Indistinguishable synapses lead to sparse networks. (English) Zbl 1472.92041

Summary: Neurons integrate information from many neighbors when they process information. Inputs to a given neuron are thus indistinguishable from one another. Under the assumption that neurons maximize their information storage, indistinguishability is shown to place a strong constraint on the distribution of strengths between neurons. The distribution of individual synapse strengths is found to follow a modified Boltzmann distribution with strength proportional to \(\exp (-\beta w)\). The model is shown to be consistent with experimental data from Caenorhabditis elegans connectivity and in vivo synaptic strength measurements. The \(1/w\) dependence helps account for the observation of many zero or weak connections between neurons or sparsity of the neural network.


92B20 Neural networks for/in biological studies, artificial life and related topics
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[1] Barabási, A.-L. (2009). Scale-free networks: A decade and beyond. Science, 325(5939), 412. ,
[2] Barbour, B., Brunel, N., Hakim, V., & Nadal, J.-P. (2007). What can we learn from synaptic weight distributions? Trends in Neurosciences, 30(12), 622-629. ,
[3] Brunel, N. (2016). Is cortical connectivity optimized for storing information? Nature Neuroscience, 19(5), 749-755. ,
[4] Brunel, N., Hakim, V., Isope, P., Nadal, J.-P., & Barbour, B. (2004). Optimal information storage and the distribution of synaptic weights: Perceptron versus Purkinje cell. Neuron, 43(5), 745-757. ,
[5] Bullmore, E., & Sporns, O. (2009). Complex brain networks: Graph theoretical analysis of structural and functional systems. Nature Reviews Neuroscience, 10(3), 186-198. ,
[6] Bullmore, E., & Sporns, O. (2012). The economy of brain network organization. Nature Reviews Neuroscience, 13(5), 336-349. ,
[7] Buzsáki, G., & Mizuseki, K. (2014). The log-dynamic brain: How skewed distributions affect network operations. Nature Reviews Neuroscience, 15(4), 264-278. ,
[8] Clopath, C., & Brunel, N. (2013). Optimal properties of analog perceptrons with excitatory weights. PLoS Computational Biology, 9(2), e1002919. ,
[9] Cossell, L., Iacaruso, M. F., Muir, D. R., Houlton, R., Sader, E. N., Ko, H., … Mrsic-Flogel, T. D. (2015). Functional organization of excitatory synaptic strength in primary visual cortex. Nature, 518(7539), 399-403. ,
[10] Delignette-Muller, M. L., & Dutang, C. (2015). fitdistrplus: An R package for fitting distributions. Journal of Statistical Software, 64(4), 1-34. ,
[11] Jackson, C. (2016). Flexsurv: A platform for parametric survival modeling in R.Journal of Statistical Software, 70(8), 1-33. doi:10.18637/jss.v070.i08,
[12] Jan, Y.-N., & Jan, L. Y. (2010). Branching out: Mechanisms of dendritic arborization. Nature Reviews Neuroscience, 11(5), 316-328. ,
[13] Kawaguchi, Y., Karube, F., & Kubota, Y. (2006). Dendritic branch typing and spine expression patterns in cortical nonpyramidal cells. Cerebral Cortex, 16(5), 696-711. ,
[14] Kouh, M. (2017). Information maximization explains the sparseness of presynaptic neural response. Neural Computation, 29(4), 888-896. , · Zbl 1414.92026
[15] Krueppel, R., Remy, S., & Beck, H. (2011). Dendritic integration in hippocampal dentate granule cells. Neuron, 71(3), 512-528. ,
[16] Larkum, M. E., Nevian, T., Sandler, M., Polsky, A., & Schiller, J. (2009). Synaptic integration in tuft dendrites of layer 5 pyramidal neurons: A new unifying principle. Science, 325(5941), 756-760. ,
[17] Lefort, S., Tomm, C., Floyd Sarria, J. C., & Petersen, C. C. H. (2009). The excitatory neuronal network of the C2 barrel column in mouse primary somatosensory cortex. Neuron, 61(2), 301-316. ,
[18] Ma, X., Kohashi, T., & Carlson, B. A. (2013). Extensive excitatory network interactions shape temporal processing of communication signals in a model sensory system. Journal of Neurophysiology, 110(2), 456-469. ,
[19] Newman, C. M. (1988). Memory capacity in neural network models: Rigorous lower bounds. Neural Networks, 1(3), 223-238. ,
[20] Polsky, A., Mel, B. W., & Schiller, J. (2004). Computational subunits in thin dendrites of pyramidal cells. Nature Neuroscience, 7(6), 621-627. ,
[21] Russo, R., Herrmann, H. J., & de Arcangelis, L. (2014). Brain modularity controls the critical behavior of spontaneous activity. Scientific Reports, 4.
[22] Schröter, M., Paulsen, O., & Bullmore, E. T. (2017). Micro-connectomics: Probing the organization of neuronal networks at the cellular scale. Nature Reviews Neuroscience, 18(3), 131-146. ,
[23] Silver, R. A. (2010). Neuronal arithmetic. Nature Reviews Neuroscience, 11(7), 474-489. ,
[24] Sjöström, P. J. (2005). Connectivity dataset.
[25] Sjöström, P. J., Rancz, E. A., Roth, A., & Häusser, M. (2008). Dendritic excitability and synaptic plasticity. Physiological Reviews, 88(2), 769-840. ,
[26] Song, S., Sjöström, P. J., Reigl, M., Nelson, S., & Chklovskii, D. B. (2005). Highly nonrandom features of synaptic connectivity in local cortical circuits. PLoS Biology, 3(3), e68. ,
[27] Spruston, N. (2008). Pyramidal neurons: Dendritic structure and synaptic integration. Nature Reviews Neuroscience, 9(3), 206-221. ,
[28] Trautmann, H., Steuer, D., Mersmann, O., & Bornkamp, B. (2014). Truncnorm: Truncated normal distribution.
[29] Varshney, L. R., Chen, B. L., Paniagua, E., Hall, D. H., & Chklovskii, D. B. (2011). Structural properties of the Caenorhabditis elegans neuronal network. PLoS Computational Biology, 7(2), e1001066. ,
[30] Varshney, L. R., Sjöström, P. J., & Chklovskii, D. B. (2006). Optimal information storage in noisy synapses under resource constraints. Neuron, 52(3), 409-423. ,
[31] WormAtlas, Altun, Z. F., Herndon, L. A., Crocker, C., Lints, R., & Hall, D. (Eds.). (2002-2017).
[32] Yoshimura, Y., Dantzker, J. L., & Callaway, E. M. (2005). Excitatory cortical neurons form fine-scale functional networks. Nature, 433(7028), 868-873. ,
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