Introduction Neurons are situated in a microenvironment composed of various biochemical and biophysical cues,where stretching is thought to have a major impact on neurons.For instance,during a moderate traumatic brain...Introduction Neurons are situated in a microenvironment composed of various biochemical and biophysical cues,where stretching is thought to have a major impact on neurons.For instance,during a moderate traumatic brain impact,the injury region in axons exhibits significant longitudinal strain;and in a rat model of spinal cord injury,the most severe axonal injury is located in the largest strain region.Stretching may result in microstructural changes in neural tissue and further leading to abnormal electrophysiological function.Hence,it is of great importance to understand the coupled mechanoelectricalbehaviors of neurons under stretching.In spite of significant experimental efforts,the underlying mechanism remains elusive,more works are needed to provide a detailed description of the process that leads to the observed phenomena.Mathematical modeling is a powerful tool that offers a quantitative description of the underlying mechanism of an observed biological phenomenon,including mechanical and electrophysiological behaviors of neurons.Thus,we developed a mechanoelectrical coupling model of neurons under stretching in this study.Mathematical model The mathematical model consists of three submodels,i.e.,the mechanical submodel,the mechanoelectrical coupling submodel and the electrophysiological submodel.The mechanical submodel deals with the relationship between stretching and the deformation of axons,which has specially considered the plastic deformation of axons.The electrophysiological submodel characterizes the feature of neuronal action potential(AP),which is based on the classical H-H model and the cable theory.The mechanoelectrical coupling submodel links the mechanical and electrophysiological submodels through strain-induced equivalent circuit parameter alteration and ion channel injury.Besides,we have discussed a more general deformation condition,where an expanded model coupling the axonal deformation and electrophysiology alteration was explored.As the most essential parameters in an electrophysiological assessment,the amplitude of the AP,the neuronal firing frequency and the electrophysiological signal conduction velocity,which could be affected by stretching,were used as outputs of the model.Results&discussion To understand the mechanoelectrical coupling of neurons under stretching,we developed a mechanoelectrical coupling model.To verify the model,we simulated a slow stretching on an axon following the experimental study in the literature,we observed that as the strain increases,the peak AP declines faster,which is consistent with the experimental data.Moreover,the reduced AP cannot be restored to the original peak,implying that the damage is irreversible.The simulation results also predict that strain induces a more frequent neuronal firing and a faster conduction.In a realistic situation,in addition to stretching,the loading condition is very complicated,which may induce complex axonal deformation(e.g., necking and swelling along the axons).We also simulated such necking deformation impairment and observed that the AP amplitude decreases at the necking region and recovers after that,indicating a blockage of the AP;and the conduction velocity decreases with the increase in deformation degree.Conclusions In this study,we developed a mechanoelectrical coupling model of neurons under stretching with consideration of axonal plastic deformation.With the model,we found that the effect of mechanical loading on electrophysiology mainly manifests as decreased membrane AP amplitude,a more frequent neuronal firing and a faster electrophysiological signal conduction.The model predicts not only stretch-induced injury but also a more gene ral necking deformation case,which may someday be revealed in future by experiments,providing a reference for the prediction and regulation of neuronal function under mechanical loadings.展开更多
基金financially supported by the National Natural Science Foundation of China ( 11522219, 11532009)the Projects of International ( Regional) Cooperation and Exchanges of NSFC ( 11761161004)+3 种基金the Natural Science Basic Research Plan in Shaanxi Province of China ( 2017JM1026,2017JM8097)the National Project Cultivating Foundation of Xi’an Medical University ( 2017GJFY23)Young Talent Support Plan of Shaanxi Provincethe China Postdoctoral Science Foundation ( 2018M631141,2018M631173)
文摘Introduction Neurons are situated in a microenvironment composed of various biochemical and biophysical cues,where stretching is thought to have a major impact on neurons.For instance,during a moderate traumatic brain impact,the injury region in axons exhibits significant longitudinal strain;and in a rat model of spinal cord injury,the most severe axonal injury is located in the largest strain region.Stretching may result in microstructural changes in neural tissue and further leading to abnormal electrophysiological function.Hence,it is of great importance to understand the coupled mechanoelectricalbehaviors of neurons under stretching.In spite of significant experimental efforts,the underlying mechanism remains elusive,more works are needed to provide a detailed description of the process that leads to the observed phenomena.Mathematical modeling is a powerful tool that offers a quantitative description of the underlying mechanism of an observed biological phenomenon,including mechanical and electrophysiological behaviors of neurons.Thus,we developed a mechanoelectrical coupling model of neurons under stretching in this study.Mathematical model The mathematical model consists of three submodels,i.e.,the mechanical submodel,the mechanoelectrical coupling submodel and the electrophysiological submodel.The mechanical submodel deals with the relationship between stretching and the deformation of axons,which has specially considered the plastic deformation of axons.The electrophysiological submodel characterizes the feature of neuronal action potential(AP),which is based on the classical H-H model and the cable theory.The mechanoelectrical coupling submodel links the mechanical and electrophysiological submodels through strain-induced equivalent circuit parameter alteration and ion channel injury.Besides,we have discussed a more general deformation condition,where an expanded model coupling the axonal deformation and electrophysiology alteration was explored.As the most essential parameters in an electrophysiological assessment,the amplitude of the AP,the neuronal firing frequency and the electrophysiological signal conduction velocity,which could be affected by stretching,were used as outputs of the model.Results&discussion To understand the mechanoelectrical coupling of neurons under stretching,we developed a mechanoelectrical coupling model.To verify the model,we simulated a slow stretching on an axon following the experimental study in the literature,we observed that as the strain increases,the peak AP declines faster,which is consistent with the experimental data.Moreover,the reduced AP cannot be restored to the original peak,implying that the damage is irreversible.The simulation results also predict that strain induces a more frequent neuronal firing and a faster conduction.In a realistic situation,in addition to stretching,the loading condition is very complicated,which may induce complex axonal deformation(e.g., necking and swelling along the axons).We also simulated such necking deformation impairment and observed that the AP amplitude decreases at the necking region and recovers after that,indicating a blockage of the AP;and the conduction velocity decreases with the increase in deformation degree.Conclusions In this study,we developed a mechanoelectrical coupling model of neurons under stretching with consideration of axonal plastic deformation.With the model,we found that the effect of mechanical loading on electrophysiology mainly manifests as decreased membrane AP amplitude,a more frequent neuronal firing and a faster electrophysiological signal conduction.The model predicts not only stretch-induced injury but also a more gene ral necking deformation case,which may someday be revealed in future by experiments,providing a reference for the prediction and regulation of neuronal function under mechanical loadings.
