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1
Skinner, F. K., J. Y. J. Chung, I. Ncube, P. A. Murray, and S. A. Campbell. "Using Heterogeneity to Predict Inhibitory Network Model Characteristics." Journal of Neurophysiology 93, no. 4 (April 2005): 1898–907. http://dx.doi.org/10.1152/jn.00619.2004.
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From modeling studies it has been known for >10 years that purely inhibitory networks can produce synchronous output given appropriate balances of intrinsic and synaptic parameters. Several experimental studies indicate that synchronous activity produced by inhibitory networks is critical to the production of population rhythms associated with various behavioral states. Heterogeneity of inputs to inhibitory networks strongly affect their ability to synchronize. In this paper, we explore how the amount of input heterogeneity to two-cell inhibitory networks affects their dynamics. Using numerical simulations and bifurcation analyses, we find that the ability of inhibitory networks to synchronize in the face of heterogeneity depends nonmonotonically on each of the synaptic time constant, synaptic conductance and external drive parameters. Because of this, an optimal set of parameters for a given cellular model with various biophysical characteristics can be determined. We suggest that this could be a helpful approach to use in determining the importance of different, underlying biophysical details. We further find that two-cell coherence properties are maintained in larger 10-cell networks. As such, we think that a strategy of “embedding” small network dynamics in larger networks is a useful way to understand the contribution of biophysically derived parameters to population dynamics in large networks.
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Vassiliev, P. M., A. A. Spasov, A. N. Kochetkov, M. A. Perfilev, and A. R. Koroleva. "Consensus ensemble neural network multitarget model of RAGE inhibitory activity of chemical compounds." Biomeditsinskaya Khimiya 67, no. 3 (2021): 268–77. http://dx.doi.org/10.18097/pbmc20216703268.
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RAGE signal transduction via the RAGE-NF-κB signaling pathway is one of the mechanisms of inflammatory reactions that cause severe complications in diabetes mellitus. RAGE inhibitors are promising pharmacological compounds that require the development of new predictive models. Based on the methodology of artificial neural networks, consensus ensemble neural network multitarget model has been constructed. This model describes the dependence of the level of the RAGE inhibitory activity on the affinity of compounds for 34 target proteins of the RAGE-NF-κB signal pathway. For this purpose an expanded database of valid three-dimensional models of target proteins of the RAGE-NF-κB signal chain was created on the basis of a previously created database of three-dimensional models of relevant biotargets. Ensemble molecular docking of known RAGE inhibitors from a verified database into the sites of added models of target proteins was performed, and the minimum docking energies for each compound in relation to each target were determined. An extended training set for neural network modeling was formed. Using seven variants of sampling by the method of artificial multilayer perceptron neural networks, three ensembles of classification decision rules were constructed to predict three level of the RAGE-inhibitory activity based on the calculated affinity of compounds for significant target proteins of the RAGE-NF-κB signaling pathway. Using a simple consensus of the second level, the predictive ability of the created model was assessed and its high accuracy and statistical significance were shown. The resultant consensus ensemble neural network multitarget model has been used for virtual screening of new derivatives of different chemical classes. The most promising substances have been synthesized and sent for experimental studies.
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Bryson, Alexander, Samuel F. Berkovic, Steven Petrou, and David B. Grayden. "State transitions through inhibitory interneurons in a cortical network model." PLOS Computational Biology 17, no. 10 (October 15, 2021): e1009521. http://dx.doi.org/10.1371/journal.pcbi.1009521.
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Inhibitory interneurons shape the spiking characteristics and computational properties of cortical networks. Interneuron subtypes can precisely regulate cortical function but the roles of interneuron subtypes for promoting different regimes of cortical activity remains unclear. Therefore, we investigated the impact of fast spiking and non-fast spiking interneuron subtypes on cortical activity using a network model with connectivity and synaptic properties constrained by experimental data. We found that network properties were more sensitive to modulation of the fast spiking population, with reductions of fast spiking excitability generating strong spike correlations and network oscillations. Paradoxically, reduced fast spiking excitability produced a reduction of global excitation-inhibition balance and features of an inhibition stabilised network, in which firing rates were driven by the activity of excitatory neurons within the network. Further analysis revealed that the synaptic interactions and biophysical features associated with fast spiking interneurons, in particular their rapid intrinsic response properties and short synaptic latency, enabled this state transition by enhancing gain within the excitatory population. Therefore, fast spiking interneurons may be uniquely positioned to control the strength of recurrent excitatory connectivity and the transition to an inhibition stabilised regime. Overall, our results suggest that interneuron subtypes can exert selective control over excitatory gain allowing for differential modulation of global network state.
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Chou, Kenny F., and Kamal Sen. "AIM: A network model of attention in auditory cortex." PLOS Computational Biology 17, no. 8 (August 27, 2021): e1009356. http://dx.doi.org/10.1371/journal.pcbi.1009356.
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Attentional modulation of cortical networks is critical for the cognitive flexibility required to process complex scenes. Current theoretical frameworks for attention are based almost exclusively on studies in visual cortex, where attentional effects are typically modest and excitatory. In contrast, attentional effects in auditory cortex can be large and suppressive. A theoretical framework for explaining attentional effects in auditory cortex is lacking, preventing a broader understanding of cortical mechanisms underlying attention. Here, we present a cortical network model of attention in primary auditory cortex (A1). A key mechanism in our network is attentional inhibitory modulation (AIM) of cortical inhibitory neurons. In this mechanism, top-down inhibitory neurons disinhibit bottom-up cortical circuits, a prominent circuit motif observed in sensory cortex. Our results reveal that the same underlying mechanisms in the AIM network can explain diverse attentional effects on both spatial and frequency tuning in A1. We find that a dominant effect of disinhibition on cortical tuning is suppressive, consistent with experimental observations. Functionally, the AIM network may play a key role in solving the cocktail party problem. We demonstrate how attention can guide the AIM network to monitor an acoustic scene, select a specific target, or switch to a different target, providing flexible outputs for solving the cocktail party problem.
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Rich, Scott, Michal Zochowski, and Victoria Booth. "Effects of Neuromodulation on Excitatory–Inhibitory Neural Network Dynamics Depend on Network Connectivity Structure." Journal of Nonlinear Science 30, no. 5 (January 4, 2018): 2171–94. http://dx.doi.org/10.1007/s00332-017-9438-6.
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Abstract Acetylcholine (ACh), one of the brain’s most potent neuromodulators, can affect intrinsic neuron properties through blockade of an M-type potassium current. The effect of ACh on excitatory and inhibitory cells with this potassium channel modulates their membrane excitability, which in turn affects their tendency to synchronize in networks. Here, we study the resulting changes in dynamics in networks with inter-connected excitatory and inhibitory populations (E–I networks), which are ubiquitous in the brain. Utilizing biophysical models of E–I networks, we analyze how the network connectivity structure in terms of synaptic connectivity alters the influence of ACh on the generation of synchronous excitatory bursting. We investigate networks containing all combinations of excitatory and inhibitory cells with high (Type I properties) or low (Type II properties) modulatory tone. To vary network connectivity structure, we focus on the effects of the strengths of inter-connections between excitatory and inhibitory cells (E–I synapses and I–E synapses), and the strengths of intra-connections among excitatory cells (E–E synapses) and among inhibitory cells (I-I synapses). We show that the presence of ACh may or may not affect the generation of network synchrony depending on the network connectivity. Specifically, strong network inter-connectivity induces synchronous excitatory bursting regardless of the cellular propensity for synchronization, which aligns with predictions of the PING model. However, when a network’s intra-connectivity dominates its inter-connectivity, the propensity for synchrony of either inhibitory or excitatory cells can determine the generation of network-wide bursting.
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Cao, Ying, Xiaoyan He, Yuqing Hao, and Qingyun Wang. "Transition Dynamics of Epileptic Seizures in the Coupled Thalamocortical Network Model." International Journal of Bifurcation and Chaos 28, no. 08 (July 2018): 1850104. http://dx.doi.org/10.1142/s0218127418501043.
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In this paper, based on the two-compartment unidirectionally coupled thalamocortical model network, we investigated the transition dynamics of epileptic seizures, by considering the inhibitory coupling strength from cortical inhibitory interneuronal (IN) population to excitatory pyramidal (PY) neuronal population as the key bifurcation parameter. The results show that in the single compartment thalamocortical model, inner-compartment inhibitory functions of IN can make the system transit from the absence seizures to the tonic oscillations. In the case of two-compartment coupled thalamocortical model network, the inter-compartment inhibitory coupling functions from the first compartment can drive the second compartment to more easily initiate the absence and tonic seizures at the lower inhibitory coupling strengths, respectively. Also, the driven functions can make the amplitudes of these seizures vary irregularly. Detailed investigations reveal that along with the various state transitions, the system consecutively undergoes Hopf bifurcations, fold of cycles bifurcations and torus bifurcations, respectively. In particular, the reinforcing inter-compartment inhibitory coupling function can induce the chaotic dynamics. We highlight the unidirectional coupling functions between two compartments which might give new insights into the propagation and evolution dynamics of epileptic seizures.
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Tiesinga, Paul H. E. "Stimulus Competition by Inhibitory Interference." Neural Computation 17, no. 11 (November 1, 2005): 2421–53. http://dx.doi.org/10.1162/0899766054796905.
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When two stimuli are present in the receptive field of a V4 neuron, the firing rate response is between the weakest and strongest response elicited by each of the stimuli when presented alone (Reynolds, Chelazzi, & Desimone, 1999). When attention is directed toward the stimulus eliciting the strongest response (the preferred stimulus), the response to the pair is increased, whereas the response decreases when attention is directed to the other stimulus (the poor stimulus). When attention is directed to either of the two stimuli presented alone, the firing rate remains the same or increases slightly, but the coherence between the neuron's spike train and the local field potential can increase (Fries, Reynolds, Rorie, & Desimone, 2001). These experimental results were reproduced in a model of a V4 neuron under the assumption that attention modulates the activity of local interneuron networks. The V4 model neuron received stimulus-specific excitation from V2 and synchronous inhibitory inputs from two local interneuron networks in V4. Each interneuron network was driven by stimulus-specific excitatory inputs from V2 and was modulated by the activity of the frontal eye fields. Stimulus competition was present because of a delay in arrival time of synchronous volleys from each interneuron network. For small delays, the firing rate was close to the rate elicited by the preferred stimulus alone, whereas for larger delays, it approached the firing rate of the poor stimulus. When either stimulus was presented alone, the neuron's response was not altered by the change in delay, but could change due to modulation of the degree of synchrony of the corresponding interneuron network. The model suggests that top-down attention biases the competition between V2 columns for control of V4 neurons primarily by changing the relative timing of inhibition, whereas changes in the degree of synchrony of interneuron networks modulate the response to a single stimulus. The new mechanism proposed here for attentional modulation of firing rate, gain modulation by inhibitory interference, is likely to have more general applicability to cortical information processing.
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YAMAZAKI, TADASHI, and SHIGERU TANAKA. "A NEURAL NETWORK MODEL FOR TRACE CONDITIONING." International Journal of Neural Systems 15, no. 01n02 (February 2005): 23–30. http://dx.doi.org/10.1142/s0129065705000037.
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We studied the dynamics of a neural network that has both recurrent excitatory and random inhibitory connections. Neurons started to become active when a relatively weak transient excitatory signal was presented and the activity was sustained due to the recurrent excitatory connections. The sustained activity stopped when a strong transient signal was presented or when neurons were disinhibited. The random inhibitory connections modulated the activity patterns of neurons so that the patterns evolved without recurrence with time. Hence, a time passage between the onsets of the two transient signals was represented by the sequence of activity patterns. We then applied this model to represent the trace eyeblink conditioning, which is mediated by the hippocampus. We assumed this model as CA3 of the hippocampus and considered an output neuron corresponding to a neuron in CA1. The activity pattern of the output neuron was similar to that of CA1 neurons during trace eyeblink conditioning, which was experimentally observed.
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Andreev, Andrey, and Vladimir Maksimenko. "Synchronization in coupled neural network with inhibitory coupling." Cybernetics and Physics, Volume 8, 2019, Number 4 (December 30, 2019): 199–204. http://dx.doi.org/10.35470/2226-4116-2019-8-4-199-204.
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A theoretical model of a network of neuron-like elements was constructed. The network included several subnetworks. The first subnetwork was used to translate a constant-amplitude signal into a spike sequence (conversion of amplitude to frequency). A similar process occurs in the brain when perceiving visual information. With an increase in the flow of information, the generation frequency of the neural ensemble participating in the processing increases. Further, the first subnetwork transmitted excitation to two large interconnected subnetworks. These subnetworks simulated the dynamics of the cortical neuronal populations. It was shown that in the presence of inhibitory coupling, the neuronal ensembles demonstrate antiphase dynamics. Various connectivity topologies and various types of neuron-like oscillators were investigated. We compare the results obtained in a discrete neuron model (Rulkov model) and a continuous-time model (Hodgkin-Huxley). It is shown that in the case of a discrete neuron model, the periodic dynamics is manifested in the alternate excitation of various neural ensembles. In the case of the continuous-time model, periodic modulation of the synchronization index of neural ensembles is observed.
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Blazis, Diana E. J., Thomas M. Fischer, and Thomas J. Carew. "A Neural Network Model of Inhibitory Information Processing in Aplysia." Neural Computation 5, no. 2 (March 1993): 213–27. http://dx.doi.org/10.1162/neco.1993.5.2.213.
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Recent cellular studies have revealed a novel form of inhibitory information processing in the siphon withdrawal reflex of the marine mollusc Aplysia: Motorneuronal output is significantly reduced by activity-dependent potentiation of recurrent inhibition within the siphon withdrawal network (Fischer and Carew 1991, 1993). This inhibitory modulation is mediated by two types of identified interneurons, L29s and L30s. In an effort to describe and analyze this and other forms of inhibitory information processing in Aplysia, and to compare it with similar processing in other nervous systems, we have constructed a neural network model that incorporates many empirically observed features of these interneurons. The model generates important aspects of the interactions of cells L29 and L30, and with no further modification, exhibits many network level phenomena that were not explicitly incorporated into the model.
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Weissenberger, Felix, Marcelo Matheus Gauy, Xun Zou, and Angelika Steger. "Mutual Inhibition with Few Inhibitory Cells via Nonlinear Inhibitory Synaptic Interaction." Neural Computation 31, no. 11 (November 2019): 2252–65. http://dx.doi.org/10.1162/neco_a_01230.
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In computational neural network models, neurons are usually allowed to excite some and inhibit other neurons, depending on the weight of their synaptic connections. The traditional way to transform such networks into networks that obey Dale's law (i.e., a neuron can either excite or inhibit) is to accompany each excitatory neuron with an inhibitory one through which inhibitory signals are mediated. However, this requires an equal number of excitatory and inhibitory neurons, whereas a realistic number of inhibitory neurons is much smaller. In this letter, we propose a model of nonlinear interaction of inhibitory synapses on dendritic compartments of excitatory neurons that allows the excitatory neurons to mediate inhibitory signals through a subset of the inhibitory population. With this construction, the number of required inhibitory neurons can be reduced tremendously.
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Vreeswijk, C. van, and H. Sompolinsky. "Chaotic Balanced State in a Model of Cortical Circuits." Neural Computation 10, no. 6 (August 1, 1998): 1321–71. http://dx.doi.org/10.1162/089976698300017214.
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The nature and origin of the temporal irregularity in the electrical activity of cortical neurons in vivo are not well understood. We consider the hypothesis that this irregularity is due to a balance of excitatory and inhibitory currents into the cortical cells. We study a network model with excitatory and inhibitory populations of simple binary units. The internal feedback is mediated by relatively large synaptic strengths, so that the magnitude of the total excitatory and inhibitory feedback is much larger than the neuronal threshold. The connectivity is random and sparse. The mean number of connections per unit is large, though small compared to the total number of cells in the network. The network also receives a large, temporally regular input from external sources. We present an analytical solution of the mean-field theory of this model, which is exact in the limit of large network size. This theory reveals a new cooperative stationary state of large networks, which we term a balanced state. In this state, a balance between the excitatory and inhibitory inputs emerges dynamically for a wide range of parameters, resulting in a net input whose temporal fluctuations are of the same order as its mean. The internal synaptic inputs act as a strong negative feedback, which linearizes the population responses to the external drive despite the strong nonlinearity of the individual cells. This feedback also greatly stabilizes the system's state and enables it to track a time-dependent input on time scales much shorter than the time constant of a single cell. The spatiotemporal statistics of the balanced state are calculated. It is shown that the autocorrelations decay on a short time scale, yielding an approximate Poissonian temporal statistics. The activity levels of single cells are broadly distributed, and their distribution exhibits a skewed shape with a long power-law tail. The chaotic nature of the balanced state is revealed by showing that the evolution of the microscopic state of the network is extremely sensitive to small deviations in its initial conditions. The balanced state generated by the sparse, strong connections is an asynchronous chaotic state. It is accompanied by weak spatial cross-correlations, the strength of which vanishes in the limit of large network size. This is in contrast to the synchronized chaotic states exhibited by more conventional network models with high connectivity of weak synapses.
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Zonca, Lou, and David Holcman. "Emergence and fragmentation of the alpha-band driven by neuronal network dynamics." PLOS Computational Biology 17, no. 12 (December 6, 2021): e1009639. http://dx.doi.org/10.1371/journal.pcbi.1009639.
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Rhythmic neuronal network activity underlies brain oscillations. To investigate how connected neuronal networks contribute to the emergence of the α-band and to the regulation of Up and Down states, we study a model based on synaptic short-term depression-facilitation with afterhyperpolarization (AHP). We found that the α-band is generated by the network behavior near the attractor of the Up-state. Coupling inhibitory and excitatory networks by reciprocal connections leads to the emergence of a stable α-band during the Up states, as reflected in the spectrogram. To better characterize the emergence and stability of thalamocortical oscillations containing α and δ rhythms during anesthesia, we model the interaction of two excitatory networks with one inhibitory network, showing that this minimal topology underlies the generation of a persistent α-band in the neuronal voltage characterized by dominant Up over Down states. Finally, we show that the emergence of the α-band appears when external inputs are suppressed, while fragmentation occurs at small synaptic noise or with increasing inhibitory inputs. To conclude, α-oscillations could result from the synaptic dynamics of interacting excitatory neuronal networks with and without AHP, a principle that could apply to other rhythms.
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CATSIGERAS, ELEONORA. "CHAOS AND STABILITY IN A MODEL OF INHIBITORY NEURONAL NETWORK." International Journal of Bifurcation and Chaos 20, no. 02 (February 2010): 349–60. http://dx.doi.org/10.1142/s0218127410025806.
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We analyze the dynamics of a deterministic model of inhibitory neuronal networks proving that the discontinuities of the Poincaré map produce a never empty chaotic set, while its continuity pieces produce stable orbits. We classify the systems in three types: the almost everywhere (a.e.) chaotic, the a.e. stable, and the combined systems. The a.e. stable are periodic and chaos appears as bifurcations. We prove that a.e. stable systems exhibit limit cycles, attracting a.e. the orbits.
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Bowman, Howard, Friederike Schlaghecken, and Martin Eimer. "A neural network model of inhibitory processes in subliminal priming." Visual Cognition 13, no. 4 (February 2006): 401–80. http://dx.doi.org/10.1080/13506280444000823.
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Sinha, Ankur, Christoph Metzner, Neil Davey, Roderick Adams, Michael Schmuker, and Volker Steuber. "Growth rules for the repair of Asynchronous Irregular neuronal networks after peripheral lesions." PLOS Computational Biology 17, no. 6 (June 1, 2021): e1008996. http://dx.doi.org/10.1371/journal.pcbi.1008996.
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Several homeostatic mechanisms enable the brain to maintain desired levels of neuronal activity. One of these, homeostatic structural plasticity, has been reported to restore activity in networks disrupted by peripheral lesions by altering their neuronal connectivity. While multiple lesion experiments have studied the changes in neurite morphology that underlie modifications of synapses in these networks, the underlying mechanisms that drive these changes are yet to be explained. Evidence suggests that neuronal activity modulates neurite morphology and may stimulate neurites to selective sprout or retract to restore network activity levels. We developed a new spiking network model of peripheral lesioning and accurately reproduced the characteristics of network repair after deafferentation that are reported in experiments to study the activity dependent growth regimes of neurites. To ensure that our simulations closely resemble the behaviour of networks in the brain, we model deafferentation in a biologically realistic balanced network model that exhibits low frequency Asynchronous Irregular (AI) activity as observed in cerebral cortex. Our simulation results indicate that the re-establishment of activity in neurons both within and outside the deprived region, the Lesion Projection Zone (LPZ), requires opposite activity dependent growth rules for excitatory and inhibitory post-synaptic elements. Analysis of these growth regimes indicates that they also contribute to the maintenance of activity levels in individual neurons. Furthermore, in our model, the directional formation of synapses that is observed in experiments requires that pre-synaptic excitatory and inhibitory elements also follow opposite growth rules. Lastly, we observe that our proposed structural plasticity growth rules and the inhibitory synaptic plasticity mechanism that also balances our AI network both contribute to the restoration of the network to pre-deafferentation stable activity levels.
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Yang, Geunbo, Wongyu Lee, Youjung Seo, Choongseop Lee, Woojoon Seok, Jongkil Park, Donggyu Sim, and Cheolsoo Park. "Unsupervised Spiking Neural Network with Dynamic Learning of Inhibitory Neurons." Sensors 23, no. 16 (August 17, 2023): 7232. http://dx.doi.org/10.3390/s23167232.
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A spiking neural network (SNN) is a type of artificial neural network that operates based on discrete spikes to process timing information, similar to the manner in which the human brain processes real-world problems. In this paper, we propose a new spiking neural network (SNN) based on conventional, biologically plausible paradigms, such as the leaky integrate-and-fire model, spike timing-dependent plasticity, and the adaptive spiking threshold, by suggesting new biological models; that is, dynamic inhibition weight change, a synaptic wiring method, and Bayesian inference. The proposed network is designed for image recognition tasks, which are frequently used to evaluate the performance of conventional deep neural networks. To manifest the bio-realistic neural architecture, the learning is unsupervised, and the inhibition weight is dynamically changed; this, in turn, affects the synaptic wiring method based on Hebbian learning and the neuronal population. In the inference phase, Bayesian inference successfully classifies the input digits by counting the spikes from the responding neurons. The experimental results demonstrate that the proposed biological model ensures a performance improvement compared with other biologically plausible SNN models.
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Armstrong, Eve, and Henry D. I. Abarbanel. "Model of the songbird nucleus HVC as a network of central pattern generators." Journal of Neurophysiology 116, no. 5 (November 1, 2016): 2405–19. http://dx.doi.org/10.1152/jn.00438.2016.
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We propose a functional architecture of the adult songbird nucleus HVC in which the core element is a “functional syllable unit” (FSU). In this model, HVC is organized into FSUs, each of which provides the basis for the production of one syllable in vocalization. Within each FSU, the inhibitory neuron population takes one of two operational states: 1) simultaneous firing wherein all inhibitory neurons fire simultaneously, and 2) competitive firing of the inhibitory neurons. Switching between these basic modes of activity is accomplished via changes in the synaptic strengths among the inhibitory neurons. The inhibitory neurons connect to excitatory projection neurons such that during state 1 the activity of projection neurons is suppressed, while during state 2 patterns of sequential firing of projection neurons can occur. The latter state is stabilized by feedback from the projection to the inhibitory neurons. Song composition for specific species is distinguished by the manner in which different FSUs are functionally connected to each other. Ours is a computational model built with biophysically based neurons. We illustrate that many observations of HVC activity are explained by the dynamics of the proposed population of FSUs, and we identify aspects of the model that are currently testable experimentally. In addition, and standing apart from the core features of an FSU, we propose that the transition between modes may be governed by the biophysical mechanism of neuromodulation.
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Dasika, Vasant K., John A. White, Laurel H. Carney, and H. Steven Colburn. "Effects of Inhibitory Feedback in a Network Model of Avian Brain Stem." Journal of Neurophysiology 94, no. 1 (July 2005): 400–414. http://dx.doi.org/10.1152/jn.01065.2004.
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The avian auditory brain stem consists of a network of specialized nuclei, including nucleus laminaris (NL) and superior olivary nucleus (SON). NL cells show sensitivity to interaural time difference (ITD), a critical cue that underlies spatial hearing. SON cells provide inhibitory feedback to the rest of the network. Empirical data suggest that feedback inhibition from SON could increase the ITD sensitivity of NL across sound level. Using a bilateral network model, we assess the effects of SON feedback inhibition. Individual cells are specified as modified leaky-integrate-and-fire neurons with time constants and thresholds that vary with inhibitory input. Acoustic sound level is reflected in the discharge rates of the model auditory-nerve fibers, which innervate the network. Simulations show that with SON inhibitory feedback, ITD sensitivity is maintained in model NL cells over a threefold range in auditory-nerve discharge rate. In contrast, without SON feedback inhibition, ITD sensitivity is significantly reduced as input rates are increased. Feedback inhibition is most beneficial in maintaining ITD sensitivity at high-input rates (simulating high sound levels). With SON inhibition, ITD sensitivity is maintained for both interaurally balanced inputs (simulating an on-center sound source) and interaurally imbalanced inputs (simulating a lateralized source). Further, the empirically observed temporal build-up of SON inhibition and the presence of reciprocal inhibitory connections between the ipsi- and contralateral SON both improve ITD sensitivity. In sum, our network model shows that inhibitory feedback can substantially increase the sensitivity and dynamic range of ITD coding in the avian auditory brain stem.
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Gelenbe, Erol. "Stability of the Random Neural Network Model." Neural Computation 2, no. 2 (June 1990): 239–47. http://dx.doi.org/10.1162/neco.1990.2.2.239.
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In a recent paper (Gelenbe 1989) we introduced a new neural network model, called the Random Network, in which “negative” or “positive” signals circulate, modeling inhibitory and excitatory signals. These signals can arrive either from other neurons or from the outside world: they are summed at the input of each neuron and constitute its signal potential. The state of each neuron in this model is its signal potential, while the network state is the vector of signal potentials at each neuron. If its potential is positive, a neuron fires, and sends out signals to the other neurons of the network or to the outside world. As it does so its signal potential is depleted. We have shown (Gelenbe 1989) that in the Markovian case, this model has product form, that is, the steady-state probability distribution of its potential vector is the product of the marginal probabilities of the potential at each neuron. The signal flow equations of the network, which describe the rate at which positive or negative signals arrive at each neuron, are nonlinear, so that their existence and uniqueness are not easily established except for the case of feedforward (or backpropagation) networks (Gelenbe 1989). In this paper we show that whenever the solution to these signal flow equations exists, it is unique. We then examine two subclasses of networks — balanced and damped networks — and obtain stability conditions in each case. In practical terms, these stability conditions guarantee that the unique solution can be found to the signal flow equations and therefore that the network has a well-defined steady-state behavior.
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Taylor, Adam L., Garrison W. Cottrell, and William B. Kristan. "Analysis of Oscillations in a Reciprocally Inhibitory Network with Synaptic Depression." Neural Computation 14, no. 3 (March 1, 2002): 561–81. http://dx.doi.org/10.1162/089976602317250906.
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We present and analyze a model of a two-cell reciprocally inhibitory network that oscillates. The principal mechanism of oscillation is short-term synaptic depression. Using a simple model of depression and analyzing the system in certain limits, we can derive analytical expressions for various features of the oscillation, including the parameter regime in which stable oscillations occur, as well as the period and amplitude of these oscillations. These expressions are functions of three parameters: the time constant of depression, the synaptic strengths, and the amount of tonic excitation the cells receive. We compare our analytical results with the output of numerical simulations and obtain good agreement between the two. Based on our analysis, we conclude that the oscillations in our network are qualitatively different from those in networks that oscillate due to postinhibitory rebound, spike-frequency adaptation, or other intrinsic (rather than synaptic) adaptational mechanisms. In particular, our network can oscillate only via the synaptic escape mode of Skinner, Kopell, and Marder (1994).
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Ouardouz, Mohamed, and Lionel Carmant. "Changes in inhibitory CA1 network in dual pathology model of epilepsy." Channels 6, no. 1 (January 2012): 18–25. http://dx.doi.org/10.4161/chan.18615.
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Ponzi, Adam P. D., and Jeff Wickens. "Input dependent cell assembly dynamics in an inhibitory spiking network model." Neuroscience Research 68 (January 2010): e213. http://dx.doi.org/10.1016/j.neures.2010.07.2511.
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Miyawaki, Yoichi, and Masato Okada. "A network model of inhibitory effects induced by transcranial magnetic stimulation." Neurocomputing 52-54 (June 2003): 837–42. http://dx.doi.org/10.1016/s0925-2312(02)00810-x.
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Omori, Toshiaki, and Tsuyoshi Horiguchi. "Dynamical Neural Network Model of Hippocampus with Excitatory and Inhibitory Neurons." Journal of the Physical Society of Japan 73, no. 3 (March 15, 2004): 749–55. http://dx.doi.org/10.1143/jpsj.73.749.
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Lee, Euiwoo, and David Terman. "Oscillatory Rhythms in a Model Network of Excitatory and Inhibitory Neurons." SIAM Journal on Applied Dynamical Systems 18, no. 1 (January 2019): 354–92. http://dx.doi.org/10.1137/18m1200877.
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Vreeswijk, C. van, and D. Hansel. "Patterns of Synchrony in Neural Networks with Spike Adaptation." Neural Computation 13, no. 5 (May 1, 2001): 959–92. http://dx.doi.org/10.1162/08997660151134280.
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We study the emergence of synchronized burst activity in networks of neurons with spike adaptation. We show that networks of tonically firing adapting excitatory neurons can evolve to a state where the neurons burst in a synchronized manner. The mechanism leading to this burst activity is analyzed in a network of integrate-and-fire neurons with spike adaptation. The dependence of this state on the different network parameters is investigated, and it is shown that this mechanism is robust against inhomogeneities, sparseness of the connectivity, and noise. In networks of two populations, one excitatory and one inhibitory, we show that decreasing the inhibitory feedback can cause the network to switch from a tonically active, asynchronous state to the synchronized bursting state. Finally, we show that the same mechanism also causes synchronized burst activity in networks of more realistic conductance-based model neurons.
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Linster, Christiane, Silke Sachse, and C. Giovanni Galizia. "Computational Modeling Suggests That Response Properties Rather Than Spatial Position Determine Connectivity Between Olfactory Glomeruli." Journal of Neurophysiology 93, no. 6 (June 2005): 3410–17. http://dx.doi.org/10.1152/jn.01285.2004.
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Olfactory responses require the representation of high-dimensional olfactory stimuli within the constraints of two-dimensional neural networks. We used a computational model of the honeybee antennal lobe to test how inhibitory interactions in the antennal lobe should be organized to best reproduce the experimentally measured input-output function in this structure. Our simulations show that a functionally organized inhibitory network, as opposed to an anatomically or all-to-all organized inhibitory network, best reproduces the input-output function of the antennal lobe observed with calcium imaging. In this network, inhibition between each pair of glomeruli was proportional to the similarity of their odor-response profiles. We conclude that contrast enhancement between odorants in the honeybee antennal lobe is best achieved when interglomerular inhibition is organized based on glomerular odor response profiles rather than on anatomical neighborhood relations.
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Arunachalam, Viswanathan, Raha Akhavan-Tabatabaei, and Cristina Lopez. "Results on a Binding Neuron Model and Their Implications for Modified Hourglass Model for Neuronal Network." Computational and Mathematical Methods in Medicine 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/374878.
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The classical models of single neuron like Hodgkin-Huxley point neuron or leaky integrate and fire neuron assume the influence of postsynaptic potentials to last till the neuron fires. Vidybida (2008) in a refreshing departure has proposed models for binding neurons in which the trace of an input is remembered only for a finite fixed period of time after which it is forgotten. The binding neurons conform to the behaviour of real neurons and are applicable in constructing fast recurrent networks for computer modeling. This paper develops explicitly several useful results for a binding neuron like the firing time distribution and other statistical characteristics. We also discuss the applicability of the developed results in constructing a modified hourglass network model in which there are interconnected neurons with excitatory as well as inhibitory inputs. Limited simulation results of the hourglass network are presented.
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Nawrot, Mark, and Randolph Blake. "A neural network model of kinetic depth." Visual Neuroscience 6, no. 3 (March 1991): 219–27. http://dx.doi.org/10.1017/s0952523800006234.
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AbstractWe propose a network model that accounts for the kinetic depth in structure from motion phenomena. Using plausible neural mechanisms, the model accounts for (1) fluctuations in perception when viewing a simple kinetic depth stimulus, (2) disambiguation of this stimulus with stereoscopic information, and (3) subsequent bias of the percept of this stimulus following stereoscopic adaptation. The model comprises two levels: a layer of monocular directionally selective motion detectors that provide input to a second layer of disparity- selective and direction-selective binocular mechanisms. The network of facilitatory and inhibitory connections between binocular mechanisms gives rise to fluctuations in network activity that mimic the fluctuations in perception of kinetic depth in the absence of disparity information. The results of a psychophysical experiment are consistent with the nature of the proposed interactions.
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Horn, D., D. Sagi, and M. Usher. "Segmentation, Binding, and Illusory Conjunctions." Neural Computation 3, no. 4 (December 1991): 510–25. http://dx.doi.org/10.1162/neco.1991.3.4.510.
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We investigate binding within the framework of a model of excitatory and inhibitory cell assemblies that form an oscillating neural network. Our model is composed of two such networks that are connected through their inhibitory neurons. The excitatory cell assemblies represent memory patterns. The latter have different meanings in the two networks, representing two different attributes of an object, such as shape and color. The networks segment an input that contains mixtures of such pairs into staggered oscillations of the relevant activities. Moreover, the phases of the oscillating activities representing the two attributes in each pair lock with each other to demonstrate binding. The system works very well for two inputs, but displays faulty correlations when the number of objects is larger than two. In other words, the network conjoins attributes of different objects, thus showing the phenomenon of “illusory conjunctions,” as in human vision.
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Manzke, Till, Mathias Dutschmann, Gerald Schlaf, Michael Mörschel, Uwe R. Koch, Evgeni Ponimaskin, Olivier Bidon, Peter M. Lalley, and Diethelm W. Richter. "Serotonin targets inhibitory synapses to induce modulation of network functions." Philosophical Transactions of the Royal Society B: Biological Sciences 364, no. 1529 (September 12, 2009): 2589–602. http://dx.doi.org/10.1098/rstb.2009.0068.
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The cellular effects of serotonin (5-HT), a neuromodulator with widespread influences in the central nervous system, have been investigated. Despite detailed knowledge about the molecular biology of cellular signalling, it is not possible to anticipate the responses of neuronal networks to a global action of 5-HT. Heterogeneous expression of various subtypes of serotonin receptors (5-HTR) in a variety of neurons differently equipped with cell-specific transmitter receptors and ion channel assemblies can provoke diverse cellular reactions resulting in various forms of network adjustment and, hence, motor behaviour. Using the respiratory network as a model for reciprocal synaptic inhibition, we demonstrate that 5-HT 1A R modulation primarily affects inhibition through glycinergic synapses. Potentiation of glycinergic inhibition of both excitatory and inhibitory neurons induces a functional reorganization of the network leading to a characteristic change of motor output. The changes in network operation are robust and help to overcome opiate-induced respiratory depression. Hence, 5-HT 1A R activation stabilizes the rhythmicity of breathing during opiate medication of pain.
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Shevtsova, Natalia, and James A. Reggia. "A Neural Network Model of Lateralization during Letter Identification." Journal of Cognitive Neuroscience 11, no. 2 (March 1999): 167–81. http://dx.doi.org/10.1162/089892999563300.
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The causes of cerebral lateralization of cognitive and other functions are currently not well understood. To investigate one aspect of function lateralization, a bihemispheric neural network model for a simple visual identification task was developed that has two parallel interacting paths of information processing. The model is based on commonly accepted concepts concerning neural connectivity, activity dynamics, and synaptic plasticity. A combination of both unsupervised (Hebbian) and supervised (Widrow-Hoff) learning rules is used to train the model to identify a small set of letters presented as input stimuli in the left visual hemifield, in the central position, and in the right visual hemifield. Each visual hemifield projects onto the contralateral hemisphere, and the two hemispheres interact via a simulated corpus callosum. The contribution of each individual hemisphere to the process of input stimuli identification was studied for a variety of underlying asymmetries. The results indicate that multiple asymmetries may cause lateralization. Lateralization occurred toward the side having larger size, higher excitability, or higher learning rate parameters. It appeared more intensively with strong inhibitory callosal connections, supporting the hypothesis that the corpus callosum plays a functionally inhibitory role. The model demonstrates clearly the dependence of lateralization on different hemisphere parameters and suggests that computational models can be useful in better understanding the mechanisms underlying emergence of lateralization.
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Viriyopase, Atthaphon, Raoul-Martin Memmesheimer, and Stan Gielen. "Cooperation and competition of gamma oscillation mechanisms." Journal of Neurophysiology 116, no. 2 (August 1, 2016): 232–51. http://dx.doi.org/10.1152/jn.00493.2015.
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Oscillations of neuronal activity in different frequency ranges are thought to reflect important aspects of cortical network dynamics. Here we investigate how various mechanisms that contribute to oscillations in neuronal networks may interact. We focus on networks with inhibitory, excitatory, and electrical synapses, where the subnetwork of inhibitory interneurons alone can generate interneuron gamma (ING) oscillations and the interactions between interneurons and pyramidal cells allow for pyramidal-interneuron gamma (PING) oscillations. What type of oscillation will such a network generate? We find that ING and PING oscillations compete: The mechanism generating the higher oscillation frequency “wins”; it determines the frequency of the network oscillation and suppresses the other mechanism. For type I interneurons, the network oscillation frequency is equal to or slightly above the higher of the ING and PING frequencies in corresponding reduced networks that can generate only either of them; if the interneurons belong to the type II class, it is in between. In contrast to ING and PING, oscillations mediated by gap junctions and oscillations mediated by inhibitory synapses may cooperate or compete, depending on the type (I or II) of interneurons and the strengths of the electrical and chemical synapses. We support our computer simulations by a theoretical model that allows a full theoretical analysis of the main results. Our study suggests experimental approaches to deciding to what extent oscillatory activity in networks of interacting excitatory and inhibitory neurons is dominated by ING or PING oscillations and of which class the participating interneurons are.
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Matadi, Maba Boniface. "Application of Lie Symmetry to a Mathematical Model that Describes a Cancer Sub-Network." Symmetry 14, no. 2 (February 17, 2022): 400. http://dx.doi.org/10.3390/sym14020400.
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In this paper, a mathematical model of a cancer sub-network is analysed from the view point of Lie symmetry methods. This model discusses a human cancer cell which is developed due to the dysfunction of some genes at the R-checkpoint during the cell cycle. The primary purpose of this paper is to apply the techniques of Lie symmetry to the model and present some approximated solutions for the three-dimensional system of first-order ordinary differential equations describing a cancer sub-network. The result shows that the phosphatase gene (Cdc25A) regulates the cyclin-dependent kinases inhibitor (P27Kip1). Furthermore, this research discovered that the activity that reverses the inhibitory effects on cell cycle progression at the R-checkpoint initiates a pathway.
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De Schutter, E., J. D. Angstadt, and R. L. Calabrese. "A model of graded synaptic transmission for use in dynamic network simulations." Journal of Neurophysiology 69, no. 4 (April 1, 1993): 1225–35. http://dx.doi.org/10.1152/jn.1993.69.4.1225.
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1. The heartbeat central pattern-generating network of the medicinal leech contains elemental neural oscillators, comprising reciprocally inhibitory pairs of segmental heart interneurons, that use graded as well as spike-mediated synaptic transmission. We are in the process of developing a general computer model of this pattern generator. Our modeling goal is to explore the interaction of membrane currents and synaptic transmission that promote oscillation in heart interneurons. As a first step toward this goal, we have developed a computer model of graded synaptic transmission between reciprocally inhibitory heart interneurons. Previously gathered voltage-clamp data of presynaptic Ca2+ currents and simultaneous postsynaptic currents and potentials (5 mM external [Ca2+]) were used as the bases of the model. 2. We assumed that presynaptic Ca2+ current was composed of distinct fast (ICaF) and slow (Icas) components because there are two distinct time courses of inactivation for this current. We fitted standard Hodgkin-Huxley equations (Eq. 1 and 2, APPENDIX) to these components using first-order activation and inactivation kinetics. 3. Graded synaptic transfer in the model is based on calculation of a dimensionless variable [P]. A portion of both IcaF and ICaS determined by a factor A contributes to [P], and a removal factor B decreases [P] (Eq. 4, APPENDIX). [P] can be roughly equated to the [Ca2+] in an unspecified volume that is effective in causing transmitter release. Transmitter release, and thus postsynaptic conductance, is related to [P]3 (Eq. 3, APPENDIX). 4. We adapted our model to voltage-clamp data gathered at physiological external [Ca2+] (2.0 mM) and tested it for shorter presynaptic voltage steps. Presynaptic Ca2+ currents and synaptic transfer were well simulated under all conditions. 5. The graded synaptic transfer model could be used in a network simulation to reproduce the oscillatory activity of a reciprocally inhibitory pair of heart interneurons. Because synaptic transmission in the model is an explicit function of presynaptic Ca2+ current, the model should prove useful to explore the interaction between membrane currents and synaptic transmission that promote and modulate oscillation in reciprocally inhibitory heart interneurons.
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Schall, Jeffrey D., Thomas J. Palmeri, and Gordon D. Logan. "Models of inhibitory control." Philosophical Transactions of the Royal Society B: Biological Sciences 372, no. 1718 (February 27, 2017): 20160193. http://dx.doi.org/10.1098/rstb.2016.0193.
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We survey models of response inhibition having different degrees of mathematical, computational and neurobiological specificity and generality. The independent race model accounts for performance of the stop-signal or countermanding task in terms of a race between GO and STOP processes with stochastic finishing times. This model affords insights into neurophysiological mechanisms that are reviewed by other authors in this volume. The formal link between the abstract GO and STOP processes and instantiating neural processes is articulated through interactive race models consisting of stochastic accumulator GO and STOP units. This class of model provides quantitative accounts of countermanding performance and replicates the dynamics of neural activity producing that performance. The interactive race can be instantiated in a network of biophysically plausible spiking excitatory and inhibitory units. Other models seek to account for interactions between units in frontal cortex, basal ganglia and superior colliculus. The strengths, weaknesses and relationships of the different models will be considered. We will conclude with a brief survey of alternative modelling approaches and a summary of problems to be addressed including accounting for differences across effectors, species, individuals, task conditions and clinical deficits. This article is part of the themed issue ‘Movement suppression: brain mechanisms for stopping and stillness’.
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Wang, Aiqun, and Nanning Zheng. "Multiplicative inhibitory velocity detector and multi-velocity motion detection neural network model." Journal of Computer Science and Technology 13, no. 1 (January 1998): 41–54. http://dx.doi.org/10.1007/bf02946613.
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TATENO, KATSUMI, HIDEYUKI TOMONARI, HATSUO HAYASHI, and SATORU ISHIZUKA. "PHASE DEPENDENT TRANSITION BETWEEN MULTISTABLE STATES IN A NEURAL NETWORK WITH RECIPROCAL INHIBITION." International Journal of Bifurcation and Chaos 14, no. 05 (May 2004): 1559–75. http://dx.doi.org/10.1142/s0218127404010138.
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We studied multistable oscillatory states of a small neural network model and switching of an oscillatory mode. In the present neural network model, two pacemaker neurons are reciprocally inhibited with conduction delay; one pacemaker neuron inhibits the other via an inhibitory nonpacemaker interneuron, and vice versa. The small network model shows bifurcations from quasi-periodic oscillation to chaos via period 3 with increase in the synaptic weight of the reciprocal inhibition. The route to chaos in the network model is different from that in the single pacemaker neuron. The network model exhibits several multistable states. In a regime of a weak inhibitory connection, in-phase beat, out-of-phase beat (period 3), and chaotic oscillation coexist at the multistable state. We can switch an oscillatory mode by an excitatory synaptic input to one of the pacemaker neurons through an afferent path. In a strong inhibitory connection regime, in-phase beat and out-of-phase beat (period 4) coexist at the multistable state. An excitatory synaptic input through the afferent path leads to the transition from the in-phase beat to the out-of-phase beat. The transition from the out-of-phase beat to the in-phase beat is induced by an inhibitory synaptic input via interneurons. A conduction delay, furthermore, causes the spontaneous transition from the in-phase beat to the out-of-phase beat. These transitions can be explained by phase response curves.
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Müller, Thomas H., D. Swandulla, and H. U. Zeilhofer. "Synaptic Connectivity in Cultured Hypothalamic Neuronal Networks." Journal of Neurophysiology 77, no. 6 (June 1, 1997): 3218–25. http://dx.doi.org/10.1152/jn.1997.77.6.3218.
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Müller, Thomas H., D. Swandulla, and H. U. Zeilhofer. Synaptic connectivity in cultured hypothalamic neuronal networks. J. Neurophysiol. 77: 3218–3225, 1997. We have developed a novel approach to analyze the synaptic connectivity of spontaneously active networks of hypothalamic neurons in culture. Synaptic connections were identified by recording simultaneously from pairs of neurons using the whole cell configuration of the patch-clamp technique and testing for evoked postsynaptic current responses to electrical stimulation of one of the neurons. Excitatory and inhibitory responses were distinguished on the basis of their voltage and time dependence. The distribution of latencies between presynaptic stimulation and postsynaptic response showed multiple peaks at regular intervals, suggesting that responses via both monosynaptic and polysynaptic paths were recorded. The probability that an excitatory event is transmitted to another excitatory neuron and results in an above-threshold stimulation was found to be only one in three to four. This low value indicates that in addition to evoked synaptic responses other sources of excitatory drive must contribute to the spontaneous activity observed in these networks. The various types of synaptic connections (excitatory and inhibitory, monosynaptic, and polysynaptic) were counted, and the observations analyzed using a probabilistic model of the network structure. This analysis provides estimates for the ratio of inhibitory to excitatory neurons in the network (1:1.5) and for the ratio of postsynaptic cells receiving input from a single GABAergic or glutamatergic neuron (3:1). The total number of inhibitory synaptic connections was twice that of excitatory connections. Cell pairs mutually connected by an excitatory and an inhibitory synapse occurred significantly more often than predicted by a random process. These results suggests that the formation of neuronal networks in vitro is controlled by cellular mechanisms that favor inhibitory connections in general and specifically enhance the formation of reciprocal connections between pairs of excitatory and inhibitory neurons. These mechanisms may contribute to network formation and function in vivo.
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Traub, R. D., R. Miles, and R. K. Wong. "Models of synchronized hippocampal bursts in the presence of inhibition. I. Single population events." Journal of Neurophysiology 58, no. 4 (October 1, 1987): 739–51. http://dx.doi.org/10.1152/jn.1987.58.4.739.
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1. We constructed model networks with 520 or 1,020 cells intended to represent the CA3 region of the hippocampus. Model neurons were simulated in enough detail to reproduce intrinsic bursting and the electrotonic flow of currents along dendritic cables. Neurons exerted either excitatory or inhibitory postsynaptic actions on other cells. The network models were simulated with different levels of excitatory and inhibitory synaptic strengths in order to study epileptic and other interesting collective behaviors in the system. 2. Excitatory synapses between neurons in the network were powerful enough so that burst firing in a presynaptic neuron would evoke bursting in its connected cells. Since orthodromic or antidromic stimulation evokes both a fast and a slow phase of inhibition, two types of inhibitory cells were simulated. The properties of these inhibitory cells were modeled to resemble those of two types of inhibitory cells characterized by dual intracellular recordings in the slice preparation. 3. With fast inhibition totally blocked, a stimulus to a single cell lead to a synchronized population burst. Thus the principles of our epileptic synchronization model, developed earlier, apply even when slow inhibitory postsynaptic potentials (IPSPs) are present, as apparently occurs in the epileptic hippocampal slice. The model performs in this way because bursting can propagate through several generations in the network before slow inhibition builds up enough to block burst propagation. This can occur, however, only if connectivity is sufficiently large. With very low connection densities, slow IPSPs will prevent the development of full synchronization. 4. We performed multiple simulations in which the fast inhibitory conductance strength was kept fixed at various levels while the strength of the excitatory synapses was varied. In each simulation, we stimulated either one or four cells. For each level of inhibition, the peak number of cells bursting depended sensitively on excitatory synaptic strength, showing a sudden increase as this strength reached a critical level. The critical excitation, which depended on the level of inhibition, corresponded to the level at which bursting can propagate from cell to cell at the particular level of inhibition. 5. We performed an analogous series of simulations in which the strength of excitatory synapses was held constant while the strength of fast inhibitory synapses was varied, stimulating a single neuron in each case. These simulations correspond to experiments that have been done in the hippocampal slice as low doses of picrotoxin are washed into a slice, gradually abolishing fast inhibition.(ABSTRACT TRUNCATED AT 400 WORDS)
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Wang, Yuan, Xia Shi, Bo Cheng, and Junliang Chen. "Neural Dynamics and Gamma Oscillation on a Hybrid Excitatory-Inhibitory Complex Network (Student Abstract)." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 10 (April 3, 2020): 13957–58. http://dx.doi.org/10.1609/aaai.v34i10.7251.
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This paper investigates the neural dynamics and gamma oscillation on a complex network with excitatory and inhibitory neurons (E-I network), as such network is ubiquitous in the brain. The system consists of a small-world network of neurons, which are emulated by Izhikevich model. Moreover, mixed Regular Spiking (RS) and Chattering (CH) neurons are considered to imitate excitatory neurons, and Fast Spiking (FS) neurons are used to mimic inhibitory neurons. Besides, the relationship between synchronization and gamma rhythm is explored by adjusting the critical parameters of our model. Experiments visually demonstrate that the gamma oscillations are generated by synchronous behaviors of our neural network. We also discover that the Chattering(CH) excitatory neurons can make the system easier to synchronize.
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Cáceres, María J., and Ricarda Schneider. "Analysis and numerical solver for excitatory-inhibitory networks with delay and refractory periods." ESAIM: Mathematical Modelling and Numerical Analysis 52, no. 5 (September 2018): 1733–61. http://dx.doi.org/10.1051/m2an/2018014.
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The network of noisy leaky integrate and fire (NNLIF) model is one of the simplest self-contained mean-field models considered to describe the behavior of neural networks. Even so, in studying its mathematical properties some simplifications are required [Cáceres and Perthame, J. Theor. Biol. 350 (2014) 81–89; Cáceres and Schneider, Kinet. Relat. Model. 10 (2017) 587–612; Cáceres, Carrillo and Perthame, J. Math. Neurosci. 1 (2011) 7] which disregard crucial phenomena. In this work we deal with the general NNLIF model without simplifications. It involves a network with two populations (excitatory and inhibitory), with transmission delays between the neurons and where the neurons remain in a refractory state for a certain time. In this paper we study the number of steady states in terms of the model parameters, the long time behaviour via the entropy method and Poincaré’s inequality, blow-up phenomena, and the importance of transmission delays between excitatory neurons to prevent blow-up and to give rise to synchronous solutions. Besides analytical results, we present a numerical solver, based on high order flux-splitting WENO schemes and an explicit third order TVD Runge-Kutta method, in order to describe the wide range of phenomena exhibited by the network: blow-up, asynchronous/synchronous solutions and instability/stability of the steady states. The solver also allows us to observe the time evolution of the firing rates, refractory states and the probability distributions of the excitatory and inhibitory populations.
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Akhmet, Marat, Madina Tleubergenova, Roza Seilova, and Zakhira Nugayeva. "Poisson Stability in Symmetrical Impulsive Shunting Inhibitory Cellular Neural Networks with Generalized Piecewise Constant Argument." Symmetry 14, no. 9 (August 23, 2022): 1754. http://dx.doi.org/10.3390/sym14091754.
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In the paper, shunting inhibitory cellular neural networks with impulses and the generalized piecewise constant argument are under discussion. The main modeling novelty is that the impulsive part of the systems is symmetrical to the differential part. Moreover, the model depends not only on the continuous time, but also the generalized piecewise constant argument. The process is subdued to Poisson stable inputs, which cause the new type of recurrent signals. The method of included intervals, recently introduced approach of recurrent motions checking, is effectively utilized. The existence and asymptotic properties of the unique Poisson stable motion are investigated. Simulation examples for results are provided. Finally, comparing impulsive shunting inhibitory cellular neural networks with former neural network models, we discuss the significance of the components of our model.
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Sanchez-Vives, Maria V., Maurizio Mattia, Albert Compte, Maria Perez-Zabalza, Milena Winograd, Vanessa F. Descalzo, and Ramon Reig. "Inhibitory Modulation of Cortical Up States." Journal of Neurophysiology 104, no. 3 (September 2010): 1314–24. http://dx.doi.org/10.1152/jn.00178.2010.
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The balance between excitation and inhibition is critical in the physiology of the cerebral cortex. To understand the influence of inhibitory control on the emergent activity of the cortical network, inhibition was progressively blocked in a slice preparation that generates spontaneous rhythmic up states at a similar frequency to those occurring in vivo during slow-wave sleep or anesthesia. Progressive removal of inhibition induced a parametric shortening of up state duration and elongation of the down states, the frequency of oscillations decaying. Concurrently, a gradual increase in the network firing rate during up states occurred. The slope of transitions between up and down states was quantified for different levels of inhibition. The slope of upward transitions reflects the recruitment of the local network and was progressively increased when inhibition was decreased, whereas the speed of activity propagation became faster. Removal of inhibition eventually resulted in epileptiform activity. Whereas gradual reduction of inhibition induced linear changes in up/down states and their propagation, epileptiform activity was the result of a nonlinear transformation. A computational network model showed that strong recurrence plus activity-dependent hyperpolarizing currents were sufficient to account for the observed up state modulations and predicted an increase in activity-dependent hyperpolarization following up states when inhibition was decreased, which was confirmed experimentally.
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Börgers, Christoph, Steven Epstein, and Nancy J. Kopell. "Gamma oscillations mediate stimulus competition and attentional selection in a cortical network model." Proceedings of the National Academy of Sciences 105, no. 46 (November 12, 2008): 18023–28. http://dx.doi.org/10.1073/pnas.0809511105.
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Simultaneous presentation of multiple stimuli can reduce the firing rates of neurons in extrastriate visual cortex below the rate elicited by a single preferred stimulus. We describe computational results suggesting how this remarkable effect may arise from strong excitatory drive to a substantial local population of fast-spiking inhibitory interneurons, which can lead to a loss of coherence in that population and thereby raise the effectiveness of inhibition. We propose that in attentional states fast-spiking interneurons may be subject to a bath of inhibition resulting from cholinergic activation of a second class of inhibitory interneurons, restoring conditions needed for gamma rhythmicity. Oscillations and coherence are emergent features, not assumptions, in our model. The gamma oscillations in turn support stimulus competition. The mechanism is a form of “oscillatory selection,” in which neural interactions change phase relationships that regulate firing rates, and attention shapes those neural interactions.
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Farah, Firas H., Vasily Grigorovsky, and Berj L. Bardakjian. "Coupled Oscillators Model of Hyperexcitable Neuroglial Networks." International Journal of Neural Systems 29, no. 03 (March 18, 2019): 1850041. http://dx.doi.org/10.1142/s0129065718500417.
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Glial populations within neuronal networks of the brain have recently gained much interest in the context of hyperexcitability and epilepsy. In this paper, we present an oscillator-based neuroglial model capable of generating Spontaneous Electrical Discharges (SEDs) in hyperexcitable conditions. The network is composed of 16 coupled Cognitive Rhythm Generators (CRGs), which are oscillator-based mathematical constructs previously described by our research team. CRGs are well-suited for modeling assemblies of excitable cells, and in this network, each represents one of the following populations: excitatory pyramidal cells, inhibitory interneurons, astrocytes, and microglia. We investigated various pathways leading to hyperexcitability, and our results suggest an important role for astrocytes and microglia in the generation of SEDs of various durations. Analysis of the resultant SEDs revealed two underlying duration distributions with differing properties. Particularly, short and long SEDs are associated with deterministic and random underlying processes, respectively. The mesoscale of this model makes it well-suited for (a) the elucidation of glia-related hypotheses in hyperexcitable conditions, (b) use as a testing platform for neuromodulation purposes, and (c) a hardware implementation for closed-loop neuromodulation.
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Kiss, Tamás, Gergő Orbán, Máté Lengyel, and Péter Érdi. "Intrahippocampal gamma and theta rhythm generation in a network model of inhibitory interneurons." Neurocomputing 38-40 (June 2001): 713–19. http://dx.doi.org/10.1016/s0925-2312(01)00358-7.
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Verret, Laure, Edward O. Mann, Giao B. Hang, Albert M. I. Barth, Inma Cobos, Kaitlyn Ho, Nino Devidze, et al. "Inhibitory Interneuron Deficit Links Altered Network Activity and Cognitive Dysfunction in Alzheimer Model." Cell 149, no. 3 (April 2012): 708–21. http://dx.doi.org/10.1016/j.cell.2012.02.046.
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Horn, D., and M. Usher. "EXCITATORY–INHIBITORY NETWORKS WITH DYNAMICAL THRESHOLDS." International Journal of Neural Systems 01, no. 03 (January 1990): 249–57. http://dx.doi.org/10.1142/s0129065790000151.
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We investigate feedback networks containing excitatory and inhibitory neurons. The couplings between the neurons follow a Hebbian rule in which the memory patterns are encoded as cell assemblies of the excitatory neurons. Using disjoint patterns, we study the attractors of this model and point out the importance of mixed states. The latter become dominant at temperatures above 0.25. We use both numerical simulations and an analytic approach for our investigation. The latter is based on differential equations for the activity of the different memory patterns in the network configuration. Allowing the excitatory thresholds to develop dynamic features which correspond to fatigue of individual neurons, we obtain motion in pattern space, the space of all memories. The attractors turn into transients leading to chaotic motion for appropriate values of the dynamical parameters. The motion can be guided by overlaps between patterns, resembling a process of free associative thinking in the absence of any input.