Markov models (MMs) represent a generalization of Hodgkin-Huxley models. They provide a versatile structure for modelling single channel data, gating currents, state-dependent drug interaction data, exchanger and pump dynamics, etc. This paper uses examples from cardiac electrophysiology to discuss aspects related to parameter estimation. (i) Parameter unidentifiability (found in 9 out of 13 of the considered models) results in an inability to determine the correct layout of a model, contradicting the idea that model structure and parameters provide insights into underlying molecular processes. (ii) The information content of experimental voltage step clamp data is discussed, and a short but sufficient protocol for parameter estimation is presented. (iii) MMs have been associated with high computational cost (owing to their large number of state variables), presenting an obstacle for multicellular whole organ simulations as well as parameter estimation. It is shown that the stiffness of models increases computation time more than the number of states. (iv) Algorithms and software programs are provided for steady-state analysis, analytical solutions for voltage steps and numerical derivation of parameter identifiability. The results provide a new standard for ion channel modelling to further the automation of model development, the validation process and the predictive power of these models.

译文

:Markov模型(MM)代表Hodgkin-Huxley模型的推广。它们为单通道数据,门控电流,状态相关的药物相互作用数据,交换器和泵动力学等建模提供了通用的结构。本文使用心脏电生理学中的示例讨论与参数估计有关的方面。 (i)参数无法识别(在所考虑模型的13个中的9个中发现)导致无法确定模型的正确布局,这与模型结构和参数可洞悉潜在分子过程的观点相矛盾。 (ii)讨论了实验电压阶跃钳位数据的信息内容,并提出了一个简短而充分的参数估计协议。 (iii)MM与高计算量相关联(由于其状态变量数量众多),这给多细胞全器官模拟以及参数估计带来了障碍。结果表明,模型的刚度比状态数更多地增加了计算时间。 (iv)提供了用于稳态分析的算法和软件程序,电压阶跃的解析解以及参数可识别性的数值推导。结果为离子通道建模提供了新的标准,以进一步促进模型开发,验证过程和这些模型的预测能力的自动化。

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