Beaumont J, Roberge F A, Lemieux D R
Institute of Biomedical Engineering, Ecole Polytechnique, Montreal, Quebec, Canada.
Math Biosci. 1993 Jun;115(2):145-86. doi: 10.1016/0025-5564(93)90070-q.
In a companion paper in this issue we show that all the parameters and functions of the Hodgkin-Huxley (HH) model can be calculated in a unique and optimal manner from voltage-clamp peak current data when the steady-state activation (x infinite) and inactivation (z infinite) characteristics are known. Assuming that x infinite and z infinite can be adequately expressed by a Boltzmann equation with two parameters, the present paper describes an optimization procedure to estimate these parameters from peak current data without any constraint on the time constants of activation and inactivation. The required voltage-clamp data are the peak ionic current value (Ip) and its time of occurrence (tp), as provided by two complementary voltage-clamp protocols involving, in each case, a single fixed value of clamp potential. The performance of the procedure was very good with simulated medium- or high-resolution data as it was then possible to determine with confidence the degrees of the gating variables. The performance was also very good with low-resolution data, provided that the degrees of the gating variables were chosen correctly. Good results were also obtained in the presence of Gaussian noise. On the other hand, estimates of x infinite and z infinite based on normalization of peak current measurements always give uncertain results that are likely to be incorrect in a number of circumstances. It is concluded that the HH model can be a useful tool for the interpretation of voltage-clamp peak current data when a reasonable database is available.
在本期的一篇配套论文中，我们表明，当稳态激活（x无穷大）和失活（z无穷大）特性已知时，霍奇金-赫胥黎（HH）模型的所有参数和函数都可以从电压钳峰值电流数据中以独特且最优的方式计算得出。假设x无穷大和z无穷大可以由具有两个参数的玻尔兹曼方程充分表示，本文描述了一种优化程序，可从峰值电流数据中估计这些参数，而对激活和失活的时间常数没有任何限制。所需的电压钳数据是峰值离子电流值（Ip）及其出现时间（tp），这由两种互补的电压钳协议提供，在每种情况下，钳制电位都有一个单一的固定值。对于模拟的中分辨率或高分辨率数据，该程序的性能非常好，因为此时可以自信地确定门控变量的程度。对于低分辨率数据，只要门控变量的程度选择正确，性能也非常好。在存在高斯噪声的情况下也获得了良好的结果。另一方面，基于峰值电流测量归一化对x无穷大和z无穷大的估计总是给出不确定的结果，在许多情况下可能是不正确的。得出的结论是，当有合理的数据库时，HH模型可以成为解释电压钳峰值电流数据的有用工具。
