goldman equation/gibbs-donnan equilibrium

  1. can anyone explain these concepts in easier-to-grasp forms? preferrably with numeric examples. thanks~
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  2. 5 Comments

  3. by   bethem
    No reply on SDN, eh?
  4. by   CRNA, DNSc
    Start with understanding the Nerst equation which refers to a single ion. EMF (millivolts) = + 61 log of concentration inside/concentration outside

    The calculated number indicates the electromotive force that would exactly oppose diffusion of a single ion across a permable membrane even in the face a concentration gradient.

    The next step is the Goldman equation which can be used to calculate the EMF required to oppose diffusion of several different ions when the membrane is permeable to more than one ion.

    Reference- Textbook of Medical Physiology by Guyton & Hall, 2006, 11th edition, pg58.

    Hope this helps!
  5. by   dfk
    Quote from bethem
    No reply on SDN, eh?
    bethem,
    not even a lick...

    Quote from CRNA, DNSc
    Start with understanding the Nerst equation which refers to a single ion. EMF (millivolts) = + 61 log of concentration inside/concentration outside

    The calculated number indicates the electromotive force that would exactly oppose diffusion of a single ion across a permable membrane even in the face a concentration gradient.

    The next step is the Goldman equation which can be used to calculate the EMF required to oppose diffusion of several different ions when the membrane is permeable to more than one ion.

    Reference- Textbook of Medical Physiology by Guyton & Hall, 2006, 11th edition, pg58.

    Hope this helps!
    thanx crna/dnsc...
    still working on it tho~
  6. by   brownie1129
    Quote from dfk
    can anyone explain these concepts in easier-to-grasp forms? preferrably with numeric examples. thanks~
    This helped me:

    Positive charges are oriented toward the outer surface of the membrane and negative charges are oriented toward the inner surface of the membrane. The lipid bilayer acts as a barrier to diffusion of ions; nongated channels allow selective movement of ions.

    Unequal distribution of electrolytes across the cell membrane - Na+ and Cl− are at higher concentrations in the ECF. K+ and large anions (proteins, organic polyphosphate compounds, nucleic acids, etc.) are at higher concentration in the ICF.

    Membrane permeability (P) or conductance (g) - Even at very high membrane potentials there is virtually no ionic current flow through the lipid bilayer because of high resistance. Nongated channels permit some diffusion of Na+, K+, and Cl− (leak currents) through the resting membrane. The resting membrane is moderately permeable to K+ and only slightly permeable to Na+ and Cl−. Relative permeabilities - PK+ : PNa+ = 1.0:0.04, therefore the membrane is about 25 more permeable to K+ than to Na+. PK+ : PCl− = 1.0:0.45, therefore the membrane is about 2.2 more permeable to K+ than to Cl−. The cell membrane is impermeable to the large intracellular anions.

    Basis for unequal ion concentrations across the membrane - Most of the anions in the intracellular fluid are large, organic anions that cannot pass through the cell membrane. These anions attract cations into the cell. Since the resting cell membrane is mostly permeable to K+, K+ ions pair up with intracellular anions. K+ is the predominant intracellular cation, while Na+ is the predominant extracellular cation. Cl- can pass through the cell membrane but is mostly paired up aawith Na+ in the ECF.

    The Na+-K+ pump - An important function is to maintain cell volume. By maintaining a low intracellular Na+ concentration, the Na+-K+ pump helps to prevent swelling and lysis of cells. During hypoxia or when the Na+-K+ pump is severely inhibited, intracellular Na+ increases, more water enters the cell by osmosis, and the cell eventually ruptures. The Na+-K+ pump balances leak currents - At rest, the leakage of Na+ and K+ are exactly balanced by the Na+-K+ pump, therefore the concentration gradients for these ions are maintained. Because the pump moves 3 Na+ out of the cell for every 2 K+ it moves into the cell it causes a net transfer of positive charges out of the cell; this constitutes a pump current.

    Diffusion Potentials - The force that causes a substance to diffuse through a solution from an area of high concentration to an area of low concentration is a chemical force; this force moves particles down their concentration gradient. As a charged particle diffuses due to a chemical force, a separation of charge develops; the attraction of opposite charges is an electrical force that acts in opposition to a chemical force. Thus, when there is unequal distribution of an ion across a membrane and the membrane is permeable to the ion, passive diffusion of the ion produces an electrical potential across the membrane.

    Equilibrium potential (or Nernst potential) - The electrical driving force that is equal and opposite to the chemical driving force. Describes a point that is reached at which the driving force of the chemical gradient for ion is exactly counteracted by the electrical attraction of the excess anions on the inside of the membrane and the electrical repulsion of the excess cations on the outside of the membrane; this is the electrochemical equilibrium.

    NOTE: The Nernst equation assumes that the membrane is freely permeable to the ion in question. In other words, the equation only holds true under conditions when the membrane is substantially permeable to the subject ion.

    Nernst equation can be thought of as a tool that converts the energy in the form of a concentration gradient into electrical units of potential difference (mV).

    Significance of Nernst potentials - For a given ion, the Nernst potential is the potential at which there is no net flux of that ion across the membrane. The greater the difference between the membrane potential and the Nernst potential of an ion(Em - Ex), the greater the driving force for movement of that ion across the membrane. If a membrane becomes more permeable to a particular ion, the resulting ionic current will cause the membrane potential to change in the direction of the Nernst potential of that ion. When a membrane is permeable to more than one ion species, each ion tends to force the membrane potential toward its own Nernst Potential. Only ions to which the membrane is permeable and who's chemical gradients are actively maintained can influence the ER. The more permeable the membrane is to a given ion, the more influence that ion will have on the membrane potential. K+ more permeable than Cl- which is more permeable to Na+. Movement of Cl− ions tends toward an equilibrium across the membrane, so the Nernst potential for Cl− is equal to the resting potential and there is no net diffusion of Cl− at rest.

    Gibbs Donnan:

    This situation is called a Gibbs-Donnan equilibrium a. The diffusible cation concentration, [K+], will be higher on the side of the impermeant anion, A- (Intracellular) b. The diffusible anion concentration [Cl-], will be lower on the side of the impermeant anion, A- (Intracellular) c. More water moves into the side of the impermeant anion than would be predicted on the basis of the [A-] alone

    PM me with your personal email and I will send you some files that may be more helpful.

    Brownie
  7. by   gatormac2112
    i have no idea about the gibbs-donnan equilibrium as i haven't studied that, but i'll give the goldman equation a go. i am not a science wiz so please correct me if i am wrong.

    a ton of cell functions have to do with concentrations of ions (na+, k+, cl-) inside and outside the cell. these different concentrations create both a chemical gradient and an electrical gradient.

    the chemical gradient is as simple as going from an area of high concentration to low concentration. for example, intracellular k+ is roughly 140meq/l and extracellular is roughly 4meq/l. since there is alot more k+ inside the cell k+ will leave the cell whenever it can (this happens through protein channels in the cell wall).

    the electrical gradient is as simple as this: ions have an electrical charge and potassium is positive (k+). also, k+ is about 100x more permeable to the cell wall than na+, so it leaves the cell much easier. as it leaves the cell to the extracellular fluid the inside of the cell becomes more negative than the outside of the cell. as you know, opposites attract, and the positive k+ ion flows back into the cell as it is attracted to the intracellular negative charge.

    therefore, there comes a point where the ions go out and then come back in---this is the point at which the equilibrium potential for that ion is reached. it can be determined by the nernst equation for each ion. this equation is basically: 61/z x log(outside concentration/inside concentration). the books do it a bit differently, but this works. the z stands for the ions valence, i.e., k+ is +1, na+ is +1, cl- is -1, ca++ is +2. lets do one for k+ and na+:

    k+ intracellular= 140meq/l
    k+ extracellular= 4meq/l

    nernst eq. potential= 61/1 x log(4/140) = -94

    na+ intracellular= 14meq/l
    na+ extracellular= 142meq/l

    nernst eq. potential= 61/1 x log(142/14) = +61

    so, you have -94 for k+ and +61 for na+. how does this help to determine the resting membrane potential for the cell? thats where the goldman equation comes in. it is basically a modified nernst equation with the each ions permeability factor thrown in. only 3 ions (k+, na+ and cl-) have any real effect on the resting membrane potential, but lets do na+ and k+ to keep it simple:

    pk = permeability to k+, pna = permeability to na+, k-out is concentration of k+ outside the cell and so on.

    goldman = 61 x log[pk(k-out) + pna(na-out)/pk(k-in) + pna(na-in)]

    as i said before, k+ is about 100x more permeable than na+. therefore, pk = 100 and pna = 1.

    61 x log 100(4)+1(142) = -86
    ...........100(140)+1(14)

    so your resting membrane potential for the cell considering the ions k+ and na+ is -86.

    does this help at all or have i just made things worse?

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