Abstract
The wiring diagram of the mouse brain has recently been mapped at a mesoscopic scale in the Allen Mouse Brain Connectivity Atlas. Axonal projections from brain regions were traced using green fluoresent proteins. The resulting data were registered to a common three-dimensional reference space. They yielded a matrix of connection strengths between 213 brain regions. Global features such as closed loops formed by connections of similar intensity can be inferred using tools from persistent homology. We map the wiring diagram of the mouse brain to a simplicial complex (filtered by connection strengths). We work out generators of the first homology group. Some regions, including nucleus accumbens, are connected to the entire brain by loops, whereas no region has non-zero connection strength to all brain regions. Thousands of loops go through the isocortex, the striatum and the thalamus. On the other hand, medulla is the only major brain compartment that contains more than 100 loops.
References
[1] Adams, H. and Tausz, A. (2011). Javaplex tutorial. Google Scholar.Search in Google Scholar
[2] Adams, H., Tausz, A., and Vejdemo-Johansson, M. (2014). Javaplex: A research software package for persistent (co) homology. In International Congress on Mathematical Software, pages 129–136. Springer.10.1007/978-3-662-44199-2_23Search in Google Scholar
[3] Anderson, K. M., Krienen, F. M., Choi, E. Y., Reinen, J. M., Yeo, B. T., and Holmes, A. J. (2018). Gene expression links functional networks across cortex and striatum. Nature communications, 9(1):1–14.10.1038/s41467-018-03811-xSearch in Google Scholar
[4] Barabási, A.-L. and Albert, R. (1999). Emergence of scaling in random networks. science, 286(5439):509–512.10.1126/science.286.5439.509Search in Google Scholar
[5] Bohland, J. W., Bokil, H., Pathak, S. D., Lee, C.-K., Ng, L., Lau, C., Kuan, C., Hawrylycz, M., and Mitra, P. P. (2010). Clustering of spatial gene expression patterns in the mouse brain and comparison with classical neuroanatomy. Methods, 50(2):105–112.10.1016/j.ymeth.2009.09.001Search in Google Scholar
[6] Bohland, J. W., Wu, C., Barbas, H., Bokil, H., Bota, M., Breiter, H. C., Cline, H. T., Doyle, J. C., Freed, P. J., Greenspan, R. J., et al. (2009). A proposal for a coordinated effort for the determination of brainwide neuroanatomical connectivity in model organisms at a mesoscopic scale. PLoS Comput Biol, 5(3):e1000334.10.1371/journal.pcbi.1000334Search in Google Scholar
[7] Chan, J. M., Carlsson, G., and Rabadan, R. (2013). Topology of viral evolution. Proceedings of the National Academy of Sciences, 110(46):18566–18571.10.1073/pnas.1313480110Search in Google Scholar
[8] Chowdhury, S. and Mémoli, F. (2018). A functorial dowker theorem and persistent homology of asymmetric networks. Journal of Applied and Computational Topology, 2(1-2):115–175.10.1007/s41468-018-0020-6Search in Google Scholar
[9] Collins, A., Zomorodian, A., Carlsson, G., and Guibas, L. J. (2004). A barcode shape descriptor for curve point cloud data. Computers & Graphics, 28(6):881–894.10.1016/j.cag.2004.08.015Search in Google Scholar
[10] Curto, C., Giusti, C., Marku, K., Pastalkova, E., and Itskov, V. (2013). Pairwise correlation graphs from hippocampal population activity have highly non-random, low-dimensional clique topology. BMC neuroscience, 14(1):1–2.10.1186/1471-2202-14-S1-P182Search in Google Scholar
[11] Dong, H. W. (2008). The Allen reference atlas: A digital color brain atlas of the C57Bl/6J male mouse. John Wiley & Sons Inc.Search in Google Scholar
[12] Edelsbrunner, H. and Harer, J. (2010). Computational topology: an introduction. American Mathematical Soc.10.1090/mbk/069Search in Google Scholar
[13] Edelsbrunner, H., Letscher, D., and Zomorodian, A. (2000). Topological persistence and simplification. In Proceedings 41st annual symposium on foundations of computer science, pages 454–463. IEEE.10.1109/SFCS.2000.892133Search in Google Scholar
[14] Giusti, C., Pastalkova, E., Curto, C., and Itskov, V. (2015). Clique topology reveals intrinsic geometric structure in neural correlations. Proceedings of the National Academy of Sciences, 112(44):13455–13460.10.1073/pnas.1506407112Search in Google Scholar
[15] Grange, P., Bohland, J. W., Okaty, B. W., Sugino, K., Bokil, H., Nelson, S. B., Ng, L., Hawrylycz, M., and Mitra, P. P. (2014). Cell-type–based model explaining coexpression patterns of genes in the brain. Proceedings of the National Academy of Sciences, 111(14):5397–5402.10.1073/pnas.1312098111Search in Google Scholar
[16] Grange, P., Hawrylycz, M., and Mitra, P. P. (2013). Computational neuroanatomy and co-expression of genes in the adult mouse brain, analysis tools for the allen brain atlas. Quantitative Biology, 1(1):91–100.10.1007/s40484-013-0011-5Search in Google Scholar
[17] Grange, P., Menashe, I., and Hawrylycz, M. (2015). Cell-type-specific neuroanatomy of cliques of autism-related genes in the mouse brain. Frontiers in computational neuroscience, 9:55.10.3389/fncom.2015.00055Search in Google Scholar
[18] Hawrylycz, M., Miller, J. A., Menon, V., Feng, D., Dolbeare, T., Guillozet-Bongaarts, A. L., Jegga, A. G., Aronow, B. J., Lee, C.-K., Bernard, A., et al. (2015). Canonical genetic signatures of the adult human brain. Nature neuroscience, 18(12):1832.10.1038/nn.4171Search in Google Scholar
[19] Josh Huang, Z. and Zeng, H. (2013). Genetic approaches to neural circuits in the mouse. Annual review of neuroscience, 36:183–215.10.1146/annurev-neuro-062012-170307Search in Google Scholar
[20] Lein, E. S., Hawrylycz, M. J., Ao, N., Ayres, M., Bensinger, A., Bernard, A., Boe, A. F., Boguski, M. S., Brockway, K. S., Byrnes, E. J., et al. (2007). Genome-wide atlas of gene expression in the adult mouse brain. Nature, 445(7124):168–176.Search in Google Scholar
[21] Menashe, I., Grange, P., Larsen, E. C., Banerjee-Basu, S., and Mitra, P. P. (2013). Co-expression profiling of autism genes in the mouse brain. PLoS Comput Biol, 9(7):e1003128.10.1371/journal.pcbi.1003128Search in Google Scholar
[22] Ng, L., Bernard, A., Lau, C., Overly, C. C., Dong, H.-W., Kuan, C., Pathak, S., Sunkin, S. M., Dang, C., Bohland, J. W., et al. (2009). An anatomic gene expression atlas of the adult mouse brain. Nature neuroscience, 12(3):356–362.10.1038/nn.2281Search in Google Scholar
[23] Oh, S. W., Harris, J. A., Ng, L., Winslow, B., Cain, N., Mihalas, S., Wang, Q., Lau, C., Kuan, L., Henry, A. M., et al. (2014). A mesoscale connectome of the mouse brain. Nature, 508(7495):207–214.10.1038/nature13186Search in Google Scholar
[24] Paus, T., Pesaresi, M., and French, L. (2014). White matter as a transport system. Neuroscience, 276:117–125.10.1016/j.neuroscience.2014.01.055Search in Google Scholar
[25] Robertson, M. M., Eapen, V., Singer, H. S., Martino, D., Scharf, J. M., Paschou, P., Roessner, V., Woods, D. W., Hariz, M., Mathews, C. A., et al. (2017). Gilles de la tourette syndrome. Nature reviews Disease primers, 3(1):1–20.10.1038/nrdp.2016.97Search in Google Scholar
[26] Rybak, I., Shevtsova, N., Paton, J., Dick, T., John, W. S., Mörschel, M., and Dutschmann, M. (2004). Modeling the pontomedullary respiratory network. Respiratory physiology & neurobiology, 143(2-3):307–319.10.1016/j.resp.2004.03.020Search in Google Scholar
[27] Saggar, M., Sporns, O., Gonzalez-Castillo, J., Bandettini, P. A., Carlsson, G., Glover, G., and Reiss, A. L. (2018). Towards a new approach to reveal dynamical organization of the brain using topological data analysis. Nature communications, 9(1):1–14.10.1038/s41467-018-03664-4Search in Google Scholar
[28] Sizemore, A. E., Giusti, C., Kahn, A., Vettel, J. M., Betzel, R. F., and Bassett, D. S. (2018). Cliques and cavities in the human connectome. Journal of computational neuroscience, 44(1):115–145.10.1007/s10827-017-0672-6Search in Google Scholar
[29] Sporns, O. (2011). The human connectome: a complex network. Annals of the New York Academy of Sciences, 1224(1):109–125.10.1111/j.1749-6632.2010.05888.xSearch in Google Scholar
[30] Stafford, J. M., Jarrett, B. R., Miranda-Dominguez, O., Mills, B. D., Cain, N., Mihalas, S., Lahvis, G. P., Lattal, K. M., Mitchell, S. H., David, S. V., et al. (2014). Large-scale topology and the default mode network in the mouse connectome. Proceedings of the National Academy of Sciences, 111(52):18745–18750.10.1073/pnas.1404346111Search in Google Scholar
[31] Swanson, L. (2004). Brain maps: structure of the rat brain. Gulf Professional Publishing.Search in Google Scholar
[32] Wasserman, L. (2018). Topological data analysis. Annual Review of Statistics and Its Application, 5:501–532.10.1146/annurev-statistics-031017-100045Search in Google Scholar
[33] Watts, D. J. and Strogatz, S. H. (1998). Collective dynamics of ‘small-world’networks. nature, 393(6684):440–442.10.1038/30918Search in Google Scholar
[34] Zomorodian, A. and Carlsson, G. (2005). Computing persistent homology. Discrete & Computational Geometry, 33(2):249–274.10.1007/s00454-004-1146-ySearch in Google Scholar
© 2020 Pascal Grange, published by De Gruyter
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