Monday, July 28, 2014

Finding the "perfect" enzyme

I got an email message yesterday from a student who is taking a summer course in biochemistry. His professor asked the class to find "most efficient enzyme known to man." The professor gave them a hint by telling them that the enzyme had something to do with nucleotide biosynthesis. The student contacted me because some of my blog posts popped up on Goggle. He (the student) was a bit confused about how to define the "perfect" enzyme.

There are two different ways of defining the "perfect" enzyme and both of them are wrong because there's no such thing. The common textbook definition picks up on the idea that the "perfect" enzyme catalyzes a reaction every time it encounters a substrate(s). These enzyme rates are referred to as "diffusion-controlled" rates since the rate is limited only by the rate at which substrate diffuses into the reaction site on the enzyme. Some enzymes can even catalyze reactions that are slightly faster than the diffusion-controlled limit.

Here's what Voet & Voet (4th edition) say (page 490) ...
Some Enzymes Have Attained Catalytic Perfection
Thus, enzymes with such values of kcat/Km must catalyze a reaction every time they encounter a substrate molecule. ... several enzymes ... have achieved this state of virtual catalytic perfection.
As I discussed in two previous posts, it's very misleading to refer to these enzymes as "perfect" enzymes since there are thousands of enzymes that get along just fine having evolved a pretty fast reaction rate that's far from the maximum value. They are good enough enzymes for the conditions of the cell. Who's to say that they haven't evolved a "perfect" solution to reaction rates even though it's not the fastest rate possible? [Better Biochemistry: The Perfect Enzyme] [Better Biochemistry: Good Enough Enzymes]. (The post on good enough enzymes has some nice data on average rate constants and average turnover numbers.)

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Better Biochemistry
The other way of defining a "perfect" enzyme is to look at something called "catalytic proficiency." That's the ratio of two rates: the maximum rate catalyzed by the enzyme and the spontaneous rate of the reaction in the absence of enzyme. (Recall that enzymes speed up reactions that will occur naturally.) There are lots of reactions that take place very, very, slowly in nature. Some of them have half-lives measured in millions or even billions of years.

Any enzyme that can catalyze such reactions at an appreciable rate is going to have a high catalytic proficiency [Enzyme Efficiency: The Best Enzyme] [The Best Enzyme]. These enzymes are better candidates for best enzymes but only one of them could be the "perfect enzyme"—if that were a meaningful term.

The leading candidate for the enzyme with the highest catalytic efficiency used to be orotidine 5′-phosphate decarboxylase (OMP decarboxylase), an enzyme involved in pyrimidine biosynthesis. That's almost certainly the enzyme that the professor wanted the students to find. However, an even better enzyme was discovered six years ago. It's uroporphyrin decarboxylase1 with at catalytic proficiency 10× higher than orotidine 5′-phosphate decarboxylase. I posted about it in 2008.

And here's how the information in that 2008 post got incorporated into the latest edition of my textbook.



There might be even more proficient enzymes that have been characterized since then. Does anyone know?

There's an ongoing debate among biochemistry teachers about the kind of information that typical students in an introductory course can handle. The students in our "honors" course can easily handle the information in this blog post but I'm not so sure about the students in our large "non-majors" course intended for students who aren't specializing in biochemistry. Some of my readers teach biochemistry. What do you think?


Image Credit: Moran, L.A., Horton, H.R., Scrimgeour, K.G., and Perry, M.D. (2012) Principles of Biochemistry 5th ed., Pearson Education Inc. page 175 [Pearson: Principles of Biochemistry 5/E]

1. Mutations in the gene for uroporphyrin decarboxylase are responsible for a common form of porphyria Porphyria cutana tarda]

14 comments :

  1. I'm a lab technician, I only have very little formal training in biochemistry. I don't find this hard to understand at all.

    I do have a question though. When you say the uncatalyzed reactions have a certain spontaneous rate, what conditions are those measured under? Does it depend on the type of reaction? I imagine some reactions have higher spontaneous rates at higher temperatures than others, and that they all generally become slower as the temperature drops?

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    1. In order to estimate the true spontaneous reaction rate under physiological conditions they have to measure them under extreme conditions of high temperature and pressure then extrapolate to the lower rates.

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    2. For some reason, this particular blog post seems rather scatter-brained to me, and I don't think students handle that aspect well. I only point that out because it seems to be an exception to most of your postings.
      As for the biochemical content, I see three points. The notion of a "perfect enzyme" is silly. Some enzymes are so efficient that effectively every molecule that binds to the active site is converted to product. And the concept of enzymatic proficiency illustrated with examples. I'd say these are within the reach of all students, even medical students.

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    3. @roger shrubber

      I'm sorry you think my post is scatter-brained but at least you grasped the main points.

      I strongly doubt that this information is within reach of all students who take undergraduate biochemistry courses. Most of them know nothing about evolution and the idea that an enzyme could have evolved to be less than perfect will seem strange to them. As you can see from my example, some textbooks talk about "achieving catalytic perfection" so I assume that even textbook authors are confused.

      I usually take Wikipedia to be a reasonable estimate of what typical biochemistry students can handle. Here's what it says about Diffusion limited enzyme.

      It is worth noting that there are not many kinetically perfect enzymes. This can be explained in terms of natural selection. An increase in catalytic speed may be favoured as it could confer some advantage to the organism. However, when the catalytic speed outstrips diffusion speed (i.e. substrates entering and leaving the active site, and also encountering substrates) there is no more advantage to increase the speed even further. The diffusion limit represents an absolute physical constraint on evolution.[1] Increasing the catalytic speed past the diffusion speed will not aid the organism in any way and so represents a global maximum in a fitness landscape. Therefore these perfect enzymes must have come about by 'lucky' random mutation which happened to spread, or because the faster speed was once useful as part of a different reaction in the enzyme's ancestry.

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    4. I've been slowly trying to digest the above but here must be too many imperfections in my digestive enzymes. I have a gut reaction that it's BS but can't de-scatter-brain my own thoughts. Among other problems I have is the apparent notion that kcat evolves rather than kcat is the result of the enzyme sequence evolving. For example, the same amino acid substitutions that improve Km could very likely also improve kcat, providing one mechanism to drive very fast catalysis. And of course the passage above equates evolution with adaption. But I suspect I'm missing something more (beyond the obvious example of enzymes that are being adapted to additional reactions where the extremely fast reaction is just a biproduct).

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  2. Two years ago there was an article (http://tinyurl.com/mc4ndhf) with a similar title in which there were some valuable comments from Joe Felsenstein that largely seem to have fallen on deaf ears. Although I read the article itself at the time I didn't read the comments (not enough of them, anyway) until yesterday, when I was searching for something else. At the end of the exchange of views someone called Anonymous said "I’m slightly surprised that Athel hasn’t popped up to explain this since he has made major contributions to metabolic control analysis". If I had seen it I probably would have, but now I'm too late to join that party. However, this new article provides a context to say that I entirely agree with Joe.

    First, however, one or two remarks about the whole concept of a perfect enzyme. I thought this was already oversold when Jeremy Knowles introduced it. He was my doctoral supervisor in the 1960s, and I was a great admirer of his work up to the end of his life. Nonetheless, catalytic perfection was a misguided idea if taken too seriously, as it has been by many who have uncritically adopted it. One point is that being a good catalyst is not the only thing a good enzyme needs to be: it also needs to be stable enough to stick around as long as it is needed, but able to be degraded when it is not, and, above all, it needs to be specific; many also need to be able to respond to regulatory signals.

    Joe's point was different, however. He was concerned with the idea that catalysing a reaction in the highly artificial conditions of a spectrophotometer is not at all the same as catalysing it in a metabolic pathway, when it is mixed with a lot of other enzymes and metabolites, and, in most cases, it has little control over the rate it has to supply: it needs to transform its substrates at the rate at which they arrive, and the best it can do its to modulate the concentrations of substrates and products to agree with that rate. As Henrik Kacser (mentioned by Joe) and others since have understood (but not yet most authors of general textbooks of biochemistry) this means that the idea of a rate-determining enzyme is largely a myth.

    One of the favourite examples of a rate-determining “key” enzyme is phosphofructokinase, which is supposed to determine the rate of glycolysis. As long ago as 1986 (nearly 30 years ago!) Heinisch reported that over-expressing phosphofructokinase in yeast had no measurable effect on the flux to ethanol. This was not a one-off anomaly, as similar results have now been found for phosphofructokinase in species as diverse as potatoes and mice. Moreover, it was exactly what was to be expected from Henrik’s analysis. It is time for biochemists to accept that a living cell is not the same as a cuvette in a spectrophotometer.

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    1. Athel,

      Thanks for "popping up"!!!

      I'm glad we agree about "perfect" enzymes. There's no such thing. We should try and get this concept out of the textbooks. It's a good candidate for your Biochemical howlers website. Incidentally, my textbook was the best of the ten textbooks you reviewed back in 2005 and since then I've corrected (or explained) the two items where I scored low on your original evaluation.

      The discussion about flux and control is very complicated. I've had a section on "flux"in my textbook for the last three editions but a lot of the feedback has been negative. It's thought to be too complicated for an introductory biochemistry course. Many of the most popular textbooks don't even mention the word "flux." (Perhaps it's not a surprise that these books are also the ones that have low scores on your Biochemistry Howlers site.)

      Joe discusses a well-known paper by Kacser and Burns (1973). The paper has been reprinted, with comments, and a free PDF is available [PDF].

      The paper is very difficult to read and understand. I gave up many years ago. I just re-read it and I am still disinclined to spend time trying to figure out the math. However, I get the main points which are ...

      1. Many reactions are near-equilibrium reactions. To the extent that the metabolite pools are not exactly at equilibrium, the rate of the enzyme is important because it determines the speed with which equilibrium is reached. If flux is high, the pools may drift away from equilibrium values. Thus, all enzymes in a pathway play a role in determining flux.

      2. In most cases, metabolite pools are at near-equilibrium values and these values are close to the steady-state values inside the cell. The rates of the various enzymes are sufficient to rapidly re-establish near-equilibrium values if they are perturbed. Adding more enzyme (e.g by over-expression) should have no effect.

      3. Some enzymes are regulated. Their rate is altered in various ways to prevent the pools of substrates and products from reaching equilibrium. Disequilibrium is a good proxy for a regulated reaction that controls flux in a pathway although it is not the only control point. Phosphofructokinase is a regulated enzyme; it's rate depends on the concentration of AMP. This makes sense since the activity of phosphofructokinase has to be curbed when cells are making glucose (gluconeogenesis). The amount of phosphofructokinase in a cell is irrelevant unless the molar quantity approaches the molarity of the regulatory molecule and that's unlikely.

      4. Part of the problem is semantic. It's best to talk about regulated enzymes and not "control points" or "control reactions" or "rate-limiting" steps.

      It is very difficult to each these concepts to students in an introductory biochemistry class or to explain them in a textbook. Part of the problem with textbook writing is that the real audience (teachers) won't adopt the book if it conflicts with what they've been teaching for years and years. Most biochemistry teachers don't understand the concept of near-equilibrium reactions and they don't understand flux. And even if they do understand these concepts, they may think that it's way beyond the level of their course.

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    2. My browser decided to crash while I was in the process of typing a (partial) reply. I'd have popped up before but I was put off by your security arrangements (doubtless introduced to reduce the amount of spam, but too complicated for an old guy like me). however, Joe told me I should comment here, and I found that getting a Google ID wasn't too difficult.

      As you'll doubtless have observed, my Biochemistry Howlers pages are in urgent need of updating, but although I could probably find the time I need access to all the current textbooks, and that's more difficult -- the library here was pretty dismal 25 years ago, and now it's virtually non-existent. (I prepared the original pages once while I killing time in the office of someone who had administrative duties that occupied a lot of his time.)

      So far as Kacser and Burns are concerned we'll have to agree to differ. If I had your encyclopaedic knowledge of biochemistry I'd be tempted to write a general textbook of my own, but there are huge swathes of biochemistry that I know little about, so it would be a disaster.

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    3. ... I need access to all the current textbooks, and that's more difficult

      What's the problem? You can buy them all on Amazon. I figure it won't cost you more than $2000 to get one copy of each of the most popular books. :-)

      Alternatively, you could fly to Toronto from Marseille and use my copies. Or, you could trust me to look up the data and give you a completely unbiased view of why my book is better than all the others.

      (I can understand why you might not want to leave Marseille for Toronto. Maybe I could come and visit you with all my textbooks?)

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  3. Let me add a point about rate-limiting-ness, from the work of Kacser and Burns. They made a measure of rate-limitingness called the Sensitivity Coefficient. For a simple linear pathway, it was the fraction of change in output divided by the fractional rate of change in the concentration of the enzyme. So if increasing the enzyme concentration by 2% increased the output of the pathway by 1%, the sensitivity coefficient of that enzyme was 0.5.

    For a pure rate-limiting enzyme the SC would be 1. What Kacser and Burns proved (very easily) was that the sum of SC's for a linear pathway would be 1. That means that if one step had an SC of (say) 0.1, none of the others could have SC's of more than 0.9.

    So typically there is (what K&B called) "molecular democracy": although some steps may have bigger SCs that others, all have an effect. No one step in a pathway is literally rate-limiting. That is a surprise -- we were all brought up on the idea that there are rate-limiting steps and non-rate-limiting steps. But in face the distinction is illusory.

    (In case anyone wants to quibble, yes, I have oversimplified slightly. The SC is actually the derivative of the logarithm if output with respect to the logarithm of enzyme concentration. But for small changes the above description will work well enough.)

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    1. Typo: "but in fact the distinction is illusory".

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    2. Let's be clear about one thing. In a typical pathway operating under normal steady-state conditions it makes no sense to identify one of the enzyme-catalyzed reactions as "rate-limiting."

      However, the activity of one of more enzymes might be regulated by covalent modification or by interaction with activators and inhibitors. If you inactivate an enzyme by covalent modification, for example, you can reduce the level of activity to the point where normal flux in the pathway is severely reduced.


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  4. A couple more points:

    1. Nowadays we say "flux control coefficient" rather than "sensitivity coefficient". This was a compromise (J. A. Burns et al. (1985) Control analysis of metabolic systems Trends Biochem. Sci. 10, 16) between Kacser and Burns's terminology and that of Reinhart Heinrich and Tom Rapoport published independently at about the same time, in which they used the term "control strength".

    2. There is an implicit assumption in Joe's argument (derived, as he says, from Kacser and Burns) that all flux control coefficients are positive, because the idea of sharing becomes more problematical when some of the shares are negative. In fact, although negative values are possible they aren't common enough or usually large enough to wreck the whole idea of sharing.

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    1. On point 1, I agree. I was not up on more recent developments in metabolic control, but the material at AC-B's web site (e.g. here) is both detailed and persuasive. Kacser and Burns's sensitivity coefficient was defined in terms of the effects of changing the concentration of the enzymes. That leaves us unclear on how to deal with a change of the properties of one of the enyzymes, as might occur with an amino acid substitution.

      On point 2, I will plead extenuating circumstances. Kacser and Burns's result is for the case of a linear pathway with no feedback of regulation. It is also for the case where the concentrations of substrates and products are far enough from equilibrium that we can talk about flux through the pathway. Given that, I believe that flux control coefficients will be positive.

      As for reality -- well, I don't even know the names of all 20 amino acids, having trained as a population biologist rather than as a biochemist or molecular biologist, so ask Athel Cornish-Bowden about that.

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