ACTION POTENTIALS use visual .net data matrix drawer tointegrate data matrix 2d barcode on .net Microsoft Windows SDK the basic p VS .NET barcode data matrix arameters of Eq. (16.

16) together by dividing through by cm0 . This yields 1/(2racm0 ) as the factor multiplying q2V/qt2. The factors multiplying the specific channel current terms are now all of the form Gx/cm0 .

Since the densities of all the channels are fixed, then each Gx will scale with the area; cm0 scales with area as well so the ratios Gx/cm0 are constant. This makes the constant 1/(2racm0 ) invariant with respect to axon diameter. Once the value of this factor that gives a stable solution to Eq.

(16.16) is found, it will work for any other axonal diameter. Denoting this factor as k gives.

s k  r a c m0 (16:17). Recall from Visual Studio .NET Data Matrix barcode 15 that ra c/pa2 (Eq. (15.

1)), where a is the radius. Note that cm0 is the capacitance of the membrane of a unit length of axon; cm0 2pacm. These substitutions give.

s ka  2c cm (16:18). This is an VS .NET data matrix barcodes important result because it tells us that the velocity increases with the square root of the axon radius. In fact, this is an old experimental result, as shown in a plot of conduction velocity versus diameter for many different squid and cuttlefish giant axons (Fig.

16.9). Equation (16.

18) and Fig. 16.9 illustrate that, for axons, bigger is faster.

Since speed helps an organism in many ways, evolution will favor large axons. The giant axon of the squid is a perfect example. This axon runs through the mantel, triggering a contraction to generate a rapid burst of locomotion.

This motion is part of. Fig: 16:9: Action potential conduction velocity is plotted versus axon diameter. Measurements were made in a wide range of axons from squid and cuttlefish of different sizes. The p curve drawn is 0.

8 diameter. (Data from Table I of Pumphrey and Young, 1938; temperature range 19.5 22.

18C). ) 15 Velocity(ms 10 0 0 10 20 3 0 Diameter( 40 m) 50 60 70 80. 16.6 M Y E L I N an escape r eflex of the animal to avoid predators, and the conduction velocity of this axon contributes to the speed of this response.. 16.6 Myelin The advanta ge of speed provided by a large axon weighs against the disadvantage of size and energy cost. In a complex nervous system with billions of neurons, too many large axons would make the nervous system unmanageably huge and consume an inordinate amount of metabolic energy. Invertebrates such as the squid generally have fewer neurons, but vertebrates have much more elaborate nervous systems and need another strategy to speed up axonal conduction.

They have achieved this with myelin, a thick insulating sheath that wraps around axons to increase their membrane resistance and reduce their capacitance (Fig. 16.10a).

This increases the conduction velocity. With myelin, a 10-mm diameter nerve fiber of a frog conducts at about 20 m s 1 (Hodgkin, 1964), which is roughly three times faster than a 100-mm diameter axon in the squid (Fig. 16.

9). Myelin sheaths do not cover the entire axon surface. There are bare spots, called nodes of Ranvier, spaced at regular intervals (Fig.

16.10b). At the node there is no myelin, so ions have unobstructed access to the membrane.

Electrical recordings from myelinated axons showed that the nodes are the sites of action potential generation. Extracellular fields recorded near a node showed that action potentials are accompanied by active inward currents (Huxley and Stampfli, 1949). Recordings at other sites detected only passive outward currents.

The Na channels, which are essential to the initiation and propagation of action potentials, are concentrated at the nodes of Ranvier. The high resistance of the myelin allows the depolarization at one node to spread over a great distance without much current loss. One way to think about this is that increasing the membrane resistance increases the length constant, l.

Myelin also reduces the capacitance so that charge entering a node can change the voltage of a greater area of axonal membrane. Both the increased resistance and reduced capacitance work together to promote rapid spread of an action potential from one node to the next. Because this entails.

(a) (b). Fig: 16:10: (a) Myelin wraps itself around an axon in a spiral form. (b) Between the sheaths of myelin are nodes of exposed axonal membrane. The nodes are spaced at regular intervals.

Arrows indicate ion entry. Action potentials propagate by jumping from node to node..

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