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P185: Higher-order interactions induced by strong shared inputs
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Safura Rashid Shomali, **Seyyed Nader Rasuli**, **Hideaki Shimazaki**

Experimental studies demonstrated that neural populations exhibit correlated spiking activity that goes beyond pairwise correlations and involves higher- order interactions [1-5]. These higher-order interactions are known to encode stimulus information or the internal state of the brain [1-5]. However, the origin of this population activity and types of presynaptic neurons inducing the higher-order interactions remain unclear. Here we investigate how the interactions [6] among groups of 3, 4, and then N neurons emerge, when they receive common inputs on top of independent noisy background inputs, assuming simple connecting motifs. Given Poissonian common inputs, we calculate the neural interactions among clusters of neurons in a _small time-window_ for the limit of the _strong common input_ ’s amplitude. When 2 or 3 neurons share excitatory/inhibitory common inputs, their pairwise and triple-wise interactions are well explained as functions of their baseline spontaneous rate, and the common-input’s rate [7].

We analytically solve the interactions for a cluster of more than 3 neurons when all of them share strong excitatory/inhibitory common input. Then, extending our analysis to the arbitrary number of N neurons we show that the N-th order interaction among neurons is still a simple function of the _postsynaptic_ and _common input_ rates. However, in larger populations, the N-th order interaction more strongly depends on the spontaneous rate of postsynaptic neuron rather than input rate. We also observe that larger number of neurons induce stronger magnitude of interactions, regardless of interaction’s sign. Moreover, shared excitatory inputs to all neurons always generate interactions with positive sign, while shared inhibitory inputs induce interactions with oscillatory signs with respect to N. Finally, we obtain the analytic result when excitatory or inhibitory inputs are shared among N-1 out of all N neurons: Surprisingly, the N-th order interactions exhibit signs opposite to those found when the common inputs is shared by all N neurons.

In all mentioned cases, when the spontaneous activity of postsynaptic neurons is low, excitatory inputs can generate strong positive/negative higher-order interactions, whereas for high spontaneous activity, inhibitory neurons can induce large absolute values of higher-order interactions. These results are valid for any _neuron model_ and solely based on the assumption of _strong common inputs_ given to neurons! Since cortical, subcortical, and retinal neurons mostly exhibit spontaneous activity less than λ=40 Hz, for small time-window of Δ=5ms, these neurons are in low spontaneous regime i.e. λΔ < 0.2. Therefore we suggest that the significant higher-order interactions observed in retina, hippocampus, and cortices reveal that motifs of strong excitatory rather than inhibitory shared inputs are present and dominant there.

Finally, we draw a table that links the strength of interactions and their signs to motifs, both for low and high spontaneous activity regimes. So based on interactions obtained from experimental data, it is possible to predict the underlying motif behind it. For example, for a specific experiment done in the hippocampal CA3 region [8], the observed negative 3rd-order, positive 4th- order, and negative 5th-order interactions leads us to the architecture of excitatory to pairs, that can generate such interactions simultaneously.

References:

1. Ohiorhenuan I. E, Mechler F, Purpura K. P, et al. Sparse coding and high-order correlations infine-scale cortical networks. Nature. 2010, 466, 617–621.

2. Montani F, Ince R. A, Senatore R, et al. The impact of high-order interactions on the rate ofsynchronous discharge and information transmission in somatosensory cortex. PHILOS TR SOC A. 2009, 367(1901), 3297-3310.

3. Yu S, Yang H, Nakahara H, Santos G. S, et al. Higher-order interactions characterized incortical activity. The Journal of Neuroscience. 2011, 31, 17514–17526.

4. Shimazaki H, Amari S.-i., Brown E. N., et al. State-space analysis of timevaryinghigher-order spike correlation for multiple neural spike train data. PLoS comp biol. 2012, 8,e1002385.

5. Ganmor, E., Segev, R., & Schneidman, E., Sparse low-order interaction network underlies ahighly correlated and learnable neural population code. PNAS. 2011, 108(23), 9679-9684.

6. Nakahara H, Amari S, Information-geometric measure for neural spikes, Neural Comp. 2002,14, 2269–2316.

7. R. Shomali S, N. Ahmadabadi M, Rasuli S.N, et al. Uncovering Network Architecture Using anExact Statistical Input-Output Relation of a Neuron Model. bioRxiv. 2019. 10.1101/479956

8. Shimazaki H, Sadeghi K, Ishikawa T, et al. Simultaneous silence organizes structured higher-order interactions in neural populations. Scientific Reports. 2015, 5, 9821.

**Speakers**

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If you missed the session or have a question, send an email to : safura@ipm.ir

Safura Rashid Shomali

Experimental studies demonstrated that neural populations exhibit correlated spiking activity that goes beyond pairwise correlations and involves higher- order interactions [1-5]. These higher-order interactions are known to encode stimulus information or the internal state of the brain [1-5]. However, the origin of this population activity and types of presynaptic neurons inducing the higher-order interactions remain unclear. Here we investigate how the interactions [6] among groups of 3, 4, and then N neurons emerge, when they receive common inputs on top of independent noisy background inputs, assuming simple connecting motifs. Given Poissonian common inputs, we calculate the neural interactions among clusters of neurons in a _small time-window_ for the limit of the _strong common input_ ’s amplitude. When 2 or 3 neurons share excitatory/inhibitory common inputs, their pairwise and triple-wise interactions are well explained as functions of their baseline spontaneous rate, and the common-input’s rate [7].

We analytically solve the interactions for a cluster of more than 3 neurons when all of them share strong excitatory/inhibitory common input. Then, extending our analysis to the arbitrary number of N neurons we show that the N-th order interaction among neurons is still a simple function of the _postsynaptic_ and _common input_ rates. However, in larger populations, the N-th order interaction more strongly depends on the spontaneous rate of postsynaptic neuron rather than input rate. We also observe that larger number of neurons induce stronger magnitude of interactions, regardless of interaction’s sign. Moreover, shared excitatory inputs to all neurons always generate interactions with positive sign, while shared inhibitory inputs induce interactions with oscillatory signs with respect to N. Finally, we obtain the analytic result when excitatory or inhibitory inputs are shared among N-1 out of all N neurons: Surprisingly, the N-th order interactions exhibit signs opposite to those found when the common inputs is shared by all N neurons.

In all mentioned cases, when the spontaneous activity of postsynaptic neurons is low, excitatory inputs can generate strong positive/negative higher-order interactions, whereas for high spontaneous activity, inhibitory neurons can induce large absolute values of higher-order interactions. These results are valid for any _neuron model_ and solely based on the assumption of _strong common inputs_ given to neurons! Since cortical, subcortical, and retinal neurons mostly exhibit spontaneous activity less than λ=40 Hz, for small time-window of Δ=5ms, these neurons are in low spontaneous regime i.e. λΔ < 0.2. Therefore we suggest that the significant higher-order interactions observed in retina, hippocampus, and cortices reveal that motifs of strong excitatory rather than inhibitory shared inputs are present and dominant there.

Finally, we draw a table that links the strength of interactions and their signs to motifs, both for low and high spontaneous activity regimes. So based on interactions obtained from experimental data, it is possible to predict the underlying motif behind it. For example, for a specific experiment done in the hippocampal CA3 region [8], the observed negative 3rd-order, positive 4th- order, and negative 5th-order interactions leads us to the architecture of excitatory to pairs, that can generate such interactions simultaneously.

References:

1. Ohiorhenuan I. E, Mechler F, Purpura K. P, et al. Sparse coding and high-order correlations infine-scale cortical networks. Nature. 2010, 466, 617–621.

2. Montani F, Ince R. A, Senatore R, et al. The impact of high-order interactions on the rate ofsynchronous discharge and information transmission in somatosensory cortex. PHILOS TR SOC A. 2009, 367(1901), 3297-3310.

3. Yu S, Yang H, Nakahara H, Santos G. S, et al. Higher-order interactions characterized incortical activity. The Journal of Neuroscience. 2011, 31, 17514–17526.

4. Shimazaki H, Amari S.-i., Brown E. N., et al. State-space analysis of timevaryinghigher-order spike correlation for multiple neural spike train data. PLoS comp biol. 2012, 8,e1002385.

5. Ganmor, E., Segev, R., & Schneidman, E., Sparse low-order interaction network underlies ahighly correlated and learnable neural population code. PNAS. 2011, 108(23), 9679-9684.

6. Nakahara H, Amari S, Information-geometric measure for neural spikes, Neural Comp. 2002,14, 2269–2316.

7. R. Shomali S, N. Ahmadabadi M, Rasuli S.N, et al. Uncovering Network Architecture Using anExact Statistical Input-Output Relation of a Neuron Model. bioRxiv. 2019. 10.1101/479956

8. Shimazaki H, Sadeghi K, Ishikawa T, et al. Simultaneous silence organizes structured higher-order interactions in neural populations. Scientific Reports. 2015, 5, 9821.

Monday July 20, 2020 9:00pm - 10:00pm CEST

Slot 14

Slot 14