Weight distributions in the fruit-fly and the mouse connectomes

By the growing number of available structural connectome data, the distributions of the synaptic weights can be determined which provides a hint at the learning mechanisms at play, both in the global and local level. In this work, we show a numerical analysis of this on the occasion of the latest large and by far, the most well-documented connectomes, the mouse visual cortex and the fruit-fly optical lobe. In literature and in the present work, the synaptic weight distributions for various connectomes follow a power-law (PL) behavior, while the local node strengths can follow heavy-tailed distributions that decay faster. We found that the degree of proofreading on connectomes drastically affects the heavyness of the distribution tails, affecting the interpretation of the structural behavior. In relation to this, there is an ongoing debate on the ubiquitous contradicting observations of lognormal (LN) and PL behavior of weight distributions. Here, we provide an explanation to resolve this by arguing on the basis of generalized central limit theorem. Finally, we show that the global synaptic weight distributions exhibit PL tails with exponents α≥3, indicating heavy-tailed, but regular connectivity, while synaptic weights around broadcaster and integrator neurons can be fitted with α<3, i.e have real scale-free fat tails. This suggests a non-random heterogeneous organization in which a few dominant synapses facilitate information flow.