更改

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,

\( V_j \) 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.

\( V_j \) 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>V_j</math>是电流<math>j</math>的[[能斯特电位]]或[[反转电位]]，<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</math>，<math>b</math>分别是<font color = "#32CD32">提升为小整数幂</font><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>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。

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\（ <math>V</math> \ ，\），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.

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。

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<font color = "#32CD32">提高到（非单位整数幂）</font>，这由对数据的经验拟合决定。

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。（？？？）

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来解决的问题。

In summary, the basic assumptions in conductance-based models are:

In summary, the basic assumptions in conductance-based models are:

建立在许多基于电导的模型中的一个常见扩展为将钙[[动力学]]方程包含在内。

建立在许多基于电导的模型中的一个常见扩展为将钙[[动力学]]方程包含在内。

例如，参见Dayan and Abbott （2001）中的第6.2节。

例如，参见Dayan and Abbott （2001）中的第6.2节。

In turn, these intrinsic characteristics affect behaviors in neuronal networks.

In turn, these intrinsic characteristics affect behaviors in neuronal networks.

建立基于电导的可兴奋细胞模型，来帮助理解促进动作电位的产生、重复放电和[[爆裂]]（？）（即[[振荡]]模式）等的潜在原理。

建立基于电导的可兴奋细胞模型，来帮助理解促进动作电位的产生、反复放电和[[簇放电]]（即[[振荡]]模式）等的潜在原理。

反过来，这些内在特征会影响神经元网络中的行为。

反过来，这些内在特征会影响神经元网络中的行为。

Mathematical distinctions in conductance-based models using dynamical system and bifurcation analyses are available. Details are described in Izhikevich (2007).

Mathematical distinctions in conductance-based models using dynamical system and bifurcation analyses are available. Details are described in Izhikevich (2007).

在使用动力系统和[[分岔理论|分岔]]分析的基于电导的模型中，可以进行数学区分。（？？？）细节在Izhikevich（2007）中有所描述。

在使用动力系统和[[分岔理论|分岔]]分析的基于电导的模型中，<font color = "#32CD32">可以进行数学区分</font>。更多细节在Izhikevich（2007）中有所描述。

== 参考文献 ==

== 参考文献 ==

== 编者推荐 ==

== 编者推荐 ==

《神经科学的数学原理》

'''《神经科学的数学原理》'''（《Mathematical Foundations of Neuroscience》）G.Bard Ermentrout, David H.Terman著 吴莹，刘深泉译