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-65 mV. The value Vm

65 mV is said to be a stable fixed point because after small perturbations above or below that value, Vm will return to it.

Next, consider the fixed point at V0 = — 59 mV. In this case, Vm(0.5)<0 for Vm< V0, and Vm(0.5)>0 for Vm>V0. This result implies that this fixed point is unstable: After small perturbations above or below V0, Vm will move away from the fixed point. The implication of this fact is that the point V0 = -59 mV serves as a threshold. For V0<-59mV, the model returns to resting potential (Fig. 9a); for V0 > —59 mV, Vm rapidly increases as the action potential begins [Fig. 9b; in these cases, Vm(t) continues to evolve, eventually bringing the cell to rest]. For these simulations, the fixed point at V0 = -59 mV corresponds exactly with the threshold for generation of an action potential (vertical dashed line in Fig. 9d).

E. Backpropagation of the Action Potential

In the traditional view, information flow in the mammalian neuron is in one direction only: The dendrite receives input from the presynaptic population, the soma integrates this information, the decision regarding whether or not to fire an action potential is made at or near the axon hillock, and the action potential is propagated to other neurons by the axon. This view has been amended in recent years as scientists have developed techniques for recording simultaneously from multiple locations within the neuron (e.g., the soma and a primary dendrite). In pyramidal neurons of layer V of neocortex, for example, suprathreshold synaptic input to the apical dendrites leads to initiation of an action potential near the soma. This action potential can then travel back from the soma toward the distal end of the apical dendrite. The reliability of backpropagation depends on recent patterns of input and spike generation. Given the crucial role of dendritic depolarization for synaptic plasticity, backpropagating action potentials may be important for experience-dependent alterations of neuronal circuitry in learning and memory.

F. Diseases Related to Mutations in Ion Channels

Given the central role that electrical excitability plays in nervous system function, it is not surprising that mutations of voltage-gated ion channels alter neuronal function. Although work in this area is just beginning, a host of maladies have been associated with nonlethal mutations of neuronal voltage-gated channels, including the following:

* Generalized epilepsy with febrile seizures, so-named because patients have fever-induced seizures that develop later in life into seizures without a clear trigger, is associated in some cases with a rare mutation of the b1 subunit of the Na+ channel. This mutation may promote epilepsy by slowing the inactivation process in neuronal Na+ channels, leaving the brain hyperexcitable.

* Benign familial neonatal epilepsy is associated with mutations that lead to reduced expression of slow, voltage-gated K+ channels of the KCNQ family, thereby leaving some neurons hyperexcitable.

* Some forms of episodic ataxia, a condition of triggered events of imbalance and uncoordinated movements, has been associated with many missense mutations of the Kv1.1 channel, which gives rise to an inactivating K+ conductance. Ataxia-associated mutations of Kv1.1 have been shown to lead to pathologically rapid deactivation, enhanced inacti-vation, and increases in the threshold of activation. These disparate changes all have the effect of broadening the neuronal action potential, but it is not known how the broadened spike may lead to ataxia.

See Also the Following Articles

ELECTRICAL POTENTIALS • ELECTROENCEPHALOGRAPHY (EEG) • EVENT-RELATED

ELECTROMAGNETIC RESPONSES • ION CHANNELS •

NEURON • NEURAL NETWORKS

Suggested Reading

Aidley, D. J., and Stanfield, P. R. (1996). Ion Channels: Molecules in Action. Cambridge Univ. Press, Cambridge, UK.

Ashcroft, F. M. (2000). Ion Channels and Disease. Academic Press, San Diego.

Hausser, M., Spruston, N., and Stuart, G. (2000). Diversity and dynamics of dendritic signaling. Science 290, 739-744.

Hille, B. (2001). Ionic Channels of Excitable Membranes, 3rd ed. Sinauer, Sunderland, MA.

Johnston, D., and Wu, S. M.-S. (1995). Foundations of Cellular Neurophysiology. MIT Press, Cambridge, MA.

Koch, C. (1999). Biophysics of Computation. Oxford Univ. Press, New York.

Koch, C.,andSegev, I. (Eds.) (1998). Methods in Neuronal Modeling, 2nd ed. MIT Press, Cambridge, MA.

Nicholls, J. G., Martin, A. R., Wallace, B. G., and Fuchs, P. A. (2000). From Neuron to Brain, 4th ed. Sinauer, Sunderland, MA.

Sakmann, B., and Neher, E. (Eds.) (1995). Single-Channel Recording, 2nd ed. Plenum, New York.

Weiss, T. F. (1996). Cellular Biophysics. MIT Press, Cambridge, MA.

White, J. A., Rubinstein, J. T., and Kay, A. R. (2000). Channel noise in neurons. Trends Neurosci. 23, 131-137.

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