Lemieux D R, Chicoine H, Roberge F A
Institute of Biomedical Engineering, Ecole Polytechnique, Montreal, Canada.
J Theor Biol. 1994 Aug 21;169(4):363-73. doi: 10.1006/jtbi.1994.1159.
This paper describes a new parameter estimation method applicable to experimental voltage-clamp records. The method is based on the Hodgkin-Huxley (HH) representation of a generic non-inactivating delayed rectifier current (IK) which can be assimilated to the delayed rectifier potassium current of cardiac cells. The model involves a single gating variable of activation (chi) of degree (lambda chi). Its parameters include the voltage-dependent steady-state characteristic (chi infinity), time constant tau chi, the degree lambda chi as a positive integer, and the maximal conductance gK. The method is based on linear optimization. It implements a series of least-squares minimization steps to calculate a first estimate of each model parameter, followed by global minimization to obtain final estimates. The required data, in the form of ionic current responses, correspond to standard voltage-clamp protocols. The effects of noise are minimized by avoiding the use of the time derivative of IK in the calculations. Simulated voltage-clamp data using either a HH model or a five-state Markov chain (MC) model served two purposes: (i) to test the performance of the HH parameter estimation method, and (ii) to study the suitability of the HH model to reproduce data generated by models other than HH. A nominal MC model was obtained by fitting its current responses to those of the HH model. Rate constants of the nominal MC model were then modified and voltage-clamp current responses were generated. Excellent results were obtained with HH and nominal MC data. Data sets generated by a 20% change in the rate constants of the nominal MC model showed that the closed-state rate constants have only a limited influence on the HH parameter estimates, whereas changes in the closed-to-open rate constants produce substantial effects. Nevertheless, a given MC data set can be fitted quite closely by a HH model. In the light of these simulation results it is indicated that an hybrid HH-MC representation of IK data would be more flexible than a straight HH model by removing some of the constraints between the rate constants, and less cumbersome than a straight MC model by substantially reducing the number of parameters to be estimated.
本文描述了一种适用于实验电压钳记录的新参数估计方法。该方法基于通用非失活延迟整流电流（IK）的霍奇金-赫胥黎（HH）表示，该电流可等同于心肌细胞的延迟整流钾电流。该模型涉及一个激活程度为（λχ）的单一门控变量（χ）。其参数包括电压依赖性稳态特性（χ∞）、时间常数τχ、作为正整数的程度λχ以及最大电导gK。该方法基于线性优化。它通过一系列最小二乘最小化步骤来计算每个模型参数的初步估计值，然后进行全局最小化以获得最终估计值。所需的数据以离子电流响应的形式呈现，对应于标准电压钳协议。通过在计算中避免使用IK的时间导数，可将噪声的影响降至最低。使用HH模型或五态马尔可夫链（MC）模型模拟的电压钳数据有两个目的：（i）测试HH参数估计方法的性能，以及（ii）研究HH模型再现除HH模型之外的其他模型生成的数据的适用性。通过将其电流响应拟合到HH模型的电流响应来获得标称MC模型。然后修改标称MC模型的速率常数并生成电压钳电流响应。使用HH和标称MC数据获得了出色的结果。由标称MC模型的速率常数变化20%生成的数据集表明，关闭状态速率常数对HH参数估计的影响有限，而关闭到开放速率常数的变化会产生实质性影响。然而，给定的MC数据集可以由HH模型非常紧密地拟合。鉴于这些模拟结果，表明IK数据的混合HH-MC表示比直接的HH模型更灵活，因为它消除了速率常数之间的一些约束，并且比直接的MC模型更简便，因为它大大减少了要估计的参数数量。
