I.  Introduction

A. The body and electricity, basic principles

- the body is electrically neutral (total), however there are areas where opposite charges are separated by a distance (membrane) - work must be done to keep them apart, energy (NRG) liberated when they come together.

- separated opposite charges have potential NRG, measured in volts; thus voltage is the difference in potential between two areas of opposite charge.

- the flow of electrical charge from one point to the other is current.

- Current (I) = Voltage (V)/Resistance (R)

- in the body electrical charges are ions; there is an unequal distribution of ions between the ICF and ECF - a voltage

- in body electrical currents are flow of ions across membranes; ions cross membranes through channels, ion channels, three types:

• passive (leakage) channels: always open.
• chemically-gated channels: open upon ligand binding.
• voltage-gated channels: open/close in response to changes in membrane potential.

- keep in mind that ions diffuse across membrane through channels down both chemical and electrical gradients.

- in the body resistance is the membrane permeability to a specific ion

B.  The resting membrane potential (RMP) -- overview (Figure 3-26)

- membrane without potential (a) -- an equal number of + and - charges on each side of the membrane

- membrane has potential (b) -- difference in relative amount of + and - charges between the two sides; separation of opposite charges across membrane

- attractive forces between separated opposite charges causes them to accumulate in a thin layer across outer and inner surface of the plasma membrane (c, d)

• fluid outside the cells and inside the cells is electrically neutral
• a very small number of charged particles present in body fluids is responsible for the RMP 

- magnitude of RMP depends on the degree of separation of the opposite charges (e)

II.  Generation and maintenance of the RMP

-  membrane potential in all living cells characterized by slight excess of positive charge outside and negative charge inside

A.  Ions responsible for generation of RMP

- ion concentration differences set up and maintained by Na⁺/K⁺ ATPase

-  plasma membrane virtually impermeable to A^- -- found only inside the cell

-  membrane has many more leakage channels for K⁺ than for Na⁺

-  note electrochemical gradients for Na⁺ and K⁺ at rest

B.  Contribution of Na⁺/K⁺ pump to RMP

-  Na⁺/K⁺ pump accounts for 10-20% of RMP

-  due to electrogenic nature of pump

- remaining 80-90% of RMP accounted for by passive diffusion of Na⁺ and K⁺ down concentration gradient

- the critical role of the Na⁺/K⁺ pump is to maintain the concentration gradients for Na+ and K+ that are DIRECTLY responsible for ion diffusion that accounts for majority of RMP

C.  Effect of K⁺ diffusion alone on RMP

- hypothetical situation:

• K⁺ and A^- distributed as usual across membrane
• free membrane permeability to K⁺ but not to A^-
• no potential as yet present

- K⁺ moves to outside along concentration gradient -- negative charges in form of A^- cannot follow to maintain electroneutrality

- as K⁺ accumulates outside membrane a membrane potential now exists

• chemical gradient for K⁺ diffusion to outside

• electrical gradient for K⁺ diffusion to inside

- initially chemical gradient for K⁺ diffusion greater than electrical gradient -- K⁺ continues to move to ECF

- as K⁺ moves out, the electrical gradient increases, chemical gradient stays the same (doesn't decrease because only infinitely small numbers of K⁺ ions need to move out to produce changes in membrane potential)

- at some point electrical gradient equals the concentration gradient -- net diffusion of ion stops

•  K⁺ is at electrochemical equilibrium:  electrical gradient counteracts concentration gradient -- no net flux.

• membrane potential that occurs at electrochemical equilibrium is the equilibrium potential for K⁺ 

• NOTE that a large concentration gradient for K⁺ still exists but no more net movement of K⁺ occurs because the concentration gradient is exactly balanced by electrical gradient

- therefore the equilibrium potential (E) for an ion is the voltage that must be applied to a membrane to stop net movement of ion along concentration gradient.

-  equilibrium potential for an ion can be calculated using the Nernst equation:

E = 61 log (Co/Ci) where

• E = equilibrium potential for an ion in mV

• 61 = a constant that incorporates the universal gas constant (R), absolute temperature (T), the ion's valence (z), and an electrical constant, Faraday; thus 61 = RT/zF

• Co = concentration of ion outside the cell in millimoles/liter (millimolars, mM)

• Ci = concentration of the ion inside the cell in mM

- solving about for K⁺, E_K+ = -90 mV

• this means that the membrane potential when K⁺ has reached electrochemical equilibrium is -90 mV

• the membrane potential is always expressed relative to the inside of the membrane

• thus E_K+ = -90 mV means that a potential of 90 mV, with the inside of the membrane negative relative to the outside, must be applied to the membrane to stop net diffusion of K+ across membrane

D.  Effect of Na⁺ diffusion alone on RMP

- hypothetical situation:

• Na⁺ and A^- distributed as usual across membrane
• free membrane permeability to Na⁺ but not to A^-
• no potential as yet present

- Na⁺ moves along concentration gradient to inside of cell

- as Na⁺ accumulates inside membrane a membrane potential now exists

• chemical gradient for Na⁺ diffusion to inside

• electrical gradient for Na⁺ diffusion to outside

- initially chemical gradient for Na⁺ diffusion greater than electrical gradient -- Na⁺ continues to move to inside of cell

- as Na⁺ moves in, the electrical gradient increases, chemical gradient stays the same

- at some point electrical gradient equals the concentration gradient -- net diffusion of ion stops, equilibrium potential for Na⁺ has been reached

- E_Na+ = + 60 mV; this means:

• a potential of 60 mV, with the inside of the membrane positive relative to outside, must be applied to the membrane to stop net diffusion of Na⁺ across membrane

E.  Effects of K⁺ and Na⁺ diffusion on the RMP 

- equilibrium potentials as discussed above only exist in theoretical or experimental conditions as the joint effects of Na⁺ and K⁺ must be taken into account

- the greater the permeability of membrane for a given ion, the greater the tendency for that ion to drive the membrane potential toward its own equilibrium potential

• at rest membrane is far more permeable to K⁺ than to Na⁺, thus K⁺ influences membrane potential far more than Na⁺
• however, during part of the action potential, the membrane become far more permeable to Na⁺ than to K⁺ -- at this point Na⁺ influences membrane potential far more than K⁺ and the membrane potential approaches the value of E_Na+

- thus at rest membrane far more permeable to K⁺ than to Na⁺

• K⁺ tends to leave cell and drive membrane potential to E_K+
• however membrane potential never reaches E_K+ because membrane very slightly permeable to Na⁺
• in other words some of the diffusion of Na⁺ neutralizes the potential created by K⁺ alone -- the RMP brought to -70 mV, slightly less than E_K+

- thus at resting potential neither Na⁺ nor K⁺ is at equilibrium -- there is continual tendency to K⁺ to passively exit and for Na⁺ to enter cell through leakage channels, down their electrochemical gradients -- however more K⁺ enters than Na⁺ leaves -- this is the basis of the RMP in all cells

- note the critical role of the Na⁺/K⁺ ATPase in maintaining the concentration gradients for Na⁺ and K⁺ constant across membrane 

• thus resting membrane potential remains constant -- even though Na⁺ and K⁺ are not at equilibrium, there is no net movement of any ions across membrane, with active transport of Na⁺ and K⁺ counterbalancing the rate of passive leakage for each ion

F.  The effect of Cl^- on RMP

-  Cl^- does not influence the membrane potential of a cell -- instead the membrane potential passively influences the Cl^- distribution across membrane

• this is because there are no active transport mechanisms for Cl^- and membrane is very permeable to Cl^-

• in the resting state, the excess of negative charge inside the membrane drives the negative Cl^- outside of the cell until a concentration gradient is created that exactly balances this electrical gradient -- thus at rest concentration of Cl^- outside the cell greater than inside

III.  Importance of RMP to excitable tissue

- nerve and muscle uses changes in RMP as communicating signals for receiving, integrating, sending information, or for contraction

- changes in membrane potential are achieved by either changing the membrane permeability to a specific ion, or by any factor that affects the ion concentration on either side of the membrane.

- changes in MP greater than RMP (more negative than RMP) -- hyperpolarization.

- changes in MP less than RMP (less negative) -- depolarization.