兴奋-抑制平衡

2022-06-14T11:59:58Z

安贞桦：

兴奋-抑制平衡

2022-06-14T11:59:48Z

安贞桦：

参考<nowiki/>http://www.scholarpedia.org/article/Balance_of_excitation_and_inhibition

此词条由神经动力学读书会词条梳理志愿者安贞桦翻译审校，未经专家审核，带来阅读不便，请见谅。

In the context of neurophysiology, '''balance of excitation and inhibition''' (E/I balance) refers to the relative contributions of excitatory and inhibitory synaptic inputs corresponding to some neuronal event, such as oscillation or response evoked by sensory stimulation.

在神经生理学背景下，'''兴奋-抑制平衡 E/I balance'''指的是对应于某些神经元事件的兴奋性和抑制性突触输入的相关贡献，如由感觉刺激引起的振荡或反应。

In the current literature, owing to the extremely wide range of conditions in which the term is applied, it has several different, albeit related, meanings.

在目前的文献中，由于该术语的应用情景极其广泛，它有几种相关但不相同的含义。

As described in more detail below, the precise meaning depends on various considerations, such as averaging across time or population of neurons that is involved; the relevant timescale; whether the synaptic activity is sustained or transient, spontaneous or evoked.

如下文更详细地描述，确切的含义取决于各种考虑因素，比如时间上的平均值或所涉及的神经元群体；相关的时间尺度；突触活动是持续的还是暂态的，是自发的还是激发的。

In general, excitatory and inhibitory inputs of a neuron are said to be balanced if across a range of conditions of interest the ratio between the two inputs is constant.

一般来说，如果在整个关心的条件范围内，兴奋性和抑制性输入之间的比率是恒定的，则称其为平衡的。

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In the cortex, interneurons responsible for inhibition comprise just a small fraction of the neurons, yet they have an important function in regulating activity of principal cells.

在皮层中，负责抑制的''' 中间神经元interneurons '''只占神经元的一小部分，但它们对调节''' 主细胞 principal cells '''的活动具有重要功能。

When inhibition is blocked pharmacologically, cortical activity becomes epileptic (Dichter and Ayala, 1987), and neurons may lose their selectivity to different stimulus features (Sillito, 1975).

当抑制作用在药理学上阻断时，皮层活动会发生癫痫（Dichter和Ayala，1987），神经元可能会失去对不同刺激特征的选择性（Sillito，1975）。

These and other data indicate that the interplay between excitation and inhibition has an important role in determining the cortical computation.

这些数据和其他数据表明，兴奋和抑制之间的相互作用在决定皮质计算中具有重要作用。

Our understanding of the relationships between these two opposing forces has advanced significantly during the recent years, mainly due to the growing use of in-vivo intracellular recording techniques.

近年来，得益于体内的''' 胞内记录intracellular recording '''技术的日益普及，我们对这两种对立力量之间的关系的理解有了显著的进步。

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== Indirect evidence for E/I balance E/I平衡的间接证据 ==

Cortical neurons receive synaptic inputs from thousands of other, mainly excitatory, neurons, most of which evoke only a sub-millivolt response (Bruno and Sakmann, 2006; Lefort et al., 2009).

皮质神经元从数千个其他神经元（主要是兴奋性神经元）接收突触输入，大多数仅仅引发亚毫伏反应（Bruno和Sakmann，2006;Lefort et al.， 2009）。

If these inputs arrive from neurons that fire at independent random times, they are expected to produce an almost constant depolarization leading to a regular firing.

如果这些输入来自在独立随机的时间点发放的神经元，则它们将产生几乎恒定的去极化，引起有规律的发放。

However, spike trains extracellularly recorded from single cortical neurons exhibit high variability.

然而，从单个皮质神经元记录的胞外''' 尖峰序列spike trains '''表现出高度的可变性。

For instance, '''the coefficient of variation''' of the inter-spike intervals (ISIs) of neurons firing in response to a sensory input for a period of several seconds, is approximately equal to 1, as expected from a Poisson process (Softky and Koch, 1993).

例如，响应于数秒内的感觉输入而放电的神经元的放电间隔（ISIs）的'''变化系数'''大约等于1，正如''' 泊松过程Poisson process '''所预期的那样（Softky和Koch，1993）。

This apparent paradox between simple probabilistic considerations and the observed statistics of cortical spike trains led to several proposed resolutions.

在简单的概率考虑和观察到的皮质尖峰序列的统计数据之间的明显矛盾，驱使人们提出了几种解释方案。

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One early resolution was that excitatory and inhibitory synaptic currents of cortical neurons are approximately balanced in strength, causing the membrane potential to hover somewhat below the spiking threshold, crossing it at random times (Shadlen and Newsome, 1994, 1998).

一个早期的解释方案是，皮质神经元的兴奋性和抑制性突触电流在强度上大致平衡，导致膜电位在放电阈值以下波动，在随机时间超过阈值（Shadlen和Newsome，1994，1998）。

Simulations, based on the random walk model of (Gerstein and Mandelbrot, 1964) demonstrated that under such a regime of synaptic inputs the ISI variability is in agreement with experimental observations (Shadlen and Newsome, 1994, 1998).

基于的'''随机游走模型random walk model'''（Gerstein和Mandelbrot，1964）的模拟表明，在这种突触输入的机制下，ISI的变化与实验观察结果一致（Shadlen和Newsome，1994，1998）。

Furthermore, computational studies of spontaneous activity in neuronal networks showed that E/I balance emerges naturally if the network is sparsely connected (van Vreeswijk and Sompolinsky, 1996; Vogels et al., 2005).

However, these early theoretical studies were based on crude estimates of the relevant parameters, and therefore cannot be regarded as definitive.

此外，对神经元网络中的自发活动的计算研究表明，如果网络是稀疏连接的，E / I平衡会自然出现（van Vreeswijk和Sompolinsky，1996; Vogels等人，2005年）。

然而，这些早期的理论研究是基于对相关参数的粗略估计，因此不能视为定论。

In fact, several follow-up studies suggested that other factors, such as synchrony, are required in order to explain the observed ISI statistics, e.g., (Stevens and Zador, 1998).

事实上，一些后续研究表明，如（Stevens和Zador，1998），为了解释观察到的ISI统计数据，需要引入其他因素，例如同步性。

Indeed, as described below, it appears that although excitation and inhibition are balanced, the membrane potential of cortical neurons does not necessarily follow the random walk trajectory predicted by these early models

(Crochet and Petersen, 2006; DeWeese and Zador, 2006; Poulet and Petersen, 2008; Okun et al., 2010; Polack et al., 2013; Sachidhanandam et al., 2013; Tan et al., 2014).

如下所述，尽管兴奋和抑制是平衡的，但皮质神经元的膜电位并不一定遵循这些早期模型预测的随机游走轨迹。

（Crochet和Petersen，2006;DeWeese和Zador，2006年;Poulet和Petersen，2008;奥坤等人， 2010;Polack et al.， 2013;Sachidhanandam等人， 2013;谭等人，2014）。

The possibility of excitation and inhibition having a comparable strength might seem implausible at first, since interneurons comprise only 15% - 25% of the population of cortical neurons.

起初兴奋和抑制具有相当强度的可能性似乎难以置信，因为中间神经元仅占皮质神经元群体的15%-25%。

However, the synaptic strength and firing rates of inhibitory interneurons are substantially higher than in excitatory neurons, thus inhibitory interneurons have an impact disproportionate to their relatively small number.

然而，抑制性中间神经元的突触强度和放电率大大高于兴奋性神经元，因此抑制性中间神经元有着与其相对较少的数量不成比例的影响。

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== Intracellular measurement of the excitatory and inhibitory synaptic inputs 兴奋性和抑制性突触输入的细胞内测量 ==

[[Image:fig1.png|thumb|350px|right|F1|Computation of synaptic conductance evoked by sensory stimulus. The average response to whisker deflection in a spiny stellate neuron in layer IV of the rat primary somatosensory cortex is recorded in current-clamp mode while injecting 4 different currents (left panel). In addition, neuron’s capacitance and leak conductance are measured (not shown). By fitting the responses to equation (1) the average excitatory and inhibitory synaptic conductances evoked by the stimulus are recovered (right panel). Adapted from (Heiss et al., 2008).

图1：由感觉刺激引起的突触电导的计算。
在注入4种不同的电流时（左图），以电流钳模式记录大鼠初级躯体感觉皮层的第IV层中，多刺星状神经元对'''晶须偏转'''的平均响应。
此外，测量了神经元电容和漏电导（未显示）。
通过将响应拟合至方程（1），'''恢复了由刺激引起的平均兴奋性和抑制性突触电导'''（右图）。改编自（Heiss等人，2008）。

]]

In a pioneering study, Borg-Graham and colleagues used intracellular recordings to directly estimate the synaptic conductance changes evoked in cortical neurons by visual stimulation (Borg-Graham et al., 1996, 1998).

在一项开创性的研究中，Borg-Graham及其同事用胞内记录直接估计通过视觉刺激在皮质神经元中引起的突触电导变化（Borg-Graham等人，1996，1998）。

The average synaptic current evoked by a stimulus is recorded in voltage-clamp mode, using several different clamping voltages.

用一些不同的钳位电压，在电压钳位模式下记录由刺激引起的平均突触电流。

Alternatively, the subthreshold response is recorded in the current-clamp mode at several different clamping currents (Anderson et al., 2000).

或者，用一些不同的钳位电流，在电流钳位模式下记录阈值下响应（Anderson等人，2000）。

The behavior of the membrane potential is approximated using a passive, single compartment, conductance-based model of the neuron, described by

膜电位的行为是用神经元的被动单'''隔室compartment'''的[[基于电导的模型]]近似的，描述如下

<math>CdV/dt = -G_{leak}(V(t)-E_{leak}) - G_{ex}(t)(V(t)-E_{ex}) - G_{in}(t)(V(t)-E_{in})+I_{inj}</math> (1)

where \(E_{leak}\) is the resting membrane potential of the neuron, \(C\) is its capacitance, \(G_{leak}\) is the mean conductance in absence of stimulation (the inverse of input resistance), \(E_{ex}\) and \(E_{in}\) are the reversal potentials of excitation and inhibition, and \(I_{inj}\) is the current injected through the recording pipette.

其中<math>E_{leak}</math>是神经元的静息膜电位，<math>C</math>是其电容，<math>G_{leak}</math>是在没有刺激的情况下的平均电导（输入电阻的倒数），<math>E_{ex}</math>和<math>E_{in}</math>是兴奋和抑制的反转电位，<math>I_{inj}</math>是通过记录移液管注入的电流。

By fitting equation (1) to the average responses at different holding potentials, the synaptic conductances evoked by the stimulus, \(G_{ex}(t)\) and \(G_{in}(t)\ ,\) can be computed (see Figure 1).

通过将方程（1）拟合到不同保持电位下的平均响应，可以计算出由刺激<math>G_{ex}(t)</math>和<math>G_{in}(t)</math>引起的突触电导（见图1）。

For an in-depth review of the method and its caveats an interested reader is referred to (Monier et al., 2008).

欲深入了解该方法及其注意事项，请参考（Monier等人，2008）。

== Selectivity of cortical excitation and inhibition to sensory stimulation 皮质兴奋的选择性和对感觉刺激的抑制 ==

Early models of the visual cortex suggested that the selectivity of cortical cells to sensory stimulation emerges from feedforward inputs.

视觉皮层的早期模型表明，皮质细胞对感觉刺激的选择性来自于前馈输入。

Later models, however, questioned this view by suggesting that cortical inhibition plays a significant role in enhancing the selectivity of cortical response.

然而，后来的模型质疑这一观点，认为皮质抑制在增强皮质响应的选择性方面起着显著的作用。

The best known example for this controversy is the emergence of orientation selectivity in primary visual cortex.

这种争议最着名的例子是初级视觉皮层中方向选择性的出现。

The feedforward model (Hubel and Wiesel, 1962) was supported by various studies (Nelson et al., 1994; Alonso and Martinez, 1998; Chung and Ferster, 1998; Martinez and Alonso, 2001), while being challenged by others (Sillito, 1975; Volgushev et al., 1996).

'''前馈模型feedforward model'''（Hubel和Wiesel，1962）得到了各种研究的支持（Nelson等人，1994;阿隆索和马丁内斯，1998年;钟和费斯特， 1998;马丁内斯和阿隆索，2001），同时受到其他人的挑战（Sillito，1975;Volgushev等人，1996年）。

The feedforward model, however, failed to predict several key experimental findings, and in particular the contrast invariance of orientation tuning (Ferster and Miller, 2000).

然而，前馈模型未能预测几个关键的实验发现，特别是方向调谐的对比不变性（Ferster和Miller，2000）。

Alternative models proposed that the tuning of inhibitory inputs is wider, so that excitation and inhibition form a 'Mexican hat' interaction pattern which sharpens the selectivity of the cells (Ben-Yishai et al., 1995; Somers et al., 1995; Hansel and Sompolinsky, 1996).

替代模型提出，抑制性输入的调谐范围更广，因此兴奋和抑制形成了'''"墨西哥帽Mexican hat"'''相互作用模式，从而提高了细胞的选择性（Ben-Yishai等人，1995;萨默斯等人，1995年;汉赛尔和索姆波林斯基，1996年）。

In the primary auditory cortex inhibition was similarly suggested to account for the sensory selectivity of the neurons (Calford and Semple, 1995; Sutter et al., 1999; Wang et al., 2002).

在初级听觉皮层中，抑制同样被认为可以解释神经元的感觉选择性（Calford和Semple，1995;萨特等人， 1999;Wang等人，2002）。

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A breakthrough in the ability to test these models was achieved by the in-vivo intracellular conductance measurement methods described above.

通过上述体内细胞内电导测量方法，在测试这些模型的能力方面取得了突破。

Over the last 15 years this approach was used in many studies to examine the sensory selectivity of excitatory and inhibitory synaptic inputs in primary sensory areas of several mammalian species.

在过去的15年中，这种方法被用于许多研究，来检查一些哺乳动物物种的主要感觉区域中兴奋性和抑制性突触输入的感觉选择性。

Direct measurements showed that to a first approximation the excitatory and inhibitory inputs are either similarly tuned, or that inhibitory inputs have a somewhat wider tuning.

直接测量表明，在一级近似下，要么兴奋性和抑制性输入被相似地调谐，要么抑制性输入具有更宽的调谐。

In cat primary visual cortex excitatory and inhibitory synaptic inputs are similarly tuned for orientation (Anderson et al., 2000), as well as for length (Anderson et al., 2001) and the direction of motion (Priebe and Ferster, 2005).

在猫的初级视觉皮层中，方向（Anderson等人，2000）以及长度（Anderson等人，2001）和运动方向（Priebe和Ferster，2005）相似地调谐兴奋性和抑制性突触输入。

In the rodent primary auditory cortex inhibition is tuned similarly or somewhat wider than excitation for both frequency and intensity (Wehr and Zador, 2003; Wu et al., 2008; Zhou et al., 2014), see Figure 2.

在啮齿动物的初级听觉皮层中，在频率和强度上的抑制与兴奋相似或略宽地调谐（Wehr和Zador，2003;吴等， 2008;Zhou等人，2014），见图2。

Therefore, in these cases the selectivity of the neurons is unlikely to emerge through inhibitory suppression of the response to non-preferred stimuli.

因此，在这些情况下，神经元的选择性不太可能通过对非偏好刺激的响应的抑制而显现。

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[[Image:fig2.jpg|frame|right|F2|An example of a neuron in the auditory cortex with frequency and intensity co-tuned excitatory and inhibitory inputs. (a) Excitatory and inhibitory synaptic conductances evoked by stimuli of different frequencies and preferred intensity have a similar tuning. The measured conductances are shown at the bottom (green – excitatory conductance, red - inhibitory conductance, black – total conductance). (b) The excitatory and inhibitory inputs are also intensity co-tuned, notation as in (a). Adapted from (Wehr and Zador, 2003).

图2：听觉皮层中神经元的示例，其频率和强度共同调谐兴奋性和抑制性输入。
（a）由不同频率和偏好强度的刺激诱发的兴奋性和抑制性突触传导具有相似的调谐。
测量的电导显示在底部（绿色-兴奋性电导，红色-抑制性电导，黑色-总电导）。
（b）兴奋性和抑制性输入也会由强度协同调谐，如（b）所示。改编自（Wehr和Zador，2003）

]]

The similar tuning of excitatory and inhibitory inputs to different features of the stimuli space appears to be a rather common organizational principle in the sensory areas, however there are several notable exceptions.

对刺激空间不同特征的兴奋性和抑制性输入的类似调谐似乎是感觉区域中相当常见的组织原则，但也有几个显著的例外。

The most prominent deviation from co-tuning was observed for orientation selectivity in the mouse primary visual cortex, where the inhibitory input is substantially more broadly tuned than the excitatory input, possibly because rodent primary visual cortex lacks orientation columns (Liu et al., 2011; Atallah et al., 2012; Li et al., 2012; Harris and Mrsic-Flogel, 2013).

在小鼠初级视觉皮层中观察到对方向选择性的最显著的协同调谐偏差，其中抑制性输入的调谐范围比兴奋性输入的调谐范围更广，可能是因为啮齿动物初级视觉皮层缺乏朝向柱（Liu等人，2011年；Atalah等人，2012年；Li等人，2012年；Harris和Mrsic Flogel，2013年）。

An opposite scenario, where inhibitory inputs have narrower selectivity, was observed for frequency tuning in layer V '''intrinsically-bursting''' (but not regular-spiking) neurons of the primary auditory cortex (Sun et al., 2013).

在初级听觉皮层的第五层'''内在簇放电'''（但不是规则的尖峰）神经元中观察到了一种相反的情况，即抑制性输入的选择性较窄（Sun等人，2013年）。

Also in the auditory cortex, some intensity-tuned neurons receive excitatory inputs which peak at the preferred intensity, whereas their inhibitory inputs increase monotonically with the stimulus strength (Wu et al., 2006), representing a case where the co-tuning of excitation and inhibition appears to break altogether.

同样在听觉皮层，一些强度调谐神经元接收到的兴奋性输入在偏好强度时达到峰值，而它们的抑制性输入随着刺激强度单调增加（Wu等人，2006年），这体现了兴奋和抑制的共同调谐发生破坏的例子。

Finally, it should be noted that the tuning of inhibitory and excitatory inputs alone is not sufficient to substantiate specific theoretical models for feature selectivity in the cortex, because broad tuning of inhibition may either reflect non-specific convergence of inputs from a population of inhibitory cells that demonstrate highly selective but non-overlapping orientation tuning curves, or simply result from the wide tuning curves of their '''innervating''' inhibitory neurons (Shapley and Xing, 2013; Section 6 below).

最后，应注意的是，仅抑制性和兴奋性输入的调谐不足以证实皮质中特征选择性的具体理论模型，因为抑制性的广泛调谐可能反映了抑制性细胞群输入的非特异性收敛，这些抑制性细胞群显示出具有高度选择性但不重叠的方向调谐曲线，或者仅仅是由于它们的'''神经支配'''抑制神经元的宽调谐曲线（Shapley和Xing，2013；下文第6节）。

== Temporal structure of sensory evoked excitation and inhibition 感觉诱发电能和抑制的时间结构 ==

In the auditory and somatosensory cortices sensory stimulation often evokes '''stereotypic''' sequence of excitation followed within a few milliseconds by inhibition (Wehr and Zador, 2003; Higley and Contreras, 2006).

在听觉和体感皮层中，感觉刺激经常唤起在随后几毫秒内受抑制的'''定型'''兴奋序列，（Wehr和Zador，2003;Higley和Contreras，2006）。

Although excitation and inhibition are similarly tuned and hence are said to be balanced, a large imbalance occurs at the fine time scale, as inhibition lags behind excitation by several milliseconds.

尽管兴奋和抑制被相似地调谐而因此被称为平衡的，但由于抑制滞后于兴奋几毫秒，在精细的时间尺度上会出现很大的不平衡。

This lag between excitation and inhibition is likely to determine the integration window for excitation, affecting the number and precise timing of action potentials (Gabernet et al., 2005).

兴奋和抑制之间的这种滞后可能决定兴奋的整合窗口，影响动作电位的数量和精确时间（Gabernet等人，2005年）。

In the auditory cortex the lag is independent of the frequency tuning of the cells (Wehr and Zador, 2003).

在听觉皮层中，滞后与细胞的频率调谐无关（Wehr和Zador，2003）。

In the somatosensory cortex, however, the delay between excitation and inhibition might be related to the stimulus tuning of the neuron, such that at the preferred stimuli the lag between excitation and inhibition is larger than at the non-preferred ones (Wilent and Contreras, 2005).

然而，在体感皮层中，兴奋和抑制之间的延迟可能与神经元的刺激调谐有关，因此相比于在非偏好刺激下，在偏好刺激下兴奋和抑制之间的延迟更大（Wilent和Contreras，2005）。

Hence, a wider time window is available for integration of excitation for the preferred stimuli, producing more action potentials.

因此，更宽的时间窗口用于对偏好刺激的兴奋整合，产生更多的动作电位。

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One of the central roles traditionally attributed to inhibition is suppression of neuronal responses during temporal integration of sensory inputs.

传统上认为抑制的核心作用之一是在感觉输入的时间整合过程中对神经元反应的抑制。

A widely known example is forward suppression in the auditory cortex, in which the response to a second click presented shortly after the first one is much weaker.

一个广为人知的例子是听觉皮层中的前向抑制，在第一次点击声后不久，对第二次点击声的反应要弱得多。

Another example is in the barrel cortex, where a response to whisker stimulation is largely suppressed if it is preceded by a stimulation of a neighboring whisker.

另一个例子是在桶状皮质中，如果之前刺激相邻的胡须，则对胡须刺激的响应在很大程度上受到抑制。

Such forward suppression was widely believed to be due to inhibition evoked by the first stimuli.

这种前向抑制当前广泛认为是由于第一次刺激引起的抑制。

However, intracellular conductance measurements found that the duration of inhibitory synaptic input evoked by the first click is too short to account for the duration of forward suppression, so that the above explanation is incomplete at the best (Wehr and Zador, 2003, 2005).

然而，对细胞内电导的测量发现，第一次点击声诱发的抑制性突触输入的持续时间太短，无法解释前向抑制的持续时间，因此上述解释充其量是不完整的（Wehr和Zador，2003，2005）。

Similarly, an intracellular recording study in the barrel cortex has shown that cross whisker suppression cannot be fully explained by a postsynaptic inhibitory mechanism (Higley and Contreras, 2003).

类似地，桶状皮质的细胞内记录研究表明，突触后抑制机制不能完全解释交叉胡须抑制（Higley and Contreras，2003）。

Although inhibition is not the primary cause for forward suppression, in other cases the ratio between the excitatory and inhibitory inputs to a neuron in a primary sensory area does depend not only on the instantaneous properties of the stimulus (its contrast, frequency, intensity, etc.) but also on its history.

虽然抑制不是前向抑制的主要原因，但在其他情况下，初级感觉区神经元的兴奋性和抑制性输入之间的比率不仅取决于刺激的瞬时特性（其对比度、频率、强度等），还取决于其历史。

One particular example is adaptation to repeated stimuli, such as clicks or whisker deflections, which under certain conditions can skew the ratio between excitatory and inhibitory inputs toward excitation (Wehr and Zador, 2005; Heiss et al., 2008).

一个特别的例子是对重复刺激的适应，例如点击声或胡须偏转，在某些条件下，这会使兴奋性和抑制性输入之间的比率向兴奋方向倾斜（Wehr和Zador，2005；Heiss等人，2008）。

Paradoxically, because of a slower recovery of inhibitory inputs from adaptation, neurons become hypersensitive shortly after the termination of the adapting stimulation (Cohen-Kashi Malina et al., 2013), which might explain why neurons in the barrel cortex respond better to non-periodic stimulation (Lak et al., 2008).

自相矛盾的是，由于从适应中恢复抑制性输入较慢，神经元在适应刺激终止后不久就会变得超敏（Cohen Kashi-Malina等人，2013年），这可能解释了为什么桶状皮质神经元对非周期性刺激的响应得更好（Lak等人，2008年）。

== E/I balance during spontaneous activity 自发活动期间的 E/I 平衡 ==

Under some anesthesia conditions and during slow wave sleep, the membrane potential of cortical neurons fluctuates between a depolarized state and hyperpolarized state.

在某些麻醉条件下和慢波睡眠期间，皮质神经元的膜电位在去极化状态和超极化状态之间波动。

This behavior is known as Up-Down activity.

此行为称为"上下活动"。

During the Down phase the neurons receive almost no synaptic inputs, so that the membrane stays near its resting potential.

在下降阶段，神经元几乎不接收突触输入，因此膜保持在其静息电位附近。

In the Up phase a barrage of synaptic inputs produces a reliable depolarization of 10-20 mV, which occasionally causes spiking (see Figure 1 in Up and down states).

在上升阶段，大量突触输入会产生10-20 mV的可靠去极化，偶尔会导致尖峰（上升和下降状态见图1）。

//

The relation between the average amounts of excitatory and inhibitory synaptic inputs during the Up phase was studied using the conductance measurement method described above.

使用上述电导测量方法研究了在上升期兴奋性和抑制性突触输入的平均数量之间的关系。

These experiments, conducted both in vitro (Shu et al., 2003) and in vivo (Haider et al., 2006), have shown that excitatory and inhibitory conductances are balanced throughout the Up phase.

这些在体外（Shu等人，2003年）和体内（Haider等人，2006年）进行的实验表明，兴奋性和抑制性传导在整个上升阶段是平衡的。

In the beginning of the Up phase, both the excitatory and the inhibitory synaptic conductances are high and they tend to progressively decrease, but their ratio remains constant and approximately equal to 1.

在上升期开始时，兴奋性和抑制性突触传导都很高，并趋于逐渐降低，但它们的比率保持不变，约等于1。

//

In awake, drug-free animals the membrane potential dynamics exhibits an entire spectrum of distinct, brain state dependent activity patterns.

在清醒、无药物的动物中，膜电位动力学表现出一整套不同的、依赖于大脑状态的活动模式。

The highly desynchronized high-conductance state, which is similar to a continuous Up phase (Crochet and Petersen 2006; Destexhe et al., 2007) represents one end of this spectrum.

高度去同步的高电导状态，类似于连续上升阶段（Crochet and Petersen 2006；Destexe et al.，2007），代表了这一套的一端。

According to an intracellular study in the cortex of awake cats, in this condition the neurons are continuously bombarded by both excitatory and inhibitory inputs, where the total inhibitory conductance is several times higher than the excitatory one (Rudolph et al., 2007), providing a confirmation for the balanced excitation-inhibition hypothesis put forward by (Shadlen and Newsome, 1994).

根据对清醒状态下猫的皮层的细胞内研究，在这种情况下，神经元连续受到兴奋性和抑制性输入的轰击，其中总抑制电导比兴奋性电导高出数倍（Rudolph等人，2007年），证实了由（Shadlen和Newsome，1994年）提出的平衡兴奋-抑制假说。

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[[Image:fig3.jpg|thumb|500px|right|F3|Excitatory and inhibitory inputs are synchronized during spontaneous activity. Two nearby neurons are simultaneously recorded when (a) both are at their resting potential, close to the reversal potential of inhibition (hyperpolarized-hyperpolarized mode); (b) both neurons are depolarized close to the reversal potential of excitation (depolarized-depolarized mode); (c-d) one of the neurons is in the hyperpolarized mode while the other is in the depolarized mode. In (a) the activity is dominated by excitatory inputs, which are seen to be highly synchronized between the neurons. Similarly, in (b) the activity is dominated by inhibitory inputs which are also highly synchronized. Finally, the mixed mode recordings (c-d) demonstrate that the excitatory and inhibitory inputs possess a high degree of synchrony. Adapted from (Okun and Lampl, 2008).

图3：在自发活动期间，兴奋性和抑制性输入是同步的。
在以下情景同时记录两个邻近的神经元
（a）两者都处于静息电位，接近抑制反转电位（超极化-超极化模式）；
（b）两个神经元都去极化，接近于兴奋的反转电位（去极化-去极化模式）；
（c-d）其中一个神经元处于超极化模式，而另一个处于去极化模式。
在（a）中，活动主要由兴奋性输入支配，在神经元之间将这种兴奋性输入视为高度同步的。
类似地，在（b）中，活动由抑制性输入支配，这些输入也是高度同步的。
最后，对混合模式的记录（c-d）表明兴奋性和抑制性输入具有高度的同步性。改编自（Okun and Lampl，2008）。

]]

The other end of the spectrum of brain states in awake mammals is the quiet wakefulness condition, which is somewhat similar to light anesthesia, and is characterized by rather short depolarizations ('bumps') and membrane potential distribution that is not bimodal, e.g., (DeWeese and Zador, 2006; Poulet and Petersen, 2008).

清醒哺乳动物大脑状态谱的另一端是安静的清醒状态，这在某种程度上类似于轻度麻醉，其特征是相当短的去极化（'''“碰撞bumps”'''）和非双峰的膜电位分布，例如（DeWeese和Zador，2006；Poulet和Petersen，2008）。

In the quiet wakefulness condition and light state of anesthesia there are no ''' stereotypic''' Up events nor does the activity resemble a single continuous Up phase, therefore the single-electrode conductance measurement method which requires averaging over multiple repeats of some stereotypic event, recorded at different holding potentials, cannot be applied.

在安静的清醒状态和轻度的麻醉状态下，没有'''定型'''的上升事件，也没有类似于单一连续上升阶段的活动，因此，无法应用单电极电导测量方法，该方法要求在不同的保持电位下记录的一些定型事件的多次重复中求平均值。

However, the substantial synchrony of synaptic inputs to closely located neurons (Lampl et al., 1999; Hasenstaub et al., 2005; Okun and Lampl, 2008; Poulet and Petersen, 2008) which exists in this case allows to continuously monitor both the excitatory and the inhibitory activity in the local network.

然而，这种情况下存在的对位置相近神经元的突触输入的实质同步性（Lampl等人，1999；Hasenstaub等人，2005；Okun和Lampl，2008；Poulet和Petersen，2008），允许持续监测局部网络中的兴奋性和抑制性活动。

Toward this end simultaneous recording from a nearby pair of neurons are used, where one cell is hyperpolarized close to the reversal potential of inhibition and the other cell is depolarized sufficiently close to the reversal potential of excitation (Okun and Lampl, 2008), Figure 3.

为此，使用一对临近神经元的同步记录，其中一个细胞超极化，接近抑制的反转电位，另一个细胞去极化，足以接近兴奋的反转电位（Okun和Lampl，2008），图3。

This method reveals that in this type of spontaneous activity the excitatory and inhibitory inputs are '''interlocked''' in time, with inhibition lagging by several milliseconds behind excitation.

该方法揭示了在这种自发活动中，兴奋性和抑制性输入在时间上是'''互锁'''的，抑制滞后于兴奋数毫秒。

Furthermore, the strength of excitatory and inhibitory inputs is (positively) correlated – large bumps typically contain both a strong excitatory and a strong inhibitory components, whereas small bumps are due to weak synaptic inputs, rather than strong inhibition that quenches the excitatory input.

此外，兴奋性和抑制性输入的强度（正）相关——大碰撞通常包含强兴奋性和强抑制性成分，而小碰撞是由于突触输入较弱，而非终止兴奋性输入的强抑制。

These correlations strongly suggest that inhibition plays important role in controlling the excitability of cortical networks at fast time scales.

这些相关性强烈表明，抑制在快速时间尺度上控制皮层网络的兴奋性方面起着重要作用。

==Current research directions 当前研究方向==

In the recent years a whole range of new genetic tools became available, particularly for the mouse (''Mus musculus'') species.

近年来，出现了一系列新的遗传工具，特别是对于小鼠（''Mus musculus''）物种。

In addition, working with awake head-fixed mice is relatively '''straightforward'''.

此外，使用清醒的头部固定的小鼠相对'''直截了当'''。

These and other recent developments are heavily relied upon in the current research which, in addition to the directions discussed in the previous sections, focuses on new aspects of E/I balance, as described in more detail below.

这些和其他最近的发展在很大程度上依赖于当前的研究，除了前面讨论的方向之外，这些当前研究还关注E/I平衡的新方面，如下面更详细地描述。

===E/I balance across brain states E/I 在大脑状态之间保持平衡===

To date, only few works investigated how brain state modulation affects E/I balance.

迄今为止，只有少数工作研究了大脑状态的调节如何影响E/I平衡。

A study of primary visual cortex found that in awake mice, when compared to animals under anesthesia, the spatial tuning of inhibitory synaptic inputs is much wider, suggesting that in awake animals the E/I balance is profoundly skewed towards inhibition (Haider et al., 2013).

对初级视觉皮层的研究发现，在与麻醉下的动物相比的清醒的小鼠中，抑制性突触输入的空间调谐要宽得多，这表明在清醒的动物中，E/I平衡显著偏向于抑制（Haider等，2013）。

However in the auditory cortex of awake mice excitation and inhibition have similar magnitude and frequency tuning (Zhou et al., 2014), in agreement with previous results in anesthetized animals.

然而，在清醒小鼠的听觉皮层中，兴奋和抑制具有相似的幅度和频率调谐（Zhou等，2014），这与之前在麻醉动物中的结果一致。

Finally, a study of ongoing activity in the barrel cortex of anesthetized rats found that a switch to lighter anesthesia induces a profound shift toward excitation, probably due to depression of inhibitory synapses in the regime of higher activity under light anesthesia (Taub et al., 2013).

最后，对麻醉大鼠桶状皮层中正在进行的活动的研究发现，向较轻麻醉的转变会引起向兴奋的深度转移，这可能是由于在轻度麻醉下较高活性状态下抑制性突触的抑制（Taub等，2013）。

At the present time it is not clear whether the differences between these studies are due to differences between brain areas, special connectivity subserving sensory tuning or other factors.

目前尚不清楚这些研究之间的差异是源于大脑区域之间的差异、促进感觉调谐的特殊连接还是其他因素。

//

In addition to differences between awake and anesthetized conditions, the effects of transition between quiet wakefulness and locomotion were recently studied.

除了清醒和麻醉条件之间的差异外，最近还研究了安静清醒和运动之间转变的影响。

Locomotion was found to have a differential effect on primary visual and auditory cortices, increasing the firing and shifting the balance towards excitation in the former (Bennett et al., 2013), while suppressing firing and equally scaling down both excitation and inhibition in the latter (Zhou et al., 2014).

最近研究发现运动对初级视觉和听觉皮层具有不同的作用，对前者提高发放并将平衡转移至兴奋（Bennett等人，2013），对后者抑制发放并同规模地减少兴奋和抑制（Zhou等人，2014）。

Hence, the impact of locomotion on brain-state and in particular on E/I balance is not uniform across the sensory cortices.

因此，运动对大脑状态的影响，特别是对E / I平衡的影响在整个感觉皮层中并不均匀。

===Interneuron classes and the E/I balance 中间神经元等级和 E/I 平衡===

In spite of constituting a minority, inhibitory interneurons in the cortex are vastly more diverse than the excitatory cells, with large variety of dendritic and axonal arborization patterns (Ramon Y Cajal, 1911; Jones 1975).

皮质中的抑制性中间神经元尽管占据少数，但比兴奋性细胞更加多样化，因为具有多种树突和轴突树枝状模式（Ramon Y Cajal，1911；Jones 1975）。

Histochemical and other methods revealed that GABAergic neurons in the cortex are subdivided into at least 4 almost non-overlapping classes (Kawaguchi and Kubota 1997; Harris and Mrsic-Flogel 2013):

组织化学和其他方法显示：皮质中的GABA能神经元至少可以细分为4个几乎不重叠的类别（Kawaguchi和Kubota 1997；Harris和Mrsic-Flogel 2013）：

Parvalbumin (PV) expressing cells, somatostatin (Sst) expressing cells, vasoactive intestinal peptide (VIP) expressing cells and neurogliaform cells (NGs).

'''小清蛋白Parvalbumin'''（PV）表达细胞，'''生长激素抑制素somatostatin'''（Sst）表达细胞，'''血管活性肠肽vasoactive intestinal peptide'''（VIP）表达细胞和'''神经胶质neurogliaform'''细胞（NGs）。

Anatomical evidence and recordings in brain-slices suggest that these classes have different roles in the E/I balance and may have different functional roles across cortical layers.

脑切片中的解剖学证据和记录表明，这些类别GABA能神经元在E/I平衡中起着不同的作用，并且在皮质层中可能具有不同的功能作用。

Current studies use molecular genetics and imaging methods to understand the role and function of each subtype.

目前的研究使用分子遗传学和成像方法来了解每种亚型的作用和功能。

//

Several converging lines of evidence indicate that PV cells constitute the major source of inhibitory current in principal cells for both spontaneous activity and sensory evoked responses.

一些趋同的证据表明，PV细胞贡献主细胞中抑制电流的主要来源，用于自发活动和感觉诱发反应。

It follows that the sensory tuning of inhibitory synaptic inputs of pyramidal cells is expected to be the same or wider than the sensory tuning of the individual PV cells.

因此，锥体细胞的抑制性突触输入的感觉调谐，预计与单个PV细胞的感觉调谐相同或更宽。

For example, for orientation tuning in the mouse visual cortex, the tuning curves of PV cells were found to be much wider than of the principal cells, explaining the wide tuning of inhibitory inputs of pyramidal neurons (Atallah et al., 2012).

例如，对于小鼠视觉皮层的方向调谐，发现PV细胞的调谐曲线比主细胞的调谐曲线宽得多，这解释了锥体神经元抑制性输入的宽广调谐（Atallah等人，2012）。

In the auditory cortex the PV cells were found to be tuned for frequency, again consistent with inhibitory inputs to pyramidal cells originating in the neighboring PV neurons (Moore and Wehr 2013; Li et al., 2014).

在听觉皮层中，发现PV细胞被频率调谐，再次与起源于邻近PV神经元对锥体细胞的抑制性输入一致（Moore和Wehr 2013;李等人，2014）。

//

The role of the other classes of inhibitory interneurons is currently investigated in many labs, in particular using the powerful new optogenetic tools.

目前，许多实验室在研究其他类型的抑制性中间神经元的作用，特别是使用强大而新的光遗传学工具。

Optogenetic stimulation was recently used to examine the effect of PV and Sst cells on orientation tuning (Atallah et al. 2012; Lee et al., 2012; Wilson et al., 2012).

光遗传学刺激最近用于研究PV和Sst细胞对方向调谐的影响（Atalah等人2012；Lee等人2012；Wilson等人2012）。

(Atallah et al. 2012) and (Wilson et al., 2012) suggest that PV cells do not alter the tuning of principal cells.

（Atalah et al.2012）和（Wilson et al.2012）表明PV细胞不会改变主细胞的调谐。

(Wilson et al., 2012) furthermore attribute to Sst cells the ability to sharpen orientation selectivity of principal cells by a subtraction effect.

In contrast, (Lee et al., 2012) report that activation of PV cells was found to sharpen the orientation tuning of principal cells.

（Wilson et al.，2012）进一步研究出Sst细胞通过减法效应增强了主细胞的方向选择性的能力。

相比之下，（Lee等人，2012年）报告发现，PV细胞的激活可以增强主细胞的方向调节。

Whether the contradiction between the studies is real or only at the level of data interpretation is not entirely clear (Lee et al., 2014; Atallah et al., 2014).

矛盾，是真实存在于在研究之间，还是说存在于数据解释层面上，尚不完全清楚（Lee等人，2014年；Atalah等人，2014年）。

==Conclusions 结论==

The available data, collected under a wide variety of conditions and in distinct cortical areas indicates that co-activation of inhibition and excitation is a basic functional principle underlying various cortical activities (Isaacson and Scanziani, 2011).

在各种条件下和不同皮质区域收集的现有数据表明，抑制和兴奋的共激活是各种皮质活动的基本功能原理（Isaacson和Scanziani，2011）。

Furthermore, the excitatory and inhibitory synaptic inputs appear to be individually matched in each pyramidal cell (Xue et al., 2014) with a high temporal precision of just a few milliseconds.

此外，兴奋性和抑制性突触输入似乎在每个锥体细胞中单独匹配（Xue等人，2014），具有仅几毫秒的高时间精度。

Yet, whether excitation and inhibition share the same sensory tuning seems to depend on various factors, including animal species, the sensory modality and brain-state.

然而，兴奋和抑制是否具有相同的感官调谐似乎取决于各种因素，包括动物种类，感觉方式和大脑状态。

//

The E/I balance was studied most extensively in the cortex, however similar principles manifest themselves in many CNS structures, such as the hippocampus (Atallah and Scanziani, 2009), superior colliculus (Populin, 2005), brain stem (Magnusson et al., 2008), spinal cord (Berg et al., 2007), prefrontal cortex (Yizhar et al., 2011) and others, not covered here in detail.

E / I平衡在皮层中得到了最广泛的研究，但是类似的原理在许多CNS结构中表现出来，例如海马体（Atallah和Scanziani，2009），上丘脑（Populin，2005），脑干（Magnusson等人，2008），脊髓（Berg等人，2007），前额叶皮层（Yizhar等人，2011）等，这里没有详细介绍。

This entry also did not describe E/I balance development and plasticity, e.g., (Froemke et al., 2007; Dorrn et al., 2010; Sun et al., 2010; Li et al. 2012).

该条目也没有描述E / I平衡发育和可塑性，例如，（Froemke等人，2007;Dorrn et al.， 2010;孙等， 2010;李等人， 2012）.

While the role of the tight coupling between excitation and inhibition is not fully clear, it is most likely to serve as a major gain mechanism that increases the accuracy and speed of neuronal response.

虽然兴奋和抑制之间紧密耦合的作用尚不完全清楚，但它最有可能作为提高神经元响应的准确性和速度的主要增益机制。

By counterbalancing the excitatory drive, inhibitory inputs greatly extend the dynamic range of excitation, allowing a fine and rapid control over the amount of depolarization of the membrane potential.

通过平衡兴奋驱动作用，抑制性输入大大扩展了兴奋的动态范围，允许精细快速地控制膜电位的去极化量。

It is apparent that achieving a certain depolarization without a counteracting inhibitory force would have required a much weaker excitatory input, increasing the error and variability of the response.

很明显，若没有用于平衡的抑制作用，则实现一定的去极化将需要更弱的兴奋性输入，从而增加响应的误差和可变性。

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== 另见 ==
[[抑制]], [[高电导状态]]

[[Category:计算神经科学]]
[[Category:神经科学]]
[[Category:突触]]
[[Category:神经元模型]]

安贞桦：

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

此词条由神经动力学读书会-词条梳理志愿者-安贞桦翻译审校，未经专家审核，带来阅读不便，请见谅。

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.

‎基于电导的模型conductance-based model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 ==
Conductance-based models are based on an equivalent circuit representation of a cell membrane as first put forth by Hodgkin and Huxley (1952).

‎基于电导的模型建立在[[‎‎Hodgkin和Huxley]]‎‎（1952）首次提出的细胞膜的一个等效电路表示的基础之上。

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，<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.

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<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>\，\）。

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，‎

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

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

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，‎

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

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。

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.

每项离子电流都与电导（电阻的倒数）和驱动力（电池）相关，这是细胞内与细胞外的介质中离子的不同浓度所导致的。

Thus,

因此

<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.

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, \( <math>g</math> \) (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。

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。

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。‎

== 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>

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

其中

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

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

<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.

\（ <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。

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\（ <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.

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.

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:

# the different ion channels in the cell membrane are independent from each other,
# activation and inactivation gating variables are voltage-dependent and independent of each other for a given ion channel type,
# each gating variable follows first-order kinetics, and
# the model cell compartment is isopotential.

总之，基于电导的模型中的基本假设为：

# 细胞膜中的不同离子通道相互独立
# 对于给定的离子通道类型，激活和失活门控变量依赖于电压且相互独立
# 每个门控变量都遵循一阶动力学
# 并且模型细胞房室是等电势的。

== 示例和变体 ==

* Hodgkin-Huxley model (1952): Original conductance-based model based on the giant axon of the squid producing action potentials. There is a sodium current with activation and inactivation variables, a potassium current with only an activation variable, and a (passive) leak current.
* [[霍奇金-赫胥黎模型]]（1952年）：原始的基于电导的模型，建立在产生[[动作电位]]的乌贼巨大轴突的基础上。模型中有具有激活和失活变量的钠电流，仅具有激活变量的钾电流，以及（被动）漏电流。
* Connor-Stevens model (1971): Extended action potential generating model using gastropod neuron somas. There is a sodium, potassium and leak current as in the Hodgkin-Huxley model, and in addition, another potassium current that is transient, the so-called A-current, is included. This current has an activation and an inactivation variable.
* Connor-Stevens模型（1971）：使用[[腹足纲神经元体]]建立的扩展动作电位生成模型。与[[霍奇金-赫胥黎模型]]一样，有钠离子项、钾离子项和漏电流项，此外，还包括另一个瞬态钾电流，即所谓的[[A电流]]。此电流项具有激活和失活变量。
* Morris-Lecar model (1981): Based on the barnacle muscle fiber. There is a calcium current with an instantaneous activation, a potassium current with an activation variable, and a (passive) leak current.

* [[Morris-Lecar模型]]（1981年）：基于[[藤壶肌纤维]]建立模型。模型中有具有瞬时激活的钙电流、具有激活变量的钾电流和（被动）漏电流。

Conductance-based models are the most common formulation used in neuronal models and can incorporate as many different ion channel types as are known for the particular cell being modeled.

A common extension found in many conductance-based models is the inclusion of an equation for calcium dynamics.

Ionic currents can be calcium-dependent in addition to voltage-dependent with calcium concentrations being controlled by calcium currents, pumps and exchangers.

For example, see section 6.2 in Dayan and Abbott (2001).

基于电导的模型是神经元模型中最常用的公式，它可以包含在要建模的特定细胞中已知的那么多的不同离子通道类型。

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。

离子电流除了对钙离子依赖，还依赖于电压，由钙离子电流、离子泵和（交换器？？？）控制的钙离子浓度。（？？？）

例如，参见Dayan and Abbott （2001）中的第6.2节。

Furthermore, as details of various ion channels are determined, variants of conductance-based models have been developed to better match the experimental data.

For example, the standard conductance-based formalism derived from Hodgkin-Huxley models has been extended to account for state-dependent inactivation without voltage dependence in fast sodium and Kv3 potassium channels (Marom and Abbott 1994).

此外，随着各种离子通道的细节确定，已经建立了基于电导的模型的变体，以更好地适应实验数据。

例如，从[[霍奇金-赫胥黎模型]]派生的标准基于电导的形式体系，已经扩展到解释快速钠通道和[[Kv3]]钾通道中没有电压依赖性的状态依赖性失活（Marom和Abbott 1994）。

The simplest conductance-based model formulation from a spatial perspective consists of a single, isopotential compartment.

Ion movement is strictly between the inside and outside of the cell.

However, to incorporate spatial complexity of cells, several compartments can be connected to represent the cell's complex morphology (see compartmental model).

A conductance-based model formulation can then be used for each compartment with additional terms added to the equations to represent the connections.

That is, current flow occurs not only between the inside and outside of the cell, but also between different regions of the cell.

从空间角度来看，最简单的基于电导的模型公式由单个等电势房室表示。

离子运动严格地在细胞内和细胞外之间进行。

然而，为了结合细胞的空间[[复杂性]]，可以连接几个房室来表示细胞的复杂形态（参见[[区室模型]]）。

然后，基于电导的模型公式可以用在每个房室，并在方程中添加其他项以表示连接。

也就是说，电流的流动不仅发生在细胞的内部和外部之间，也发生在细胞的不同区域之间。

== 其他问题 ==
Conductance-based models for excitable cells are developed to help understand underlying mechanisms that contribute to action potential generation, repetitive firing and bursting (i.e., oscillatory patterns) and so on.

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。

反过来，这些内在特征会影响神经元网络中的行为。

However, as the number of currents included in conductance-based models expands, it becomes more difficult to understand and predict the resulting model dynamics due to the increasing number of differential equations.

For example, the original Hodgkin-Huxley model is a 4th order system of ODEs.

Efforts have been made not only to capture the qualitative dynamics of conductance-based models (e.g., FitzHugh-Nagumo model) but also to reduce the complexity of the system (e.g., Kepler et al. 1992).

然而，随着基于电导的模型中包含的电流项数量的增加，由于微分方程数量的增加，对由此产生的模型的动力学行为的理解和预测变得更加困难。

例如，最初的[[霍奇金-赫胥黎模型]]是一个 4 阶[[ODE]]系统。

人们不仅努力建立基于电导的模型的定性动力学（例如，[[FitzHugh-Nagumo模型]]），而且还降低了系统的复杂性（例如，Kepler等人，1992年）。

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。

== 参考文献 ==

* Connor JA and Stevens CF. "Prediction of repetitive firing behaviour from voltage clamp data on an isolated neurone soma." J Physiol. 1971 Feb;213(1):31-53.
* Dayan P and Abbott LF. "Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems." The MIT Press, 2001.
* Hille B. "Ion Channels of Excitable Membranes". 3rd ed. Sinauer Associates Inc. Sunderland, MA, 2001.
* Hodgkin AL and Huxley AF. "A quantitative description of membrane current and its application to conduction and excitation in nerve." J Physiol. 1952 Aug;117(4):500-44.
* Izhikevich EM. "Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting." The MIT Press, 2007.
* Kepler TB, Abbott LF, Marder E. "Reduction of conductance-based neuron models." Biol Cybern. 1992, 66:381-387.
* Koch C. "Biophysics of Computation: Information processing in single neurons." Oxford University Press, New York, 1999.
* Marom S and Abbott LF. "Modeling state-dependent inactivation of membrane currents." Biophys J. 1994 Aug;67(2):515-20.
* Morris C and Lecar H. "Voltage oscillations in the barnacle giant muscle fiber." Biophys J. 1981 Jul;35(1):193-213.
* Willms AR. "NEUROFIT: software for fitting Hodgkin-Huxley models to voltage-clamp data." J Neurosci Meth. 2002, 121:139-150.

'''Internal references'''

* Eugene M. Izhikevich (2006) Bursting. Scholarpedia, 1(3):1300.
* Eugene M. Izhikevich and Richard FitzHugh (2006) FitzHugh-Nagumo model. Scholarpedia, 1(9):1349.

== 外部链接 ==

* Frances K. Skinner's website

== 参见 ==

Hodgkin-Huxley Model, Morris-Lecar Model, Hindmarsh-Rose Model, Dynamical Systems, Bifurcations, Excitability, NEURON, GENESIS, Neural Oscillators
{| class="wikitable"
|Sponsored by: Eugene M. Izhikevich, Editor-in-Chief of Scholarpedia, the peer-reviewed open-access encyclopedia
|-
|Reviewed by: Prof. Leonid L. Rubchinsky, Indiana University Purdue University, Indianapolis, IN, and Indiana University School of Medicine, Indianapolis, IN, USA
|-
|Reviewed by: Astrid A. Prinz, Emory University, Atlanta, Georgia
|-
|Accepted on: 2006-11-22 15:04:01 GMT
|}
Categories:

* Computational Neuroscience
* Neuroscience
* Dynamical Systems
* Models of Neurons

== 编者推荐 ==
《神经科学的数学原理》