How long does it take to synthetize a molecule of leucine anyway?

Bora Zivkovic asked this question on A Blog Around the Clock: How long does it take to synthesize a molecule of leucine anyway?.

A dozen or so years ago, I drove my Biochemistry prof to tears with questions - she had 200 people in front of her and she tried hard to make Biochem interesting enough not to get us all bored to tears, and she was pretty good at that, as much as it is possible not to make people bored to tears with Biochem. But my questions exasperated her mainly because she could not answer them, because, as I learned later, the field of biochemistry was not able to answer those questions yet at the time: questions about dynamics - how fast is a reaction, how long it takes for a pathway to go from beginning to end, how many individual molecules are synthesized per unit of time?, etc.

Bora, I'm sorry your Professor wasn't able to answer your questions. The answers have been known for decades. Perhaps she didn't know the answers, or perhaps there was another reason why she didn't answer.

The rate of enzymatic reactions is part of the field of enzyme kinetics. The material is usually covered in introductory biochemistry. The particular value you were looking for is called the catalytic constant, k_cat. It represents the number of moles of substrate converted to product per second per mole of enzyme under saturating conditions. In other words, it's the maximum speed of an enzyme. This is also called the turnover number.

Typical values for most enzymes are between 10² and 10³. What this means is that a given enzyme can catalyze between 100 and 1000 reactions per second.

A metabolic pathway in cells is a series of reactions where a substrate is converted to a product in several steps. The pathway for leucine biosynthesis is well known. It begins with pyruvate, which is converted in three reactions to α-ketoisovalerate. That intermediate can be converted directly to valine or it can serve as the substrate for a series of four reactions leading to leucine.

All of the enzymes have been studied. I'd have to look up all of the k_cat values to give you a precise answer but it's easy to give a reasonable estimate.¹

Biochemical pathways operate, for the most part, under near-equilibrium conditions. What this means is that there is a steady state concentration of all reactants in the pathway. These concentrations correspond to the equilibrium values for each reaction.

The flux in a pathway depends on how quickly the end product is utilized. Under normal conditions leucine will be used up in protein synthesis at a nearly constant rate but that rate might rise if the cell is growing rapidly and it might fall if the cell is starved for nutrients. When leucine synthesis is required, for whatever reason, it's maximum rate of synthesis will be equal to the turnover number of the slowest enzyme in the pathway.

You can safely assume that this will be between 100 and 1000 molecules per second per enzyme. That's the answer you should have been given. In a big mammalian cell growing in tissue culture there will be lots and lots of enzyme and the flux could be a million molecules per second. It will be much less in smaller cells that are not growing.

The key to understanding metabolic pathways is to appreciate that there is a pool of leucine in the cell and a pool of the last intermediate. These pools of metabolites are at steady-state concentrations and the enzyme is constantly making leucine and converting leucine back to the intermediate because that's what happens under equilibrium conditions. The rates of the forward and reverse reactions are equal, and fast.

As soon as the leucine pool is depleted there will be some net synthesis of leucine made from the pool of the last intermediate to restore the steady-state equilibrium concentrations. The rate of this reaction is very rapid.²

Then the pool of the last intermediate is replenished from the second-last intermediate etc. etc. All of these reactions are rapid. Most students seem to think that there are no intermediates and when leucine is needed the enzymes have to grab a pyruvate molecule and run through the entire pathway to make a new molecule of leucine. Such a pathway is impossible.

Well, the field is starting to catch up with my questions lately - adding the temporal dimension to the understanding of what is going on inside the cell. In today's issue of PLoS Biology, there is a new article that is trying to address exactly this concern: Dynamics and Design Principles of a Basic Regulatory Architecture Controlling Metabolic Pathways:

That's an interesting paper but it doesn't answer any of your questions.

The paper address the induction of enzymes in yeast. When yeast cells grow in the presence of leucine they turn off synthesis of the pathway enzymes because there's no need to synthesize leucine when it's available in the medium. If you then shift the cells to leucine free medium they will begin to make the leucine pathway enzymes. It takes about one hour to make signifcant amounts of enzyme.

Enzyme induction has been studied for over 50 years. The diagram below is from Monod's Nobel Lecture of 1965. The current PLoS paper adds some information to this field but, with all due respect, it is not a breakthrough and it does not answer fundamental questions in biochemistry that were unknown when you were a student. You may not have been aware of kinetic studies when you were a student but that's a reflection on the quality of your education and not on what was known in biochemistry at the time.

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1. Perhaps your biochemistry Professor didn't want to spend the time looking up all the details? Whenever I get a question like that I assign the task to the student. It's a good exercise for them to search through the scientific literature to find the answer to their own question. It also helps them appreciate why their Professor may not have had the answer at her fingertips.

2. For the sake of simplicity, I'm ignoring regulation. Some enzymes in the pathway might be regulated in which case the steady-state concentrations might not correspond to the equilibrium concentrations. This doesn't make much difference when it comes to addressing Bora's questions.