Understanding the structure–function relationship in a neuronal network is one of the major challenges in neuroscience research. Despite increasing researches at circuit connectivity and neural network structure, their structure-based biological interpretability remains unclear. Based on the attractor theory, here we develop an analytical framework that links neural circuit structures and their functions together through fixed point attractor in Caenorhabditis elegans. In this framework, we successfully established the structural condition for the emergence of multiple fixed points in C. elegans connectome. Then we construct a finite state machine to explain how functions related to bistable phenomena at the neural activity and behavioral levels are encoded. By applying the proposed framework to the command circuit in C. elegans, we provide a circuit level interpretation for the forward-reverse switching behaviors. Interestingly, network properties of the command circuit and first layer amphid interneuron circuit can also be inferred from their functions in this framework. Our research indicates the reliability of the fixed point attractor bridging circuit structure and functions, suggesting its potential applicability to more complex neuronal circuits in other species.
Objective. Reconstruction of connectomes at the cellular scale is a prerequisite for understanding the principles of neural circuits. However, due to methodological limits, scientists have reconstructed the connectomes of only a few organisms such as C. elegans, and estimated synaptic strength indirectly according to their size and number. Approach. Here, we propose a graph network model to predict synaptic connections and estimate synaptic strength by using the calcium activity data from C. elegans. Main results. The results show that this model can reliably predict synaptic connections in the neural circuits of C. elegans, and estimate their synaptic strength, which is an intricate and comprehensive reflection of multiple factors such as synaptic type and size, neurotransmitter and receptor type, and even activity dependence. In addition, the excitability or inhibition of synapses can be identified by this model. We also found that chemical synaptic strength is almost linearly positively correlated to electrical synaptic strength, and the influence of one neuron on another is non-linearly correlated with the number between them. This reflects the intrinsic interaction between electrical and chemical synapses. Significance. Our model is expected to provide a more accessible quantitative and data-driven approach for the reconstruction of connectomes in more complex nervous systems, as well as a promising method for accurately estimating synaptic strength.
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