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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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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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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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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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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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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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Marinazzo, Daniele, Hilbert J. Kappen, and Stan C. A. M. Gielen. "Input-Driven Oscillations in Networks with Excitatory and Inhibitory Neurons with Dynamic Synapses." Neural Computation 19, no. 7 (July 2007): 1739–65. http://dx.doi.org/10.1162/neco.2007.19.7.1739.
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Previous work has shown that networks of neurons with two coupled layers of excitatory and inhibitory neurons can reveal oscillatory activity. For example, Börgers and Kopell (2003) have shown that oscillations occur when the excitatory neurons receive a sufficiently large input. A constant drive to the excitatory neurons is sufficient for oscillatory activity. Other studies (Doiron, Chacron, Maler, Longtin, & Bastian, 2003; Doiron, Lindner, Longtin, Maler, & Bastian, 2004) have shown that networks of neurons with two coupled layers of excitatory and inhibitory neurons reveal oscillatory activity only if the excitatory neurons receive correlated input, regardless of the amount of excitatory input. In this study, we show that these apparently contradictory results can be explained by the behavior of a single model operating in different regimes of parameter space. Moreover, we show that adding dynamic synapses in the inhibitory feedback loop provides a robust network behavior over a broad range of stimulus intensities, contrary to that of previous models. A remarkable property of the introduction of dynamic synapses is that the activity of the network reveals synchronized oscillatory components in the case of correlated input, but also reflects the temporal behavior of the input signal to the excitatory neurons. This allows the network to encode both the temporal characteristics of the input and the presence of spatial correlations in the input simultaneously.
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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.
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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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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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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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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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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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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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Hu, Xiaolin, and Zhigang Zeng. "Bridging the Functional and Wiring Properties of V1 Neurons Through Sparse Coding." Neural Computation 34, no. 1 (January 1, 2022): 104–37. http://dx.doi.org/10.1162/neco_a_01453.
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Abstract The functional properties of neurons in the primary visual cortex (V1) are thought to be closely related to the structural properties of this network, but the specific relationships remain unclear. Previous theoretical studies have suggested that sparse coding, an energy-efficient coding method, might underlie the orientation selectivity of V1 neurons. We thus aimed to delineate how the neurons are wired to produce this feature. We constructed a model and endowed it with a simple Hebbian learning rule to encode images of natural scenes. The excitatory neurons fired sparsely in response to images and developed strong orientation selectivity. After learning, the connectivity between excitatory neuron pairs, inhibitory neuron pairs, and excitatory-inhibitory neuron pairs depended on firing pattern and receptive field similarity between the neurons. The receptive fields (RFs) of excitatory neurons and inhibitory neurons were well predicted by the RFs of presynaptic excitatory neurons and inhibitory neurons, respectively. The excitatory neurons formed a small-world network, in which certain local connection patterns were significantly overrepresented. Bidirectionally manipulating the firing rates of inhibitory neurons caused linear transformations of the firing rates of excitatory neurons, and vice versa. These wiring properties and modulatory effects were congruent with a wide variety of data measured in V1, suggesting that the sparse coding principle might underlie both the functional and wiring properties of V1 neurons.
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Miehl, Christoph, and Julijana Gjorgjieva. "Stability and learning in excitatory synapses by nonlinear inhibitory plasticity." PLOS Computational Biology 18, no. 12 (December 2, 2022): e1010682. http://dx.doi.org/10.1371/journal.pcbi.1010682.
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Synaptic changes are hypothesized to underlie learning and memory formation in the brain. But Hebbian synaptic plasticity of excitatory synapses on its own is unstable, leading to either unlimited growth of synaptic strengths or silencing of neuronal activity without additional homeostatic mechanisms. To control excitatory synaptic strengths, we propose a novel form of synaptic plasticity at inhibitory synapses. Using computational modeling, we suggest two key features of inhibitory plasticity, dominance of inhibition over excitation and a nonlinear dependence on the firing rate of postsynaptic excitatory neurons whereby inhibitory synaptic strengths change with the same sign (potentiate or depress) as excitatory synaptic strengths. We demonstrate that the stable synaptic strengths realized by this novel inhibitory plasticity model affects excitatory/inhibitory weight ratios in agreement with experimental results. Applying a disinhibitory signal can gate plasticity and lead to the generation of receptive fields and strong bidirectional connectivity in a recurrent network. Hence, a novel form of nonlinear inhibitory plasticity can simultaneously stabilize excitatory synaptic strengths and enable learning upon disinhibition.
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Morita, Kenji, Masato Okada, and Kazuyuki Aihara. "Selectivity and Stability via Dendritic Nonlinearity." Neural Computation 19, no. 7 (July 2007): 1798–853. http://dx.doi.org/10.1162/neco.2007.19.7.1798.
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Inspired by recent studies regarding dendritic computation, we constructed a recurrent neural network model incorporating dendritic lateral inhibition. Our model consists of an input layer and a neuron layer that includes excitatory cells and an inhibitory cell; this inhibitory cell is activated by the pooled activities of all the excitatory cells, and it in turn inhibits each dendritic branch of the excitatory cells that receive excitations from the input layer. Dendritic nonlinear operation consisting of branch-specifically rectified inhibition and saturation is described by imposing nonlinear transfer functions before summation over the branches. In this model with sufficiently strong recurrent excitation, on transiently presenting a stimulus that has a high correlation with feed- forward connections of one of the excitatory cells, the corresponding cell becomes highly active, and the activity is sustained after the stimulus is turned off, whereas all the other excitatory cells continue to have low activities. But on transiently presenting a stimulus that does not have high correlations with feedforward connections of any of the excitatory cells, all the excitatory cells continue to have low activities. Interestingly, such stimulus-selective sustained response is preserved for a wide range of stimulus intensity. We derive an analytical formulation of the model in the limit where individual excitatory cells have an infinite number of dendritic branches and prove the existence of an equilibrium point corresponding to such a balanced low-level activity state as observed in the simulations, whose stability depends solely on the signal-to-noise ratio of the stimulus. We propose this model as a model of stimulus selectivity equipped with self-sustainability and intensity-invariance simultaneously, which was difficult in the conventional competitive neural networks with a similar degree of complexity in their network architecture. We discuss the biological relevance of the model in a general framework of computational neuroscience.
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Ahmadian, Yashar, Daniel B. Rubin, and Kenneth D. Miller. "Analysis of the Stabilized Supralinear Network." Neural Computation 25, no. 8 (August 2013): 1994–2037. http://dx.doi.org/10.1162/neco_a_00472.
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We study a rate-model neural network composed of excitatory and inhibitory neurons in which neuronal input-output functions are power laws with a power greater than 1, as observed in primary visual cortex. This supralinear input-output function leads to supralinear summation of network responses to multiple inputs for weak inputs. We show that for stronger inputs, which would drive the excitatory subnetwork to instability, the network will dynamically stabilize provided feedback inhibition is sufficiently strong. For a wide range of network and stimulus parameters, this dynamic stabilization yields a transition from supralinear to sublinear summation of network responses to multiple inputs. We compare this to the dynamic stabilization in the balanced network, which yields only linear behavior. We more exhaustively analyze the two-dimensional case of one excitatory and one inhibitory population. We show that in this case, dynamic stabilization will occur whenever the determinant of the weight matrix is positive and the inhibitory time constant is sufficiently small, and analyze the conditions for supersaturation, or decrease of firing rates with increasing stimulus contrast (which represents increasing input firing rates). In work to be presented elsewhere, we have found that this transition from supralinear to sublinear summation can explain a wide variety of nonlinearities in cerebral cortical processing.
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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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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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Netoff, Theoden I., Matthew I. Banks, Alan D. Dorval, Corey D. Acker, Julie S. Haas, Nancy Kopell, and John A. White. "Synchronization in Hybrid Neuronal Networks of the Hippocampal Formation." Journal of Neurophysiology 93, no. 3 (March 2005): 1197–208. http://dx.doi.org/10.1152/jn.00982.2004.
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Understanding the mechanistic bases of neuronal synchronization is a current challenge in quantitative neuroscience. We studied this problem in two putative cellular pacemakers of the mammalian hippocampal theta rhythm: glutamatergic stellate cells (SCs) of the medial entorhinal cortex and GABAergic oriens-lacunosum-moleculare (O-LM) interneurons of hippocampal region CA1. We used two experimental methods. First, we measured changes in spike timing induced by artificial synaptic inputs applied to individual neurons. We then measured responses of free-running hybrid neuronal networks, consisting of biological neurons coupled (via dynamic clamp) to biological or virtual counterparts. Results from the single-cell experiments predicted network behaviors well and are compatible with previous model-based predictions of how specific membrane mechanisms give rise to empirically measured synchronization behavior. Both cell types phase lock stably when connected via homogeneous excitatory-excitatory (E-E) or inhibitory-inhibitory (I-I) connections. Phase-locked firing is consistently synchronous for either cell type with E-E connections and nearly anti-synchronous with I-I connections. With heterogeneous connections (e.g., excitatory-inhibitory, as might be expected if members of a given population had heterogeneous connections involving intermediate interneurons), networks often settled into phase locking that was either stable or unstable, depending on the order of firing of the two cells in the hybrid network. Our results imply that excitatory SCs, but not inhibitory O-LM interneurons, are capable of synchronizing in phase via monosynaptic mutual connections of the biologically appropriate polarity. Results are largely independent of synaptic strength and synaptic kinetics, implying that our conclusions are robust and largely unaffected by synaptic plasticity.
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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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Qi, Yi, Rubin Wang, Xianfa Jiao, and Ying Du. "The Effect of Inhibitory Neuron on the Evolution Model of Higher-Order Coupling Neural Oscillator Population." Computational and Mathematical Methods in Medicine 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/174274.
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We proposed a higher-order coupling neural network model including the inhibitory neurons and examined the dynamical evolution of average number density and phase-neural coding under the spontaneous activity and external stimulating condition. The results indicated that increase of inhibitory coupling strength will cause decrease of average number density, whereas increase of excitatory coupling strength will cause increase of stable amplitude of average number density. Whether the neural oscillator population is able to enter the new synchronous oscillation or not is determined by excitatory and inhibitory coupling strength. In the presence of external stimulation, the evolution of the average number density is dependent upon the external stimulation and the coupling term in which the dominator will determine the final evolution.
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Xu, Ailei, Ying Du, Rubin Wang, and Jinde Cao. "Interaction between Different Cells in Olfactory Bulb and Synchronous Kinematic Analysis." Discrete Dynamics in Nature and Society 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/808792.
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Olfactory bulb plays an important part in signal encoding of olfactory system. The interaction between excitatory mitral cell (MC) and inhibitory granule cell (GC) is particularly crucial. In this paper, the current situation of synchronous oscillation in the network of olfactory system is firstly introduced. Then we set up a dynamical model of MC and GC in the olfactory bulb. The simulation shows the firing patterns of single MC and single GC, as well as these two kinds of cells having a coupling relationship. The results indicate that MCs have an excitatory effect on GCs, and GCs have an inhibitory effect on MCs. The firing pattern varies with different synaptic strength. In addition, we set up simple olfactory network models, discussing the influence of ring-like and grid-like neuronal networks of GCs on the synchronization of two MCs. Different types of firing synchronization are quantified by means of ISI-distance method. The numerical analysis indicates that grid-like neuronal network can make MCs synchronize better.
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Garrido, Jesús A., Niceto R. Luque, Silvia Tolu, and Egidio D’Angelo. "Oscillation-Driven Spike-Timing Dependent Plasticity Allows Multiple Overlapping Pattern Recognition in Inhibitory Interneuron Networks." International Journal of Neural Systems 26, no. 05 (June 8, 2016): 1650020. http://dx.doi.org/10.1142/s0129065716500209.
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The majority of operations carried out by the brain require learning complex signal patterns for future recognition, retrieval and reuse. Although learning is thought to depend on multiple forms of long-term synaptic plasticity, the way this latter contributes to pattern recognition is still poorly understood. Here, we have used a simple model of afferent excitatory neurons and interneurons with lateral inhibition, reproducing a network topology found in many brain areas from the cerebellum to cortical columns. When endowed with spike-timing dependent plasticity (STDP) at the excitatory input synapses and at the inhibitory interneuron–interneuron synapses, the interneurons rapidly learned complex input patterns. Interestingly, induction of plasticity required that the network be entrained into theta-frequency band oscillations, setting the internal phase-reference required to drive STDP. Inhibitory plasticity effectively distributed multiple patterns among available interneurons, thus allowing the simultaneous detection of multiple overlapping patterns. The addition of plasticity in intrinsic excitability made the system more robust allowing self-adjustment and rescaling in response to a broad range of input patterns. The combination of plasticity in lateral inhibitory connections and homeostatic mechanisms in the inhibitory interneurons optimized mutual information (MI) transfer. The storage of multiple complex patterns in plastic interneuron networks could be critical for the generation of sparse representations of information in excitatory neuron populations falling under their control.
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Kim, Christopher M., and Carson C. Chow. "Training Spiking Neural Networks in the Strong Coupling Regime." Neural Computation 33, no. 5 (April 13, 2021): 1199–233. http://dx.doi.org/10.1162/neco_a_01379.
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Abstract Recurrent neural networks trained to perform complex tasks can provide insight into the dynamic mechanism that underlies computations performed by cortical circuits. However, due to a large number of unconstrained synaptic connections, the recurrent connectivity that emerges from network training may not be biologically plausible. Therefore, it remains unknown if and how biological neural circuits implement dynamic mechanisms proposed by the models. To narrow this gap, we developed a training scheme that, in addition to achieving learning goals, respects the structural and dynamic properties of a standard cortical circuit model: strongly coupled excitatory-inhibitory spiking neural networks. By preserving the strong mean excitatory and inhibitory coupling of initial networks, we found that most of trained synapses obeyed Dale's law without additional constraints, exhibited large trial-to-trial spiking variability, and operated in inhibition-stabilized regime. We derived analytical estimates on how training and network parameters constrained the changes in mean synaptic strength during training. Our results demonstrate that training recurrent neural networks subject to strong coupling constraints can result in connectivity structure and dynamic regime relevant to cortical circuits.
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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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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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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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Li, Licong, Jin Zhou, Hongji Sun, Jing Liu, Hongrui Wang, Xiuling Liu, and Changyong Wang. "A Computational Model to Investigate GABA-Activated Astrocyte Modulation of Neuronal Excitation." Computational and Mathematical Methods in Medicine 2020 (September 15, 2020): 1–13. http://dx.doi.org/10.1155/2020/8750167.
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Gamma-aminobutyric acid (GABA) is critical for proper neural network function and can activate astrocytes to induce neuronal excitability; however, the mechanism by which astrocytes transform inhibitory signaling to excitatory enhancement remains unclear. Computational modeling can be a powerful tool to provide further understanding of how GABA-activated astrocytes modulate neuronal excitation. In the present study, we implemented a biophysical neuronal network model to investigate the effects of astrocytes on excitatory pre- and postsynaptic terminals following exposure to increasing concentrations of external GABA. The model completely describes the effects of GABA on astrocytes and excitatory presynaptic terminals within the framework of glutamatergic gliotransmission according to neurophysiological findings. Utilizing this model, our results show that astrocytes can rapidly respond to incoming GABA by inducing Ca2+ oscillations and subsequent gliotransmitter glutamate release. Elevation in GABA concentrations not only naturally decreases neuronal spikes but also enhances astrocytic glutamate release, which leads to an increase in astrocyte-mediated presynaptic release and postsynaptic slow inward currents. Neuronal excitation induced by GABA-activated astrocytes partly counteracts the inhibitory effect of GABA. Overall, the model helps to increase knowledge regarding the involvement of astrocytes in neuronal regulation using simulated bath perfusion of GABA, which may be useful for exploring the effects of GABA-type antiepileptic drugs.
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Lu, Lulu, Zhuoheng Gao, Zhouchao Wei, and Ming Yi. "Working memory depends on the excitatory–inhibitory balance in neuron–astrocyte network." Chaos: An Interdisciplinary Journal of Nonlinear Science 33, no. 1 (January 2023): 013127. http://dx.doi.org/10.1063/5.0126890.
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Previous studies have shown that astrocytes are involved in information processing and working memory (WM) in the central nervous system. Here, the neuron–astrocyte network model with biological properties is built to study the effects of excitatory–inhibitory balance and neural network structures on WM tasks. It is found that the performance metrics of WM tasks under the scale-free network are higher than other network structures, and the WM task can be successfully completed when the proportion of excitatory neurons in the network exceeds 30%. There exists an optimal region for the proportion of excitatory neurons and synaptic weight that the memory performance metrics of the WM tasks are higher. The multi-item WM task shows that the spatial calcium patterns for different items overlap significantly in the astrocyte network, which is consistent with the formation of cognitive memory in the brain. Moreover, complex image tasks show that cued recall can significantly reduce systematic noise and maintain the stability of the WM tasks. The results may contribute to understand the mechanisms of WM formation and provide some inspirations into the dynamic storage and recall of memory.
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Lefebvre, J., A. Longtin, and V. G. Leblanc. "Oscillatory response in a sensory network of ON and OFF cells with instantaneous and delayed recurrent connections." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 368, no. 1911 (January 28, 2010): 455–67. http://dx.doi.org/10.1098/rsta.2009.0229.
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A neural field model with multiple cell-to-cell feedback connections is investigated. Our model incorporates populations of ON and OFF cells, receiving sensory inputs with direct and inverted polarity, respectively. Oscillatory responses to spatially localized stimuli are found to occur via Andronov–Hopf bifurcations of stationary activity. We explore the impact of multiple delayed feedback components as well as additional excitatory and/or inhibitory non-delayed recurrent signals on the instability threshold. Paradoxically, instantaneous excitatory recurrent terms are found to enhance network responsiveness by reducing the oscillatory response threshold, allowing smaller inputs to trigger oscillatory activity. Instantaneous inhibitory components do the opposite. The frequency of these response oscillations is further shaped by the polarity of the non-delayed terms.
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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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Lourenço, C., and A. Babloyantz. "Control of Chaos in Networks with Delay: A Model for Synchronization of Cortical Tissue." Neural Computation 6, no. 6 (November 1994): 1141–54. http://dx.doi.org/10.1162/neco.1994.6.6.1141.
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The unstable periodic orbits of chaotic dynamics in systems described by delay differential equations are considered. An orbit is stabilized successfully, using a method proposed by Pyragas. The system under investigation is a network of excitatory and inhibitory neurons of moderate size, describing cortical activity. The relevance of the results for synchronized cortical activity is discussed.
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Stasenko, Sergey V., and Victor B. Kazantsev. "Information Encoding in Bursting Spiking Neural Network Modulated by Astrocytes." Entropy 25, no. 5 (May 1, 2023): 745. http://dx.doi.org/10.3390/e25050745.
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We investigated a mathematical model composed of a spiking neural network (SNN) interacting with astrocytes. We analysed how information content in the form of two-dimensional images can be represented by an SNN in the form of a spatiotemporal spiking pattern. The SNN includes excitatory and inhibitory neurons in some proportion, sustaining the excitation–inhibition balance of autonomous firing. The astrocytes accompanying each excitatory synapse provide a slow modulation of synaptic transmission strength. An information image was uploaded to the network in the form of excitatory stimulation pulses distributed in time reproducing the shape of the image. We found that astrocytic modulation prevented stimulation-induced SNN hyperexcitation and non-periodic bursting activity. Such homeostatic astrocytic regulation of neuronal activity makes it possible to restore the image supplied during stimulation and lost in the raster diagram of neuronal activity due to non-periodic neuronal firing. At a biological point, our model shows that astrocytes can act as an additional adaptive mechanism for regulating neural activity, which is crucial for sensory cortical representations.
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Cai, Zhiting, Curtis L. Neveu, Douglas A. Baxter, John H. Byrne, and Behnaam Aazhang. "Inferring neuronal network functional connectivity with directed information." Journal of Neurophysiology 118, no. 2 (August 1, 2017): 1055–69. http://dx.doi.org/10.1152/jn.00086.2017.
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This study brings together the techniques of voltage-sensitive dye recording and information theory to infer the functional connectome of the feeding central pattern generating network of Aplysia. In contrast to current statistical approaches, the inference method developed in this study is data driven and validated by conductance-based model circuits, can distinguish excitatory and inhibitory connections, is robust against synaptic plasticity, and is capable of detecting network structures that mediate motor patterns.
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Zheng, Meihong, Takami Matsuo, Ai Miyamoto, and Osamu Hoshino. "Tonically Balancing Intracortical Excitation and Inhibition by GABAergic Gliotransmission." Neural Computation 26, no. 8 (August 2014): 1690–716. http://dx.doi.org/10.1162/neco_a_00612.
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For sensory cortices to respond reliably to feature stimuli, the balancing of neuronal excitation and inhibition is crucial. A typical example might be the balancing of phasic excitation within cell assemblies and phasic inhibition between cell assemblies. The former controls the gain of and the latter the tuning of neuronal responses. A change in ambient GABA concentration might affect the dynamic behavior of neurons in a tonic manner. For instance, an increase in ambient GABA concentration enhances the activation of extrasynaptic receptors, augments an inhibitory current, and thus inhibits neurons. When a decrease in ambient GABA concentration occurs, the tonic inhibitory current is reduced, and thus the neurons are relatively excited. We simulated a neural network model in order to examine whether and how such a tonic excitatory-inhibitory mechanism could work for sensory information processing. The network consists of cell assemblies. Each cell assembly, comprising principal cells (P), GABAergic interneurons (Ia, Ib), and glial cells (glia), responds to one particular feature stimulus. GABA transporters, embedded in glial plasma membranes, regulate ambient GABA levels. Hypothetical neuron-glia signaling via inhibitory (Ia-to-glia) and excitatory (P-to-glia) synaptic contacts was assumed. The former let transporters import (remove) GABA from the extracellular space and excited stimulus-relevant P cells. The latter let them export GABA into the extracellular space and inhibited stimulus-irrelevant P cells. The main finding was that the glial membrane transporter gave a combinatorial excitatory-inhibitory effect on P cells in a tonic manner, thereby improving the gain and tuning of neuronal responses. Interestingly, it worked cooperatively with the conventional, phasic excitatory-inhibitory mechanism. We suggest that the GABAergic gliotransmission mechanism may provide balanced intracortical excitation and inhibition so that the best perceptual performance of the cortex can be achieved.
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VOLK, DANIEL. "EPILEPTIC SEIZURES IN A DISCRETE MODEL OF NEURAL NETWORKS OF THE BRAIN." International Journal of Modern Physics C 10, no. 05 (July 1999): 815–21. http://dx.doi.org/10.1142/s0129183199000632.
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A discrete model of a neural network of excitatory and inhibitory neurons is presented which yields oscillations of its global activity. Different types of dynamics occur depending on the selection of parameters: oscillating population activity as well as randomly fluctuating but mainly constant activity. For certain sets of parameters the model also shows temporary transitions from apparently random to periodic behavior in one run, similar to an epileptic seizure.
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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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Frost, W. N., and E. R. Kandel. "Structure of the network mediating siphon-elicited siphon withdrawal in Aplysia." Journal of Neurophysiology 73, no. 6 (June 1, 1995): 2413–27. http://dx.doi.org/10.1152/jn.1995.73.6.2413.
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1. The network mediating siphon-elicited siphon withdrawal in Aplysia is a useful model system for cellular studies of simple forms of learning and memory. Here we describe three new cells in this circuit, L33, L34, and L35, and several new connections among the following network neurons: LE, L16, L29, L30, L32, L33, L34, and L35. On the basis of these findings we present an updated diagram of the network. Altogether, 100 neurons have now been identified in the abdominal ganglion that can participate in both siphon-elicited and spontaneous respiratory pumping siphon withdrawals. 2. Two features of the interneuronal population may have important behavioral functions. First, the L29 interneurons make fast and slow excitatory connections onto the LFS cells, which may be important for transforming brief sensory neuron discharges into the long-lasting motor neuron firing that underlies withdrawal duration. Second, inhibitory interneurons are prominent in the network. The specific connectivity of certain of these interneurons is appropriate to block potentially interfering inhibitory inputs from other networks during execution of the behavior. 3. Deliberate searches have so far revealed very few excitatory interneuronal inputs to the network interneurons and motor neurons within the abdominal ganglion. These results, together with intracellular studies by others, are more consistent at present with a relatively dedicated rather than a highly distributed organizational scheme for the siphon-elicited siphon withdrawal circuitry.
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Liljenstrom, H., and M. E. Hasselmo. "Cholinergic modulation of cortical oscillatory dynamics." Journal of Neurophysiology 74, no. 1 (July 1, 1995): 288–97. http://dx.doi.org/10.1152/jn.1995.74.1.288.
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1. The effect of cholinergic modulation on cortical oscillatory dynamics was studied in a computational model of the piriform (olfactory) cortex. The model included the cholinergic suppression of neuronal adaptation, the cholinergic suppression of intrinsic fiber synaptic transmission, the cholinergic enhancement of interneuron activity, and the cholinergic suppression of inhibitory synaptic transmission. 2. Electroencephalographic (EEG) recordings and field potential recordings from the piriform cortex were modeled with a simplified network in which cortical pyramidal cells were represented by excitatory input/output functions with gain parameters dependent on previous activity. The model incorporated distributed excitatory afferent input and excitatory connections between units. In addition, the model contained two sets of inhibitory units mediating inhibition with different time constants and different reversal potentials. This model can match effectively the patterns of cortical EEG and field potentials, showing oscillatory dynamics in both the gamma (30-80 Hz) and theta (3-10 Hz) frequency range. 3. Cholinergic suppression of neuronal adaptation was modeled by reducing the change in gain associated with previous activity. This caused an increased number of oscillations within the network in response to shock stimulation of the lateral olfactory tract, effectively replicating the effect of carbachol on the field potential response in physiological experiments. 4. Cholinergic suppression of intrinsic excitatory synaptic transmission decreased the prominence of gamma oscillations within the network, allowing theta oscillations to predominate. Coupled with the cholinergic suppression of neuronal adaptation, this caused the network to shift from a nonoscillatory state into an oscillatory state of predominant theta oscillations. This replicates the longer term effect of carbachol in experimental preparations on the EEG potential recorded from the cortex in vivo and from brain-slice preparations of the hippocampus in vitro. Analysis of the model suggests that these oscillations depend upon the time constant of neuronal adaptation rather than the time constant of inhibition or the activity of bursting neurons. 5. Cholinergic modulation may be involved in switching the dynamics of this cortical region between those appropriate for learning and those appropriate for recall. During recall, the spread of activity along intrinsic excitatory connections allows associative memory function, whereas neuronal adaptation prevents the spread of activity between different patterns. During learning, the recall of previously stored patterns is prevented by suppression of intrinsic excitatory connections, whereas the response to the new patterns is enhanced by suppression of neuronal adaptation.
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Dasgupta, Debanjan, and Sujit Kumar Sikdar. "Heterogeneous network dynamics in an excitatory-inhibitory network model by distinct intrinsic mechanisms in the fast spiking interneurons." Brain Research 1714 (July 2019): 27–44. http://dx.doi.org/10.1016/j.brainres.2019.02.013.
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Bush, Paul C., David A. Prince, and Kenneth D. Miller. "Increased Pyramidal Excitability and NMDA Conductance Can Explain Posttraumatic Epileptogenesis Without Disinhibition: A Model." Journal of Neurophysiology 82, no. 4 (October 1, 1999): 1748–58. http://dx.doi.org/10.1152/jn.1999.82.4.1748.
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Partially isolated cortical islands prepared in vivo become epileptogenic within weeks of the injury. In this model of chronic epileptogenesis, recordings from cortical slices cut through the injured area and maintained in vitro often show evoked, long- and variable-latency multiphasic epileptiform field potentials that also can occur spontaneously. These events are initiated in layer V and are synchronous with polyphasic long-duration excitatory and inhibitory potentials (currents) in neurons that may last several hundred milliseconds. Stimuli that are significantly above threshold for triggering these epileptiform events evoke only a single large excitatory postsynaptic potential (EPSP) followed by an inhibitory postsynaptic potential (IPSP). We investigated the physiological basis of these events using simulations of a layer V network consisting of 500 compartmental model neurons, including 400 principal (excitatory) and 100 inhibitory cells. Epileptiform events occurred in response to a stimulus when sufficient N-methyl-d-aspartate (NMDA) conductance was activated by feedback excitatory activity among pyramidal cells. In control simulations, this activity was prevented by the rapid development of IPSPs. One manipulation that could give rise to epileptogenesis was an increase in the threshold of inhibitory interneurons. However, previous experimental data from layer V pyramidal neurons of these chronic epileptogenic lesions indicate: upregulation, rather than downregulation, of inhibition; alterations in the intrinsic properties of pyramidal cells that would tend to make them more excitable; and sprouting of their intracortical axons and increased numbers of presumed synaptic contacts, which would increase recurrent EPSPs from one cell onto another. Consistent with this, we found that increasing the excitability of pyramidal cells and the strength of NMDA conductances, in the face of either unaltered or increased inhibition, resulted in generation of epileptiform activity that had characteristics similar to those of the experimental data. Thus epileptogenesis such as occurs after chronic cortical injury can result from alterations of intrinsic membrane properties of pyramidal neurons together with enhanced NMDA synaptic conductances.
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Hui, Qing, Wassim M. Haddad, James M. Bailey, and Tomohisa Hayakawa. "A Stochastic Mean Field Model for an Excitatory and Inhibitory Synaptic Drive Cortical Neuronal Network." IEEE Transactions on Neural Networks and Learning Systems 25, no. 4 (April 2014): 751–63. http://dx.doi.org/10.1109/tnnls.2013.2281065.
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Szi Hui, Tan, and Mohamad Khairi Ishak. "Spike neuron optimization using deep reinforcement learning." IAES International Journal of Artificial Intelligence (IJ-AI) 10, no. 1 (March 1, 2021): 175. http://dx.doi.org/10.11591/ijai.v10.i1.pp175-183.
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Deep reinforcement learning (DRL) which involved reinforcement learning and artificial neural network allows agents to take the best possible actions to achieve goals. Spiking Neural Network (SNN) faced difficulty in training due to the non-differentiable spike function of spike neuron. In order to overcome the difficulty, Deep Q network (DQN) and Deep Q learning with normalized advantage function (NAF) are proposed to interact with a custom environment. DQN is applied for discrete action space whereas NAF is implemented for continuous action space. The model is trained and tested to validate its performance in order to balance the firing rate of excitatory and inhibitory population of spike neuron by using both algorithms. Training results showed both agents able to explore in the custom environment with OpenAI Gym framework. The trained model for both algorithms capable to balance the firing rate of excitatory and inhibitory of the spike neuron. NAF achieved 0.80% of the average percentage error of rate of difference between target and actual neuron rate whereas DQN obtained 0.96%. NAF attained the goal faster than DQN with only 3 steps taken for actual output neuron rate to meet with or close to target neuron firing rate.
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Bernacchia, Alberto, and Xiao-Jing Wang. "Decorrelation by Recurrent Inhibition in Heterogeneous Neural Circuits." Neural Computation 25, no. 7 (July 2013): 1732–67. http://dx.doi.org/10.1162/neco_a_00451.
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The activity of neurons is correlated, and this correlation affects how the brain processes information. We study the neural circuit mechanisms of correlations by analyzing a network model characterized by strong and heterogeneous interactions: excitatory input drives the fluctuations of neural activity, which are counterbalanced by inhibitory feedback. In particular, excitatory input tends to correlate neurons, while inhibitory feedback reduces correlations. We demonstrate that heterogeneity of synaptic connections is necessary for this inhibition of correlations. We calculate statistical averages over the disordered synaptic interactions and apply our findings to both a simple linear model and a more realistic spiking network model. We find that correlations at zero time lag are positive and of magnitude [Formula: see text], where K is the number of connections to a neuron. Correlations at longer timescales are of smaller magnitude, of order K−1, implying that inhibition of correlations occurs quickly, on a timescale of [Formula: see text]. The small magnitude of correlations agrees qualitatively with physiological measurements in the cerebral cortex and basal ganglia. The model could be used to study correlations in brain regions dominated by recurrent inhibition, such as the striatum and globus pallidus.
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Popovici, C., A. Pătraşcu Cutaru, L. Tuţă, G. Roşu, Lars Ole Fichte, and O. Baltag. "Biological neural network model based on a non-linear stochastic system." IOP Conference Series: Materials Science and Engineering 1254, no. 1 (September 1, 2022): 012025. http://dx.doi.org/10.1088/1757-899x/1254/1/012025.
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Abstract As a contribution to recent activities in the field of modelling electro-biological phenomena, we would like to present an investigation on the electrical properties of a network of neuron and propose a simplified model for brain activity, based on a biological neural network represented by a non-linear system with stochastic components. The network’s fundamental element is represented by Izhikevich model, and including several types of responses, grouped into excitatory and inhibitory response. The network’s electrical activity is compared to a biological signal obtained from an electroencephalogram recording, and it is noted that the correlation between the biological and the simulated signal increases with the number of neurons in the network.
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CARTLING, BO. "GENERATION OF ASSOCIATIVE PROCESSES IN A NEURAL NETWORK WITH REALISTIC FEATURES OF ARCHITECTURE AND UNITS." International Journal of Neural Systems 05, no. 03 (September 1994): 181–94. http://dx.doi.org/10.1142/s0129065794000207.
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A recent neural network model of cortical associative memory incorporating neuronal adaptation by a simplified description of its underlying ionic mechanisms is extended towards more realistic network units and architecture. Excitatory units correspond to groups of adapting pyramidal neurons and inhibitory units to groups of nonadapting interneurons. The network architecture is formed from pairs of one pyramidal and one interneuron unit each with inhibitory connections within and excitatory connections between pairs. The degree of adaptability of the pyramidal units controls the character of the network dynamics. An intermediate adaptability generates limit cycles of transitions between stored patterns and regulates oscillation frequencies in the range of theta rhythms observed in the brain. In particular, neuronal adaptation can impose a direction of transitions between overlapping patterns also in a symmetrically connected network. The model permits a detailed analysis of the transition mechanisms. Temporal sequences of patterns thus formed may constitute parts of associative processes, such as recall of stored sequences or search of pattern subspaces. As a special case, neuronal adaptation can accomplish pattern segmentation by which overlapping patterns are temporally resolved. The type of limit cycles produced by neuronal adaptation may also be of significance for central pattern generators, also for networks involving motor neurons. The applied learning rule of Hebbian type is compared to a modified version also common in neural network modelling. It is also shown that the dependence of the network dynamic behaviour on neuronal adaptability, from fixed point attractors at weak adaptability towards more complex dynamics of limit cycles and chaos at strong adaptability, agrees with that recently observed in a more abstract version of the model. The present description of neuronal adaptation is compared to models based on dynamic firing thresholds.
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Börgers, Christoph, and Nancy Kopell. "Synchronization in Networks of Excitatory and Inhibitory Neurons with Sparse, Random Connectivity." Neural Computation 15, no. 3 (March 1, 2003): 509–38. http://dx.doi.org/10.1162/089976603321192059.
Full textAbstract:
In model networks of E-cells and I-cells (excitatory and inhibitory neurons, respectively), synchronous rhythmic spiking often comes about from the interplay between the two cell groups: the E-cells synchronize the I-cells and vice versa. Under ideal conditions—homogeneity in relevant network parameters and all-to-all connectivity, for instance—this mechanism can yield perfect synchronization. We find that approximate, imperfect synchronization is possible even with very sparse, random connectivity. The crucial quantity is the expected number of inputs per cell. As long as it is large enough (more precisely, as long as the variance of the total number of synaptic inputs per cell is small enough), tight synchronization is possible. The desynchronizing effect of random connectivity can be reduced by strengthening the E→I synapses. More surprising, it cannot be reduced by strengthening the I→E synapses. However, the decay time constant of inhibition plays an important role. Faster decay yields tighter synchrony. In particular, in models in which the inhibitory synapses are assumed to be instantaneous, the effects of sparse, random connectivity cannot be seen.