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Biology By the Numbers

I’ve been meaning to write about this paper in PNAS for a while. The authors (from Cal Tech and the Weizmann Institute) have set up a new web site, are calling for a more quantitative take on biological questions. They say that modern techniques are starting to give up meaningful inputs, and that we’re getting to the point where this perspective can be useful. A web site, Bionumbers, has been set up to provide ready access to data of this sort, and it’s well worth some time just for sheer curiosity’s sake.
But there’s more than that at work here. To pick an example from the paper, let’s say that you take a single E. coli bacterium and put it into a tube of culture medium, with only glucose as a carbon source. Now, think about what happens when this cell starts to grow and divide, but think like a chemist. What’s the limiting reagent here? What’s the rate-limiting step? Using the estimates for the size of a bacterium, its dry mass, a standard growth rate, and so on, you can arrive at a rough figure of about two billion sugar molecules needed per cell division.
Of course, bacteria aren’t made up of glucose molecules. How much of this carbon got used up just to convert it to amino acids and thence to proteins (the biggest item on the ledger by far, it turns out), to lipids, nucleic acids, and so on? What, in other words, is the energetic cost of building a bacterium? The estimate is about four billion ATPs needed. Comparing that to those two billion sugar molecules, and considering that you can get up to 30 ATPs per sugar under aerobic conditions, and you can see that there’s a ten to twentyfold mismatch here.
Where’s all the extra energy going? The best guess is that a lot of it is used up in keeping the cell membrane going (and keeping its various concentration potentials as unbalanced as they need to be). What’s interesting is that a back-of-the-envelope calculation can quickly tell you that there’s likely to be some other large energy requirement out there that you may not have considered. And here’s another question that follows: if the cell is growing with only glucose as a carbon source, how many glucose transporters does it need? How much of the cell membrane has to be taken up by them?
Well, at the standard generation time in such media of about forty minutes, roughly 10 to the tenth carbon atoms need to be brought in. Glucose transporters work at a top speed of about 100 molecules per second. Compare the actual surface area of the bacterial cell with the estimated size of the transporter complex. (That’s about 14 square nanometers, if you’re wondering, and thinking of it in those terms gives you the real flavor of this whole approach). At six carbons per glucose, then, it turns out that roughly 4% of the cell surface must taken up with glucose transporters.
That’s quite a bit, actually. But is it the maximum? Could a bacterium run with a 10% load, or would another rate-limiting step (at the ribosome, perhaps?) make itself felt? I have to say, I find this manner of thinking oddly refreshing. The growing popularity of synthetic biology and systems biology would seem to be a natural fit for this kind of thing.
It’s all quite reminiscent of the famous 2002 paper (PDF) “Can A Biologist Fix a Radio”, which called (in a deliberately provocative manner) for just such thinking. (The description of a group of post-docs figuring out how a radio works in that paper is not to be missed – it’s funny and painful/embarrassing in almost equal measure). As the author puts it, responding to some objections:

One of these arguments postulates that the cell is too complex to use engineering approaches. I disagree with this argument for two reasons. First, the radio analogy suggests that an approach that is inefficient in analyzing a simple system is unlikely to be more useful if the system is more complex. Second, the complexity is a term that is inversely related to the degree of understanding. Indeed, the insides of even my simple radio would overwhelm an average biologist (this notion has been proven experimentally), but would be an open book to an engineer. The engineers seem to be undeterred by the complexity of the problems they face and solve them by systematically applying formal approaches that take advantage of the ever-expanding computer power. As a result, such complex systems as an aircraft can be designed and tested completely in silico, and computer-simulated characters in movies and video games can be made so eerily life-like. Perhaps, if the effort spent on formalizing description of biological processes would be close to that spent on designing video games, the cells would appear less complex and more accessible to therapeutic intervention.

But I’ll let the PNAS authors have the last word here:

“It is fair to wonder whether this emphasis on quantification really brings anything new and compelling to the analysis of biological phenomena. We are persuaded that the answer to this question is yes and that this numerical spin on biological analysis carries with it a number of interesting consequences. First, a quantitative emphasis makes it possible to decipher the dominant forces in play in a given biological process (e.g., demand for energy or demand for carbon skeletons). Second, order of magnitude BioEstimates merged with BioNumbers help reveal limits on biological processes (minimal generation time or human-appropriated global net primary productivity) or lack thereof (available solar energy impinging on Earth versus humanity’s demands). Finally, numbers can be enlightening by sharpening the questions we ask about a given biological problem. Many biological experiments report their data in quantitative form and in some cases, as long as the models are verbal rather than quantitative, the theor y will lag behind the experiments. For example, if considering the input–output relation in a gene-regulatory net work or a signal- transduction network, it is one thing to say that the output goes up or down, it is quite another to say by how much.


47 comments on “Biology By the Numbers”

  1. RB Woodweird says:

    “I have to say, I find this manner of thinking oddly refreshing.”
    I agree. I think it is because as chemists, we are always thinking about the actual vs the theoretical yield of reactions and processes. I don’t know that biologists or even biochemists work that way.

  2. imatter says:

    As a chemist, I am fascinated how biologists run experiments. But in reality, these are just basic scientific thought processes that should be in common in all disciplines.

  3. lazybratsche says:

    I’m a young biologist that would love to mix in a bit of the quantitative approach with the usual biology. In undergrad, I attempted to apply what I learned in diff eq and computer modeling courses to some of my upper level bio courses. This was met with a lot of blank stares from the bio profs (who didn’t want to try to follow any math), and similar non-comprehension from the math profs (who would point out flaws in the math, but didn’t care about its use in biology). Even now, the PIs I work with give me a look of blank derision whenever I even mention systems biology.
    It’s a shame that biologists are so bad at math, and react to it with near hostility.

  4. Timbo says:

    I was always inclined to think of biology as a very complex form of chemistry but it was always evident that my biologist friends didn’t do that that often. Maybe that is because when their head starts to hurt (as mine sometimes does) they retract to a more macroscopic way of thinking.

  5. Cloud says:

    The bionumbers database is a good idea.
    However, there are all sorts of people taking quantitative approaches to biology, and some of these fields have been around for a long time. Lazybratsche- if you really want to pursue the use of math to better understand biology, I think you want to look at biomathematics, bioengineering, and/or computational biology. You’ll find graduate programs in all of these disciplines.
    Biologists aren’t stupid. In the cases where these approaches yield useful information, that information tends to get used. Most bioengineers, biomathematicians, and computational biologists that I know collaborate extensively with other types of biologists. However, just like not all chemists make extensive use of theoretical chemistry in their work, not all biologists make extensive use of mathematical approaches in their work. There is nothing wrong with that- judge the work by whether it is advancing knowledge, not by whether the people doing it think the way you think they should.

  6. barry says:

    Four billion ATP molecules might suffice for an external machine to build a dead bacterium, but we shouldn’t be surprised that it takes more for a live bacterium to build itself. Call it housekeeping.

  7. Frodo says:

    #4 Timbo,
    In “Jurassic Park”, Crichton uses a lot of math to point out the complexity of biological systems. He takes that to another level by using math to make a point about scientific ethics. The “scientists” in the book are blinded by the “magic” their biological experiment unleashes. The mathmatician uses logic to show them the folly of their efforts. For some people, when biology is involved, we overlay a cloud of mystery to systems that aren’t as “magical” as they really are.
    In addition, most biology degrees don’t require advanced math courses.
    Isaac Newton would like this subject.

  8. Beckman says:

    Michael Crichton also succumbed in “State of Fear” to the common mistake that Cal Tech is spelled as two words. Caltech, one word.

  9. Bored says:

    My favorite Crichton subject, close to home, is the biolab “Wildfire” in “The Andromeda Strain.” If a major accident occures at the lab, a nuclear bomb goes off in the basement.
    Having something like that in the lab basement might make Derek’s list of “Things I Won’t Work With” a little longer, I would think. Heck, I’d be careful just turning on the coffee pot.

  10. Timbo says:

    #7 Frodo
    I think I should rewatch all of my childhood movies!

  11. Cloud says:

    Timbo, you just made at least half of us feel very old.
    I was in college when Jurassic Park came out. I saw it with a bunch of biologists, one of whom actually blurted out “oh, bad idea!” when they got to the bit about using amphibians DNA as filler.

  12. Derek Lowe says:

    Tell me about it. When that movie came out, I was on my third different drug discovery project in industry. Maybe fourth. Time, it does that marching on thing.

  13. metaphysician says:

    See, these days, its clear your better off using bird DNA for filler.
    ( after all, there’s no way the raptors could accidentally develop wings 😉 )

  14. Anonymous says:

    Dr. Ian Malcolm: “I’ll tell you the problem with the scientific power that you’re using here: it didn’t require any discipline to attain it. You read what others had done and you took the next step. You didn’t earn the knowledge for yourselves, so you don’t take any responsibility… for it. You stood on the shoulders of geniuses to accomplish something as fast as you could and before you even knew what you had you patented it and packaged it and slapped it on a plastic lunchbox, and now you’re selling it!”
    Kind of spooky, considering this blog…

  15. Vince says:

    I agree with you, Cloud, on some level but as someone that calls neurobiology home and has spent a good deal of time in the areas of bioengineering and biophysics, your general grad student kind of sucks when it comes to understanding and describing biology as a mathematically definable system.
    I am constantly in awe of the number of ‘biology’ grad students I come into contact with who, when you attempt to talk about topics such as senescence, just provide hand-waving excuses about the complexity of the system or some such answer. Which is fine, but they’re arguments are hollow and indefinable: which is a problem that stems from an lacking toolset from which to classify systems. Really? Those ‘random’ metabolic or molecular network graphs aren’t just a jumble of lines? You can define those? …a network-motiff?!?
    I’ll never forget my conversation with a biopsychology grad who was trying to convince me about quantum mechanical computations in the brain. Ohh, it has to be entanglement…. A cursory knowledge of the numbers involved, the thermodynamics involved, should lead to a general inkling something’s wrong. kBT?!? he answered with surprise and I walked away.
    Not to be down on biologists, but I find that bioengineers and biophysicists have a better mental framework and are much better equipt to look at biology as a system that can be defined, explained and tweaked. Biologists are too easy to wave their hands and walk away.

  16. Bacteriologist says:

    The chemists have to understand that each bacterium is like one individual person with a complete life of its own. Just like no two humans behave similar in a given situation, so is with each bacterium of a bacterial species. But together as a colony they generally show a calculated mob behavior.
    I am not suggesting even remotely that Math is ineffective while studying bacteria, but only cautioning that it does not support Bacteriology in the manner it does in Chemistry.
    One has to have an understanding of different sciences (Physics, Math, Chemistry…) to be an effective bacteriologist…and only then can he work well with a Medicinal Chemist to identify the right weapon against the pathogenic bacteria.

  17. RKN says:

    As a result, such complex systems as an aircraft can be designed and tested completely in silico […]
    Except we’ve been told that cells, unlike aircraft, have not been designed. I’m just saying!
    Seriously, it seems to me understandable that much of molecular biology has been largely non-quantitative up to now, but going forward it’s inexcusable if it doesn’t become more so. Even then, it’s going to be only a few who do it seriously since, based on my experience, many students of biology can’t even explain what a t-test measures.
    As to your question: where’s all the ATP going, maybe back into the media? I don’t know, don’t bacteria have ATP exporters in their cell membranes? In mammals, if you have a biomolecule at excess concentration then it goes to urine. So maybe bacteria are just “pissing” the excess away?

  18. Forest Gump says:

    Possibly a very obvious question that will be shot down in 30 seconds, but if the only thing you’re putting into your system is glucose, then where is the nitrogen coming from for the proteins etc? If there’s another input into the system, surely this will change the sums won’t it?

  19. Bored says:

    While on the semi sci-fi topic, Asimov stated long ago in the “Foundation” series that there can be no predictive theory of History (i.e. the future) because there are too many variables. I think he meant that you can’t KNOW all the variables in a complex system, and so can’t ever explain everything in mathematical terms. You can get a good approximation, maybe. That is partly what calculus is about.

  20. Vader says:

    He didn’t say glucose was the only thing being put in the system; only that it is the only carbon source in the system. Nitrogen can be supplied as either ammonium or nitrate; the former is already in the right oxidation state for production of amino acids, while the latter has to be reduced first, which costs some energy.
    Hope that helps.

  21. Jim Hu says:

    The estimate is about four billion ATPs needed. Comparing that to those two billion sugar molecules, and considering that you can get up to 30 ATPs per sugar under aerobic conditions, and you can see that there’s a ten to twentyfold mismatch here.

    What? You get 30 ATP if you take the glucose all the way to CO2, in which case none of those C atoms are part of the dry weight being discussed in the 2B estimate. If we assume E. coli growing in minimal + 0.2% glucose exhausts the glucose at a cell density of ~10^9/ml, that works out to about 6B molecules of glucose/cell. In other words, E. coli burns more than it uses to make another cell.
    Where does the 4B ATPs number come from?
    caveat: I may have screwed up the quick calculation. I’m a biologist, after all!

  22. bamh1d says:

    Excuse me. As someone with a graduate degree in quantitative biology and (too) many years in drug discovery research, I’d like to share a few thoughts on this topic. In general, the reason most biologists choose to work in the field is because of the challenge of working with complex, dynamic systems. Because the tools available are usually inadequate to even describe, much less understand these systems even in a steady state, the biologist’s approach is usually, and necessarily, descriptive; hence the hand waving about the parts that are not understood. Of course, this approach collides loudly and painfully with the scientist’s preference to rationalize the universe, and consequently results in a tendency toward reductionism for all concerned. So both the chemist and biologist are fooling themselves. The biologist, because he is using a very limited set of tools to work on a system for which the variables are usually inadequately described, much less defined, and the med chemist, for pretending that an apparent understanding of the SAR or selectivity profile of whatever chemical series is currently under study is sufficient to understand, and by extension control, a disease state in a whole population of live mammals. So please, no more chest beating about the relative scientific rigor of biologists and chemists working with inadequately understood systems.
    A couple of other thoughts: much of the work presented on the Bionumbers Web site is based on measurements averaged over populations numbering in the millions, usually microbial populations. The relative simplicity of microbes and the convenience with which these populations can be manipulated makes it easier to do the analysis and interpret the results. However, most biologists will tell you that for those reasons, microbial results do not extrapolate well to results obtained with mouse cells in culture, and are certainly not predictive of results obtained with a population of few dozen live mice.
    Also, the molecular biologists and their progeny, the molecular cell biologists, come in for a fair amount of deserved criticism on this site. However, I would point out that at least as far as drug discovery is concerned, in general terms their work is not so different from that of the med chemist. Both the biologist and chemist are working with artificial constructs in an attempt to probe and then manipulate a complex biological system. Both are limited by the tools that are conveniently at hand, and for that reason both are taking necessary short cuts to try to both expand and at the same time accelerate an expensive process. Let’s remember that back in the golden age (1960-1990) drug discovery was conducted testing a relatively small number of compounds directly in live animal models using relatively simplistic endpoints. In other words, with limited input (and impact) by both the med chemist and biologist. Let’s also remember that this was basically the age of natural products, in which many generations of evolution substituted for pseudo-knowledge to provide the chemistry that achieved a useful biological response. Finally, let’s consider that the (in my opinion, largely unsuccessful) attempt to expand and systematize drug discovery during the 90s was based on the idea that the available tools were adequate or sufficiently extendible to support that objective in a cost-effective manner.

  23. Jim Hu says:

    Of course as soon as I posted my comment, I saw the mistake in my calcs. At this level of accuracy 6 = 2. The number is very sensitive to the actual titer of cells grown in glucose.

  24. Cloud says:

    Vince- sure, most pure biologists aren’t going to be great at defining their systems mathematically. That isn’t their strength. But the smart ones are willing to collaborate with the people who ARE good at defining biological systems mathematically. And the smart bioengineers/biomaths types go looking for those collaborations, because they need the input data and someone to help test the hypotheses their models suggest.
    The cross-fertilization between bench biology and the more mathematically inclined isn’t as good as it could be, but I don’t think the blame for that lies entirely with the bench biologists.
    And there were a lot of things I couldn’t do in grad school that I can do now.

  25. AR says:

    One of the problems with applying strict mathematics to cellular biology is it doesn’t take futile cycling into consideration. Here’s a one real world example. There should be one to one stoichiometry between consumption of NADPH and insertion of oxygen into a compound via cytochrome P450 oxidative metabolism. In principle you ought to be able to just measure NADPH consumption and be able to figure the amount of parent drug metabolism – but it doesn’t work. The compound binds loosely in a lazy enzyme pocket – some P450 enzymes are just built that way in order to accommodate a lot of different substrates. Anyway, NADPH is consumed, but the non-metabolized drug falls off. This can be repeated time and time again for no rhythm or reason that is known before oxygen insertion.

  26. coprolite says:

    I am educated and trained as a biologist but have been employed as a chemist in a number of positions, and I have seen a lot of different approaches to the wee beasties and the stuff that makes them run. No doubt it takes a balanced contribution all disciplines to create a balanced view of a process. If you want to point the finger at one group of people being unable to understand the complexities of a biological system you should see there are three fingers pointing back at you.
    Lazybrat, are you sure the blank stares were a result of others ignorance, or maybe they were a reaction to yours?
    I love the Ian Malcolm talk, easily one of my favorite characters.

  27. Three Pines says:

    I agree with your comment, but would replace “calculus” with “statistics”.

  28. mad says:

    This is laughable. Comparing the approach biologists use to study new systems where even the basic components (enzymes/proteins) are entire fields of study to that of an engineer fixing a basic radio already having the knowledge of the man made components is flawed. It assumes a biologist has never seen a radio before but that an engineer has all the modern knowledge of engineering to fix something that’s a basic lesson in a 101 class?
    If this were the case a biologist would fix a radio by reading the literature on how to fix a radio.
    I understand the message about incorporating more math in biology but observing the apple falling from the tree usually precedes making equations to explain its behavior. Definig what happnes in the very beginign and thats what bilogists are tryin to do There are plenty of people trying to do more at great failure (which is fine they shoudl keep trying ans will one day get it). The authors are just a bit ignorant. This is a typical grass is always greener scenario…Ah yeah complex math that will make it all obvious!

  29. Gandalf the Orange says:

    #28 mad
    Yes, all of the chemists, physicists, researchers, and just about every other scientist or scientist-to-be under the sun on this blog are just a bit ignorant. We are glad you have set us all straight.

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