1. Department of Physics in Science College, Nanjing University of Aeronautics and Astronautics, Nanjing 210016 2. Research Center of Complex Systems Science, University of Shanghai for Science and Technology, Shanghai 200093 3. Department of Mathematics, College of Logistic Engineering of PLA, Nanjing 210016 4. College of Civil Aviation, Nanjing University of Aeronautics and Astronautics, Nanjing 210016 5. Institute of Physics, Academia Sinica, Nankang, Taipei 11529 6. National Center for Theoretical Sciences, Tsing Hua University, Hsinchu 30013
The distribution of the geometric distances of connected neurons is a practical factor underlying neural networks in the brain. It can affect the brain’s dynamic properties at the ground level. Karbowski derived a power-law decay distribution that has not yet been verified by experiment. In this work, we check its validity using simulations with a phenomenological model. Based on the in vitro twodimensional development of neural networks in culture vessels by Ito, we match the synapse number saturation time to obtain suitable parameters for the development process, then determine the distribution of distances between connected neurons under such conditions. Our simulations obtain a clear exponential distribution instead of a power-law one, which indicates that Karbowski’s conclusion is invalid, at least for the case of in vitro neural network development in two-dimensional culture vessels.
M. J. Chacron, L. Maler, and J. Bastian, Electroreceptor neuron dynamics shape information transmission, Nat. Neurosci. 8(5), 673 (2005)
https://doi.org/10.1038/nn1433
2
L. Agnati, L. Santarossa, S. Genedani, E. Canela, G. Leo, R. Franco, A. Woods, C. Lluis, S. Ferré, and K. Fuxe, On the nested hierarchical organization of CNS: Basic characteristics of neuronal molecular networks, Comput. Neurosci. 3146, 24 (2004)
https://doi.org/10.1007/978-3-540-27862-7_2
3
E. Bullmore and O. Sporns, Complex brain networks: Raph theoretical analysis of structural and functional systems, Nat. Rev. Neurosci. 10(3), 186 (2009)
https://doi.org/10.1038/nrn2575
4
C. L. Leveroni, M. Seidenberg, and A. R. Mayer, Neural systems underlying recognition of familiar and newly learned daces, J. Neurosci. 20(2), 878 (2000)
5
G. Shahaf and S. Marom, Learning in networks of cortical neurons, J. Neurosci. 21(22), 8782 (2001)
6
X. Liang, J. H. Wang, and Y. He, Human connectome: Structural and functional brain networks, Chin. Sci. Bull. 55(16), 1565 (2010)
https://doi.org/10.1360/972009-2150
7
P. Hagmann, M. Kurant, X. Gigandet, P. Thiran, V. J. Wedeen, R. Meuli, and J. P. Thiran, Mapping human whole-brain structural networks with diffusion MRI, PLoS One 2(7), e597 (2007)
https://doi.org/10.1371/journal.pone.0000597
R. Kötter, Online retrieval, processing, and visualization of primate connectivity data from the CoCoMac database, Neuroinformatics 2(2), 127 (2004)
https://doi.org/10.1385/NI:2:2:127
10
D. Ito, H. Tamate, M. Nagayama, T. Uchida, S. N. Kudoh, and K. Gohara, Minimum neuron density for synchronized bursts in a rat cortical culture on multielectrode arrays, Neuroscience 171(1), 50 (2010)
https://doi.org/10.1016/j.neuroscience.2010.08.038
11
D. Ito, T. Komatsu, and K. Gohara, Measurement of saturation processes in glutamatergic and GABAergic synapse densities during long-term development of cultured rat cortical networks, Brain Res. 1534, 22 (2013)
https://doi.org/10.1016/j.brainres.2013.08.004
12
J. Karbowski, Optimal wiring principle and plateaus in the degree of separation for cortical neurons, Phys. Rev. Lett. 86(16), 3674 (2001)
https://doi.org/10.1103/PhysRevLett.86.3674
13
M. Miller and A. Peters, Maturation of rat visual cortex (II): A combined Golgi-electron microscope study of pyramidal neurons, J. Comparative Neurology 203(4), 555 (1981)
https://doi.org/10.1002/cne.902030402
14
B. Hayes and A. Roberts, Synaptic junction development in the spinal cord of an Amphibian Embryo: An electron microscope study, Z. Zellforsch. 137, 251 (1973)
https://doi.org/10.1007/BF00307433
15
C. G. Dotti, C. A. Sullivan, and G. A. Banker, The establishment of polarity by hippocampal neurons in culture, J. Neurosci. 8(4), 1454 (1988)
16
M. Kaiser, C. C. Hilgetag, and A. van Ooyen, A simple rule for axon outgrowth and synaptic competition generates realistic connection lengths and filling fractions, Cereb. Cortex 19(12), 3001 (2009)
https://doi.org/10.1093/cercor/bhp071
17
M. Ercsey-Ravasz, N. T. Markov, C. Lamy, D. C. Van Essen, K. Knoblauch, Z. Toroczkai, and H. Kennedy, A predictive network model of cerebral cortical connectivity based on a distance rule, Neuron 80(1), 184 (2013)
https://doi.org/10.1016/j.neuron.2013.07.036
18
M. Kaiser and C. C. Hilgetag, Nonoptimal component placement, but short processing paths, due to longdistance projections in neural systems, PLOS Comput. Biol. 2(7), e95 (2006)
https://doi.org/10.1371/journal.pcbi.0020095
