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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 ==

Conductance-based models are based on an equivalent circuit representation of a cell membrane as first put forth by Hodgkin and Huxley (1952).  

Conductance-based models are based on an equivalent circuit representation of a cell membrane as first put forth by Hodgkin and Huxley (1952).  

These models represent a minimal biophysical interpretation for an excitable cell in which current flow across the membrane is due to charging of the membrane capacitance, \( I_C \ ,\) and movement of ions across ion channels.  

These models represent a minimal biophysical interpretation for an excitable cell in which current flow across the membrane is due to charging of the membrane capacitance,<math>I_C</math>,and movement of ions across ion channels.  

这些模型代表了可兴奋细胞的最小生物物理解释（？），其中电流能够跨膜流动的原因是膜电容的充电，\（I_C\，\）以及离子在离子通道上的运动。

这些模型代表了可兴奋细胞的最小生物物理解释（？），其中电流能够跨膜流动的原因是膜电容的充电，<math>I_C</math>以及离子在离子通道上的运动。

In its simplest version, a conductance-based model represents a neuron by a single isopotential electrical compartment, neglects ion movements between subcellular compartments, and represents only ion movements between the inside and outside of the cell.  

In its simplest version, a conductance-based model represents a neuron by a single isopotential electrical compartment, neglects ion movements between subcellular compartments, and represents only ion movements between the inside and outside of the cell.  

在其最简单的版本中，基于电导的模型通过单个等势电房室表示‎‎神经元‎‎，忽略了亚细胞房室之间的离子运动，并且仅表示细胞内部和外部之间的离子运动。

在其最简单的版本中，基于电导的模型通过单个等势电房室表示‎‎神经元‎‎，忽略了亚细胞房室之间的离子运动，并且仅表示细胞内部和外部之间的离子运动。

Ion channels are selective for particular ionic species, such as sodium (\(Na\)) or potassium (\(K\)), giving rise to currents \( I_{Na} \) or \( I_K \ ,\) respectively.  

Ion channels are selective for particular ionic species, such as sodium<math>Na</math> or potassium<math>K</math>, giving rise to currents<math>I_{Na}</math> \) or(<math>I_K</math>\ ,\) respectively.  

离子通道对特定的离子种类具有选择性，例如对钠（\（Na\））或钾（\（K\）），分别产生电流\（I_{Na} \）或\（I_K\，\）。

离子通道对特定的离子种类具有选择性，例如对钠（\（<math>Na</math>\））或钾（\（<math>K</math>\）），分别产生电流\（<math>I_{Na}</math> \）或\（<math>I_K</math>\，\）。

Thus, the total membrane current, \( I_m(t) \ ,\) is the sum of the capacitive current and the ionic current,

Thus, the total membrane current, \( <math>I_m(t)</math> \ ,\) is the sum of the capacitive current and the ionic current,

因此，总膜电流 \（ I_m（t） \ ，\） 为电容电流和离子电流之和，‎

因此，总膜电流 \（ <math>I_m(t)</math> \ ，\） 为电容电流和离子电流之和，‎

\( I_m(t) = I_C + I_{ionic} \ ,\) where

\( <math>I_m(t) = I_C + I_{ionic}</math> \ ,\) where

\( I_C = C_m dV(t)/dt \ .\)

\( <math>I_C = C_m dV(t)/dt</math> \ .\)

In the Hodgkin-Huxley model, the original conductance-based model,

In the Hodgkin-Huxley model, the original conductance-based model,

在‎‎霍奇金-赫胥黎模型‎‎中，基于电导的原始模型，‎

在‎‎霍奇金-赫胥黎模型‎‎中，基于电导的原始模型，‎

\( I_{ionic} = I_{Na} + I_K + I_L \ .\)

\( <math>I_{ionic} = I_{Na} + I_K + I_L</math> \ .\)

The leak current, \( I_L \ ,\) approximates the passive properties of the cell.  

The leak current, \( <math>I_L</math> \ ,\) approximates the passive properties of the cell.  

‎漏电流 <math> I_L </math> 用于近似神经元的被动属性。

‎漏电流 <math> I_L </math> 用于近似神经元的被动属性。

这在图‎‎1‎‎的原理图中用电阻上的箭头表示。

这在图‎‎1‎‎的原理图中用电阻上的箭头表示。

The voltage dependence or non-constant nature of the conductance, \( g \) (1/resistance) of ion channels is captured using "activation" and "inactivation" '''gating variables''' which are described using first-order kinetics.  

The voltage dependence or non-constant nature of the conductance, \( <math>g</math> \) (1/resistance) of ion channels is captured using "activation" and "inactivation" '''gating variables''' which are described using first-order kinetics.  

离子通道的电压依赖性或电导的非恒定性\（ g \） （1/电阻） 用"激活"和"失活"‎‎的门控变量来‎‎体现，这些变量用一阶动力学方程来描述。

离子通道的电压依赖性或电导的非恒定性\（ <math>g</math> \） （1/电阻） 用"激活"和"失活"‎‎的门控变量来‎‎体现，这些变量用一阶动力学方程来描述。

This is represented with an arrow across the resistor in the schematic representation of Figure 1.  

This is represented with an arrow across the resistor in the schematic representation of Figure 1.  

这在图‎‎1‎‎的原理图中用电阻上的箭头表示。

这在图‎‎1‎‎的原理图中用电阻上的箭头表示。

A current due to ionic species \( S \) with an activation gating variable, \( a \ ,\) but no inactivation variable, would be given by \( g_S = \overline{g}_S \times a \ ,\) where \( a \) is described by first-order kinetics and \( \overline{g}_S \) represents the maximal conductance for the particular ion channel.

A current due to ionic species \( <math>S</math> \) with an activation gating variable, \( <math>a</math> \ ,\) but no inactivation variable, would be given by \( <math>g_S = \overline{g}_S \times a</math> \ ,\) where \( <math>a</math> \) is described by first-order kinetics and \( <math>\overline{g}_S</math> \) represents the maximal conductance for the particular ion channel.

由具有激活门控变量但没有失活变量的离子种类引起的电流，由<math> g_S = \overline{g}_S \times a \ ，</math>给出，其中\（a \）由一阶动力学描述，\（\overline{g}_S \）表示特定离子通道的最大电导。‎

由具有激活门控变量但没有失活变量的离子种类引起的电流，由<math> g_S = \overline{g}_S \times a \ ，</math>给出，其中\（<math>a</math> \）由一阶动力学描述，\（<math>\overline{g}_S</math> \）表示特定离子通道的最大电导。‎

== 公式、参数和假设 ==

== 公式、参数和假设 ==

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\[ C_m dV/dt = \Sigma_j g_j （V_j - V） + I_{ext} \]

从上述理论基础来看，基于电导的模型的标准公式给出为\[ <math>C_m dV/dt = \Sigma_j g_j （V_j - V） + I_{ext}</math> \]

where

where

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。

\（ <math>V_j</math> \） 是电流的能斯特电位或反转电位 \（ <math>j<math> \ ，\） \（ （<math>V - V_j</math>） \） 称为 \（ <math>j</math> \ ，\） 的驱动力，而 \（ <math>I_{ext}</math> \） 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。？？？

\（ <math>a</math>， <math>b</math> \） 是分别提升为小整数幂 \（ <math>x</math>， <math>y</math> \ ，\） 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。

\（ <math>a_{\infty}</math>， <math>b_{\infty}</math> \） 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。

\（ <math>\tau</math> \） 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）。

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）。

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。

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。

电导不仅取决于跨膜电位\（ <math>V</math> \ ，\），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.