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Membrane Potential
Membrane potential
Separation of charges across the membrane
Or
Difference in relative number of cations and anions
in the ECF
Separated charges create the
ability to do work
Membrane potential is measured
in millivolts
1mv = 1/1000 volts
Chapter 3 The Plasma Membrane and
Membrane Potential
Human Physiology by Lauralee Sherwood Š2007
Brooks/Cole-Thomson Learning
Which has the greatest membrane potential?
Plasma membrane of all
living cells has a
membrane potential
(polarized electrically)
Due to differences in
concentration and
permeability of key ions ie
Na+ K+ and large
intracellular proteins b/w
ECF & ICF
Nerve and muscle cells
Excitable cells
Have ability to produce rapid,
transient changes in their membrane
potential when excited which serves as
electric signals
Resting membrane potential (RMP)
Constant membrane potential present in cells of
non excitable tissues and those of excitable
tissues when they are at rest
Generation and maintenance of
RMP
The unequal distribution of a few key ions b/w the
ICF and ECF and their selective movement through
the plasma membrane are responsible for the
electrical properties of the membrane
In body electric charges are carried by ions .
So the ions primarily responsible for the generation of
resting membrane potential are Na+
, K+
, and A-
Resting Membrane Potential
The Resting Potential
inside
outside
Resting potential of neuron = -70mV
+
-
+
-
+
-
+
-
+
-
Table 3-3, p. 75
The concentration difference of Na+
and K+ are maintained by the Na+ K+
pump.
Since the plasma membrane is
impermeable to proteins so A- are
inside the membrane
More permeability of K+ as
compared to Na+ in resting state
The plasma membrane is more
permeable to K+ in resting state than
Na+ because the membrane has got
more leak channels for K+ than for
Na+
Moreover the hydrated form of K+ is
smaller than the hydrated form of Na+
Key point
Concentration gradient
for K is towards
outside and for Na is
towards inside but the
electric gradient for
both of these ions is
towards the negatively
charged side of the
membrane
Normal value of RMP in different cells
Resting membrane potentials for cells generally
range: -20 mV to -200mV

TYPE OF CELL RMP
SKELETAL MUSCLE - 90 mvs
SMOOTH MUSCLE - 60mvs
CARDIAC MUSCLE - 85 to - 90 mvs
NERVE CELL - 70 mvs
Effect of sodium-potassium pump on
membrane potential
Makes only a small direct contribution to
membrane potential through its unequal
transport of positive ions
Only 20% of the MP is directly generated
by Na K pump
80% of the MP is caused by the passive
diffusion of Na and K down the
concentration gradient
Effect of movement of K+
alone on MP (K+ equilibrium
potential)
Plasma membrane
ECF ICF
Concentration
gradient for K+
Electrical
gradient for K+
EK+ = –94mV
•.•MEMBRANE POTENTIAL CAUSED BY DIFUSION OF K IONS
= -94 MV (K+ equilibrium potential)
•Nernst equation:
•Used to calculate the equilibrium potential caused by
single ion
•EMF= ± 61 Log conc. outside
____________
Conc inside
•. Therefore : for K+ ion
•EMF= ± 61 log conc. Of K+ Outside
____________
conc. Of K+ inside
EMF = Âą 61 log 4
____
140
= 61 log 1
____
35
= - 61 × (-1.54) because log of 1/35 is -1.54
= - 94 mvs
Effect of movement of Na+ alone on
MP (Na+ equilibrium potential)
Plasma membrane
ECF ICF
Concentration
gradient for Na+
Electrical
gradient for Na+
ENa+ = +61 mV
•Similarly for Na ions
•EMF = ± 61 log conc. Outside
______________
conc. Inside
= +61 log 150/15
= +61 × 1 (log of 10=1)
= +61 mvs
Goldman equation:
Used to calculate the equilibrium potential of 2 or more
ions
Therefore combining the equilibrium potential of K (-94)
& Na (+61)
= - 86 mVs
The membrane is so impermeable
to Chloride that you drop it from
the equation
Maintaining the Resting Potential by
Na+ K+ pump
Na+ ions are actively transported (this uses
energy) to maintain the resting potential.
The sodium-potassium pump (a membrane
protein) exchanges three Na+
ions for two K+
ions.
since more +ve ions move outside so causes
negativity of -4 mvs on inside
inside
outside
Na+
Na+
K+
K+
Na+
NET RMP
Net RMP = - 86 - 4 = -90mvs
This means when the cell is at rest it has negativity of
-90 mvs inside i.e. inside the cell there is 90 mvs more
negative as compared to outside the cell
Resting Membrane Potential summary
Ionic differences are the consequence of:
•Different membrane permeabilities due to passive
ion channels for Na+
, K+
,and Cl-
•Operation of the sodium-potassium pump
Fig. 3-23, p. 79
Plasma membrane
ECF ICF Relatively large net
diffusion of K+
outward establishes
an EK+ of –90 mV
No diffusion of A–
across membrane
Relatively small net
diffusion of Na+
inward neutralizes
some of the
potential created by
K+
alone
Resting membrane potential = –
70 mV
(A–
= Large intracellular anionic proteins)
Fig. 3-22, p. 78
Fig. 3-22, p. 78
Usefulness?
Neurons and muscle fibers can alter membrane
potential to send signals and create motion.
 So called excitable tissues because when they are
excited by appropriate stimulation they can rapidly
and transiently alter membrane permeabilities to the
involved ions so bringing fluctuations in membrane
potential which bring about nerve impulse in nerve
cells and triggering contraction in muscle cells
Changes in ion movement
in turn are brought about by
changes in membrane
permeability in response to
a triggering agent or a
stimuli
•The stimulus:
It is an external force or event which when applied to an
excitable tissue produces a characteristic response.
Examples of various types of stimuli are:
1)Electrical: use to produce an action potential in
neurons .
2)Hormonal: hormones are released i.e. adrenaline act on
heart to increases its rate
3)Thermal: stimulation of thermal receptors in skin by hot
or cold objects.
4)Electromagnetic receptor: stimulation of rods & cone
of retina by light.
5)Chemical: stimulation of taste receptors on the tongue
6)Sound: stimulation of auditory hair cells
•Sub-threshold stimuli:
A stimulus which is too weak to produce a response
•Threshold stimuli:
Minimum strength of stimulus that can produce excitation is
called threshold stimuli.
Electrical signals are produced by changes in ion
movement across the plasma membrane
Triggering agent (stimulus)
 Change in membrane permeability
Alter ion flow by opening and closing of gates
Membrane potential fluctuates
Electrical signal generated
Types of electrical signals
Two types of signals are produced by a change in
membrane potential:
graded potentials (short-distance signals)
action potentials (long-distance signals)
Terminology Associated with Changes in
Membrane PotentialF8-7, F8-8
• Polarization-
•Depolarization- a decrease in the potential difference between the inside and
outside of the cell.
•Hyperpolarization- an increase in the potential difference between the inside and
outside of the cell.
• Repolarization- returning to the RMP from either direction.
•Overshoot- when the inside of the cell becomes +ve due to the reversal of the
membrane potential polarity.
Terminologies
Polarization
Depolarization
Repolarization
Hyperpolarization
Graded Potentials
Short-lived, local changes in membrane potential
(either depolarizations or hyperpolarizations)
Cause passive current flow that decreases in
magnitude with distance so serve as short distance
signals
Their magnitude varies directly with the strength of
the stimulus – the stronger the stimulus the more the
voltage changes and the farther the current goes
Sufficiently strong graded potentials can initiate
action potentials
Graded Potentials
The Stronger a triggering event, the larger the
resultant graded potential
Graded Potential spread by passive Current flow.
Graded potentials die over short distances
K+ leaks out of the membrane
Decremental: gradually decreases
If strong enough, graded potentials trigger action
potentials
The wave of depolarization or
hyperpolarization which moves
through the cell with a graded
potential is known as local current
flow.
Current Flow During a Graded Potential
Chapter 4 Principles of Neural and Hormonal
Communication
Human Physiology by Lauralee Sherwood Š2010
Brooks/Cole, Cengage Learning
Chapter 4 Principles of Neural
and Hormonal Communication
Human Physiology by Lauralee
Sherwood Š2010 Brooks/Cole,
Cengage Learning
Graded Potential
Occurs in small, specialized region of excitable cell
membranes
Magnitude of graded potential varies directly with the
magnitude of the triggering event
Examples of graded potentials are:
1)Receptor potential.
2)Post synaptic potential
3)Slow wave potential
4)End plate potential
5)Pace maker potential
•A graded potential depolarization is called
excitatory postsynaptic potential (EPSP). A
graded potential hyperpolarization is called an
inhibitory postsynaptic potentials (IPSP).
•They occur in the cell body and dendrites of the
neuron.
Changes in Membrane Potential
Graded Potentials
Voltage changes in graded
potentials are decremental,
the charge is quickly lost
through the permeable
plasma membrane
short- distance signal
•Graded potentials travel through the neuron until they reach the trigger zone. If
they depolarize the membrane above threshold voltage (about -55 mV in
mammals), an action potential is triggered and it travels down the axon.
F8-10
Graded Potentials Above Threshold
Voltage Trigger Action Potentials
Action Potentials (APs)
The AP is a brief, rapid large change in
membrane potential during which potential
reverses so that inside of the excitable cell
transiently becomes more +ve than the outside.
APs do not decrease in strength with distance so
serve as long distance signals.
Events of AP generation and transmission are
the same for skeletal muscle cells and neurons
Course of the Action Potential
The action potential begins with a partial
depolarization [A].
When the excitation threshold is reached there is a
sudden large depolarization [B].
This is followed rapidly by repolarization [C] and a
brief hyperpolarization [D].
Membrane
potential
(mV)
[A]
[B] [C]
[D] excitation threshold
Time (msec)
-70
+40
0
0 1 2 3
Marked changes in membrane
permeability and ion movement lead to
an action potential (AP)
Passive diffusion of K+ makes greatest contribution to
the RMP due to more permeability of plasma
membrane to K+ through leak channels at rest.
During an AP marked changes in membrane
permeability to Na+ and K+ take place permitting
rapid fluxes down their electrochemical gradient
These ions carry the current responsible for the
potential changes that occur during an AP
Action potential takes place as
a result of the triggered
opening and subsequent closing
of 2 specific types of channels
Voltage gated Na+ channels
Voltage gated K+ channels
ROLE OF VOLTAGE GATED Na+
CHANNEL & VOLTAGE GATED K+
CHANNELS IN ACTION POTENTIAL
Voltage gated Na+ channels
 Most important channels during AP
It has two gates:
ACTIVATION GATES: At RMP activation gates are
closed so no Na+ influx at RMP thru these channels
These activation gates open when membrane
potential become less negative than during resting
state then the activation gates of these voltage gated
channels open so increasing Na+ permeability to 500-
5000 fold.
Inactivation of Na+ channels
The same increase in voltage that open the activation
gates also closes the inactivation gates but closing of
gates is a slower process than opening so large
amount of Na+ influx has occurred
Another important feature of Na+ channels
inactivation is that the inactivation gate will not
reopen until the membrane potential returns to or
near the original RMP.
•.
Voltage gated K+ channel
During RMP Voltage gated K+ channels are closed
The same stimulus which open voltage gated Na+
channels also open voltage gated K+ channel
Due to slow opening of these channels they open just
at the same time that the Na+ channels are beginning
to close because of inactivation.
So now decrease Na+ influx and simultaneous
increase in K+ out flux cause membrane potential to
go back to resting state (recovery of RMP)
These channels close when membrane potential
reaches back to RMP
•.
Phases of action potential
Depolarization
Repolarization
Hyperpolarizatio
n
Initiation of action potential
To initiate an AP a triggering event causes the
membrane to depolarize from the resting potential of
-90 mvs.
Depolarization proceeds slowly at first until it reaches
a critical level known as threshold potential. i.e.
-65 mvs . At threshold explosive depolarization occurs.
 An AP will not occur until the initial rise in membrane
potential reaches a threshold level.
 This occurs when no. of Na+ entering the cell
becomes greater than the no. of K+ leaving the
cell.
Threshold and Action Potentials
Threshold Voltage– membrane is depolarized by
15 to 20 mV
Subthreshold stimuli produce subthreshold
depolarizations and are not translated into APs
Stronger threshold stimuli produce depolarizing
currents that are translated into action potentials
All-or-None phenomenon – action potentials
either happen completely, or not at all
depending on threshold
Action Potential: Resting
StateNa+
and K+
channels are closed
Each Na+
channel has two voltage-regulated gates
Activation gates –
closed in the resting
state
Inactivation gates –
open in the resting
state
Depolarization opens the activation gate (rapid)
and closes the inactivation gate (slower) The gate
for the K+
is slowly opened with depolarization.
Depolarization Phase
Na+
activation gates open quickly and Na+
enters
causing local depolarization which opens more
activation gates and cell interior becomes
progressively less negative. Rapid depolarization and
polarity reversal.
Threshold – a critical level of depolarization
(-55 to -60 mV) where
depolarization becomes
self-generating
Positive Feedback?
Repolarization Phase
Sodium inactivation gates of Na+
channels close.
As sodium gates close, the slow voltage-sensitive K+
gates open and K+
leaves the cell following its
electrochemical gradient and the internal negativity of
the neuron is restored
Hyperpolarization
The slow K+
gates remain open longer than is needed
to restore the resting state. This excessive efflux causes
hyperpolarization of the membrane
The neuron is
insensitive to
stimulus and
depolarization
during this time
Depolarization increases the probability of
producing nerve impulses. Hyperpolarization
reduces the probability of producing nerve
impulses.
Role of the Sodium-Potassium Pump
Repolarization restores the resting electrical
conditions of the neuron, but does not restore the
resting ionic conditions
Ionic redistribution is accomplished by the
sodium-potassium pump following
repolarization
Importance of Action Potential
Generation
Nerve traffic, muscle contraction, hormone
release, G.I. secretions, Cognitive thought,
etc.
Action Potentials are required for the
senses - Sight, hearing, and touch are all
dependent on action potentials for
transmission of information to the brain
Threshold stimuli (Graded Potential) cause
the.generation of an action potential
Role of Calcium ions in Action
potential
Calcium pump in almost all cells of the body
maintain the calcium gradient with high Ca in ECF
as compared to ICF.
In addition to Ca pumps there are voltage gated Ca
channels which are slightly permeable to Na+ as well
as to Ca++ ions.
So when they open both Na and Ca flow to the
interior of the fiber. So called Ca Na channels.
They are slow to open requiring 20 times as long for
activation as Na channels so called slow channels in
contrast to Na channels which are fast channels.
Ca++ channels are numerous in smooth muscles and
cardiac muscle. In some smooth muscles the fast
Na+ channels are hardly present so that the AP are
caused almost entirely by activation of slow Ca++
channels.
Increased permeability of Na channels
when there is deficit of Ca ions
The conc. Of Ca ions in ECF has profound effect on
the voltage level at which the Na channels become
activated.
So when there is a deficit of Calcium ions in the
ECF the voltage gated Na channels open by very little
increase of MP from its normal very negative level.
so nerve fiber become highly excitable .
When Ca levels fall 50% below normal spontaneous
discharge occurs in some peripheral nerves causing
tetany. Its lethal when respiratory muscles are
involved.
Cause:
Ca bind to the exterior surface of the voltage gated
Na channels protein molecule.
The +ve charge of Ca ions in turn alter the electrical
state of the channel protein itself.
So altering the voltage level required to open the
sodium gates.
Propagation of
Action Potential
A single action
potential involves
only a small portion
of the total excitable
cell membrane and
then the action
potential is self-
propagating and
moves away from the
stimulus (point of
origin)
Direction of Action potential
AP travels in all directions away from the stimulus
until the entire membrane is depolarized
Conduction of Action Potentials
Two types of propagation
Contiguous conduction
 Conduction in unmyelinated fibers
 Action potential spreads along every portion of the
membrane
Saltatory conduction
 Rapid conduction in myelinated fibers
 Impulse jumps over sections of the fiber covered with
insulating myelin
Nerve or muscle impulse
The transmission of the depolarization process along
a nerve or muscle fibre is called impulse
An action potential in the axon of a neuron is called a nerve
impulse and is the way neurons communicate.
Parts of neuron and signal
transmission in nerve trunks
Myelination
Most mammalian axons are myelinated.
The myelin sheath is provided by oligodendrocytes and
Schwann cells.
MYELIN
Myelin
Primarily composed of lipids sphingomyelin
Formed by oligodendrocytes in CNS
Formed by Schwann cells in PNS
• Myelin is insulating, preventing passage of ions
over the membrane as it is made up of lipids so
water soluble ions cannot permeate so current
cannot leak out in the ECF
Myelination
In PNS each
Schwann cell
myelinates 1mm
of 1 axon by
wrapping round
& round axon
Electrically
insulates axon
• The resistance of the
membrane to current leak
out of the cell and the
diameter of the axon
determine the speed of AP
conduction.
• Large diameter axons
provide a low resistance to
current flow within the axon
and this in turn, speeds up
conduction.
•Myelin sheath which wraps around vertebrate axons prevents current leak out of
the cells. Acts like an insulator, for example, plastic coating surrounding electric
wires. It is devoid of any passage ways.
• However, portions of the axons lack the myelin sheath and these are called
Nodes of Ranvier. They are present at about 1 mm intervals along the length
of axons . High concentration of Na+
channels are found at these nodes so AP
occurs only at nodes
2 ways to increase AP propagation speed
Saltatory Conduction (Saltere means jump
or leap) • When depolarization
reaches a node, Na+
enters
the axon through open
channels.
• At the nodes, Na+
entry
reinforces the depolarization
to keep the amplitude of the
AP constant
• However, it speeds up again when the depolarization encounters the next node.
•The apparent leapfrogging of APs from node to node along the axon is called
saltatory conduction.
•Myelinated fibers conduct impulses about 50 times faster
than unmyelinated fibers of comparable size
F8-22
•Saltatory conduction in myelinated fibers
from node to node
•As no ions can flow through myelin sheath they can
flow with ease through node of ranvier.
•Therefore, action potential or flow of electrical
currents occurs from node to node in a jumping
manner known as saltatory conduction
Importance of saltatory
conduction
•Increases the conduction velocity through myelinated
nerve fiber.
•Conserves energy for the axon
Multiple Sclerosis
• In demylinating diseases, such as
multiple sclerosis, the loss of
myelin in the nervous system
slows down the conduction of APs.
Multiple sclerosis patients
complain of muscle weakness,
fatigue, difficulty with walking
Plateau in some action
potentials
In cardiac muscle the excited muscle membrane
does not repolarize immediately after
depolarization ; instead the potential remains on a
plateau near the peak of the spike potential only
then does repolarization begins.
Plateau prolongs the period of depolarization so
prolongs the contraction of heart muscle
Cause of plateau
It is due to combination of factors:
1) First two types of channels causes depolarization
a)Voltage gated Na+ channels called fast channels for
spike potential
b)Slow Ca++ Na+ channels for plateau portion
2) The voltage gated K+ channels are slower than usual
to open, often not opening until the end of plateau
this delays the return of the MP towards normal
resting value
•.
The Action Potential Types
Rhythmicity of some excitable
tissues
Repetitive self induced discharges occurs normally in
the heart , in most smooth muscles and in neurons of
the CNS.
The rhythmical discharges causes:
1. Rhythmical beat of the heart
2.Rhythmical peristalsis of intestine
3. Rhythmical control of respiration
Re- excitation process necessary for
spontaneous rhythmicity
For spontaneous rhythmicity to occur, the
membbrane even in its natural state must be
permeable enough to Na + ions or to Ca and Na thru
slow channels
The resting membrane potential in the rhythmical
control center of the heart is only -60 - -70mvs
This is not enough –ve voltage to keep the Na and Ca
channels totally closed .
So following sequence of events take place:
1. Some Na and Ca ions flow inside
2.This increases the membrane voltage in +ve
direction which further increases membrane
permeability .
3. Still more ions flow inside
4.+ve feed back mechanism
5.AP is generated
6.Then membrane repolarizes
7.Again depolarization and new AP
8.This cycle repeats again and again & causes self
induced rhythmical excitation of the excitable tissue
RHYTHMICITY IN EXICATABLE TISSUESRHYTHMICITY IN EXICATABLE TISSUES
REPETITIVE,SPONT
ANEOUS AND SELF
INDUCED DISCHARGE
RHYTHIMICITY
OCCUR IN HEART
PACEMAKER,
PERISTALSIS OF
INTESTINE etc
Chapter 4 Principles of Neural
and Hormonal Communication
Human Physiology by Lauralee
Sherwood Š2010 Brooks/Cole,
Cengage Learning
Graded Potential vs Action
Potential
Principles of Action Potentials
1. The All or Nothing Principle:
Action Potentials occur in all or none fashion
depending on the strength of the stimulus
2. The Refractory Period:
Responsible for setting up limit on the frequency of
Action Potentials
All-or-None Principle
• If any portion of the membrane is depolarized
to threshold an AP is initiated which
will go to its maximum height.
• A triggering event stronger than one necessary
to bring the membrane to threshold does not
produce a large AP.
• However a triggering event that fails to
depolarize the membrane to threshold does
not trigger the AP at all.
All or none principle
Thus an excitable membrane either respond to a
triggering event with maximal Action potential that
spread throughout the membrane in a non
decremental manner or it does not respond with an
AP at all. This is called all or non law.
Importance
The importance of threshold phenomenon
is that it allows some discrimination b/w
important and unimportant stimuli .
Stimulus too weak to bring the membrane
potential to threshold do not initiate
action potentials and therefore do not
transmit the signals.
Refractory period
(unresponsive or stubborn)
A new action potential cannot
occur in an excitable membrane as
long as the membrane is still
depolarized from the preceding
action potential.
Refractory Periods
Absolute refractory
period:
Membrane cannot produce
another AP because Na+
channels are inactivated and
no amount of excitatory
signal applied to these
channels at this point will
open the inactivation gates.
Relative refractory period
occurs when VG K+
channels are open, making
it harder to depolarize to 7-38
Absolute Refractory Period
The absolute refractory period is the time from
the opening of the Na+
activation gates until the
closing of inactivation gates
When a section of membrane is generating an AP and
Na+
channels are open, the neuron cannot respond to
another stimulus
Relative Refractory Period
The relative refractory period is the interval following the
absolute refractory period when:
Na+
gates are closed
K+
gates are open
Repolarization is occurring
During this period, the threshold level is elevated,
allowing only strong stimuli to generate an AP (a
strong stimulus can cause more frequent AP
generation) a large suprathreshold graded potential can
start a second AP by activating Na+
channels which
have been reset
• Absolutely refractory period- a second AP will not occur until the first is over.
The gates on the Na+
channel have not reset.
•Relatively refractory period- a large suprathreshold graded potential can start
a second AP by activating Na+
channels which have been reset.
Refractory Periods Limit the Frequency of
APs
F8-17
Significance of refractory
period
By the time the original site has recovered from its
refractory period and is capable of being
restimulated by normal current flow the AP has
been rapidly propagated in forward direction only
and is so far away that it no longer influence the
original site so ensure one way propagation of the
action potential
• Refractory periods limit the rate at which signals
can be transmitted down a neuron. Limit is
around 100 impulses/s.
• The greater the RP the greater the delay before a
new AP can be initiated and lower the frequency
with which a nerve cell can respond to repeated
or on going stimulation
Refractory Periods Limit the Frequency of APs
Refractory Periods
Frequency of Action Potential Firing is
Proportional to the Size of the Graded
Potential
The amount of neurotransmitter released from the axon terminal is
proportional to the frequency of action potentials.
F8-18
Factors Affecting Excitability of Nerve
1-Increase excitability:1-Increase excitability:
-Increase Na permeability (Depolarize):-Increase Na permeability (Depolarize):
Low extracellularLow extracellular Ca++
--Increase extracellularIncrease extrac K concentration..
2-Decrease excitability (membrane stabilizers)2-Decrease excitability (membrane stabilizers)
--Decreased Na permeability:Decreased Na permeability:
High extracellularHigh extracellular, Ca++ and local anesthesia
--Decrease extracellularDecrease extracellular K+ concentration.
.
•Membrane stabilizers :
•In addition to the factors that increases membrane
excitability still others which decreases excitability of the
membrane called membrane stabilizing factors.
•For e.g. high ECF Ca++ decreases membrane permeability
to Na+ and simultaneously reduces excitability so Ca++ are
said to be a membrane stabilizer
•Local anesthetics: they r also membrane stabilizers. E.g.
procaine and tetracaine. They act directly on the
activation gates of Na++ making it much more difficult for
these gates to open so reducing membrane excitability.
•Graded potential Action Potential
May be positive (depolarize) always begin with dep.
Or negative (hyperpolarize)
Graded: proportional to stimulus All or none
Strength
Reversible, returns to RMP if stimulation Irreversible: goes to
Ceases before threshold is reached completion once
it begin
Local: has effect for only short distance general
Decremental: signal grows weaker Non decremental
with distance

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Membrane Potential Explained

  • 2. Membrane potential Separation of charges across the membrane Or Difference in relative number of cations and anions in the ECF
  • 3. Separated charges create the ability to do work Membrane potential is measured in millivolts 1mv = 1/1000 volts
  • 4. Chapter 3 The Plasma Membrane and Membrane Potential Human Physiology by Lauralee Sherwood Š2007 Brooks/Cole-Thomson Learning Which has the greatest membrane potential?
  • 5. Plasma membrane of all living cells has a membrane potential (polarized electrically) Due to differences in concentration and permeability of key ions ie Na+ K+ and large intracellular proteins b/w ECF & ICF
  • 6. Nerve and muscle cells Excitable cells Have ability to produce rapid, transient changes in their membrane potential when excited which serves as electric signals
  • 7. Resting membrane potential (RMP) Constant membrane potential present in cells of non excitable tissues and those of excitable tissues when they are at rest
  • 8. Generation and maintenance of RMP The unequal distribution of a few key ions b/w the ICF and ECF and their selective movement through the plasma membrane are responsible for the electrical properties of the membrane In body electric charges are carried by ions . So the ions primarily responsible for the generation of resting membrane potential are Na+ , K+ , and A-
  • 10. The Resting Potential inside outside Resting potential of neuron = -70mV + - + - + - + - + -
  • 12. The concentration difference of Na+ and K+ are maintained by the Na+ K+ pump. Since the plasma membrane is impermeable to proteins so A- are inside the membrane
  • 13. More permeability of K+ as compared to Na+ in resting state The plasma membrane is more permeable to K+ in resting state than Na+ because the membrane has got more leak channels for K+ than for Na+ Moreover the hydrated form of K+ is smaller than the hydrated form of Na+
  • 14. Key point Concentration gradient for K is towards outside and for Na is towards inside but the electric gradient for both of these ions is towards the negatively charged side of the membrane
  • 15. Normal value of RMP in different cells Resting membrane potentials for cells generally range: -20 mV to -200mV  TYPE OF CELL RMP SKELETAL MUSCLE - 90 mvs SMOOTH MUSCLE - 60mvs CARDIAC MUSCLE - 85 to - 90 mvs NERVE CELL - 70 mvs
  • 16. Effect of sodium-potassium pump on membrane potential Makes only a small direct contribution to membrane potential through its unequal transport of positive ions Only 20% of the MP is directly generated by Na K pump 80% of the MP is caused by the passive diffusion of Na and K down the concentration gradient
  • 17. Effect of movement of K+ alone on MP (K+ equilibrium potential)
  • 18. Plasma membrane ECF ICF Concentration gradient for K+ Electrical gradient for K+ EK+ = –94mV
  • 19. •.•MEMBRANE POTENTIAL CAUSED BY DIFUSION OF K IONS = -94 MV (K+ equilibrium potential) •Nernst equation: •Used to calculate the equilibrium potential caused by single ion •EMF= Âą 61 Log conc. outside ____________ Conc inside
  • 20. •. Therefore : for K+ ion •EMF= Âą 61 log conc. Of K+ Outside ____________ conc. Of K+ inside EMF = Âą 61 log 4 ____ 140 = 61 log 1 ____ 35 = - 61 × (-1.54) because log of 1/35 is -1.54 = - 94 mvs
  • 21. Effect of movement of Na+ alone on MP (Na+ equilibrium potential)
  • 22. Plasma membrane ECF ICF Concentration gradient for Na+ Electrical gradient for Na+ ENa+ = +61 mV
  • 23. •Similarly for Na ions •EMF = Âą 61 log conc. Outside ______________ conc. Inside = +61 log 150/15 = +61 × 1 (log of 10=1) = +61 mvs
  • 24. Goldman equation: Used to calculate the equilibrium potential of 2 or more ions Therefore combining the equilibrium potential of K (-94) & Na (+61) = - 86 mVs
  • 25. The membrane is so impermeable to Chloride that you drop it from the equation
  • 26. Maintaining the Resting Potential by Na+ K+ pump Na+ ions are actively transported (this uses energy) to maintain the resting potential. The sodium-potassium pump (a membrane protein) exchanges three Na+ ions for two K+ ions. since more +ve ions move outside so causes negativity of -4 mvs on inside inside outside Na+ Na+ K+ K+ Na+
  • 27. NET RMP Net RMP = - 86 - 4 = -90mvs This means when the cell is at rest it has negativity of -90 mvs inside i.e. inside the cell there is 90 mvs more negative as compared to outside the cell
  • 28. Resting Membrane Potential summary Ionic differences are the consequence of: •Different membrane permeabilities due to passive ion channels for Na+ , K+ ,and Cl- •Operation of the sodium-potassium pump
  • 30. Plasma membrane ECF ICF Relatively large net diffusion of K+ outward establishes an EK+ of –90 mV No diffusion of A– across membrane Relatively small net diffusion of Na+ inward neutralizes some of the potential created by K+ alone Resting membrane potential = – 70 mV (A– = Large intracellular anionic proteins) Fig. 3-22, p. 78
  • 32. Usefulness? Neurons and muscle fibers can alter membrane potential to send signals and create motion.  So called excitable tissues because when they are excited by appropriate stimulation they can rapidly and transiently alter membrane permeabilities to the involved ions so bringing fluctuations in membrane potential which bring about nerve impulse in nerve cells and triggering contraction in muscle cells
  • 33. Changes in ion movement in turn are brought about by changes in membrane permeability in response to a triggering agent or a stimuli
  • 34. •The stimulus: It is an external force or event which when applied to an excitable tissue produces a characteristic response. Examples of various types of stimuli are: 1)Electrical: use to produce an action potential in neurons . 2)Hormonal: hormones are released i.e. adrenaline act on heart to increases its rate 3)Thermal: stimulation of thermal receptors in skin by hot or cold objects. 4)Electromagnetic receptor: stimulation of rods & cone of retina by light. 5)Chemical: stimulation of taste receptors on the tongue 6)Sound: stimulation of auditory hair cells
  • 35. •Sub-threshold stimuli: A stimulus which is too weak to produce a response •Threshold stimuli: Minimum strength of stimulus that can produce excitation is called threshold stimuli.
  • 36. Electrical signals are produced by changes in ion movement across the plasma membrane Triggering agent (stimulus)  Change in membrane permeability Alter ion flow by opening and closing of gates Membrane potential fluctuates Electrical signal generated
  • 37. Types of electrical signals Two types of signals are produced by a change in membrane potential: graded potentials (short-distance signals) action potentials (long-distance signals)
  • 38. Terminology Associated with Changes in Membrane PotentialF8-7, F8-8 • Polarization- •Depolarization- a decrease in the potential difference between the inside and outside of the cell. •Hyperpolarization- an increase in the potential difference between the inside and outside of the cell. • Repolarization- returning to the RMP from either direction. •Overshoot- when the inside of the cell becomes +ve due to the reversal of the membrane potential polarity.
  • 40. Graded Potentials Short-lived, local changes in membrane potential (either depolarizations or hyperpolarizations) Cause passive current flow that decreases in magnitude with distance so serve as short distance signals Their magnitude varies directly with the strength of the stimulus – the stronger the stimulus the more the voltage changes and the farther the current goes Sufficiently strong graded potentials can initiate action potentials
  • 41. Graded Potentials The Stronger a triggering event, the larger the resultant graded potential Graded Potential spread by passive Current flow. Graded potentials die over short distances K+ leaks out of the membrane Decremental: gradually decreases If strong enough, graded potentials trigger action potentials
  • 42. The wave of depolarization or hyperpolarization which moves through the cell with a graded potential is known as local current flow.
  • 43. Current Flow During a Graded Potential Chapter 4 Principles of Neural and Hormonal Communication Human Physiology by Lauralee Sherwood Š2010 Brooks/Cole, Cengage Learning
  • 44. Chapter 4 Principles of Neural and Hormonal Communication Human Physiology by Lauralee Sherwood Š2010 Brooks/Cole, Cengage Learning Graded Potential Occurs in small, specialized region of excitable cell membranes Magnitude of graded potential varies directly with the magnitude of the triggering event
  • 45. Examples of graded potentials are: 1)Receptor potential. 2)Post synaptic potential 3)Slow wave potential 4)End plate potential 5)Pace maker potential
  • 46. •A graded potential depolarization is called excitatory postsynaptic potential (EPSP). A graded potential hyperpolarization is called an inhibitory postsynaptic potentials (IPSP). •They occur in the cell body and dendrites of the neuron.
  • 47. Changes in Membrane Potential
  • 48. Graded Potentials Voltage changes in graded potentials are decremental, the charge is quickly lost through the permeable plasma membrane short- distance signal
  • 49. •Graded potentials travel through the neuron until they reach the trigger zone. If they depolarize the membrane above threshold voltage (about -55 mV in mammals), an action potential is triggered and it travels down the axon. F8-10 Graded Potentials Above Threshold Voltage Trigger Action Potentials
  • 50. Action Potentials (APs) The AP is a brief, rapid large change in membrane potential during which potential reverses so that inside of the excitable cell transiently becomes more +ve than the outside. APs do not decrease in strength with distance so serve as long distance signals. Events of AP generation and transmission are the same for skeletal muscle cells and neurons
  • 51. Course of the Action Potential The action potential begins with a partial depolarization [A]. When the excitation threshold is reached there is a sudden large depolarization [B]. This is followed rapidly by repolarization [C] and a brief hyperpolarization [D]. Membrane potential (mV) [A] [B] [C] [D] excitation threshold Time (msec) -70 +40 0 0 1 2 3
  • 52. Marked changes in membrane permeability and ion movement lead to an action potential (AP) Passive diffusion of K+ makes greatest contribution to the RMP due to more permeability of plasma membrane to K+ through leak channels at rest. During an AP marked changes in membrane permeability to Na+ and K+ take place permitting rapid fluxes down their electrochemical gradient These ions carry the current responsible for the potential changes that occur during an AP
  • 53. Action potential takes place as a result of the triggered opening and subsequent closing of 2 specific types of channels Voltage gated Na+ channels Voltage gated K+ channels
  • 54. ROLE OF VOLTAGE GATED Na+ CHANNEL & VOLTAGE GATED K+ CHANNELS IN ACTION POTENTIAL
  • 55. Voltage gated Na+ channels  Most important channels during AP It has two gates: ACTIVATION GATES: At RMP activation gates are closed so no Na+ influx at RMP thru these channels These activation gates open when membrane potential become less negative than during resting state then the activation gates of these voltage gated channels open so increasing Na+ permeability to 500- 5000 fold.
  • 56. Inactivation of Na+ channels The same increase in voltage that open the activation gates also closes the inactivation gates but closing of gates is a slower process than opening so large amount of Na+ influx has occurred Another important feature of Na+ channels inactivation is that the inactivation gate will not reopen until the membrane potential returns to or near the original RMP.
  • 58. Voltage gated K+ channel During RMP Voltage gated K+ channels are closed The same stimulus which open voltage gated Na+ channels also open voltage gated K+ channel Due to slow opening of these channels they open just at the same time that the Na+ channels are beginning to close because of inactivation. So now decrease Na+ influx and simultaneous increase in K+ out flux cause membrane potential to go back to resting state (recovery of RMP) These channels close when membrane potential reaches back to RMP
  • 60. Phases of action potential Depolarization Repolarization Hyperpolarizatio n
  • 61.
  • 62.
  • 63. Initiation of action potential To initiate an AP a triggering event causes the membrane to depolarize from the resting potential of -90 mvs. Depolarization proceeds slowly at first until it reaches a critical level known as threshold potential. i.e. -65 mvs . At threshold explosive depolarization occurs.  An AP will not occur until the initial rise in membrane potential reaches a threshold level.  This occurs when no. of Na+ entering the cell becomes greater than the no. of K+ leaving the cell.
  • 64. Threshold and Action Potentials Threshold Voltage– membrane is depolarized by 15 to 20 mV Subthreshold stimuli produce subthreshold depolarizations and are not translated into APs Stronger threshold stimuli produce depolarizing currents that are translated into action potentials All-or-None phenomenon – action potentials either happen completely, or not at all depending on threshold
  • 65.
  • 66.
  • 67. Action Potential: Resting StateNa+ and K+ channels are closed Each Na+ channel has two voltage-regulated gates Activation gates – closed in the resting state Inactivation gates – open in the resting state Depolarization opens the activation gate (rapid) and closes the inactivation gate (slower) The gate for the K+ is slowly opened with depolarization.
  • 68.
  • 69. Depolarization Phase Na+ activation gates open quickly and Na+ enters causing local depolarization which opens more activation gates and cell interior becomes progressively less negative. Rapid depolarization and polarity reversal. Threshold – a critical level of depolarization (-55 to -60 mV) where depolarization becomes self-generating Positive Feedback?
  • 70.
  • 71. Repolarization Phase Sodium inactivation gates of Na+ channels close. As sodium gates close, the slow voltage-sensitive K+ gates open and K+ leaves the cell following its electrochemical gradient and the internal negativity of the neuron is restored
  • 72.
  • 73. Hyperpolarization The slow K+ gates remain open longer than is needed to restore the resting state. This excessive efflux causes hyperpolarization of the membrane The neuron is insensitive to stimulus and depolarization during this time
  • 74. Depolarization increases the probability of producing nerve impulses. Hyperpolarization reduces the probability of producing nerve impulses.
  • 75. Role of the Sodium-Potassium Pump Repolarization restores the resting electrical conditions of the neuron, but does not restore the resting ionic conditions Ionic redistribution is accomplished by the sodium-potassium pump following repolarization
  • 76. Importance of Action Potential Generation Nerve traffic, muscle contraction, hormone release, G.I. secretions, Cognitive thought, etc. Action Potentials are required for the senses - Sight, hearing, and touch are all dependent on action potentials for transmission of information to the brain Threshold stimuli (Graded Potential) cause the.generation of an action potential
  • 77.
  • 78. Role of Calcium ions in Action potential Calcium pump in almost all cells of the body maintain the calcium gradient with high Ca in ECF as compared to ICF. In addition to Ca pumps there are voltage gated Ca channels which are slightly permeable to Na+ as well as to Ca++ ions. So when they open both Na and Ca flow to the interior of the fiber. So called Ca Na channels. They are slow to open requiring 20 times as long for activation as Na channels so called slow channels in contrast to Na channels which are fast channels.
  • 79. Ca++ channels are numerous in smooth muscles and cardiac muscle. In some smooth muscles the fast Na+ channels are hardly present so that the AP are caused almost entirely by activation of slow Ca++ channels.
  • 80. Increased permeability of Na channels when there is deficit of Ca ions The conc. Of Ca ions in ECF has profound effect on the voltage level at which the Na channels become activated. So when there is a deficit of Calcium ions in the ECF the voltage gated Na channels open by very little increase of MP from its normal very negative level. so nerve fiber become highly excitable . When Ca levels fall 50% below normal spontaneous discharge occurs in some peripheral nerves causing tetany. Its lethal when respiratory muscles are involved.
  • 81. Cause: Ca bind to the exterior surface of the voltage gated Na channels protein molecule. The +ve charge of Ca ions in turn alter the electrical state of the channel protein itself. So altering the voltage level required to open the sodium gates.
  • 82. Propagation of Action Potential A single action potential involves only a small portion of the total excitable cell membrane and then the action potential is self- propagating and moves away from the stimulus (point of origin)
  • 83. Direction of Action potential AP travels in all directions away from the stimulus until the entire membrane is depolarized
  • 84. Conduction of Action Potentials Two types of propagation Contiguous conduction  Conduction in unmyelinated fibers  Action potential spreads along every portion of the membrane Saltatory conduction  Rapid conduction in myelinated fibers  Impulse jumps over sections of the fiber covered with insulating myelin
  • 85.
  • 86.
  • 87.
  • 88.
  • 89. Nerve or muscle impulse The transmission of the depolarization process along a nerve or muscle fibre is called impulse An action potential in the axon of a neuron is called a nerve impulse and is the way neurons communicate.
  • 90. Parts of neuron and signal transmission in nerve trunks
  • 91. Myelination Most mammalian axons are myelinated. The myelin sheath is provided by oligodendrocytes and Schwann cells.
  • 92. MYELIN Myelin Primarily composed of lipids sphingomyelin Formed by oligodendrocytes in CNS Formed by Schwann cells in PNS • Myelin is insulating, preventing passage of ions over the membrane as it is made up of lipids so water soluble ions cannot permeate so current cannot leak out in the ECF
  • 93. Myelination In PNS each Schwann cell myelinates 1mm of 1 axon by wrapping round & round axon Electrically insulates axon
  • 94. • The resistance of the membrane to current leak out of the cell and the diameter of the axon determine the speed of AP conduction. • Large diameter axons provide a low resistance to current flow within the axon and this in turn, speeds up conduction. •Myelin sheath which wraps around vertebrate axons prevents current leak out of the cells. Acts like an insulator, for example, plastic coating surrounding electric wires. It is devoid of any passage ways. • However, portions of the axons lack the myelin sheath and these are called Nodes of Ranvier. They are present at about 1 mm intervals along the length of axons . High concentration of Na+ channels are found at these nodes so AP occurs only at nodes 2 ways to increase AP propagation speed
  • 95.
  • 96. Saltatory Conduction (Saltere means jump or leap) • When depolarization reaches a node, Na+ enters the axon through open channels. • At the nodes, Na+ entry reinforces the depolarization to keep the amplitude of the AP constant • However, it speeds up again when the depolarization encounters the next node. •The apparent leapfrogging of APs from node to node along the axon is called saltatory conduction. •Myelinated fibers conduct impulses about 50 times faster than unmyelinated fibers of comparable size F8-22
  • 97. •Saltatory conduction in myelinated fibers from node to node •As no ions can flow through myelin sheath they can flow with ease through node of ranvier. •Therefore, action potential or flow of electrical currents occurs from node to node in a jumping manner known as saltatory conduction
  • 98. Importance of saltatory conduction •Increases the conduction velocity through myelinated nerve fiber. •Conserves energy for the axon
  • 99.
  • 100. Multiple Sclerosis • In demylinating diseases, such as multiple sclerosis, the loss of myelin in the nervous system slows down the conduction of APs. Multiple sclerosis patients complain of muscle weakness, fatigue, difficulty with walking
  • 101. Plateau in some action potentials In cardiac muscle the excited muscle membrane does not repolarize immediately after depolarization ; instead the potential remains on a plateau near the peak of the spike potential only then does repolarization begins. Plateau prolongs the period of depolarization so prolongs the contraction of heart muscle
  • 102. Cause of plateau It is due to combination of factors: 1) First two types of channels causes depolarization a)Voltage gated Na+ channels called fast channels for spike potential b)Slow Ca++ Na+ channels for plateau portion 2) The voltage gated K+ channels are slower than usual to open, often not opening until the end of plateau this delays the return of the MP towards normal resting value
  • 105. Rhythmicity of some excitable tissues Repetitive self induced discharges occurs normally in the heart , in most smooth muscles and in neurons of the CNS. The rhythmical discharges causes: 1. Rhythmical beat of the heart 2.Rhythmical peristalsis of intestine 3. Rhythmical control of respiration
  • 106. Re- excitation process necessary for spontaneous rhythmicity For spontaneous rhythmicity to occur, the membbrane even in its natural state must be permeable enough to Na + ions or to Ca and Na thru slow channels The resting membrane potential in the rhythmical control center of the heart is only -60 - -70mvs This is not enough –ve voltage to keep the Na and Ca channels totally closed .
  • 107. So following sequence of events take place: 1. Some Na and Ca ions flow inside 2.This increases the membrane voltage in +ve direction which further increases membrane permeability . 3. Still more ions flow inside 4.+ve feed back mechanism 5.AP is generated 6.Then membrane repolarizes 7.Again depolarization and new AP 8.This cycle repeats again and again & causes self induced rhythmical excitation of the excitable tissue
  • 108. RHYTHMICITY IN EXICATABLE TISSUESRHYTHMICITY IN EXICATABLE TISSUES REPETITIVE,SPONT ANEOUS AND SELF INDUCED DISCHARGE RHYTHIMICITY OCCUR IN HEART PACEMAKER, PERISTALSIS OF INTESTINE etc
  • 109. Chapter 4 Principles of Neural and Hormonal Communication Human Physiology by Lauralee Sherwood Š2010 Brooks/Cole, Cengage Learning
  • 110. Graded Potential vs Action Potential
  • 111. Principles of Action Potentials 1. The All or Nothing Principle: Action Potentials occur in all or none fashion depending on the strength of the stimulus 2. The Refractory Period: Responsible for setting up limit on the frequency of Action Potentials
  • 112. All-or-None Principle • If any portion of the membrane is depolarized to threshold an AP is initiated which will go to its maximum height. • A triggering event stronger than one necessary to bring the membrane to threshold does not produce a large AP. • However a triggering event that fails to depolarize the membrane to threshold does not trigger the AP at all.
  • 113. All or none principle Thus an excitable membrane either respond to a triggering event with maximal Action potential that spread throughout the membrane in a non decremental manner or it does not respond with an AP at all. This is called all or non law.
  • 114. Importance The importance of threshold phenomenon is that it allows some discrimination b/w important and unimportant stimuli . Stimulus too weak to bring the membrane potential to threshold do not initiate action potentials and therefore do not transmit the signals.
  • 115. Refractory period (unresponsive or stubborn) A new action potential cannot occur in an excitable membrane as long as the membrane is still depolarized from the preceding action potential.
  • 116.
  • 117. Refractory Periods Absolute refractory period: Membrane cannot produce another AP because Na+ channels are inactivated and no amount of excitatory signal applied to these channels at this point will open the inactivation gates. Relative refractory period occurs when VG K+ channels are open, making it harder to depolarize to 7-38
  • 118. Absolute Refractory Period The absolute refractory period is the time from the opening of the Na+ activation gates until the closing of inactivation gates When a section of membrane is generating an AP and Na+ channels are open, the neuron cannot respond to another stimulus
  • 119. Relative Refractory Period The relative refractory period is the interval following the absolute refractory period when: Na+ gates are closed K+ gates are open Repolarization is occurring During this period, the threshold level is elevated, allowing only strong stimuli to generate an AP (a strong stimulus can cause more frequent AP generation) a large suprathreshold graded potential can start a second AP by activating Na+ channels which have been reset
  • 120. • Absolutely refractory period- a second AP will not occur until the first is over. The gates on the Na+ channel have not reset. •Relatively refractory period- a large suprathreshold graded potential can start a second AP by activating Na+ channels which have been reset. Refractory Periods Limit the Frequency of APs F8-17
  • 121. Significance of refractory period By the time the original site has recovered from its refractory period and is capable of being restimulated by normal current flow the AP has been rapidly propagated in forward direction only and is so far away that it no longer influence the original site so ensure one way propagation of the action potential
  • 122. • Refractory periods limit the rate at which signals can be transmitted down a neuron. Limit is around 100 impulses/s. • The greater the RP the greater the delay before a new AP can be initiated and lower the frequency with which a nerve cell can respond to repeated or on going stimulation Refractory Periods Limit the Frequency of APs
  • 124. Frequency of Action Potential Firing is Proportional to the Size of the Graded Potential The amount of neurotransmitter released from the axon terminal is proportional to the frequency of action potentials. F8-18
  • 125. Factors Affecting Excitability of Nerve 1-Increase excitability:1-Increase excitability: -Increase Na permeability (Depolarize):-Increase Na permeability (Depolarize): Low extracellularLow extracellular Ca++ --Increase extracellularIncrease extrac K concentration.. 2-Decrease excitability (membrane stabilizers)2-Decrease excitability (membrane stabilizers) --Decreased Na permeability:Decreased Na permeability: High extracellularHigh extracellular, Ca++ and local anesthesia --Decrease extracellularDecrease extracellular K+ concentration. .
  • 126. •Membrane stabilizers : •In addition to the factors that increases membrane excitability still others which decreases excitability of the membrane called membrane stabilizing factors. •For e.g. high ECF Ca++ decreases membrane permeability to Na+ and simultaneously reduces excitability so Ca++ are said to be a membrane stabilizer •Local anesthetics: they r also membrane stabilizers. E.g. procaine and tetracaine. They act directly on the activation gates of Na++ making it much more difficult for these gates to open so reducing membrane excitability.
  • 127. •Graded potential Action Potential May be positive (depolarize) always begin with dep. Or negative (hyperpolarize) Graded: proportional to stimulus All or none Strength Reversible, returns to RMP if stimulation Irreversible: goes to Ceases before threshold is reached completion once it begin Local: has effect for only short distance general Decremental: signal grows weaker Non decremental with distance

Editor's Notes

  1. Figure 3.23: Counterbalance between passive Na+ and K+ leaks and the active Na+–K+ pump. At resting membrane potential, the passive leaks of Na+ and K+ down their electrochemical gradients are counterbalanced by the active Na+–K+ pump, so no net movement of Na+ and K+ takes place, and membrane potential remains constant.
  2. Figure 3.22: Effect of concurrent K+ and Na+ movement on establishing the resting membrane potential.
  3. ×××