Distribution Of Synaptic Weights Research Articles

Temporal-specific complexity of spiking patterns in spontaneous activity induced by a dual complex network structure

Temporal fluctuation of neural activity in the brain has an important function in optimal information processing. Spontaneous activity is a source of such fluctuation. The distribution of excitatory postsynaptic potentials (EPSPs) between cortical pyramidal neurons can follow a log-normal distribution. Recent studies have shown that networks connected by weak synapses exhibit characteristics of a random network, whereas networks connected by strong synapses have small-world characteristics of small path lengths and large cluster coefficients. To investigate the relationship between temporal complexity spontaneous activity and structural network duality in synaptic connections, we executed a simulation study using the leaky integrate-and-fire spiking neural network with log-normal synaptic weight distribution for the EPSPs and duality of synaptic connectivity, depending on synaptic weight. We conducted multiscale entropy analysis of the temporal spiking activity. Our simulation demonstrated that, when strong synaptic connections approach a small-world network, specific spiking patterns arise during irregular spatio-temporal spiking activity, and the complexity at the large temporal scale (i.e., slow frequency) is enhanced. Moreover, we confirmed through a surrogate data analysis that slow temporal dynamics reflect a deterministic process in the spiking neural networks. This modelling approach may improve the understanding of the spatio-temporal complex neural activity in the brain.

Absence of Repetitive Correlation Patterns Between Pairs of Adjacent Neocortical Neurons in vivo.

Neuroanatomy suggests that adjacent neocortical neurons share a similar set of afferent synaptic inputs, as opposed to neurons localized to different areas of the neocortex. In the present study, we made simultaneous single-electrode patch clamp recordings from two or three adjacent neurons in the primary somatosensory cortex (S1) of the ketamine-xylazine anesthetized rat in vivo to study the correlation patterns in their spike firing during both spontaneous and sensory-evoked activity. One difference with previous studies of pairwise neuronal spike firing correlations was that here we identified several different quantifiable parameters in the correlation patterns by which different pairs could be compared. The questions asked were if the correlation patterns between adjacent pairs were similar and if there was a relationship between the degree of similarity and the layer location of the pairs. In contrast, our results show that for putative pyramidal neurons within layer III and within layer V, each pair of neurons is to some extent unique in terms of their spiking correlation patterns. Interestingly, our results also indicated that these correlation patterns did not substantially alter between spontaneous and evoked activity. Our findings are compatible with the view that the synaptic input connectivity to each neocortical neuron is at least in some aspects unique. A possible interpretation is that plasticity mechanisms, which could either be initiating or be supported by transcriptomic differences, tend to differentiate rather than harmonize the synaptic weight distributions between adjacent neurons of the same type.

Stochastic neural field theory of wandering bumps on a sphere

We use a combination of group theoretic and perturbation methods to analyze the stochastic wandering of bump solutions in a neural field model on the sphere S2. We first construct an explicit bump solution in the absence of external inputs and noise, by taking the synaptic weight distribution to be the sum of first-order spherical harmonics. The corresponding neural field equation is equivariant under the action of the special orthogonal group SO(3), which implies that the bump is marginally stable with respect to rotations of the sphere. We then carry out an amplitude–phase decomposition of the solution in the presence of a weakly biased external input and weak noise, and use this to derive a pair of stochastic differential equations for the wandering of the bump, expressed in terms of angular coordinates on the sphere. The stochastic dynamics is a non-trivial generalization of the corresponding phase dynamics describing the wandering of a bump on a ring network with SO(2) symmetry, since SO(3) is non-abelian and S2 is a curved manifold.

Synaptic modifications driven by spike-timing-dependent plasticity in weakly coupled bursting neurons.

In the course of development, sleep, or mental disorders, certain neurons in the brain display spontaneous spike-burst activity. The synaptic plasticity evoked by such activity is here studied in the presence of spike-timing-dependent plasticity (STDP). In two chemically coupled bursting model neurons, the spike-burst activity can translate the STDP related to pre- and postsynaptic spike activity into burst-timing-dependent plasticity (BTDP), based on the timing of bursts of pre- and postsynaptic neurons. The resulting BTDP exhibits exponential decays with the same time scales as those of STDP. In weakly coupled bursting neuron networks, the synaptic modification driven by the spike-burst activity obeys a power-law distribution. The model can also produce a power-law distribution of synaptic weights. Here, the considered bursting behavior is made of stereotypical groups of spikes, and bursting is evenly spaced by long intervals.

Spike burst-pause dynamics of Purkinje cells regulate sensorimotor adaptation.

Cerebellar Purkinje cells mediate accurate eye movement coordination. However, it remains unclear how oculomotor adaptation depends on the interplay between the characteristic Purkinje cell response patterns, namely tonic, bursting, and spike pauses. Here, a spiking cerebellar model assesses the role of Purkinje cell firing patterns in vestibular ocular reflex (VOR) adaptation. The model captures the cerebellar microcircuit properties and it incorporates spike-based synaptic plasticity at multiple cerebellar sites. A detailed Purkinje cell model reproduces the three spike-firing patterns that are shown to regulate the cerebellar output. Our results suggest that pauses following Purkinje complex spikes (bursts) encode transient disinhibition of target medial vestibular nuclei, critically gating the vestibular signals conveyed by mossy fibres. This gating mechanism accounts for early and coarse VOR acquisition, prior to the late reflex consolidation. In addition, properly timed and sized Purkinje cell bursts allow the ratio between long-term depression and potentiation (LTD/LTP) to be finely shaped at mossy fibre-medial vestibular nuclei synapses, which optimises VOR consolidation. Tonic Purkinje cell firing maintains the consolidated VOR through time. Importantly, pauses are crucial to facilitate VOR phase-reversal learning, by reshaping previously learnt synaptic weight distributions. Altogether, these results predict that Purkinje spike burst-pause dynamics are instrumental to VOR learning and reversal adaptation.

Propagation delays determine neuronal activity and synaptic connectivity patterns emerging in plastic neuronal networks.

In plastic neuronal networks, the synaptic strengths are adapted to the neuronal activity. Specifically, spike-timing-dependent plasticity (STDP) is a fundamental mechanism that modifies the synaptic strengths based on the relative timing of pre- and postsynaptic spikes, taking into account the spikes' temporal order. In many studies, propagation delays were neglected to avoid additional dynamic complexity or computational costs. So far, networks equipped with a classic STDP rule typically rule out bidirectional couplings (i.e., either loops or uncoupled states) and are, hence, not able to reproduce fundamental experimental findings. In this review paper, we consider additional features, e.g., extensions of the classic STDP rule or additional aspects like noise, in order to overcome the contradictions between theory and experiment. In addition, we review in detail recent studies showing that a classic STDP rule combined with realistic propagation patterns is able to capture relevant experimental findings. In two coupled oscillatory neurons with propagation delays, bidirectional synapses can be preserved and potentiated. This result also holds for large networks of type-II phase oscillators. In addition, not only the mean of the initial distribution of synaptic weights, but also its standard deviation crucially determines the emergent structural connectivity, i.e., the mean final synaptic weight, the number of two-neuron loops, and the symmetry of the final connectivity pattern. The latter is affected by the firing rates, where more symmetric synaptic configurations emerge at higher firing rates. Finally, we discuss these findings in the context of the computational neuroscience-based development of desynchronizing brain stimulation techniques.

The research on dynamic properties of the small world neural network based on the synaptic plasticity

The artificial neural network has the ability of the information processing and storage, good adaptability, strong learning function, association function and fault tolerance function. The research on the artificial neural network is mostly focused on the dynamic properties due to fact that the applications of artificial neural networks are related to its dynamic properties. At present, the researches on the neural network are based on the hierarchical network which can not simulate the real neural network. As a high level of abstraction of real complex systems, the small world network has the properties of biological neural networks. In the study, the small world network was constructed and the optimal parameter of the small word network was chosen based on the complex network theory firstly. And then based on the regulation mechanism of the synaptic plasticity and the topology of the small world network, the small world neural network was constructed and dynamic properties of the neural network were analyzed from the three aspects of the firing properties, dynamic properties of synaptic weights and complex network properties. The experimental results showed that with the increase of the time, the firing patterns of excitatory and inhibitory neurons in the small world neural network didn't change and the firing time of the neurons tended to synchronize; the synaptic weights between the neurons decreased sharply and eventually tended to be steady; the connections in the neural network were weakened and the efficiency of the information transmission was reduced, but the small world attribute was stable. The dynamic properties of the small world neural network vary with time, and the dynamic properties can also interact with each other: the firing synchronization of the neural network can affect the distribution of synaptic weights to the minimum, and then the dynamic changes of the synaptic weights can affect the complex network properties of the small world neural network.

Delay-Induced Multistability and Loop Formation in Neuronal Networks with Spike-Timing-Dependent Plasticity

Spike-timing-dependent plasticity (STDP) adjusts synaptic strengths according to the precise timing of pre- and postsynaptic spike pairs. Theoretical and computational studies have revealed that STDP may contribute to the emergence of a variety of structural and dynamical states in plastic neuronal populations. In this manuscript, we show that by incorporating dendritic and axonal propagation delays in recurrent networks of oscillatory neurons, the asymptotic connectivity displays multistability, where different structures emerge depending on the initial distribution of the synaptic strengths. In particular, we show that the standard deviation of the initial distribution of synaptic weights, besides its mean, determines the main properties of the emergent structural connectivity such as the mean final synaptic weight, the number of two-neuron loops and the symmetry of the final structure. We also show that the firing rates of the neurons affect the evolution of the network, and a more symmetric configuration of the synapses emerges at higher firing rates. We justify the network results based on a two-neuron framework and show how the results translate to large recurrent networks.

Intracellular Dynamics in Cuneate Nucleus Neurons Support Self-Stabilizing Learning of Generalizable Tactile Representations.

How the brain represents the external world is an unresolved issue for neuroscience, which could provide fundamental insights into brain circuitry operation and solutions for artificial intelligence and robotics. The neurons of the cuneate nucleus form the first interface for the sense of touch in the brain. They were previously shown to have a highly skewed synaptic weight distribution for tactile primary afferent inputs, suggesting that their connectivity is strongly shaped by learning. Here we first characterized the intracellular dynamics and inhibitory synaptic inputs of cuneate neurons in vivo and modeled their integration of tactile sensory inputs. We then replaced the tactile inputs with input from a sensorized bionic fingertip and modeled the learning-induced representations that emerged from varied sensory experiences. The model reproduced both the intrinsic membrane dynamics and the synaptic weight distributions observed in cuneate neurons in vivo. In terms of higher level model properties, individual cuneate neurons learnt to identify specific sets of correlated sensors, which at the population level resulted in a decomposition of the sensor space into its recurring high-dimensional components. Such vector components could be applied to identify both past and novel sensory experiences and likely correspond to the fundamental haptic input features these neurons encode in vivo. In addition, we show that the cuneate learning architecture is robust to a wide range of intrinsic parameter settings due to the neuronal intrinsic dynamics. Therefore, the architecture is a potentially generic solution for forming versatile representations of the external world in different sensor systems.

Transient and Persistent UP States during Slow-wave Oscillation and their Implications for Cell-Assembly Dynamics

The membrane potentials of cortical neurons in vivo exhibit spontaneous fluctuations between a depolarized UP state and a resting DOWN state during the slow-wave sleeps or in the resting states. This oscillatory activity is believed to engage in memory consolidation although the underlying mechanisms remain unknown. Recently, it has been shown that UP-DOWN state transitions exhibit significantly different temporal profiles in different cortical regions, presumably reflecting differences in the underlying network structure. Here, we studied in computational models whether and how the connection configurations of cortical circuits determine the macroscopic network behavior during the slow-wave oscillation. Inspired by cortical neurobiology, we modeled three types of synaptic weight distributions, namely, log-normal, sparse log-normal and sparse Gaussian. Both analytic and numerical results suggest that a larger variance of weight distribution results in a larger chance of having significantly prolonged UP states. However, the different weight distributions only produce similar macroscopic behavior. We further confirmed that prolonged UP states enrich the variety of cell assemblies activated during these states. Our results suggest the role of persistent UP states for the prolonged repetition of a selected set of cell assemblies during memory consolidation.

Logarithmic distributions prove that intrinsic learning is Hebbian.

In this paper, we present data for the lognormal distributions of spike rates, synaptic weights and intrinsic excitability (gain) for neurons in various brain areas, such as auditory or visual cortex, hippocampus, cerebellum, striatum, midbrain nuclei. We find a remarkable consistency of heavy-tailed, specifically lognormal, distributions for rates, weights and gains in all brain areas examined. The difference between strongly recurrent and feed-forward connectivity (cortex vs. striatum and cerebellum), neurotransmitter (GABA (striatum) or glutamate (cortex)) or the level of activation (low in cortex, high in Purkinje cells and midbrain nuclei) turns out to be irrelevant for this feature. Logarithmic scale distribution of weights and gains appears to be a general, functional property in all cases analyzed. We then created a generic neural model to investigate adaptive learning rules that create and maintain lognormal distributions. We conclusively demonstrate that not only weights, but also intrinsic gains, need to have strong Hebbian learning in order to produce and maintain the experimentally attested distributions. This provides a solution to the long-standing question about the type of plasticity exhibited by intrinsic excitability.

Logarithmic distributions prove that intrinsic learning is Hebbian

In this paper, we present data for the lognormal distributions of spike rates, synaptic weights and intrinsic excitability (gain) for neurons in various brain areas, such as auditory or visual cortex, hippocampus, cerebellum, striatum, midbrain nuclei. We find a remarkable consistency of heavy-tailed, specifically lognormal, distributions for rates, weights and gains in all brain areas examined. The difference between strongly recurrent and feed-forward connectivity (cortex vs. striatum and cerebellum), neurotransmitter (GABA (striatum) or glutamate (cortex)) or the level of activation (low in cortex, high in Purkinje cells and midbrain nuclei) turns out to be irrelevant for this feature. Logarithmic scale distribution of weights and gains appears to be a general, functional property in all cases analyzed. We then created a generic neural model to investigate adaptive learning rules that create and maintain lognormal distributions. We conclusively demonstrate that not only weights, but also intrinsic gains, need to have strong Hebbian learning in order to produce and maintain the experimentally attested distributions. This provides a solution to the long-standing question about the type of plasticity exhibited by intrinsic excitability.

Cortical Dynamics in Presence of Assemblies of Densely Connected Weight-Hub Neurons.

Experimental measurements of pairwise connection probability of pyramidal neurons together with the distribution of synaptic weights have been used to construct randomly connected model networks. However, several experimental studies suggest that both wiring and synaptic weight structure between neurons show statistics that differ from random networks. Here we study a network containing a subset of neurons which we call weight-hub neurons, that are characterized by strong inward synapses. We propose a connectivity structure for excitatory neurons that contain assemblies of densely connected weight-hub neurons, while the pairwise connection probability and synaptic weight distribution remain consistent with experimental data. Simulations of such a network with generalized integrate-and-fire neurons display regular and irregular slow oscillations akin to experimentally observed up/down state transitions in the activity of cortical neurons with a broad distribution of pairwise spike correlations. Moreover, stimulation of a model network in the presence or absence of assembly structure exhibits responses similar to light-evoked responses of cortical layers in optogenetically modified animals. We conclude that a high connection probability into and within assemblies of excitatory weight-hub neurons, as it likely is present in some but not all cortical layers, changes the dynamics of a layer of cortical microcircuitry significantly.

Distributed synaptic weights in a LIF neural network and learning rules

Leaky integrate-and-fire (LIF) models are mean-field limits, with a large number of neurons, used to describe neural networks. We consider inhomogeneous networks structured by a connectivity parameter (strengths of the synaptic weights) with the effect of processing the input current with different intensities.We first study the properties of the network activity depending on the distribution of synaptic weights and in particular its discrimination capacity. Then, we consider simple learning rules and determine the synaptic weight distribution it generates. We outline the role of noise as a selection principle and the capacity to memorize a learned signal.

Exact firing time statistics of neurons driven by discrete inhibitory noise

Neurons in the intact brain receive a continuous and irregular synaptic bombardment from excitatory and inhibitory pre- synaptic neurons, which determines the firing activity of the stimulated neuron. In order to investigate the influence of inhibitory stimulation on the firing time statistics, we consider Leaky Integrate-and-Fire neurons subject to inhibitory instantaneous post- synaptic potentials. In particular, we report exact results for the firing rate, the coefficient of variation and the spike train spectrum for various synaptic weight distributions. Our results are not limited to stimulations of infinitesimal amplitude, but they apply as well to finite amplitude post-synaptic potentials, thus being able to capture the effect of rare and large spikes. The developed methods are able to reproduce also the average firing properties of heterogeneous neuronal populations.

Self-organization of complex cortex-like wiring in a spiking neural network model

Understanding the structure and dynamics of cortical connectivity is vital to understanding cortical function. Experimental data strongly suggest that local recurrent connectivity in the cortex is significantly non-random, exhibiting above-chance bidirectionality, an overrepresentation of certain triangular motifs, and a heavy-tailed distribution of synaptic efficacies [1]. Additional evidence suggests a significant distance dependency to connectivity over a local scale of a few hundred microns [2], and particular patterns of synaptic turnover dynamics [3]. It is currently not understood how many of these non-random features arise. Gaining understanding, then, of the processes that lead to these complexities would provide valuable insights into the development and computational functionality of the cortex. While previous work has attempted to model some of the individual features of local cortical wiring, there is no model that comprehensively begins to account for all of them. Here we present a spiking network model of a Layer V-like cortical slice culture (panel B) that, via the interactions of a few simple biologically motivated plasticity mechanisms, qualitatively reproduces many of these non-random effects, such as synaptic weight (panel A) and triangular motif distribution (panel C) Additionally, it reproduced experimentally observed synaptic growth and efficacy dynamics [3]. These plasticity mechanisms include spike timing dependent plasticity, synaptic normalization, homeostatic firing threshold adaptation, pruning of zero-efficacy synaptic connections, and the distance-dependent generation of new synaptic connections. As a spiking, topographic extension to the previously developed SORN family of models [4,5], there is also evidence suggesting that these plasticity mechanisms endow recurrent networks with powerful learning abilities. Our model suggests that mechanisms of self-organization arising from a small number of plasticity rules provide a parsimonious explanation for numerous experimentally observed non-random features of recurrent cortical wiring. Figure 1 Panel A: Mature synaptic weight distribution (in logarithmic space) for a simulation run with associated Gaussian (lognormal in linear space) fit. Panel B: Topological graph of mature network for a simulation run. Panel C: Triangular motif count (relative ...

Balancing the critical period of spiking neurons with attractor-less STDP

Attractor-based (multiplicative) STDP has been called a biologically more realistic form of spike timing dependent plasticity than attractor-less (additive) variants [1-4], as it produces unimodal distributions of synaptic weights [5,6] when given poisson-distributed random input spike trains [1,2,4,7-9]. While unimodal weight distributions have been observed as an outcome in some in vitro experiments [5], the actual biochemical process that changes synaptic connection strengths has yet to be fully understood. Unfortunately, attractor-based STDP has been repeatedly shown to be computationally less powerful than attractor-less STDP [9] and successful implementations of attractor-based STDP used attractors that were either very weak [8] or very close to some minimum weight [2,3], causing a more additive-like [2,8] behaviour of the plasticity rule. We therefore examined possible biological interpretations of attractor-less STDP rules while keeping in mind that any STDP rule is just an abstraction from the hidden biophysical reality. We show how unimodal weight distributions can reliably result from attractor-less STDP when negative synaptic drift is combined with activity-independent synaptic growth. A bimodal distribution is then only formed when non-random (polychromous [10]) poisson-distributed inputs are presented to a neuron [11]. In practice, this produces a plasticity rule that keeps the postsynaptic neuron unselective and responsive to a broad range of inputs while receiving only random spikes, but quickly allows the neuron's receptive field to become highly selective as soon as some inputs start repeating a non-random ordering of spikes. This stabilization procedure preserves STDP's sensitivity to temporally shifted correlations in input spike data, which in turn gives us several beneficial features for biologically more realistic and computationally more powerful [12] implementations of plasticity in spiking neural networks.

The influence of strong connections on dynamics of neuron population with long-tailed synaptic weight distribution

This work is devoted to exploring the influence of long-tailed synaptic weights distribution on neural population dynamics. We show numerically that both strong sparse and very weak connections pay crucial role for spontaneous activity whereas they almost do not influence on driven population activity. Moreover, according to obtained results, we suggest that neurons with strong connections form multiple chains, which are the core of spontaneous activity, whereas neurons with weak connections pay little role of partially enhancing of population activity.

A Lognormal Recurrent Network Model for Burst Generation during Hippocampal Sharp Waves.

The strength of cortical synapses distributes lognormally, with a long tail of strong synapses. Various properties of neuronal activity, such as the average firing rates of neurons, the rate and magnitude of spike bursts, the magnitude of population synchrony, and the correlations between presynaptic and postsynaptic spikes, also obey lognormal-like distributions reported in the rodent hippocampal CA1 and CA3 areas. Theoretical models have demonstrated how such a firing rate distribution emerges from neural network dynamics. However, how the other properties also display lognormal patterns remain unknown. Because these features are likely to originate from neural dynamics in CA3, we model a recurrent neural network with the weights of recurrent excitatory connections distributed lognormally to explore the underlying mechanisms and their functional implications. Using multi-timescale adaptive threshold neurons, we construct a low-frequency spontaneous firing state of bursty neurons. This state well replicates the observed statistical properties of population synchrony in hippocampal pyramidal cells. Our results show that the lognormal distribution of synaptic weights consistently accounts for the observed long-tailed features of hippocampal activity. Furthermore, our model demonstrates that bursts spread over the lognormal network much more effectively than single spikes, implying an advantage of spike bursts in information transfer. This efficiency in burst propagation is not found in neural network models with Gaussian-weighted recurrent excitatory synapses. Our model proposes a potential network mechanism to generate sharp waves in CA3 and associated ripples in CA1 because bursts occur in CA3 pyramidal neurons most frequently during sharp waves.

Self-Organized Near-Zero-Lag Synchronization Induced by Spike-Timing Dependent Plasticity in Cortical Populations.

Several cognitive tasks related to learning and memory exhibit synchronization of macroscopic cortical areas together with synaptic plasticity at neuronal level. Therefore, there is a growing effort among computational neuroscientists to understand the underlying mechanisms relating synchrony and plasticity in the brain. Here we numerically study the interplay between spike-timing dependent plasticity (STDP) and anticipated synchronization (AS). AS emerges when a dominant flux of information from one area to another is accompanied by a negative time lag (or phase). This means that the receiver region pulses before the sender does. In this paper we study the interplay between different synchronization regimes and STDP at the level of three-neuron microcircuits as well as cortical populations. We show that STDP can promote auto-organized zero-lag synchronization in unidirectionally coupled neuronal populations. We also find synchronization regimes with negative phase difference (AS) that are stable against plasticity. Finally, we show that the interplay between negative phase difference and STDP provides limited synaptic weight distribution without the need of imposing artificial boundaries.