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Mathematical Biology Is Our Secret Weapon In the Fight Against Disease (scientificamerican.com)

An anonymous reader shares excerpts from a Scientific American article: In recent years, increasingly detailed experimental procedures have lead to a huge influx in the biological data available to scientists. This data is being used to generate hypotheses about the complexity of previously abstruse biological systems. In order to test these hypotheses, they must be written down in the form of a model which can be interrogated to determine whether it correctly mimics the biological observations. Mathematics is the natural language in which to do this. In addition, the advent of, and subsequent increase in, computational ability over the last 60 years has enabled us to suggest and then interrogate complex mathematical models of biological systems. The realisation that biological systems can be treated mathematically, coupled with the computational ability to build and investigate detailed biological models, has led to the dramatic increase in the popularity of mathematical biology. Maths has become a vital weapon in the scientific armoury we have to tackle some of the most pressing questions in medical, biological and ecological science in the 21st century. By describing biological systems mathematically and then using the resulting models, we can gain insights that are impossible to access though experiments and verbal reasoning alone. Mathematical biology is incredibly important if we want to change biology from a descriptive into a predictive science -- giving us power, for example, to avert pandemics or to alter the effects of debilitating diseases.

57 comments

  1. Potential yet to be shown by XXongo · · Score: 2
    The article doesn't really show much in the way of mathematics used in biology. It's rather more cheerleading for mathematics in biology than really showing its power.

    Mathematics is really great, surely it must have some application in biology, but the article is more about potential that actuality.

    1. Re:Potential yet to be shown by Jamu · · Score: 1

      I'm wondering what they were using before...

      --
      Who ordered that?
    2. Re:Potential yet to be shown by interkin3tic · · Score: 2

      Even the stock photo.

      "Hey, we got an article about math and biology... Hmm... what about this image? Or This? No, what the fuck am I talking about? That's math! Biology isn't math! Biology is slimy and fuzzy, not math! Definitely go with a decades old picture of Ebola using EM which is nearly 100 years old. Yup, definitely, math is useful to biology in that engineers and physicists build toys like electron microscopes for biologists to get slime all over."

      For the record, I'm firmly in the category of biologists who do slimy squishy stuff and have computers and engineers do all the mathy stuff for me... but... still man, stereotypes aren't good even if I am that stereotype...

    3. Re:Potential yet to be shown by Anonymous Coward · · Score: 0

      You can use math to invent algorithms that try to figure out how protein folding works (folding@home).

    4. Re:Potential yet to be shown by Anonymous Coward · · Score: 0

      Statistics is essential to biology. In fact, like any other science, it's worthless without it.

    5. Re:Potential yet to be shown by Anonymous Coward · · Score: 0

      Mice

  2. They are just now figuring this out? by Brett+Buck · · Score: 4, Insightful

    Are they suggesting that the characteristics of physical systems can be represented by mathematical equations? And that these mathematical models may be used to predict the characteristics of physical systems that may not even exist yet?

          My God, who would have ever thought this possible or valuable? They are leading biological science boldly into the 17th century!

            If only there was some device and a standardized language with which to create these mathematical models without having to completely defined the models in closed form. Perhaps to "simulate" (to coin a phrase) these systems in an abstract way.

    1. Re:They are just now figuring this out? by Anonymous Coward · · Score: 1

      No, they've known it for ages. Hardy-Weinberg dates to 1908, Lotka-Volterra to 1910. Ideas of exponential and geometric growth have been around much longer.

      Mathematical models for HIV infection were created within years of the discovery of AIDS.

      This article is not news.

    2. Re:They are just now figuring this out? by grasshoppa · · Score: 3, Interesting

      This is why I take "expert" dietary recommendations with a huge grain of salt ( which isn't, as it turns out, the devil it once was. Joining coffee and eggs on the pile of things which "may or may not be good or horrible for you" ).

      It's staggering not only how much we don't know about how our bodies really work, but also how confident "we" are in what we only think we know. I'm also amazed at slow new information is propagated out. For instance; we knew in the 80s, the 80s that fat wasn't the dietary enemy that had been made out in previous studies ( well, "studies" given their methodology included throwing out data that didn't agree with their conclusions ), yet it would take another 30+ years before that started becoming general knowledge. In the meanwhile, increased sugar based diets ravaged the population.

      We're still just stumbling around blind on this.

      --
      Mod me down with all of your hatred and your journey towards the dark side will be complete!
    3. Re:They are just now figuring this out? by Anonymous Coward · · Score: 0

      I've got a bold new theory about how we can use mathematics to study and model the movement of money through our economy.

      I'm pretty sure this is groundbreaking stuff.

    4. Re:They are just now figuring this out? by Anonymous Coward · · Score: 1

      You sound like someone who has no real insight into the problem. I work at the intersection of mechanistic and quantitative sciences.

      The issue is not everything is quantitative, and mathematics is only really good for things you can quantify. There is a reason why math is the handmaiden of physics, less so chemistry, and even less so biology.

      Biology has a tremendous amount of representations that are "mechanistic" and are useful in that form. Forcing that kind of representation into a mathematical mold makes the the knowledge unwieldy and in many cases, useless. Category theory does not even begin to capture that kind of representation.

      We are starting to see a lot of biologists getting into bioinformatics, but there are still large swaths of biology that are not amenable to mathematical analysis.

    5. Re:They are just now figuring this out? by WrongMonkey · · Score: 2

      You're being flip, but the problem is that even the most simplest biological systems cannot be simulated. Its not that we don't know the math, but the math in intractable. Just calculating a simple physical property, like solubility of a particular protein, will bring the fastest supercomputers to their knees.

    6. Re:They are just now figuring this out? by Anonymous Coward · · Score: 0

      Mathematics imposes constraints on economic agents that the biggest players in markets relax. Math requires preference relations to be transitive, for example; yet financial firms choose A over B and B over A at the same time, and profit by loaning out parts of the perfectly-hedged portfolio short-term. Math's fundamental axioms are too restrictive to model nature.

    7. Re:They are just now figuring this out? by Anonymous Coward · · Score: 0

      Nature is inconsistent, and math has chosen consistency over completeness. Math can thus be only a poor model of nature.

    8. Re:They are just now figuring this out? by Anonymous Coward · · Score: 0

      Surely the lack of computational power is more of an issue than the problem of describing processes using mathematics. I don't see how category theory would come into play here, but a useful model that is tractable without a quantum computer is still abstracting away lots of low level details and requires experimental verification like any hypothesis. Some researchers are trying to apply engineering methods to big biological systems like a cell by describing them using abstract models that are tractable but still useful. Biology, just like physics and chemistry benefit from the coarse-graining.

    9. Re:They are just now figuring this out? by Anonymous Coward · · Score: 0

      Math requires preference relations to be transitive

      Many mathematical relations are not transitive.

      Math's fundamental axioms are too restrictive to model nature.

      I don't know if you're ignorant or trying to fool someone.

    10. Re:They are just now figuring this out? by Anonymous Coward · · Score: 0

      Nature is inconsistent, and math has chosen consistency over completeness.

      Since the context is math, this is incoherent.
      Yes, an inconsistent system is complete, but only because you can prove every statement is true. In other words, it's useless.
      "Nature is inconsistent" kind of sounds profound, but I suspect you're just equivocating and hand-waving.
      Would you care to elaborate?

    11. Re:They are just now figuring this out? by Anonymous Coward · · Score: 0

      The mathematical functions that model agents in markets require transitivity of preference relations. Without such mathematical constraints, neoclassical economics cannot prove that markets create Pareto-optimal equilibriums.

      Please see Arnsperger and Varoufakis, What is Neoclassical Economics?:

      We label the second feature of neoclassical economics methodological instrumentalism: all behaviour is preference-driven or, more precisely, it is to be understood as a means for maximising preference-satisfaction.

      And:

      People could, and should, be modelled as if they possessed consistent preferences which guide their behaviour automatically.

      Preferences are not consistent and often intransitive. Indeed, advertising actively seeks to make consumers' preferences intransitive and inconsistent, to prefer the worse product over the better. But the math required to prove markets find value most efficiently, and the predictions based on mathematical models that have constraints that all math is subject to (i.e., if 3 > 2 > 1, 1 cannot be greater than 2 or 3), prevent math from providing an adequate model for economic behavior.

      That is why math economic models fail to predict accurately.

    12. Re:They are just now figuring this out? by Anonymous Coward · · Score: 0

      A photon is a wave and a particle.

      The sun's corona is hotter than its surface.

      Jupiter's magnetic field is inconsistent with any other.

      "This statement is a lie" can't be modeled by math, math has to ban the sentence. But the sentence is a valid natural language formulation. Thus, math cannot adequately model natural language.

    13. Re:They are just now figuring this out? by Anonymous Coward · · Score: 0

      No, the problem is not just one of computation but one of representation. Not everything can be represented mathematically while still remaining useful.
      That is not to say that mathematical modeling is not useful -- merely that it is limited in its applicability to large classes of problems of practical significance.

    14. Re:They are just now figuring this out? by Anonymous Coward · · Score: 0

      A photon is a wave and a particle - in a consistent way - they always behave like this.

      The sun's corona is consistently hotter than it's surface.

      Jupiter's magnetic field is inconsistent with other planets because the other planets are not exactly like Jupiter.

      On the other hand, water boils at different temperatures depending on pressure. If differences in pressure are accounted for, water boils at a very consistent temperature.

      One cannot consistently let alone ever predict a radio active decay event. However, all radioactive isotopes have consistent half lives.

      Natural language is not natural in the same sense as natural laws when it comes to physics, chemistry and biology.

    15. Re:They are just now figuring this out? by Anonymous Coward · · Score: 0

      Do you have a single example of something useful that cannot be represented mathematically?

    16. Re:They are just now figuring this out? by Anonymous Coward · · Score: 0

      A photon is a wave and a particle.

      No, it is not. If it's one, then it is guaranteed not to be the other. This is described elegantly with maths (non-commuting linear operators.) Not so much with natural language.

    17. Re:They are just now figuring this out? by Anonymous Coward · · Score: 0

      Alright, it is the show-me-an-example time. My education is insufficient to imagine a natural system that exists in a sphere of the Earth that couldn't be represented explicitly or implicitly. It's all linear algebra, right? ;)

    18. Re:They are just now figuring this out? by Anonymous Coward · · Score: 0

      Do you have a single example? Just one would prove your point.

    19. Re:They are just now figuring this out? by Anonymous Coward · · Score: 0

      Sorry, I was the one asking the question from the AC who knew category theory (kung-fu). I should have formed my post more as a question. ;)

  3. It's All Math by Anonymous Coward · · Score: 1

    Obligatory xkcd.

    1. Re:It's All Math by Anonymous Coward · · Score: 0

      I was right!

      (guessed which xkcd you were linking to)

  4. Pandemics saved mankind before... by Anonymous Coward · · Score: 0

    Devil's advocate here:

    Pandemics have saved the world before. Before the Black Plague, the life of most people in the Western world was of groaning slavery as a serf with infant mortality off the charts and an average lifespan less than our current drinking age here in the US. The Black Plague, once the ruling class had too few backs to flog, eventually made life bearable, if not prosperous for the average person. Instead of subsistence farming, luxury items like olives could be grown. Trade increased, and the Renaissance happened. Had the plague not happened, Europe would still be under tiny little dukedoms and duchies still fighting it out today.

    Look at modern times. We are heading back to that scenario. Revolutions are pretty much pointless where one helicopter can turf thousands of protesters or empty a town of life with a Sarin gas canister. It is only a matter of time before we go back to groaning serfdom worldwide again. It might just be another pandemic might save the world as we know it, allowing technology and advances to prosper again.

    1. Re:Pandemics saved mankind before... by Anonymous Coward · · Score: 0

      Trade increased, and the Renaissance happened

      Are you sure?

      Land was plentiful, wages high, and serfdom had all but disappeared. A century later, as population growth resumed, the peasants again faced deprivation and famine.

  5. Oh great.... by sconeu · · Score: 2

    You just revealed our secret weapon to the germs!!!! Now they will find a defense against our mathematics!!!

    --
    General Relativity: Space-time tells matter where to go; Matter tells space-time what shape to be.
  6. The answer by rtkluttz · · Score: 1

    Douglas Adams is chuckling to himself. The answer to life the universe and everything really is 42.

    --
    Digital is, by definition, imperfect. Analog is the way to go.
  7. Mathematical Marketing by geekmux · · Score: 1

    TFS was a fantastic sales pitch.

    Now show me how mathematical biology can showcase its benefit.

    I might note that over the last 60 years, we've seen everything from AIDS to Zika attack mankind, so pardon me if I'm skeptical as hell as to it's ability to predict or avert pandemics. Sadly, even Ebola enjoyed a fashionable resurgence after a 20-year hiatus.

    It's also rather obvious that great financial benefit stems from perpetually treating issues rather than curing them, proving that the ultimate virus that has yet to be eradicated is Greed.

    1. Re:Mathematical Marketing by cstacy · · Score: 1

      I'm skeptical as hell as to it's ability to predict or avert pandemics.

      http://www.healthmap.org/about

  8. A bigger challenge than you may think by Goldsmith · · Score: 4, Insightful

    I'm a physicist working on tools that quantitatively measure biologic interactions. A common use for my tools is for a pharma company to take a set of molecules that they have determined through modeling will interact (inhibit activity, enhance activity, etc.) with a target protein and we measure whether that actually happens directly at the molecular level.

    So why hasn't this been done before?

    Biology is not just complex, it's also very often overgeneralized and poorly understood. It's dogma (literally) in biology that a cell using a particular sequence of DNA to build a protein will always build the same protein. This is not true. Two "identical" proteins are almost certainly chemically different. Biology to date has dealt with collections and statistical averages of protein function and genetic activity. The measurements used to work in biology, to date, use simplified environments (gels, buffers, simplified model organisms) and reporting methods that interfere with the molecular function of the biological system (fluorescence, dye binding), but these methods and approaches have been necessary to make progress.

    At this point, most biologists either have forgotten, or never appreciated, that these systems are measuring secondary effects and generalizations of true biological function. Convincing them that a quantitative, direct, math-and-physics based approach to biology can produce helpful information is an enormous cultural challenge. When presented with data showing that a correlative measurement (i.e. fluorescence) disagrees with a direct physics based measurement (i.e. an electronic biosensor), biologists will tend to believe the secondary measurement over the direct measurement.

    As direct measurement tools and simulations become more widely used, there will need to be a change in the way biologists think about their measurements, and that's not going to be a comfortable thing for them. There is an opportunity for folks in computational and physical science to lead the way and show them that our approaches to problem solving are valid and helpful.

    1. Re:A bigger challenge than you may think by Anonymous Coward · · Score: 0

      Thanks for your insight into this question.

    2. Re:A bigger challenge than you may think by Anonymous Coward · · Score: 2, Interesting

      I'm an engineer that works with biologists doing academic biological research. I'm going to have to disagree on some points, or at least ask for clarification.

      The example you gave of "dogma" is definitely not held as sacrosanct among biologists. There are a wide number of well understood mechanisms that lead to varying protein structure based on a single DNA sequence. While its often a working assumption the DNA translates to protein through a direct and repeatable route, which is many ways is a good assumption, I would say the vast majority, if not all, of PhD level biologists I interact with understand that that is not an absolute.

      And again, I'm actually fairly shocked by the statement "At this point, most biologists either have forgotten, or never appreciated, that these systems are measuring secondary effects and generalizations of true biological function" as that is so contradictory to my experience. Biologists will hammer each other on that very point. At conferences, in grant reviews, in paper reviews, and informally. Someone who makes claims off of a single measurement type will be pushed to make other measurements, at genetic, protein, and functional levels.

      As to the statement that "Convincing them that a quantitative, direct, math-and-physics based approach to biology can produce helpful information is an enormous cultural challenge." Again, I disagree. I have no trouble finding collaborators. Everyone wants an engineer (or biophysicist, or mathematician) on their team. Some of the most respected speakers at the last American Society of Cell Biologists meeting I attended were from hard sciences.

      And I wouldn't accuse of this, but I will say, there is a huge class of problems in biology that is not, at the moment, amenable to more direct measurements or rigorous physical modeling. And I have seen, many times, a math heavyweight or physics heavyweight weigh in on a problem without understanding the known complexities let alone the "unknown unknowns". And there is regularly pushback from biologists, because that is, quite bluntly, unhelpful.

      But give the average biologist a rigorous, validated tool that they can use in their lab (cost, accessibility, etc) to make DIRECT measurements of something? It will get snapped up immediately. I have zero problem convincing collaborators of the usefulness of AFM, or superresolution microscopy, or nanorheology, etc as long as it provides a truly direct measurement of what they are interested in.

      I'm certainly not going to make a claim that what you described doesn't exist at all, but I've been in academic research for almost 2 decades now, spanning multiple fields, multiple institutions across the US, have overseas collaborators, etc, and that is just not something I've ever seen. For example, I'm currently helping a collaborator with intracellular pH measurements, and we are using several correlative methods. And we are using several because if we only used one, we would get push back from paper reviewers. They would be THRILLED to have a direct measurement device, provided it was reasonable in cost and actually worked.

      Biology is becoming more and more quantitative every year. In my experience, that is embraced and sought out by researchers...it just makes their jobs easier.

    3. Re:A bigger challenge than you may think by Anonymous Coward · · Score: 0

      To add my two cents:
      Some Biological Processes, take Photosynthesis as an example, have "mechanisms" that work at the Femtosecond scale. We are now just at the point of making the tools, that can make the tools, that can examine them. (Light Sources.)
      Modeling a Nuke is vastly simpler, where the interesting things happen at the Microsecond to Millisecond scale, and you are dealing with very few fundamental players, mostly Neutrons. But even that requires a farm of Supercomputers. Classified Supercomputers.
      Even something as simple as Water, which most Biology involves, gets downright weird at the Femtosecond level, where it's not H2O, but bunches of Hs and Os hooking up in very short lived volatile relationships. Horny little bastards.
      Frankly, trying to Model Proteins is just too damn ambitious. We don't even understand the basics of Methane production, or CO2 disassociation. Just how does a CO2 Molecule get taken apart?
      I remember the old Berkeley Computational Chemistry Division. After spending a few million dollars, they finally just gave up for a couple of decades. Too difficult. Computational Chemistry is now back, but just barely.
      With the Math involved, it's like the other tools. We have to make the Math that makes the Math, and we are a long way from that.

    4. Re:A bigger challenge than you may think by Goldsmith · · Score: 1

      I wish this person had logged in to respond to my comment.

      There is a difference between academic collaboration, that carries with it added resources and funding, and making a decision to change the tooling in your lab. When AFMs are standard in biology labs, then it's an acceptable biology tool. Right now, they're an acceptable tool for an engineer or physicist to use when helping a biologist. That's very good, but we're not all the way there.

      Another way to look at this is that there are no collaborators for ELISA or western blot on the team. Those are standard tools. When the same is true of these new techniques, the culture will have been switched.

      Also... The Central Dogma of Molecular Biology

    5. Re:A bigger challenge than you may think by Anonymous Coward · · Score: 0

      Original AC...I don't have an account, I don't comment enough to make it worthwhile.

      Perhaps I don't quite understand your point about AFMs being standard in biology labs. AFMs are damn expensive, and (except for some of the newer ones) require significant expertise to even operate. It is, at the current stage of technology and/or funding, infeasible to have AFMs in even a significant percentage of biology labs. This, and dozens of examples like it, are why collaboration is *essential* in modern biology. No investigator can be an expert in everything, nor can a single lab cultivate the broad range of expertise and expensive equipment necessary to answer questions.

      Note, I'm not limiting collaboration to just "hard science" collaborating with "life science". With the proliferation of new tools and techniques, most created out of a drive for increased quantification and directness, you often see biologists form collaborations with each other just because of the sheer scope of the expertise needed to answer research questions. To take your example, western blotting, I agree is mostly very common, but that's due to the relatively ease of learning as well as low cost of the assay more then the acceptance in the field. Another example, chromatin immunoprecipitation (ChIP), very similar (in concept) but much more difficult and expensive technique, is something that people often collaborate to bring that expertise into the project. For a few projects I collaborated with a biologist that was an expert on MALDI-TOF proteomics...a well accepted technique that you will not see in every lab simply due to the expense and expertise associated with it. Hell, I recently collaborated with a group where I did FISH and they did single-cell transcriptomics. Again, both well-accepted techniques in biology that would be staggeringly infeasible to have every lab build their own expertise in. Another example, I've been brought in as a collaborator because I work with lenti...a relatively common and well accepted technique that it just doesn't make sense for every lab that needs it to culture and maintain that expertise.

      And finally, the "Central Dogma" refers more to the direction of information, ie DNA->protein (and not the other way around), and less about the purity of the information transfer. To quote Crick in the original statement of the dogma:

      "The Central Dogma. This states that once ‘information’ has passed into protein it cannot get out again. In more detail, the transfer of information from nucleic acid to nucleic acid, or from nucleic acid to protein may be possible, but transfer from protein to protein, or from protein to nucleic acid is impossible. Information means here the precise determination of sequence, either of bases in the nucleic acid or of amino acid residues in the protein."

      Second, it is very much not a dogma, to quote Crick again:

      "As it turned out, the use of the word dogma caused almost more trouble than it was worth. Many years later Jacques Monod pointed out to me that I did not appear to understand the correct use of the word dogma, which is a belief that cannot be doubted. I did apprehend this in a vague sort of way but since I thought that all religious beliefs were without foundation, I used the word the way I myself thought about it, not as most of the world does, and simply applied it to a grand hypothesis that, however plausible, had little direct experimental support."

      Even if that wasn't Crick's view, I assure you, you won't get push back form biologists on the concept that there are copy errors, chemical modifications, etc, at the DNA/RNA/Protein levels...this is well understood and basic stuff.

  9. Natural language is a better model than math by Anonymous Coward · · Score: 0

    they must be written down in the form of a model which can be interrogated to determine whether it correctly mimics the biological observations. Mathematics is the natural language in which to do this

    I think natural language is better than math for modeling nature. Math relies on axioms of consistency and transitivity that nature is not constrained by. Math is unnatural to interrogate, whereas natural language is, well, natural to us and therefore it is easier to interrogate a model using natural language.

    Natural language is the natural language to model nature. Math is too constrained by philosophical assumptions about consistency.

    1. Re:Natural language is a better model than math by Anonymous Coward · · Score: 0

      Truth and logic. Apparently this isn't enough for the idiot above.

    2. Re:Natural language is a better model than math by Anonymous Coward · · Score: 0

      Math relies on axioms of consistency and transitivity that nature is not constrained by.

      Thus proving that your statement is naturally bollocks.

  10. "abstruse" by Anonymous Coward · · Score: 0

    That word is rather ... abstruse.

  11. Another obligitory XKCD by RatherBeAnonymous · · Score: 1

    https://www.xkcd.com/793/

    P.S. I was a physics major, once upon a time.
    P.P.S I am guilty of having done what is portrayed in that comic.
    P.P.P.S I had a physic prof comment on me looking down on chemistry, "as you should." I *think* the comment was tongue-in-cheek.

    1. Re:Another obligitory XKCD by TeknoHog · · Score: 1

      And the obligatory followup: https://xkcd.com/1831/

      --
      Escher was the first MC and Giger invented the HR department.
    2. Re:Another obligitory XKCD by Goldsmith · · Score: 1

      That's a good one!

      It's our responsibility as physicists to maintain our reputations. That's generally done by covering our ears, closing our eyes and saying "LA LA LA LA" really loud whenever anyone starts talking about complex and interesting problems in the other sciences. (It's either that, or claim to have "already solved that problem 50 years ago.") I forgot to do that once, and now I work with biologists every day.

  12. Except that by paiute · · Score: 1

    Human biochemistry reveals wrinkles we did not know about all the time. A company might spend a billion dollars developing a drug only to find in clinical trials that some previously unknown enzyme or receptor or feedback mechanism makes the drug unmarketable. Mathematical models can't work well if there are these unknown sitting there waiting. They can't be predicted. They have to be found the hard way by wet biochemistry investigation. It would be like trying to use math when new integers keep showing up between the old ones.

    --
    If Slashdot were chemistry it would look like this:Cadaverine
    1. Re:Except that by iMadeGhostzilla · · Score: 1

      Reminds me of this quote, “Logic excludes – by definition – nuances, and Truth resides exclusively in the nuances.” - Ernest Renan

    2. Re:Except that by Anonymous Coward · · Score: 0

      Logic excludes illogic. Also, Ernest Renan was full of shit.

  13. Descriptive science? by Anonymous Coward · · Score: 0

    Science is predictive. Period. Get on our level biology.

  14. Re: Tlfheqy are just now figuring this out? by Anonymous Coward · · Score: 0

    While lkoklp