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Biophysics of ComputationInformation Processing in Single Neurons$
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Christof Koch

Print publication date: 1998

Print ISBN-13: 9780195104912

Published to Oxford Scholarship Online: November 2020

DOI: 10.1093/oso/9780195104912.001.0001

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Beyond Hodgkin And Huxley: Calcium And Calcium- Dependent Potassium Currents

Beyond Hodgkin And Huxley: Calcium And Calcium- Dependent Potassium Currents

(p.212) 9 Beyond Hodgkin And Huxley: Calcium And Calcium- Dependent Potassium Currents
Biophysics of Computation

Christof Koch

Oxford University Press

The cornerstone of modern biophysics is the comprehensive analysis by Hodgkin and Huxley (1952a,b,c,d) of the generation and propagation of action potentials in the squid giant axon. The basis of their model is a fast sodium current INa and a delayed potassium current IK (which here we also refer to as IDR)- The last 40 years of research have shown that impulse conduction along axons can be successfully analyzed in terms of one or both of these currents. Nonetheless, their equations do not capture—nor were they intended to capture—a number of important biophysical phenomena, such as adaptation of the firing frequency to long-lasting stimuli or bursting, that is, the generation of two to five spikes within 5-20 msec. Moreover, the transmission of electrical signals within and between neurons involves more than the mere circulation of stereotyped pulses. These impulses must be set up and generated by subthreshold processes. The differences between the firing behavior of most neurons and the squid giant axon reflect the roles of other voltage-dependent ionic conductances than the two described by Hodgkin and Huxley. Over the last two decades, more than several dozen membrane conductances have been characterized (Hagiwara, 1983; Llinás, 1988; Hille, 1992). They differ in principal carrier, voltage, and time dependence, dependence on the presence of intracellular calcium and on their susceptibility to modulation by synaptic inputs and second messengers. Our knowledge of these conductances and the role they play in impulse formation has accelerated rapidly in recent years as a result of various technical innovations such as single-cell isolation, patch clamping, and molecular techniques. We will here describe the most important of these conductances and briefly characterize each one. In order to understand more completely the functional role of these conductances in determining the response of the cell to input, empirical equations that approximate their behavior under physiological conditions must be developed and compared against the physiological preparations. In a remarkable testimony to the power and the generality of the Hodgkin-Huxley approach, the majority of such phenomenological models has used their methodology of describing individual ionic conductances in terms of activating and inactivating particles with first-order kinetics (see Chap. 6).

Keywords:   Activation gating particles, Bursting, Calcium currents, Delayed rectifier, Firing frequency adaptation, Gain control, Inactivation gating particles, LT spikes, Metabotropic receptors, Potassium currents, Saddle-node bifurcation

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