The Resting Membrane Potential

The different passive and active transport systems are coordinated in a living cell to maintain intracellular ions and other solutes at concentrations compatible with life. Consequently, the cell does not equilibrate with the extracellular fluid, but rather exists in a steady state with the extracellular solution. For example, intracellular Na+ concentration (10 mmol/L in a muscle cell) is much lower than extracellular Na+ concentration (140 mmol/L), so Na+ enters the cell by passive transport through nongated Na+ channels. The rate of Na+ entry is matched, however, by the rate of active transport of Na+ out of the cell via the sodium-potassium pump (Fig. 2.16). The net result is that intracellular Na+ is maintained constant and at a low level, even though Na+ continually enters and leaves the cell. The reverse is true for K.+ , which is maintained at a high concentration inside the cell relative to the outside. The passive exit of K+ through nongated K+ channels is matched by active entry via the pump (see Fig. 2.16). Maintenance of this steady state with ion concentrations inside the cell different from those outside the cell is the basis for the difference in electrical potential across the plasma membrane or the resting membrane potential.

Passive exit K+

Passive exit K+

Electrochemical Gradient

^FGUREIMH^^ The concept of a steady state. Na+ enters a ^mmmmmmmmm cejj through nongated Na+ channels, moving passively down the electrochemical gradient. The rate of Na+ en try is matched by the rate of active transport of Na+ out of the cell via the Na+/K+-ATPase. The intracellular concentration of Na+ remains low and constant. Similarly, the rate of passive K+ exit through nongated K+ channels is matched by the rate of active transport of K+ into the cell via the pump. The intracellular K+ concentration remains high and constant. During each cycle of the ATPase, two K+ are exchanged for three Na+ and one molecule of ATP is hydrolyzed to ADP. Large type and small type indicate high and low ion concentrations, respectively.

^FGUREIMH^^ The concept of a steady state. Na+ enters a ^mmmmmmmmm cejj through nongated Na+ channels, moving passively down the electrochemical gradient. The rate of Na+ en try is matched by the rate of active transport of Na+ out of the cell via the Na+/K+-ATPase. The intracellular concentration of Na+ remains low and constant. Similarly, the rate of passive K+ exit through nongated K+ channels is matched by the rate of active transport of K+ into the cell via the pump. The intracellular K+ concentration remains high and constant. During each cycle of the ATPase, two K+ are exchanged for three Na+ and one molecule of ATP is hydrolyzed to ADP. Large type and small type indicate high and low ion concentrations, respectively.

Ion Movement Is Driven by the Electrochemical Potential

If there are no differences in temperature or hydrostatic pressure between the two sides of a plasma membrane, two forces drive the movement of ions and other solutes across the membrane. One force results from the difference in the concentration of a substance between the inside and the outside of the cell and the tendency of every substance to move from areas of high concentration to areas of low concentration. The other force results from the difference in electrical potential between the two sides of the membrane, and it applies only to ions and other electrically charged solutes. When a difference in electrical potential exists, positive ions tend to move toward the negative side, while negative ions tend to move toward the positive side.

The sum of these two driving forces is called the gradient (or difference) of electrochemical potential across the membrane for a specific solute. It measures the tendency of that solute to cross the membrane. The expression of this force is given by:

Co where |x represents the electrochemical potential (A^, is the difference in electrochemical potential between two sides of the membrane); Ci and Co are the concentrations of the solute inside and outside the cell, respectively; Ei is the electrical potential inside the cell measured with respect to the electrical potential outside the cell (Eo),- R is the universal gas constant (2 cal/mol-K),- T is the absolute tem perature (K); z is the valence of the ion; and F is the Faraday constant (23 cal/mV-mol). By inserting these units in equation 5 and simplifying, the electrochemical potential will be expressed in cal/mol, which are units of energy. If the solute is not an ion and has no electrical charge, then z = 0 and the last term of the equation becomes zero. In this case, the electrochemical potential is defined only by the different concentrations of the uncharged solute, called the chemical potential. The driving force for solute transport becomes solely the difference in chemical potential.

Net Ion Movement Is Zero at the Equilibrium Potential

Net movement of an ion into or out of a cell continues as long as the driving force exists. Net movement stops and equilibrium is reached only when the driving force of electrochemical potential across the membrane becomes zero. The condition of equilibrium for any permeable ion will be A^, = 0. Substituting this condition into equation 5, we obtain:

Equation 6, known as the Nernst equation, gives the value of the electrical potential difference (Ej — Eo) necessary for a specific ion to be at equilibrium. This value is known as the Nernst equilibrium potential for that particular ion and it is expressed in millivolts (mV), units of voltage. At the equilibrium potential, the tendency of an ion to move in one direction because of the difference in concentrations is exactly balanced by the tendency to move in the opposite direction because of the difference in electrical potential. At this point, the ion will be in equilibrium and there will be no net movement. By converting to log10 and assuming a physiological temperature of 37°C and a value of + 1 for z (for Na+ or K+), the Nernst equation can be expressed as:

61 log1(

Since Na+ and K+ (and other ions) are present at different concentrations inside and outside a cell, it follows from equation 7 that the equilibrium potential will be different for each ion.

The Resting Membrane Potential Is Determined by the Passive Movement of Several Ions

The resting membrane potential is the electrical potential difference across the plasma membrane of a normal living cell in its unstimulated state. It can be measured directly by the insertion of a microelectrode into the cell with a reference electrode in the extracellular fluid. The resting membrane potential is determined by those ions that can cross the membrane and are prevented from attaining equilibrium by active transport systems. Potassium, sodium, and chloride ions can cross the membranes of every living cell, and each of these ions contributes to the resting membrane potential. By contrast, the permeability of the membrane of most cells to divalent ions is so low that it can be ignored in this context.

The Goldman equation gives the value of the membrane potential (in mV) when all the permeable ions are accounted for:

where PK, PNa, and PCl represent the permeability of the membrane to potassium, sodium, and chloride ions, respectively; and brackets indicate the concentration of the ion inside (i) and outside (o) the cell. If a certain cell is not permeable to one of these ions, the contribution of the impermeable ion to the membrane potential will be zero. If a specific cell is permeable to an ion other than the three considered in equation 8, that ion's contribution to the membrane potential must be included in the equation.

It can be seen from equation 8 that the contribution of any ion to the membrane potential is determined by the membrane's permeability to that particular ion. The higher the permeability of the membrane to one ion relative to the others, the more that ion will contribute to the membrane potential. The plasma membranes of most living cells are much more permeable to potassium ions than to any other ion. Making the assumption that PNa and PCl are zero relative to PK, equation 8 can be simplified to:

which is the Nernst equation for the equilibrium potential for K+ (see equation 6). This illustrates two important points:

• In most cells, the resting membrane potential is close to the equilibrium potential for K+.

• The resting membrane potential of most cells is dominated by K+ because the plasma membrane is more permeable to this ion compared to the others.

As a typical example, the K+ concentrations outside and inside a muscle cell are 3.5 mmol/L and 155 mmol/L, respectively. Substituting these values in equation 7 gives an equilibrium potential for K+ of —100 mV, negative inside the cell relative to the outside. The resting membrane potential in a muscle cell is —90 mV (negative inside). This value is close to, although not the same as, the equilibrium potential for K+.

The reason the resting membrane potential in the muscle cell is less negative than the equilibrium potential for K+ is as follows. Under physiological conditions, there is passive entry of Na+ ions. This entry of positively charged ions has a small but significant effect on the negative potential inside the cell. Assuming intracellular Na+ to be 10 mmol/L and extracellular Na+ to be 140 mmol/L, the Nernst equation gives a value of +70 mV for the Na+ equilibrium potential (positive inside the cell). This is far from the resting membrane potential of —90 mV. Na+ makes only a small contribution to the resting membrane potential because membrane permeability to Na+ is very low compared to that of K + .

The contribution of Cl— ions need not be considered because the resting membrane potential in the muscle cell is the same as the equilibrium potential for Cl—. Therefore, there is no net movement of chloride ions.

In most cells, as shown above using a muscle cell as an example, the equilibrium potentials of K + and Na+ are different from the resting membrane potential, which indicates that neither K + ions nor Na+ ions are at equilibrium.

Consequently, these ions continue to cross the plasma membrane via specific nongated channels, and these passive ion movements are directly responsible for the resting membrane potential.

The Na+/K+-ATPase is important indirectly for maintaining the resting membrane potential because it sets up the gradients of K + and Na+ that drive passive K+ exit and Na+ entry. During each cycle of the pump, two K+ ions are moved into the cell in exchange for three Na+, which are moved out (see Fig. 2.16). Because of the unequal exchange mechanism, the pump's activity contributes slightly to the negative potential inside the cell.

Essentials of Human Physiology

Essentials of Human Physiology

This ebook provides an introductory explanation of the workings of the human body, with an effort to draw connections between the body systems and explain their interdependencies. A framework for the book is homeostasis and how the body maintains balance within each system. This is intended as a first introduction to physiology for a college-level course.

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Responses

  • nicolas kerr
    How does active and passive transport help maintain a cells intracellular concentration of k?
    5 years ago
  • Wolfgang
    Is resting membrane potential maintained by passive transport?
    4 years ago
  • Chris
    What solutes are in high concentration inside a resting cell?
    4 years ago
  • melba
    Which ions are actively transported through the cell membrane to maintain a resting potential?
    4 years ago
  • dirk
    What is the resting potential for skeletal muscle?
    7 months ago

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