1. Factors Affecting Ion Transport Through the Membrane • under normal resting conditions. • The flow of ions through the cell membrane depends mainly on three factors: • the ratio of ion concentrations on both sides of the membrane • the voltage across the membrane,and • the membrane permeability. • The effects of concentration differences and membrane voltages on the flow of ions may be made commensurable if, instead of the concentration ratio, the corresponding Nernst voltage is considered. The force affecting the ions is then proportional to the differencebetween the membrane voltage and the Nernst voltage. • Regarding membrane permeability, we note that if the biological membrane consisted solely of a lipid bilayer, as described earlier, all ionic flow would be greatly impeded. However, specialized proteins are also present which cross the membrane and contain aqueous channels. Such channels are specific for certain ions; they also include gates which are sensitive to membrane voltage. The net result is that membrane permeability is different for different ions, and it may be affected by changes in the transmembrane voltage, and/or by certain ligands. • As mentioned in Section 3.4.1, Hodgkin and Huxley (1952a) formulated a quantitative relation called the independence principle. According to this principle the flow of ions through the membrane does not depend on the presence of other ions. Thus, the flow of each type of ion through the membrane can be considered independent of other types of ions. The total membrane current is then, by superposition, the sum of the currents due to each type of ions. ION FLOW THROUGH THE MEMBRANE

2. Membrane Ion Flow in a Cat Motoneuron We discuss the behavior of membrane ion flow with an example. For the cat motoneuron the following ion concentrations have been measured

3. For each ion, the following equilibrium voltages may be calculated from the Nernst equation: VNa = -61 log10(15/150) = +61 mV VK = -61 log10(150/5.5) = -88 mV VCl = +61 log10(9/125) = -70 mV The resting voltage of the cell was measured to be -70 mV.

4. When Hodgkin and Huxley described the electric properties of an axon in the beginning of the 1950s, they believed that two to three different types of ionic channels (Na+, K+, and Cl-) were adequate for characterizing the excitable membrane behavior. The number of different channel types is, however, much larger. In 1984, Bertil Hille summarized what was known at that time about ion channels. He considered that about four to five different channel types were present in a cell and that the genome may code for a total number of 50 different channel types. Now it is believed that each cell has at least 50 different channel types and that the number of different channel proteins reaches one thousand.

5. Graphical Illustration of the Membrane Ion Flow The flow of potassium and sodium ions through the cell membrane (shaded) and the electrochemical gradient causing this flow are illustrated. For each ion the clear stripe represents the ion flux; the width of the stripe, the amount of the flux; the inclination (i.e., the slope), the strength of the electrochemical gradient.

6. Membrane conductance changes during a propagating nerve impulse K. S. Cole and H. J. Curtis (1939) showed that the impedance of the membrane decreased greatly during activation and that this was due almost entirely to an increase in the membrane conductance. That is, the capacitance does not vary during activation. This is a numerical solution of Equation 4.31 (after Hodgkin and Huxley, 1952d)

8. An electric circuit representation of a membrane patch The equivalent circuit model of an axon

9. This figure illustrates the components of the membrane conductance, namely GNa and GK, and their sum Gmduring a propagating nerve impulse and the corresponding membrane voltage Vm.

10. The components of the membrane current during the propagating nerve impulse The figure illustrates the membrane voltage Vm during activation, the sodium and potassium conductances GNa and GK, the transmembrane current Im as well as its capacitive and ionic components ImC and ImI, which are illustrated for a propagating nerve impulse (Noble, 1966).

11. From the figure can be made: • The potential inside the membrane begins to increase before the sodium conductance starts to rise, owing to the local circuit current originating from the proximal area of activation. In this phase, the membrane current is mainly capacitive, because the sodium and potassium conductances are still low. • The local circuit current depolarizes the membrane to the extent that it reaches threshold and activation begins. • The activation starts with an increasing sodium conductance. As a result, sodium ions flow inward, causing the membrane voltage to become less negative and finally positive.

12. The potassium conductance begins to increase later on; its time course is much slower than that for the sodium conductance. • When the decrease in the sodium conductance and the increase in the potassium conductance are sufficient, the membrane voltage reaches its maximum and begins to decrease. At this instant (the peak of Vm), the capacitive current is zero (dV/dt = 0) and the membrane current is totally an ionic current.

13. The terminal phase of activation is governed by the potassium conductance which, through the outflowing potassium current, causes the membrane voltage to become more negative. Because the potassium conductance is elevated above its normal value, there will be a period during which the membrane voltage is more negative than the resting voltage - that is, the membrane is hyperpolarized. • Finally, when the conductances reach their resting value, the membrane voltage reaches its resting voltage..