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PROFESSOR: So, all right.
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Today we're going to pick up on where we left off before, when we looked at
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how proteins function, and we saw in particular how an enzyme functions.
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Remember this enzyme triose phosphate isomerase?
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It took one particular molecule called G3P, and it changed it into another
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molecule, DHAP.
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And it did that by stabilizing this transition state, this intermediate,
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and by preventing other reactions from going on that would destroy our happy
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little transition state molecule.
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Well, that's just one chemical transformation.
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That alone is not enough to explain what Buchner found in that experiment
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we talked about in very first lecture.
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What Buchner found, remember, was that if you took a glass of fruit juice and
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you put it out, it would ferment.
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You would get, starting with sugar, carbon dioxide and ethanol.
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Well, there's a long and complicated pathway to go from carbon dioxide and
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ethanol and that's what we're going to talk about today, biochemical pathways
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that string together transformations.
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So let's dive in.
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As always, we're obliged to put up the coat of arms here--
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function, biochemistry, protein, genetics, gene.
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And we're still over here working on the first part.
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So we've got protein structure under control.
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We've got the amino acids.
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We understand how their various different chemical properties control
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the shapes of proteins.
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We've talked about our enzyme--
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our enzyme triose phosphate isomerase, TIM amongst friends.
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And we talked about how triose phosphate isomerase has an active
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site, and that active site it stabilizes that transition state to
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help us go from G3P to DHAP.
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But does that have to do with how we go from our glass of fruit juice,
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which has yeast in it--
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and the fruit juice has a six carbon sugar.
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Let's say it has glucose or some other six carbon sugar.
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The six carbon sugar-- remember, C6H12O6--
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and it's going to ferment.
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We call a six carbon sugar a hexose.
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It's going to ferment this hexose into carbon dioxide plus ethanol.
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How does it do that?
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Does it do that in one magic step?
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No.
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It turns out it does it via a pathway of steps.
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It starts with our molecule, our hexose--
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C6H12O6, our sugar here--
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and it passes it through steps.
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A goes to B goes to C goes to D until finally gets to our
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final products here.
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That's a pathway.
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And what we want to do is understand the logic of pathways.
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How do pathways work?
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So we understood a simple aspect of pathways.
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Let's pull that up.
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We understood a simple aspect of pathways, but now we really want to
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understand the logic of pathways, and let's start with the
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energetics of pathways.
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In fact, let's just start simply with the energetics of a single reaction,
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one reaction in a long pathway like that.
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You'll recall we had our G3P goes to DHAP, and it's TIM that does that.
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And G3P over here, DHAP over here, had a slightly lower energy state.
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Free energy was lower, and it was lower by about--
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I think we said minus 1.86 kilocalories per mole.
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And we talked about that big activation barrier to get there and
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how triose phosphate isomerase lowered that activation barrier.
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But the point was there was a difference in the energy states and it
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was minus 1.86, so DHAP was more favorable than G3P.
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Does that mean that if you have G3P, all of it will get converted to DHAP?
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What do you think?
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Why not?
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DHAP is more favorable.
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STUDENT: Wouldn't it depend on the diffusion and the access to TIM?
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PROFESSOR: Let's say there's lots of triose phosphate isomerase around,
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tons and tons of it, not a problem.
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It can defuse to the enzyme, and you're very patient.
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So I throw in G3P.
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This energy--
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we write this energy, by the way delta G0 prime.
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That's favorable to a lower energy state.
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And it makes enormous sense that if that's a lower energy state, all of it
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is going to go to the lower energy state.
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That's the obvious thing.
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It's like falling down the stairs, right?
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The problem is although that makes enormous sense, it's wrong.
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It's just not the way it works.
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It really is very confusing.
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But the way chemistry really works is it involves these equilibria.
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If all of the molecules end up over there in DHAP, that's a very uneven,
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unlikely distribution and we have this problem of entropy.
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Entropy says we can't have all those molecules over there on this side.
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Then there's a statistical distribution, and it turns out that
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what happens depends on both the free energies but also concentrations.
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If you had a tube that was only DHAP, the more favored state, and triose
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phosphate isomerase, TIM would run some of that reaction backward, some.
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Now you wouldn't get all G3P.
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In fact, you'd only get about 5% that would get converted to G3P.
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But that's the important thing to think about is there's an energetic
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consideration and what's called entropic consideration.
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And it has to do with those concentrations.
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And so we have to actually understand how does that work?
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Well, the way it works, the way you know which way a reaction is going to
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run, whether all this will get converted to all that or this will get
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converted 5% back to that depends on this number, delta G, which is not
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delta G0 prime, because it doesn't have a 0 prime on it.
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Yeah.
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Good, you got that.
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What it is is delta G0 prime plus a term that has to do with entropy with
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relative concentrations.
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So it has a RT--
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that's a constant there, and that's temperature in degrees Kelvin--
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and it has the natural logarithm of the concentrations of the products and
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the reactants.
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So if our reaction was A converted to B, then it would be the log of B over
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the log of A. That's the key thing.
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And if delta G is negative, the reaction is going to run forward.
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It's favorable.
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We're going to do all that much chemistry, but this bit of chemistry
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is pretty important to know.
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And if delta G is positive, the reaction will actually
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run the other way.
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It'll run primarily backward because it's unfavorable when you balance out
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the considerations of the energy and the concentration.
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Such let's actually try this out in practice.
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Suppose I gave you a reaction here where the concentrations were equal.
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If the concentrations are equal-- the concentration of B and the
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concentration of A--
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then what's their ratio?
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STUDENT: One.
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PROFESSOR: One.
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And the log of one is zero, and so this doesn't matter.
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And it just is all determined by delta G0 prime.
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So delta G0 prime is really telling you the way the reaction will run if
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the concentrations are equal.
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So when they're equal, that tells us it's going to go from G3P to DHAP.
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But suppose I have just a huge amount of B and very little A. What
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will this ratio be?
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A big number.
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And what's the log of a big number?
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STUDENT: A big number.
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PROFESSOR: A big number.
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And when I add this big number to a negative number, it could be positive.
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So if there's enough B around, then this'll be positive and the reaction
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will go the other way.
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So for example, let's try to check that out.
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We'll try it with our triose phosphate isomerase numbers here.
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And we're going to say suppose I gave you a ratio of 30 to 1.
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Suppose we had G3P to DHAP was 30 to 1--
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sorry, was 1 to 30.
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I had a lot of DHAP, a lot of the product, 1 to 30.
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Then when we plug it in here, let's see what delta G will be.
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Delta G will be--
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delta G0 prime was minus 1.86.
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We've got to know what RT is.
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Now, RT depends on the temperature.
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So do we have to know what temperature our reaction is going on at?
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It turns out we don't, because it's the temperature degrees Kelvin, and in
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degrees Kelvin you'll live your life at essentially the
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same degrees Kelvin.
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You know if even you're running a fever or something like that or if
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your yeast is growing at a slightly lower temperature, for all practical
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purposes for all of biology, RT equals 0.6.
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It doesn't matter.
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So we can actually say this is just 0.6.
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If you're doing high temperature stuff and super low temperature stuff you
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care, but for us it's just 0.6.
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So, 0.6 times the log of 30 over 1.
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And if you do that arithmetic, you should come up
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with a positive number--
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positive number about 0.18, I think, although maybe somebody will get
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another number there.
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That's what I got.
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So that tells you it's a positive number, and that tells you when
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there's 30 times as much DHAP, the reaction will actually
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be generating G3P.
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Any questions about that?
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It's a little counterintuitive.
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Anything sensible you'd think would all go to the low energy
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state, but it doesn't.
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It bounces back and forth due to this entropy consideration,
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and this tells us--
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in fact, if you solve the equation, what would happen if we asked about
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when delta G equals 0?
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Does the reaction run forward or backward?
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Neither.
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It's at equilibrium.
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And so if you set that equal to 0, you could solve for the concentration,
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which would be at equilibrium.
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And that concentration, the equilibrium concentration for our
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reaction there is about 1 G3P to 22 DHAPs.
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That's where the reaction is balanced perfectly at equilibrium.
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OK, yes, please?
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STUDENT: So at equilibrium, does that mean that there's no
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reactions going on?
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PROFESSOR: So no molecule at all moving from the left to right or the
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right to left.
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STUDENT: Does it mean that they're moving equal amounts?
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PROFESSOR: What do you think?
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STUDENT: They're moving equal amounts?
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PROFESSOR: I think they're moving in equal amounts, aren't they, because,
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you see, each molecule doesn't know what the other molecules are doing.
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It's a mass action kind of thing.
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Every molecule is doing its thing.
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It bounces into triose phosphate isomerase, it converts
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to the other thing.
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But the thing is when there's a lot of these guys, DHAPs are bouncing into
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triose phosphate isomerase and converting back the other way.
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And when there are a lot of G3Ps, they're bouncing.
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Every molecule's behaving independently, and what's really
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happening is we're counting out the dynamic equilibrium, not a static
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equilibrium.
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It's not all the molecules decide we voted which we're going to
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be and we stay that.
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They're constantly moving back and forth.
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And this is the dynamic equilibrium that's obtained.
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OK?
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All right.
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That's it for energetics.
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Yes, please?
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STUDENT: Where are we considering the enzyme in the equation?
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PROFESSOR: Where are we considering the enzyme in the equation?
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How does the enzyme change delta G0 prime?
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It doesn't.
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The enzyme actually had no effect on these energetics.
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It had no effect on whether the reaction is
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running forward or backward.
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All of that is determined-- because that enzyme is just a catalyst.
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It's not changed, it doesn't do anything, it doesn't
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change the energy states.
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What does it do?
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It helps speed up that reaction, because in the absence of that enzyme
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TIM we'd have to wait for it to get over by thermal noise, thermal energy,
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over that barrier.
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All TIM does is speeds it up, and that's a really important observation.
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The enzyme doesn't change a thing other than the speed with which this
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is all going--
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and that other thing I told you, it protects that intermediate sometimes
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from a side reaction.
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But it's all about speed.
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As we talked about, the enzyme speeds it up merely by a factor of 10 to the
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10th, and the 10 to the 10th, as you remember, was the difference between
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one second and three centuries.
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But if you don't care, if you're very patient, it's quite immaterial.
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OK.
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I'm not that patient.
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Life isn't that patient, and that's why the evolution of enzymes was so
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very important.
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Before you go on, take a moment and answer this question about favorable
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and unfavorable chemical reactions.
19997
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