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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.


Reconstruction of a random balanced network of LIF neurons with α-shaped PSCs. The reconstruction was performed for τ=10 ms, d=1.7 ms (obtained through cross-validation) and ds=0.1 ms. a GMM fit for the PDF of the reconstructed synaptic weight matrix (black solid curve) and individual components (colored solid lines); colored bars under the curves show the distributions of the reconstructed synaptic weights classified using the ground truth synaptic connectivity matrix as in Fig. 3, approximated as histograms of n=200 bins. The scale of the vertical axis is logarithmic, except for the first decade, which is in linear scale. b, c Histograms and Gaussian KDEs approximating the PDFs of the base rates and self-connection weights
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Fig5: Reconstruction of a random balanced network of LIF neurons with α-shaped PSCs. The reconstruction was performed for τ=10 ms, d=1.7 ms (obtained through cross-validation) and ds=0.1 ms. a GMM fit for the PDF of the reconstructed synaptic weight matrix (black solid curve) and individual components (colored solid lines); colored bars under the curves show the distributions of the reconstructed synaptic weights classified using the ground truth synaptic connectivity matrix as in Fig. 3, approximated as histograms of n=200 bins. The scale of the vertical axis is logarithmic, except for the first decade, which is in linear scale. b, c Histograms and Gaussian KDEs approximating the PDFs of the base rates and self-connection weights

Mentions: After determining τ=10 ms and d=1.7 ms through the cross-validation procedure, we used these values to estimate the connectivity and base rates. The results of the connectivity reconstruction on the training dataset were processed in the same way as in the previous subsection and are presented in Fig. 5, with further details on the classification of synaptic connections in Table 3. We find that the reconstruction quality as defined by classification into the groups of excitatory, inhibitory and connections closely matches the performance on the ideal dataset analyzed in the previous section, despite the mismatch in models and the suboptimal choice of τ and d. Note that in this experiment, the recovered values of synaptic weights in mV cannot be compared directly to the ones that were used in the simulation which produced the data due to the differences between GLM and LIF models, unlike in the first experiment described in Section 3.1. However, this does not matter for the purposes of classification.Fig. 5


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

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

Reconstruction of a random balanced network of LIF neurons with α-shaped PSCs. The reconstruction was performed for τ=10 ms, d=1.7 ms (obtained through cross-validation) and ds=0.1 ms. a GMM fit for the PDF of the reconstructed synaptic weight matrix (black solid curve) and individual components (colored solid lines); colored bars under the curves show the distributions of the reconstructed synaptic weights classified using the ground truth synaptic connectivity matrix as in Fig. 3, approximated as histograms of n=200 bins. The scale of the vertical axis is logarithmic, except for the first decade, which is in linear scale. b, c Histograms and Gaussian KDEs approximating the PDFs of the base rates and self-connection weights
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Related In: Results  -  Collection

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Fig5: Reconstruction of a random balanced network of LIF neurons with α-shaped PSCs. The reconstruction was performed for τ=10 ms, d=1.7 ms (obtained through cross-validation) and ds=0.1 ms. a GMM fit for the PDF of the reconstructed synaptic weight matrix (black solid curve) and individual components (colored solid lines); colored bars under the curves show the distributions of the reconstructed synaptic weights classified using the ground truth synaptic connectivity matrix as in Fig. 3, approximated as histograms of n=200 bins. The scale of the vertical axis is logarithmic, except for the first decade, which is in linear scale. b, c Histograms and Gaussian KDEs approximating the PDFs of the base rates and self-connection weights
Mentions: After determining τ=10 ms and d=1.7 ms through the cross-validation procedure, we used these values to estimate the connectivity and base rates. The results of the connectivity reconstruction on the training dataset were processed in the same way as in the previous subsection and are presented in Fig. 5, with further details on the classification of synaptic connections in Table 3. We find that the reconstruction quality as defined by classification into the groups of excitatory, inhibitory and connections closely matches the performance on the ideal dataset analyzed in the previous section, despite the mismatch in models and the suboptimal choice of τ and d. Note that in this experiment, the recovered values of synaptic weights in mV cannot be compared directly to the ones that were used in the simulation which produced the data due to the differences between GLM and LIF models, unlike in the first experiment described in Section 3.1. However, this does not matter for the purposes of classification.Fig. 5

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.