New Insights on Critical Transitions of Single-Neuron Dynamics

H. Hea, b, K. Zhanga, H. Yanc, J. Wanga, b, d aState Key Laboratory of Electroanalytical Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun, Jilin 130022, China bSchool of Applied Chemistry and Engineering, University of Science and Technology of China, Hefei, Anhui 230026, China cCenter for Theoretical Interdisciplinary Sciences, Wenzhou Institute, University of Chinese Academy of Sciences, Wenzhou, Zhejiang 325001, China dDepartment of Chemistry and of Physics and Astronomy, State University of New York at Stony Brook, Stony Brook, New York 11794-3400, United States

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Many theoretical models depicting excitable cells stem from the Hodgkin-Huxley model. Over the past few decades, quantitative studies on its electrophysiology and nonlinear dynamics have yielded considerable progress. In this study, we employ a landscape and flux theory to statistically explore the global dynamic characteristics of the classical Hodgkin-Huxley neuron. We quantify the underlying landscape and flux to address global stability. Our results provide an intuitive understanding of a global picture of the dynamic system. By quantifying the average curl flux, we reveal that it serves as the dynamical origin for the emergence of a new state and a dynamical indicator for bifurcation. In addition, we quantitatively calculate the entropy production, identifying it as an essential thermodynamic indicator for bifurcation. The time asymmetry of the cross-correlations can be directly computed from existing experimental time series, offering a practical indicator for bifurcation analysis. This paper presents our findings and their implications for a better understanding of the behavior of excitable cells.

DOI:10.12693/APhysPolA.146.102 topics: non-equilibrium Hodgkin-Huxley (HH) neuron dynamics, landscape, curl flux, critical transition