State-of-the-art techniques allow researchers to record large numbers of spike trains in parallel for many hours. With enough such data, we should be able to infer the connectivity among neurons. Here we develop a method for reconstructing neuronal circuitry by applying a generalized linear model (GLM) to spike cross-correlations. Our method estimates connections between neurons in units of postsynaptic potentials and the amount of spike recordings needed to verify connections. The performance of inference is optimized by counting the estimation errors using synthetic data. This method is superior to other established methods in correctly estimating connectivity. By applying our method to rat hippocampal data, we show that the types of estimated connections match the results inferred from other physiological cues. Thus our method provides the means to build a circuit diagram from recorded spike trains, thereby providing a basis for elucidating the differences in information processing in different brain regions.

The activity patterns of subthalamic nucleus (STN) neurons are intimately linked to motor function and dysfunction and arise through the complex interaction of intrinsic properties and inhibitory and excitatory synaptic inputs. In many neurons, hyperpolarizationactivated cyclic nucleotide-gated (HCN) channels play key roles in intrinsic excitability and synaptic integration both under normal conditions and in disease states. However, in STN neurons, which strongly express HCN channels, their roles remain relatively obscure. To address this deficit, complementary molecular and cellular electrophysiological, imaging, and computational approaches were applied to the rat STN. Molecular profiling demonstrated that individual STN neurons express mRNA encoding several HCN subunits, with HCN2 and 3 being the most abundant. Light and electron microscopic analysis showed that HCN2 subunits are strongly expressed and distributed throughout the somatodendritic plasma membrane. Voltage-, current-, and dynamic-clamp analysis, two-photon Ca 2ϩ imaging, and computational modeling revealed that HCN channels are activated by GABA A receptor-mediated inputs and thus limit synaptic hyperpolarization and deinactivation of low-voltage-activated Ca 2ϩ channels. Although HCN channels also limited the temporal summation of EPSPs, generated through two-photon uncaging of glutamate, this action was largely shunted by GABAergic inhibition that was necessary for HCN channel activation. Together the data demonstrate that HCN channels in STN neurons selectively counteract GABA A receptor-mediated inhibition arising from the globus pallidus and thus promote single-spike activity rather than rebound burst firing.

A phase response curve (PRC) characterizes the signal transduction between oscillators such as neurons on a fixed network in a minimal manner, while spike-timing-dependent plasiticity (STDP) characterizes the way of rewiring networks in an activity-dependent manner. This paper demonstrates that these two key properties both related to the interaction times of oscillators work synergetically to carve functionally useful circuits. STDP working on neurons that prefer asynchrony converts the initial asynchronous firing to clustered firing with synchrony within a cluster. They get synchronized within a cluster despite their preference to asynchrony because STDP selectively disrupts intracluster connections, which we call wireless clustering. Our PRC analysis reveals a triad mechanism: the network structure affects how the PRC is read out to determine the synchrony tendency, the synchrony tendency affects how the STDP works, and STDP affects the network structure, closing the loop.

State-of-the-art techniques allow researchers to record large numbers of spike trains parallel for many hours. With enough such data, we should be able to infer the connectivity among neurons. Here we develop a computationally realizable method for reconstructing neuronal circuitry by applying a generalized linear model (GLM) to spike crosscorrelations. Our method estimates interneuronal connections in units of postsynaptic potentials and the amount of spike recording needed for verifying connections. The performance of inference is optimized by counting the estimation errors using synthetic data from a network of Hodgkin-Huxley type neurons. By applying our method to rat hippocampal data, we show that the numbers and types of connections estimated from our calculations match the results inferred from other physiological cues. Our method provides the means to build a circuit diagram from recorded spike trains, thereby providing a basis for elucidating the differences in information processing in different brain regions.

Dynamical behavior of a biological neuronal network depends significantly on the spatial pattern of synaptic connections among neurons. While neuronal network dynamics has extensively been studied with simple wiring patterns, such as all-to-all or random synaptic connections, not much is known about the activity of networks with more complicated wiring topologies. Here, we examined how different wiring topologies may influence the response properties of neuronal networks, paying attention to irregular spike firing, which is known as a characteristic of in vivo cortical neurons, and spike synchronicity. We constructed a recurrent network model of realistic neurons and systematically rewired the recurrent synapses to change the network topology, from a localized regular and a "small-world" network topology to a distributed random network topology. Regular and small-world wiring patterns greatly increased the irregularity or the coefficient of variation (Cv) of output spike trains, whereas such an increase was small in random connectivity patterns. For given strength of recurrent synapses, the firing irregularity exhibited monotonous decreases from the regular to the random network topology. By contrast, the spike coherence between an arbitrary neuron pair exhibited a non-monotonous dependence on the topological wiring pattern. More precisely, the wiring pattern to maximize the spike coherence varied with the strength of recurrent synapses. In a certain range of the synaptic strength, the spike coherence was maximal in the small-world network topology, and the long-range connections introduced in this wiring changed the dependence of spike synchrony on the synaptic strength moderately. However, the effects of this network topology were not really special in other properties of network activity.

Many mechanisms of neural processing rely critically upon the synaptic connectivity between neurons. As our ability to simultaneously record from large populations of neurons expands, the ability to infer network connectivity from this data has become a major goal of computational neuroscience. To address this issue, we employed several different methods to infer synaptic connections from simulated spike data from a realistic local cortical network model. This approach allowed us to directly compare the accuracy of different methods in predicting synaptic connectivity. We compared the performance of model-free (coherence measure and transfer entropy) and model-based (coupled escape rate model) methods of connectivity inference, applying those methods to the simulated spike data from the model networks with different network topologies. Our results indicate that the accuracy of the inferred connectivity was higher for highly clustered, near regular, or small-world networks, while accuracy was lower for random networks, irrespective of which analysis method was employed. Among the employed methods, the model-based method performed best. This model performed with higher accuracy, was less sensitive to threshold changes, and required less data to make an accurate assessment of connectivity. Given that cortical connectivity tends to be highly clustered, our results outline a powerful analytical tool for inferring local synaptic connectivity from observations of spontaneous activity.

It is well known that a sparsely coded network in which the activity level is extremely low has intriguing equilibrium properties. In the present work, we study the dynamical properties of a neural network designed to store sparsely coded sequential patterns rather than static ones. Applying the theory of statistical neurodynamics, we derive the dynamical equations governing the retrieval process which are described by some macroscopic order parameters such as the overlap. It is found that our theory provides good predictions for the storage capacity and the basin of attraction obtained through numerical simulations. The results indicate that the nature of the basin of attraction depends on the methods of activity control employed. Furthermore, it is found that robustness against random synaptic dilution slightly deteriorates with the degree of sparseness.

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