Greetings! My name is Jon and I'm a 1st year grad student in neurobiology. It's been a while since I had to solve for these types of equations and feel embarrassed that I forgot how to math(haha).
Anyway I'm trying to calculate the flow of ions across a membrane which must be at an equilibrium(an equal number of different kinds of ions must flow together). It uses something called Donnan's Rule:
K+(inside)/K+(outside) = CL-(outside)/CL-(inside)
K+(inside)= 150
K+(outside) =50
CL-(outside)= 150
CL-(inside) = 50
In order to satisfy space-charge neutrality, equal amounts of K+ and CL- must be moved from outside to inside
So to rewrite the formula, let X be the amount of ions that must be moved from outside to inside. Then the above formula is rewritten:
(150 + X) = (150 - X)
(150 - X) (50 + X)
The professor gave this problem as an example and didn't show his work but the answer he derived was 30, which when you plug it in, makes sense as 180/120 is 1.5 which is equivalent to 120/80- 1.5 making the two fractions equivalent, and shows that 30 ions of Cl and K must move from outside to inside.
So even though this isn't a neurobio/chem forum, the math doesn't make sense to me.
I initially tried to cross multiply and maybe that's where I messed up? Using distributions I derived this:
(150 + X)(50 + X) = (150 - X)(150 - X)
Simplified using distribution:
7500 +200X + X2 = 22500 -300X - X2
Then:
7500 +200X + X2 = 22500 -300X - X2
(Add 300 to both sides)
7500 +500X + X2 = 22500 - X2
(Then add X2 to both sides)
This is the part that screws me up....
7500 +500X +2X2 = 22500
(Subtracted 7500 from both sides)
2X2 + 500X = 15000
If this were just 500X= 15000 I'd get X= 30 by dividing both sides by 500 unfortunately that 2X2 is lingering there which screws me up. I'm not sure if I was supposed to factor for X or something? Seems like a lot of work for a class that's more conceptual than mathematical. Am I going about this the wrong way and is there a more parsimonious and efficient(and time saving) method I can do to derive the answer? Thank you in advance and sorry if this is childsplay for you mathologists!
Anyway I'm trying to calculate the flow of ions across a membrane which must be at an equilibrium(an equal number of different kinds of ions must flow together). It uses something called Donnan's Rule:
K+(inside)/K+(outside) = CL-(outside)/CL-(inside)
K+(inside)= 150
K+(outside) =50
CL-(outside)= 150
CL-(inside) = 50
In order to satisfy space-charge neutrality, equal amounts of K+ and CL- must be moved from outside to inside
So to rewrite the formula, let X be the amount of ions that must be moved from outside to inside. Then the above formula is rewritten:
(150 + X) = (150 - X)
(150 - X) (50 + X)
So even though this isn't a neurobio/chem forum, the math doesn't make sense to me.
I initially tried to cross multiply and maybe that's where I messed up? Using distributions I derived this:
(150 + X)(50 + X) = (150 - X)(150 - X)
Simplified using distribution:
7500 +200X + X2 = 22500 -300X - X2
Then:
7500 +200X + X2 = 22500 -300X - X2
(Add 300 to both sides)
7500 +500X + X2 = 22500 - X2
(Then add X2 to both sides)
This is the part that screws me up....
7500 +500X +2X2 = 22500
(Subtracted 7500 from both sides)
2X2 + 500X = 15000
If this were just 500X= 15000 I'd get X= 30 by dividing both sides by 500 unfortunately that 2X2 is lingering there which screws me up. I'm not sure if I was supposed to factor for X or something? Seems like a lot of work for a class that's more conceptual than mathematical. Am I going about this the wrong way and is there a more parsimonious and efficient(and time saving) method I can do to derive the answer? Thank you in advance and sorry if this is childsplay for you mathologists!
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