Concentration and Permeability of Ions PDF

### Concentration and Permeability of Ions - The cells of excitable tissues - namely, nerve and muscle cells, have the ability to produce rapid, transient changes in their membrane potential when excited. - These brief fluctuations in potential serve as electrical signals. - The constant membrane p...

### Concentration and Permeability of Ions - The cells of excitable tissues - namely, nerve and muscle cells, have the ability to produce rapid, transient changes in their membrane potential when excited. - These brief fluctuations in potential serve as electrical signals. - The constant membrane potential present in the cells of nonexcitable tissues and those of excitable tissues when they are at rest (i.e., when they are not producing electrical signals) is known as the **resting membrane potential**. - We focus first on the generation and maintenance of the resting membrane potential and then on the changes that take place in excitable tissues during electrical signaling. ### The Unequal Distribution of Key Ions - The unequal distribution of key ions between the ICF and the ECF and their selective movement through the plasma membrane are responsible for the electrical properties of the membrane - The ions primarily responsible for the generation of the resting membrane potential are: - Sodium (Na+) - Potassium (K+) - Anions (A-; large, negatively charged intracellular proteins) - Other ions (e.g. calcium, magnesium, chloride, bicarbonate, and phosphate) do not make a significant contribution to the resting membrane potential in most cells, but they do play other important roles in the body. ### Concentrations and Relative Permeabilities of Ions - The concentrations and relative permeabilities of the ions critical to membrane electrical activity are compared in Table 3-1. - Note that Na+ is in greater concentration in the extracellular fluid and K+ is in much higher concentration in the intracellular fluid. - These concentration differences are maintained by the Na+-K+ pump with the expense of energy (ATP). - Because the plasma membrane is virtually impermeable to A-, these large, negatively charged proteins are found only inside the cell. - They are synthesized from amino acids transported into the cell. - They remain trapped within the cell once synthesized. - In addition to the active carrier mechanism, Na+ and K+ can passively cross the membrane through specific protein channels. - It is usually much easier for K+ than for Na+ to get through the membrane because, typically, the membrane has many more channels open for passive K+ movement than for passive Na+ movement. - At resting membrane potential in a nerve cell, the membrane is about 50 to 75 times as permeable to K+ as to Na+. - Knowledge of the relative concentrations and permeabilities of these ions allows us to analyze the forces acting across the plasma membrane. - This analysis includes the following aspects: 1. The effect that the movement of K+ alone would have on membrane potential 2. The effect of Na+ alone 3. The situation that exists in the cells when both K+ and Na+ effects are taking place concurrently. ### Effect of the Movement of Potassium Alone on Membrane Potential: K+ Equilibrium Potential - Remember, throughout this discussion the concentration gradient for K+ is always outward and the concentration gradient for Na+ is always inward because the Na+-K+ pump maintains a higher concentration of K+ inside the cell and a higher concentration of Na+ outside the cell. - Note as well that because K+ and Na+ are both cations (+ charges), the electrical gradient for both of these ions is always toward the negatively charged side of the membrane. - In our first hypothetical situation, we will examine the driving forces affecting the movement of K+ across the plasma membrane. - As Table 3-1 shows, the concentration of K+ is higher inside the cell than outside; therefore, there is a concentration gradient that favors the movement of K+ out of the cell. - Figure 3-1 illustrates what happens when K+ leaves the cell, making the inside of the cell more negative relative to the outside and thereby establishing a membrane potential. - The membrane potential, however, is negative, meaning the negatively charged interior favors the movement of cations such as K+ to the inside of the cell. - As a result, two opposing forces would now be acting on K+: the concentration gradient tending to move K+ out of the cell, and the electrical gradient tending to move these same ions into the cell. - Eventually, the net outward concentration gradient and the net inward electrical gradient become balanced, so there is no net movement of K+ across the membrane. - The potential that would exist at this equilibrium is known as the K+ equilibrium potential Ex+. - At this point, because of the exactly equal opposing electrical gradient, a large concentration gradient for K+ would still exist, but no more net movement of K+ would occur out of the cell. (Figure 3-1) - The membrane potential at Ek+ is -90 mV. - By convention, the sign always designates the polarity of the excess charge on the inside of the membrane. - A membrane potential of -90 mV means that the potential is of a magnitude of 90 mV, with the inside being negative relative to the outside; a +90 mV would have the same strength, but the inside would be more positive. - The equilibrium potential for a given ion of differing concentrations across a membrane can be calculated by means of the Nernst equation, as follows: - $E = 61 log \frac{C_o}{C_i}$ - Where: - E = equilibrium potential for ion in mV - 61 = constant that incorporates the universal gas constant (R), absolute temperature (T), the ion's valence (z) (when the valence is 1+, as for K+ and Na+), an electrical constant known as Faraday (F), along with the conversion of the natural logarithm (ln) to the logarithm to base 10 (log) - 61 = RT/zF. For any ion with a valence other than 1+, 61 must be divided by z to calculate a Nernst potential. - Co = concentration of the ion outside the cell in millimoles/litre (millimolar; mM) - Ci = concentration of the ion inside the cell in mM - Given that the ECF concentration of K+ is 5 mM and the ICF concentration is 150 mM, - $E_{K+} = 61 log \frac{5 mM}{150 mM} = 61 log \frac{1}{30}$ - Because the log of $\frac{1}{30}$ = -1.447, - $E_{k+} 61 \times (-1.477) = -90mV$ - Because 61 is a constant, the equilibrium potential is essentially a measure of the membrane potential (i.e., the magnitude of the electrical gradient) that exactly counterbalances the concentration gradient (i.e., the ratio between the ion's concentration outside and inside the cell) that exists for the ion. - Note that the larger the concentration gradient is for an ion, the greater the ion's equilibrium potential. - A comparably greater opposing electrical gradient would be required to counterbalance the larger concentration gradient. ### Effect of Movement of Sodium Alone on Membrane Potential: K+ Equilibrium Potential - Figure 3-2 illustrates another hypothetical situation, this time for the movement of Na+ alone across the membrane. - In this case, the concentration gradient for Na+ would move this ion into the cell, producing a buildup of positive charges inside the membrane and leaving negative charges unbalanced outside - primarily in the form of chloride (Cl-). - (Na+ and Cl- [i.e., salt] are the predominant ECF ions.) - Net inward movement would continue until equilibrium was established by the development of an opposing electrical gradient that exactly counterbalances the concentration gradient. - This is the same principle as occurs with K+, but in the opposite direction. - Given the concentrations for Na+, the Na+ equilibrium potential, $E_{Na+}$ would be +60 mV. - In this case the inside of the cell would be positive. - The magnitude of $E_{Na+}$ is somewhat less than that of $E_{k+}$ (60 mV compared with 90 mV). - Because the concentration gradient for Na+ is not as large as that for K+ (see Table 3-1), the opposing electrical gradient (membrane potential) for Na+ is not as great as that for K+ at equilibrium.