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Chemical Potential and Molecular Transport Across a Permeability Barrier
Solute Transport in Plants
1. Physical & Chemical Principles Governing Transport
Chemical Potential
Passive & Active Transport
2. Molecular Mechanisms Governing Transport
Ion Transport Across Membranes
Nernst Equation
Membrane Transport Proteins
Channels
Carriers
Pumps
Active Transport
Primary & Secondary
Aquaporins
ABC Binding Cassettes
Development of a Diffusion Potential and a Charge Separation
Chemical Potential Equation
Nonionizing Solute
Membrane preferentially permeable to K+
uj = uj* + RTlnCj
uj = chemical potential of a solute (Joules mol-1)
uj* = chemical potential of a solute under
u us
Charge imbalance
across membrane
K+ diffuses faster
Æ Charge separation
Æ diffusion potential
Chemical Potential
Nonionizing Solute like Sucrose
μ~i = μ* + RT ln C i
Chemical Potential Inside the Cell
μ~ o = μ* + RT ln C o
Chemical Potential Outside the Cell
s
s
s
s
s
Δμ~ = μ~i − μ~ o
s
s
s
i
C
Δμ~ = RT ln s
s
Co
s
s
Chemical Potential Difference
Between inside and outside of cell
Chemical Potential Difference is
a Concentration Difference
standard conditions
RTlnCj = concentration component (activity)
Chemical Potential
Nonionizing Solute like Sucrose
C i Chemical Potential Difference is
~
Δμ = RT ln s a Concentration Difference
s
Co
s
C i 1.0
~
s =
= 10 Higher concentration inside cell Positive Δμ s
~
o
0
.
1
Positive Δμ Movement Out of Cell
C
s
s
Higher concentration outside cell Negative
Δμ~
C i 0.1
s
s =
= 0.1 Negative Δμ~ Movement Into Cell
o
s
1
.
0
C
s
Chemical Potential
Ionizing Solute like Potassium (K+)
Chemical Potential of an Ionizing Solute
u = uj* + RTlnCj + zjFE
uj = chemical potential of a solute (Joules mol-1)
Δμ~
uj* = chemical potential of a solute under standard conditions
Δμ~
RTlnCj = concentration component (activity)
zjFE = electrical potential component
Zj = electrostatic charge of an ion (e.g. +1 for a monovalent cation)
F = Faraday’s constant
(charge on 1 mole of protons)
E = electric potential of a solution (relative to ground)
Nerst Equation & Electrochemical Potential
0.0
μ *j + ( RT ln C oj + z j FE o ) = μ *j + ( RT ln C ij + z j FE i )
Difference in Electrical Potential at Equilibrium
At equilibrium, Electrochemical potential must be equal on both sides of a membrane
Rearranging the equation
or
ΔE j = E i − E o =
Ei − Eo =
o
RT ⎛⎜ C j ⎞⎟
ln i
z j F ⎜⎝ C j ⎟⎠
o
RT ⎛⎜ C j ⎞⎟
ln i
z j F ⎜⎝ C j ⎟⎠
= μ~i + − μ~ o+
K+
K
K+
[ ] + ZFE ) − (RT ln[K ] + ZFE )
[K ] + F (E − E )
= ( RT ln
[K ]
= ( RT ln K
Δμ~
K+
o
RT ⎛⎜ C j ⎞⎟
ln
z j F ⎜⎝ C ij ⎟⎠
Application of Nernst Potential
For a univalent cation at 25 C
⎛ Co ⎞
ΔE j = 59mV log⎜ ji ⎟
⎜C ⎟
⎝ j⎠
Distinguishing between active
and passive transport.
If Co is 10x > Ci Æ Voltage drop = 59mV
+ i
+ o
i
o
+ i
i
o
+ o
Chemical
Potential = Concentration +
Difference Difference
Electrical
Potential
Difference
Nerst Equation
Difference in Electrical Potential at Equilibrium
Nernst equation
1. Applies to ions
2. At equilibrium, concentration difference is
balanced by electrical potential difference
3.
ΔE j
Voltage Drop is balanced by the Concentration difference
ΔE j = E i − E o =
= Chemical Potential Difference
K
ΔE j = E i − E o =
c oj ⎞
2.3RT ⎛
⎜⎜ log i ⎟⎟
zjF ⎝
cj ⎠
o
RT ⎛⎜ C j ⎞⎟
ln
z j F ⎜⎝ C ij ⎟⎠
Application of Nernst Potential
For a univalent cation at 25 C
⎛ Co ⎞
ΔE j = 59mV log⎜ ji ⎟
⎜C ⎟
⎝ j⎠
Distinguishing between active
and passive transport.
If Co is 10> Ci, Voltage drop = 59mV
Conclusions about ion movement based on Nernst Potentials in Pea Root Cells
Relevance of Proton Pumping in Plasma Membrane
(Dashed lines fi passive transport
Solid lines fi active transport)
1. K+ can accumulate passively in cytosol &
vacuole.
2.
Na+1
Ca+2
and
are actively transported
out of cytosol or into vacuole.
3. All anions are actively transported into
cytosol from external environment.
4. Anions like NO3- and H2PO4- are
transported from vacuole to cytosol.
5. Protons transported out of cytosol to
external environment
1. ATPase pumps protons out of cell, causing generation of a
membrane potential.
2. Pumping protons out creates more negative potential in cytosol:
1. Driving force for passive diffusion of K+ into cell.
2. Responsible for proton cotransport of anions into cytosol
3. In soil, H+ displaces other nutrient cations.
Lyotropic series
Al+3>H+>Ca+2>Mg+2>K+1=NH+4>Na+1
Membrane Transport Proteins
1. Channels
2. Carriers
3. Pumps & Primary active transport
4. Secondary active transport
Symport
Antiport
5. Aquaporins
6. ABC Binding Cassettes
Membrane Transport Proteins - Channels
1. Transmembrane protein with
specific size and charge
2. Transport is always passive.
3. Usually limited to ions & water.
4. Channels variation regulated by
1. Hormones
2. Voltage
3. Light
5. Rapid ≈ 108 molecules/second
6. K+ Channels may be
1. Inward rectifying
1. E.g. in stomatal opening
2. Outward rectifying
1. E.g. in stomatal closing
Membrane Transport Proteins - Carriers
1. Proteins but pores don’t cross
membrane
2. Carriers bind transported molecules.
3. Highly specific.
4. Rate: 100-1000 molecules/second
(106 times slower than channel transport)
5. Saturation kinetics.
6. Can be passive = facilitated diffusion
or active transport.
Membrane Transport Proteins - Primary Active Transport
1. Require source of energy
1. ATP…called ATPases
2. Oxidation-reduction
3. Light (bacteriorhodopsin)
2. 1o Active Transport Membrane
Proteins = Pumps
3. Transport:
1. Protons
2. Ions
3. Large Organic Molecules
4. Can be electrogenic
1. Leads to charge imbalance
5. Can be electroneutral
1. No change in electrical potential
Proton Transport in a plant cell
Membrane Transport Proteins
Channels
Carriers
Pumps
Solute
Concentration
Accumulated Protons
Kinetic Analyses of Transport
Distinguishing between simple diffusion
and Carrier Transport.
Carrier transport Æ saturation kinetics
Membrane Potential Relies on ATP
Membrane potential of a pea cell
Solute transport properties can change
over a range of concentrations
1. Cyanide poisons
respiration.
ATP synthesis
blocked by CN-
Solute transport
Can be both carrier-mediated or through channels
Water Diffusion Across Cell Membrane
Sucrose transport in soybean cells
Channel? mediated
Diffusion
across cell
membrane
Diffusion
through
aquaporin
Carrier-mediated
Roles of aquaporins
1. Water diffusion
2. Uncharged solute movement
3. CO2 ?
Plasma Membrane H+ - ATPase
1. P-type ATPase fi enzyme is
phosphorylated as part of catalytic cycle.
Vacuolar H+ - ATPase
1. Electrogenic proton pumps transport protons
from cytosol to vacuole.
2. 10 membrane-spanning domains
3. Regulated by pH, temperature, [ATP]
2. V-type ATPase fi enzyme is like F-ATPase
(ATPsynthase) in mitochondria.
4. Inhibited by orthovanadate (a phosphate
analog)
3. Rotation of subunits drives proton transport
across the membrane.
5. Enzyme has an autoinhibitory domain
4. Inhibited by bafilomycin and high [nitrate]
1. Influenced by light, hormones,
pathogen attack
5. Functions of Vacuolar H+ - ATPase
2. H+ - ATPase activation by
1. Dephosphorylation of residues
This will
1. Drive anion uptake into vacuoles due
to electrical component
2. Drive cation and sugar uptake by
secondary transport (antiport).
6. Lemons are sour because of hyperacidification
Membrane Transport Proteins
Secondary Active Transport
1. Acidifies vacuolar sap to pH 5.5.
1. Symport
1. Anions
2. Sugars
3. Amino Acids
2. Antiport
1. Sodium
ATP Binding Cassette Transporters
Transport at the Tonoplast
ABC transporters
Æ use the energy of ATP hydrolysis directly
form a phosphorylated intermediate during catalysis
Æ pump organic molecules … large anionic molecules
Æ Glutathione (Glu-Cys-Gly) conjugates with molecules being transported
Conjugates going into vacuole
Herbicides …detoxificaiton
Heavy metals chelated to polypeptides…detoxification
Anthocyanins…pigment accumulation
Conjugates going into vacuole
anti-fungal terpenes across the plasma membrane
ATP
Binding
Cassette
Transporters
Transport at the Plasma Membrane
End
Solute Movement
Transport at the Plasma Membrane