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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.


Unregularized and ℓ1-regularized reconstruction of a random balanced network of LIF neurons with α-shaped PSCs and distributed parameters. The colored solid step lines show PDFs approximated with histograms of n=200 bins of the reconstructed synaptic weights corresponding to the classification via k-means clustering. Vertical lines demarking the boundaries between distributions designate the points that are equidistant from the identified centroids. The colored bars under the curves represent PDFs estimated by histograms of n=200 bins, classified using the ground truth connectivity matrix, as in Figs. 3 and 5
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Fig6: Unregularized and ℓ1-regularized reconstruction of a random balanced network of LIF neurons with α-shaped PSCs and distributed parameters. The colored solid step lines show PDFs approximated with histograms of n=200 bins of the reconstructed synaptic weights corresponding to the classification via k-means clustering. Vertical lines demarking the boundaries between distributions designate the points that are equidistant from the identified centroids. The colored bars under the curves represent PDFs estimated by histograms of n=200 bins, classified using the ground truth connectivity matrix, as in Figs. 3 and 5

Mentions: The estimation results for this dataset are shown in Fig. 6 and Table 5 (left panel and left part of the table respectively). The PDFs of the reconstructed synaptic weights were approximated using Gaussian KDE. Obviously, the individual components of the PDF were distorted, because instead of using optimal values for τi and di, we used rather arbitrarily chosen fixed values for all neurons and connections. However, more importantly, as the components of the original PDF of synaptic weights were broad distributions rather than δ-functions, the resulting recovered distribution components are strongly non-Gaussian. Therefore, in this case the EM procedure for GMM fails to converge to reasonable means and variances, and is no longer a viable choice to perform the classification of connections.Fig. 6


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

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

Unregularized and ℓ1-regularized reconstruction of a random balanced network of LIF neurons with α-shaped PSCs and distributed parameters. The colored solid step lines show PDFs approximated with histograms of n=200 bins of the reconstructed synaptic weights corresponding to the classification via k-means clustering. Vertical lines demarking the boundaries between distributions designate the points that are equidistant from the identified centroids. The colored bars under the curves represent PDFs estimated by histograms of n=200 bins, classified using the ground truth connectivity matrix, as in Figs. 3 and 5
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4493949&req=5

Fig6: Unregularized and ℓ1-regularized reconstruction of a random balanced network of LIF neurons with α-shaped PSCs and distributed parameters. The colored solid step lines show PDFs approximated with histograms of n=200 bins of the reconstructed synaptic weights corresponding to the classification via k-means clustering. Vertical lines demarking the boundaries between distributions designate the points that are equidistant from the identified centroids. The colored bars under the curves represent PDFs estimated by histograms of n=200 bins, classified using the ground truth connectivity matrix, as in Figs. 3 and 5
Mentions: The estimation results for this dataset are shown in Fig. 6 and Table 5 (left panel and left part of the table respectively). The PDFs of the reconstructed synaptic weights were approximated using Gaussian KDE. Obviously, the individual components of the PDF were distorted, because instead of using optimal values for τi and di, we used rather arbitrarily chosen fixed values for all neurons and connections. However, more importantly, as the components of the original PDF of synaptic weights were broad distributions rather than δ-functions, the resulting recovered distribution components are strongly non-Gaussian. Therefore, in this case the EM procedure for GMM fails to converge to reasonable means and variances, and is no longer a viable choice to perform the classification of connections.Fig. 6

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.