查看Ch12 Physiology of Neurons的源代码

=== 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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