Ch12 Physiology of Neurons
(→树突中的信号传导) |
(→树突减弱突触电位) |
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=== 树突减弱突触电位 === | === 树突减弱突触电位 === | ||
<b style=color:#0ae>Dendrites attenuate synaptic potentials</b> | <b style=color:#0ae>Dendrites attenuate synaptic potentials</b> | ||
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| + | Dendrites tend to be long and thin. Their cytoplasm has relatively low electrical resistivity, and their membrane has relatively high resistivity. These are the properties of a leaky electrical cable, which is the premise for cable theory (see p. 201). Leaky cables are like leaky garden hoses; if ionic current (or water) enters at one end, the fraction of it that exits at the other end depends on the number of channels (or holes) in the cable (hose). A good hose has no holes and all the water makes it through, but most dendrites have a considerable number of channels that serve as leaks for ionic current (see Fig. 7-22). | ||
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| + | 树突往往又长又细。它们的细胞质具有相对较低的电阻率,并且它们的膜具有相对较高的电阻率。这些是漏电电缆的特性,这是电缆理论的前提(见第 201 页)。漏水的电缆就像漏水的花园软管;如果离子电流(或水)从一端进入,则从另一端流出的离子电流的比例取决于电缆(软管)中的通道(或孔)的数量。一根好的软管没有孔,所有的水都可以通过,但大多数树枝晶都有相当数量的通道,作为离子电流的泄漏(见图 7-22)。 | ||
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| + | Cable theory predicts how much current flows down the length of the dendrite through the cytoplasm and how much of it leaks out of the dendrite across the membrane. As summarized in Table 7-3, we can express the leakiness of the membrane by the resistance per unit area of dendritic membrane (specific membrane resistance, Rm), which can vary widely among neurons. The intracellular resistance per cross-sectional area of dendrite (specific resistivity of the cytoplasm, Ri) is also important in determining current flow inasmuch as a very resistive cytoplasm forces more current to flow out across the membrane rather than down the axis of the dendrite. Another important factor is cable diameter; thick dendrites let more current flow toward the soma than thin dendrites do. Figure 7-22C illustrates the consequences of a point source of steady current flowing into a leaky, uniform, infinitely long cable made of purely passive membrane. The transmembrane voltage generated by the current falls off exponentially with distance from the site of current injection. The steepness with which the voltage falls off is defined by the length constant (λ; see p. 201), which is the distance over which a steady voltage decays by a factor of 1/e (~37%). Estimates of the parameter values vary widely, but for brain neurons at rest, reasonable numbers are ~50,000 Ω ⋅ cm2 for Rm and 200 Ω ⋅ cm for Ri. If the radius of the dendrite (a) is 1 μm (10−4 cm), we can estimate the length constant of a dendrite by applying Equation 7-8. | ||
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| + | 电缆理论预测有多少电流沿着树突的长度流过细胞质,以及有多少电流穿过膜从树突中泄漏出来。如表 7-3 所示,我们可以通过树突状膜的每单位面积阻力(比膜阻力,Rm)来表示膜的泄漏,这在神经元之间可能有很大差异。树突每个横截面积的细胞内电阻(细胞质的比电阻率 Ri)在确定电流流动方面也很重要,因为非常电阻的细胞质会迫使更多的电流流过膜而不是沿着树突的轴流出。另一个重要因素是电缆直径;厚树突比薄树突让更多的电流流向 SOMA 。图 7-22C 说明了稳定电流的点源流入由纯无源膜制成的泄漏、均匀、无限长电缆的后果。电流产生的跨膜电压随着距电流注入部位的距离呈指数下降。电压下降的陡峭度由长度常数(λ;见第 201 页)定义,这是稳态电压衰减 1/e 倍 (~37%) 的距离。参数值的估计值差异很大,但对于静止的脑神经元,合理的数字是 Rm 的 ~50,000 Ω ⋅ cm 2 和 Ri 的 200 Ω ⋅ cm。如果枝晶 (a) 的半径为 1 μm (10-4 cm),我们可以通过应用公式 7-8 来估计枝晶的长度常数。 | ||
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| + | Because dendrite diameters vary greatly, λ should also vary greatly. For example, assuming the same cellular properties, a thin dendrite with a radius of 0.1 μm would have a λ of only 354 μm, whereas a thick one with a radius of 5 μm would have a λ of 2500 μm. Thus, the graded signal voltage spreads farther in a thick dendrite. | ||
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| + | 由于枝晶直径变化很大,因此 λ 也应该变化很大。例如,假设具有相同的蜂窝特性,半径为 0.1 μm 的薄枝晶的 λ 仅为 354 μm,而半径为 5 μm 的厚枝晶的 λ 为 2500 μm。因此,渐变信号电压在厚树晶中扩散得更远。 | ||
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| + | Real dendrites are certainly not infinitely long, uniform, and unbranched, nor do they have purely passive membranes. Thus, quantitative analysis of realistic dendrites is complex. The termination of a dendrite decreases attenuation because current cannot escape farther down the cable. Branching increases attenuation because current has more paths to follow. Most dendrites are tapered. Gradually expanding to an increased diameter progressively increases λ and thus progressively decreases attenuation. Real membranes are never completely passive because all have voltagegated channels, and therefore their Rm values can change as a function of voltage and time. Finally, in the working brain, cable properties are not constant but may vary dynamically with ongoing brain activity. For example, as the general level of synaptic input to a neuron rises (which might happen when a brain region is actively engaged in a task), more membrane channels will open and thus Rm will drop as a function of time, with consequent shortening of dendritic length constants. However, all these caveats do not alter the fundamental qualitative conclusion: voltage signals are attenuated as they travel down a dendrite. | ||
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| + | 真正的树突肯定不是无限长、均匀和无支链的,它们也没有纯粹的钝膜。因此,对真实树突的定量分析很复杂。枝晶的端接减少了衰减,因为电流无法从电缆中逃逸到更远的地方。分支会增加衰减,因为电流有更多的路径可以遵循。大多数树突是锥形的。逐渐膨胀到增加的直径会逐渐增加 λ,从而逐渐降低衰减。真正的膜从来都不是完全无源的,因为所有膜都有电压门控通道,因此它们的 Rm 值会随着电压和时间的变化而变化。最后,在工作的大脑中,电缆特性不是恒定的,但可能会随着持续的大脑活动而动态变化。例如,随着神经元的突触输入的一般水平升高(当大脑区域积极参与一项任务时可能发生),更多的膜通道将打开,因此 Rm 将随时间而下降,从而导致树突长度常数缩短。然而,所有这些警告都不会改变基本的定性结论:电压信号在沿着树突传播时会衰减。 | ||
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| + | So far, we have described only how a dendrite might attenuate a sustained voltage change. Indeed, the usual definition of length constant applies only to a steady-state voltage shift. An important complication is that the signal attenuation along a cable depends on the frequency components of that signal—how rapidly voltage changes over time. When Vm varies over time, some current is lost to membrane capacitance (see p. 158), and less current is carried along the dendrite downstream from the source of the current. Because action potentials and EPSPs entail rapid changes in Vm, with the fastest of them rising and falling within a few milliseconds, they are attenuated much more strongly than the steady-state λ implies. If Vm varies in time, we can define a λ that depends on signal frequency (λAC, where AC stands for “alternating current”). When signal frequency is zero (i.e., Vm is steady), λ = λAC. However, as frequency increases, λAC may fall sharply. Thus, dendrites attenuate high-frequency (i.e., rapidly changing) signals more than low-frequency or steady signals. Another way to express this concept is that most dendrites tend to be low-pass filters in that they let slowly changing signals pass more easily than rapidly changing ones. | ||
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| + | 到目前为止,我们只描述了枝晶如何衰减持续的电压变化。事实上,长度常数的通常定义仅适用于稳态电压偏移。一个重要的复杂之处在于,沿电缆的信号衰减取决于该信号的频率分量,即电压随时间变化的速度。当 Vm 随时间变化时,一些电流会损失到膜电容上(参见第 158 页),并且沿电流源下游的枝晶携带的电流较少。因为动作电位和 EPSP 会导致 Vm 的快速变化,其中最快的在几毫秒内上升和下降,因此它们的衰减比稳态 λ 所暗示的要强得多。如果 Vm 随时间变化,我们可以定义一个取决于信号频率的 λ(λAC,其中 AC 代表“交流电”)。当信号频率为零时(即 Vm 稳定),λ = λAC。然而,随着频率的增加,λAC 可能会急剧下降。因此,树突比低频或稳定信号更能衰减高频(即快速变化)信号。另一种表达这个概念的方式是,大多数树枝状往往是低通滤波器,因为它们让缓慢变化的信号比快速变化的信号更容易通过。 | ||
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| + | Figure 12-2A shows how an EPSP propagates along two different dendrites with very different length constants. If we assume the synapses trigger EPSPs of similar size in the end of each dendrite, then the dendrites with the longer λ deliver a larger signal to the axon hillock. How do leaky dendrites manage to communicate a useful synaptic signal to the soma? The problem is solved in two ways. The first solution deals with the passive properties of the dendrite membrane. The length (l) of dendrites tends to be relatively small in comparison to their λ; thus, none extends more than one or two steady-state length constants (i.e., the l/λ ratio is <1). One way that dendrites achieve a small l/λ ratio is to have a combination of diameter and Rm that gives them a large λ. Another way is that dendrites are not infinitely long cables but “terminated” cables. Figure 12-2B shows that a signal is attenuated more in an infinitely long cable (curve a) than in a terminated cable whose length (l) is equal to λ (curve b). The attenuation of a purely passive cable would be even less if the terminated cable had a λ 10-fold greater than l (curve c). Recall that in our example in Figure 12-2A, such a 10-fold difference in λ underlies the difference in the amplitudes of the EPSPs arriving at the axon hillock. | ||
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| + | 图 12-2A 显示了 EPSP 如何沿着两个长度常数非常不同的不同树突传播。如果我们假设突触在每个树突的末端触发相似大小的 EPSP,那么具有较长 λ 的树突向轴突小丘传递更大的信号。泄漏的树突如何设法将有用的突触信号传达给 soma?这个问题可以通过两种方式来解决。第一种解决方案涉及枝晶膜的被动特性。与它们的 λ 相比,枝晶的长度 (l) 往往相对较小;因此,没有一个扩展超过一个或两个稳态长度常数(即 L/λ 比为 <1)。枝晶实现小 l/λ 比的一种方法是将直径和 Rm 组合在一起,从而获得较大的 λ。另一种方法是树突不是无限长的电缆,而是“端接”的电缆。图 12-2B 显示,无限长电缆(曲线 a)中的信号衰减大于长度 (l) 等于 λ 的端接电缆(曲线 b)中的信号衰减。如果端接电缆的 λ 大于 l 10 倍(曲线 c),则纯无源电缆的衰减会更小。回想一下,在图 12-2A 的示例中,λ 的 10 倍差异是到达轴突小丘的 EPSP 振幅差异的基础。 | ||
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| + | The second solution to the attenuation problem is to endow dendrites with voltage-gated ion channels (see pp. 182–199) that enhance the signal more than would be expected in a purely “passive” system (curve d). We discuss the properties of such “active” cables in the next section. | ||
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| + | 衰减问题的第二种解决方案是赋予树突电压门控离子通道(参见第 182-199 页),这比纯“无源”系统(曲线 d)中预期的信号增强更多。我们将在下一节讨论这种 “有源” 电缆的特性。 | ||
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2024年12月25日 (三) 17:22的版本
神经元生理学
本页英文内容取自:经典教材医学生理学(第三版) (Medical Physiology, 3rd Edtion, Walter F Boron, published in 2016)
中文内容由 BH1RBH (Jack Tan) 粗糙翻译
蓝色 【注】 后内容为 BH1RBH (Jack Tan) 所加之注释
目录 |
1 Overview
1.1 神经元接收、组合、转换、存储和发送信息
Neurons receive, combine, transform, store, and send information
Neurons have arguably the most complex job of any cell in the body. Consequently, they have an elaborate morphology and physiology. Each neuron is an intricate computing device. A single neuron may receive chemical input from tens of thousands of other neurons. It then combines these myriad signals into a much simpler set of electrical changes across its cellular membrane. The neuron subsequently transforms these ionic transmembrane changes according to rules determined by its particular shape and electrical properties and transmits a single new message through its axon, which itself may contact and inform hundreds of other neurons. Under the right circumstances, neurons also possess the property of memory; some of the information coursing through a neuron’s synapses may be stored for periods as long as years.
神经元可以说是体内任何细胞中最复杂的工作。因此,它们具有复杂的形态和生理学。每个神经元都是一个复杂的计算设备。单个神经元可以接收来自数以万计的其他神经元的化学输入。然后,它将这些无数信号组合成一组更简单的细胞膜电变化。神经元随后根据其特定形状和电特性决定的规则转换这些离子跨膜变化,并通过其轴突传递一条新信息,轴突本身可以接触并通知数百个其他神经元。在适当的情况下,神经元也具有记忆的特性;通过神经元突触传输的一些信息可以存储长达数年。
This general scheme of neuronal function applies to most neurons in the vertebrate nervous system. However, the scheme is endlessly variable. For example, each region of the brain has several major classes of neurons, and each of these classes has a physiology adapted to perform specific and unique functions. In this chapter, the general principles of neuronal function are outlined, and the almost unlimited variability contained within the general schema is discussed.
这种神经元功能的一般方案适用于脊椎动物神经系统中的大多数神经元。然而,这个方案是无穷无尽的。例如,大脑的每个区域都有几大类神经元,每类神经元都有适应于执行特定和独特功能的生理学。在本章中,概述了神经元功能的一般原理,并讨论了一般图式中包含的几乎无限的可变性。
1.2 神经信息从树突流向胞体,从轴突流向突触
Neural information flows from dendrite to soma to axon to synapse
Numerous dendrites converge on a central soma, or cell body, from which a single axon emerges and branches multiple times (see Fig. 10-1). Each branch culminates at a presynaptic terminal that contacts another cell. In most neurons, dendrites are the principal synaptic input sites, although synapses may also be found on the soma, on the axon hillock (the region of the soma neighboring the axon), or even directly on the axons. In some primary sensory neurons, the dendrites themselves are transducers of environmental energy. Regardless of their source, signals—in the form of voltage changes across the membrane—typically flow from dendrites to soma to axon and finally to synapses on the next set of cells. Under some circumstances electrical signals may also propagate in the opposite direction, from the soma outward along dendrites to their tips.
许多树突聚集在一个中央体细胞或细胞体上,单个轴突从中出现并多次分枝(见图 10-1)。每个分支在与另一个细胞接触的突触前末端结束。在大多数神经元中,树突是主要的突触输入位点,尽管突触也可能出现在体细胞、轴突小丘(与轴突相邻的胞体区域)甚至直接在轴突上。在一些初级感觉神经元中,树突本身是环境能量的传感器。无论它们的来源如何,信号(以跨膜电压变化的形式)通常从树突流向胞体,再流向轴突,最后流向下一组细胞上的突触。在某些情况下,电信号也可能沿相反方向传播,从胞体沿着树突向外传播到它们的尖端。
Excitatory input to a neuron usually generates an inward flow of positive charge (i.e., an inward current) across the dendritic membrane. Because the interior of a resting neuron is polarized negatively with respect to the external environment, this inward current, which makes the membrane voltage more positive (i.e., less negative), is said to depolarize the cell. Conversely, inhibitory input to a neuron usually generates an outward current and, thus, hyperpolarization.
神经元的兴奋性输入通常产生穿过树突状膜的向内正电荷流(即向内电流)。因为静息神经元的内部相对于外部环境呈负极化,所以这种使膜电压更正(即负更小)的向内电流被称为细胞去极化。相反,对神经元的抑制性输入通常会产生向外的电流,从而产生超极化。
If the neuron receives its input from a neighboring cell through a chemical synapse, neurotransmitters trigger currents by activating ion channels. If the cell is a sensory neuron, environmental stimuli (e.g., chemicals, light, mechanical deformation) activate ion channels and produce a flow of current. The change in membrane potential (Vm) caused by the flow of charge is called a postsynaptic potential (PSP) if it is generated at the postsynaptic membrane by a neurotransmitter and a receptor potential if it is generated at a sensory nerve ending by an external stimulus. In the case of synaptic transmission, the postsynaptic Vm changes may be either positive or negative. If the neurotransmitter is excitatory
如果神经元通过化学突触接收来自邻近细胞的输入,神经递质就会通过激活离子通道来触发电流。如果细胞是感觉神经元,环境刺激(例如化学物质、光、机械变形)会激活离子通道并产生电流。由电荷流动引起的膜电位 (Vm) 变化如果由神经递质在突触后膜产生,则称为突触后电位 (PSP),如果它是在感觉神经末梢由外部刺激产生的,则称为受体电位。在突触传递的情况下,突触后 Vm 变化可能是阳性或阴性的。如果神经递质是兴奋性的
and produces a depolarizing PSP, we refer to the PSP as an excitatory postsynaptic potential (EPSP; see p. 210). On the other hand, if the neurotransmitter is inhibitory and produces a hyperpolarizing PSP, the PSP is an inhibitory postsynaptic potential (IPSP). In all cases, the stimulus produces a Vm change that may be graded from small to large depending on the strength or quantity of input stimuli (see p. 174). Stronger sensory stimuli generate larger receptor potentials; similarly, more synapses activated together generate larger PSPs. A graded response is one form of neural coding whereby the size and duration of the input are encoded as the size and duration of the change in the dendritic Vm.
并产生去极化 PSP,我们将 PSP 称为兴奋性突触后电位 (EPSP;见第 210 页)。另一方面,如果神经递质具有抑制性并产生超极化 PSP,则 PSP 是抑制性突触后电位 (IPSP)。在所有情况下,刺激都会产生 Vm 变化,根据输入刺激的强度或数量,该变化可以从小到大分级(见第 174 页)。更强的感觉刺激产生更大的受体电位;同样,更多的突触一起激活会产生更大的 PSP。分级反应是神经编码的一种形式,其中输入的大小和持续时间被编码为树突状 Vm 变化的大小和持续时间。
The synaptic (or receptor) potentials generated at the ends of a dendrite are communicated to the soma, usually with substantial attenuation of the signal (Fig. 12-1A). Extended cellular processes such as dendrites behave like leaky electrical cables (see pp. 201–203). As a consequence, dendritic potentials usually decline in amplitude before reaching the soma. As an EPSP reaches the soma, it may also combine with EPSPs arriving via other dendrites on the cell; this behavior is a type of spatial summation and can lead to EPSPs that are substantially larger than those generated by any single synapse (see Fig. 12-1B, C). Temporal summation occurs when EPSPs arrive rapidly in succession; when the first EPSP has not yet dissipated, a subsequent EPSP tends to add its amplitude to the residual of the preceding EPSP (see Fig. 12-1D).
树突末端产生的突触(或受体)电位被传达给胞体,通常信号会大幅衰减(图 12-1A)。延伸的细胞过程,如树突,表现得像泄漏的电缆(见第 201-203 页)。因此,树突状电位通常在到达胞体之前振幅下降。当 EPSP 到达胞体时,它也可能与通过细胞上其他树突到达的 EPSP 结合;这种行为是一种空间求和,可导致 EPSP 比任何单个突触产生的 EPSP 大得多(参见图 12-1B、C)。当 EPSP 连续快速到达时,就会发生时间求和;当第一个 EPSP 尚未消散时,随后的 EPSP 倾向于将其振幅添加到前一个 EPSP 的残差中(见图 12-1D)。
The tendency for synaptic and receptor potentials to diminish with distance along a dendrite puts significant limitations on their signaling abilities. If nothing else happened, these depolarizing potentials would simply dwindle back to the resting membrane potential as they spread through the soma and down into the axon. At best, this passive signal might be carried a few millimeters, clearly inadequate for commanding a toe to wiggle when the axon of the motor neuron stretching from the spinal cord to the muscles moving the foot might be 1000 mm long. Some amplification is therefore necessary for certain inputs to generate effective signals to and from the central nervous system (CNS). Amplification is provided in the form of regenerating action potentials. If the Vm change in the soma is large enough to reach the threshold voltage (see p. 173), the depolarization may trigger one or more action potentials between the soma and axon, as shown in Figure 12-1B to D. Action potentials are large, rapid fluctuations in Vm. As described in Chapter 7, an action potential is an efficient, rapid, and reliable way to carry a signal over long distances. However, notice that generation of action potentials entails another transformation of neuronal information: the neuron converts the graded-voltage code of the dendrites (i.e., the PSPs) to a temporal code of action potentials in the axon. The initiation site for action potentials in many types of neurons is the axon initial segment, the first stretch of unmyelinated axon past the soma.
突触电位和受体电位随树突距离的增加而减弱的趋势对它们的信号传导能力造成了重大限制。如果没有其他事情发生,这些去极化电位在通过胞体扩散并向下扩散到轴突时,只会减少回静息膜电位。充其量,这个被动信号可能被携带了几毫米,当从脊髓延伸到移动脚部的肌肉的运动神经元的轴突可能长达 1000 毫米时,显然不足以命令脚趾摆动。因此,某些输入需要一些放大才能产生进出中枢神经系统 (CNS) 的有效信号。放大以再生动作电位的形式提供。如果胞体中的 Vm 变化足够大以达到阈值电压(参见第 173 页),则去极化可能会触发胞体和轴突之间的一个或多个动作电位,如图 12-1B 至 D 所示。如第 7 章所述,动作电位是一种长距离传输信号的有效、快速和可靠的方式。然而,请注意,动作电位的产生需要神经元信息的另一种转换:神经元将树突的分级电压代码(即 PSP)转换为轴突中动作电位的时间代码。在许多类型的神经元中,动作电位的起始位点是轴突初始段,即通过体细胞的第一段无髓轴突。
Action potentials are fixed in amplitude, not graded, and have uniform shape. So how is information encoded by action potentials? This question has no simple answer and is still hotly debated. Because one axonal spike looks like another (with slight exceptions), neurons can vary only the number of spikes and their timing. For a single axon, information may be encoded by the average rate of action potential firing, the total number of action potentials, their temporal pattern, or some combination of these mechanisms. Figure 12-1 illustrates that as the synaptic potential in the soma increases in size, the resultant action potentials occur more frequently, and the burst of action potentials in the axon lasts longer. Notice also that by the time the signal has propagated well down the axon, the transformation has become complete—the graded potential has waned and vanished, whereas the action potentials have retained their size, number, and temporal pattern. The final output of the neuron is entirely encoded by these action potentials. When action potentials reach axonal terminals, they may trigger the release of a neurotransmitter at the next set of synapses, and the cycle begins again.
动作电位的振幅是固定的,没有分级,并且具有均匀的形状。那么动作电位是如何编码信息的呢?这个问题没有简单的答案,至今仍备受争议。因为一个轴突尖峰看起来与另一个轴突尖峰相似(除了轻微的例外),神经元只能改变尖峰的数量及其时间。对于单个轴突,信息可能由动作电位的平均放电速率、动作电位的总数、它们的时间模式或这些机制的某种组合进行编码。图 12-1 表明,随着胞体中突触电位的大小增加,产生的动作电位发生得更频繁,轴突中动作电位的爆发持续时间更长。还要注意,当信号沿着轴突传播时,转化已经完成——分级电位已经减弱和消失,而动作电位则保留了它们的大小、数量和时间模式。神经元的最终输出完全由这些动作电位编码。当动作电位到达轴突末梢时,它们可能会触发下一组突触处神经递质的释放,循环再次开始。
2 树突中的信号传导
SIGNAL CONDUCTION IN DENDRITES
The word dendrite is derived from the Greek word dendron [tree], and indeed some dendrites resemble tree branches or roots. Inspired by trees, no doubt, the anatomist Camillo Golgi suggested in 1886 that the function of dendrites is to collect nutrients for the neuron. The truth is analogous but more interesting: dendrites arborize through a volume of brain tissue so that they can collect information in the form of synaptic input. The dendrites of different types of neurons exhibit a great diversity of shapes. Dendrites are often extensive, accounting for up to 99% of a neuron’s membrane. The dendrites of a single neuron may receive as many as 200,000 synaptic inputs. The electrical and biochemical properties of dendrites are quite variable from cell to cell, and they have a profound influence on the transfer of information from synapse to soma.
树突一词源自希腊语 dendron [树],确实有些树突类似于树枝或根。毫无疑问,受到树木的启发,解剖学家卡米洛·高尔基 (Camillo Golgi) 在 1886 年提出,树突的功能是为神经元收集营养。事实是类似的,但更有趣:树突在一定体积的脑组织中形成树状,以便它们可以以突触输入的形式收集信息。不同类型神经元的树突表现出多种形状。树突通常很广泛,占神经元膜的 99%。单个神经元的树突可以接收多达 200,000 个突触输入。树突的电学和生化特性因细胞而异,它们对信息从突触到体细胞的传递有深远的影响。
2.1 树突减弱突触电位
Dendrites attenuate synaptic potentials
Dendrites tend to be long and thin. Their cytoplasm has relatively low electrical resistivity, and their membrane has relatively high resistivity. These are the properties of a leaky electrical cable, which is the premise for cable theory (see p. 201). Leaky cables are like leaky garden hoses; if ionic current (or water) enters at one end, the fraction of it that exits at the other end depends on the number of channels (or holes) in the cable (hose). A good hose has no holes and all the water makes it through, but most dendrites have a considerable number of channels that serve as leaks for ionic current (see Fig. 7-22).
树突往往又长又细。它们的细胞质具有相对较低的电阻率,并且它们的膜具有相对较高的电阻率。这些是漏电电缆的特性,这是电缆理论的前提(见第 201 页)。漏水的电缆就像漏水的花园软管;如果离子电流(或水)从一端进入,则从另一端流出的离子电流的比例取决于电缆(软管)中的通道(或孔)的数量。一根好的软管没有孔,所有的水都可以通过,但大多数树枝晶都有相当数量的通道,作为离子电流的泄漏(见图 7-22)。
Cable theory predicts how much current flows down the length of the dendrite through the cytoplasm and how much of it leaks out of the dendrite across the membrane. As summarized in Table 7-3, we can express the leakiness of the membrane by the resistance per unit area of dendritic membrane (specific membrane resistance, Rm), which can vary widely among neurons. The intracellular resistance per cross-sectional area of dendrite (specific resistivity of the cytoplasm, Ri) is also important in determining current flow inasmuch as a very resistive cytoplasm forces more current to flow out across the membrane rather than down the axis of the dendrite. Another important factor is cable diameter; thick dendrites let more current flow toward the soma than thin dendrites do. Figure 7-22C illustrates the consequences of a point source of steady current flowing into a leaky, uniform, infinitely long cable made of purely passive membrane. The transmembrane voltage generated by the current falls off exponentially with distance from the site of current injection. The steepness with which the voltage falls off is defined by the length constant (λ; see p. 201), which is the distance over which a steady voltage decays by a factor of 1/e (~37%). Estimates of the parameter values vary widely, but for brain neurons at rest, reasonable numbers are ~50,000 Ω ⋅ cm2 for Rm and 200 Ω ⋅ cm for Ri. If the radius of the dendrite (a) is 1 μm (10−4 cm), we can estimate the length constant of a dendrite by applying Equation 7-8.
电缆理论预测有多少电流沿着树突的长度流过细胞质,以及有多少电流穿过膜从树突中泄漏出来。如表 7-3 所示,我们可以通过树突状膜的每单位面积阻力(比膜阻力,Rm)来表示膜的泄漏,这在神经元之间可能有很大差异。树突每个横截面积的细胞内电阻(细胞质的比电阻率 Ri)在确定电流流动方面也很重要,因为非常电阻的细胞质会迫使更多的电流流过膜而不是沿着树突的轴流出。另一个重要因素是电缆直径;厚树突比薄树突让更多的电流流向 SOMA 。图 7-22C 说明了稳定电流的点源流入由纯无源膜制成的泄漏、均匀、无限长电缆的后果。电流产生的跨膜电压随着距电流注入部位的距离呈指数下降。电压下降的陡峭度由长度常数(λ;见第 201 页)定义,这是稳态电压衰减 1/e 倍 (~37%) 的距离。参数值的估计值差异很大,但对于静止的脑神经元,合理的数字是 Rm 的 ~50,000 Ω ⋅ cm 2 和 Ri 的 200 Ω ⋅ cm。如果枝晶 (a) 的半径为 1 μm (10-4 cm),我们可以通过应用公式 7-8 来估计枝晶的长度常数。
Because dendrite diameters vary greatly, λ should also vary greatly. For example, assuming the same cellular properties, a thin dendrite with a radius of 0.1 μm would have a λ of only 354 μm, whereas a thick one with a radius of 5 μm would have a λ of 2500 μm. Thus, the graded signal voltage spreads farther in a thick dendrite.
由于枝晶直径变化很大,因此 λ 也应该变化很大。例如,假设具有相同的蜂窝特性,半径为 0.1 μm 的薄枝晶的 λ 仅为 354 μm,而半径为 5 μm 的厚枝晶的 λ 为 2500 μm。因此,渐变信号电压在厚树晶中扩散得更远。
Real dendrites are certainly not infinitely long, uniform, and unbranched, nor do they have purely passive membranes. Thus, quantitative analysis of realistic dendrites is complex. The termination of a dendrite decreases attenuation because current cannot escape farther down the cable. Branching increases attenuation because current has more paths to follow. Most dendrites are tapered. Gradually expanding to an increased diameter progressively increases λ and thus progressively decreases attenuation. Real membranes are never completely passive because all have voltagegated channels, and therefore their Rm values can change as a function of voltage and time. Finally, in the working brain, cable properties are not constant but may vary dynamically with ongoing brain activity. For example, as the general level of synaptic input to a neuron rises (which might happen when a brain region is actively engaged in a task), more membrane channels will open and thus Rm will drop as a function of time, with consequent shortening of dendritic length constants. However, all these caveats do not alter the fundamental qualitative conclusion: voltage signals are attenuated as they travel down a dendrite.
真正的树突肯定不是无限长、均匀和无支链的,它们也没有纯粹的钝膜。因此,对真实树突的定量分析很复杂。枝晶的端接减少了衰减,因为电流无法从电缆中逃逸到更远的地方。分支会增加衰减,因为电流有更多的路径可以遵循。大多数树突是锥形的。逐渐膨胀到增加的直径会逐渐增加 λ,从而逐渐降低衰减。真正的膜从来都不是完全无源的,因为所有膜都有电压门控通道,因此它们的 Rm 值会随着电压和时间的变化而变化。最后,在工作的大脑中,电缆特性不是恒定的,但可能会随着持续的大脑活动而动态变化。例如,随着神经元的突触输入的一般水平升高(当大脑区域积极参与一项任务时可能发生),更多的膜通道将打开,因此 Rm 将随时间而下降,从而导致树突长度常数缩短。然而,所有这些警告都不会改变基本的定性结论:电压信号在沿着树突传播时会衰减。
So far, we have described only how a dendrite might attenuate a sustained voltage change. Indeed, the usual definition of length constant applies only to a steady-state voltage shift. An important complication is that the signal attenuation along a cable depends on the frequency components of that signal—how rapidly voltage changes over time. When Vm varies over time, some current is lost to membrane capacitance (see p. 158), and less current is carried along the dendrite downstream from the source of the current. Because action potentials and EPSPs entail rapid changes in Vm, with the fastest of them rising and falling within a few milliseconds, they are attenuated much more strongly than the steady-state λ implies. If Vm varies in time, we can define a λ that depends on signal frequency (λAC, where AC stands for “alternating current”). When signal frequency is zero (i.e., Vm is steady), λ = λAC. However, as frequency increases, λAC may fall sharply. Thus, dendrites attenuate high-frequency (i.e., rapidly changing) signals more than low-frequency or steady signals. Another way to express this concept is that most dendrites tend to be low-pass filters in that they let slowly changing signals pass more easily than rapidly changing ones.
到目前为止,我们只描述了枝晶如何衰减持续的电压变化。事实上,长度常数的通常定义仅适用于稳态电压偏移。一个重要的复杂之处在于,沿电缆的信号衰减取决于该信号的频率分量,即电压随时间变化的速度。当 Vm 随时间变化时,一些电流会损失到膜电容上(参见第 158 页),并且沿电流源下游的枝晶携带的电流较少。因为动作电位和 EPSP 会导致 Vm 的快速变化,其中最快的在几毫秒内上升和下降,因此它们的衰减比稳态 λ 所暗示的要强得多。如果 Vm 随时间变化,我们可以定义一个取决于信号频率的 λ(λAC,其中 AC 代表“交流电”)。当信号频率为零时(即 Vm 稳定),λ = λAC。然而,随着频率的增加,λAC 可能会急剧下降。因此,树突比低频或稳定信号更能衰减高频(即快速变化)信号。另一种表达这个概念的方式是,大多数树枝状往往是低通滤波器,因为它们让缓慢变化的信号比快速变化的信号更容易通过。
Figure 12-2A shows how an EPSP propagates along two different dendrites with very different length constants. If we assume the synapses trigger EPSPs of similar size in the end of each dendrite, then the dendrites with the longer λ deliver a larger signal to the axon hillock. How do leaky dendrites manage to communicate a useful synaptic signal to the soma? The problem is solved in two ways. The first solution deals with the passive properties of the dendrite membrane. The length (l) of dendrites tends to be relatively small in comparison to their λ; thus, none extends more than one or two steady-state length constants (i.e., the l/λ ratio is <1). One way that dendrites achieve a small l/λ ratio is to have a combination of diameter and Rm that gives them a large λ. Another way is that dendrites are not infinitely long cables but “terminated” cables. Figure 12-2B shows that a signal is attenuated more in an infinitely long cable (curve a) than in a terminated cable whose length (l) is equal to λ (curve b). The attenuation of a purely passive cable would be even less if the terminated cable had a λ 10-fold greater than l (curve c). Recall that in our example in Figure 12-2A, such a 10-fold difference in λ underlies the difference in the amplitudes of the EPSPs arriving at the axon hillock.
图 12-2A 显示了 EPSP 如何沿着两个长度常数非常不同的不同树突传播。如果我们假设突触在每个树突的末端触发相似大小的 EPSP,那么具有较长 λ 的树突向轴突小丘传递更大的信号。泄漏的树突如何设法将有用的突触信号传达给 soma?这个问题可以通过两种方式来解决。第一种解决方案涉及枝晶膜的被动特性。与它们的 λ 相比,枝晶的长度 (l) 往往相对较小;因此,没有一个扩展超过一个或两个稳态长度常数(即 L/λ 比为 <1)。枝晶实现小 l/λ 比的一种方法是将直径和 Rm 组合在一起,从而获得较大的 λ。另一种方法是树突不是无限长的电缆,而是“端接”的电缆。图 12-2B 显示,无限长电缆(曲线 a)中的信号衰减大于长度 (l) 等于 λ 的端接电缆(曲线 b)中的信号衰减。如果端接电缆的 λ 大于 l 10 倍(曲线 c),则纯无源电缆的衰减会更小。回想一下,在图 12-2A 的示例中,λ 的 10 倍差异是到达轴突小丘的 EPSP 振幅差异的基础。
The second solution to the attenuation problem is to endow dendrites with voltage-gated ion channels (see pp. 182–199) that enhance the signal more than would be expected in a purely “passive” system (curve d). We discuss the properties of such “active” cables in the next section.
衰减问题的第二种解决方案是赋予树突电压门控离子通道(参见第 182-199 页),这比纯“无源”系统(曲线 d)中预期的信号增强更多。我们将在下一节讨论这种 “有源” 电缆的特性。
2.2 树突状膜具有电压门控离子通道
Dendritic membranes have voltage-gated ion channels
3 躯体中尖峰模式控制
CONTROL OF SPIKING PATTERNS IN THE SOMA
3.1 神经元可以将简单的输入转换为各种输出模式
Neurons can transform a simple input into a variety of output patterns
3.2 本征发射模式由动力学相对较慢的各种离子流决定
Intrinsic firing patterns are determined by a variety of ion currents with relatively slow kinetics
4 轴突传导
AXONAL CONDUCTION
4.1 轴突专门用于快速、可靠和高效的电信号传输
Axons are specialized for rapid, reliable, and efficient transmission of electrical signals
4.2 动作电位通常在初始节段启动
Action potentials are usually initiated at the initial segment
4.3 有髓轴突的传导速度随直径线性增加
Conduction velocity of a myelinated axon increases linearly with diameter
4.4 脱髓鞘轴突缓慢、不可靠或根本不传导动作电位
Demyelinated axons conduct action potentials slowly, unreliably, or not at all
5 Reference
- Smith et al. Insights into inner ear function and disease through novel visualizatio of the ductus reuniens, a semila communication between hearing and balance mechanisms. JARO (2022)
- http://www.cochlea.eu/en/cochlea
- http://www.cochlea.eu/en/cochlea/cochlear-fluids