Resilience of Nematode Connectomes Based on Network Dimension-reduced Method

Abstract

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The whole map of nematode connectomes provides important structural data for exploring the behavioral mechanism of nematodes, but to further reveal the functional importance and resilience pattern of nematode neurons, it is necessary to effectively couple the regulatory relationship between neurons and their topology. Here, with a typical signal excitation function we propose a model to capture the interacting relationship between the neurons, because a differential equation depicts the activity of a neuron, n neurons mean we need high-D differential equations to capture the neural network. With mean-field theory, we decouple this N-dimension question into a one-dimension problem mathematically. In our framework, we emphatically analyze the characteristics, similarities and differences of the structure and dynamical behaviors of the neuronal system for Caenorhabditis elegans and Pristionchus pacificus. The comparing results of simulating method and theoretical approach show that the most important homologous neurons between C.elegans and P.pacificus are I2 and NSM, which may lead to their different behavior characteristics of predation and prey. At the same time, we expect that the xeff index can be used to reveal the importance of neurons for the functional evolution and degeneration of neural networks from a dynamic perspective. In the hermaphroditic and male C.elegans, we test the control level of the intermediate neuron groups over the output neuron groups and the single neuron. These results suggest that our theoretical approach can be used to reveal the effects of bio-connectivity groups, potentially enabling us to explore the interaction relationship of neural networks in humans and animals.

Keywords

• resilience
• mean-field theory
• network dynamics
• nematodes connectomes
• neural networks