Ion movement across membranes problem set

Ion movement across membranes

problem set

UNI Plant Physiology

2009

How to use this program

• Go slowly– The challenge isn’t to understand– The challenge is to absorb & retain

• Respond, rather than just read– Right 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

Principles: charge & concentration

• Ions have charge (makes them ions)– Ions move to region of opposite charge

• This is downhill energetically

– Ions move from a region of the 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

How much push/pull? Concentration vs charge

• The force exerted by ___ mV charge – Fill it in now if you can (but don’t write on the screen)– 59 mV

• Equals• The force exerted by ___ times concentration

difference– Fill it in 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

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)

Principles: membrane charge

• Normal cells have charge (potential) across membrane– Usually + outside, - 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– Cell usually do what is necessary to maintain fairly

constant charge despite ion movement• Exceptions: guard cells, nerve cells, phloem depolarization

Example #1 – 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

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]

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

[X+] = ?

+

ΔV = 59 mV

_

[H]

[X+] = 10 mM

[L]

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]





• Ion has + charge• Cell is + inside (unusual)



[X+] = 1 mM

[X+] = ?

+

_

ΔV = 59 mV


• Where does ion “want” to go?– Check the charges– Ion is +– Inside is +– Ions will go outside if possible – Draw the arrow



[X+] = 1 mM

[X+] = ?

_

ΔV = 59 mV

+

[H]

[L]




• 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

[X+] = ?

_

ΔV = 59 mV

+

[H]

[X+] = 0.1 mM

[L]


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


– Push in from concentration difference =– Pull out from charge differences– No net movement– Equilibrium of electrochemical potential (ECP)




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]





• Ion has - charge• Cell is - inside (usual)



[X-] = 1 mM

[X-] = ?

_

+

ΔV = 59 mV


• Where does ion “want” to go?– Check the charges– Ion is -– Inside is -– Ions will go outside if possible – Draw the arrow



[X-] = 1 mM

[X-] = ?

_

ΔV = 59 mV

+

[H]

[L]







[X-] = 1 mM

[X+] = ?

+

ΔV = 59 mV

_

[H]

[X-] = 0.1 mM

[L]

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






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]





• Ion has - charge• Cell is + inside (normal)



[X-] = 1 mM

[X-] = ?

+

_

ΔV = 59 mV


• Where does ion “want” to go?– Check the charges– Ion is -– Inside is +– Ions will go inside if possible – Draw the arrow



[X-] = 1 mM

[X-] = ?

_

ΔV = 59 mV

+

[H]

[L]






• Inside must be 1 mM X 10 =?– Write it down – = 10 mM

[X-] = 1 mM

[X+] = ?

_

ΔV = 59 mV

+

[H]

[X-] = 10 mM

[L]


positively charged interior because of the attraction of the charges





– 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]





• Ion has + charge• Cell is - inside (normal)



[X+] = 10 mM

[X+] = ?

_

+

ΔV = 118 mV


• Where does ion “want” to go?– Check the charges– Ion is +– Inside is –– Ions will go inside if possible – Draw the arrow



[X+] = 10 mM

[X+] = ?

+

ΔV = 118 mV

_

[H]

[L]


– 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



• Inside must be 10 mM X 100 =?– Write it down – = 1000 mM = 1 M

[X+] = 10 mM

[X+] = ?

+

ΔV = 118 mV

_

[H]

[X+] = 1000 mM

[L]


negatively charged interior because of the attraction of the charges







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]





• Ion has - charge• Cell is - inside (usual)



[X-] = 10 mM

[X-] = ?

_

+

ΔV = 118 mV


• Where does ion “want” to go?– Check the charges– Ion is -– Inside is -– Ions will go outside if possible – Draw the arrow



[X-] = 10 mM

[X-] = ?

_

ΔV = 118 mV

+

[H]

[L]


– 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




[X-] = 10 mM

[X+] = ?

+

ΔV = 118 mV

_

[H]

[X-] = 0.1 mM

[L]


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






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]

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

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

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

Problems to solve

• We have a cell concentration situation, and want to know if energy is necessary to transport the ion to get to and maintain the situation we have.

• Steps– Calculate equilibrium value of concentration– See if the actual measurements agree

• Is the inside and the outside at ECP equilibrium?

• Is energy required? • Why do you say this?

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

[K+] = ?

+

ΔV = 118 mV

_

[H]

[L]

[K+] = 100 mM

100X

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)

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.



sides



[NO3-] = 0.1 mM

[NO3-] = ?

+

ΔV = 118 mV

_

[H]

[L]

[NO3-] = 0.001 mM

100X


[NO3-]= 0.1

mM

+

ΔV = 118 mV

_

[NO3-] = 0.001

mM


[NO3-] = 0.1

mM

+

ΔV = 118 mV

_

[NO3-] = 1 mM

Actual (measured)


• 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.



sides



[Na+] = 10 mM

[Na+] = ?

+

ΔV = 118 mV

_

[H]

[L][Na+] = 1000 mM

100X


[Na+] = 10 mM

+

ΔV = 118 mV

_

[K+] = 1000 mM


[Na+] = 10 mM

+

ΔV = 118 mV

_

[K+] = 0.1 mM

Actual (measured)


[NO3-]= 0.1

mM

+

ΔV = 118 mV

_

[NO3-] = 0.001

mM


[NO3-] = 0.1

mM

+

ΔV = 118 mV

_

[NO3-] = 1 mM

Actual (measured)


• 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.

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

• This is all going on simultaneously in each cell

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

Ion movement across membranes problem set

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