Download The changing rates of Hexose Transport – problem calculations

The changing rates of Hexose Transport – problem calculations
Wine making (Oenology) requires sophisticated math and biology skills.
Check out this link: http://enologyaccess.org/Resources/VEN124/VEN124_11.htm
Wine makers (Oenologists) need to be able to recognize when a problem is occurring with fermentation and
how to fix the problem.
The graph below shows a normal fermentation with two different sugars. Notice that Glucose and fructose are
not consumed at the same rate by yeast cells. You must understand that the same hexose transporters
translocate both sugars (Glucose & Fructose) across the cell membrane.
According to the graph:
Initial (starting) Glucose levels:
___________ ________
(Units)
Initial (starting) Fructose levels:
___________ ________
What are your sig figs?
(Units)
Initial (starting) Total Sugar levels:
___________ ________
Do these numbers add up?
(Units)
Which sugar is more effectively bound and transported by the hexose transporters? ______________________
Why would that be? __________________________________________________________________________
___________________________________________________________________________________________
If fermentation stalls, which sugar will probably be in greater abundance? _______________________
At what time is half of the Glucose transported?
___________ ________
(hint! ½ is NOT 50(g/L)
(Units)
At what time is half of the Fructose transported?
___________ ________
(Units)
Under these conditions:
At what rate do hexose transporters transport the first half of the initial Glucose?
___________ ________
(Units)
At what rate do hexose transporters transport first half of the initial Fructose?
___________ ________
(Units)
Our reference is sugar remaining in solution. Our rates should be negative, because our slopes are negative.
Let’s agree that Glucose Transport is complete by 90 hours and Fructose transport is complete by 110 hours.
Why could this this agreement be considered “iffy”? _______________________________________________
___________________________________________________________________________________________
On this agreement:
Calculate the time interval to transport the second half of the initial Glucose: ___________ ________
(Units)
Calculate the time interval to transport the second half of the initial Fructose: ___________ ________
(Units)
Under these conditions:
At what rate do hexose transporters transport the second half of the Glucose remaining?
___________ ________
(Units)
At what rate do hexose transporters transport the second half of Fructose remaining?
___________ ________
(Units)
If you showed this graph to your physics teacher, she/he would remark that constant acceleration does not
apply making the math very complicated. OK, let’s see if we can keep this simple without resorting to Calculus.
The formula for rate change is Δ rate = ratefinal – rateinitial
When comparing the two time intervals, does the Glucose transport change rates? Calculate Δ rateGlucose
___________ ________
(Units)
What does the calculated Δ rateGlucose indicate? ____________________________________________________
___________________________________________________________________________________________
When comparing the two time intervals, does the Fructose transport change rates? Calculate Δ rateFructose
___________ ________
(Units)
What does the calculated Δ rateFructose indicate? ____________________________________________________
____________________________________________________________________________________________
Remind me, what time was half of the initial Fructose transported? Let’s call that time F1/2
F1/2= ___________ ________
(Units)
At F1/2, what was the level of total sugar?
At F1/2, total sugar = ________ ________
(Units)
At F1/2, what was the level of Glucose?
At F1/2, Glucose
= ________ ________
(Units)
At F1/2, what was the level of Fructose?
At F1/2, Fructose
= ________ ________
(Units)
OK, now explain why our Δ rateGlucose and our Δ rateFructose are different: _______________________________
__________________________________________________________________________________________
__________________________________________________________________________________________
__________________________________________________________________________________________
__________________________________________________________________________________________
An Oenologist asks you about the transport efficiency of hexose transporters. You reply that hexose
transporters can transport Glucose more efficiently than Fructose. The An Oenologist then asks you for a
number; how much more efficient is Glucose transport than Fructose Transport? Explain how you would
provide a number: _________________________________________________________________________
__________________________________________________________________________________________
__________________________________________________________________________________________
__________________________________________________________________________________________
__________________________________________________________________________________________
__________________________________________________________________________________________
__________________________________________________________________________________________
Use this graph to do your calculations!
The changing rates of Hexose Transport – problem calculations
Wine making (Oenology) requires sophisticated math and biology skills.
Check out this link: http://enologyaccess.org/Resources/VEN124/VEN124_11.htm
Wine makers (Oenologists) need to be able to recognize when a problem is occurring with fermentation and
how to fix the problem.
The graph below shows a normal fermentation with two different sugars. Notice that Glucose and fructose are
not consumed at the same rate by yeast cells. You must understand that the same hexose transporters
translocate both sugars (Glucose & Fructose) across the cell membrane.
According to the graph:
:
Initial (starting) Glucose levels:
__120___
Initial (starting) Fructose levels:
___120____
___g/L__
(Units)
___ g/L __
What are your sig figs? 2
(Units)
Initial (starting) Total Sugar levels:
____240____
__ g/L ___
Do these numbers add up? Yes
(Units)
Which sugar is more effectively bound and transported by the hexose transporters? _______Glucose ______
Why would that be? ________Any reasonable answer that indicates induced fit can have preferable binding
according to 3D shape of substrate ____________________________________________________________
If fermentation stalls, which sugar will probably be in greater abundance? _______Fructose_____
At what time is half of the Glucose transported?
____35_____ __h___
(hint! ½ is NOT 50(g/L)
(Units)
At what time is half of the Fructose transported?
____55_____ ___ h ____
(Units)
Under these conditions:
At what rate do hexose transporters transport the first half of the initial Glucose?
Rate = -60 g/L
35 h
___ -1.7____ __g/L h__
(Units)
At what rate do hexose transporters transport first half of the initial Fructose?
Rate = -60 g/L
55 h
___ -1.1 ____ __ g/L h __
(Units)
Our reference is sugar remaining in solution. Our rates should be negative, because our slopes are negative.
Let’s agree that Glucose Transport is complete by 90 hours and Fructose transport is complete by 110 hours.
Why could this this agreement be considered “iffy”? _______________ Shallow approaches to asymptotes can
be difficult to estimate_______________________________________________________________________
On this agreement:
Calculate the time interval to transport the second half of the initial Glucose: __55____
____h___
(Units)
Calculate the time interval to transport the second half of the initial Fructose: ___55______
____ h ___
(Units)
Under these conditions:
At what rate do hexose transporters transport the second half of the Glucose remaining?
Rate =
- 60 g/L
55 h
___ -1.1_____ ___g/L h___
(Units)
At what rate do hexose transporters transport the second half of Fructose remaining?
Rate =
- 60 g/L
55 h
___ -1.1_____ ___g/L h___
(Units)
If you showed this graph to your physics teacher, she/he would remark that constant acceleration does not
apply making the math very complicated. OK, let’s see if we can keep this simple without resorting to Calculus.
The formula for rate change is Δ rate = ratefinal – rateinitial
When comparing the two time intervals, does the Glucose transport change rates? Calculate Δ rateGlucose
Δ rate = (-1.1) g/L h – (-1.7 g/l h)
____ + 0.6____ ___ g/l h ___
(Units)
What does the calculated Δ rateGlucose indicate? ____The rate of Glucose transport is leveling off (the negative
slope is becoming less negative). ______________________________________________________________
When comparing the two time intervals, does the Fructose transport change rates? Calculate Δ rateFructose
Δ rate = (-1.1) g/L h – (-1.1 g/l h)
____ 0 ____ ___ g/l h ___
(Units)
What does the calculated Δ rateFructose indicate? __________ The rate of Fructose transport is not changing! __
__________________________________________________________________________________________
Remind me, what time was half of the initial Fructose transported? Let’s call that time F1/2
F1/2= ____55____ ___h____
(Units)
At F1/2, what was the level of total sugar?
At F1/2, total sugar = ___70 - 80__
___ g/l ____
(Units)
At F1/2, what was the level of Glucose?
At F1/2, Glucose
= ___10 - 20___ ___ g/l ____
(Units)
At F1/2, what was the level of Fructose?
At F1/2, Fructose
= ___60___ ___ g/l ____
(Units)
OK, now explain why our Δ rateGlucose and our Δ rateFructose are different: _______ Glucose removal from solution
is leveling off – therefore the rate change is positive. This is because as glucose concentrations drops, Glucose
transport kinetics slows. Fructose concentrations are also dropping. However Fructose kinetics remain constant
because Glucose competition has been diminished. ________________________________________________
An Oenologist asks you about the transport efficiency of hexose transporters. You reply that hexose
transporters can transport Glucose more efficiently than Fructose. The An Oenologist then asks you for a
number; how much more efficient is Glucose transport than Fructose Transport? Explain how you would
provide a number: ____________________ Many interesting answers are possible. The concept of a “fair race”
would indicate to me that comparing equal levels of both Glucose and Fructose at the outset and comparing
how long it takes to drop half their levels would allow a ready comparison of Glucose’s 35 hours to Fructose’s 55
hours. _________ By this criterion, Glucose uptake is 1.7 X more efficient than Fructose by the same hexose
transporters ________________________________________________________________________________