P204 Brain-like networks emerge from distance dependence and preferential attachment Aitor Morales-Gregorio*1, Karolína Korvasová1
1Faculty of Mathematics and Physics, Charles University, Prague, Czechia
*Email: aitor.morales-gregorio@matfyz.cuni.cz Introduction Neurons in the brain are not randomly connected to each other. Neuronal networks have low density, high local clustering, short path lengths, heavy-tailed weight and degree distributions, and distance-dependent connection probability. These properties enable efficient information processing. However, standard network generating algorithms cannot produce networks to show all these brain-like properties. Here, we show that distance-dependent connection probability in combination with preferential attachment can generate brain-like networks that match the properties of the neuronal networks from six animal species: C. Elegans [1], Platynereis [2], Drosophila [3,4], Mouse [5,6], Marmoset [7], and Macaque [8].
Methods Networks are created by iterative growth, mimicking how neurons would naturally grow. Neurons are randomly positioned inside a sphere, the distance between them calculated, and multiplied by the exponential kernel [9], thus creating the distance-dependent probability. An empty network is initialized, to which a new connection is added in each iteration drawn from the distance-dependent probability. The iteration stops when the target density is reached. To achieve heavy-tailed distributions we study preferential attachment, i.e. a higher probability of connection for edges with high weight (weight-preferential) or nodes with high degree (degree-preferential).
Results The neuronal networks of six animals have low density, high local clustering, short global path lengths, and heavy-tailed weight and degree distributions. We show that distance dependence alone can create small-world networks with high clustering and short path lengths, but fails to produce heavy-tailed weight or degree distributions. Including weight-preferential attachment enables the creation of networks that also have heavy-tailed weight distributions, but not of the degrees. Finally, we show that degree-preferential attachment together with distance dependence produces brain-like networks that simultaneously have all the mentioned properties, and can match the experimentally measured networks of six different animal species.
Discussion Our algorithm can match the properties of the neuronal networks of six different animals, suggesting these could be general principles of neural network development. It is well-known that neurons at large distances are less likely to be connected, in part because these connections are metabolically more expensive to establish and maintain than short-range ones. The large neuropil branching of some neurons increases the probability of connections with them, which we capture via the degree-preferential mechanism. In conclusion, distance dependence and preferential attachment are biologically realistic mechanisms that can produce networks closely matching both invertebrate and vertebrate brains.
Acknowledgements This work received funding from the Programme Johannes Amos Comenius (OP JAK) under the project 'MSCA Fellowships CZ - UK3' (reg. n. CZ.02.01.01/00/22\_010/0008220); and from Charles University grant PRIMUS/24/MED/007 References [1] Varshney et al (2011) PLoS CB 7:e1001066 [2] Randel et al (2014) eLife 3:e02730 [3] Takemura et al (2013) Nature 500:175-181 [4] Scheffer et al (2020) eLife 9:e57443 [5] MICrONs Consortium et al (2021) bioRxiv 2021.07.28.454025 [6] Gămănuţ et al (2018) Neuron 97(3):698-715 [7] Majka et al (2020) Nature Communications 11:1133 [8] Markov et al (2014) Cerebral Cortex 24(1):17-36 [9] Ercsey-Ravasz et al (2013) Neuron 80(1):184-197
