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Paul Miller - One of the best experts on this subject based on the ideXlab platform.
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Attractor-State itinerancy in neural circuits with synaptic depression.
Journal of mathematical neuroscience, 2020Co-Authors: Bolun Chen, Paul MillerAbstract:Neural populations with strong excitatory recurrent connections can support bistable States in their mean firing rates. Multiple fixed points in a network of such bistable units can be used to model memory retrieval and pattern separation. The stability of fixed points may change on a slower timescale than that of the dynamics due to short-term synaptic depression, leading to transitions between quasi-stable point Attractor States in a sequence that depends on the history of stimuli. To better understand these behaviors, we study a minimal model, which characterizes multiple fixed points and transitions between them in response to stimuli with diverse time- and amplitude-dependencies. The interplay between the fast dynamics of firing rate and synaptic responses and the slower timescale of synaptic depression makes the neural activity sensitive to the amplitude and duration of square-pulse stimuli in a nontrivial, history-dependent manner. Weak cross-couplings further deform the basins of attraction for different fixed points into intricate shapes. We find that while short-term synaptic depression can reduce the total number of stable fixed points in a network, it tends to strongly increase the number of fixed points visited upon repetitions of fixed stimuli. Our analysis provides a natural explanation for the system’s rich responses to stimuli of different durations and amplitudes while demonstrating the encoding capability of bistable neural populations for dynamical features of incoming stimuli.
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Attractor-State itinerancy in neural circuits with synaptic depression
2019Co-Authors: Bolun Chen, Paul MillerAbstract:Neural populations with strong excitatory recurrent connections can support bistable States in their mean firing rates. Multiple fixed points in a network of such bistable units can be used to model memory retrieval and pattern separation. The stability of fixed points may change on a slower timescale than that of the dynamics due to short-term synaptic depression, leading to transitions between quasi-stable point Attractor States in a sequence that depends on the history of stimuli. To better understand these behaviors, we study a minimal model, which characterizes multiple fixed points and transitions between them in response to stimuli with diverse time- and amplitude-dependences. The interplay between the fast dynamics of firing rate and synaptic responses and the slower timescale of synaptic depression makes the neural activity sensitive to the amplitude and duration of square-pulse stimuli in a non-trivial, history-dependent manner. Weak cross-couplings further deform the basins of attraction for different fixed points into intricate shapes. Our analysis provides a natural explanation for the system9s rich responses to stimuli of different durations and amplitudes while demonstrating the encoding capability of bistable neural populations for dynamical features of incoming stimuli.
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Itinerancy between Attractor States in neural systems
Current opinion in neurobiology, 2016Co-Authors: Paul MillerAbstract:Converging evidence from neural, perceptual and simulated data suggests that discrete Attractor States form within neural circuits through learning and development. External stimuli may bias neural activity to one Attractor State or cause activity to transition between several discrete States. Evidence for such transitions, whose timing can vary across trials, is best accrued through analyses that avoid any trial-averaging of data. One such method, hidden Markov modeling, has been effective in this context, revealing State transitions in many neural circuits during many tasks. Concurrently, modeling efforts have revealed computational benefits of stimulus processing via transitions between Attractor States. This review describes the current State of the field, with comments on how its perceived limitations have been addressed.
Anders Lansner - One of the best experts on this subject based on the ideXlab platform.
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A cortical Attractor network with martinotti cells driven by facilitating synapses
PloS one, 2012Co-Authors: Pradeep Krishnamurthy, Gilad Silberberg, Anders LansnerAbstract:The population of pyramidal cells significantly outnumbers the inhibitory interneurons in the neocortex, while at the same time the diversity of interneuron types is much more pronounced. One acknowledged key role of inhibition is to control the rate and patterning of pyramidal cell firing via negative feedback, but most likely the diversity of inhibitory pathways is matched by a corresponding diversity of functional roles. An important distinguishing feature of cortical interneurons is the variability of the short-term plasticity properties of synapses received from pyramidal cells. The Martinotti cell type has recently come under scrutiny due to the distinctly facilitating nature of the synapses they receive from pyramidal cells. This distinguishes these neurons from basket cells and other inhibitory interneurons typically targeted by depressing synapses. A key aspect of the work reported here has been to pinpoint the role of this variability. We first set out to reproduce quantitatively based on in vitro data the di-synaptic inhibitory microcircuit connecting two pyramidal cells via one or a few Martinotti cells. In a second step, we embedded this microcircuit in a previously developed Attractor memory network model of neocortical layers 2/3. This model network demonstrated that basket cells with their characteristic depressing synapses are the first to discharge when the network enters an Attractor State and that Martinotti cells respond with a delay, thereby shifting the excitation-inhibition balance and acting to terminate the Attractor State. A parameter sensitivity analysis suggested that Martinotti cells might, in fact, play a dominant role in setting the Attractor dwell time and thus cortical speed of processing, with cellular adaptation and synaptic depression having a less prominent role than previously thought.
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A cortical Attractor network with dynamic synapses
BMC Neuroscience, 2011Co-Authors: Pradeep Krishnamurthy, Gilad Silberberg, Anders LansnerAbstract:Neocortical inhibitory interneurons play a critical role in shaping the network activity patterns by directly controlling the firing rates of pyramidal cells (PC) [1]. Evidences are accumulating for the possible role of Martinotti cells (MC), which are dendrite-targeting interneurons that receive strongly facilitating synapses from PC, as opposed to basket cells (BC) that are soma targeting and receive strongly depressing synapses [2]. We have previously developed a network model of neocortical layers 2/3 [3] and we here extend this set-up to explore the possible division of labour between basket and Martinotti cells. We used single-compartment cells taken from Pospischill et al. [4] and implemented in NEURON [5]. Short-term depression and facilitation were incorporated for all glutamatergic and GABAergic synapses according to the formalism of Tsodyks & Markram [6] with parameters tuned from traces provided by Silberberg et al. [2]. We commenced with reproducing in our model the PC – MC microcircuit, as previously described by Silberberg & Markram [2], and reproduced (a) frequency dependent disynaptic inhibition of PC and (b) frequency dependent recruitment of MC (Figure (Figure1A).1A). Thereafter, we integrated this microcircuit into our cortical network model to study the effects of MC on the Attractor dwell time while the network is spontaneously hopping between the Attractor States (stored memories) in the absence of external input. Raster plot and average firing rate (Figure (Figure1B)1B) show that BC that receive depressing synapses has a high firing rate at the beginning of the Attractor State which then tapers off. On the other hand, MC that receive facilitating synapses display a late onset of activation and tend to terminate an ongoing Attractor State. Cortex is provided with many mechanisms, e.g. spike frequency adaptation, synaptic depression of PC-PC synapses and late firing MC, to control its activity levels and termination of Attractors. However, our simulations show that MC inhibition could be a dominating factor, the high divergence of MC to PC connections also assists this. Figure 1 (A) PC-MC microcircuitry showing the disynaptic pathway between the PC mediated by MC showing frequency dependent recuitment and frequency dependent disynaptic inhibition of PC. (B) Raster plot (top) and average firing rate (bottom) of all the cells. ...
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Low spiking rates in a population of mutually exciting pyramidal cells
Network: Computation in Neural Systems, 1995Co-Authors: Erik Fransén, Anders LansnerAbstract:In a recurrent artificial neural network, the units active in an Attractor State typically reach their maximum activity value while the others are quiescent. In contrast, recordings of cortical cell activity in vivo rarely reveal cells firing at their maximum rate. This discrepancy has been one of the main arguments against using Attractor networks as models of cortical associative memory.In this study we show that low-rate sustained after-activity can be obtained in a simulated network of mutually exciting pyramidal cells. This is achieved by assuming that the synapses in the network are of a saturating type. When the application of a monoamine neuromodulator is simulated, after-activity with firing rates around 60 s−1 can be produced. The firing pattern of the network was found to be similar to that of the experimentally most comparable system, the disinhibited hippocampal slice. The results obtained are robust against simulated biological variation and background noise.
Per Bak - One of the best experts on this subject based on the ideXlab platform.
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Self-organized critical system with no stationary Attractor State.
Physical review. E Statistical nonlinear and soft matter physics, 2002Co-Authors: Simon F Nørrelykke, Per BakAbstract:A simple model economy with interacting producers and consumers is introduced. When driven by extreme dynamics, the model self-organizes not to an Attractor State, but to an asymptote, on which the economy has a constant rate of deflation, is critical, and exhibits avalanches of activity with power-law distributed sizes. This example demonstrates that self-organized critical behavior occurs in a larger class of systems than so far considered: systems not driven to an attractive fixed point, but, e.g., an asymptote, may also display self-organized criticality.
Edmund T. Rolls - One of the best experts on this subject based on the ideXlab platform.
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A non-reward Attractor theory of depression.
Neuroscience and biobehavioral reviews, 2016Co-Authors: Edmund T. RollsAbstract:A non-reward Attractor theory of depression is proposed based on the operation of the lateral orbitofrontal cortex and supracallosal cingulate cortex. The orbitofrontal cortex contains error neurons that respond to non-reward for many seconds in an Attractor State that maintains a memory of the non-reward. The human lateral orbitofrontal cortex is activated by non-reward during reward reversal, and by a signal to stop a response that is now incorrect. Damage to the human orbitofrontal cortex impairs reward reversal learning. Not receiving reward can produce depression. The theory proposed is that in depression, this lateral orbitofrontal cortex non-reward system is more easily triggered, and maintains its Attractor-related firing for longer. This triggers negative cognitive States, which in turn have positive feedback top-down effects on the orbitofrontal cortex non-reward system. Treatments for depression, including ketamine, may act in part by quashing this Attractor. The mania of bipolar disorder is hypothesized to be associated with oversensitivity and overactivity in the reciprocally related reward system in the medial orbitofrontal cortex and pregenual cingulate cortex.
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A computational neuroscience approach to schizophrenia and its onset
Neuroscience and biobehavioral reviews, 2010Co-Authors: Edmund T. Rolls, Gustavo DecoAbstract:a b s t r a c t Computational neuroscience integrate-and-fire Attractor network models can be used to understand the factors that alter the stability of cortical networks in the face of noise caused for example by neuronal spiking times. A reduction of the firing rates of cortical neurons caused for example by reduced NMDA receptor function (present in schizophrenia) can lead to instability of the high firing rate Attractor States that normally implement short-term memory and attention, contributing to the cognitive and negative symptoms of schizophrenia. Reduced cortical inhibition caused by a reduction of GABA neurotransmis- sion (present in schizophrenia) can lead to instability of the spontaneous firing States of cortical networks, leading to a noise-induced jump to a high firing rate Attractor State even in the absence of external inputs, contributing to the positive symptoms of schizophrenia. We consider how effects occurring at the time of late adolescence including synaptic pruning, decreases in grey matter volume, and changes in GABA- mediated inhibition and dopamine may contribute to the onset in some individuals of schizophrenia at this time.
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Sequential Memory: A Putative Neural and Synaptic Dynamical Mechanism
Journal of cognitive neuroscience, 2005Co-Authors: Gustavo Deco, Edmund T. RollsAbstract:A key issue in the neurophysiology of cognition is the problem of sequential learning. Sequential learning refers to the ability to encode and represent the temporal order of discrete elements occurring in a sequence. We show that the short-term memory for a sequence of items can be implemented in an autoassociation neural network. Each item is one of the Attractor States of the network. The autoassociation network is implemented at the level of integrate-and-fire neurons so that the contributions of different biophysical mechanisms to sequence learning can be investigated. It is shown that if it is a property of the synapses or neurons that support each Attractor State that they adapt, then everytime the network is made quiescent (e.g., by inhibition), then the Attractor State that emerges next is the next item in the sequence. We show with numerical simulations implementations of the mechanisms using (1) a sodium inactivation-based spike-frequency-adaptation mechanism, (2) a Ca2+-activated K+ current, and (3) short-term synaptic depression, with sequences of up to three items. The network does not need repeated training on a particular sequence and will repeat the items in the order that they were last presented. The time between the items in a sequence is not fixed, allowing the items to be read out as required over a period of up to many seconds. The network thus uses adaptation rather than associative synaptic modification to recall the order of the items in a recently presented sequence.
Pradeep Krishnamurthy - One of the best experts on this subject based on the ideXlab platform.
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A cortical Attractor network with martinotti cells driven by facilitating synapses
PloS one, 2012Co-Authors: Pradeep Krishnamurthy, Gilad Silberberg, Anders LansnerAbstract:The population of pyramidal cells significantly outnumbers the inhibitory interneurons in the neocortex, while at the same time the diversity of interneuron types is much more pronounced. One acknowledged key role of inhibition is to control the rate and patterning of pyramidal cell firing via negative feedback, but most likely the diversity of inhibitory pathways is matched by a corresponding diversity of functional roles. An important distinguishing feature of cortical interneurons is the variability of the short-term plasticity properties of synapses received from pyramidal cells. The Martinotti cell type has recently come under scrutiny due to the distinctly facilitating nature of the synapses they receive from pyramidal cells. This distinguishes these neurons from basket cells and other inhibitory interneurons typically targeted by depressing synapses. A key aspect of the work reported here has been to pinpoint the role of this variability. We first set out to reproduce quantitatively based on in vitro data the di-synaptic inhibitory microcircuit connecting two pyramidal cells via one or a few Martinotti cells. In a second step, we embedded this microcircuit in a previously developed Attractor memory network model of neocortical layers 2/3. This model network demonstrated that basket cells with their characteristic depressing synapses are the first to discharge when the network enters an Attractor State and that Martinotti cells respond with a delay, thereby shifting the excitation-inhibition balance and acting to terminate the Attractor State. A parameter sensitivity analysis suggested that Martinotti cells might, in fact, play a dominant role in setting the Attractor dwell time and thus cortical speed of processing, with cellular adaptation and synaptic depression having a less prominent role than previously thought.
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A cortical Attractor network with dynamic synapses
BMC Neuroscience, 2011Co-Authors: Pradeep Krishnamurthy, Gilad Silberberg, Anders LansnerAbstract:Neocortical inhibitory interneurons play a critical role in shaping the network activity patterns by directly controlling the firing rates of pyramidal cells (PC) [1]. Evidences are accumulating for the possible role of Martinotti cells (MC), which are dendrite-targeting interneurons that receive strongly facilitating synapses from PC, as opposed to basket cells (BC) that are soma targeting and receive strongly depressing synapses [2]. We have previously developed a network model of neocortical layers 2/3 [3] and we here extend this set-up to explore the possible division of labour between basket and Martinotti cells. We used single-compartment cells taken from Pospischill et al. [4] and implemented in NEURON [5]. Short-term depression and facilitation were incorporated for all glutamatergic and GABAergic synapses according to the formalism of Tsodyks & Markram [6] with parameters tuned from traces provided by Silberberg et al. [2]. We commenced with reproducing in our model the PC – MC microcircuit, as previously described by Silberberg & Markram [2], and reproduced (a) frequency dependent disynaptic inhibition of PC and (b) frequency dependent recruitment of MC (Figure (Figure1A).1A). Thereafter, we integrated this microcircuit into our cortical network model to study the effects of MC on the Attractor dwell time while the network is spontaneously hopping between the Attractor States (stored memories) in the absence of external input. Raster plot and average firing rate (Figure (Figure1B)1B) show that BC that receive depressing synapses has a high firing rate at the beginning of the Attractor State which then tapers off. On the other hand, MC that receive facilitating synapses display a late onset of activation and tend to terminate an ongoing Attractor State. Cortex is provided with many mechanisms, e.g. spike frequency adaptation, synaptic depression of PC-PC synapses and late firing MC, to control its activity levels and termination of Attractors. However, our simulations show that MC inhibition could be a dominating factor, the high divergence of MC to PC connections also assists this. Figure 1 (A) PC-MC microcircuitry showing the disynaptic pathway between the PC mediated by MC showing frequency dependent recuitment and frequency dependent disynaptic inhibition of PC. (B) Raster plot (top) and average firing rate (bottom) of all the cells. ...
