatogastric ganglion of the American lobster as our biological cell, we experimentally prepared 86 networks using five biological neurons, four model neurons, and heterogeneous synapse strengths between 1 and 10,000 nS. In 77% of networks, our method was robust to biological noise and accurately predicted the phasic relationships. In 3%, our method was inaccurate. The remaining 20% were not amenable to analysis because our theoretical assumptions were violated. The high failure rate for excitation compared with inhibition was due to differential effects of noise and feedback on excitatory versus inhibitory coupling and suggests that CPGs dominated by excitatory synapses would require precise tuning to function, which may explain why CPGs rely primarily on inhibitory synapses.

Neuronal identification of signal periodicity by balanced inhibition

Many animals, including men, use periodicity information, e.g., amplitude modulations of acoustic stimuli, as a vital cue to auditory object formation. The underlying neuronal mechanisms, however, still remain a matter of debate. Here, we mathematically analyze a model for periodicity identification that relies on the interplay of excitation and delayed inhibition. Our analytical results show how the maximal response of such a system varies systematically with the time constants of excitation and inhibition. The model reliably identifies signal periodicity in the range from about ten to several hundred Hertz. Importantly, the model relies on biologically plausible parameters only. It works best for excitatory and inhibitory neuronal couplings of equal strength, the so-called 'balanced inhibition'. We show how balanced inhibition can serve to identify low-frequency signal periodicity and how variation of a single parameter, the inhibitory time constant, can tune the system to different frequencies.

Burst synchronization of electrically and chemically coupled map-based neurons

Burst synchronization and burst dynamics of a system consisting of two map-based neurons coupled through electrical or chemical synapses are discussed. Some basic characteristic quantities are introduced to describe burst synchronization and burst dynamics of neurons. It is observed that excitatory coupling leads to in-phase burst synchronization but inhibitory coupling results in anti-phase one. By using the basic characteristics of burst dynamics, the effects of the intrinsic bursting properties and the coupling schemes on complex bursting behaviors are also presented for both inhibitory and excitatory couplings. The results are instructive to identify bursting behaviors through experimental data.

Noise shaping in neural populations

Many neurons display intrinsic interspike interval correlations in their spike trains. However, the effects of such correlations on information transmission in neural populations are not well understood. We quantified signal processing using linear response theory supported by numerical simulations in networks composed of two different models: One model generates a renewal process where interspike intervals are not correlated while the other generates a nonrenewal process where subsequent interspike intervals are negatively correlated. Our results show that the fractional rate of increase in information rate as a function of network size and stimulus intensity is lower for the nonrenewal model than for the renewal one. We show that this is mostly due to the lower amount of effective noise in the nonrenewal model. We also show the surprising result that coupling has opposite effects in renewal and nonrenewal networks: Excitatory (inhibitory coupling) will decrease (increase) the information rate in renewal networks while inhibitory (excitatory coupling) will decrease (increase) the information rate in nonrenewal networks. We discuss these results and their applicability to other classes of excitable systems.

Inhibitory Coupling between Inhibitory Interneurons in the Spinal Cord Dorsal Horn

Local inhibitory interneurons in the dorsal horn play an important role in the control of excitability at the segmental level and thus determine how nociceptive information is relayed to higher structures. Regulation of inhibitory interneuron activity may therefore have critical consequences on pain perception. Indeed, disinhibition of dorsal horn neuronal networks disrupts the balance between excitation and inhibition and is believed to be a key mechanism underlying different forms of pain hypersensitivity and chronic pain states. In this context, studying the source and the synaptic properties of the inhibitory inputs that the inhibitory interneurons receive is important in order to predict the impact of drug action at the network level. To address this, we studied inhibitory synaptic transmission in lamina II inhibitory interneurons identified under visual guidance in spinal slices taken from transgenic mice expressing enhanced green fluorescent protein (EGFP) under the control of the GAD promoter. The majority of these cells fired tonically to a long depolarizing current pulse. Monosynaptically evoked inhibitory postsynaptic currents (eIPSCs) in these cells were mediated by both GABAA and glycine receptors. Consistent with this, both GABAA and glycine receptor-mediated miniature IPSCs were recorded in all of the cells. These inhibitory inputs originated at least in part from local lamina II interneurons as verified by simultaneous recordings from pairs of EGFP+ cells. These synapses appeared to have low release probability and displayed potentiation and asynchronous release upon repeated activation. In summary, we report on a previously unexamined component of the dorsal horn circuitry that likely constitutes an essential element of the fine tuning of nociception.

Divide and conquer: resonance induced by competitive interactions

We study an Ising model in a network with disorder induced by the presence of both attractive and repulsive links and subjected to a periodic subthreshold signal. By means of numerical simulations and analytical calculations we give evidence that the global response of the system reaches a maximum value for a given fraction of the number of repulsive interactions. The model can represent a network of spin-like neurons with excitatory and inhibitory couplings, or a simple opinion spreading model. In this context, attractive/repulsive links represent friends and enemies. “Divide and Conquer” refers to the fact that in order to force a society to adopt a new point of view, it helps to break its homogeneity by fostering enmities amongst its members.

Reciprocal inhibitory coupling: Measure and control of chaos on a biophysically motivated model of bursting

Bursting activity is an interesting feature of the temporal organization in many cell firing patterns. This complex behavior is characterized by clusters of spikes (action potentials) interspersed with phases of quiescence. As shown in experimental recordings, concerning the electrical activity of real neurons, the analysis of bursting models reveals not only patterned periodic activity but also irregular behavior 1,2]. The interpretation of experimental results, particularly the study of the influence of coupling on chaotic bursting oscillations, is of great interest from physiological and physical perspectives. The inability to predict the behavior of dynamical systems in presence of chaos suggests the application of chaos control methods, when we are more interested in obtaining regular behavior. In the present article, we focus our attention on a specific class of biophysically motivated maps, proposed in the literature to describe the chaotic activity of spiking–bursting cells [Cazelles B, Courbage M, Rabinovich M. Anti-phase regularization of coupled chaotic maps modelling bursting neurons. Europhys Lett 2001;56:504–9]. More precisely, we study a map that reproduces the behavior of a single cell and a map used to examine the role of reciprocal inhibitory coupling, specially on two symmetrically coupled bursting neurons. Firstly, using results of symbolic dynamics, we characterize the topological entropy associated to the maps, which allows us to quantify and to distinguish different chaotic regimes. In particular, we exhibit numerical results about the effect of the coupling strength on the variation of the topological entropy. Finally, we show that complicated behavior arising from the chaotic coupled maps can be controlled, without changing of its original properties, and turned into a desired attracting time periodic motion (a regular cycle). The control is illustrated by an application of a feedback control technique developed by Romeiras et al. [Romeiras FJ, Grebogi C, Ott E, Dayawansa WP. Controlling chaotic dynamical systems. Physica D 1992;58:165–92]. This work provides an illustration of how our understanding of chaotic bursting models can be enhanced by the theory of dynamical systems.

Diffusively Coupled Chemical Oscillators in a Microfluidic Assembly

Fascillating: Inhibitory coupling by bromine among nanoliter aqueous droplets containing the Belousov–Zhabotinsky (BZ) reaction solution produces anti-phase oscillations and stationary Turing patterns (see picture; reduced catalyst in red, oxidized catalyst in blue). By choosing the fundamental oscillator and the scavenger added to the connecting medium, it should be possible to construct systems with controllable degrees of inhibitory or excitatory coupling.

Loss of phase-locking in non-weakly coupled inhibitory networks of type-I model neurons

Synchronization of excitable cells coupled by reciprocal inhibition is a topic of significant interest due to the important role that inhibitory synaptic interaction plays in the generation and regulation of coherent rhythmic activity in a variety of neural systems. While recent work revealed the synchronizing influence of inhibitory coupling on the dynamics of many networks, it is known that strong coupling can destabilize phase-locked firing. Here we examine the loss of synchrony caused by an increase in inhibitory coupling in networks of type-I Morris-Lecar model oscillators, which is characterized by a period-doubling cascade and leads to mode-locked states with alternation in the firing order of the two cells, as reported recently by Maran and Canavier (J Comput Nerosci, 2008) for a network of Wang-Buzsáki model neurons. Although alternating-order firing has been previously reported as a near-synchronous state, we show that the stable phase difference between the spikes of the two Morris-Lecar cells can constitute as much as 70% of the unperturbed oscillation period. Further, we examine the generality of this phenomenon for a class of type-I oscillators that are close to their excitation thresholds, and provide an intuitive geometric description of such "leap-frog" dynamics. In the Morris-Lecar model network, the alternation in the firing order arises under the condition of fast closing of K( + ) channels at hyperpolarized potentials, which leads to slow dynamics of membrane potential upon synaptic inhibition, allowing the presynaptic cell to advance past the postsynaptic cell in each cycle of the oscillation. Further, we show that non-zero synaptic decay time is crucial for the existence of leap-frog firing in networks of phase oscillators. However, we demonstrate that leap-frog spiking can also be obtained in pulse-coupled inhibitory networks of one-dimensional oscillators with a multi-branched phase domain, for instance in a network of quadratic integrate-and-fire model cells. Finally, for the case of a homogeneous network, we establish quantitative conditions on the phase resetting properties of each cell necessary for stable alternating-order spiking, complementing the analysis of Goel and Ermentrout (Physica D 163:191-216, 2002) of the order-preserving phase transition map.