Biological Membranes - A. N. Ogurtsov 2012

Electrogenesis of Biomembranes
Electrical Potentials of Biomembranes
Resting Potential

Membrane potentials are subdivided into resting potentials and action potentials.

The resting potential (resting voltage) refers to the steady-state electrical potential difference that can be recorded between the inner and outer surfaces of a membrane in the unexcited state. Since Introduction/36.html">Biological Membranes separate compartments that are isolated from one another, the resting potential is determined by two factors:

1) the difference in ion concentrations on opposite sides of the membrane;

2) the diffusion of ions across the membrane.

The magnitude of the resting Membrane Potential is approximately 70 mV, with The Cell Cytosol always negatively charged relative to the positively charged extracellular environment. Given the small thickness of a biological membrane (around 3.5 nm), the potential gradient across the membrane (the electrostatic field strength) is 200,000 V/cm.

Both the transmembrane ion concentration gradient and the membrane potential play a decisive role in numerous biological processes. For instance, an increase in cytosolic Ca²⁺ concentration serves as a crucial regulatory signal that, for example, triggers Muscle cell contraction or initiates the secretion of digestive Enzymes in pancreatic Cells. In many animal cells, the combined effect of the Na⁺ ion concentration gradient and the membrane potential drives the Transmembrane Movement of Amino Acids and other molecules against their concentration gradient via symport or antiport mechanisms. Another example is the propagation of nerve impulses along Neurons, which is governed by The activity of Ion Channels.

For clarity, let us consider a model system in which two electrolyte solutions—with ion concentrations corresponding to the physiological concentrations of potassium and sodium ions in the cytosol and extracellular fluid—are separated by a membrane that is impermeable to potassium and sodium ions (Figure 89). The electrical potential across such a membrane is zero.

If the concentration of a given ion inside the cell, c_in, differs from its outside concentration, c_out, and the membrane is permeable to this ion, a flux of charged particles across the membrane arises. This disrupts the electrical neutrality of the system and establishes an internal-to-external potential difference φ_M = φ_in - φ_out, which will counteract any further movement of ions across the membrane.

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Figure 89 - Schematic diagram modeling the ionic COMPOSITION OF THE cytosol and extracellular fluid

Upon establishment of equilibrium, the electrochemical potentials on both sides of the membrane become equal

Since

Another form of this equation, with the membrane potential φ_M = φ_in - φ_out isolated on the left-hand side, is known as the Nernst equation for the equilibrium membrane potential

If the membrane potential is generated by The transport of K⁺ ions, for which [K⁺]_in > [K⁺]_out and z = +1, the equilibrium membrane potential is negative and takes the form

For Na⁺ ions: [Na⁺]_in < [Na⁺]_out, z = +1,

For Cl^- ions: [Cl^-]_in < [Cl^-]_out, z = -1,

At T = 300 K and z = +1 (taking into account that ln x = 2.3 log x)

from which it follows that

The resting membrane potential in most cells is very close to the equilibrium potential for potassium ions. Based on this, Bernstein suggested as early as 1902 that the resting membrane potential arises from the diffusion of potassium ions out of the cell through specific channels in the membrane.

This hypothesis was subsequently confirmed experimentally, leading to the discovery and characterization of Membrane Proteins that form channels allowing various ions to cross the membrane selectively.

Indeed, when selective ion channels for sodium (Figure 90(a)) or potassium (Figure 90(b)) are present in the membrane, the resulting movement of ions driven by the concentration gradient leads to charge Separation across the membrane, thereby generating a membrane potential.

Figure 90 - The Role of selective ion channels in membrane potential generation: a - sodium channels, b - potassium channels

For The sodium and potassium ion concentrations shown in Figure 83, the membrane potential resulting from the transmembrane movement of sodium ions will be φ = -59 mV (Figure 90(a)), whereas in the case of selective Transmembrane Transport of potassium ions, the membrane potential will be φ = +59 mV (Figure 90(b)).

The experimentally measured membrane potentials and ion concentrations, along with the potential values calculated using the Nernst equation for two cell types, are presented in Table 5.

Table 5 - Content of K⁺, Na⁺, Cl^- ions, equilibrium potentials φ⁰_M, and resting potentials φ^e_M of certain cells

Using the principles of electrostatics, let us estimate The amount of ions that must cross from the Cytoplasm into the extracellular fluid to establish a potential difference of the order of 10^-1 V.

The cell radius is r = 10 μm = 10^-5 m. The specific membrane capacitance (capacitance per unit area) is C_s = 10^-2 F/m².

The membrane surface area is S = 4πr² ≈ 4π∙10^-10 m² ≈ 10^-9 m². Consequently, the total membrane capacitance is C = C_s ∙ S ≈ 10^-2 F/m² ∙ 10^-9 m² = 10^-11 F.

Treating the membrane as a capacitor, the magnitude of the charge of each sign on its surface is |q| = Cφ ≈ 10^-11 ∙ 10^-1 = 10^-12 C, which corresponds to

moles of ions.

The volume of a cell with this radius is

The resulting change in intracellular ion concentration due to the efflux of 10^-17 moles of ions is

This concentration change is negligible compared to the intracellular concentration of potassium ions (Table 5), amounting to merely 10^-4 % of the internal potassium content.

Thus, establishing the Nernst equilibrium membrane potential requires the translocation of a vanishingly small number of ions across the membrane compared to their total pool within the cell.