The current-voltage relationship of a hypothetical cell containing selective channels for Na+, K+, and Cl- is illustrated in Figure 2.4. The graph represents the membrane currents at various membrane voltages. Each ion current is calculated using Ohm's law, the Nernst equilibrium potential for each ion (ECl, EK, and ENa), and the membrane conductance for each ion. The overall current-voltage relationship for the entire cell is also depicted. The total cell current (Icell) is determined using the chord conductance equation (Eq.2.7). As 80% of the cell conductance is due to K+, the resting membrane voltage (Vm) of -64.4 mV is close to the Nernst equilibrium potential for K+.

The chord conductance equation (Eq. 2.7) is often referred to as the chord conductance equation. It states that Vm will approximate the Nernst equilibrium potential of the ion with the highest membrane conductance. In Figure 2.4, since 80% of the membrane conductance is attributed to K+, Vm closely resembles the Nernst equilibrium potential for K+ (EK+). During rest, most cells have a high conductance to K+, resulting in Vm approximating EK+. Additionally, the magnitude of EK+ greatly influences Vm, which in turn is affected by changes in the extracellular concentration of K+. For instance, if the intracellular [K+] is 120 mEq/L and the extracellular [K+] is 4 mEq/L, EK+ is -90.8 mV. If the extracellular [K+] increases to 7 mEq/L, EK+ becomes -79.9 mV, leading to a depolarization of Vm. Conversely, if the extracellular [K+] decreases to 2 mEq/L, EK+ becomes -109.4 mV, resulting in a hyperpolarization of Vm.

Figure 2.5 illustrates a nerve action potential and the changes in Na+ and K+ conductances (G and GK+, respectively) as well as the membrane potential (Vm). During rest, the membrane exhibits high K+ conductance, causing Vm to be close to the Nernst equilibrium potential for K+ (EK+). With the initiation of the action potential, there is a significant increase in Na+ conductance, causing Vm to approach the Nernst equilibrium potential for Na+ (ENa+). This increase in Na+ conductance is transient, and thereafter, K+ conductance rises above its initial value, resulting in hyperpolarization of the cell as Vm approaches EK+. Once the K+ conductance returns to its baseline value, Vm returns to its resting value of -70 mV.

[Modified from Levy MN, Koeppen BM, Stanton BA. Berne & Levy’s Principles of Physiology. 4th ed. St. Louis: Mosby; 2006.]
•Fig. 2.4 Current-Voltage Relationship of a Hypothetical Cell Containing Na+-, K+-, and Cl−-Selective Channels. Membranecurrentsareplottedoverarangeofmembranevoltages(i.e.,current-voltagerelationships).EachioncurrentiscalculatedwiththeuseofOhm’slaw,theNernstequilibriumpotentialfortheion(ECl,EK,andENa),andthemembraneconductancefortheion.Thecurrent-voltagerelationshipforthewholecellisalsoshown.Totalcellcurrent(Icell)wascalculatedwiththechordconductanceequation(see
Eq.2.7).Because80%of cellconductanceisduetoK+ ,therestingmembranevoltage(Vm)of−64.4mVisneartothatoftheNernstequilibriumpotentialforK+ .
Equation 2.7 where ˜G = G ++ G ++ G −.
Inspection of
Eq. 2.7 , which is often called the chord conductance equation, reveals that the Vm will be near to the Nernst equilibrium potential of the ion to which the membrane has the highest conductance. In
Fig. 2.4 , 80% of the membrane conductance is attributable to K+; as a result, Vm is near to the Nernst equilibrium potential for K+ (EK+). For most cells at rest, the membrane has a high conductance to K+ , and thus the Vm approximates EK+. Moreover, the Vm is greatly influenced by the magnitude of EK+ , which in turn is greatly influenced by changes in the [K+] of the ECF. For example, if the intracellular [K+] is 120 mEq/L and the extracellular [K+] is 4 mEq/L, EK+ has a value of −90.8 mV. If the extracellular [K+] is increased to 7 mEq/L, EK+ would be −79.9 mV. This change in EK+ depolarizes the Vm (i.e., Vm is less negative). Conversely, if the extracellular [K+] is decreased to 2 mEq/L, EK+ becomes −109.4 mV, and the Vm hyperpolarizes (i.e., Vm is more negative).
•Fig. 2.5 Nerve Action Potential Showing the Changes in Na+ and K+ Conductances ( G and GK+ , Respectively) and the Membrane
Potential (Vm). Atrest,themembranehasahighK+ conductance,andVmisneartheNernstequilibriumpotentialforK+ (EK+ ).Withtheinitiationoftheactionpotential,thereisalargeincreaseintheNa+ conductanceofthemembrane,andtheVmapproachestheNernstequilibriumpotentialforNa+ (ENa+ ).TheincreaseinNa+ conductanceistransient,andtheK+ conductancethenincreasesaboveitsvaluebeforetheactionpotential.ThishyperpolarizesthecellasVmapproachesEK+.AstheK+ conductancereturnstoitsbaselinevalue,Vmreturnstoitsrestingvalueof−70mV.(ModifiedfromLevyMN,KoeppenBM,StantonBA.Berne & Levy’s Principles of Physiology. 4thed.St.Louis:Mosby;2006.)