ZOO 3200 Lecture Notes - Lecture 3: Osmosis, Active Transport, Tonicity
2 May 2018
School
Department
Course
Professor
Ionic properties of the intra and extracellular compartments
!
Diffusion (Fick's law)
!
Osmosis
!
Nernst equation
!
Donnan equilibrium and Donnan potential
!
Outline:
Reading: Chapter 5 (pages 99-124)
Class Exercise: Donnan equilibrium calculation
Every cell of multicellular animals maintains concentrations of
inorganic solutes inside the cell that are very different from those
outside
!
Interior
Exterior
[Na+]
10mM
120mM
[K+]
140
2.5
[Ca2+]
< 10^-3
2
[Cl-]
3-4
120
[A-]
140
low
Mammal cell:
!
490 Na+
!
10 K+
!
500 Cl-
!
Environment (seawater)
○
490 Na+
!
10 K+
!
500 Cl-
!
Blood
○
70 Na+
!
200 K+
!
100 Cl-
!
630 other
!
Cell
○
Marine Invertebrates:
!
Gradient of sodium in and potassium out applies to all
multicellular animals
!
Electrical communication
○
E.g. ATP production by mitochondria
!
E.g. sodium gradient used to bring many things into
cells (sugars, amino acids)
!
Energy in electrical and chemical gradients can be used to
do work
○
Importance of ion/electric gradients:
!
Passice distribution -Donnan equilibrium
○
Active transport
○
Causes of ion distribution differences in cells:
!
Glucose diffuses in net fashion in the direction of
equilibrium, which is the direction that equalizes
concentration on the two sides of the membrane
○
More molecules pass through the membrane by this
chance process due to density of glucose molecules on
either side
!
As glucose molecules on the high concentration side
collides with other molecules, its random motions can line it
up to pass through a pore to the side with a lower
concentration
○
Example: simple diffusion viewed macroscopically and
microscopically
!
Entropy -random walks in 3 dimensions
○
Driving force:
!
Ionic Properties of the Intra-& Extracellular Compartments
The net rate of diffusion of a solute across a membrane
!
J -rate of diffusion or quantity of solute diffusing per unit
time (mmoles cm-2 s-1)
○
P -permeability
"
MW -molecular weight
"
D = P/ (sq.rt(MW))
!
D -diffusion coefficient (cm2/s)
○
C1 -value of high concentration (mmoles/cm3)
○
C2 -value of low concentration (mmoles/cm3)
○
X -distance separating C1 from C2 (cm)
○
J = D* (C1-C2)/X
!
Note: 0.5 M = 0.5 moles per L = 0.5 mmoles/ml = 0.5 mmoles/cm3
!
Hydration shells cause molecules to become
larger
"
Na+ binds water strongly, the
hydration shell is stable and moves
together with the cation
◊
Any Na+ movement
(retention/excretion) is followed by
H2O movement
◊
Na+ is the most hydrated ion, typically
with 4 or 6 water molecules in the first
layer, depending on the environment,
!
The more salt in ECF, the more water in
ECF, the higher volume and BP
!
K+ has a higher permeability across
cell membrane than Na+
◊
K+ is larger and has 8 more elections
shielding postively-charged nucleus, so
K+ makes transient associations with
water rather than a discrete hydration
layer (hydrated K+ is smaller than Na+)
!
Hydration of Na+ and K+ cations:
"
Size can be affected by hydration
!
Size of particle -larger particles will diffuse more slowly
(affects permeability)
○
Concentration -increases J
○
Permeability -increases J
○
Distance separating C1 from C2 -decreases J
○
Temperature -increases J
○
Factors that determine the diffusion coefficient:
!
Fick's Law of Diffusion
Diffusion of water through a semipermeable membrane from a
region of low solute concentration to a region of high solute
concentration
!
This would cause cells to swell
○
Water stops moving when the hydrostatic pressure = osmotic
pressure
!
Osmosis depends on the numberof solute particles in
solution not the type of particles
○
Freshwater animals gain water by osmosis
!
Hyperosmotic Solution -there is a higher solute
concentration in the environment (cell shrinks)
○
Hyposmotic Solution -there is a higher solute concentration
in the cell (cell swells)
○
Isomotic Solution -solute concentrations in cell are equal to the
environment (stays the same size)
!
Salt added to an isotonic solution --> hypertonic solution
(cell shrinks)
○
Urea added to an isotonic solution --> remains as a isotonic
solution
○
*membrane is impermeable to Na+ and Cl-but is permeant
to urea (so diffusion occurs)
○
Tonicity -effect of tonicity depends on the differences in
osmolarity, but also on the permeability of the membrane to the
solutes
!
Hypertonic solutions causes cells to shrink (lose water)
○
Isotonic solutions results in no change in cell volume
○
Hypotonic solutions causes cells to shrink (gains water)
○
Red blood cells in…
!
Osmosis
At equilibrium, the ratio of positively charged permeable ions
equals the ratio of negatively charged permeable ions
!
[K+]I/ [K+]II = [Cl-]II / [Cl-]I
○
The number of positive charges must equal the number of
negative charged on each side of the membrane
○
Mathematically expressed:
!
[K+]I = [A-]I + [Cl-]I
○
[K+]II = [Cl-]II
○
But, in real ells there are a large number of negatively charged,
impermeable molecules (proteins, nucleic acids…etc ) - these will
be represented as A-
!
Movements of solutes across a permeable membrane is
determined by both the chemical and electrical gradients
(the electrochemical gradient) *note equilibrium does not
mean that there are equal ion concentrations on either side
of the membrane
○
High -low concentration gradient
!
Positive -negative electrical gradient
!
Fast diffusion
!
Reinforcing concentration and electrical effects:
○
High -low concentration gradient
!
Negative -positive electrical gradient
!
Slow diffusion
!
Opposing concentration and electrical effects:
○
Electrochemical Gradients:
!
[Na+]in + [K+]in = [Cl-]in + [A-]in
○
[Na+]out + [K+]out = [Cl-]out **anionic proteins are only
inside the cell (not in ECF)
○
Principle of Electroneutrality
!
How an electrical charge is produced across a membrane
(Donnan potential)
○
The Donnan Equilibrium predicts that the distribution of
ions across a membrane will be unequal if the membrane is
impermeable to one or more types of charged particles
○
Used to calculate the potential difference across a
membrane due to unequal distribution of an ion
!
E -electrical potential (V or mV)
"
R -universal gas constant (8.312
joules/degree/mole)
"
T -absolute temperature (K)
"
z -sign and valence of ion
"
F -Faraday constant (96,500 coulombs per
mole)
"
E = RT/zF ln([ion outside]/[ion inside) = 2.3026
RT/zF log10 ([ion out]/[ion in])
!
Nernst Equation:
○
Donnan Equilibrium:
!
*see slide
○
Approximately obeys the Donnan rule
"
The internal and external [K]*[Cl] products are
about equal, and the Nernstian equilibrium
potential for both K and Cl are approximately
equal to the resting potential
"
Frog muscle
!
Does not obey the Donnan rule
"
The internal and external [K]*[Cl] products are
not equal, and the Nernstian equilibrium
potentials are different for K and Cl, and
different from the resting potential
"
Squid axon
!
Origin of the resting membrane potential:
○
Ionic charge separation occurs only within nanometers
of membranes
!
Within a few nanometers of the membrane on either
side, net positive and negative charge concentrations
may accumulate late because the lipid bilayers in a
cell membrane can maintain separation of oppositely
charged ions
!
The net charge in any given region of bulk
solution is zero
"
Farther away (in the bulk solution on either side),
positive and negative charges are mixed at random
!
Electrochemical Gradients:
○
100mM K+ on both sides
"
50 mM Cl-on the left, 100mM Cl-on the right
(shifts to the left)
"
50mM Proteins on left (none on right)
"
The osmolarity in 200mM on both sides
"
Initial:
!
114mM K+ on left, 86mM K+ on right
"
64mM Cl-on left, 86mM Cl-on right
"
Still 50mM proteins on left
"
H2O moves to the left side
"
E (Donnan potential) = -7.1mV
"
Osmolarity on the left is 228mM and 172mM
on the right
"
*note the osmotic imbalance
"
Final:
!
Example:
○
Donnan equilibrium occurs if cells are poisoned (can't
make ATP) or Na/K ATPase is inhibited --> cells
swell
!
If this process continues, the cells will
inevitably rupture
"
Water will continuously move into the cell by osmosis
!
Other consequences of the Donnan potential
○
Donnan Potential:
!
Most ubiquitous system in animal cells
!
The presence of ATP-driven Na+ and K+ pump is
nature's way of preventing cells from rupturing by
continuously pushing out excess ions
!
The sodium pump in the cell membrane
○
The sodium pump renders the membrane impermeable
to sodium, setting up a second Donnan Equilibrium
!
The earlier Donnan effect with respect to the
impermeable anionic colloids balances the latter
Donnan effect of impermeable extracellular sodium
!
The balancing act between these two effect is by way
of allowing cells to maintain and regulate normal cell
volume in living functions
!
The pup together with the membrane's low permeability to
sodium effectively prevents sodium from entering the cell
○
Preventing cells from swelling and rupturing:
!
Passive Distribution -Donnan Equilibrium & Potential
Summary: permeability of membranes to specific ions has major
consequences in determining membrane potentials and concentration
gradients
[A-] = molar
equivalent of
negative charges
carried by other
molecules and
ions (primarily
large proteins)
Diffusion & Osmosis
#$%&'()*+,-./0.12.&, 34+,5637
35895,:;
Ionic properties of the intra and extracellular compartments
!
Diffusion (Fick's law)
!
Osmosis
!
Nernst equation
!
Donnan equilibrium and Donnan potential
!
Outline:
Reading: Chapter 5 (pages 99-124)
Class Exercise: Donnan equilibrium calculation
Every cell of multicellular animals maintains concentrations of
inorganic solutes inside the cell that are very different from those
outside
!
Interior Exterior
[Na+] 10mM 120mM
[K+] 140 2.5
[Ca2+] < 10^-3 2
[Cl-] 3-4 120
[A-] 140 low
Mammal cell:
!
490 Na+
!
10 K+
!
500 Cl-
!
Environment (seawater)
○
490 Na+
!
10 K+
!
500 Cl-
!
Blood
○
70 Na+
!
200 K+
!
100 Cl-
!
630 other
!
Cell
○
Marine Invertebrates:
!
Gradient of sodium in and potassium out applies to all
multicellular animals
!
Electrical communication
○
E.g. ATP production by mitochondria
!
E.g. sodium gradient used to bring many things into
cells (sugars, amino acids)
!
Energy in electrical and chemical gradients can be used to
do work
○
Importance of ion/electric gradients:
!
Passice distribution -Donnan equilibrium
○
Active transport
○
Causes of ion distribution differences in cells:
!
Glucose diffuses in net fashion in the direction of
equilibrium, which is the direction that equalizes
concentration on the two sides of the membrane
○
More molecules pass through the membrane by this
chance process due to density of glucose molecules on
either side
!
As glucose molecules on the high concentration side
collides with other molecules, its random motions can line it
up to pass through a pore to the side with a lower
concentration
○
Example: simple diffusion viewed macroscopically and
microscopically
!
Entropy -random walks in 3 dimensions
○
Driving force:
!
Ionic Properties of the Intra-& Extracellular Compartments
The net rate of diffusion of a solute across a membrane
!
J -rate of diffusion or quantity of solute diffusing per unit
time (mmoles cm-2 s-1)
○
P -permeability
"
MW -molecular weight
"
D = P/ (sq.rt(MW))
!
D -diffusion coefficient (cm2/s)
○
C1 -value of high concentration (mmoles/cm3)
○
C2 -value of low concentration (mmoles/cm3)
○
X -distance separating C1 from C2 (cm)
○
J = D* (C1-C2)/X
!
Note: 0.5 M = 0.5 moles per L = 0.5 mmoles/ml = 0.5 mmoles/cm3
!
Hydration shells cause molecules to become
larger
"
Na+ binds water strongly, the
hydration shell is stable and moves
together with the cation
◊
Any Na+ movement
(retention/excretion) is followed by
H2O movement
◊
Na+ is the most hydrated ion, typically
with 4 or 6 water molecules in the first
layer, depending on the environment,
!
The more salt in ECF, the more water in
ECF, the higher volume and BP
!
K+ has a higher permeability across
cell membrane than Na+
◊
K+ is larger and has 8 more elections
shielding postively-charged nucleus, so
K+ makes transient associations with
water rather than a discrete hydration
layer (hydrated K+ is smaller than Na+)
!
Hydration of Na+ and K+ cations:
"
Size can be affected by hydration
!
Size of particle -larger particles will diffuse more slowly
(affects permeability)
○
Concentration -increases J
○
Permeability -increases J
○
Distance separating C1 from C2 -decreases J
○
Temperature -increases J
○
Factors that determine the diffusion coefficient:
!
Fick's Law of Diffusion
Diffusion of water through a semipermeable membrane from a
region of low solute concentration to a region of high solute
concentration
!
This would cause cells to swell
○
Water stops moving when the hydrostatic pressure = osmotic
pressure
!
Osmosis depends on the numberof solute particles in
solution not the type of particles
○
Freshwater animals gain water by osmosis
!
Hyperosmotic Solution -there is a higher solute
concentration in the environment (cell shrinks)
○
Hyposmotic Solution -there is a higher solute concentration
in the cell (cell swells)
○
Isomotic Solution -solute concentrations in cell are equal to the
environment (stays the same size)
!
Salt added to an isotonic solution --> hypertonic solution
(cell shrinks)
○
Urea added to an isotonic solution --> remains as a isotonic
solution
○
*membrane is impermeable to Na+ and Cl-but is permeant
to urea (so diffusion occurs)
○
Tonicity -effect of tonicity depends on the differences in
osmolarity, but also on the permeability of the membrane to the
solutes
!
Hypertonic solutions causes cells to shrink (lose water)
○
Isotonic solutions results in no change in cell volume
○
Hypotonic solutions causes cells to shrink (gains water)
○
Red blood cells in…
!
Osmosis
At equilibrium, the ratio of positively charged permeable ions
equals the ratio of negatively charged permeable ions
!
[K+]I/ [K+]II = [Cl-]II / [Cl-]I
○
The number of positive charges must equal the number of
negative charged on each side of the membrane
○
Mathematically expressed:
!
[K+]I = [A-]I + [Cl-]I
○
[K+]II = [Cl-]II
○
But, in real ells there are a large number of negatively charged,
impermeable molecules (proteins, nucleic acids…etc ) - these will
be represented as A-
!
Movements of solutes across a permeable membrane is
determined by both the chemical and electrical gradients
(the electrochemical gradient) *note equilibrium does not
mean that there are equal ion concentrations on either side
of the membrane
○
High -low concentration gradient
!
Positive -negative electrical gradient
!
Fast diffusion
!
Reinforcing concentration and electrical effects:
○
High -low concentration gradient
!
Negative -positive electrical gradient
!
Slow diffusion
!
Opposing concentration and electrical effects:
○
Electrochemical Gradients:
!
[Na+]in + [K+]in = [Cl-]in + [A-]in
○
[Na+]out + [K+]out = [Cl-]out **anionic proteins are only
inside the cell (not in ECF)
○
Principle of Electroneutrality
!
How an electrical charge is produced across a membrane
(Donnan potential)
○
The Donnan Equilibrium predicts that the distribution of
ions across a membrane will be unequal if the membrane is
impermeable to one or more types of charged particles
○
Used to calculate the potential difference across a
membrane due to unequal distribution of an ion
!
E -electrical potential (V or mV)
"
R -universal gas constant (8.312
joules/degree/mole)
"
T -absolute temperature (K)
"
z -sign and valence of ion
"
F -Faraday constant (96,500 coulombs per
mole)
"
E = RT/zF ln([ion outside]/[ion inside) = 2.3026
RT/zF log10 ([ion out]/[ion in])
!
Nernst Equation:
○
Donnan Equilibrium:
!
*see slide
○
Approximately obeys the Donnan rule
"
The internal and external [K]*[Cl] products are
about equal, and the Nernstian equilibrium
potential for both K and Cl are approximately
equal to the resting potential
"
Frog muscle
!
Does not obey the Donnan rule
"
The internal and external [K]*[Cl] products are
not equal, and the Nernstian equilibrium
potentials are different for K and Cl, and
different from the resting potential
"
Squid axon
!
Origin of the resting membrane potential:
○
Ionic charge separation occurs only within nanometers
of membranes
!
Within a few nanometers of the membrane on either
side, net positive and negative charge concentrations
may accumulate late because the lipid bilayers in a
cell membrane can maintain separation of oppositely
charged ions
!
The net charge in any given region of bulk
solution is zero
"
Farther away (in the bulk solution on either side),
positive and negative charges are mixed at random
!
Electrochemical Gradients:
○
100mM K+ on both sides
"
50 mM Cl-on the left, 100mM Cl-on the right
(shifts to the left)
"
50mM Proteins on left (none on right)
"
The osmolarity in 200mM on both sides
"
Initial:
!
114mM K+ on left, 86mM K+ on right
"
64mM Cl-on left, 86mM Cl-on right
"
Still 50mM proteins on left
"
H2O moves to the left side
"
E (Donnan potential) = -7.1mV
"
Osmolarity on the left is 228mM and 172mM
on the right
"
*note the osmotic imbalance
"
Final:
!
Example:
○
Donnan equilibrium occurs if cells are poisoned (can't
make ATP) or Na/K ATPase is inhibited --> cells
swell
!
If this process continues, the cells will
inevitably rupture
"
Water will continuously move into the cell by osmosis
!
Other consequences of the Donnan potential
○
Donnan Potential:
!
Most ubiquitous system in animal cells
!
The presence of ATP-driven Na+ and K+ pump is
nature's way of preventing cells from rupturing by
continuously pushing out excess ions
!
The sodium pump in the cell membrane
○
The sodium pump renders the membrane impermeable
to sodium, setting up a second Donnan Equilibrium
!
The earlier Donnan effect with respect to the
impermeable anionic colloids balances the latter
Donnan effect of impermeable extracellular sodium
!
The balancing act between these two effect is by way
of allowing cells to maintain and regulate normal cell
volume in living functions
!
The pup together with the membrane's low permeability to
sodium effectively prevents sodium from entering the cell
○
Preventing cells from swelling and rupturing:
!
Passive Distribution -Donnan Equilibrium & Potential
Summary: permeability of membranes to specific ions has major
consequences in determining membrane potentials and concentration
gradients
[A-] = molar
equivalent of
negative charges
carried by other
molecules and
ions (primarily
large proteins)
Diffusion & Osmosis
#$%&'()*+,-./0.12.&, 34+,5637 35895,:;
Document Summary
Ionic properties of the intra and extracellular compartments. Ionic properties of the intra- & extracellular compartments. Every cell of multicellular animals maintains concentrations of inorganic solutes inside the cell that are very different from those outside. [a-] = molar equivalent of negative charges carried by other molecules and ions (primarily large proteins) Gradient of sodium in and potassium out applies to all multicellular animals. Energy in electrical and chemical gradients can be used to do work. E. g. sodium gradient used to bring many things into cells (sugars, amino acids) Glucose diffuses in net fashion in the direction of equilibrium, which is the direction that equalizes concentration on the two sides of the membrane. As glucose molecules on the high concentration side collides with other molecules, its random motions can line it up to pass through a pore to the side with a lower concentration.
