Abstract
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.
Highlights
Due to special physiological structure and easy modeling, nematode has become the primary model to reveal the neurons structure and functional mechanism for humans and animals [1, 2]
According to the theory of symmetry group, they found that the symmetry of the neural network has directly biological significance, and its correctness can be strictly proved by using the mathematical form of symmetry group
To verify the correctness of our dimension-reduced method for the system resilience of xeff, we use the ODE45 function to solve the neural dynamics of Eq 1, which can ensure we get the numerical results of xi
Summary
Due to special physiological structure and easy modeling, nematode has become the primary model to reveal the neurons structure and functional mechanism for humans and animals [1, 2]. Even Witvliet et al reconstructed full brain of eight isogenic Caenorhabditis elegans individuals across postnatal stages to investigate how it changes with age [5] This contributes to a more detailed and accurate understanding and exploration of human and animal behavior at the neuronal level, as well as an analysis of the functional importance of individual neurons at the systemic level. According to the theory of symmetry group, they found that the symmetry of the neural network has directly biological significance, and its correctness can be strictly proved by using the mathematical form of symmetry group This form makes it possible to understand the importance of the structure-function relationship [17]. The results remain reliable with a small amount of disturbance to the reference connectors, but large disturbances are likely to cause distortion
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