Ion channels

Ion channels are critical determinants of the electrical behavior of membranes

This chapter and the following three chapters focus on the properties of the cell membrane that determine the overall electrical behavior of the cell. To put this material in its proper context, consider a typical neuron, such as the α motor neuron illustrated in Fig. 5.1 . The cell body (soma) contains the nucleus, mitochondria, and the endoplasmic reticulum, which is the site of protein synthesis. Two types of processes usually extend from the cell body. Dendrites are relatively short, small-diameter processes that branch extensively and receive signals from other neurons. The axon is a cylindrical process that can be more than 1 m long in humans and much longer in some large animals and is responsible for transmitting signals to other neurons or effector cells. The axon begins at a region of the soma called the axon hillock and terminates in small branches that make contact with as many as 1000 other neurons, or other cell types like muscle and endocrine cells. Specialized junctions ( synapses ) are formed at the points of contact between neurons and are sites of communication between the cells ( Chapters 12 and 13 ). The main electrical functions of a cell like the α motor neuron are as follows: (1) to sum, or integrate, electrical inputs from a large number of other neurons; (2) to generate an action potential (AP), which is a rapid, transient membrane depolarization, if the inputs reach a critical level; and (3) to propagate the AP signal to the nerve terminals. All these processes depend on the activity of several types of ion channels . The channels are integral membrane proteins that form water-filled (aqueous) pores through which selected ions can permeate.

The primary role of the neuronal cell body and dendrite membranes ( Fig. 5.1 ) is to integrate, over both space and time, the activity of all synaptic inputs impinging on the cell and communicate this information to the axon hillock. The characteristics of this integrative process are determined largely by the passive electrical properties of the membrane, which are described in Chapter 6 . When the V _m at the axon hillock ( Fig. 5.1 ) reaches threshold, an AP is generated. Threshold behavior and the generation of the AP are caused primarily by two types of ion channels in nerves, voltage-gated Na ⁺ and K ⁺ channels. The properties of these channels and their roles in the generation of the AP are presented in Chapter 7 . Once the AP has been generated, it is conducted, or propagated , at full amplitude (i.e., it is “ all or none ”; Chapter 7 ) along the axon to the nerve terminals. AP propagation depends on both the passive properties of the membrane and the dynamic activity of the voltage-gated Na ⁺ and K ⁺ channels.

Distinct types of ion channels have several common properties

Ion channels increase the permeability of the membrane to ions

The permeability of a pure phospholipid bilayer membrane to ions (e.g., Na ⁺ , K ⁺ , Cl ⁻ , and Ca ²⁺ ) is extremely small: the permeability coefficients for these ions are in the range of 10 ⁻¹¹ to 10 ⁻¹³ cm/sec ( Chapter 2 ). Because of this low intrinsic permeability, ions can cross membranes only by two special mechanisms: by reversibly binding to a carrier protein ( Chapters 10 and 11 ) or by diffusion through an aqueous pore ( Fig. 5.2 ). The maximum transport rate for carriers is on the order of 5000 ions per second. This is much too slow to generate the rapid changes in V _m that are required for neuronal signaling. Excitation of nerve and muscle (i.e., the generation and propagation of the AP; Chapter 7 ) and neuronal signaling require much faster ion movements. The rate of ion movement by diffusion through a small pore in the membrane is usually several orders of magnitude faster than the transport rate of carriers ( Box 5.1 ).

BOX 5.1

Calculation of the Rate of Ion Movement Through an Aqueous Pore

The diffusion equation ( Chapter 2 ) can be used to calculate the rate of ion movement across a membrane through an aqueous pore. The equation is

$J\text{=-}D\frac{\text{Δ}C}{\text{Δ}x}$

where J is the flux per unit area (in mol/cm ² /sec), D is the diffusion coefficient, Δ C is the concentration difference across the membrane, and Δ x is the pore length. We will assume that the pore is a cylinder with radius r _p . To calculate a flux in units of mol/sec, we multiply both sides of the flux equation by the cross-sectional area of the pore (π × r _p ² ):

$J(\text{mol/sec)}\text{=-}\pi \text{×}{r}_{\text{p}}^{\text{2}}\text{×}D\frac{\text{Δ}C}{\text{Δ}x}$

We assume that (1) D for the ion in the pore is the same as in bulk solution (2 × 10 ⁻⁵ cm ² /sec), (2) r _p is 3 × 10 ⁻⁸ cm, (3) Δ C is 100 mM, and (4) Δ x is 5 × 10 ⁻⁷ cm. Plugging these values into Equation B5.1 gives

$\begin{array}{c}J\text{=}\pi \text{×}{\left(3\text{×}{10}^{\text{-}8}\text{cm}\right)}^2\text{×}2\text{×}{10}^{\text{-}5}\frac{{\text{cm}}^2}{\sec }\\ \text{×}\frac{0.1\frac{\text{mol}}{{10}^3{\text{cm}}^3}}{5\text{×}{10}^{\text{-}7}\text{cm}}\approx 1\text{×}{10}^{\text{-}17}\frac{\text{mol}}{\sec }\end{array}$

Multiplying by Avogadro’s number (6.022 × 10 ²³ ions/mol) gives the flux as approximately 6 million ions per second, which is approximately 1000 times faster than the maximum rate of carrier-mediated transport ( Chapter 11 ).