1,721,156 research outputs found
Dynamics of networks of randomly connected excitatory and inhibitory spiking neurons
No full textRecent advances in the understanding of the dynamics of populations of spiking neurones are reviewed. These studies shed Light on how a population of neurones can follow arbitrary Variations in input stimuli, how the dynamics of the population depends on the type of noise, and how recurrent connections influence the dynamics. The importance of inhibitory feedback for the generation of irregularity in single cell behaviour is emphasized. Examples of computation that recurrent networks with excitatory and inhibitory cells can perform are then discussed. Maintenance of a network state as an attractor of the system is discussed as a model for working memory function, in both object and spatial modalities. These models can be used to interpret and make predictions about electrophysiological data in the awake monkey. (C) 2000 Elsevier Science Ltd. Published by Editions scientifiques et medicales Elsevier SAS
Storage capacity of networks with discrete synapses and sparsely encoded memories
Full text linkAttractor neural networks (ANNs) are one of the leading theoretical
frameworks for the formation and retrieval of memories in networks of
biological neurons. In this framework, a pattern imposed by external inputs to
the network is said to be learned when this pattern becomes a fixed point
attractor of the network dynamics. The storage capacity is the maximum number
of patterns that can be learned by the network. In this paper, we study the
storage capacity of fully-connected and sparsely-connected networks with a
binarized Hebbian rule, for arbitrary coding levels. Our results show that a
network with discrete synapses has a similar storage capacity as the model with
continuous synapses, and that this capacity tends asymptotically towards the
optimal capacity, in the space of all possible binary connectivity matrices, in
the sparse coding limit. We also derive finite coding level corrections for the
asymptotic solution in the sparse coding limit. The result indicates the
capacity of network with Hebbian learning rules converges to the optimal
capacity extremely slowly when the coding level becomes small. Our results also
show that in networks with sparse binary connectivity matrices, the information
capacity per synapse is larger than in the fully connected case, and thus such
networks store information more efficiently
Dynamics of the firing probability of noisy integrate-and-fire neurons
No full textCortical neurons in vivo undergo a continuous bombardment due to synaptic activity, which acts as a major source of noise. Here, we investigate the effects of the noise filtering by synapses with various levels of realism on integrate-and-fire neuron dynamics. The noise input is modeled by white (for instantaneous synapses) or colored (for synapses with a finite relaxation time) noise. Analytical results for the modulation of firing probability in response to an oscillatory input current are obtained by expanding a Fokker-Planck equation for small parameters of the problem-when both the amplitude of the modulation is small compared to the background firing rate and the synaptic time constant is small compared to the membrane time constant. We report here the detailed calculations showing that if a synaptic decay time constant is included in the synaptic current model, the firing-rate modulation of the neuron due to an oscillatory input remains finite in the high-frequency limit with no phase lag. In addition, we characterize the low-frequency behavior and the behavior of the high-frequency limit for intermediate decay times. We also characterize the effects of introducing a rise time to the synaptic currents and the presence of several synaptic receptors with different kinetics. In both cases, we determine, using numerical simulations, an effective decay time constant that describes the neuronal response completely
Dynamic control of sequential retrieval speed in networks with heterogeneous learning rules
Full text linkTemporal rescaling of sequential neural activity has been observed in multiple brain areas during behaviors involving time estimation and motor execution at variable speeds. Temporally asymmetric Hebbian rules have been used in network models to learn and retrieve sequential activity, with characteristics that are qualitatively consistent with experimental observations. However, in these models sequential activity is retrieved at a fixed speed. Here, we investigate the effects of a heterogeneity of plasticity rules on network dynamics. In a model in which neurons differ by the degree of temporal symmetry of their plasticity rule, we find that retrieval speed can be controlled by varying external inputs to the network. Neurons with temporally symmetric plasticity rules act as brakes and tend to slow down the dynamics, while neurons with temporally asymmetric rules act as accelerators of the dynamics. We also find that such networks can naturally generate separate 'preparatory' and 'execution' activity patterns with appropriate external inputs
Unsupervised Learning of Persistent and Sequential Activity.
Full text linkTwo strikingly distinct types of activity have been observed in various brain structures during delay periods of delayed response tasks: Persistent activity (PA), in which a sub-population of neurons maintains an elevated firing rate throughout an entire delay period; and Sequential activity (SA), in which sub-populations of neurons are activated sequentially in time. It has been hypothesized that both types of dynamics can be "learned" by the relevant networks from the statistics of their inputs, thanks to mechanisms of synaptic plasticity. However, the necessary conditions for a synaptic plasticity rule and input statistics to learn these two types of dynamics in a stable fashion are still unclear. In particular, it is unclear whether a single learning rule is able to learn both types of activity patterns, depending on the statistics of the inputs driving the network. Here, we first characterize the complete bifurcation diagram of a firing rate model of multiple excitatory populations with an inhibitory mechanism, as a function of the parameters characterizing its connectivity. We then investigate how an unsupervised temporally asymmetric Hebbian plasticity rule shapes the dynamics of the network. Consistent with previous studies, we find that for stable learning of PA and SA, an additional stabilization mechanism is necessary. We show that a generalized version of the standard multiplicative homeostatic plasticity (Renart et al., 2003; Toyoizumi et al., 2014) stabilizes learning by effectively masking excitatory connections during stimulation and unmasking those connections during retrieval. Using the bifurcation diagram derived for fixed connectivity, we study analytically the temporal evolution and the steady state of the learned recurrent architecture as a function of parameters characterizing the external inputs. Slow changing stimuli lead to PA, while fast changing stimuli lead to SA. Our network model shows how a network with plastic synapses can stably and flexibly learn PA and SA in an unsupervised manner
STDP in a bistable synapse model based on CaMKII and associated signaling pathways
Full text linkThe calcium/calmodulin-dependent protein kinase II (CaMKII) plays a key role in the induction of long-term postsynaptic modifications following calcium entry. Experiments suggest that these long-term synaptic changes are all-or-none switch-like events between discrete states. The biochemical network involving CaMKII and its regulating protein signaling cascade has been hypothesized to durably maintain the evoked synaptic state in the form of a bistable switch. However, it is still unclear whether experimental LTP/LTD protocols lead to corresponding transitions between the two states in realistic models of such a network. We present a detailed biochemical model of the CaMKII autophosphorylation and the protein signaling cascade governing the CaMKII dephosphorylation. As previously shown, two stable states of the CaMKII phosphorylation level exist at resting intracellular calcium concentration, and high calcium transients can switch the system from the weakly phosphorylated (DOWN) to the highly phosphorylated (UP) state of the CaMKII (similar to a LTP event). We show here that increased CaMKII dephosphorylation activity at intermediate Ca(2+) concentrations can lead to switching from the UP to the DOWN state (similar to a LTD event). This can be achieved if protein phosphatase activity promoting CaMKII dephosphorylation activates at lower Ca(2+) levels than kinase activity. Finally, it is shown that the CaMKII system can qualitatively reproduce results of plasticity outcomes in response to spike-timing dependent plasticity (STDP) and presynaptic stimulation protocols. This shows that the CaMKII protein network can account for both induction, through LTP/LTD-like transitions, and storage, due to its bistability, of synaptic changes
Irregular persistent activity induced by synaptic excitatory feedback
Full text linkNeurophysiological experiments on monkeys have reported highly irregular persistent activity during the performance of an oculomotor delayed-response task. These experiments show that during the delay period the coefficient of variation (CV) of interspike intervals (ISI) of prefrontal neurons is above 1, on average, and larger than during the fixation period. In the present paper, we show that this feature can be reproduced in a network in which persistent activity is induced by excitatory feedback, provided that (i) the post-spike reset is close enough to threshold , (ii) synaptic efficacies are a non-linear function of the pre-synaptic firing rate. Non-linearity between presynaptic rate and effective synaptic strength is implemented by a standard short-term depression mechanism (STD). First, we consider the simplest possible network with excitatory feedback: a fully connected homogeneous network of excitatory leaky integrate-and-fire neurons, using both numerical simulations and analytical techniques. The results are then confirmed in a network with selective excitatory neurons and inhibition. In both the cases there is a large range of values of the synaptic efficacies for which the statistics of firing of single cells is similar to experimental data
The statistics of repeating patterns of cortical activity can be reproduced by a model network of stochastic binary neurons
No full textCalcium imaging of the spontaneous activity in cortical slices has revealed repeating spatiotemporal patterns of transitions between so-called down states and up states (Ikegaya et al., 2004). Here we fit a model network of stochastic binary neurons to data from these experiments, and in doing so reproduce the distributions of such patterns. We use two versions of this model: (1) an unconnected network in which neurons are activated as independent Poisson processes; and (2) a network with an interaction matrix, estimated from the data, representing effective interactions between the neurons. The unconnected model (model 1) is sufficient to account for the statistics of repeating patterns in 11 of the 15 datasets studied. Model 2, with interactions between neurons, is required to account for pattern statistics of the remaining four. Three of these four datasets are the ones that contain the largest number of transitions, suggesting that long datasets are in general necessary to render interactions statistically visible. We then study the topology of the matrix of interactions estimated for these four datasets. For three of the four datasets, we find sparse matrices with long-tailed degree distributions and an overrepresentation of certain network motifs. The remaining dataset exhibits a strongly interconnected, spatially localized subgroup of neurons. In all cases, we find that interactions between neurons facilitate the generation of long patterns that do not repeat exactly
Characteristics of sequential activity in networks with temporally asymmetric Hebbian learning.
Full text linkSequential activity has been observed in multiple neuronal circuits across species, neural structures, and behaviors. It has been hypothesized that sequences could arise from learning processes. However, it is still unclear whether biologically plausible synaptic plasticity rules can organize neuronal activity to form sequences whose statistics match experimental observations. Here, we investigate temporally asymmetric Hebbian rules in sparsely connected recurrent rate networks and develop a theory of the transient sequential activity observed after learning. These rules transform a sequence of random input patterns into synaptic weight updates. After learning, recalled sequential activity is reflected in the transient correlation of network activity with each of the stored input patterns. Using mean-field theory, we derive a low-dimensional description of the network dynamics and compute the storage capacity of these networks. Multiple temporal characteristics of the recalled sequential activity are consistent with experimental observations. We find that the degree of sparseness of the recalled sequences can be controlled by nonlinearities in the learning rule. Furthermore, sequences maintain robust decoding, but display highly labile dynamics, when synaptic connectivity is continuously modified due to noise or storage of other patterns, similar to recent observations in hippocampus and parietal cortex. Finally, we demonstrate that our results also hold in recurrent networks of spiking neurons with separate excitatory and inhibitory populations
From spiking neuron models to linear-nonlinear models.
Full text linkNeurons transform time-varying inputs into action potentials emitted stochastically at a time dependent rate. The mapping from current input to output firing rate is often represented with the help of phenomenological models such as the linear-nonlinear (LN) cascade, in which the output firing rate is estimated by applying to the input successively a linear temporal filter and a static non-linear transformation. These simplified models leave out the biophysical details of action potential generation. It is not a priori clear to which extent the input-output mapping of biophysically more realistic, spiking neuron models can be reduced to a simple linear-nonlinear cascade. Here we investigate this question for the leaky integrate-and-fire (LIF), exponential integrate-and-fire (EIF) and conductance-based Wang-Buzsáki models in presence of background synaptic activity. We exploit available analytic results for these models to determine the corresponding linear filter and static non-linearity in a parameter-free form. We show that the obtained functions are identical to the linear filter and static non-linearity determined using standard reverse correlation analysis. We then quantitatively compare the output of the corresponding linear-nonlinear cascade with numerical simulations of spiking neurons, systematically varying the parameters of input signal and background noise. We find that the LN cascade provides accurate estimates of the firing rates of spiking neurons in most of parameter space. For the EIF and Wang-Buzsáki models, we show that the LN cascade can be reduced to a firing rate model, the timescale of which we determine analytically. Finally we introduce an adaptive timescale rate model in which the timescale of the linear filter depends on the instantaneous firing rate. This model leads to highly accurate estimates of instantaneous firing rates
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