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DBL%20Hendrix%20small.png College chemistry, 1983

Derek Lowe The 2002 Model

Dbl%20new%20portrait%20B%26W.png After 10 years of blogging. . .

Derek Lowe, an Arkansan by birth, got his BA from Hendrix College and his PhD in organic chemistry from Duke before spending time in Germany on a Humboldt Fellowship on his post-doc. He's worked for several major pharmaceutical companies since 1989 on drug discovery projects against schizophrenia, Alzheimer's, diabetes, osteoporosis and other diseases. To contact Derek email him directly: derekb.lowe@gmail.com Twitter: Dereklowe

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February 18, 2010

Biology By the Numbers

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Posted by Derek

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.
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Comments (35) + TrackBacks (0) | Category: Biological News | Who Discovers and Why


COMMENTS

1. RB Woodweird on February 18, 2010 9:14 AM writes...

"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.

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2. imatter on February 18, 2010 10:47 AM writes...

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.

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3. lazybratsche on February 18, 2010 10:49 AM writes...

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.

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4. Timbo on February 18, 2010 11:01 AM writes...

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.

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5. Cloud on February 18, 2010 12:23 PM writes...

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.

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6. barry on February 18, 2010 12:47 PM writes...

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.

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7. Frodo on February 18, 2010 1:09 PM writes...

#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.

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8. Beckman on February 18, 2010 1:44 PM writes...

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

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9. Bored on February 18, 2010 1:54 PM writes...

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.

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10. Timbo on February 18, 2010 2:28 PM writes...

#7 Frodo

I think I should rewatch all of my childhood movies!

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11. Cloud on February 18, 2010 3:50 PM writes...

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.

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12. Derek Lowe on February 18, 2010 3:54 PM writes...

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.

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13. metaphysician on February 18, 2010 6:34 PM writes...

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 ;-) )

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14. Anonymous on February 18, 2010 8:32 PM writes...

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...

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15. Vince on February 18, 2010 9:21 PM writes...

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,