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Conductance-based models are the simplest possible biophysical representation of an excitable cell, such as a neuron, in which its protein molecule ion channels are represented by conductances and its lipid bilayer by a capacitor.
Conductance-based models are the simplest possible biophysical representation of an excitable cell, such as a neuron, in which its protein molecule ion channels are represented by conductances and its lipid bilayer by a capacitor.
<font color = "#ff8000">基于电导的模型conductance-based model</font>是可兴奋细胞（如神经元）最简单的生物物理表示，其中它的蛋白质分子离子通道用电导表示，它的磷脂双分子层用电容表示。
<font color="#ff8000">基于电导的模型conductance-based model</font>是可兴奋细胞（如神经元）最简单的生物物理表示，其中它的蛋白质分子离子通道用电导表示，它的磷脂双分子层用电容表示。
== 理论基础 ==
== 理论基础 ==
From the theoretical basis described above, the standard formulation for a conductance-based model is given as <math> C_m dV/dt = \Sigma_j g_j (V_j - V) + I_{ext} </math>
From the theoretical basis described above, the standard formulation for a conductance-based model is given as <math> C_m dV/dt = \Sigma_j g_j (V_j - V) + I_{ext} </math>
从上述理论基础来看，基于电导的模型的标准公式给出为\[ C_m dV/dt = \Sigma_j g_j （V_j - V） + I_{ext} \]
where
where
其中
其中
for each j. \( V_j \) is the Nernst potential or reversal potential for current \( j \ ,\) \( (V - V_j) \) is called the driving force for \( j \ ,\) and \( I_{ext} \) is an external current that may be present. \( a, b \) are gating variables raised to small integer powers \( x, y \ ,\) respectively. \( a_{\infty}, b_{\infty} \) are the steady-state gating variable functions that are typically sigmoidal in shape. \( \tau \) is the time constant, which can be voltage-dependent. Further details and equation descriptions can be found in many texts such as Hille (2001) and Koch (1999). Thus, conductance-based models consist of a set of ordinary differential equations (ODEs), as derived from current flow in a circuit representation following Kirchoff's laws. The number of differential equations in the set of model equations depends on the number of different ion channel types being represented with their particular activation and inactivation gating variables. The conductances can depend not only on transmembrane potential \( V \ ,\) but also on concentrations of different ions, for example, the concentration of calcium.
for each j. \( V_j \) is the Nernst potential or reversal potential for current \( j \ ,\) \( (V - V_j) \) is called the driving force for \( j \ ,\) and \( I_{ext} \) is an external current that may be present. \( a, b \) are gating variables raised to small integer powers \( x, y \ ,\) respectively. \( a_{\infty}, b_{\infty} \) are the steady-state gating variable functions that are typically sigmoidal in shape. \( \tau \) is the time constant, which can be voltage-dependent. Further details and equation descriptions can be found in many texts such as Hille (2001) and Koch (1999). Thus, conductance-based models consist of a set of ordinary differential equations (ODEs), as derived from current flow in a circuit representation following Kirchoff's laws. The number of differential equations in the set of model equations depends on the number of different ion channel types being represented with their particular activation and inactivation gating variables. The conductances can depend not only on transmembrane potential \( V \ ,\) but also on concentrations of different ions, for example, the concentration of calcium.
\（ V_j \） 是电流的能斯特电位或反转电位 \（ j \ ，\） \（ （V - V_j） \） 称为 \（ j \ ，\） 的驱动力，而 \（ I_{ext} \） 是可能存在的外部电流。
\（ a， b \） 是分别提升为小整数幂 \（ x， y \ ，\） 的门控变量。？？？
\（ a_{\infty}， b_{\infty} \） 是稳态门控变量函数，其形状通常为 sigmoid。
\（ \tau \） 是时间常数，取决于电压。
进一步的细节和方程描述可以在许多文本中找到，如Hille（2001）和Koch（1999）。
因此，基于电导的模型由一组常微分方程（ODE）组成，根据基尔霍夫定律从电路表示的电流推导得出。
模型方程组中微分方程的数量取决于不同离子通道类型的数量，这些离子通道类型用其特定的激活和失活门控变量表示。
电导不仅取决于跨膜电位\（ V \ ，\），还取决于不同离子的浓度，例如钙离子的浓度。
The parameters in conductance-based models are determined from empirical fits to voltage-clamp experimental data (e.g., see Willms 2002), assuming that the different currents can be adequately separated using pharmacological manipulations and voltage-clamp protocols. As shown in the model formulation, the activation and inactivation variables can be raised to a non-unity integer power, and this is dictated by empirical fits to the data.
The parameters in conductance-based models are determined from empirical fits to voltage-clamp experimental data (e.g., see Willms 2002), assuming that the different currents can be adequately separated using pharmacological manipulations and voltage-clamp protocols. As shown in the model formulation, the activation and inactivation variables can be raised to a non-unity integer power, and this is dictated by empirical fits to the data.
基于电导的模型中的参数是通过经验拟合和电压钳实验数据确定的（例如，参见Willms 2002），假设可以使用药理学操作和电压钳方案充分分离不同的电流。如模型公式所示，激活和失活变量可以提高到（非单位整数幂）（？？？），这是由对数据的经验拟合决定的。
Since (i) it is rarely possible to obtain estimates of all parameter values in a conductance-based mathematical model from experimental data alone, and (ii) the model construct is necessarily a simplification of the biological cell, it is important to consider various optimization techniques to help constrain the problem for which the conductance-based model was developed to address.
Since (i) it is rarely possible to obtain estimates of all parameter values in a conductance-based mathematical model from experimental data alone, and (ii) the model construct is necessarily a simplification of the biological cell, it is important to consider various optimization techniques to help constrain the problem for which the conductance-based model was developed to address.
由于（i）仅从实验数据中很难获得基于电导的数学模型中所有参数值的估计，并且（ii）模型构建必然是生物细胞的简化，因此重要的是要考虑各种优化技术，以帮助约束建立基于电导的模型以解决的问题。（？？？）
In summary, the basic assumptions in conductance-based models are:
In summary, the basic assumptions in conductance-based models are: