Passive Membrane Properties
• Two physical properties of shape the axons response
– Resistance (ohms Ω): a measure of an objects opposition
to the passage of current
– Capacitance: Storage of charges (+ & -) across two
plates separated by a non-conductive material
– Nonconductive material = cell membrane
– Two plates = intra- and extracellular fluid
– Capacitance measured in Farads
Electrical Model of Membrane
Thursday, May 6, 2010
Unit Membrane
Passive Membrane Properties
The Length Constant
• Voltage change diminishes with distance
from current injection sit?
• λ=Length constant
–
Current flow is influenced by the
membrane resistance (rm) and internal
Resistance (ri)
•
Resistors values add normally when in series
but reciprocally when in parallel
•
Current tends to flow through the shortest path
(rm)
Thursday, May 6, 2010
Passive Membrane Properties
The Length Constant
• Voltage change diminishes with distance
from current injection sit?
• λ=Length constant
–
Current flow is influenced by the
membrane resistance (rm) and internal
Resistance (ri)
•
Resistors values add normally when in series
but reciprocally when in parallel
•
Current tends to flow through the shortest path
(rm)
Thursday, May 6, 2010
Passive Membrane Properties:
The Time Constant
• A capacitor
– Stores charge on two plates
separated by nonconductive
material
– Since the charges have to move it
takes time to charge the plates
•
This results ramp in the rate of change
of Vm in response to injected current
Charging delay due to
capacitance
τ=Cm*Rm
Thursday, May 6, 2010
Resting Membrane Potential
• Membrane potential is determined by
– Selective permeability of the membrane
– Ions moving towards their electrochemical
equilibrium
•
Some molecules (e.g. ions) can flow
freely across membranes through
channels in membrane
•
Large negatively charged proteins (A-)
can not cross the membrane
•
In this example K+ moves down its
concentration gradient but A- can not
cross the membrane
•
The result: charge separation &
measurable membrane potential
Thursday, May 6, 2010
Equilibrium Potential
Inner
chamber
• Negative net charge on the
inner face & positive net
charge on outer face tend to
move K+ back into cell
• Electrochemical equilibrium:
– When the electrical force
equal the chemical forces
there is no ‘net’ flow of ions
across the membrane
• We can use the Nernst
Equation to calculate an ion’s
equilibrium potential
Thursday, May 6, 2010
–90 mV
Outer
chamber
140 mM
5 mM
KCI
KCI
K+
Cl–
Potassium
channel
(a) Membrane selectively permeable to K+
Equilibrium Potential
Inner
chamber
• Negative net charge on the
inner face & positive net
charge on outer face tend to
move K+ back into cell
• Electrochemical equilibrium:
– When the electrical force
equal the chemical forces
there is no ‘net’ flow of ions
across the membrane
• We can use the Nernst
Equation to calculate an ion’s
equilibrium potential
Thursday, May 6, 2010
–90 mV
Outer
chamber
140 mM
5 mM
KCI
KCI
K+
Cl–
Potassium
channel
(a) Membrane selectively permeable to K+
Eion=62 mV * (log[ion]o/[ion]i)
Equilibrium Potential
–90 mV
Inner
chamber
• Negative net charge on the
inner face & positive net
charge on outer face tend to
move K+ back into cell
• Electrochemical equilibrium:
– When the electrical force
equal the chemical forces
there is no ‘net’ flow of ions
across the membrane
• We can use the Nernst
Equation to calculate an ion’s
equilibrium potential
Thursday, May 6, 2010
Outer
chamber
140 mM
5 mM
KCI
KCI
K+
Cl–
Potassium
channel
(a) Membrane selectively permeable to K+
Eion=62 mV * (log[ion]o/[ion]i)
EK = 62 mV
( log
5 mM
140 mM
)
= –90 mV
Equilibrium Potential (Eion)
• Use the Nernst equation to calculate a membrane’s
Equilibrium Potential (Eion) for different ions:
Eion = 62 mV (log[ion]outside/[ion]inside)
–90 mV
Inner
chamber
+62 mV
Outer
chamber
140 mM
KCI
15 mM
NaCI
5 mM
KCI
EK = -90Mv
150 mM
NaCI
ENa=+62Mv
Cl–
K+
Cl–
Potassium
channel
(a) Membrane selectively permeable to K+
(
EK = 62 mV log
5 mM
140 mM
)
= –90 mV
Na+
Sodium
channel
(b) Membrane selectively permeable to Na+
ENa = 62 mV
mM )
(log 150
15 mM
The number of ions involved is small
Thursday, May 6, 2010
= +62 mV
Membrane Potential
• Very few ions required to generate the membrane
potential
– In a 1µM x 0.001µM 6 ions on either side of the
membrane are responsible for generating the -90mV
membrane potential
Inner
chamber
–90 mV
Outer
140 mM
5 mM
KCI
KCI
K+
Cl–
Potassium
channel
(a) Membrane selectively permeable
Thursday, May 6, 2010
Energy is Required to Maintain the Vm
• Energy is required to maintain Vm
– With time Na+ and K+ electrochemical gradients will run
down
– ATP-dependent Na-K pumps maintain the Na+ and K+
concentration gradients
Thursday, May 6, 2010
The Goldman Equation:
• Describers the relative contribution of
multiples ions to the membrane potential
(Em) at rest
• PK & PNa the relative permeability of K+ and Na+
• [x]i & [x]o concentration of the ion x inside and outside the cell
Thursday, May 6, 2010
Membranes of Neurons and Muscles are Excitable
• Record the response of
the membrane potential
to the injection of current
• The response depends
on whether the current
was hyperpolarizing or
depolarizing
–
Cells response to
injection of negative is
linear
–
Cells response to
injection of positive
current is nonlinear
–
Voltage Threshold
Thursday, May 6, 2010
Ac#on Poten#al are defined as all or nothing
• Once the membrane poten.al reaches the voltage threshold the ac.on poten.al is triggered • Shape of the ac.on Poten.al defined by changes in Ion permeability • Threshold represents the point where PNa exceeds PK
Thursday, May 6, 2010
Hodgkin Cycle
Physical Bases of the of the Ac#on Poten#al
We can use the Goldman-Katz
Equation to decipher the Action
Potential
Thursday, May 6, 2010
Physical Bases of the of the Ac#on Poten#al
• At rest: Pk high rela#ve to other ions
– Δ Em~Ek
• Rising phase: Na+ channels open
– Δ Em~ENa
• Falling phase: Na+ channels inac#vate & voltage sensi#ve K+ open PNa
– Δ Em~EK
• Recovery Phase: Na+ is closed & voltage sensi#ve K+ open
– Δ Em~EK Thursday, May 6, 2010
Physical Bases of the of the Ac#on Poten#al
Thursday, May 6, 2010
Patch Clamp: Viewing the Current One Channel at a Time Fig. 11-17
Fig. 11-18
• Can use a special electrode to recorded current flowing through a single channel during an ac.on poten.al – Inward current flows through the Na+ channel
– Outward current flows through K+ channels
• Note: the channels are ‘gated’
– Currents flows during a narrow #me window (on/
off)
Thursday, May 6, 2010
Voltage Clamp Experiments
Fig. 11-19
• The membrane poten#al is held at a predetermined value
– You can measure the amount of current required to hold Vm at the predetermined voltage
– Hyperpolarize to -­‐100mV : Observe a capaci.ve current
– Depolarize to 0mV: observe both the inward and outward currents
Thursday, May 6, 2010
Voltage-­‐Clamp as a Tool
• Examine the inward and outward currents under different condi#ons to characterize ac#on poten#al
– Inward current is dependent upon Na+
• Manipulate [Na+]out/ [Na+]in
– Outward current is carried through K+ dependent • Manipulate K+ or use TEA to block K+ channels
Thursday, May 6, 2010
Manipulate ion concentrations
Use toxins that block specific ion
channels
15
Na+ Channels are Voltage Sensitive
• The Na+ channel has a
domain that serves as a
voltage sensory
– The voltage sensory detects
changes in Vm
– Triggers change in the
structure of the Na+
channel
• In response the channel
opens
Voltage Sensory is one of
several functional domains
Thursday, May 6, 2010
Propaga.on of Ac.on Poten.als
• Consider capacitance – The channel is closed un#l it senses a depolariza#on
– The voltage shiX the channel senses is due to capaci#ve currents
Thursday, May 6, 2010
Propaga#on of Ac#on Poten#als
• Ac#on poten#als propagate by regenera#ng along the axon
• At the site where the ac#on poten#al is generated (the axon hillock) ionic currents depolarizes the neighboring region of the axon membrane
Capacitive currents are
responsible to the initial
depolarization of the
membrane
Thursday, May 6, 2010
Ac#on Poten#al Propaga#on
• Ac.on poten.als travel in only one direc.on toward the synap.c terminals
• Inac.vated Na+ channels behind the zone of depolariza.on prevent the ac.on poten.al from traveling backward
Thursday, May 6, 2010