Physiology 5th Ed.
DIFFUSION POTENTIALS AND EQUILIBRIUM POTENTIALS
Ion Channels
Ion channels are integral, membrane-spanning proteins that, when open, permit the passage of certain ions. Thus, ion channels are selective and allow ions with specific characteristics to move through them. This selectivity is based on both the size of the channel and the charges lining it. For example, channels lined with negative charges typically permit the passage of cations but exclude anions; channels lined with positive charges permit the passage of anions but exclude cations. Channels also discriminate on the basis of size. For example, a cation-selective channel lined with negative charges might permit the passage of Na+ but exclude K+; another cation-selective channel (e.g., nicotinic receptor on the motor end plate) might have less selectivity and permit the passage of several different small cations.
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Ion channels are controlled by gates, and, depending on the position of the gates, the channels may be open or closed. When a channel is open, the ions for which it is selective can flow through it by passive diffusion, down the existing electrochemical gradient. When the channel is closed, the ions cannot flow through it, no matter what the size of the electrochemical gradient. The conductance of a channel depends on the probability that it is open. The higher the probability that the channel is open, the higher is its conductance or permeability.
The gates on ion channels are controlled by three types of sensors. One type of gate has sensors that respond to changes in membrane potential (i.e., voltage-gated channels); a second type of gate responds to changes in signaling molecules (i.e., second-messenger-gated channels); and a third type of gate responds to changes in ligands such as hormones or neurotransmitters (i.e., ligand-gated channels).
Voltage-gated channels have gates that are controlled by changes in membrane potential. For example, the activation gate on the nerve Na+channel is opened by depolarization of the nerve cell membrane; opening of this channel is responsible for the upstroke of the action potential. Interestingly, another gate on the Na+ channel, an inactivation gate, is closed by depolarization. Because the activation gate responds more rapidly to depolarization than the inactivation gate, the Na+ channel first opens and then closes. This difference in response times of the two gates accounts for the shape and time course of the action potential.
Second messenger-gated channels have gates that are controlled by changes in levels of intracellular signaling molecules such as cyclic adenosine monophosphate (cyclic AMP) or inositol 1,4, 5-triphosphate (IP3). Thus, the sensors for these gates are on the intracellular side of the ion channel. For example, the gates on Na+ channels in cardiac sinoatrial node are opened by increased intracellular cyclic AMP.
Ligand-gated channels have gates that are controlled by hormones and neurotransmitters. The sensors for these gates are located on the extracellular side of the ion channel. For example, the nicotinic receptor on the motor end plate is actually an ion channel that opens when acetylcholine (ACh) binds to it; when open, it is permeable to Na+ and K+ ions.
Diffusion Potentials
A diffusion potential is the potential difference generated across a membrane when a charged solute (an ion) diffuses down its concentration gradient. Therefore, a diffusion potential is caused by diffusion of ions. It follows, then, that a diffusion potential can be generated only if the membrane is permeable to that ion. Furthermore, if the membrane is not permeable to the ion, no diffusion potential will be generated no matter how large a concentration gradient is present.
The magnitude of a diffusion potential, measured in millivolts (mV), depends on the size of the concentration gradient, where the concentration gradient is the driving force. The sign of the diffusion potential depends on the charge of the diffusing ion. Finally, as noted, diffusion potentials are created by the movement of only a few ions, and they do not cause changes in the concentration of ions in bulk solution.
Equilibrium Potentials
The concept of equilibrium potential is simply an extension of the concept of diffusion potential. If there is a concentration difference for an ion across a membrane and the membrane is permeable to that ion, a potential difference (the diffusion potential) is created. Eventually, net diffusion of the ion slows and then stops because of that potential difference. In other words, if a cation diffuses down its concentration gradient, it carries a positive charge across the membrane, which will retard and eventually stop further diffusion of the cation. If an anion diffuses down its concentration gradient, it carries a negative charge, which will retard and then stop further diffusion of the anion. The equilibrium potential is the diffusion potential that exactly balances or opposes the tendency for diffusion down the concentration difference. At electrochemical equilibrium, the chemical and electrical driving forces acting on an ion are equal and opposite, and no further net diffusion occurs.
The following examples of a diffusing cation and a diffusing anion illustrate the concepts of equilibrium potential and electrochemical equilibrium:
Example of Na+ Equilibrium Potential
Figure 1-11 shows two solutions separated by a theoretical membrane that is permeable to Na+ but not to Cl−. The NaCl concentration is higher in Solution 1 than in Solution 2. The permeant ion, Na+, will diffuse down its concentration gradient from Solution 1 to Solution 2, but the impermeant ion, Cl−, will not accompany it. As a result of the net movement of positive charge to Solution 2, an Na+ diffusion potential develops and Solution 2 becomes positive with respect to Solution 1. The positivity in Solution 2 opposes further diffusion of Na+, and eventually it is large enough to prevent further net diffusion. The potential difference that exactly balances the tendency of Na+ to diffuse down its concentration gradient is the Na+ equilibrium potential. When the chemical and electrical driving forces on Na+ are equal and opposite, Na+ is said to be at electrochemical equilibrium. This diffusion of a few Na+ions, sufficient to create the diffusion potential, does not produce any change in Na+ concentration in the bulk solutions.
Figure 1-11 Generation of an Na+ diffusion potential.
Example of Cl− Equilibrium Potential
Figure 1-12 shows the same pair of solutions as in Figure 1-11; however, in Figure 1-12, the theoretical membrane is permeable to Cl− rather than to Na+. Cl− will diffuse from Solution 1 to Solution 2 down its concentration gradient, but Na+ will not accompany it. A diffusion potential will be established, and Solution 2 will become negative relative to Solution 1. The potential difference that exactly balances the tendency of Cl− to diffuse down its concentration gradient is the Cl− equilibrium potential. When the chemical and electrical driving forces on Cl− are equal and opposite, then Cl− is at electrochemical equilibrium. Again, diffusion of these few Cl− ions will not change the Cl−concentration in the bulk solutions.
Figure 1-12 Generation of a Cl− diffusion potential.
Nernst Equation
The Nernst equation is used to calculate the equilibrium potential for an ion at a given concentration difference across a membrane, assuming that the membrane is permeable to that ion. By definition, the equilibrium potential is calculated for one ion at a time.Thus,
where
EX
= Equilibrium potential (mV) for a given ion, X
= Constant (60 mV at 37°C)
z
= Charge on the ion (+1 for Na+; +2 for Ca2+; −1 for Cl−)
Ci
= Intracellular concentration of X (mmol/L)
Ce
= Extracellular concentration of X (mmol/L)
In words, the Nernst equation converts a concentration difference for an ion into a voltage. This conversion is accomplished by the various constants: R is the gas constant, T is the absolute temperature, and F is Faraday’s constant; multiplying by 2.3 converts natural logarithm to log10.
By convention, membrane potential is expressed as intracellular potential relative to extracellular potential. Hence, a transmembrane potential difference of −70 mV means 70 mV, cell interior negative.
Typical values for equilibrium potential for common ions, calculated as previously described and assuming typical concentration gradients across cell membranes, are as follows:
ENa+ = +65 mV
ECa2+ = +120 mV
EK+ = -85 mV
ECl- = -90 mV
It is useful to keep these values in mind when considering the concepts of resting membrane potential and action potentials.
SAMPLE PROBLEM. If the intracellular [Ca2+] is 10−7 mol/L and the extracellular [Ca2+] is 2 × 10−3 mol/L, at what potential difference across the cell membrane will Ca2+ be at electrochemical equilibrium? Assume that 2.3RT/F = 60 mV at body temperature (37°C).
SOLUTION. Another way of posing the question is to ask what the membrane potential will be, given this concentration gradient across the membrane, if Ca2+ is the only permeant ion. Remember, Ca2+ is divalent, so z = +2. Thus,
Because this is a log function, it is not necessary to remember which concentration goes in the numerator. Simply complete the calculation either way to arrive at 129 mV, and then determine the correct sign with an intuitive approach. The intuitive approach depends on the knowledge that, because the [Ca2+] is much higher in ECF than in ICF, Ca2+ will tend to diffuse down this concentration gradient from ECF into ICF, making the inside of the cell positive. Thus, Ca2+ will be at electrochemical equilibrium when the membrane potential is +129 mV (cell interior positive).
Be aware that the equilibrium potential has been calculated at a given concentration gradient for Ca2+ ions. With a different concentration gradient, the calculated equilibrium potential would be different.
Driving Force
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When dealing with uncharged solutes, the driving force for net diffusion is simply the concentration difference of the solute across the cell membrane. However, when dealing with charged solutes (i.e., ions), the driving force for net diffusion must consider both concentration difference and electrical potential difference across the cell membrane.
The driving force on a given ion is the difference between the actual, measured membrane potential (Em) and the ion’s calculated equilibrium potential (EX). In other words, it is the difference between Em and what that ion would “like” the membrane potential to be (its equilibrium potential, as calculated by the Nernst equation). The driving force on a given ion, X, is therefore calculated as:
Net driving force (mV) = Em – Ex
where
Driving force
= Driving force (mV)
Em
= Actual membrane potential (mV)
EX
= Equilibrium potential for X (mV)
When the driving force is negative (i.e., Em is more negative than the ion’s equilibrium potential), that ion X will enter the cell if it is a cation and will leave the cell if it is an anion. In other words, ion X “thinks” the membrane potential is too negative and tries to bring the membrane potential toward its equilibrium potential by diffusing in the appropriate direction across the cell membrane. Conversely, if the driving force is positive (Em is more positive than the ion’s equilibrium potential), then ion X will leave the cell if it is a cation and will enter the cell if it is an anion; in this case, ion X “thinks” the membrane potential is too positive and tries to bring the membrane potential toward its equilibrium potential by diffusing in the appropriate direction across the cell membrane. Finally, if Em is equal to the ion’s equilibrium potential, then the driving force on the ion is zero, and the ion is, by definition, at electrochemical equilibrium.
Ionic Current
Ionic current (IX), or current flow, occurs when there is movement of an ion across the cell membrane. Ions will move across the cell membrane through ion channels when two conditions are met: (1) there is a driving force on the ion and (2) the membrane has a conductance to that ion (i.e., its ion channels are open). Thus,
Ix = Gx (Em – Ex)
Where
IX
= ionic current (mAmps)
GX
= ionic conductance (1/ohms), where conductance is the reciprocal of resistance
Em − EX
= driving force on ion X (mV)
You will notice that the equation for ionic current is simply a rearrangement of Ohm’s law, where V = IR or I = V/R (where V is the same thing as E). Because conductance (G) is the reciprocal of resistance (R), I = G × V.
The direction of ionic current is determined by the direction of the driving force, as described in the previous section. The magnitude of ionic current is determined by the size of the driving force and the conductance. For a given conductance, the greater the driving force, the greater the current flow. For a given driving force, the greater the conductance, the greater the current flow. Lastly, if either the driving force or the conductance of an ion is zero, there can be no diffusion of that ion across the cell membrane and no current flow.
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