Potassium Uptake

1
Potassium Uptake

• Over 90 of soil K is unavailable
• Most in the form of mica or feldspar
• Free K is easily leached
• Moves towards plant via bulk flow and diffusion
• Cannot effectively diffuse across the membrane

2
Membranes

• Act as semipermeable barriers
• 7 nm in thickness
• Diffusion is limited to small non polar molecules
• Lipid bilayer contains numerous proteins (30 of
  cell protein)
• These are largely involved in transport processes

3
Transporter Types
4
Potassium Transporters

• There are both high affinity and low affinity K
  transporters
• The low affinity transporter is an ion channel
• Works for K ion influx
• Can move 106 ions sec-1

5
Ion Channels

• Three general types
• Voltage gated
• Ligand gated
• Gap junction
• First 2 can transport against gradient
• How?

6
Ficks Law of Diffusion

• influx M PM Me A e
• PM is the permeability coefficient
• effluxM PM Mi A i
• At equilibrium
• Me A e Mi A i or
• Ai /A e Me/ M I g
• g Donnan Equilibrium

7
Donnan Equilbrium

• g 1 when all ions are free to permeate the
  membrane
• However, if charges are not free to diffuse (i.e
  - charged proteins Pi) a new equilibrium must
  be established
• Must still have Me Ae
• But now Mi Ai Pi

8
http//www.geocities.com/le_chatelier_uk/electroch
emistry.html
9
Donnan Equilibrium

• Now Mi gt Ai
• Therefore Me/ M i lt 1
• Also total ion concentration is larger on the
  inside than outside and a concentration gradient
  has been established for M
• These conditions are only applicable to K, Na and
  Cl

10
Chemical Equilibrium

• Membranes act as barriers
• Gradients can be established
• Chemical gradient
• m m RTlnC zFE VP mgh
• Effect of gravity(g) and pressure (P) are
  effectively zero in membrane biophysics

11
Chemical Potential

• The chemical potential can be rewritten
• m m RTlnC zFE
• m chemical potential
• m chemical potential at STP
• R gas constant, T Temperature, C
  concentration, z charge F Faradays constant
  E electrical voltage

12
Deriving the Nernst Equation

• If the molecule is neutral, then z is zero and
  the chemical potential is only dependant on the
  concentration
• However ions have a charge
• Combining chemical potential with the principles
  of Donnan equilibrium, one derives the Nernst
  Equation

13
Nernst Equation

• Cells establish potential across the membrane
• Must compare the chemical and electrical
  potentials inside and outside the membrane
• Rearrange the chemical potential formula to
  include the compartmentation
• Note m is cancelled

14
Nernst Equation

• Dm moutside - minside RTln (Coutside /
  Cinside) zF (Eoutside - Einside)
• Dm (difference in chemical potential)
• There the Dm is driven by a concentration
  gradient and an electrical gradient
• Thus an electrical charge will allow a chemical
  to move against its concentration gradient

15
Nernst Equation

• Rearranging the formula to derive electrical
  component results in the Nernst potential (DEn)
• DEn (2.3RT)/zF log (Coutside / Cinside)
• or (RT)/zF ln (Coutside / Cinside)
• Solve for K were z 1
• DEn 59 log (Ke/ K i )

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What does this mean?

• If a electrical potential of 59mV can be
  generated a 10 fold concentration difference can
  be maintained by simple diffusion
• Changing electrical potential shifts equilibrium
  causing a conformational change on the low
  affinity K ion channel
• Channel open (milliseconds) and K enters cell
  along its concentration gradient

17
Developing Electrochemical Potentials

• Membrane potentials will range from 20 - 200 mV
• Potential can be altered by
• Increasing intercellular anion concentration
• Active transport of H ions to the outside