electrical properties of cell membrane
DESCRIPTION
neuro educationTRANSCRIPT
OBJECTIVES
1. Define diffusion potential of an ion and simply conclude how to calculate it
2. Discuss the concept of charge separation.
3. Explain the methods of calculation of equilibrium potential when the membrane is permeable to several ions.
4. Define Donnan equilibrium and discuss its consequences
5. Apply this knowledge to a practical instance.
BASICS FACTSMolecular Gradients
Na+
K+
Mg2+
Ca2+
H+
HCO3-
Cl-
SO42-
PO3-
protein
inside(in mM)
14
140
0.5
10-4
(pH 7.2)
10
5-15
2
75
40
outside(in mM)
142
4
1-2
1-2
(pH 7.4)
28
110
1
4
5
1. lipid-soluble molecules move readily across the membrane (rate depends on lipid solubility)
2. H2O soluble molecules cross via channels or pores
(a) (b)
Diffusion
1. Ungated Determined by size, shape, distribution of charge, et2.Gated voltage (e.g. voltage-dependent Na+ channels) chemically (e.g. nicotinic ACh receptor channels.
Characteristics:
Na+
in
outNa+ and other ions
Ion Channels
Ion concentrations
Cell Membrane in resting state
K+
Na+Cl-K+ A-
Outside of Cell
Inside of Cell
Na+ Cl-
Cell Membrane is Semi-Permeable
Cell Membrane at rest
Na+ Cl-K+
Na+ Cl-K+ A-
Outside of Cell
Inside of Cell
(K+) can pass through to equalize its concentration
Na+ and Cl- cannot pass through
Result - inside is negative relative to outside
- 55 to -100mv
- +- +- +
- +
Hydration Shells
- +
- +
- +
- +
- +- +
- +
-
+
- +
- +-
+ -
+
- +
- +
- +
- +
- +
- +
- + -
+
- +
- +
In H2O, without a membrane
hydrated Cl- is smaller than hydrated Na+ therefore faster:
Cl-Cl-
Na+
Basic ConceptsForces that determine ionic movement
Volt;- A charge difference between 2 points in space
1. Electrostatic forces1. Opposite charges attract2. Identical charges repel
2. Concentration forces1. Diffusion – movement of ions through semipermeable
membrane2. Osmosis – movement of water from region of high
concentration to low
ELECTRONEUTRAL DIFFUSSION
HIGH SALT CONC;
LOW SALT CONC;
+
-
BARRIER SEPARATES THE TWO SOLUTIONS
+
-+
-
+
-+
-+
-+
-+
-
ELECTRONEUTRAL DIFFUSSION
HIGH SALT CONC;
LOW SALT CONC;
+
-
BARRIER REMOVED
+
-
+-
+-
+-+
-+
-+
-
+ -
CHARGE SEPARATION = ELECTRICAL POTENTIAL
is the potential difference generated across a membrane when a charged solute (an ion) diffuses down its concentration gradient.
( caused by diffusion of ions.)
can be generated only if the membrane is permeable to that ion.
FEATURES;-1. if not permeable to the ion, no DP will be generated no matter how large a conc; gradient is present.
2. magnitude/Unit =, measured in mV,
3. depends on the size of the concentration gradient, where the concentration gradient is the driving force.
4. Sign of the DP depends on the charge of the diffusing ion.
5. DP are created by the movement of only a few ions, and they do not cause changes in the concentration of ions in bulk solution.
Diffusion Potentials(DP)
EP(electrochemical equilibrium), is the DIFFUSION POTENTIAL that exactly balances or opposes the tendency for diffusion down the concentration difference. At the chemical and electrical driving
forces acting on an ion are equal and opposite, FEATURES;-
1.1.Membrane is polarizedpolarized
2.More –ve particles in than out
3. Bioelectric Potential i.e,battery1. Potential for ion movement2. Current
EQUILIBRIUM POTENTIAL (EP)
At Electrochemical EquilibriumAt Electrochemical Equilibrium:
4.Concentration gradient for
the ion is exactly balanced
by the electrical gradient
5.No net flux of the ion
6.No requirement for any
sort of energy-driven pump
to maintain the concentration
gradient
Electrical potential (EMF)
The Nernst potential (equilibrium potential) is the theoretical intracellular electrical potential that would be equal in magnitude but opposite in direction to the concentration force.
When will the
negatively charged molecules stop entering the cell?
- at which an ion will be in electrochemical equilibrium.
At this potential: total energy inside = total energy outside
Electrical Energy Term: zFV
Chemical Energy Term: RT.ln[Ion]
Z is the charge, 1 for Na+ and K+, 2 for Ca2+ and Mg2+, -1 for Cl-
F is Faraday’s Constant = 9.648 x 104 Coulombs / mole
R is the Universal gas constant = 8.315 Joules / °Kelvin * mole
T is the absolute temperature in °Kelvin
Equilibrium potential (mV) , Eion =
EK = -90mV ENa = +60mv
i
o
K K
K
ZF
RTE
][
][log
1. Cell membranes form an insulating barrier that acts
like a parallel plate capacitor (1 μF /cm2)
2. Only a small number of ions must cross the membrane to create a significant voltage difference
3. Bulk neutrality of internal and external solution
4. Cells need channels to regulate their volume
5. Permeable ions move toward electrochemical equilibrium
6. Eion =calculated as NERST POTENTIAL
7. Electrochemical equilibrium does not depend on permeability,
only on the concentration gradient
CAPACITANCE
Electrical properties
The membrane potential
In the resting state, the intracellular space contains more negative ions than the extracellular space
difference of -50 to +120mV
THE MEMBRANE POTENTIAL
MEMBRANE
ExtracellularFluid Intracellular
Fluid
Na+
K+K+
Sodium channel is less open causing sodium to be slower
Potassium channel is more open causing potassium to be faster
+ - MEMRANE POTENTIAL(ABOUT 90 -120 mv)
1. Cell membrane acts as a barrier--ICF from mixing with ECF2. 2 solutions have different concentrations of their ions. Furthermore, this difference in
concentrations leads to a difference in charge of the solutions..
3. Therefore,+ve ions will tend to gravitate towards -ve solution. Likewise, -ve ions will tend to gravitate towards +ve solution.
4. Then the difference between the inside voltage and outside voltage is determined membrane potential.
When a membrane is permeable to several different ions, DP developed depends on:
1.Polarity of the electrical charge of ions.
2. Permeability of the membrane (P) to each ion.
3. Concentration of each ion in two compartments separated by the membrane.
MP is calculated by Goldman-Hodgkin-Katz equation.
icliNaiK
ocloNaoK
m ClPNaPKP
ClPNaPKP
F
RTV
][][][
][][][log
Membrane Potential: Goldman Equation
1. P = permeabilityAt rest: PK: PNa: PCl = 1.0 : 0.4 : 0.45
2. Net potential movement for all ions 3. Known Vm:Can predict direction of movement of any ion ~
NOTE:P’ = permeability
EQUIVALENT ELECTRICAL CIRCUIT MODEL
1. With unequal distribution of ions and differential resting conductances to those ions,
2. We can use the Nernst equation and Ohm’s law in an equivalent circuit model to predict a stable resting membrane potential of -75 mV, as is seen in many cells
NB, this is a steady state and not an equilibrium, since K+ and Na+ are not at their equilibrium potentials; there is a continuous flux of those ions at the RMP
RMP Em = (EK * gK) + (ENa * gNa) + (ECl * gCl)gNa + gK + gCl
Chord Conductance Equation
ClE
Clg
Nag
Kg
Clg
NaE
Clg
Nag
Kg
Nag
KE
Clg
Nag
Kg
Kg
Vm
1.Vm = EK+ +ENa+ + ECl-....
Vm = membrane potential, not equal to Eion;
2.Weighted avg of equilibrium potentials of all ions to which membrane is
permeable
3.Esp. K+, Na+, Cl-; changes in ECF K+ alters RMP in all cells
Passive distribution Donnan equilibrium
The ratio of positively charged permeable ions equals the ratio of negatively charged permeable ions
III
K+
Cl-
III
[K+] = [K+]
[Cl-] = [Cl-]
Start Equilibrium
Mathematically expressed:
•Another way of saying the number of positive charges must equal the number of negative charges on each side of the membrane
[ ] [ ]
[ ] [ ]I II
II I
K Cl
K Cl
1. BUT, in real cells there are a large number of negatively charged, impermeable molecules (proteins, nucleic acids, other ions)
2. call them A-
III
K+
Cl-
Start
A- III
[K+] > [K+]
[Cl-] < [Cl-]
Equilibrium
A-
III
[K+] > [K+]
[Cl-] < [Cl-]
Equilibrium
A- [K+]I = [A-]I + [Cl-]I
[K+]II = [Cl-]II
If [A-]I is large, [K+]I must also be largeA=phosphate anions+ protiens macromolecules
+’ve = -’ve+’ve = -’ve
space-charge neutrality
-----------
+++++++++++
EXAMPLE
1. The product of Diffusible Ions is the same on the two sides of a membrane.
33 K+
33 Cl-
67 K+
50 Pr -
17 Cl-Step 2
66 Osmoles 134 Osmoles
50 K+ 50 K+
50 Cl- 50 Pr -Initial
100 Osmoles 100 Osmoles
Final
33 ml 67 ml
33 K+
33 Cl-
67 K+
50 Pr -
17 Cl-
Total Volume100 ml
IonsMove
H2Omoves
Human Potentials
1. Strong potentials in muscles--EMG, ECG (electromyogram
and electrocardiogram).
2. Weaker potentials from brain--EEGs.
3. Evoked potentials allow study of changes.
4. Computer averaging allows study of deep brain potentials:
Event-related potentials in sensory systems and cognition.