Tuesday, November 11, 2008

Enzyme Efficiency: The Best Enzyme

One of the first things you learn about enzymes is that they catalyze, or speed up, reactions that would normally take place at a much slower rate. This is a difficult concept for students to understand because they're used to thinking of biochemical reactions in terms of reactions that would never happen without an enzyme.

The trick in understanding the role of enzymes is to appreciate the difference in rates between the enzyme-catalyzed reaction and the spontaneous reaction. While it's true that all enzyme-catalyzed reactions would eventually proceed even in the absence of enzyme, the rate of the spontaneous reaction might be way too slow. We often emphasize that the spontaneity of a reaction can be determined from the thermodynamics (i.e. if ΔG <0 the reaction is spontaneous) but we sometimes forget to show real data on how fast such a reaction can occur under physiological conditions. Typical rates for enzyme-catalyzed reactions are described by a constant called kcat.1 These values are usually in the range of 100-1000 reactions per second but there are some enzymes than have rates of over 1,000,000 reactions per second.

Spontaneous reactions can often approach these rates but, as you might imagine, the ones that require enzymes are very much slower. Proteins, for example, will eventually break down into amino acids but the rate of the reaction is so slow that spontaneous protein degradation is not a problem in living cells. In order to degrade proteins for food, we need to make enzymes such as chymotrypsin, trypsin, pepsin, and elastin to do the job at a faster rate.

Most of the important metabolic reactions take years in the absence of enzyme. The spontaneous degradation of a protein, for example, takes about 100 years (rate constant ~ 4 × 10-9). Since chymotrypsin catalzyes this reaction at a rate of about 1000 molecules per second, this means that the enzyme speeds up the reaction by a factor of more than 1011 (100 billion times)!

This value (1011) is sometimes called the catalytic proficiency of an enzyme although for technical reasons we won't go into here, the real measure of catalytic proficiency is higher by several orders of magnitude.1 The catalytic proficiency of chymotrypsin is 2 × 1016.

Naturally, this invites a comparison with those enzymes showing the greatest rate enhancements. But there's a problem. You can measure spontaneous rates that are on the order of a few years because you don't have to wait until the reaction goes to completion. But if the spontaneous reaction takes hundreds of years it can be difficult to measure—even the most dedicated graduate student won't wait that long!

Fortunately there are a few tricks that will make the job easier. You can observe the spontaneous reaction at high temperatures, for example, and calculate what the rate would be at physiological temperatures. That's what Radzicka and Wolfenden did in 1995 when they reported that the spontaneous decarboxylation of ornithine 5′-phosphate (OMP) had a rate constant of 3 × 10-16 s-1. This is a half-life of 78 million years.

The enzyme that catalyzes this reaction is ornithine 5′-phosphate decaboxlyase and up until last week it was the record holder with a catalytic proficiency of 2 × 1023. (OMP decarboxylase catalyzes an essential step in the synthesis of pyrimidine nucleotides that are required to make RNA and DNA.)

That record has now been broken. Lewis and Wolfenden (2008) studied a reaction catalyzed by uroporphyrinogen decarboxylase, an enzyme involved in the synthesis of porphyrins such as heme, the cofactor in hemoglobin, and the chlorophylls. There were able to model the reaction and determine that the rate of spontaneous decarboxylation is 9.5 × 10-18 s-1, which corresponds to a half-life of 2.3 billion years! Lewis and Wolfenden published a chart showing typical half-lives of spontaneous reactions.

The catalytic proficiency of uroporphyrinogen decarboxylase is 2.5 × 1024, a new record.

Into the textbook it goes.

1. A better description of an enzyme's real rate constant is kcat/Km.

Radzicka, A. and Wolfenden, R. (1995) A proficient enzyme. Science 267:90-93.

Lewis,C.A. Jr. and Wolfenden, R. (2008) Uroporphyrinogen decarboxylation as a benchmark for the catalytic proficiency of enzymes. Proc. Natl. Acad. Sci. (USA) published online November 6, 2008 [Abstract] [doi:10.1073/pnas.0809838105]


  1. Into the textbook it goes

    Doubt it.

    1. Described is a perfectly mediorce enzyme, with kcat/Km of only ~ 3e6. There are a number of enzymes that are 100X better catalysts, with kcat/Km > 2e8.

    2. The big number that is supposed to awe everyone is based on *extrapolation* of the experimentally derived spontaneous rate.

    3. The Fig.3's legend says that a linear fitting was used for the Arrhenius plot. In other words, a common (and severe) mistake was made by applying equal weights to the data spanning 3 orders of magnitude. Jeez, and I thought these days every Biochem 101 student is taught to NOT ever derive anything from linearized plots! That no estimated standard deviations of the fit's parameters are mentioned anywhere in the paper is only all too telling...

    4. Considering the above, it's anyone guess how close to reality the extrapolation from >100C down to 25C is. (And that is even *assuming* that Arrhenius plot is linear over the entire range of 150-20C - which may not be true; life is full of nonlinear Arrhenius plots).

    5. On top of the problems above, the study did not use the actual sustrate. It used a much smaller compound that is part of the porphyrinogen. This had to do with obvious experimental limitations but it is far from given that PAA and porphyrinogen have identical sponataneous rates of decarboxylation! At a minimum, a full quantum mechanics calculation of the electron density distribution should have been carried out and provided to prove that it is reasonable to assume the near equivalence. (That's not difficult to do these days but it was evidently not done). That the macrocycle ring has absolutely no influence on the chemistry of pyrroles is a very dubious assumption, IMHO.

    All in all, a shaky ground for any quantitative claims. Seems like a typical PNAS paper from old times.

  2. I agree with most of DK's comments, so I won't repeat the arguments. The main one where I have reservations is

    a common (and severe) mistake was made by applying equal weights to the data spanning 3 orders of magnitude.

    Effectively the authors have assumed uniform lognormal errors, approximately the same as saying that they are uniform in coefficient of variation. This may often be closer to the truth than the more usual assumption that they have unform variance. Of course, the important point is that the weighting should be based on the real (preferably measured, but that means virtually never!) error distribution, not on whatever is most convenient for calculation. The only case that I know of where an experimentally determined distribution of error in a enzyme in an experiment turned out to be close to uniform variance was the original study of Lineweaver and Burk way back in 1934. However, don't look at the paper that everyone refers to but few have read; look at the one they wrote in the same year with W. E. Deming (a real statistician) in J. Amer. Chem. Soc. 56, 225-230.

    An additional point is that we are really being asked to be impressed at how slow the uncatalysed reaction is, not how fast the catalysed reaction is. But who cares about that? Humans learned how to accelerate very slow processes by many orders of magnitude at least 4000 years ago (for example, building of the pyramids or Stonehenge -- large chunks of rock move exceedingly slowly, if at all, in nature) , but they only learned how to double the rate of a fast process in the past couple of centuries (for example the speed of a car compared with that of a galloping horse).

  3. athel says,

    An additional point is that we are really being asked to be impressed at how slow the uncatalysed reaction is, not how fast the catalysed reaction is. But who cares about that?

    I do.

    It's hard to get students to learn this conceptual stuff. That's why I'm always looking for examples to illustrate the difference between so-called "spontaneity" (deltaG) and rate.

    This looks pretty good to me even with the qualifications noted by dk. In the textbook I'll say that the rate is only an estimate.