Topic 9.7: Coupled Reactions

Coupled reactions: making reactions run uphill

The cold pack goes because its total delta G naught is negative. But making ATP has a K of about five times ten to the minus six, and nothing climbs that far uphill on its own, so how does life manage it? There are two ways to run an unfavorable process. One is energy from outside, like plugging in your phone, where electricity pays to run the battery’s reaction backwards, and a cell run that way is called an electrolytic cell.

Sunlight is another outside source. This is the same forest two hours earlier, where all day the leaves have been turning carbon dioxide and water into glucose and oxygen. That’s photosynthesis, with a delta G naught of about plus two thousand eight hundred eighty kilojoules for every mole of glucose, and light pays for all of it. Follow the energy in almost any animal’s food back far enough, the firefly’s included, and you end up at sunlight on leaves like these.

Match each process with the outside energy that drives it. Which pairing is right? But a firefly can’t plug into the wall or photosynthesize, so it uses the other way, and makes its ATP by coupling that uphill reaction to a downhill one, burning its food with oxygen, which is roughly photosynthesis run backwards.

Here’s our well model again, with three wells. A turning into I is uphill by eighteen kilojoules per mole, so almost every bead stays in A. Now I’ll connect a reaction that uses I: I plus B makes P, downhill by thirty. Each bead that reaches I falls on into P before it can slide back, so A keeps draining, and the beads pile up in P.

This works because I is shared, made by one reaction and used up by the other. Add the reactions and I cancels, and add their delta G naught values and you get plus eighteen minus thirty, minus twelve kilojoules per mole. So the overall reaction, A plus B making P, is favored, with a K of about one hundred thirty.

But the partner has to be strong enough. If the second step is only minus ten, the total is plus eight, still uphill, and most of the beads stay home. And the partner has to connect to it. This tray’s reaction is downhill by a hundred, but it doesn’t make or use I, so A doesn’t budge; a favorable reaction nearby does nothing without a shared intermediate. Now you pick the partner that makes the overall reaction favored, with a negative total delta G naught.

Coupling with ATP

Now real molecules. The first thing a cell does with glucose is attach a phosphate group, and glucose plus phosphate making glucose-6-phosphate is uphill, with a delta G naught prime of plus thirteen point eight and a K prime of about four thousandths. ATP plus water making ADP and phosphate is the reaction you already worked out, minus thirty point five.

Now we add them, and I’ll ask you the question: what shows up on both sides? Phosphate and water, so they cancel, and what’s left is glucose plus ATP making glucose-6-phosphate plus ADP. The delta G naught values add too: plus thirteen point eight plus minus thirty point five is minus sixteen point seven kilojoules per mole, so K prime is about eight hundred fifty, far toward glucose-6-phosphate.

In the real enzyme, the phosphate never floats free. ATP hands its last phosphate group straight to glucose, and adding the equations, with phosphate canceling as the common intermediate, is the bookkeeping that gives the overall delta G naught. And if this shows up on the AP exam, this is the sentence that earns the point. The two reactions share a common intermediate, and adding them gives an overall delta G naught that’s negative, so the overall reaction is thermodynamically favored.

Now a harder one. A to I has a delta G naught of plus eighteen kilojoules per mole, and two I plus B making P has minus sixty. What’s delta G naught for two A plus B making P, in kilojoules per mole?

What really lights a firefly

Now let’s answer the question from the start and go inside his lantern. These branching tubes carry air deep inside, and that matters, because oxygen is part of the reaction. The light comes from an enzyme called luciferase. Here’s luciferase, here’s the molecule that will make the light, called luciferin, and here’s ATP.

Step one: ATP hands its AMP piece to luciferin, and the other two phosphates leave together. That makes luciferyl-AMP, an activated luciferin that’s ready to react. ATP’s AMP piece ends up inside the activated molecule, so the firefly is spending ATP to build it, a coupled reaction just like the glucose one.

Step two: oxygen attacks the activated molecule, the AMP lets go, and a tiny four-membered ring forms, so strained that it snaps almost at once. Carbon dioxide breaks off, and what’s left, oxyluciferin, holds a lot of extra energy.

Step three: it lets that energy go as a single photon of yellow-green light, and luciferase comes out unchanged, ready for the next one. Now the arithmetic I promised. Firefly light is yellow-green, around five hundred sixty nanometers, so let’s find the energy of one mole of those photons.

Use E equals h c over lambda for one photon, then multiply by Avogadro’s number. What’s the energy of one mole of five-hundred-sixty-nanometer photons, in kilojoules?

Now compare. Each luciferin uses one ATP and can make at most one photon, and splitting ATP into AMP gives forty-five point six kilojoules per mole, while a mole of photons costs two hundred fourteen, almost five times more. The thirty point five you saw earlier, for ATP to ADP, is even smaller, and even inside a living cell, where ATP gives up to about twice these standard values, it isn’t close. ATP can’t pay for this light.

So what does? Step two does: luciferin reacting with oxygen, and that strained ring snapping, releases enough energy to make the photon. ATP’s job was to get luciferin ready, and oxygen pays for the light. If you guessed ATP too, you’re in good company. And now you can show exactly why it can’t be the whole story.

So delta G naught tells you how far a reaction goes, through K, and whether a salt dissolves comes down to enthalpy and entropy weighed against each other. And an uphill reaction can happen if something pays for it: light, electricity, or a partner that shares a piece with it. Every one of those flashes is a coupled reaction, paid for in the end by oxygen, and now you can prove it.