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== 树突中的信号传导 ==
<b style=color:#f80>SIGNAL CONDUCTION IN DENDRITES</b>

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%。<b style=color:#0b0>单个神经元的树突</b>可以接收多达 <b style=color:#f80>200,000 个突触输入</b>。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。

=== 树突减弱突触电位 ===
<b style=color:#0ae>Dendrites attenuate synaptic potentials</b>

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。

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=== 树突状膜具有电压门控离子通道 ===
<b style=color:#0ae>Dendritic membranes have voltage-gated ion channels</b>

All mammalian dendrites have voltage-gated ion channels that influence their signaling properties. Dendritic characteristics vary from cell to cell, and the principles of dendritic signaling are being studied intensively. Most dendrites have a relatively low density of voltage-gated channels (see pp. 182–199) that may amplify, or boost, synaptic signals by adding additional inward current as the signals propagate from distal dendrites toward the soma. We have already introduced the principle of an active cable in curve d of Figure 12-2B. If the membrane has voltage-gated channels that are able to carry more inward current (often Na+ or Ca2+) under depolarized conditions, a sufficiently strong EPSP would drive Vm into the activation range of the voltagegated channels. These voltage-gated channels would open, and their additional inward current would add to that generated initially by the synaptic channels. Thus, the synaptic signal would fall off much less steeply with distance than in passive dendrite. Voltage-gated channels can be distributed all along the dendrite and thus amplify the signal along the entire dendritic length, or they can be clustered at particular sites. In either case, voltage-gated channels can boost the synaptic signal considerably, even if the densities of channels are far too low for the generation of action potentials.

所有哺乳动物树突都具有影响其信号传导特性的电压门控离子通道。树突状特征因细胞而异，并且正在深入研究树突状信号转导的原理。大多数树突具有相对较低的电压门控通道密度（参见第 182-199 页），当信号从远端树突传播到体细胞时，可以通过增加额外的向内电流来放大或增强突触信号。我们已经在图 12-2B 的曲线 d 中介绍了有源电缆的原理。如果膜具有电压门控通道，能够在去极化条件下携带更多的向内电流（通常是 Na + 或 Ca2 + ），则足够强的 EPSP 会将 Vm 驱动到电压门控通道的激活范围内。这些电压门控通道将打开，它们额外的向内电流将添加到突触通道最初产生的电流中。因此，突触信号随距离的下降幅度比被动树突要小得多。电压门控通道可以沿树突分布，从而沿整个树突长度放大信号，或者它们可以聚集在特定位置。在任何一种情况下，电压门控通道都可以显着增强突触信号，即使通道的密度太低而无法产生动作电位。


An even more dramatic solution, used by a few types of dendrites, is to have such a high density of voltage-gated ion channels that they can produce action potentials, just as axons can. One of the best-documented examples is the Purkinje cell, which is the large output neuron of the cerebellum. As Rodolfo Llinás and colleagues have shown, when the dendrites of Purkinje cells are stimulated strongly, they can generate large, relatively broad action potentials that are mediated by voltage-gated Ca2+ channels (Fig. 12-3). Such Ca2+ spikes can sometimes propagate toward—or even into—the soma, but these Ca2+ action potentials do not continue down the axon. Instead, they may trigger fast Na+-dependent action potentials that are generated by voltage-gated Na+ channels in the initial segment. The Na+ spikes carry the signal along the axon in the conventional way. Both types of spikes occur in the soma, where the Na+ spikes are considerably quicker and larger than the dendritic Ca2+ spikes. The faster Na+ spikes propagate only a short distance backward into the dendritic tree because the rapid time course of the Na+ spike is strongly attenuated by the inherent filtering properties of the dendrites (i.e., the λAC is smaller for the rapid frequencies of the Na+ action potentials than for the slower Ca2+ action potentials). The dendrites of certain other neurons of the CNS, including some pyramidal cells of the cerebral cortex, can also generate spikes that are dependent on Ca2+, Na+, or both.

几种类型的树突使用的一种更引人注目的解决方案是具有如此高密度的电压门控离子通道，以至于它们可以产生动作电位，就像轴突一样。记录最充分的例子之一是浦肯野细胞，它是小脑的大输出神经元。正如 Rodolfo Llinás 及其同事所表明的那样，当浦肯野细胞的树突受到强烈刺激时，它们可以产生由电压门控 Ca2+ 通道介导的大的、相对广泛的动作电位（图 12-3）。这种 Ca2+ 尖峰有时可以向体细胞传播，甚至传播到体细胞中，但这些 Ca2+ 动作电位不会继续沿轴突向下移动。相反，它们可能会触发由初始段中的电压门控 Na+ 通道产生的快速 Na+ 依赖性动作电位。Na+ 尖峰以传统方式沿轴突传递信号。这两种类型的尖峰都发生在体细胞中，其中 Na+ 尖峰比树突状 Ca2+ 尖峰更快、更大。较快的 Na + 尖峰仅向后传播一小段距离到树突树中，因为 Na + 尖峰的快速时间过程被树突固有的过滤特性强烈衰减（即，对于 Na + 动作电位的快速频率，λAC 比对于较慢的 Ca2 + 动作电位）。CNS 的某些其他神经元的树突，包括大脑皮层的一些锥体细胞，也可以产生依赖于 Ca2+、Na+ 或两者兼而有之的尖峰。


Dendritic action potentials, when they exist at all, tend to be slower and weaker, and with higher thresholds, than those in axons. The reason is probably that one of the functions of dendrites is to collect and to integrate information from a large number of synapses (often thousands). If each synapse were capable of triggering an action potential, there would be little opportunity for most of the synaptic inputs to have a meaningful influence on a neuron’s output. The cell’s dynamic range would be truncated; that is, a very small number of active synapses would bring the neuron to its maximum firing rate. However, if dendrites are only weakly excitable, the problem of signal attenuation along dendritic cables can be solved while the cell still can generate an output (i.e., the axonal firing rate) that is indicative of the proportion of its synapses that are active.

树突动作电位（如果存在）往往比轴突中的动作电位更慢、更弱，并且阈值更高。原因可能是树突的功能之一是收集和整合来自大量突触（通常是数千个）的信息。如果每个突触都能够触发动作电位，那么大多数突触输入几乎没有机会对神经元的输出产生有意义的影响。单元格的动态范围将被截断;也就是说，极少量的活跃突触会使神经元达到其最大放电速率。然而，如果树突只是弱可激发的，则可以解决沿树突电缆的信号衰减问题，而细胞仍然可以产生指示其活跃突触比例的输出（即轴突放电率）。


Another advantage of voltage-gated channels in dendrites may be the selective boosting of high-frequency synaptic input. Recall that passive dendrites attenuate signals of high frequency more than those of low frequency. However, if dendrites possess the appropriate voltage-gated channels, with fast gating kinetics, they will be better able to communicate high-frequency synaptic input.

树突中电压门控通道的另一个优势可能是高频突触输入的选择性增强。回想一下，无源枝晶比低频信号更能衰减高频信号。然而，如果树突具有适当的电压门控通道，具有快速门控动力学，它们将能够更好地传达高频突触输入。

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