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Ion movement across membranes problem set (#2)

Ion movement across membranes problem set (#2). UNI Plant Physiology 2005. How to use this program. Go slowly The challenge isn’t to understand The challenge is to absorb & retain Respond, rather than just read Write the answers on your own sheet

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Ion movement across membranes problem set (#2)

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  1. Ion movement across membranes problem set (#2) UNI Plant Physiology 2005

  2. How to use this program • Go slowly • The challenge isn’t to understand • The challenge is to absorb & retain • Respond, rather than just read • Write the answers on your own sheet • Own sheet already used? Write in a different color • Go through it one step at a time • Repeat until it makes sense

  3. Principles: charge & concentration • Ions have charge (makes them ions) • Cations are positive (+), anions are negative (-) • Ions move to region of opposite charge • This is downhill energetically • Ions move away from region of same charge • This is downhill energetically • Ions exist at a concentration • Independent concentrations for each kind • Ions move from higher to lower concentration • This is downhill energetically

  4. How much push/pull? Concentration vs charge • The force exerted by ___ mV charge • Fill in the blank if you can • 59 mV • Equals • The force exerted by ___ times the concentration difference • Fill in the blank if you can • 10 times concentration difference • Most cells have closer to 118 mV charge • = what concentration difference? • 10X for the first 59 mV times 10X for the second 59 mV • = 100X

  5. Principles: adding forces • Charge and electrical attraction may • Add together to move the ion in the same direction • Tend to move the ion in opposite directions • Exactly balance each other • This is equilibrium • Ions will move until equilibrium is established • This is the result of moving downhill energetically • It could happen slowly or quickly, but it will happen • Unless there is absolutely no route across the membrane for this ion (rare)

  6. Principles: membrane charge • Normal cells have charge (potential) across membrane • Usually positive (+) outside, negative (-) inside • What determines the potential (charge)? • Cell pumps protons (inside to out) • Protons come from organic acids inside • Major source of normal cell charge • Ions (+ or -) move across membrane • Cells usually do what is necessary to maintain fairly constant charge despite ion movement • Exceptions: guard cells, nerve cells, phloem depolarization

  7. [X+] = 1 mM [X+] = ? _ ΔV = 59 mV + Example #1 – a (setup) • Cell at equilibrium • Waited until it stopped changing • Sitting in lots of solution • Cell is -inside (normal) • Membrane electrical potential = 59 mV • Outside conc of the ion of interest = 1 mM • Want to know conc inside (at equilibrium)

  8. Example #1 – b (where to go?) • Where does ion “want” to go? • Check the charges • Ion is + • Inside is – • Ions will go inside if possible • Draw the arrow • After the ion moves • One side of membrane will have high [H] concentration • One side will have low [L] conc • Write these on the correct side [X+] = 1 mM [L] [X+] = ? [H] _ ΔV = 59 mV +

  9. Example #1 – c (how much?) • Membrane potential = 59 mV • Inside and outside concen-trations will differ by 10X • One will be 10 times the other • Is the inside high or low? • Look at H, L • Inside is high concentration side • Outside conc of ion of interest = 1 mM • Won’t change (large volume) • This is low concentration side • Inside must be 1 mM X 10 =? • Write it down • = 10 mM [X+] = 1 mM [L] [X+] = ? [X+] = 10 mM [H] _ ΔV = 59 mV +

  10. Example #1 – d (the story) • The positively charged ion moved to the negatively charged interior because of the attraction of the charges • As the concentration built up inside, the concentration differences tended to push the ion out • Ions will move until equilibrium is reached • At equilibrium (wait a long time) • Push out from concentration difference = • Pull in from charge differences • No net movement • Equilibrium of electrochemical potential (ECP) • Not concentration alone • Not charge alone • Combined effect: ECP • ECP of K+ outside = ECP of K+ inside • Membrane maintains original charge (regulated by other ion movement) • Effect (force) of 59 mV equals effect (force) of 10X concentration difference • Consequence: It’s easy to get cations into cells—just open the channels [X+] = 1 mM [L] [X+] = ? [X+] = 10 mM [H] _ ΔV = 59 mV +

  11. [X+] = 1 mM [X+] = ? + ΔV = 59 mV _ Example #2 – a (setup) • Cell at equilibrium • Waited until it stopped changing • Sitting in lots of solution • Outside conc of the ion of interest = 1 mM • Ion has + charge • Cell is + inside (unusual) • Membrane potential = 59 mV • Want to know conc inside (at equilibrium)

  12. Example #2 – b (where to go?) • Where does ion “want” to go? • Check the charges • Ion is + • Inside is + • Ions will go outside if possible • Draw the arrow • After the ion moves • One side of membrane will have high [H] concentration • One side will have low [L] conc • Write these on the correct side [X+] = 1 mM [H] [X+] = ? [L] + ΔV = 59 mV _

  13. Example #2 – c (how much?) • Membrane potential = 59 mV • Inside and outside concen-trations will differ by 10X • One will be 10 times the other • Is the inside high or low? • Look at H, L • Inside is low concentration side • Outside conc of ion of interest = 1 mM • Won’t change (large volume) • This is high concentration side • Inside must be 1 mM / 10 =? • Write it down • = 0.1 mM [X+] = 1 mM [H] [X+] = ? [X+] = 0.1 mM [L] + ΔV = 59 mV _

  14. Example #2 – d (the story) • The positively charged ion moved to the negatively charged exterior because of the attraction of the charges • As the concentration is lowered inside, the concentration differences tended to pull the ion in • Ions will move until equilibrium is reached • At equilibrium (wait a long time) • Push in from concentration difference = • Pull out from charge differences • No net movement • Equilibrium of electrochemical potential (ECP) • Not concentration alone • Not charge alone • Combined effect: ECP • ECP of K+ outside = ECP of K+ inside • Membrane maintains original charge (regulated by other ion movement) • Effect (force) of 59 mV equals effect (force) of 10X concentration difference • Consequence: It would be hard to get cations into cells, but this isn’t a problem because the cells aren’t normally charged this way [X+] = 1 mM [H] [X+] = ? [X+] = 0.1 mM [L] + ΔV = 59 mV _

  15. [X-] = 1 mM [X-] = ? _ ΔV = 59 mV + Example #3 – a (setup) • Cell at equilibrium • Waited until it stopped changing • Sitting in lots of solution • Outside conc of the ion of interest = 1 mM • Ion has - charge • Cell is - inside (usual) • Membrane potential = 59 mV • Want to know conc inside (at equilibrium)

  16. Example #3 – b (where to go?) • Where does ion “want” to go? • Check the charges • Ion is - • Inside is - • Ions will go outside if possible • Draw the arrow • After the ion moves • One side of membrane will have high [H] concentration • One side will have low [L] conc • Write these on the correct side [X-] = 1 mM [H] [X-] = ? [L] _ ΔV = 59 mV +

  17. Example #3 – c (how much?) • Membrane potential = 59 mV • Inside and outside concen-trations will differ by 10X • One will be 10 times the other • Is the inside high or low? • Look at H, L • Inside is low concentration side • Outside conc of ion of interest = 1 mM • Won’t change (large volume) • This is high concentration side • Inside must be 1 mM / 10 =? • Write it down • = 0.1 mM [X-] = 1 mM [H] [X+] = ? [X-] = 0.1 mM [L] _ ΔV = 59 mV +

  18. Example #3 – d (the story) • The negatively charged ion moved to the positively charged exterior because of the attraction of the charges • As the concentration is lowered inside, the concentration differences tended to push the ion in • Ions will move until equilibrium is reached • At equilibrium (wait a long time) • Push in from concentration difference = • Pull out from charge differences • No net movement • Equilibrium of electrochemical potential (ECP) • Not concentration alone • Not charge alone • Combined effect: ECP • ECP of K+ outside = ECP of K+ inside • Membrane maintains original charge (regulated by other ion movement) • Effect (force) of 59 mV equals effect (force) of 10X concentration difference • Consequence: It is hard to get lots of anions into cells. As a result, cells usually use some other mechanism (such as cotransport or countertransport) to do the job. [X-] = 1 mM [H] [X+] = ? [X-] = 0.1 mM [L] _ ΔV = 59 mV +

  19. [X-] = 1 mM [X-] = ? + ΔV = 59 mV _ Example #4 – a (setup) • Cell at equilibrium • Waited until it stopped changing • Sitting in lots of solution • Outside conc of the ion of interest = 1 mM • Ion has - charge • Cell is + inside (normal) • Membrane potential = 59 mV • Want to know conc inside (at equilibrium)

  20. Example #4 – b (where to go?) • Where does ion “want” to go? • Check the charges • Ion is - • Inside is + • Ions will go inside if possible • Draw the arrow • After the ion moves • One side of membrane will have high [H] concentration • One side will have low [L] conc • Write these on the correct side [X-] = 1 mM [L] [X-] = ? [H] + ΔV = 59 mV _

  21. Example #4 – c (how much?) • Membrane potential = 59 mV • Inside and outside concen-trations will differ by 10X • One will be 10 times the other • Is the inside high or low? • Look at H, L • Inside is high concentration side • Outside conc of ion of interest = 1 mM • Won’t change (large volume) • This is low concentration side • Inside must be 1 mM X 10 =? • Write it down • = 10 mM [X-] = 1 mM [L] [X+] = ? [X-] = 10 mM [H] + ΔV = 59 mV _

  22. Example #4 – d (the story) • The negatively charged ion moved to the positively charged interior because of the attraction of the charges • As the concentration built up inside, the concentration differences tended to push the ion out • Ions will move until equilibrium is reached • At equilibrium (wait a long time) • Push out from concentration difference = • Pull in from charge differences • No net movement • Equilibrium of electrochemical potential (ECP) • Not concentration alone • Not charge alone • Combined effect: ECP • ECP of K+ outside = ECP of K+ inside • Membrane maintains original charge (regulated by other ion movement) • Effect (force) of 118 mV equals effect (force) of 100X concentration difference • Consequence: It would be easy to get anions into the cell, but alas, the membrane is not normally charged this way, so this isn’t a realistic example. [X-] = 1 mM [L] [X+] = ? [X-] = 10 mM [H] + ΔV = 59 mV _

  23. Example #5 – a (setup) • Cell at equilibrium • Waited until it stopped changing • Sitting in lots of solution • Outside conc of the ion of interest = 10 mM • Ion has + charge • Cell is - inside (normal) • Membrane potential = 59 mV • Want to know conc inside (at equilibrium) [X+] = 10 mM [X+] = ? ΔV = 118 mV + _

  24. Example #5 – b (where to go?) • Where does ion “want” to go? • Check the charges • Ion is + • Inside is – • Ions will go inside if possible • Draw the arrow • After the ion moves • One side of membrane will have high [H] concentration • One side will have low [L] conc • Write these on the correct side [X+] = 10 mM [L] [X+] = ? [H] _ ΔV = 118 mV +

  25. Example #5 – c (how much?) • Membrane potential = 118 mV • Inside and outside concentrations will differ by 10 x 10 • 10X for first 59 mV, 10X for second • One will be 100 times the other • Is the inside high or low? • Look at H, L • Inside is high concentration side • Outside conc of ion of interest = 1 mM • Won’t change (large volume) • This is low concentration side • Inside must be 10 mM X 100 =? • Write it down • = 1000 mM = 1 M [X+] = 10 mM [L] [X+] = ? [X+] = 1000 mM [H] _ ΔV = 118 mV +

  26. Example #5 – d (the story) • The positively charged ion moved to the negatively charged interior because of the attraction of the charges • As the concentration built up inside, the concentration differences tended to push the ion out • Ions will move until equilibrium is reached • At equilibrium (wait a long time) • Push out from concentration difference = • Pull in from charge differences • No net movement • Equilibrium of electrochemical potential (ECP) • Not concentration alone • Not charge alone • Combined effect: ECP • ECP of K+ outside = ECP of K+ inside • Membrane maintains original charge (regulated by other ion movement) • Effect (force) of 59 mV equals effect (force) of 10X concentration difference • Consequence: It’s REALLY easy to get cations into cells—just open the channels, which is what cells usually do. [X+] = 10 mM [L] [X+] = ? [X+] = 100 mM [H] _ ΔV = 118 mV +

  27. [X-] = 10 mM [X-] = ? _ ΔV = 118 mV + Example #6 – a (setup) • Cell at equilibrium • Waited until it stopped changing • Sitting in lots of solution • Outside conc of the ion of interest = 10 mM • Ion has - charge • Cell is - inside (usual) • Membrane potential = 59 mV • Want to know conc inside (at equilibrium)

  28. Example #6 – b (where to go?) • Where does ion “want” to go? • Check the charges • Ion is - • Inside is - • Ions will go outside if possible • Draw the arrow • After the ion moves • One side of membrane will have high [H] concentration • One side will have low [L] conc • Write these on the correct side [X-] = 10 mM [H] [X-] = ? [L] _ ΔV = 118 mV +

  29. Example #6 – c (how much?) • Membrane potential = 118 mV • Inside and outside concentrations will differ by 10 x 10 • 10X for first 59 mV, 10X for second • One will be 100 times the other • Is the inside high or low? • Look at H, L • Inside is low concentration side • Outside conc of ion of interest = 10 mM • Won’t change (large volume) • This is high concentration side • Inside must be 10 mM / 100 =? • Write it down • = 0.1 mM [X-] = 10 mM [H] [X+] = ? [X-] = 0.1 mM [L] _ ΔV = 118 mV +

  30. Example #6 – d (the story) • The negatively charged ion moved to the positively charged exterior because of the attraction of the charges • As the concentration is lowered inside, the concentration differences tended to push the ion in • Ions will move until equilibrium is reached • At equilibrium (wait a long time) • Push in from concentration difference = • Pull out from charge differences • No net movement • Equilibrium of electrochemical potential (ECP) • Not concentration alone • Not charge alone • Combined effect: ECP • ECP of K+ outside = ECP of K+ inside • Membrane maintains original charge (regulated by other ion movement) • Effect (force) of 118 mV equals effect (force) of 100X concentration difference • Consequence: It is hard to get lots of anions into cells. As a result, cells usually use some other mechanism (such as cotransport or countertransport) to do the job. [X-] = 1 mM [H] [X+] = ? [X-] = 0.1 mM [L] _ ΔV = 118 mV +

  31. In nature, cations (+) • Usually go in through channels because the charge will pull in as much as the cell needs • No direct energy required: passive transport • Examples: K+, Ca2+, Mg2+ • It’s a problem keeping undesirable cations (Na+) out—they may need active transport to escort them back out when they leak in

  32. In nature, anions • Are hard to get in, because the membrane charge tends to drive them out • Are still needed in large quantities (NO3-, PO43-) • So they tend to be cotransported in, coupled with a cation that “wants” to go in • Anions are often hitchhikers

  33. Protons, friend of transport • Proton pumps are the source of much of the + charge on the outside • They leave behind negatively charged organic acids (etc.) • This makes it easy to get cations in passively • Protons “want” to go back inside • Anions hitch a ride (cotransport) in with protons

  34. Problems to solve • We have a concentration of a particular ion inside and outside a cell • We want to know if transport energy is necessary to have that cell concentration • Steps • Calculate equilibrium value of concentration • See if the actual measurements agree • Are the inside and the outside at ECP equilibrium? • Is energy required? • Why do you say this?

  35. Example #7determine equilibrium concentration • Decide whether the inside will be high or low concentration • Check the charges • Draw the arrow • Write [H] and [L] on correct sides • Use the membrane potential to calculate the concentration difference • Write it down • Do the arithmetic [K+] = 1 mM [L] [K+] = ? [K+] = 100 mM [H] 100X ΔV = 118 mV _ +

  36. Equilibrium (predicted) Actual (measured) [K+] = 1 mM [K+] = 1 mM [K+] = 100 mM [K+] = 100 mM _ _ ΔV = 118 mV ΔV = 118 mV + + Example #7 compare equilibrium & actual values

  37. Example #7: Ask the questions • ECP equilibrium • Is the ECP of K+ inside the cell the same as the ECP of K+ outside the cell? • For the predicted? Yes, we used the equilibrium state to get the predicted values • For the measured? Yes, because the measured values are the same as the predicted values • Is transport energy required to maintain this state? No, because the ECP of K+ is the same on both sides of the membrane.

  38. Example #8determine equilibrium concentration • Decide whether the inside will be high or low concentration • Check the charges • Draw the arrow • Write [H] and [L] on correct sides • Use the membrane potential to calculate the concentration difference • Write it down • Do the arithmetic [NO3-] = 0.1 mM [H] [NO3-] = 0.001 mM [NO3-] = ? [L] 100X ΔV = 118 mV _ +

  39. Equilibrium (predicted) Actual (measured) [NO3-]= 0.1 mM [NO3-] = 0.1 mM [NO3-] = 0.001 mM [NO3-] = 1 mM _ _ ΔV = 118 mV ΔV = 118 mV + + Example #8 compare equilibrium & actual values

  40. Example #8: Ask the questions • ECP equilibrium • Is the ECP of NO3- inside the cell the same as the ECP of NO3- outside the cell? • For the predicted? Yes, we used the equilibrium state to get the predicted values • For the measured? No, because the measured values are higher than the predicted values • Is transport energy required to maintain this state? Yes, because the ECP of NO3- is higher on the inside of the membrane than on the outside.

  41. Example #9determine equilibrium concentration • Decide whether the inside will be high or low concentration • Check the charges • Draw the arrow • Write [H] and [L] on correct sides • Use the membrane potential to calculate the concentration difference • Write it down • Do the arithmetic [Na+] = 10 mM [L] [Na+] = 1000 mM [Na+] = ? [H] 100X ΔV = 118 mV _ +

  42. Equilibrium (predicted) Actual (measured) [Na+] = 10 mM [Na+] = 10 mM [K+] = 1000 mM [K+] = 0.1 mM _ _ ΔV = 118 mV ΔV = 118 mV + + Example #9 compare equilibrium & actual values

  43. Equilibrium (predicted) Actual (measured) [NO3-]= 0.1 mM [NO3-] = 0.1 mM [NO3-] = 0.001 mM [NO3-] = 1 mM _ _ ΔV = 118 mV ΔV = 118 mV + + Example #8 compare equilibrium & actual values

  44. Example #9: Ask the questions • ECP equilibrium • Is the ECP of Na+ inside the cell the same as the ECP of Na+ outside the cell? • For the predicted? Yes, we used the equilibrium state to get the predicted values • For the measured? No, because the measured values are lower than the predicted values • Is transport energy required to maintain this state? Yes, because the ECP of Na+ is lower on the inside of the membrane than on the outside.

  45. In nature • A cell has an ECP difference (or not) • For each different ion • At the same time, in the same cell • So the cell is busy • Opening channels to allow some cations in • Using energy to remove undesirable cations • Cotransporting to bring in anions • All going on simultaneously in each cell

  46. In conclusion • Membranes are busy places • You can understand what’s going on • It all depends on ECP • Not just concentration • Not just electrical charge • Both combined: ECP

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