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Reconstruction of recurrent synaptic connectivity of thousands of neurons from simulated spiking activity.

Zaytsev YV, Morrison A, Deger M - J Comput Neurosci (2015)

Bottom Line: Previous methods, including those of the same class, did not allow recurrent networks of that order of magnitude to be reconstructed due to prohibitive computational cost and numerical instabilities.Finally, we successfully reconstruct the connectivity of a hidden synfire chain that is embedded in a random network, which requires clustering of the network connectivity to reveal the synfire groups.Our results demonstrate how synaptic connectivity could potentially be inferred from large-scale parallel spike train recordings.

View Article: PubMed Central - PubMed

Affiliation: Simulation Laboratory Neuroscience - Bernstein Facility for Simulation and Database Technology, Institute for Advanced Simulation, Jülich Aachen Research Alliance, Jülich Research Center, Jülich, Germany, yury@zaytsev.net.

ABSTRACT
Dynamics and function of neuronal networks are determined by their synaptic connectivity. Current experimental methods to analyze synaptic network structure on the cellular level, however, cover only small fractions of functional neuronal circuits, typically without a simultaneous record of neuronal spiking activity. Here we present a method for the reconstruction of large recurrent neuronal networks from thousands of parallel spike train recordings. We employ maximum likelihood estimation of a generalized linear model of the spiking activity in continuous time. For this model the point process likelihood is concave, such that a global optimum of the parameters can be obtained by gradient ascent. Previous methods, including those of the same class, did not allow recurrent networks of that order of magnitude to be reconstructed due to prohibitive computational cost and numerical instabilities. We describe a minimal model that is optimized for large networks and an efficient scheme for its parallelized numerical optimization on generic computing clusters. For a simulated balanced random network of 1000 neurons, synaptic connectivity is recovered with a misclassification error rate of less than 1 % under ideal conditions. We show that the error rate remains low in a series of example cases under progressively less ideal conditions. Finally, we successfully reconstruct the connectivity of a hidden synfire chain that is embedded in a random network, which requires clustering of the network connectivity to reveal the synfire groups. Our results demonstrate how synaptic connectivity could potentially be inferred from large-scale parallel spike train recordings.

No MeSH data available.


Identification of an embedded synfire chain by clustering connectivity estimated from “background” spiking activity. The grouping by rows delineates the panels produced on the basis of the ground truth connectivity, connections estimated using the GLM model, and lagged cross-correlation data. The grouping by columns lays out the panels presenting the connectivity matrices where the order of the neuron identifiers have been randomized, recovered by clustering and defined by the sequence in which the neurons were originally wired up. a, d, g Ground truth and MLE reconstructed synaptic weights, as well as lagged cross-correlation coefficient matrices for randomized neuron identifier order. c, f The red rectangles correspond to the connections from one chain link to the next. Thin blue bands identify inhibitory neurons that belong to the synfire chain. The wide blue band corresponds to the inhibitory neurons that are not part of the chain. b, e The interpretation of the bigger red rectangles and the wide blue band is the same as above, except that all inhibitory neurons are now grouped together. The thin red rectangles at the bottom correspond to the groups of inhibitory neurons in the synfire chain receiving incoming connections from all excitatory neurons in the previous link. The clustering process that produced the reordering and the dendrograms is illustrated in steps in Fig. 8. g, h, i The lagged cross-correlation matrix is symmetric by construction. Therefore, the dendrograms at the top and on the right of panel h are identical (unlike b, e). Diagonal entries (all 1) were excluded here.h, i The red rectangles correspond to groups of neurons that exhibit positively correlated firing activity, while inhibitory neurons display negative correlation, marked by the blue bands
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Fig9: Identification of an embedded synfire chain by clustering connectivity estimated from “background” spiking activity. The grouping by rows delineates the panels produced on the basis of the ground truth connectivity, connections estimated using the GLM model, and lagged cross-correlation data. The grouping by columns lays out the panels presenting the connectivity matrices where the order of the neuron identifiers have been randomized, recovered by clustering and defined by the sequence in which the neurons were originally wired up. a, d, g Ground truth and MLE reconstructed synaptic weights, as well as lagged cross-correlation coefficient matrices for randomized neuron identifier order. c, f The red rectangles correspond to the connections from one chain link to the next. Thin blue bands identify inhibitory neurons that belong to the synfire chain. The wide blue band corresponds to the inhibitory neurons that are not part of the chain. b, e The interpretation of the bigger red rectangles and the wide blue band is the same as above, except that all inhibitory neurons are now grouped together. The thin red rectangles at the bottom correspond to the groups of inhibitory neurons in the synfire chain receiving incoming connections from all excitatory neurons in the previous link. The clustering process that produced the reordering and the dendrograms is illustrated in steps in Fig. 8. g, h, i The lagged cross-correlation matrix is symmetric by construction. Therefore, the dendrograms at the top and on the right of panel h are identical (unlike b, e). Diagonal entries (all 1) were excluded here.h, i The red rectangles correspond to groups of neurons that exhibit positively correlated firing activity, while inhibitory neurons display negative correlation, marked by the blue bands

Mentions: In Fig. 9, the clustered matrices (middle column) are contrasted with the matrices in randomized (left column) and original ordering (right column), i.e. the initial indexing of neurons that we used to define the neuron groups of the synfire chain network. An identical clustering procedure was applied to the ground truth connectivity matrix (Fig. 9a–c) and the one obtained from MLE estimation using the recorded spike trains (Fig. 9d–f). Note that, as explained at the end of Section 3.2, the reconstructed values of the synaptic weights in the second row cannot be directly compared to the original synaptic strengths.Fig. 9


Reconstruction of recurrent synaptic connectivity of thousands of neurons from simulated spiking activity.

Zaytsev YV, Morrison A, Deger M - J Comput Neurosci (2015)

Identification of an embedded synfire chain by clustering connectivity estimated from “background” spiking activity. The grouping by rows delineates the panels produced on the basis of the ground truth connectivity, connections estimated using the GLM model, and lagged cross-correlation data. The grouping by columns lays out the panels presenting the connectivity matrices where the order of the neuron identifiers have been randomized, recovered by clustering and defined by the sequence in which the neurons were originally wired up. a, d, g Ground truth and MLE reconstructed synaptic weights, as well as lagged cross-correlation coefficient matrices for randomized neuron identifier order. c, f The red rectangles correspond to the connections from one chain link to the next. Thin blue bands identify inhibitory neurons that belong to the synfire chain. The wide blue band corresponds to the inhibitory neurons that are not part of the chain. b, e The interpretation of the bigger red rectangles and the wide blue band is the same as above, except that all inhibitory neurons are now grouped together. The thin red rectangles at the bottom correspond to the groups of inhibitory neurons in the synfire chain receiving incoming connections from all excitatory neurons in the previous link. The clustering process that produced the reordering and the dendrograms is illustrated in steps in Fig. 8. g, h, i The lagged cross-correlation matrix is symmetric by construction. Therefore, the dendrograms at the top and on the right of panel h are identical (unlike b, e). Diagonal entries (all 1) were excluded here.h, i The red rectangles correspond to groups of neurons that exhibit positively correlated firing activity, while inhibitory neurons display negative correlation, marked by the blue bands
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Fig9: Identification of an embedded synfire chain by clustering connectivity estimated from “background” spiking activity. The grouping by rows delineates the panels produced on the basis of the ground truth connectivity, connections estimated using the GLM model, and lagged cross-correlation data. The grouping by columns lays out the panels presenting the connectivity matrices where the order of the neuron identifiers have been randomized, recovered by clustering and defined by the sequence in which the neurons were originally wired up. a, d, g Ground truth and MLE reconstructed synaptic weights, as well as lagged cross-correlation coefficient matrices for randomized neuron identifier order. c, f The red rectangles correspond to the connections from one chain link to the next. Thin blue bands identify inhibitory neurons that belong to the synfire chain. The wide blue band corresponds to the inhibitory neurons that are not part of the chain. b, e The interpretation of the bigger red rectangles and the wide blue band is the same as above, except that all inhibitory neurons are now grouped together. The thin red rectangles at the bottom correspond to the groups of inhibitory neurons in the synfire chain receiving incoming connections from all excitatory neurons in the previous link. The clustering process that produced the reordering and the dendrograms is illustrated in steps in Fig. 8. g, h, i The lagged cross-correlation matrix is symmetric by construction. Therefore, the dendrograms at the top and on the right of panel h are identical (unlike b, e). Diagonal entries (all 1) were excluded here.h, i The red rectangles correspond to groups of neurons that exhibit positively correlated firing activity, while inhibitory neurons display negative correlation, marked by the blue bands
Mentions: In Fig. 9, the clustered matrices (middle column) are contrasted with the matrices in randomized (left column) and original ordering (right column), i.e. the initial indexing of neurons that we used to define the neuron groups of the synfire chain network. An identical clustering procedure was applied to the ground truth connectivity matrix (Fig. 9a–c) and the one obtained from MLE estimation using the recorded spike trains (Fig. 9d–f). Note that, as explained at the end of Section 3.2, the reconstructed values of the synaptic weights in the second row cannot be directly compared to the original synaptic strengths.Fig. 9

Bottom Line: Previous methods, including those of the same class, did not allow recurrent networks of that order of magnitude to be reconstructed due to prohibitive computational cost and numerical instabilities.Finally, we successfully reconstruct the connectivity of a hidden synfire chain that is embedded in a random network, which requires clustering of the network connectivity to reveal the synfire groups.Our results demonstrate how synaptic connectivity could potentially be inferred from large-scale parallel spike train recordings.

View Article: PubMed Central - PubMed

Affiliation: Simulation Laboratory Neuroscience - Bernstein Facility for Simulation and Database Technology, Institute for Advanced Simulation, Jülich Aachen Research Alliance, Jülich Research Center, Jülich, Germany, yury@zaytsev.net.

ABSTRACT
Dynamics and function of neuronal networks are determined by their synaptic connectivity. Current experimental methods to analyze synaptic network structure on the cellular level, however, cover only small fractions of functional neuronal circuits, typically without a simultaneous record of neuronal spiking activity. Here we present a method for the reconstruction of large recurrent neuronal networks from thousands of parallel spike train recordings. We employ maximum likelihood estimation of a generalized linear model of the spiking activity in continuous time. For this model the point process likelihood is concave, such that a global optimum of the parameters can be obtained by gradient ascent. Previous methods, including those of the same class, did not allow recurrent networks of that order of magnitude to be reconstructed due to prohibitive computational cost and numerical instabilities. We describe a minimal model that is optimized for large networks and an efficient scheme for its parallelized numerical optimization on generic computing clusters. For a simulated balanced random network of 1000 neurons, synaptic connectivity is recovered with a misclassification error rate of less than 1 % under ideal conditions. We show that the error rate remains low in a series of example cases under progressively less ideal conditions. Finally, we successfully reconstruct the connectivity of a hidden synfire chain that is embedded in a random network, which requires clustering of the network connectivity to reveal the synfire groups. Our results demonstrate how synaptic connectivity could potentially be inferred from large-scale parallel spike train recordings.

No MeSH data available.