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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.
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<font color = "#32CD32">最小生物物理解释</font>，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.
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.
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（\（<math>Na</math>\））或钾（\（<math>K</math>\）），分别产生电流\（<math>I_{Na}</math> \）或\（<math>I_K</math>\，\）。
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, \( <math>I_m(t)</math> \ ,\) 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 \（ <math>I_m(t)</math> \ ，\） 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，
<math>I_m(t) = I_C + I_{ionic}</math>，其中
<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，
<math>I_{ionic} = I_{Na} + I_K + I_L</math>
The leak current, \( <math>I_L</math> \ ,\) approximates the passive properties of the cell.
The leak current, \( <math>I_L</math> \ ,\) approximates the passive properties of the cell.
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.
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\（ <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。
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.
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.
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\（<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。
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\[ <math>C_m dV/dt = \Sigma_j g_j （V_j - V） + I_{ext}</math> \]
从上述理论基础来看，基于电导的模型的标准公式给出为<math>C_m dV/dt = \Sigma_j g_j (V_j - V) + I_{ext}</math>
where
where
with
with
<math> da/dt = [a_{\infty}(V) - a]/\tau_a(V) </math> and
<math> da/dt = [a_{\infty}(V) - a]/\tau_a(V) </math> 以及
<math> db/dt = [b_{\infty}(V) - b]/\tau_b(V) </math>
<math> db/dt = [b_{\infty}(V) - b]/\tau_b(V) </math>
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.
对每个j。
<br>
\( V_j \) 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.
<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。
<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。？？？
<math>a_{\infty}</math>， <math>b_{\infty}</math> \） 是稳态门控变量函数，其形状通常为 sigmoid。
\（ <math>\tau</math> \） 是时间常数，取决于电压。
\（ <math>\tau</math> \） 是时间常数，取决于电压。