Lecture notes
• Taken in part from:
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Adley, D. J. (1991) The Physiology of Excitable Cells, Cambridge,3ed.
Calabrese, R. C., Gordon, J., Hawkins, R., & Qian, Ning. (1995) Essentials of neural Science and Behavior.
Study guide and practice problems. Appleton & Lange
Davson, H. (1970) A Textbook of General Physiology, 4th Ed., Williams and Wilkins
Hille, B. (1992) Ionic Channels of Excitable Membranes, 2ed., Sinauer.
Levitan, I. B. & Kaczmarek, L. K. (1991) The Neuron: Cell and Molecular biology, Oxford.
Mathews, G. G. (1998) Cellular Physiology of Nerve and Muscle, Blackwell Science
CELL
MEMBRANE
• 1) KEEPS THE CELL INTACKT (IN
PART)
• 2) PERMEABLE TO SMALL MOLECULES
• 3) IMPERMEABLE TO LARGE
MOLECULES.
DIFFUSION
PHYSICAL PROCESS THAT
EQUILIBRATES FREELY
MOVING SUBSTANCES
CELLULAR COMPARTMENTS
• INTRACELLULAR SPACE – The fluid
space surrounded by the plasma
membrane or cell wall.
• EXTRACELLULAR SPACE – The fluid
space surrounding the outside of a plasma
membrane of a cell or cell wall.
COMPOSITIONS OF PARTICLAS
WITHIN AND OUTSIDE PLASMA
MEBRANES
PLASMA MEMBRANE
FREEZE FRACTURE TECHNIQUE
FRACTURE IS NOT ALONG
CRYSTAL PLANES
OSMOLARITY
• CONCENTRATION OF WATER IN
SOLUTIONS CONTAINING DIFFERENT
DISSOLVED SUBSTANCES.
Osmolarity (cont.)
• THE HIGHER THE OSMOLARITY OF A
SOLUTION THE LOWER THE
CONCENTRATION OF WATER IN THAT
SOLUTION.
MOLARITY
• THE MOLECULAR WEIGHT, IN GRAMS,
OF A SUBSTANCE DISOLVED IN 1
LITER OF SOLUTION. (1 M)
Molarity (cont.)
• 1 MOLE OF DISOLVED PARTICLES PER
LITER IS SAID TO HAVE 1 OSMAL
MOLALITY
• MOLES OF SOLUTION PER KILOGRAM
OF SOLVENT
• Takes into account that large dissolved
molecules (protein of high molecular
weight) displace a greater volume of
water than small molecules
Example
• Glucose, sucrose do not greatly dissolve
in water. Number of water molecules does
not change.
Osmolarity
• Osmolarity takes into account how many
dissolved particles result from each
molecule of the dissolved substance.
• 0.1 M glucose solution is 0.1 Osm
solution.
• Glucose, sucrose and urea molecules do
not dissociate when dissolved in water.
• 0.1M glucose is a 0.1 Osm solution
Osmolarity for dissociated
substances
0.1 M NaCl = 0.1 M Na + 0.1M Cl = 0.2 Osm
300 Osm
•
•
•
•
300 mM glucose
150 mM NaCl
100 mM NaCl + 100 mM Sucrose
75 mM NaCl + 75 mM KCl
Mixing
• The mixing is caused by the random
independent motion of individual
molecules (temperature dependent).
Two separate actions
• Random movement of the solute
(glucose)
• Random movement of the solvent (water).
Osmosis
• WHEN SOLUTIONS OF DIFFERENT
OSMOLARITY ARE PLACED IN
CONTACT WITH A BARRIER THROUGH
WHICH WATER WILL MOVE ACROSS
THE BARRIER, WATER WILL MOVE
FROM THAT SIDE WITH THE GREATER
NUMBER OF WATER MOLECULES PER
UNIT VOLUME (Higher Osmolarity) TO
THAT SIDE WITH THE LESSER WATER
MOLECULES PER UNIT VOLUME (Lower
Osmolarity).
Home experiment
•
•
•
•
Mason or Kerr quart jar.
Dark Molasses
Large Carrot
Glass Tube
Observable change
• Mechanism is the same, diffusion. The
results of the process is observable
because the water moving into the carrot
displaces the molasses forcing the
molasses up the tube which can be seen.
Work done by osmosis moves
piston from left to right
compartment
Osmotic Pressure
• Suppose that one could measure the force
necessary to just keep the water from
moving into compartment A.
• That force divided by the cross sectional
area of the piston would be the osmotic
pressure of the system.
Aqua pores
• Pores have now been found that transfer
only water and not ions.
OSMOTIC CHANGE IN VOL.
OSMOTIC BALALANCE VS CELL
VOLUME
• [S]in = [S]out
• [S]in + [P]in = [S]out
NO NET CHANGE WHEN IN
BALANCE
• IF A SUBSTANCE IS AT DIFFUSION
EQUILIBRIUM ACROSS THE CELL
MEMBARANE, THERE IS NO NET
MOVEMENT OF THAT SUBSTANCE
ACROSS THAT MEMBRANE.
Osm vs. cell volume (cont.)
• REQUIRES THAT:
•
[S]in = [S]out
•
and
•
[S]in + [P]in = [S]out
• BE SIMULATENEOUSLY TRUE AT
EQUILIBRIUM.
• How do cells in nature solve
the simultaneous condition?
Solution 1
• MAKE THE CELL IMPERMEANT TO
WATER
• Certain epithelial cells (skin) are
impermanent to water
Solution 2
• PUT THE CONTENTS OF THE CELL
WITHIN AN INELASTIC WALL
• Plant cell’s solution
Solution 3
• MAKE THE CELL MEMBRANE
IMPERMEANT TO SELECTED
EXTRACELLULAR SOLUTES
Impermeant sucrose & protein
ECF Osm. Lower than ICF
ECF has permeant solute, ECF &
ICF initially equal
ECF contains a mixture of
permeant and impermeant solutes
• [UREA]in + [P]in = [UREA]out +
[SUCROSE]out
IONS IN SOLUTION (WATER)
• Ions in solution behave much like particles
in solution.
Na+, K+, Cl-, Ca2+
• When they move they carry their charge
with them.
• Some channels are non selective as to the
type of cation.
• The movement of ions down their
concentration gradient can do work.
Size of ion depends on it ability
to hold a water “cloud”
Most channels only allow one
species of ion to pass, a uniport
+
Na
channel. Water cloud must
be stripped away
Current through channels
follows Ohm’s law
CATION & ANIONS
• Positively charged particles in solution
tend to congregate near the negative pole
of a battery.
• Negatively charged particles tend to
congregate near the positive poles.
DIFFUSION POTENTIAL
• DIFFERENTIAL DISTRIBUTION OF IONS
IN SOLUTION BETWEEN TWO
DIFFERENT COMAPARTMENTS, WITH
A COMUNICATING CHANNEL, GIVE
RISE TO A VOLTAGE GRADIANT IN THE
SOLUTION.
Concentration Cell
• Different concentration of electrolyte XY in
solution.
• Membrane permeable to only X+
Diffusion
• Concentration in 1 is greater than 2 by
twice as much
Diffusion
• If the barrier is moved, twice as many X+
moves down its gradient from
compartment 1 to compartment 2, carrying
a positive charge.
Charge separation
• Movement of charges from 1 to 2 sets up
a potential difference between the two
compartments.
• This charge separation is in the direction
of 2 to 1, opposite to the diffusion gradient.
• As the potential difference grows it will
become increasing harder to move X+
from 1 to 2.
• More and more X+ will move from 2 to 1
Equilibrium Potential
• An equilibrium position is reached at which
the electrical (tending to move X+ from 2 to
1) just balances the chemical or
concentration gradient (tending to move X+
from 1 to 2).
Voltage
1) The potential difference that builds up in
the above system is expressed as
voltage (in mVolts).
2) That is, when charges are separated, a
potential energy condition is constructed.
3) Volt is and expression that describes this
potential difference in electrical terms.
Voltage (cont.)
Voltage should be thought of as a
gradient. A gradient implies looking at two
places or states with respect to one
another.
Electrical conventions 1
If Compartment 1 is the reference chamber,
Compartment 2 is said to be positive with
respect to compartment 1. (A volt meter
will point toward the positive pole).
Electrical conventions 2
If the compartment 2 is the reference
chamber, compartment 2 is negative with
respect to compartment 1. (The voltmeter
will point to the left chamber).
Voltage (cont.)
2) This can be thought of as an
electromotive force.
Charge separation gives rise to a difference
of electrical potential (volts).
The voltage across the membrane (Vm) is
called: membrane potential.
Vm = Vin - Vout
Voltage (cont.)
3) Think of this voltage as a driving force for the
movement of charges in space.
We will use the convention that the direction of
current flow is the direction of the net movement
of the positive charges (Franklin’s convention)
That is, in ionic solutions cations (+ charges)
move in the direction of the electrical current
• When current flows in a cell (either cations or
anions) the potential across the cell is disturbed,
its degree of polarization is changed.
• Depolarization is a reduction in the degree of
negativity (reduced charge separation) across
the membrane.
• An increase in charge separation leads to more
negativity called hyperpolarization.
Ohm’s Law
• Voltage is proportional to current.
•
V∞I
• If the two are related you must have a
proportionality constant.
V = RI
Where V is in volts, R is resistance, in ohms
and I is in amperes. R is the slope of the line
relating volts to current
Equilibrium Potential
• A potential can be calculated for each
species of ions which represents the
balance between the electromotive force
(separation of charge) and diffusion
(differential concentration gradient) for a
given species of ion across a selectively
permeable membrane.
Temperature effect
• There is a temperature coefficient that is
implied in the Nernst equation. Increasing
the temperature increases the random
motion of the molecules in solution. This
increase will increase the probability of a
given ion to go through the channel.
Nernst Equation
• If one wants to know the dynamic value of
the diffusion flow one would have to do
work to stop the flow.
• Assume an increment of work is done to
just stop the flow of K down its gradient
but no greater work.
Sources of energy driving the
Nernst equation
• Diffusion gradient.
• The generated electrical field (Separation
of Charge).
• These two forces work in opposite
directions.
• The differential concentrations (Diffusion)
Diffusion gradient of K
Work opposing diffusion
• δWc = δn(R)(T) ln([x]out/[x]in)
Where
δW = increment of work
δn = increment of number of moles moved.
R = gas constant (8.314 J deg-1 mole-1)
T = absolute temperature
X = molar concentrations of solute in
compartment 1 an 2
Work of opposing electromotive
force
• Work of electromotive force opposing diffusion
δWe = δn (zFE)
δWe = increment of work.
δn = moles moved against an electrical
gradient.
Z = valence of the ion moved.
F = Faraday’s constant (96,500).
E = the potential difference between the
two compartments.
At Equilibrium, no net movement of
X
•
•
δWe = δWc
or
δn (z) (FE) = δn (R)(T)ln([X]1/[X]2)
• Solving for E
Nernst Equation
• E = (RT/zF)ln([X]1/[X]2)
•
or
• E = (25/z)ln([X]1/[X]2)
•
or
• enumerating the constants
• E = (58/z)log10([X1/X]2)
•
at 18o C
• E is in millivolts.
CRITICAL PROPERTIES OF THE
NERNST EQUATION
• Applies to only one ion at a time. Each ion
will have its own equilibrium potential.
Property 1
• Applies only to those ions that can cross
the membrane.
Property 2
• At equilibrium ions move across the
membrane, but there is no net change in
the number of ions that move per unit
time.
Nernst equation (cont)
• If you exceed the equilibrium potential in
excitable cells, the direction of current flow
will be reversed and ions will flow in the
opposite direction up hill (more on this
later).
Implications
• If the concentration in one of the two
chambers is changed, the voltage E must
change.
• If the voltage changes, the ratio of the two
compartments change and the
concentrations must change with respect
to each other.
The Effect External Δ Potassium
Ion Concentrations on Membrane
Potentials
The Resting Membrane
Potential
• There is a resting membrane potential for
all cells.
• Requires: Selectively permeable
membrane, diffusion gradient, separation
of charge