Membrane Potentials

Question 1

What is the relationship of K+, Na+, and Cl- concentrations inside and outside the cell?

What is standard osmolarity?

Answer 1

• K+ concentration is generally high intracellularly and lower extracellularly, while Na+ and Cl- are high extracellularly and lower intracellularly
• standard osmolarity: 285 mOsM

Question 2

What are the differences between voltage-gated channels vs. ligand-gated channels?

Answer 2

• voltage gated channels have gates controlled by change in membrane potential (e.g. sodium and potassium channels)
• ligand-gated channels have gates controlled by binding of ligand, such as a NT (e.g. acetylcholine receptors)

Question 3

• potential difference generated across membrane when ion diffuses down conc gradient
• magnitude of diffusion depends on size of conc gradient
• conc gradient is driving force
• usually measured in millivolts (mV)

Answer 3

diffusion potential

Question 4

What determines equilibrium potential within a cell?

Answer 4

• chemical forces (conc gradient) and electrical forces (electrical potential)
• can be mathematically calculated by the Nernst equation

Question 5

What is the simplified Nernst equation? (yes, you do need to know this and be able to use it)

Answer 5

(when RT/F at 37 degrees = 26.8 mV and ln(x) = 2.3log(x))

Question 6

What are the approximate conc of the following ions in ECF and ICF?

a) Na+
b) K+
c) Ca2+
d) Cl-

Answer 6

a) Na+: ECF (140) and ICF (14)
b) K+: ECF (4) and ICF (120)
c) Ca2+: ECF (2.5) and ICF (0.0001)
d) Cl-: ECF (105) and ICF (10)

Question 7

What are the typical values for equilibrium potential for these ions in skeletal muscle?

a) Na+
b) K+
c) Ca2+
d) Cl-

Answer 7

a) Na+: +65 mV
b) K+: -95 mV
c) Ca2+: +120 mV
d) Cl-: -90 mV

Question 8

What is the difference in diffusion equilibrium for charged vs uncharged substances?

Answer 8

uncharged substances (e.g. sucrose_ are only influenced by conc gradient as the driving force, electrical force does not influence equilibrium stated in uncharged substances

Question 9

What must driving force for net diffusion of ions account for?

What is the equation for net driving force?

Answer 9

• must account for conc gradient and electrical potential across membrane
• net driving force (mV) = Em- Ex

(Em = membrane potential (mV) and Ex = equilibrium potential for given ion (mV)

Question 10

What will occur within the cell if:

• driving force is negative (Em is more negative that Ex):
• driving force is positive (Em is more positive that Ex):
• driving force is zero (Em and Ex are equal):

Answer 10

• driving force is negative (Em is more negative that Ex): cation will enter the cell, anion will leave the cell
• driving force is positive (Em is more positive that Ex): cation will leave the cell, anion will enter the cell
• driving force is zero (Em and Ex are equal): no net movement of ions

Question 11

What is the equation for ionic current? (current generated by movement of charged ions across membrane)

Answer 11

ionic current = Gx (driving force of given ion)

• this equation is a rearrangement of Ohm’s law equation (V=IR) where V is voltage (same as E) and R is resistance
• since G is the reciprocal of resistance, Ohm’s law equation can be arranged to estimate ionic current: I = G x V

LOL I LOVE HOW I THOUGHT I WOULD BE DONE W/ PHYSICS IN MED SCHOOL, LOLOLOL GUESS NOT

Question 12

What are the two factors that affect ionic current across cell membrane?

Answer 12

• difference between equilibrium potential for given ion and actual membrane potential (i.e. driving force = Em - Ex): larger the difference between Em and Ex, the larger the imbalance between electrical and conc gradients, thus a larger net movement of given ion
• permeability of membrane to given ion: if perm high, ionic current at particular value of driving force will be higher than if permeability was low, permeability is closely related to conductance (an index of ability of an ion to carry current across a membrane, for a given driven force the greater the conductance the greater the current flow)

Question 13

What two factors determine the membrane potential?

Answer 13

• ion concentrations: conc gradients (e.g. sodium-potasium ATPase)
• relative ion permeabilities: determine relative importance of particular ion in governing where Em lies, ions w/ highest permeabilities/conductances at rest will make greatest contribution to resting membrane potential (if cell membrane is highly permeable to ion, that ion can respond readily to deviations away from its equilibrium potential and Em will tend to be near that equilbrium potential)

Question 14

• equation that gives a quantitative relation between Em on one hand and ion conc and permeabilities on other hand
• interpretation: combination of outwardly directed K+ gradient (product of sod-pot ATPase activity) and high permeability of membrane to K+ makes the ICF electrically negative w/ respect to ECF; however, the finite permeability of membrane to Na+ and Cl- prevents the membrane potential from reaching the Nernst potential for K+

Answer 14

Goldman-Hodgkin-Katz equation

Question 15

What is the role of the sodium-potassium ATPase pump?

Answer 15

• electrogenic contribution: 3 Na+ ions pumped out of the cell for every 2 K+ ions pumped into the cell
• maintains conc gradients of Na+ and K+

Question 16

• alternate equation to the Goldman equation
• considers the equilibrium potential for each ion by its relative conductance
• ions w/ highest conductance drive membrane potential toward their equilibrium, ions w/ low conductance have little influence on membrane potential

Answer 16

Chord conductance equation

Question 17

• this potential is generated by a transient dramatic increase in sodium permeability (and conductance) due to the activation of voltage-gated Na+ channels
• this potential is the basic signal of the nervous system

Answer 17

action potential

Question 18

What are the characteristics of an action potential?

Answer 18

• triggered by depolarization
• threshold level of depolarization must be reached to trigger AP
• all or nothing events
• propagation of AP’s from one site to the next is nondecremental (magnitude is preserved)
• at hte peak of the AP, membrane potential reverses sign becoming inside positive
• after a neuron/cell fire an AP, there is a brief period in which it is impossible to trigger another AP (i.e. absolute refractory period)

Question 19

Describe the following parts and phases of the action potential:

• resting membrane potential:
• threshold potential:
• depolarizing phase:
• peak:
• overshoot:
• repolarization phase:
• undershoot:
• hyperpolarizing phase:

Answer 19

• resting membrane potential: steady state; cell interior negative (~ -70 mV)
• threshold potential: membrane potential at which the depolarization level is enough to trigger an AP
• depolarizing phase: membrane potential becomes less negative than the resting membrane potential (Na+ influx dominates, causes inward current, becomes self-sustained giving rise to upstroke)
• peak: maximum amplitude (depolarization) of the AP
• overshoot: membrane potential transiently overshoots zero, and the inside of the cell becomes positive w/ respect to the outside for a brief period of time
• repolarization phase: upstroke is terminated, and the membrane repolarizes to the resting level
• undershoot: (hyperpolarizing afterpotential) when the AP repolarizes toward the normal resting membrane potential, it transiently becomes more negative than normal
• hyperpolarizing phase: the membrane potential becomes more negative than the resting membrane potential

Question 20

What is the relation of ion concentration within the cell and action potential?

Answer 20

• Na+ increases during the action potential, it’s concentration generally follows the same pattern as the action potential does on an mV x time graph, while K+ begins increasing once the AP has reached its peak and K+ is highest when the AP is going into undershoot (declining)
• conduction state of sodium channel depends on membrane potential (since it is a voltage-gated sodium channel)
• when membrane is depolarized, permeability of Na+ increases, allowing Na+ ions to carry positive charge into the cell, this depolarizes cell further, causing greater increase in permeability of Na+ and more depolarization
• this process is explosive and tends to continue until all sodium channels are open and membrane potential has been driven up near equilibrium potential of Na+

Question 21

What causes the Em (membrane potential) to return to rest after the action potential?

Answer 21

1. depolarization-induced increase in permeability of Na+ (pNa) is transient
2. there is a delayed, voltage-dependent increase in permeability of K+ (pK)

Question 22

How do ions (Na+ in particular) control repolarization after an action potential?

Answer 22

• the voltage-dependent sodium channel is controlled by activation/inactivation (acts as if flow of Na+ is controlled by two independent gates)
• activation gate: closed when membrane potential is equal to or more negative than the usual resting membrane potential (prevents Na+ from entering the cell at resting potential)
• inactivation gate: open at resting membrane potential
• both gates: respond to depolarization but w/ different speeds and in opposite directions (act opens rapidly in response to depolarization, inact closes sowly in response to depolarization)
• immediately after depolarization, both gates are open allowing Na+ to enter the cell
• ~1-2 ms after act gate is still open, but inact gate has responded by closing
• as a result: permeability of Na+ first increases in response to depolarization, then declines again even if depolarization were maintained in some way
• delayed decline in Na+ permeability upon depolarization is called sodium channel inactivation

Question 23

How do the voltage-dependent potassium channels respond during an AP?

Answer 23

• channels are closed at resting membrane potential
• act gates slowly open upon depolarization (slow activation)
• permeability of K+ increases w/ a delay following depolarization, K+ current is outward

Question 24

Describe the following refractory periods in relation to the AP:

• absolute refractory period:
• relative refractory period:

Answer 24

• absolute refractory period: when inactivation gates of voltage-gated sodium channels are closed, no amnt of depolarization can cause the cell to fire an AP, prevents influx of Na+ necessary to trigger the AP, no AP can occur
• relative refractory period: overlaps w/ hyperpolarization phase (undershoot), during which conductance to K+ is higher than normal, AP can be evoked but only if a greater than usual depolarizing current is applied

Question 25

- process that occurs when the nerve or muscle cell is held at **depolarized level** in a **sustained manner** - occurs b/c depolarization closes inactivation gates on Na+ channels, if depolarization occurs slowly enough **Na+ channels close** and **remained closed** - depolarization will slowly activate K+ channels, increasing K+ conductance - initial depolarization of resting membrane potential but **net reduction in cell excitability** b/c sustained depolarization closes inactivation gates on Na+ channels; **cell is less likely to fire an AP** **- can occur in hyperkalemia**

Answer 25

accommodation

Question 26

What is the relationship of hyperkalemia and muscle physiology?

Answer 26

- in a hyperkalemic state, K+ equilibrium potential and resting membrane potential become less negative (depolarized), which can lead to **muscle spasms** - muscle spasms is followed by prolonged weakness - **weakness**: act gates open on Na+ channels in response to depolarization and inact gates on Na+ channel slowly close in response, prolonged depolarization causes **inact gates to remain closed** and when these are closed the **Na+ channels are closed** regardless of the position of act gates, for upstroke to occur both sets of Na+ gates must be open but if inact gates are closed **no AP can occur** - **neuromuscular sx**: related to alterations in generation of AP - eventually the increased K+ uptake within cells leads to hypokalemia within the blood

Question 27

What is the relationship of hypokalemia and muscle physiology?

Answer 27

- **in skeletal muscle**: reduction of K+ will hyperpolarize cell membrane (resting potential more electronegative) which impairs the muscle's ability to depolarize and contract, leading to muscle weakness - **periodic paralysis**: rare neuromuscular disorder, classified as hypokalemic when episodes occur in a/w hypokalemia, attacks occur suddenly w/ generalized weakness, attacks may be triggered by rest after vigorous exercise, stress, or high carb meal (often w/ several hour delay), often a/w increased release of epi or insulin which cause movement of K+ into cells and hypokalemia in the blood

Question 28

- blocks voltage-gated sodium channels, the inward Na+ current of the upstroke of AP does not occur - propagation of the AP, which depends on depolarizing inward current, is prevented

Answer 28

lidocaine

Question 29

- self-propagating wave of depolarization that sweeps across axon/nerve/muscle fiber - local currents spread from active regions to adjacent inactive regions

Answer 29

action potential propagation

Question 30

What are the electrical properties of the axon?

Answer 30

- channels alone do not control spread of electrical current - **spread of current**: depends on nature of conducting and insulating medium (e.g. cell membranes, ECF, ICF) - **important factors**: electrical resistance of aqueous solutions and cell membrane, and membrane capacitance - **electronic spread of voltage changes**: occurs by flow of electrical current carried by ions in ICF and ECF, along pathways of least electrical resistance - **two main pathways**: flow across membrane (Rm) and move down axon (Ri) - amnt of current taking each path depends on relative resistances of two pathways, **more current flows down path w/ less resistance**

Question 31

- determine the way in which graded potentials and AP's propagate over space/time in axon - two important properties: time constant (τ) and length constant (λ)

Answer 31

cable properties (determine conduction velocity)

Question 32

What factors affect the time constant (𝜏)?

Answer 32

- **equation**: 𝜏 = 𝑅𝑚𝐶𝑚 (membrane resistane = 𝑅𝑚, membrane capacitance = 𝐶𝑚) - **when Rm is high, 𝜏 increases** (current does not readily flow across cell membrane, making it difficult to change membrane potential) - **when Cm is high, 𝜏 increases** (injected current must discharge the membrane capacitor before it can depolarize the membrane

Question 33

What affect does the time constant (𝜏) have on action potential propagation?

Answer 33

- 𝜏 influences spread of voltage changes in time, thus velocity of signal propagation - shorter 𝜏 = more quickly a neighboring region of membrane will be brought to threshold (faster the speed of impulse propagation)

Question 34

What affect does the length constant (λ) have on spread of voltage changes in space?

Answer 34

- **λ depends on three resistance elements**: membrane, external, and internal resistance (Rm, Ro, and Ri) - Ri is much larger than Ro, so Ro can be ignored - the longer the λ, the farther down the axon a voltage change spreads - **λ will be longest (i.e. current travels farthest) when**: diameter of nerve is large (Ri low), or Rm is high (e.g. myelinated axon) **- the longer the λ, the less loss of signal there will be**

Question 35

What would happen if the Rm were made higher and Ri could be made lower?

Answer 35

- pathway of the axon would be favored - a larger portion of current would continue along the inside - depolarization resulting from AP would decay less rapidly along axon - rate of propagation would increase

Question 36

How has nature increased the speed of AP propagation?

Answer 36

Two strategies: - **increase diameter of axon to decrease Ri** (when axon is wider, it offers larger cross-sectional area to the internal flow of current; strategy adopted by many invertebrate animals; variation in size of axons among vertebrates - **increase internal diameter by wrapping axon w/ extra layers of insulation (myelin) to increase Rm** (myelin sheath forces a larger portion of current flowing as a result of a voltage change to move down the interior of the axon)

Question 37

What are the effects of myelin sheath on the AP

Answer 37

- increases Rm - decreases membrane capacitance (Cm) - effects on Rm and Cm result in increased conduction velocity - increases distance between conducting ICF and ECF, effective capacitance of membrane decreases (smaller number of charges need to be added to inside in order to reach depolarization) - depolarization will spread faster (decreases 𝜏) and farther

Question 38

- periodic breaks in myelin sheath - influx of Na+ carrying the depolarizing current during initiate of AP has access to the axon membrane through these gaps - depolarization at one gap spreads along interior of axon to next node, where it sets up a new AP - AP leaps along axon, jumping from gap to gap (saltatory conduction) - **saltatory conduction**: dramatically improves speed w/ which thin axon can conduct AP along its length

Answer 38

nodes of ranvier

Question 39

- most common demyelinating disease of the CNS - loss of myelin sheath results in: decrease in membrane resistance results in current leak out across membrane during conduction, local currents decay more rapidly as they flow down axon (decreased length constant), failure to conduct AP occurs - demyelinated axons do not have sufficient number of sodium channels on internodal segements and generation of closely spced AP's is diminished - sx of condition: weakness of LE's, numbness, paresthesia, blurred vision, pain w/ eye movements

Answer 39

multiple sclerosis (MS)