Weight distributions in the fruit-fly and the mouse connectomes

Abstract

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 [&ge;] 3, indicating heavy-tailed, but regular connectivity, while synaptic weights around broadcaster and integrator neurons can be fitted with < 3, i.e have real scale-free fat tails. This suggests a non-random heterogenous organization in which a few dominant synapses facilitate information flow. Graphical Abstract O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=83 SRC="FIGDIR/small/687553v2_ufig1.gif" ALT="Figure 1"> View larger version (16K): org.highwire.dtl.DTLVardef@1b4d11corg.highwire.dtl.DTLVardef@cc09corg.highwire.dtl.DTLVardef@1397515org.highwire.dtl.DTLVardef@135b653_HPS_FORMAT_FIGEXP M_FIG C_FIG HighlightsO_LIAnalyses of the latest large visual connectomes, the mouse visual cortex and male fruit-fly optic lobe, despite being evolutionarily distant showed that their global synaptic weight distributions follow a powerlaw (PL) while their local node strengths follow heavy-tailed behavior that decays faster than a PL providing a hint at the critical learning mechanisms at play C_LIO_LIWe briefly illustrate that the degree of proofreading of datasets can affect the heaviness of the weight distribution tails C_LIO_LIThe node strength distributions P (s) for these visual connectomes are found to exhibit dual PL scaling mainly due to the node degree P (k) heterogeneity with low-k nodes contributing to the low-s regime, and high-k nodes to the heavy tails. C_LIO_LIEdge weight assignments are also found to be non-random and also modulate the behavior of the node strength distributions, although their correlation is below 1% C_LIO_LIWe propose an explanation for the deviation of the local behavior from the PL which may resolve the contradicting observation of lognormals and PLs related to critical behavior C_LIO_LIThe synaptic weights of links originating and terminating from source and sink nodes are found to also exhibit PL behaviors with exponent less than 3 indicating that they are scale-free C_LI