{"title":"C 型和 N 型失活异构电压门控钾通道的数学模型。","authors":"Kees McGahan, James Keener","doi":"10.3389/fncel.2024.1418125","DOIUrl":null,"url":null,"abstract":"<p><p>Voltage gated potassium channels can be composed of either four identical, or different, pore-forming protein subunits. While the voltage gated channels with identical subunits have been extensively studied both physiologically and mathematically, those with multiple subunit types, termed heteromeric channels, have not been. Here we construct, and explore the predictive outputs of, mechanistic models for heteromeric voltage gated potassium channels that possess either N-type or C-type inactivation kinetics. For both types of inactivation, we first build Markov models of four identical pore-forming inactivating subunits. Combining this with previous results regarding non-inactivating heteromeric channels, we are able to define models for heteromeric channels containing both non-inactivating and inactivating subunits of any ratio. We simulate each model through three unique voltage clamp protocols to identify steady state properties. In doing so, we generate predictions about the impact of adding additional inactivating subunits on a total channel's kinetics. We show that while N-type inactivating subunits appear to have a non-linear impact on the level of inactivation the channel experiences, the effect of C-type inactivating subunits is almost linear. Finally, to combat the computational issues of working with a large number of state variables we define model reductions for both types of heteromeric channels. For the N-type heteromers we derive a quasi-steady-state approximation and indicate where the approximation is appropriate. 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We show that while N-type inactivating subunits appear to have a non-linear impact on the level of inactivation the channel experiences, the effect of C-type inactivating subunits is almost linear. Finally, to combat the computational issues of working with a large number of state variables we define model reductions for both types of heteromeric channels. For the N-type heteromers we derive a quasi-steady-state approximation and indicate where the approximation is appropriate. 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引用次数: 0
摘要
电压门控钾通道可以由四个相同或不同的孔形成蛋白亚基组成。虽然对具有相同亚基的电压门控通道进行了广泛的生理学和数学研究,但对具有多种亚基类型的通道(称为异构体通道)还没有进行过研究。在这里,我们构建了具有 N 型或 C 型失活动力学的异构体电压门控钾通道的机理模型,并探索了这些模型的预测结果。对于这两种类型的失活,我们首先建立了四个相同的孔形成失活亚基的马尔可夫模型。结合之前关于非失活异构体通道的研究结果,我们能够定义包含任意比例的非失活亚单位和失活亚单位的异构体通道模型。我们通过三种独特的电压钳制协议对每种模型进行模拟,以确定稳态特性。在此过程中,我们预测了添加额外失活亚基对整个通道动力学的影响。我们发现,虽然 N 型失活亚基似乎对通道的失活水平有非线性影响,但 C 型失活亚基的影响几乎是线性的。最后,为了解决处理大量状态变量的计算问题,我们定义了两种异构通道的模型还原。对于 N 型异构体,我们推导出一个准稳态近似值,并指出该近似值的适用范围。对于 C 型异构体,我们能够写出明确的模型还原,将超过 10 维的模型还原为 2 维。
Mathematical models of C-type and N-type inactivating heteromeric voltage gated potassium channels.
Voltage gated potassium channels can be composed of either four identical, or different, pore-forming protein subunits. While the voltage gated channels with identical subunits have been extensively studied both physiologically and mathematically, those with multiple subunit types, termed heteromeric channels, have not been. Here we construct, and explore the predictive outputs of, mechanistic models for heteromeric voltage gated potassium channels that possess either N-type or C-type inactivation kinetics. For both types of inactivation, we first build Markov models of four identical pore-forming inactivating subunits. Combining this with previous results regarding non-inactivating heteromeric channels, we are able to define models for heteromeric channels containing both non-inactivating and inactivating subunits of any ratio. We simulate each model through three unique voltage clamp protocols to identify steady state properties. In doing so, we generate predictions about the impact of adding additional inactivating subunits on a total channel's kinetics. We show that while N-type inactivating subunits appear to have a non-linear impact on the level of inactivation the channel experiences, the effect of C-type inactivating subunits is almost linear. Finally, to combat the computational issues of working with a large number of state variables we define model reductions for both types of heteromeric channels. For the N-type heteromers we derive a quasi-steady-state approximation and indicate where the approximation is appropriate. With the C-type heteromers we are able to write an explicit model reduction bringing models of greater than 10 dimensions down to 2.
期刊介绍:
Frontiers in Cellular Neuroscience is a leading journal in its field, publishing rigorously peer-reviewed research that advances our understanding of the cellular mechanisms underlying cell function in the nervous system across all species. Specialty Chief Editors Egidio D‘Angelo at the University of Pavia and Christian Hansel at the University of Chicago are supported by an outstanding Editorial Board of international researchers. This multidisciplinary open-access journal is at the forefront of disseminating and communicating scientific knowledge and impactful discoveries to researchers, academics, clinicians and the public worldwide.