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 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) [X + ] = 1 mM [X + ] = ? _ + ΔV = 59 mV

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 [X + ] = ? + ΔV = 59 mV _ [H] [L]

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

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 [X + ] = ? + ΔV = 59 mV _ [H] [X + ] = 10 mM [L]

11 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) [X + ] = 1 mM [X + ] = ? + _ ΔV = 59 mV

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 [X + ] = ? _ ΔV = 59 mV + [H] [L]

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

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 [X + ] = ? _ ΔV = 59 mV + [H] [X + ] = 0.1 mM [L]

15 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) [X - ] = 1 mM [X - ] = ? _ + ΔV = 59 mV

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 [X - ] = ? _ ΔV = 59 mV + [H] [L]

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

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 [X + ] = ? + ΔV = 59 mV _ [H] [X - ] = 0.1 mM [L]

19 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) [X - ] = 1 mM [X - ] = ? + _ ΔV = 59 mV

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 [X - ] = ? _ ΔV = 59 mV + [H] [L]

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

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 [X + ] = ? _ ΔV = 59 mV + [H] [X - ] = 10 mM [L]

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 [X + ] = ? + ΔV = 118 mV _ [H] [L]

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

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 [X + ] = ? + ΔV = 118 mV _ [H] [X + ] = 100 mM [L]

27 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) [X - ] = 10 mM [X - ] = ? _ + ΔV = 118 mV

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 [X - ] = ? _ ΔV = 118 mV + [H] [L]

29 Example #6 – c (how much?) Membrane potential = 118 mV –I–Inside and outside concentrations will differ by 10 x 10 –1–10X for first 59 mV, 10X for second –O–One will be 100 times the other Is the inside high or low? –L–Look at H, L –I–Inside is low concentration side Outside conc of ion of interest = 10 mM –W–Won’t change (large volume) –T–This is high concentration side Inside must be 10 mM / 100 =? –W–Write it down –=–= 0.1 mM [X - ] = 10 mM [X + ] = ? + ΔV = 118 mV _ [H] [X - ] = 0.1 mM [L]

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 [X + ] = ? + ΔV = 118 mV _ [H] [X - ] = 0.1 mM [L]

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 +, Ca 2+, Mg 2+ 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 (NO 3 -, PO 4 3- ) 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 #7 determine 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 [K + ] = ? + ΔV = 118 mV _ [H] [L] [K + ] = 100 mM 100X

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

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 #8 determine 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 [NO 3 - ] = 0.1 mM [NO 3 - ] = ? + ΔV = 118 mV _ [H] [L] [NO 3 - ] = mM 100X

39 Example #8 compare equilibrium & actual values [NO 3 - ]= 0.1 mM + ΔV = 118 mV _ [NO 3 - ] = mM Equilibrium (predicted) [NO 3 - ] = 0.1 mM + ΔV = 118 mV _ [NO 3 - ] = 1 mM Actual (measured)

40 Example #8: Ask the questions ECP equilibrium –Is the ECP of NO 3 - inside the cell the same as the ECP of NO 3 - 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 NO 3 - is higher on the inside of the membrane than on the outside.

41 Example #9 determine 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 [Na + ] = ? + ΔV = 118 mV _ [H] [L] [Na + ] = 1000 mM 100X

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

43 Example #8 compare equilibrium & actual values [NO 3 - ]= 0.1 mM + ΔV = 118 mV _ [NO 3 - ] = mM Equilibrium (predicted) [NO 3 - ] = 0.1 mM + ΔV = 118 mV _ [NO 3 - ] = 1 mM Actual (measured)

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