How the Gibbs-Donnan equilibrium conditions and diffusion through a semipermeable membrane are involved in creating the resting membrane potential

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Introduction

The resting membrane potential (RMP) is an electrical potential difference in cells, occurring across their plasma membranes. The cytoplasm of the cell is electrically negative in comparison to the surrounding extracellular fluid, this difference in electrical charge gives rise to the RMP. The RMP is essential for the functioning of many electrically excitable cells including, neuronal cells, smooth and skeletal muscle cells, as well as cardiac myocytes, which through electrical impulses control the contractility of the heart.

During this essay the generation of the resting membrane potential will be explored, including the effects of the Gibbs-Donnan equilibrium conditions, the structure and function of the plasma membrane, and how, with the diffusion of ions through a semi permeable membrane they give rise to the RMP. (Levy, N. et al.2006)

Plasma Membrane

The plasma membrane asserts tight control over the interstitial environment of the cell, this is achieved through the formation of a phospholipid bilayer containing protein constituents (ref). Phospholipids are distributed into two leaflets within the bilayer, with the hydrophobic portions facing inwards and the hydrophilic tails of the phospholipids facing the aqueous environment, the presence of phospholipids give the membrane its capacitance. Integral membrane proteins and ion channel proteins span the length of the membrane, like that of the Na+-K+ pump and Sodium-Potassium leak channels discussed later, which aid in the conductance of the cell membrane. The inter and extracellular surfaces of the membrane are negatively charged, due to the presence of acidic phospholipids and the anionic nature of proteins at biological pH, this negative charge on the outer membranes with respect to extra and intracellular fluid is known as the zeta potential, which causes the formation of a small electrical field (ref); This electrical field works to achieve electroneutrality with opposing charged particles, and by doing so aids in the formation of concentration gradients. Changes to surface charges within the plasma membrane, such as ionic concentrations, can therefore effect the resting membrane potential and the ability of a cell to reach threshold (Sperelakis, N. 1998).

Concentration gradient and Electrical Potential

To understand how the flow of ions contribute to the RMP, the formation of a concentration gradient and electrical potential must first be understood. Molecules diffuse from an area of high concentration to an area of lower concentration, if two aqueous compartments separated by a membrane were formed, containing equal concentrations of the X molecule then no diffusion would occur between compartments (Figure 1). However if the concentration of X increased in compartment A, then the ion would flow down its concentration gradient into compartment B until equilibrium is reached between compartments. However diffusion is more complexed in biological compartments as ions are found in the form of cations and anions. If an X+ion was placed in compartment A, which contained a higher concentration of X+than compartment B, then X+ would again flow down its concentration gradient into compartment B, however X+ now also flows against its concentration gradient back into compartment A, due to the electrical potential difference across the membrane, generated by the loss of cations from compartment A, causing an increase in negativity, and an increase in X+in compartment B, increasing electrical charge opposing cations (Figure 2); This movement of ions causes a potential difference to arise between compartments, increased movement of X+ down its concentration gradient, increases the potential difference, and decreases the ability of X+ to move against its electrical gradients, thus an equilibrium is reached between the concentration gradient and electrical gradient, known as the equilibrium potential (Aidley, D.1989).

Gibbs-Donnan Equilibrium

The cytoplasm of eukaryotic cells contain permeable ions as well as many impermeable ionised molecules that cannot penetrate the cell membrane, such as proteins, nucleic acids and glycoprotein's. Many of these intracellular molecules are negatively charged at physiological pH, causing a notable effect on the concentration gradient and electrical potential of permeable cations and anions across the plasma membrane. The effect of impermeable intracellular anionic molecules therefore influences the resting membrane potential, this is known as a Gibbs-Donnan equilibrium.

Again consider two aqueous compartments separated by a semi permeable membrane, compartment A contains Na+ and proteins (Pr-), compartment B contains Na+ and Cl- (Figure 3a). The semi permeable membrane is permeable to Na+, Cl- and Water but impermeable to Pr-. Compartment A and B contain 0.1 molar solutions of Na protinate and NaCl respectively, as the concentration of Cl- is higher in compartment B it diffuses down its concentration gradient into compartment A, this is turn causes the creation of an electrical potential as compartment A increases in negativity due to the anionic properties of Cl-, prompting a flux of K+ down its electrical gradient from compartment B to A. Equilibrium will eventually occur between compartments so that the concentration of Na+ and Cl- are equal (Figure 3b):

[Na+]A[Cl-]A= [Na+]B[Cl-]B

This is known as Gibbs-Donnan equilibrium conditions (Sperelakis, N.1998). However it must be noted from the equations that only the permeate ions satisfy the gibbs-donnan equilibrium conditions, the impermeable Pr- are not included as they are unable to diffuse and reach equilibrium (Sperelakis, N.1998). Applying the Nernst equation for either Na+ or Cl- results in a negative electrical potential, this is due to the impermeable protein ions in chamber A (Sperelakis, N.1998), these negative impermeable intracellular anions therefore contribute to the negativity of the cytoplasm in relation to the extracellular fluid, contributing to the resting membrane potential (Donnan, F).

Another property of Gibbs-Donnan equilibria should be noted, looking at figure 3b it can be seen that the net concentration of NaCl in chamber A is greater than that of chamber B, this is due to the presence of protein anions in chamber A when establishing electrochemical equilibrium between ions, and is a general property of Gibbs-Donnan equilibria (Levy, N. et al.2006). Finally it is important to mention the equilibrium state of water, as previously mentioned chamber A contains a higher concentration of ions than chamber B, therefore there is a large osmotic gradient between the two chambers; This leads to a flux of water from chamber B to A, however, the osmotic effects of water influx on chamber A acts to dilute ion concentrations building up within the chamber, therefore hydrostatic pressure in chamber A would be insufficient to oppose water influx, leading to a depletion of water and NaCl ions from chamber B (Sperelakis, N.1998); However this situation does not resemble true Gibbs-Donnan equilibrium conditions, where by the build up of osmotic pressure in chamber A would resist the further osmotic influx of water, resulting in swelling of the chamber, if it were to be enclosed, such as a living cell (Sperelakis, N.1998). If unopposed gibbs-donnan equilibrium would cause the cytoplasm of living cells to have an osmotic pressure greater than that of the surrounding extracellular fluid, as water enters cells, control over cell volume may be lost (Sperelakis, N.1998). However this is not the case due to the cells ability to transport ions (Levy, N. et al.2006).

Ion transport

The resting membrane potential within skeletal muscle cells is around -80mV, this is due to the differing ion concentrations between the cytoplasm and surrounding extracellular fluid (ref), this difference in ion concentrations is maintained by the active transport of ions against there electrochemical gradient, powered by metabolic energy (ref). The ion pump of most importance to preserving potential difference across the cell membrane is the Na+/K+ATPase, this pumps out three Na+ in exchange for two extracellular K+, through the hydrolysis of a membrane bound ATPase, this ratio of 3:2 leaves the cytoplasm negative in respect to the extracellular fluid, and is therefore termed an electrogenic pump (Huang, F.et al.2009). Although the Na+/K+ATPase is responsible for only a small amount of the RMP between 12-16mV in skeletal myoblasts (Sperelakis, N.1998), overtime inhibition can lead to lack of cell excitability due to the accumulation of small depolarisations.

Ion Diffusion

To understand how Na+, K+ diffuse across the plasma membrane causing the RMP, their intra and extracellular concentrations must be established (Figure 4). Each ion is capable of establishing a RMP, therefore the potential depends on several factors, the permeability of the membrane to each ion, the intra and extracellular concentrations of each ion and the polarity of the ions (Guyton and Hall.2000). Firstly if the membrane is only permeable to a certain ion then that ion will be solely responsible for the generation of the RMP, for example, in a nerve fibre K+ concentration is greater in the cytoplasm than the extracellular fluid, if the membrane were only permeable to K+, then K+ would diffuse down its concentration gradient into the extracellular fluid until opposed by its electrical gradient, this would leave the cytoplasm with a negative charge of around -94mV with respect to the extracellular fluid, thus K+ would be responsible for a resting membrane potential of -94mV, as this is the Nernst potential for K+ (Guyton and Hall.2000). However the RMP cannot be caused by one ion alone, as the nerve cells has a RMP of -90mV, and the Nernst's potentials for K+ and Na+ are -94mV and +61mV respectively, therefore if the RMP was caused by one univalent ion it would be equal to that of their Nernst potential (Guyton and Hall.2000).

Due to the Nernst potential of K+, it can be assumed that this ion is the major contributor to the RMP, the cytoplasmic concentration of K+ is 35times higher than that of its extracellular concentration, and it diffuses through the membrane via Potassium-Sodium leak channels in which its is 100 times more permeable to than Na+ (Guyton and Hall. 2000). However Na+ also contributes to the RMP by low amounts of Na+ diffusing through the Potassium-Sodium leak channels, this small amount of diffusion leads to a ratio of 0:1 Na+ in the cytoplasm to the extracellular fluid, giving a Nernst potential of +61mV (Guyton and Hall. 2000). Using the Nernst potentials for Na+ and k+ in theGoldman-Hodgkin-Katz equationtheir contribution to the RMP can be established, this results in an internal membrane potential of -86mV (Guyton and Hall. 2000). The remaining -4mV comes from the contribution of the previously mentioned electrogenic Na+-K+ pump, leading to a RMP of -90mV in nerve fibres (Guyton and Hall. 2000).

Conclusion

To conclude, the RMP arises due to a combination of several factors most of which have been covered in the preceding discussions. The cell membranes structural properties allow for the capacitance and conductance of electrical charges, as well as the generation of electrical fields due to the negatively charged outer membrane, this works to aid in the formation of concentration gradients by which ions flow. In the presence of ionic species which are unable to permeate the cell membrane, such as anionic intracellular proteins, a Gibbs-Donnan equilibrium occurs, in which the distribution of permeable ions favour the intracellular environment due to the presence of impermeable anionic molecules, this disruption of ionic concentrations across the plasma membrane coupled with the presence of impermeable anionic molecules, brings about a negative intracellular environment, and thus a potential difference across the membrane. However in a closed system such as the eukaryotic cell, the Gibbs-Donnan equilibrium leads to a greater intracellular osmotic pressure, if unopposed this would lead to a loss of control over cell volume, therefore ion transporters are in place to dissipate ion concentration, like that of the Na+-K+ ATPase. The exchange ratio of 3:2 potassium for sodium respectively, performed by the Na+-K+ ATPase also contributes to the electronegative intracellular environment, and thus the resting membrane potential. The major cause of the RMP is however down to the diffusion of potassium into the extracellular fluid via Sodium-Potassium leak channels, coupled with the low extracellular diffusion of sodium and the aforementioned Na+-K+ ATPase and Gibbs-Donnan equilibrium conditions, the resting membrane potential is formed.

References

Sperelakis, N. 1998.Cell Physiology Source Book. Second edition. Californa: Academic Press.

Aidley, D. 1989.The Physiology of Excitable Cells. Third Edition. Cambridge: Cambridge University Press.

Levy, N. et al. 2006.Principles of Physiology. Fourth edition. Philadelphia: Elsevier Mosby.

Huang, F. el al. 2009. Distribution of the Na/K pumps' turnover rates As a function of membrane potential, temperature, and ion concentration gradients and effect of fluctuations.Journal of Physical Chemistry B113(23), pp. 8096-8102.

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