Cell Biology by the Numbers

Cell Biology by the Numbers,
by Ron Milo and Rob Phillips.

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’ll 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.

Physical Biology of the Cell

Physical Biology of the Cell,
by Phillips, Kondev, and Theriot.

I spent some time this week looking over the recently published textbook Physical Biology of the Cell, by Rob Phillips, Jane Kondev, and Julie Theriot. In some ways this book is a competitor of the 4th edition of Intermediate Physics for Medicine and Biology (it is always good to know your competition). Bernard Chasan reviewed Physical Biology of the Cell in the November 2010 issue of the American Journal of Physics.

The authors of this book are, in a very real sense, missionaries. They want to convince a wide audience to share their enthusiasm for and commitment to a more quantitative and scientifically rigorous approach to cell biology than is normally encountered in the teaching literature.

To achieve this goal, they set out a program of quantitative model building based on physical principles…. What the authors describe (awkwardly but evocatively) as the mathematizing of the semiqualitative models of cell biology (referred to as “cartoons” in some circles) has now become central to cell biology—as evidenced by a half a dozen recent texts and the relatively new and thriving discipline of systems biology. The work being reviewed is the latest and most comprehensive attempt to foster and advocate for this approach…

At the center of their approach is the art of model making—well presented with the aid of some excellent figures, which show the choices needed to model proteins, as one example. The main point is that modeling requires a simplifying choice, which emphasizes one view of the protein and essentially ignores others. If it suits your purposes to model the protein as a collection of hydrophobic and hydrophilic amino acid residues—a good model for protein folding—then you cannot at the same time consider the protein as a two state system.

After skimming through Physical Biology of the Cell (I wish I had time to read it thoroughly), I have several observations.

1. The second half of Intermediate Physics for Medicine and Biology (IPMB) is about clinical medical physics: imaging and therapy. None of this appears in Physical Biology of the Cell (PBC). Also, in IPMB Russ Hobbie and I steer clear of molecular biology, saying in the preface that “molecular biophysics has been almost completely ignored: excellent texts already exist, and this is not our area of expertise.” PBC is all molecular and cellular. The main overlap between the two books is several chapters in PBC that cover similar topics as are in the first half of IPMB. So, I guess IPMB and PBC are not really in direct competition. However, if I was Phil Nelson, author of Biological Physics: Energy, Information, Life, I might be concerned about market share.
2. PBC is illustrated by Nigel Orme. Let me be frank; Orme’s drawings are much better than what we have in IPMB. One thing I like about PBC is that you can skip the text altogether and just look at the pictures, and still learn the gist of the subject. Figure 1.4 showing the genetic code reminds me of the sort of graphics that Edward Tufte promotes in The Visual Display of Quantitative Information. The authors of PBC state in the acknowledgments “this book would never have achieved its present incarnation without the close and expert collaboration of our gifted illustrator, Nigel Orme, who is responsible for the clarity and visual appeal of the more than 550 figures found in these pages, as well as the overall design of the book.” As generous as this tribute is, it may be an understatement. Then, just when I thought the artwork couldn’t get any better, I found that PBC contains several beautiful figures contributed by David Goodsell, author of The Machinery of Life.
3. In the 4th edition of IPMB, Russ and I added an initial section exploring the relative size of biological objects. In PBC, a similar discussion fills the entire Chapter 2. There is lots of numerical estimating in this chapter, reminding me of the Bionumbers website. Chapter 3 looks at different temporal scales, which is more difficult to show visually than spatial scales (Russ and I didn’t try), although Orme’s drawings do a pretty good job. Chapter 4 of PBC looks at the many model systems used in biology, with an eye toward history (Mendel’s pea plants, hemoglobin and the structure of a protein, the bacteriophage in genetics, etc.). Great reading.
4. Some subjects—such as diffusion, fluid dynamics, thermodynamics, and bioelectricity—are covered in both PBC and IPMB. Which book explains these topics better? Obviously I am biased, but I suggest that Russ and I develop the physics in a more detailed and systematic way, starting from the fundamentals, whereas Phillips, Kondev and Theriot present the physics rather quickly, and then apply it to many interesting biological applications. I would say that PBC does for molecular and cellular biology what Air and Water by Mark Denny does for physiology: use physics and math to explain biological concepts quantitatively. Russ and I, on the other hand, teach physics using biological examples. The difference is more about approach, tone, and point-of-view than about substance. The reader can look at both books and draw their own conclusions.
5. PBC has a few nice homework problems, but I prefer IPMB’s more extensive collection. The student learns more by doing than by reading.
6. The final chapter in PBC, “Wither Physical Biology,” is an excellent summary of the “the role of quantitative analysis in the study of living matter.” Anyone working at the interface between physics and biology must read these ten pages.

Phillips, Kondev, and Theriot ought to have the last word, so I will finish this blog entry by quoting PBC’s eloquent closing paragraph.

The act of writing this book has convinced each of us that the study of living matter is one of the most exciting frontiers in human thought. Just as the makings of the large scale universe are being revealed by ever more impressive telescopes, living matter is now being viewed in ways that were once as unimaginable as was going to the Moon. Despite the muscle-enhancing weight of this book, we feel that we have only scratched the surface of the rich and varied applications of physical reasoning to biological problems. Our overall goal has been to communicate a style of thinking about problems where we have done our best to illustrate the power of the style using examples chosen from biological systems that are well defined and usually well studied from a biological perspective. As science moves forward into the twenty-first century, it is our greatest hope that synthetic approaches for understanding the natural world from biological, physical, chemical, and mathematical perspectives simultaneously will enrich all of these fields and illuminate the world around us. We can only hope the reader has at least a fraction of the pleasure in answering that charge as we have had in attempting to describe the physical biology of the cell.

iBioMagazine

I recently discovered iBioMagazine, which I highly recommend. The iBioMagazine website describes its goals.

iBioMagazine offers a collection of short (less than 15 min) talks that highlight the human side of research. iBioMagazine goes 'behind-the-scenes' of scientific discoveries, provides advice for young scientists, and explores how research is practiced in the life sciences. New topics will be covered in each quarterly issue. Subscribe to be notified when a new iBioMagazine is released.

Here are some of my favorites:

Bruce Alberts, Editor-in-Chief of Science magazine and coauthor of The Molecular Biology of the Cell, tells about how he learned from failure.

Former NIH director Harold Varmus explains why he became a scientist.

Young researchers participating in a summer course at the Marine Biological Laboratory at Woods Hole explain why they became scientists.

Hugh Huxley discusses his development of the sliding filament theory of muscle contraction. Of particular interest is that Huxley began his career as a physics student, and then changed to biology. Andrew Huxley (no relation), of Hodgkin and Huxley fame, independently developed a similar model.

Finally, readers of Intermediate Physics for Medicine and Biology should be sure to listen to Rob Phillips’ wonderful talk about the role of quantitative thinking and mathematical modeling in biology. Phillips is coauthor of the textbook Physical Biology of the Cell, which I have discussed earlier in this blog.

Forman Acton (1920 – 2014)

Numerical Methods That Work,
by Forman Acton.

The American computer scientist Forman Acton died ten years ago this Sunday. In Intermediate Physics for Medicine and Biology, Russ Hobbie and I cite Acton’s Numerical Methods That Work. For readers interested in using computers to model biological processes, I recommend this well written and engaging book.

Before he died, Acton donated funds to establish the Forman Acton Foundation. Here is how their website describes his life:

Forman Sinnickson Acton was born in Salem City, and he went on to change the world.

Born on August 10, 1920, he began his education in the Salem City school system before attending private boarding school at Phillips Exeter Academy and college at Princeton University. He graduated with two degrees in engineering toward the end of World War II, during which he served in the Army Corps of Engineers and worked on a team involved in the Manhattan Project.

After his service, he earned his doctorate in mathematics from Carnegie Institute of Technology, helped the Army develop the world’s first anti-aircraft missiles and became a pioneer in the evolving field of computer science.

Acton conducted research and taught at Princeton from 1952 to 1990, during which time he wrote textbooks on mathematics at his cabin on Woodmere Lake in Quinton Township, Salem County. When he turned 80, he joined the Lower Alloways Creek pool to stay in shape, swimming six days a week for 14 years.

He died on February 18, 2014, in Woodstown, New Jersey, but not before he anonymously donated thousands of dollars toward scholarships for Salem City School District students, some of whom were just then graduating from college. Before he passed, he made it clear to friends and confidants that he wanted these students to have access to the incredible educational experiences he enjoyed.

Eight months after his passing, the Forman S. Acton Educational Foundation was officially incorporated to ensure that all of Salem’s youth also have a chance to change the world.

Sometimes I will read a passage and say to myself “That’s exactly what students studying from IPMB need to hear.” I feel this way about Acton’s preface to Numerical Methods That Work. Russ and I include many homework problems in IPMB so the student can gain experience with the art of mathematical modeling. Below, in Acton’s words, is why we do that. Just replace phrases like “solving equations numerically” with “building models mathematically” and his words apply equally well to IPMB.

Numerical equation solving is still largely an art, and like most arts it is learned by practice. Principles are there, but even they remain unreal until you actually apply them. To study numerical equation solving by watching someone else do it is rather like studying portrait painting by the same method. It just won’t work. The principle reason lies in the tremendous variety within the subject…

The art of solving problems numerically arises in two places: in choosing the proper method and in circumventing the main road-blocks that always seem to appear. So throughout the book I shall be urging you to go try the problems—mine or yours.

I have tried to make my explanations clear, but sad experience has shown that you will not really understand what I am talking about until you have made some of the same mistakes I have made. I hesitate to close a preface with a ringing exhortation for you to go forth to make fruitful mistakes; somehow it doesn’t seem quite the right note to strike! Yet, the truth it contains is real. Guided, often laborious, experience is the best teacher for an art.

 

Calculus Made Easy

Intermediate Physics for Medicine and Biology assumes the reader knows calculus. Most medical doctors and biologists have studied some calculus, but I’m not sure they remember much of it. And most high school students, and even college freshman, have yet to take their first calculus course. What should these readers of IPMB do if they don’t know any calculus?  

Calculus Made Easy,
by Silvanus Thompson.

What these readers need is a quick and easy way to learn calculus without delving into all the subtle and complicated details. How can they do that? Read the delightful old book Calculus Made Easy, by Silvanus Thompson. Here’s the prologue:

Considering how many fools can calculate, it is surprising that it should be thought either a difficult or a tedious task for any other fool to learn how to master the same tricks. 

Some calculus-tricks are quite easy. Some are enormously difficult. The fools who write the textbooks of advanced mathematics — and they are mostly clever fools — seldom take the trouble to show you how easy the easy calculations are. On the contrary, they seem to desire to impress you with their tremendous cleverness by going about it in the most difficult way. 

Being myself a remarkably stupid fellow, I have had to unteach myself the difficulties, and now beg to present to my fellow fools the parts that are not hard. Master these thoroughly, and the rest will follow. What one fool can do, another can.

I know what you’re thinking: “That sounds like just what I need, but how much is it going to cost me?” The good news is that you can access the book for free online, at http://calculusmadeeasy.org.

Silvanus P. Thompson

The author, Silvanus Phillips Thompson (1851–1916), was an English physicist and a fellow of the Royal Society. I have a particular fondness for physicists from the Victorian era, especially one such as Thompson who was interested in science education and whose strength was his ability to explain difficult concepts clearly.

For those of you turned off by the dated style of Calculus Made Easy, written in 1910, I suggest Quick Calculus or Used Math instead. For those who, like me, love the Victorian style, I recommend Flatland by Edwin Abbott.

Enjoy!

Calculus Made Easy, by Silvanus P. Thompson, Part 1/2. A LibriVox audiobook. 

https://www.youtube.com/watch?v=hF2FLi5UnlE

 

Calculus Made Easy, by Silvanus P. Thompson, Part 2/2. A LibriVox audiobook.

https://www.youtube.com/watch?v=uqQtQNTKo-A

Bionumbers

One feature of the 4th edition of Intermediate Physics for Medicine and Biology that distinguishes it from many other medical or biological textbooks is its focus on analyzing biomedical topics quantitatively. This point of view is also promoted at the BIONUMB3R5 (bionumbers) website, established by researchers in the systems biology department at Harvard. There is also a BIONUMB3R5 wiki where many researchers are coming together to provide new insights into key numbers in biology.

I particularly like the “Bionumber of the Month” feature. The March 2010 entry (“What are the Time Scales for Diffusion in Cells”) could easily be made into a homework problem for Chapter 4 of Intermediate Physics for Medicine and Biology. The January 2010 entry (“What is Faster, Transcription or Translation?”) is fascinating.

Transcription, the synthesis of mRNA from DNA, and translation, the synthesis of protein from mRNA, are the main pillars of the central dogma of molecular biology. How do the speeds of these two processes compare? …

Transcription of RNA by RNA polymerase in E. coli cells proceeds at a maximal speed of about 40–80 bp/sec… Translation by the ribosome in E. coli proceeds at a maximal speed of about 20 aa/sec… Interestingly, since every 3 base pairs code for one amino acid, the rates of the two processes are quite similar…

The “collection of fundamental numbers in molecular biology” found at the bionumbers website has the same tone as the first section of Chapter 1 in Intermediate Physics for Medicine and Biology, in which Russ Hobbie and I look at the relative size of biological objects. The collection contains this gem: “concentration of 1 nM in a cell the volume of E. coli is ~ 1 molecule/cell.”

The bionumbers website arose from an article by Rob Phillips and Ron Milo in the Proceedings of the National Academy of Sciences (Volume 106, pages 21465–21471, 2009), “A Feeling for the Numbers in Biology.” The abstract of their paper is given below:

Although the quantitative description of biological systems has been going on for centuries, recent advances in the measurement of phenomena ranging from metabolism to gene expression to signal transduction have resulted in a new emphasis on biological numeracy. This article describes the confluence of two different approaches to biological numbers. First, an impressive array of quantitative measurements make it possible to develop intuition about biological numbers ranging from how many gigatons of atmospheric carbon are fixed every year in the process of photosynthesis to the number of membrane transporters needed to provide sugars to rapidly dividing Escherichia coli cells. As a result of the vast array of such quantitative data, the BioNumbers web site has recently been developed as a repository for biology by the numbers. Second, a complementary and powerful tradition of numerical estimates familiar from the physical sciences and canonized in the so-called “Fermi problems” calls for efforts to estimate key biological quantities on the basis of a few foundational facts and simple ideas from physics and chemistry. In this article, we describe these two approaches and illustrate their synergism in several particularly appealing case studies. These case studies reveal the impact that an emphasis on numbers can have on important biological questions.

Russ and I introduce similar order-of-magnitude estimates (Fermi problems) in Chapter 1 of our book (for example, see homework problems 1–4, which are new in the 4th edition). One of my favorite Fermi problems, which I first encountered in the book Air and Water by Mark Denny, is to calculate the concentration of oxygen molecules in blood and in air, and compare them. Not too surprisingly, they are nearly the same (about 8 mM). I suspect the bionumbers folks would enjoy Air and Water. (I hope they would enjoy Intermediate Physics for Medicine and Biology, too.)

For those of you who find all of this interesting but prefer video over text, see the bionumbers video on YouTube.

Bionumbers: The data base of useful biological numbers. 

https://www.youtube.com/embed/psE0H1ejxKE

Learning Biology

Suppose you are a physicist, mathematician, or engineer who wants to change your research direction toward biology and medicine. How do you learn biology? Let’s assume you don’t quit your day job, so you have limited time. Here are my suggestions.

1. 

   Machinery of Life,
   by David Goodsell.

   Read The Machinery of Life (2nd edition), by David Goodsell. I discussed this book a few weeks ago in this blog. It’s visual, easy to read, not too long, cheap, and doesn’t get bogged down in details. It’s a great introduction; this is where I would start.
2. If you haven’t had an introductory biology class, you might consider taking this online biology class from MIT. It’s free, it has homework assignments and quizzes so you can assess your learning, and you can work at your own schedule. For those who prefer an online class to reading a book, this is the thing to do.
3. If you would prefer reading an introductory biology textbook, a popular one is Campbell Biology by Reece et al., now in its 10th edition. The MIT online course mentioned above and the introductory biology classes here at Oakland University use this book. Its advantages are that it covers all of biology and it is written for introductory students. Its disadvantages are that it is expensive and long. I am not an expert on the different intro biology textbooks; there may be others just as good.

4. 

   The Eighth Day of Creation,
   by Horace Freeland Judson.

   I like to learn a subject by studying its history. If you want to try this, I suggest: The Double Helix by James Watson (of Watson and Crick) and The Eighth Day of Creation by Horace Freeland Judson. Watson’s book is a classic: a first-person account the discovery of the structure of DNA. It is well written, controversial, and should be read by anyone interested in science. Judson’s book is longer and more comprehensive; a fantastic book.
5. The textbook Physical Biology of the Cell by Phillips et al. was written by physicists trying to learn biology. Also from a physicist’s point of view are Biological Physics and Physical Models of Living Systems, both by Philip Nelson. These books don’t cover all of biology, but a physicist may like them.
6. I learned a lot of biology in high school reading Isaac Asimov books. They often take a historical approach, and are qualitative, interesting, clearly written, fairly short, and cheap. I worry about recommending them because biology has progressed so much over the last few decades that these books from the 1960s are out-of-date. However, I suspect they are still useful introductions, and I suggest The Wellsprings of Life, The Genetic Code, The Human Body, The Human Brain, and A Short History of Biology.
7. Some books from my ideal bookshelf cover parts of biology from the point of view of a physicist: Air and Water by Mark Denny, Scaling: Why is Animal Size so Important? by Knut Schmidt-Nielsen, and Random Walks in Biology by Howard Berg. Steven Vogel has many books you might like, including Life in Moving Fluids, Vital Circuits, and Life’s Devices. 
8. Nothing in biology makes sense except in light of evolution. To learn about evolution, read the books of Stephen Jay Gould. I enjoyed his collections of essays from the magazine Natural History. Start with Ever Since Darwin.



Textbook of Medical Physiology,
by Guyton and Hall.

9. Once you have a general biology background, what comes next? When I was in graduate school, I sat in on the Vanderbilt Medical School’s Physiology class and their Biochemistry class. These are the two courses that I encourage Oakland University Medical Physics graduate students to take. Typical textbooks are Guyton and Hall’s Textbook of Medical Physiology, now in its 13th edition, and Nelson and Cox's Lehninger Principles of Biochemistry, now in its 6th edition. Both books are long, expensive, and detailed. If interested in cell and molecular biology, a leading text is Molecular Biology of the Cell by Bruce Alberts and Alexander Johnson. 
10. If you have the time, you can do what Russ Hobbie did: between 1971 and 1973 he audited all the courses medical students take in their first two years at the University of Minnesota. Finally, you can always purchase a copy of the 5th edition of Intermediate Physics for Medicine and Biology!

If readers of the blog have their own recommendations, please add them in the comments.