Enzymes and Reversibility of Reactions

Question

Richard Feynman mentions in the third chapter of The Feynman Lectures:

So the real system is in the GDP-GTP transformation; in the dark the GTP which has been stored up during the day is used to run the whole cycle around the other way. An enzyme you see, does not care in which direction the reaction goes, for if it did it would violate one of the laws of physics. 1

Which law of physics is Feynman referring to and how would it "caring" violate it?

Chapter 3 Vol. I of The Feynman Lectures, just search for "violate"

Answer 1

I think Feynman is referring to the second law of thermodynamics.

The entire statement is this:

The most important feature of the cycle of Fig. 3–1 is the transformation from GDP to GTP (guanosine-di-phosphate to guanosine-tri-phosphate) because the one substance has much more energy in it than the other. Just as there is a “box” in certain enzymes for carrying hydrogen atoms around, there are special energy-carrying “boxes” which involve the triphosphate group. So, GTP has more energy than GDP and if the cycle is going one way, we are producing molecules which have extra energy and which can go drive some other cycle which requires energy, for example the contraction of muscle. The muscle will not contract unless there is GTP. We can take muscle fiber, put it in water, and add GTP, and the fibers contract, changing GTP to GDP if the right enzymes are present. So the real system is in the GDP-GTP transformation; in the dark the GTP which has been stored up during the day is used to run the whole cycle around the other way. An enzyme, you see, does not care in which direction the reaction goes, for if it did it would violate one of the laws of physics.

Now, there are some mistakes here. For instance, GTP is not used in the muscle contraction but ATP. Perhaps this was not quite known during Feynman's times. Coming to the point, I think what Feynman means is that external work has to be done by the enzyme (that catalyses the GTP-GTP exchange) if it is actually moving the chemical equilibrium towards one side (against what would happen in an uncatalyzed condition). Some enzymes can actually do that (shift equilibria and catalyse one sided reactions), by using energy from ATP hydrolysis or other energetic transformations but since they are performing work by using energy from an external source, they are also not violating the second law.

That's the essence of the second law of thermodynamics: you cannot move heat from a cold reservoir to a hot reservoir unless external work is done. We don't have "heat" here but there concept is the same for chemical energy and reaction rates.

Answer 2

Actually I don't think Feynman is referring to the second law. Although he is wandering some way off topic in this piece, I believe he's referring to the fact that for all fundamental building-block physical theories, such as electromagnetism, quantum mechanics and Newtonian mechanics, any solution to the relevant equations can be reversed in time to find another solution. That is, fundamental physical laws don't know the difference between past to future and future to past time progression: they work in exactly the same way in both cases. The same holds for general relativity although it is less relevant there because people most often tend to think of the spacetime manifold rather than time evolution. So if the enzyme "cared" or "knew" which way the reaction were going, its behavior would tell against at least one of these fundamental theories of physics which are all reversible.

Imagine a glass falling from a table, hitting the floor and shivvering into thousands of shards. That process conforms with all the fundamental physical theories that govern it: the mechanics of motion and the solid state physics that governs how objects stay together as a whole. Now imagine that we could freeze the time evolution, and change the motion state of every glass shard flying off the impact so that its velocity vector were pointed exactly in the opposite direction, before letting the physical process keep going. You would also have to reverse the direction of the wavefronts of all the acoustic waves travelling off into the floor and air as well as the wavefronts of the electromagnetic radiation produced by the impact. We would see all the shards coming together at the impact site, the glass reassembling itself (the edges would line up so that the chemical bonds would all reform) and jumping back onto the table unblemished! This, believe it or not, is a valid solution to all the relevant equations of physics here, just as valid as the one where the glass falls and shatters.

Feynman here is alluding to something in thermodynamics known as Loschmidt's Paradox: the problem of explaining why physical processes seem to have a preferred direction when the underlying laws are time-reversible. The answer is the second law of thermodynamics whose modern accepted explanation seems to be that the universe, somehow, began in an exquisitely low entropy state such that any "random walk" in phase space undergone by a physical system will increase the system's entropy with overwhelming probability. The same would not be true if the universe began in or near a maximum entropy state. This leaves the mystery as to why the universe began in that state; a highly readable account of these ideas is to be found in:

Roger Penrose, "The Road to Reality: A Complete Guide to the Laws of the Universe", Chapter 27 "The Big Bang and its Thermodynamic Legacy"