Friday, July 8, 2016

Cell Biology by the Numbers

Six years ago I wrote an entry in this blog about the bionumbers website. Now Ron Milo and Rob Phillips have turned that website into a book: Cell Biology by the Numbers. Milo and Phillips write
One of the central missions of our book is to serve as an entry point that invites the reader to explore some of the key numbers of cell biology. We hope to attract readers of all kinds—from seasoned researchers, who simply want to find the best values for some number of interest, to beginning biology students, who want to supplement their introductory course materials. In the pages that follow, we provide a broad collection of vignettes, each of which focuses on quantities that help us think about sizes, concentrations, energies, rates, information content, and other key quantities that describe the living world.
One part of the book that readers of Intermediate Physics for Medicine and Biology might find useful is their “rules of thumb”. I reproduce a few of them here
• 1 dalton (Da) = 1 g/mol ~ 1.6 × 10-24 g.
• 1 nM is about 1 molecule per bacterial volume [E. coli has a volume of about 1 μm3].
• 1 M is about one per 1 nm3.
• Under standard conditions, particles at a concentration of 1 M are ~ 1 nm apart.
• Water molecule volume ~ 0.03 nm3, (~0.3 nm)3.
• A small metabolite diffuses 1 nm in ~1 ns.
The book consists of a series of vignettes, each phrased as a question. Here is an excerpt form one.
Which is bigger, mRNA or the protein it codes for?

The role of messenger RNA molecules (mRNAs), as epitomized in the central dogma, is one of fleeting messages for the creation of the main movers and shakers of the cell—namely, the proteins that drive cellular life. Words like these can conjure a mental picture in which an mRNA is thought of as a small blueprint for the creation of a much larger protein machine. In reality, the scales are exactly the opposite of what most people would guess. Nucleotides, the monomers making up an RNA molecule, have a mass of about 330 Da. This is about three times heavier that the average amino acid mass, which weighs in at ~110 Da. Moreover, since it takes three nucleotides to code for a single amino acid, this implies an extra factor of three in favor of mRNA such that the mRNA coding a given protein will be almost an order of magnitude heavier.
It’s obvious once someone explains it to you. Here is another that I liked.
What is the pH of a cell?

…Even though hydrogen ions appear to be ubiquitous in the exercise sections of textbooks, their actual abundance inside cells is extremely small. To see this, consider how many ions are in a bacterium or mitochondrion of volume 1 μm3 at pH 7. Using the rule of thumb that 1 nM corresponds to ~ 1 molecule per bacterial cell volume, and recognizing that pH 7 corresponds to a concentration of 10-7 M (or 100 nM), this means that there are about 100 hydrogen ions per bacterial cell…This should be contrasted with the fact that there are in excess of a million proteins in that same cellular volume.
This one surprised me.
What are the concentrations of free matabolites in cells?

…The molecular census of metabolites in E. coli reveals some overwhelmingly dominant molecular players. The amino acid glutamate wins out…at about 100 mM, which is higher than all other amino acids combined…Glutamate is negatively charged, as are most of the other abundant metabolites in the cell. This stockpile of negative charges is balanced mostly by a corresponding positively changed stockpile of free potassium ions, which have a typical concentration of roughly 200 mM.
Somehow, I never realized how much glutamate is in cells. I also learned all sorts of interesting facts. For instance, a 5% by weight mixture of alcohol in water (roughly equivalent to beer) corresponds to a 1 M concentration. I guess the reason this does not wreak havoc on your osmotic balance is that alcohol easily crosses the cell membrane. Apparently yeast use the alcohol they produce to inhibit the growth of bacteria. This must be why John Snow found that during the 1854 London cholera epidemic, the guys working (and, apparently, drinking) in the brewery were immune.

I’ll give you one more example. Milo and Phillips analyze how long it will take a substrate to collide with a protein.
…Say we drop a test substrate molecule into a cytoplasm with a volume equal to that of a bacterial cell. If everything is well mixed and there is no binding, how long will it take for the substrate molecule to collide with one specific protein in the cell? The rate of enzyme substrate collisions is dictated by the diffusion limit, which as shown above, is equal to ~ 109 s-1M-1 times the concentration. We make use of one of our tricks of the trade, which states that in E. coli, a single molecule (say, our substrate) has an effective concentration of about 1 nM (that is, 10-9 M). The rate of collisions is thus 109 s-1M-1 × 10-9 M. That is, they will meet within a second on average. This allows us to estimate that every substrate molecule collides with each and every protein in the cell on average about once per second.
Each and every one, once per second! The beauty of this book, and the value of making these order-of-magnitude estimates, is to provide such insight. I cannot think of any book that has provided me with more insight than Cell Biology by the Numbers.

Readers of IPMB will enjoy CBbtN. It is well written and the illustrations by Nigel Orme are lovely. It may have more cell biology than readers of IPMB are used to (Russ Hobbie and I are macroscopic guys), but that is fine. For those who prefer video over text, listen to Rob Phillips and Ron Milo give their views of life in the videos below.

I will give Milo and Phillips the last word, which could also sum up our goals for IPMB.
We leave our readers with the hope that they will find these and other questions inspiring and will set off on their own path to biological numeracy. 

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