更改

参考<nowiki/>http://www.scholarpedia.org/article/Conductance-based_models

参考<nowiki/>http://www.scholarpedia.org/article/Conductance-based_models

== 理论基础 ==

== 理论基础 ==

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, \( I_C \ ,\) and movement of ions across ion channels.  

这些模型代表了可兴奋电池的最小生物物理解释（？），其中电流跨膜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，\（I_C\，\）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.  

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

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

‎漏电流 \（ I_L \ ，\） 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。

Each ionic current is associated with a conductance (inverse of resistance) and a driving force (battery) which is due to the different concentrations of ions in the intracellular and extracellular media of the cell.  

Each ionic current is associated with a conductance (inverse of resistance) and a driving force (battery) which is due to the different concentrations of ions in the intracellular and extracellular media of the cell.  

因此

因此

\( I_{ionic} = g_{Na}(V) [V(t) - V_{Na}] + g_K(V) [V(t) - V_K] + g_L [V(t) - V_L] \ .\)

<math> I_{ionic} = g_{Na}(V) [V(t) - V_{Na}] + g_K(V) [V(t) - V_K] + g_L [V(t) - V_L] . </math>

This is illustrated in Figure 1.  

This is illustrated in Figure 1.  

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 \( S \) 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.

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\（ g_S = \overline{g}_S \times a \ ，\）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\（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。‎

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

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>

where

where

<math>\( g_j = \overline{g}_j a_j^x b_j^y \) </math>

<math> g_j = \overline{g}_j a_j^x b_j^y </math>

with

with

\( da/dt = [a_{\infty}(V) - a]/\tau_a(V) \) and

<math> da/dt = [a_{\infty}(V) - a]/\tau_a(V) </math> and

\( db/dt = [b_{\infty}(V) - b]/\tau_b(V) \)

<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. \( V_j \) 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.