“The Machinery of Life” by David Goodsell is full of illustrations like the ones show in the article and really gave me a sense of what k might imagine when reading about the cell.
“Cell Biology by the Numbers” by Ron Milo and Rob Philips is full of order of magnitude calculations of about the processes of the cell. How fast are they, over what distance, how much, etc.
There's a searchable database of bionumbers[1], and a draft version of "by the Numbers" officially online[2].
[1] https://bionumbers.hms.harvard.edu/search.aspx [2] https://www.dropbox.com/s/gvpleqtcv8scro4/cellBiologyByTheNu...
Every part of this passage is a shockingly accurate description of myself. I felt that I was bad at math and did a biochem degree because it meant I could skip Cal III. Now, I'm a computational biologist and I've mostly made up with math.
One of the most fascinating parts to me was DNA transcription. The engineering is quite precise.
Found the video I was referring to: https://www.youtube.com/watch?v=7Hk9jct2ozY
For illustration, consider the classic animation of a walking kinesin towing a vesicle. One could jiggle-ify it. But that won't convey that during every step, the vesicle has done a "balloon in a hurricane" exploration of every possible position it can reach while remaining tethered. Won't clarify that the very very misleading "I'm just a peaceful barge" vibe is entirely animation fantasy. Secondary content could have been added to defuse this negative educational impact, but the choice was made to optimize for, and I'm quoting, "pretty".
Jiggle-ification takes perhaps the biggest educational downside of these animations, and makes it even more misleading.
One thing that these animations always remind me of is that speeds at that level are tied to size. We're use to a world where birds and cars are faster than pollen and insects (mostly), but the fidgety twerking of all those big proteins is due to collisions with higher-velocity, invisibly small molecules like water (Brownian motion). When was the last time a pollen grain made you flinch? Everything is kinetic/EM energy exchange; everything is in the gray area between Newtonian and quantum physics. (Shout out to Einstein, but also Boltzmann through Dirac.)
The painting is wonderful. Yes, it's a snapshot in time of a dynamic state. All paintings are!
> The first time I did these calculations, I felt an intense appreciation for biology. And now, I want everyone else to feel the same. We ought to teach students of biology to think as mathematicians: to carefully quantify biology, to think in absolute units, and to develop a feeling for the organism.
It was interesting to read this article, but I think I would’ve understood a lot more if this entire piece had been (or were) an animated video that described it. Text and a few animations don’t do enough justice for the passion, knowledge and detail that’s in this article, IMO.
Bit nitpicky here but ... he wrote a typical E. coli cell.
Naturally bacteria have different size ranges, depending on many factors - nutrients, temperature, genome and so forth; e. g. look at how huge Thiomargarita namibiensis is.
But the 1 µm as average here given for E. coli, is not correct:
https://bionumbers.hms.harvard.edu/bionumber.aspx?id=117344&...
Length 1.78±0.54 μm
So while +/- at the lower end may be 1.24 µm, the max range here would be 2.42 µm, which is what I had more in mind (e. g. roughly about 2µm). I don't have all of the data to be able to say which is the exact value, but I think the website at bionumbers.hms.harvard.ed is more realistic, so I would say that E. coli's best average is more at 2µm than 1µm.
[1] https://commons.wikimedia.org/wiki/File:E._coli_Bacteria_(73...
Hold up, My own inexpert "numerical intuition" is having problems here.
If polymerase converts 40 bases/sec, and travels ~20m /sec, how on earth is one base pair 2 meters long?
I assume what the author means is that the average conversion work done by each protein is 40 base pairs per second, however it spends most the time "seeking" rather than "converting"?
Maybe an educational text for the laymen has summarised this recently but I'm not aware of one. Most Biology from your school days have been rewritten.
I will have to re-read Molecular Biology of the Cell, 7th Edition, 2022. I read the 3th edition and it has changed dramatically since.
You can download it on Anna's Archive or order it at the usual suspects https://www.amazon.com/s?k=Molecular+Biology+of+the+Cell%2C+...
The first few Units cover all the basics: chemistry of life and energy, molecular biology, cell biology, and genetics. From there you can branch out into anything.
Curious how perspectives vary. I would have said there's basically nothing available, textbooks being horribly wretched.
I don't know of anything which takes a "bottom up", rough quantitative, engineering first-principles intro to cell bio, let alone to biology. No whys and hows of building close to thermal noise energy levels. No focus on pervasive multi-scale cross-cutting strategies for localization and compartmentalization. No energy budgets, not feel for reasonable numbers, no... sigh. When you see a nifty foundational insight mentioned in passing in a research talk, it's a really good bet it won't be in textbooks any year soon. One of the causal threads leading up to TFA, the Harvard bionumbers database, was born out of someone's 'it's absurdly hard to find numbers'.
Chatting with a cell bio tome publisher years ago, about what absurdly implausible resources would be needed to do something transformatively better, the snark for "but it has 100 authors!" was "nifty - and how many for the second page?". Maybe now with AI we can start nibbling away at this faster.
I didn't get the "miles of DNA" reference. A single strand of DNA is approx 3 meter in length when uncoiled. Now I'm thinking how many strands may be replicated at a time.
Very true, these books are qualitative. There's a bit of basic math around delta-G for reactions and Chi-sq tests for genetic associations, but the conventional undergraduate introductory biology course is 99% descriptive.
There are reasonable arguments for taking that approach. These courses are foundations for subsequent study, with the intended outcome that students have a broad but shallow understanding of core basic ideas. Lots of biology makes intuitive, mechanistic, and visual sense, much like introductory computer science and introductory chemistry.
Obviously applied math plays a key role in biology but it tends to address specific needs like protein structure prediction, dynamic modeling of transcription/translation and metabolism, inferring phylogeny, high-throughput 'omics analysis, network simulation of epidemic outbreaks, and so on. These are great to study, but without the broader context the understanding would be relatively fragmented, lacking the big picture.
Rereading OP's question:
> good modern starting points to someone who would want to learn more about how living beings work (from bottom up)?
I interpret that as wanting a general understanding, starting with chemistry and working upwards towards evolution and populations. That's all in the standard two-semester introductory course, hence my book recommendation.
If that's wrong and OP wants a math-centric approach, here are a few gems:
Physical Biology of the Cell, Phillips, et. al
An Introduction to Systems Biology, Alon
Evolutionary Dynamics, Nowack
For me, success means "robust structural intuition". Perhaps frame it as understanding that's robust to adversarial noise? To fuzzing testing? If you fuzz content, changing numbers, inserting negations and lies, how extreme before there's a "wait, that doesn't make sense"?
Merely quantitative isn't sufficient. An Ideal Gas Law chapter problem, with numbers for solid Argon - mindless plug-and-chug - is not this success. But a sense of reasonable values, yes. Contrast the first-tier med student, asked for red blood cell size, who failing to recall it as a factoid, is quantitatively lost, retreating to "really really small".
Similarly, "descriptive" can be deep structure and constraints of a domain, focused on building structural intuition, or at least trying for it, or an embrace of "stamp collecting" focused on regurgitation.
I nod to "foundations for subsequent study, with the intended outcome that students have a broad but shallow understanding of core basic ideas. Lots of biology makes intuitive, mechanistic, and visual sense, much like [...] introductory chemistry. [...] without the broader context the understanding would be relatively fragmented, lacking the big picture." But then contrast it with content presenting a not-broad and quite-shallow take, that pervasively fails to engage with the domain's core structure. And then, even on its own shallow terms, still fails outcome-wise: First-tier institution students, coming to intro genetics from intro bio, lacking even a firm grasp of central dogma? Stoichiometry students not even thinking of atoms as real physical objects? So I see "wonderful books" and think "wat?!? - how about profoundly and pervasively dysfunctionally unhelpful books?".
Perhaps at root, there might be different visions of what a "big picture map" best looks like??? Maybe picture a human surface map, vs a USGS topography and geology one. Do details clarify by exposing patterns, or obscure as clutter? Does underlying structure? Do year-to-year research insights provide opportunity and motivation for frequent rewrites, or is there relative stability and slow evolution? Are labels and vocabulary treated as foundational, or as relatively unimportant? If you haven't seen part of the map, how important is being able to sketch it in plausibly? If fragmented into puzzle pieces, how important is being able to fit them together? How important is seeing why things are the way they are?
Maybe the contrast between a slim tourist guidebook, versus walking in conversation with someone who deeply understands the history and society and structure of a city? Both are accessible experiences. Conversation that's numerate will be richer than non. But while the guidebook can provide a bit of orientation, it's not even trying to leave you insightful and deeply clued in.
Thanks again. I'd not thought of the fuzzing analogy before.
There was a flurry of papers in the early 2000s that aimed to generalize biological robustness, borrowing from ideas and math from engineering. You might find these interesting:
https://www-users.york.ac.uk/~lsdc1/SysBiol/kitano.robustnes...
https://link.springer.com/article/10.1038/msb4100179
https://www.cs.unibo.it/~babaoglu/courses/cas02-03/papers/Ro...
> An Ideal Gas Law chapter problem, with numbers for solid Argon -
Ha!
> First-tier institution students, coming to intro genetics from intro bio, lacking even a firm grasp of central dogma?
Yeah, unfortunately this is a real problem: Foundational biology courses (intro, genetics, cell bio) overwhelm students with a firehose of facts that must be learned or you flunk out. Later, in upper-level undergrad and grad school, those facts start connecting, and biology becomes lots more interesting and actually easier to study.
> Are labels and vocabulary treated as foundational, or as relatively unimportant?
Vocabulary is a big deal in biology. Many terms carry associated meaning, for example polymerase chain reaction helps describe the mechanism, and TAQ polymerase reminds you that heat is important. Bone morphogenic protein says a lot.
That said, plenty of biology terms are pretty useless. Ribosome doesn't provide much intuition other than RNA is involved, and Golgi apparatus is even worse. Many gene names are arbitrary, reflecting a lack of knowledge at the time of discovery. Some are just dorky like sonic hedgehog.
Good undergrad biology books have big, carefully written glossaries in the back, these are absolutely invaluable.
> How important is seeing why things are the way they are?
It's important to internalize: 1) Biology is just physics and chemistry. 2) Millions of years of evolution and randomness produced all these arbitrary biological systems with their endless complexity. That's why living organisms are nothing like rational engineered systems, despite all the shared physics.
> If you haven't seen part of the map, how important is being able to sketch it in plausibly? If fragmented into puzzle pieces, how important is being able to fit them together?
For me, studying any big subject with lots of details, context really helps. It's easy for me to get lost in the details and lose motivation unless the ideas plug into some bigger picture. That's true even if I only want tourist-level knowledge.
Regards such cross-cutting insights, I'm tempted to see what an LLM, given a order-100 author tome, where the expertise is applied mostly silo-wise, might make of something vaguely like "Edit this to emphasize modularity (see doc). And weave that story across chapters. And...". But I suspect a good breath-wise pass would require similar order massed expertise.
Hmm... just now doing a quick and sloppy spot check, suggests current AIs might be coaxed to draft a "simplified tree of life" using the regulatory miRNA family ratchet (and Hox clusters, TF families) as a lineage regulatory/complexity budget. That's potentially much easier to do than it's been in years past. So maybe the blocker of "massive expertise resources required, but there's little incentive", might be destabilized by AI?
> Later, [...] connecting, and biology becomes lots more interesting and actually easier to study
So my question is, can this be done much much earlier? A kindergarten sci ed person suggested their kids have a human right to understand their world now, not a lifetime (for them) later. Seems an intriguingly audacious goal. Riffing on above, might one create a K-accessible/empowering fun little tree of life?
Our collective focus seems elsewhere. From MCAT to early primary, I've heard "Yes, <that> would be a nice way to explain <concept>, providing better understanding. But my students are soon taking <next high-stakes exam>, and that's not on the exam. Our time together is limited, so I'd be doing them a disservice if I <didn't teach to the test>."
Perhaps the texts are fine and something extra is needed. A formative AI tutor? Or perhaps texts and tests could use a massive refresh. Or perhaps something non-textual is needed. Tens of hours living in novel AR cell sims? Or some combo. But I find the status quo rather piteous.
Viewing science education as disaster triage chain of care, there's a distinction between stabilization and patient packaging, just surviving handoff vs not having to redo. If intro genetics is burning time on something which could have been taught in primary but wasn't, and was taught unsuccessfully in middle school, again in HS, and again in intro bio... maybe change is needed and available? Order-of-magnitude size is a part of most every physical sciences intro class, and there was a NSF "nanotech" push to primary, so how many times and years might a first-tier med student have been "taught" it, 10-ish?, before having little clue how big a red blood cell is?
One teaches with the students, outcomes, and material at hand. So material which pervasively leverages scaling doesn't exist; and outcomes don't require/permit it; and students have no sense of scale; so such material would be undeployable; and sci ed research doesn't deal with the undepoyable; so we've no idea what it might look like or gain; so there's little research funding; and thus little progress over time. I think of us as being wedged, or in a local optimum with search temperature dialed unhelpfully low.
Sorry for my latency. Thank you again for the comments.
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