The functional significance of correlations between action potentials of neurons is still a matter of vivid debate. In particular, it is presently unclear how much synchrony is caused by afferent synchronized events and how much is intrinsic due to the connectivity structure of cortex. The available analytical approaches based on the diffusion approximation do not allow to model spike synchrony, preventing a thorough analysis. Here we theoretically investigate to what extent common synaptic afferents and synchronized inputs each contribute to correlated spiking on a fine temporal scale between pairs of neurons. We employ direct simulation and extend earlier analytical methods based on the diffusion approximation to pulse-coupling, allowing us to introduce precisely timed correlations in the spiking activity of the synaptic afferents. We investigate the transmission of correlated synaptic input currents by pairs of integrate-and-fire model neurons, so that the same input covariance can be realized by common inputs or by spiking synchrony. We identify two distinct regimes: In the limit of low correlation linear perturbation theory accurately determines the correlation transmission coefficient, which is typically smaller than unity, but increases sensitively even for weakly synchronous inputs. In the limit of high input correlation, in the presence of synchrony, a qualitatively new picture arises. As the non-linear neuronal response becomes dominant, the output correlation becomes higher than the total correlation in the input. This transmission coefficient larger unity is a direct consequence of non-linear neural processing in the presence of noise, elucidating how synchrony-coded signals benefit from these generic properties present in cortical networks.
Whether spike timing conveys information in cortical networks or whether the firing rate alone is sufficient is a matter of controversial debate, touching the fundamental question of how the brain processes, stores, and conveys information. If the firing rate alone is the decisive signal used in the brain, correlations between action potentials are just an epiphenomenon of cortical connectivity, where pairs of neurons share a considerable fraction of common afferents. Due to membrane leakage, small synaptic amplitudes and the non-linear threshold, nerve cells exhibit lossy transmission of correlation originating from shared synaptic inputs. However, the membrane potential of cortical neurons often displays non-Gaussian fluctuations, caused by synchronized synaptic inputs. Moreover, synchronously active neurons have been found to reflect behavior in primates. In this work we therefore contrast the transmission of correlation due to shared afferents and due to synchronously arriving synaptic impulses for leaky neuron models. We not only find that neurons are highly sensitive to synchronous afferents, but that they can suppress noise on signals transmitted by synchrony, a computational advantage over rate signals.
This article discusses the compositional structure of hand movements by analyzing and modeling neural and behavioral data obtained from experiments where a monkey (Macaca fascicularis) performed scribbling movements induced by a search task. Using geometrically based approaches to movement segmentation, it is shown that the hand trajectories are composed of elementary segments that are primarily parabolic in shape. The segments could be categorized into a small number of classes on the basis of decreasing intra-class variance over the course of training. A separate classification of the neural data employing a hidden Markov model showed a coincidence of the neural states with the behavioral categories. An additional analysis of both types of data by a data mining method provided evidence that the neural activity patterns underlying the behavioral primitives were formed by sets of specific and precise spike patterns. A geometric description of the movement trajectories, together with precise neural timing data indicates a compositional variant of a realistic synfire chain model. This model reproduces the typical shapes and temporal properties of the trajectories; hence the structure and composition of the primitives may reflect meaningful behavior.
voluntary-movements; scribbling; compositionality; hand-motion-model; synfire chains; motion-primitives
The diversity of neuron models used in contemporary theoretical neuroscience to investigate specific properties of covariances in the spiking activity raises the question how these models relate to each other. In particular it is hard to distinguish between generic properties of covariances and peculiarities due to the abstracted model. Here we present a unified view on pairwise covariances in recurrent networks in the irregular regime. We consider the binary neuron model, the leaky integrate-and-fire (LIF) model, and the Hawkes process. We show that linear approximation maps each of these models to either of two classes of linear rate models (LRM), including the Ornstein–Uhlenbeck process (OUP) as a special case. The distinction between both classes is the location of additive noise in the rate dynamics, which is located on the output side for spiking models and on the input side for the binary model. Both classes allow closed form solutions for the covariance. For output noise it separates into an echo term and a term due to correlated input. The unified framework enables us to transfer results between models. For example, we generalize the binary model and the Hawkes process to the situation with synaptic conduction delays and simplify derivations for established results. Our approach is applicable to general network structures and suitable for the calculation of population averages. The derived averages are exact for fixed out-degree network architectures and approximate for fixed in-degree. We demonstrate how taking into account fluctuations in the linearization procedure increases the accuracy of the effective theory and we explain the class dependent differences between covariances in the time and the frequency domain. Finally we show that the oscillatory instability emerging in networks of LIF models with delayed inhibitory feedback is a model-invariant feature: the same structure of poles in the complex frequency plane determines the population power spectra.
correlations; linear response; Hawkes process; leaky integrate-and-fire model; binary neuron; linear rate model; Ornstein–Uhlenbeck process
Structural plasticity governs the long-term development of synaptic connections in the neocortex. While the underlying processes at the synapses are not fully understood, there is strong evidence that a process of random, independent formation and pruning of excitatory synapses can be ruled out. Instead, there must be some cooperation between the synaptic contacts connecting a single pre- and postsynaptic neuron pair. So far, the mechanism of cooperation is not known. Here we demonstrate that local correlation detection at the postsynaptic dendritic spine suffices to explain the synaptic cooperation effect, without assuming any hypothetical direct interaction pathway between the synaptic contacts. Candidate biomolecular mechanisms for dendritic correlation detection have been identified previously, as well as for structural plasticity based thereon. By analyzing and fitting of a simple model, we show that spike-timing correlation dependent structural plasticity, without additional mechanisms of cross-synapse interaction, can reproduce the experimentally observed distributions of numbers of synaptic contacts between pairs of neurons in the neocortex. Furthermore, the model yields a first explanation for the existence of both transient and persistent dendritic spines and allows to make predictions for future experiments.
Structural plasticity has been observed even in the adult mammalian neocortex – in seemingly static neuronal circuits structural remodeling is continuously at work. Still, it has been shown that the connection patterns between pairs of neurons are not random. In contrast, there is evidence that the synaptic contacts between a pair of neurons cooperate: several experimental studies report either zero or about 3–6 synapses between neuron pairs. The mechanism by which the synapses cooperate, however, has not yet been identified. Here we propose a model for structural plasticity that relies on local processes at the dendritic spine. We combine and extend the previous models and determine the equilibrium probability distribution of synaptic contact numbers of the model. By optimizing the parameters numerically for each of three reference datasets, we obtain equilibrium contact number distributions that fit the references very well. We conclude that the local dendritic mechanisms that we assume suffice to explain the cooperative synapse formation in the neocortex.
Synfire chains, sequences of pools linked by feedforward connections, support the propagation of precisely timed spike sequences, or synfire waves. An important question remains, how synfire chains can efficiently be embedded in cortical architecture. We present a model of synfire chain embedding in a cortical scale recurrent network using conductance-based synapses, balanced chains, and variable transmission delays. The network attains substantially higher embedding capacities than previous spiking neuron models and allows all its connections to be used for embedding. The number of waves in the model is regulated by recurrent background noise. We computationally explore the embedding capacity limit, and use a mean field analysis to describe the equilibrium state. Simulations confirm the mean field analysis over broad ranges of pool sizes and connectivity levels; the number of pools embedded in the system trades off against the firing rate and the number of waves. An optimal inhibition level balances the conflicting requirements of stable synfire propagation and limited response to background noise. A simplified analysis shows that the present conductance-based synapses achieve higher contrast between the responses to synfire input and background noise compared to current-based synapses, while regulation of wave numbers is traced to the use of variable transmission delays.
Recurrent network dynamics; Feedforward network; Synchrony; Synaptic conductance; Synfire chain; Storage capacity
Correlations in spike-train ensembles can seriously impair the encoding of
information by their spatio-temporal structure. An inevitable source of
correlation in finite neural networks is common presynaptic input to pairs of
neurons. Recent studies demonstrate that spike correlations in recurrent neural
networks are considerably smaller than expected based on the amount of shared
presynaptic input. Here, we explain this observation by means of a linear
network model and simulations of networks of leaky integrate-and-fire neurons.
We show that inhibitory feedback efficiently suppresses pairwise correlations
and, hence, population-rate fluctuations, thereby assigning inhibitory neurons
the new role of active decorrelation. We quantify this decorrelation by
comparing the responses of the intact recurrent network (feedback system) and
systems where the statistics of the feedback channel is perturbed (feedforward
system). Manipulations of the feedback statistics can lead to a significant
increase in the power and coherence of the population response. In particular,
neglecting correlations within the ensemble of feedback channels or between the
external stimulus and the feedback amplifies population-rate fluctuations by
orders of magnitude. The fluctuation suppression in homogeneous inhibitory
networks is explained by a negative feedback loop in the one-dimensional
dynamics of the compound activity. Similarly, a change of coordinates exposes an
effective negative feedback loop in the compound dynamics of stable
excitatory-inhibitory networks. The suppression of input correlations in finite
networks is explained by the population averaged correlations in the linear
network model: In purely inhibitory networks, shared-input correlations are
canceled by negative spike-train correlations. In excitatory-inhibitory
networks, spike-train correlations are typically positive. Here, the suppression
of input correlations is not a result of the mere existence of correlations
between excitatory (E) and inhibitory (I) neurons, but a consequence of a
particular structure of correlations among the three possible pairings (EE, EI,
The spatio-temporal activity pattern generated by a recurrent neuronal network
can provide a rich dynamical basis which allows readout neurons to generate a
variety of responses by tuning the synaptic weights of their inputs. The
repertoire of possible responses and the response reliability become maximal if
the spike trains of individual neurons are uncorrelated. Spike-train
correlations in cortical networks can indeed be very small, even for neighboring
neurons. This seems to be at odds with the finding that neighboring neurons
receive a considerable fraction of inputs from identical presynaptic sources
constituting an inevitable source of correlation. In this article, we show that
inhibitory feedback, abundant in biological neuronal networks, actively
suppresses correlations. The mechanism is generic: It does not depend on the
details of the network nodes and decorrelates networks composed of excitatory
and inhibitory neurons as well as purely inhibitory networks. For the case of
the leaky integrate-and-fire model, we derive the correlation structure
analytically. The new toolbox of formal linearization and a basis transformation
exposing the feedback component is applicable to a range of biological systems.
We confirm our analytical results by direct simulations.
Large-scale neuromorphic hardware systems typically bear the trade-off between detail level and required chip resources. Especially when implementing spike-timing dependent plasticity, reduction in resources leads to limitations as compared to floating point precision. By design, a natural modification that saves resources would be reducing synaptic weight resolution. In this study, we give an estimate for the impact of synaptic weight discretization on different levels, ranging from random walks of individual weights to computer simulations of spiking neural networks. The FACETS wafer-scale hardware system offers a 4-bit resolution of synaptic weights, which is shown to be sufficient within the scope of our network benchmark. Our findings indicate that increasing the resolution may not even be useful in light of further restrictions of customized mixed-signal synapses. In addition, variations due to production imperfections are investigated and shown to be uncritical in the context of the presented study. Our results represent a general framework for setting up and configuring hardware-constrained synapses. We suggest how weight discretization could be considered for other backends dedicated to large-scale simulations. Thus, our proposition of a good hardware verification practice may rise synergy effects between hardware developers and neuroscientists.
neuromorphic hardware; wafer-scale integration; large-scale spiking neural networks; spike-timing dependent plasticity; synaptic weight resolution; circuit variations; PyNN; NEST
NEST is a widely used tool to simulate biological spiking neural networks. Here we explain the improvements, guided by a mathematical model of memory consumption, that enable us to exploit for the first time the computational power of the K supercomputer for neuroscience. Multi-threaded components for wiring and simulation combine 8 cores per MPI process to achieve excellent scaling. K is capable of simulating networks corresponding to a brain area with 108 neurons and 1012 synapses in the worst case scenario of random connectivity; for larger networks of the brain its hierarchical organization can be exploited to constrain the number of communicating computer nodes. We discuss the limits of the software technology, comparing maximum filling scaling plots for K and the JUGENE BG/P system. The usability of these machines for network simulations has become comparable to running simulations on a single PC. Turn-around times in the range of minutes even for the largest systems enable a quasi interactive working style and render simulations on this scale a practical tool for computational neuroscience.
supercomputer; large-scale simulation; spiking neural networks; parallel computing; computational neuroscience
The CoCoMac database contains the results of several hundred published axonal tract-tracing studies in the macaque monkey brain. The combined results are used for constructing the macaque macro-connectome. Here we discuss the redevelopment of CoCoMac and compare it to six connectome-related projects: two online resources that provide full access to raw tracing data in rodents, a connectome viewer for advanced 3D graphics, a partial but highly detailed rat connectome, a brain data management system that generates custom connectivity matrices, and a software package that covers the complete pipeline from connectivity data to large-scale brain simulations. The second edition of CoCoMac features many enhancements over the original. For example, a search wizard is provided for full access to all tables and their nested dependencies. Connectivity matrices can be computed on demand in a user-selected nomenclature. A new data entry system is available as a preview, and is to become a generic solution for community-driven data entry in manually collated databases. We conclude with the question whether neuronal tracing will remain the gold standard to uncover the wiring of brains, thereby highlighting developments in human connectome construction, tracer substances, polarized light imaging, and serial block-face scanning electron microscopy.
CoCoMac; macaque; connectivity; database; axonal tracing