11 Schr¨odinger’s “What is Life?” at 75
Rob Phillips ∗ Division of Biology and Biological Engineering and Department of Physics, CaliforniaInstitute of Technology, Pasadena, California, U.S.A ∗ E-mail: [email protected] “These facts are easily the most interesting that science has revealed in our day.” -Erwin Schr¨odingerin “What is Life?”, discussing how the “dislocation of just a few atoms” in a gene can bring about a“well-defined change in the large-scale hereditary characteristics of the organism.”
Abstract st century science.
1. Background: The Author, His Book and its Readers
Erwin Schr¨odinger is one of the luminaries of twentieth-century physics. His insights into the workingsof the microscopic world were codified in the famed wave equation that bears his name and gave rise(among many other things) to the s, p and d orbitals we all learn about in our first real encounter withthis world in high-school chemistry. Schr¨odinger was born and raised in Austria, the only child of a highlyintellectual family with a father deeply interested in botany, leaving Schr¨odinger himself with a sincereand enduring interest in the living world. In his Autobiographical Sketches he recounts that because ofdiscussions with his father, “I had virtually devoured The Origin of Species” ...Of course I soon becamean ardent follower of Darwinism (and still am today) [1].”In the late 1930s after the
Anschluss , Schr¨odinger had to flee the Nazis and turn his back on hisprofessorship in Graz, Austria. Fortunately, Irish prime minister ´Eamon de Valera was in the processof establishing the Institute for Advanced Studies in Dublin, and it was there that the great physicistrelocated. Later, speaking of his 17 years in Dublin, Schr¨odinger called them “the happiest years ofmy life,” and it was in the context of his life there that he offered the public lectures that ultimatelybecame the book we celebrate here (see Figure 1 for the cover page of the 1944 edition). To get a deepersense of the impressive intellect that Schr¨odinger brought to bear on topics far and wide such as hisgift for languages (including English, Spanish and ancient Greek), the breadth of his accomplishments inphysics and his personal lifestyle, there are several excellent sources [2, 3, 4]. Noted physicist Max Born’sautobiography gives us an impression of the regard Schr¨odinger commanded among his intellectual peers:“His private life seemed strange to bourgeois people like ourselves. But all this does not matter. He wasa most lovable person, independent, amusing, temperamental, kind and generous, and he had a mostperfect and efficient brain.” a r X i v : . [ q - b i o . O T ] F e b Figure 1.
The 1944 edition of Erwin Schr¨odinger’s “What is Life?,” published by Cambridge University Press. The bookresulted from a series of public lectures offered by Schr¨odinger in Dublin in 1943.
Schr¨odinger’s “What is Life?” constitutes a long argument in which he sets himself the task of nothingless than the search for “unified, all-embracing knowledge” to describe the natural phenomenon we referto as life. In the section entitled “The General Character and Purpose of the Investigation,” he articulateshis quest for universal knowledge more precisely by asking the oft-quoted question “How can the eventsin space and time which take place within the spatial boundary of a living organism be accounted forby physics and chemistry?” And it is to answering that question that the entirety of the long argumentthat follows is devoted. He asserts that the intellectual ledger sheet was not yet balanced, with the dataoutpacing corresponding conceptual understanding that “accounts” for them, words that remain true tothis day. Indeed, to really put forth a critical reading of Schr¨odinger’s text, we need to understand whathe means by the word “account,” a point that was overlooked by many of his most ardent critics andwhich serves as the first key point of this essay.
Most contemporary discussions of Schr¨odinger’s book focus not on its content but on its influence ona generation of biologists. As a result, it seems important to touch briefly on that story before turning tothe main argument that Schr¨odinger’s call for a physics of the living world remains valid today. Nearlya decade before the publication of the structure of DNA by Watson and Crick, Schr¨odinger was alreadythinking about what came to be known as the coding problem. As Horace Freeland Judson tells us inhis classic history of modern biology, “The Eighth Day of Creation” [5]: “The earliest mention of codingthat counts was Erwin Schr¨odinger’s, in 1944 in ‘What is Life?’ ...The fascination of the book lay in theclarity with which Schr¨odinger approached the gene not as an algebraic unit but as a physical substancethat had to be almost perfectly stable and yet express immense variety.” The influence of Schr¨odinger’sbook on some of the founders of modern biology is evidenced by Figure 2, which shows a letter from theyoung Francis Crick to the elderly master.With the historical preliminaries behind us, we turn instead to a different question: to what extent isSchr¨odinger’s classic relevant to the practice of biology and physics here and now? I argue that the vastmajority of what Schr¨odinger had to say remains unfinished business. This makes it an opportune timeat this three-quarters of a century milestone to ask what would it look like for the entirety of modernscience, with no allegiance to any particular sub-discipline within science, to revisit the question of the“physical aspect of the living cell?” The remainder of the essay centers on two key points: (i) Schr¨odingerargues that the part of the natural world we refer to as life needs to be “accounted for” in physical termsand (ii) the quest to do such accounting will lead to new physics, not only helping us make sense of life,but also enriching physics itself.
2. The Meaning of “Accounting for the Living Organism”
Schr¨odinger’s charge was to find out how the actions within the walls of a living organism can “beaccounted for by physics and chemistry.” When he uses the words “account for” what I think he hadin mind was the idea that our understanding of some phenomenon of interest can be seen as resultingfrom an appeal to some underlying principle, that that appeal is formulated in mathematical language insuch a way that observed phenomena are seen as quantitative consequences of these underlying principlesand that the resulting insights make it possible to make statements about phenomena not yet seen ormeasurements not yet made.
A fitting analogy for what Schr¨odinger meant when talking of “accounting for” some class of phe-nomenon “by physics and chemistry” is provided by his own work, for which he is so deservedly famous.In the mid- and late 19th century, there was an explosion in our factual knowledge about the light given off
Figure 2.
Letter from Crick and Watson to Schr¨odinger openly acknowledging the importance of “What is Life?” totheir careers. by and absorbed by different chemical elements in the form of their atomic spectra as shown in Figure 3.Just as with our current proliferation of gene and protein names and the burdensome nomenclature forthe pathways that connect them, the era of factual discovery in atomic spectra saw a proliferation of fas-cinating and complicated spectral nomenclature with concepts such as the D-line of Na and the differentseries such as the Balmer, Lyman, Brackett and Paschen series that are observed in the H spectrum (fora sense of the enormity of the factual diversity of these lines see [6]). But what set the wavelength ofabsorbed or emitted light for a given element, or the number of spectral lines in a series?Understanding in physics demands that factual knowledge based on experiments be complemented by conceptual knowledge. Precisely the same kind of unified, all-embracing knowledge that Schr¨odinger wasspeaking of in “What is Life?” was earlier needed for thinking about the huge diversity of special casesfound in atomic spectra (for an enlightening description of the history of the study of atomic spectra,see Mehra and Rechenberg [7]). Nearly a century of struggle followed the discovery and experimentalcharacterization of spectral lines as evidenced by the words of Max Planck in 1902: “If the questionconcerning the nature of white light may thus be regarded as being solved, the answer to a closely relatedbut no less important question - the question concerning the nature of light of the spectral lines - seemsto belong among the most difficult and complicated problems which have ever been posed in opticsor electrodynamics.” [8] One outcome of these struggles (see Figure 3) was the discovery of empiricalformulae that gave a phenomenological mathematical description of the measured wavelengths of variousspectral lines seen in Figure 3(A) of the form1 λ = R (cid:18) p − n (cid:19) , (1)where λ is the wavelength of the spectral line in question, R is a phenomenological parameter known asthe Rydberg constant, later “accounted for” by physical understanding, and p and n are integers. SCHRÖDINGER’S ACCOUNTTHE SPECTRUM OF HYDROGEN(A)(B) (C)EMPIRICISM’S FIRST INSIGHT w a v e l e n g t h ( n m ) . red . blue . violet . . . = R –1 λ Figure 3.
Accounting for the spectrum of hydrogen. (A) The spectrum of hydrogen with the wavelengths of variousspectral lines reported in nm. (B) The Balmer formula for the wavelengths of the spectral lines featuring the Rydbergconstant, R . (C) Page from the English translation of Schr¨odinger’s paper on wave mechanics in which he shows that theequation that now bears his name amazingly gives rise to precisely the energy levels found earlier by Niels Bohr thatexplain the spectrum of hydrogen. To account for such phenomenological understanding requires us to construct theories that explainwhy spectral lines are described by such a formula and what determines the phenomenological constant R . Niels Bohr’s theory of the hydrogen atom gave a first tentative conceptual success where he positedthat the electron orbits are restricted to certain quantized values with energies E n = − Z me h ε n , (2)with m the mass of the electron, e the elementary charge of the electron, h the symbol for Planck’sconstant and ε the permittivity of free space. Here the steps towards accounting take the form of thestunning realization that the empirical Rydberg constant can in fact be written as R = me h cε ≈ . × m − . (3)Erwin Schr¨odinger’s great atomic triumph, shown in Figure 3, was the insight that he could interpret thediscrete energy levels of atomic systems in much the same way that we interpret the musical notes froma guitar string or an organ pipe using wave equations.Our digression into the niceties of how theoretical understanding “accounted” for the many complex-ities of spectral lines and so much more about the complicated microscopic world is meant to serve as aninvitation to the kind of physical frameworks that Schr¨odinger might have had in mind when discussingliving matter and using the words to “account for” a given phenomenon. Though Schr¨odinger clearly left the door open for quantum insights into the phenomenon of life,much of his thinking centers on what is now known as statistical physics. In the 19 th century, statisticalphysics arose in response to other phenomena demanding his type of accounting. By then, mechanicshad dominated as an explanatory framework for more than a century, from Newton’s 1687 presentationof his “System of the World,” until the middle of the 19th century when questions about the natureof heat began to take center stage [9, 10]. We can use Schr¨odinger’s language in that context as: howcan our experience of temperature and heat be accounted for by the mechanical motions of materialparticles? The quest to answer that question took the better part of a century, culminating in the twinedifices of statistical physics and thermodynamics, but also leaving in its wake unresolved problems suchas the specific heats of crystalline solids that would have to await the quantum theory for their properresolution [11].Statistical physics was clearly much on Schr¨odinger’s mind in his Dublin years as evidenced not onlyby “What is Life?,” which is full of deep insights into the subject that can be read with great profitwith no reference to biology whatsoever, but also by his 1946 book, “Statistical Thermodynamics,” still amasterful treatise that one can learn from to this day. Schr¨odinger was schooled in the Austrian traditionof Ludwig Boltzmann’s statistical physics, having only missed having one of the great founders (alongwith Maxwell and Gibbs) of statistical mechanics as a professor by a year or two due to Boltzmann’s tragicsuicide. But this did not stop Schr¨odinger from being steeped in the tradition of statistical physics thatultimately became central not only to our scientific understanding of classical physics, but also to the waywe view the quantum world he helped uncover. For Schr¨odinger as announced in his AutobiographicalSketches, “no perception in physics has ever seemed more important to me than that of Boltzmann -despite Planck and Einstein,” a resounding testament to the statistical physics sensibilities he broughtto the table in his thinking about the nature of life, and the shortcomings of which led to his belief inthe ultimate need for “new physics” to account for living matter [1].As an introduction to the shortcomings of the physics of Schr¨odinger’s time to account for the livingorganism, Chapter 1 of “What is Life?” introduces “The Classical Physicist’s Approach to the Subject.”Schr¨odinger reminds us that statistical mechanics is the central conceptual framework used until thattime to interpret the collective properties of matter. To that end, he begins by providing a beautiful andcompelling introduction to the key ideas of statistical physics. Why? Because, as he points out, “it is inrelation to the statistical point of view that the structure of the vital parts of living organisms differs soentirely from that of any piece of matter that we physicists and chemists have ever handled physically inour laboratories or mentally at our writing desks.” This idea of what Schr¨odinger dubs a “difference instatistical structure” between conventional and living matter is a theme that permeates the entirety ofhis short book. The first chapter thus lays the general groundwork for what follows by giving a highlysimplified but profound view of statistical physics. There, he raises many of the themes that dominatemodern biology including the roles played by stochastic effects, small numbers, adaptation, accuracy andnoise in the reproducible processes of cells and organisms.In Chapters 2-5, he brings the general arguments of Chapter 1 to bear on his first big specific question:how is genetic information so stably passed from one generation to the next, despite how few atoms areimplicated in the gene (as we will discuss in the next section)? Indeed, Schr¨odinger argues that thestability of the genetic material is inconsistent with the then-known laws of statistical physics. Though itis mind-boggling to consider, one could say that in some sense biological information is more stable thanis the Earth itself. In the 50 million or so years since the Indian subcontinent collided with Asia, 8000 mmountains have been thrust up from the Earth, while at the same time, the Hox genes that confer bodyplans in animals from flies to humans have passed from one generation to the next such that the familyresemblances are completely evident when we compare sequences from different organisms. By focusingon the nature of the hereditary molecule now known to be DNA, Schr¨odinger foreshadowed the agendafor the DNA-centric perspective that colors much of modern biological investigation.After concluding that the stability of genetic information leaves puzzles for the physics of his (andour) day, Schr¨odinger then turns to another set of biological phenomena that defy the physics of his time.Here he focuses on what in modern guise we might call the physico-chemical basis of the self-organizationof living matter. One of the most disturbing of human tendencies is how we all become accustomed tothe wonders around us, whether in our science or in our lives. One example that I find remarkable is seenon transatlantic flights where, as we pass over the glaciers of Greenland, nearly all passengers have theirshades closed without even a thought of what lies below. I might recast Schr¨odinger’s question aboutthe physico-chemical basis of the organization of living cells thus: how do the elements of the periodictable, when sculpted by the consumption of energy at the nanometer scale through ATP hydrolysis, cometogether and form remarkable structures such as the insect eye or the dynamic and constantly-renewingouter segment of animal photoreceptors? These amazing rhodopsin-filled structures are a reminder to dothe scientific equivalent of opening the shades over Greenland and marvel at living cells as collections ofatoms from the periodic table that produce “endless forms most beautiful and most wonderful.”Let’s look a little more closely at the way that Schr¨odinger examined the capacity of statistical physicsto account (or not) for living matter. As a first example of the statistical structure of classical physics, hetackles the question of paramagnetism (how the tiny individual magnets of single atoms conspire to giverise to the macroscopic phenomenon of magnetism and how it depends upon temperature). The magneticphenomenon results from a competition between the energy advantage that comes from aligning spinswith an applied magnetic field and the entropy that comes from those spins adopting random orientations.The key point is the recognition that the thermal energy scale, k B T ≈ . ATP ORDER FROM ORDERORDER FROM DISORDERSchrödinger’s concentration gradient Order at the population scaleOrder at the cellular scale Order at theorganismal scaleOrder at the molecular scale The Bicoid morphogen gradient in
Drosophila max XL Figure 4.
Schr¨odinger’s order from disorder and order from order. In the top panel, Schr¨odinger illustrated the way thatstrictly random motions of atoms or molecules could give rise to reproducible patterns of concentration (left). Moderndevelopmental biology has borne that out in the form of morphogen gradients such as the gradient of the transcriptionfactor Bicoid in the fly embryo shown here schematically beneath the graph. The length ( L ) of the embryo is plotted indimensionless units x/L . The profile of Bicoid can be thought of as emerging from the “disordered” processes of diffusionand protein degradation. In the bottom panel, the expenditure of energy at very small scales in the form of ATPhydrolysis leads to order at the cellular scale, the organismal scale and even the population scale. Speaking of the jostling of these Brownian particles, Schr¨odinger poetically muses: “Their movementsare determined by the thermic whims of the surrounding medium; they have no choice. If they hadsome locomotion of their own, they might nevertheless succeed in getting from one place to another -but with some difficulty, since the heat motion tosses them like a small boat in a rough sea.” Again, thestatistical structure of classical physics reveals that ordered states with the mathematical precision of anexponential function such as the concentration gradient shown in Figure 4 in fact emerge from the secondlaw of thermodynamics which tells us that systems evolve towards states of maximum entropy, yielding akind of order from disorder. Turing’s paper showing an even more subtle and beautiful example of orderfrom disorder was still a decade in the future [12].Once these foundations have been laid, Schr¨odinger starts homing in on biological phenomena byconsidering the “limits of accuracy of measuring,” the insight being that there are limits to such mea-surement due to the natural fluctuations of the measuring device itself, a phenomenon perhaps even moreimportant in living organisms than in the experimenter’s apparatus. Indeed, in my view, in this section,Schr¨odinger foreshadowed one of the most important themes of modern physical biology, namely, howliving organisms defy the strictures of equilibrium physics. These questions arise in settings ranging fromthe origins of high fidelity polymerization and the emergence of the concept of kinetic proofreading [13, 14]to the measurement of concentration differences by cells performing chemotaxis [15] to the emergenceof herds with orientational order in apparent defiance of fundamental physical theorems [16]. The topicof fidelity in biological polymerization was also brilliantly undertaken by Linus Pauling [17], but from amolecular perspective rather than the conceptual point of view adopted by Schr¨odinger.Schr¨odinger starts his discussion on the limits of accuracy of measuring with an analysis of the kindsof torsional balance apparatus used by Cavendish (gravity) and Coulomb (electrostatics) to measure theclassic inverse-square laws. His point is that as the apparatus gets smaller and smaller, the deflectionsinduced by the forces of interest will be comparable in magnitude to those induced by thermal motion.Questions of biological accuracy and precision have now become a centerpiece of rigorous thinking inmodern biology in the form of the Berg-Purcell limit, but more generally in the context of how wellliving organisms can sense their environments, whether in the context of hearing or seeing, or in thedetection of chemical messengers [18]. Schr¨odinger himself understood precisely the physics question inplay, noting: “The uncontrollable effect of the heat motion competes with the effect of the force to bemeasured and makes the single deflection observed insignificant. You have to multiply observations, inorder to eliminate the effect of the Brownian movement of your instrument. This example is, I think,particularly illuminating in our present investigation. For our organs of sense, after all, are a kind ofinstrument. We can see how useless they would be if they became too sensitive.”But this is all more than pretty words. Schr¨odinger wants to describe these physical challenges to theliving organism quantitatively. He notes the monotonous repetition of this same statistical principle inthe inorganic world, but wants his listeners and readers to know that there is a simple mathematical law,the “so-called √ n law,” that tells us the size of the fluctuations to be expected in a system containing n atoms or molecules. Schr¨odinger summarizes that law as: “The laws of physics and physical chemistryare inaccurate within a probable relative error of the order of 1 / √ n , where n is the number of moleculesthat co-operate to bring about the law - to produce its validity with such regions of space or time (orboth) that matter, for some considerations or for some particular experiment.” These ideas are centralto modern biological enquiry. For example, when photosynthetic bacteria divide, they have to carry withthem copies of a photosynthetic organelle known as the carboxysome, with only a few (3-6) copies per cell.During the division process, they have special machinery to prevent these unwanted 1 / √ n partitioningerrors [19]. By way of contrast, partitioning errors in transcription factors are a demonstrable part of thereason for noisy gene expression [20, 21]. And yet, and here is the crux of the whole book, “The classicalphysicist’s expectation, far from being trivial, is wrong.” As seen by the carboxysome example, livingorganisms have found ways to insulate themselves from the all-important √ n law and many of the otherstrictures of equilibrium statistical physics.As I will elaborate on below, one way to think of that “wrongness” is summarized in the bottompanel of Figure 4 which hints at the need for a statistical physics of the phenomena that emerge whenenergy is invested to keep those systems out of equilibrium, an enterprise that has been undertaken togreat effect in recent decades (for a flavor of this new physics, see [22]). To further elaborate on why theclassical physicist’s expectation is wrong, let’s revisit Schr¨odinger’s quantitative analysis of the questionof the stability of the genetic information.
3. Fermi Problems in Schr¨odinger Style
Numbers sharpen our questions. Schr¨odinger appreciated this sharpness and used quantitative es-timates as a key part of his arguments. In the world of physics, numerical estimates to describe somephenomenon of interest are sometimes known as Fermi problems and are a model for the power of order-of-magnitude reasoning to clarify both our questions and our thinking in response to those questions.Their name refers to a style of thinking brought to an art form by Italo-American physicist Enrico Fermi,who could estimate his way to numerical answers to questions ranging from the number of piano tuners ina big American city, to the heat loss in our homes if we forget to install storm windows, to the yield of theatomic explosion in the Trinity Test of 1945. Fermi brought this same approach [23] to critical questionsin the science challenges he faced in his professional life as a physicist. For example, the design of thefirst successful nuclear reactor - built upon a string of systematic preliminary studies, each characterized0by numerical estimates on topics such as neutron diffusion - led Fermi to predict the precise moment thatthe Stagg Field nuclear reactor would reach a self-sustained nuclear reaction [24].Schr¨odinger’s book draws from the same Fermi-problem inkwell. In fact, Schr¨odinger’s short manifestogives perhaps the best example of a physicist working through Fermi problems in plain view that I haveseen in written form. Over and over, Schr¨odinger poses questions of the form: what sets the scale ofX?, the quintessential framing of questions in order-of-magnitude thinking. Examples include: what setsthe relative scale of organisms and atoms, what is the size of a gene and how much energy is needed tomaintain the stability of the gene?Having laid down his statistical mechanical and order-of-magnitude thinking foundations, Schr¨odingerwas now prepared to take up the question of the size of a gene. His musing on this question is motivatedby the statistical structure of classical physics and his interest in how biological systems deal with the √ n law introduced above. His argument is that if the number of atoms associated with a gene is small, thenthe natural fluctuations of such systems would impact the stability of genetic information. Concretely,he wonders, how many atoms are associated with a gene and if that number is small in the sense of the √ n law, then how do these genes safeguard themselves from the inevitable statistical fluctuations presentin any collection of atoms? To examine the question of the size of a gene, Schr¨odinger performs several different estimates whichare illustrated in Figure 5. Note the painstaking and often misguided detective work involved in answeringsuch a deep question as the size of the gene before it was even widely accepted that DNA is the geneticmaterial. Schr¨odinger begins with two entirely independent estimates of the size of the gene. The first,shown in Figure 5(A) builds on the subsection of his book entitled “Crossing-over. Location of properties”in which he explains how maps like the classic case for
Drosophila of Alfred Sturtevant are discovered.As seen in the figure, when there is a crossing over event, we can ask the frequency with which two genesend up on the same strand together. The more likely that occurrence, the closer those two genes are onthe chromosome and from these frequencies an actual map of gene positions on the chromosome can bedivined. Given one of these maps of a chromosome, Schr¨odinger proposes a strictly order-of-magnitudeupper bound on the size of a gene based on the size of a chromosome and the number of “properties”(i.e., genes) per each chromosome. As he notes, the estimate provides a bound, because at the time ofhis writing, the entirety of the genes on a chromosome had not yet been mapped. The concept of theestimate is reasonable as is indicated for a bacterial genome in Figure 5(D). The second such estimateis a very clever (though “wrong”) idea of using the banded patterns of chromosomes as a measure ofgene size. As seen in Figure 5(B), if we consider the 23 chromosomes (Schr¨odinger refers to 24 pairs ofchromosomes, true for chimps, but not humans) with their banding patterns, this estimate would saythat the size of a gene is much larger than we know to be true.He really hits his stride when considering a third estimate of the size of a gene as seen in Figure 5(C).This is the point in the story where Schr¨odinger’s reports on the work of Max Delbr¨uck and coworkers,inspiring Perutz’s remark “In retrospect, the chief merit of “What is Life?” is its popularization ofthe Timof´eeff, Zimmer and Delbr¨uck paper that would otherwise have remained unknown outside thecircles of geneticists and radiation biologists” [26]. As seen in the figure, experiments on ionization ofgases allowed for a measure of radiation intensity that could then be directly translated into a tool forexamining radiation damage in DNA. By measuring the radiation-induced mutation rate, an estimatefor the size of a gene could be made leading to the idea that a gene involves roughly 1000 atoms. Ourmodern understanding of the DNA double helix tells us that a base has f ew ×
10 atoms, meaning thata typical thousand nucleotide bacterial gene would involve on the order of f ew × atoms, a bit morethan a factor of 10 larger than Schr¨odinger’s estimate. Though his estimate is too low for the size of anentire gene and a little too large for the size of a basepair, it is an impressive use of indirect reasoningto arrive at molecular dimensions that conjures images of the way Benjamin Franklin, Lord Rayleigh,1 cynR T S X A Y Z Ilac E. coli genome≈ 4.6 × bp oriC µ m 2 nm≈1000 bp 0.34nm 1 nm nm MMPP Sturtevant’s symbols: B C P R M y w v m r
X chromosome locations: 0.0 1.5 30.7 33.7 57.6modern symbols:yellowbody whiteeyes vermillioneyes miniaturewings rudimentarywingsPP ′ P ′ P ′ P ′ Pcrossing-over V bp = � r h ≈ 1 nm V gene = N bp V bp ≈ 10 nm V gene ≈ V chromosome N bands N bands ≈ 25 x-raysx-rays photon ( υ )“MUTATIONS”IN AIR MUTATIONS INLIVING MATTER+N hits = r N hits = r ρ living matter V gene V box ρ air d dL LP cut =ESTIMATE Drosophila
Gene density on the
E. coli chromosomeMutation rate as a functionof radiation dosageThe crossing-over process The estimate of gene sizeThe estimate of gene sizeThe estimate of gene sizeThe estimate of gene size
Figure 5.
The size of a gene. The first estimate exploited the beautiful insights into mapping genes on chromosomes(originally in
Drosophila ) to figure out the mean spacing of genes. Given the gene number and the size of chromosomesthis approach would yield helpful insights. Schr¨odinger’s second estimate uses banding patterns on chromosomes on themistaken assumption that each band is a gene. The Delbr¨uck estimate was based on the mutation rate induced by x-rays.A modern estimate uses the number of base pairs in a gene and the very useful rule that the volume of a base pair is1 nm . For more details of the paper of Timof´eeff-Ressovsky, Zimmer and Delbr¨uck that measured the data shown onmutation rate and radiation dosage, see the book “Creating a Physical Biology” which includes its translation [25]. physics (not biology) to account for these phenomena. Schr¨odinger then goes farther by noting“Thus we have come to the conclusion that an organism and all the biologically relevant processes that itexperiences must have an extremely ‘many-atomic’ structure and must be safeguarded against haphazard,‘single-atomic’ events attaining too great an importance.” All of this kind of “what sets the scale of X”thinking brought Schr¨odinger to precisely the same place that was arrived at 30 years later in a differentway by John Hopfield and Jacques Ninio when they presented a theory of just the kind of “safeguarding”called for in “What is Life?” and that now goes under the name of kinetic proofreading [13, 14].
4. The Biological Frontiers of Physics: New Laws to Be Expected in the Organism
Having made his arguments about the shortcomings of the statistical physics of his time to accountfor the stability of living matter, Schr¨odinger closes the book with some higher-level thinking on theimplications of living matter for the future of physics. In their great book “The Evolution of Physics,”Albert Einstein and Leopold Infeld make it very clear how physics has repeatedly been driven forwardby new experimental measurements (think Faraday and electromagnetic induction) that demand theemergence of new concepts [29]. At the beginning of the 19 th century, the concept of entropy, one ofthe foundational ideas of modern science, had not even been conceived or defined, but an increasinglysophisticated experimental program revealing the character of temperature and heat demanded it. Sim-ilarly, although the idea of “field theory” was implicit in the development of continuum mechanics bygreat thinkers such as Euler, it would have to await the labors of Faraday, Maxwell and others beforeit took the proportions that would lead Einstein and Infeld to say “A new concept appears in physics,the most important invention since Newton’s time: the field. It needed great scientific imagination torealize that it is not the charges nor the particles, but the field in the space between the charges andthe particles which is essential for the description of physical phenomena.” The question is: to deliveron Schr¨odinger’s call to “account for” the phenomena of life, what new experiments and concepts doesexpanding our domain of physical enquiry into the realm of the living demand?My reading of Schr¨odinger’s book is that he is arguing that, just as the phenomena of heat andelectrodynamics forced upon us a myriad of new concepts such as temperature, entropy, the electric fieldand radiation pressure, the phenomena of the living world similarly demand the continued evolutionof physics through new concepts. In his section on “New Laws to Be Expected in the Organism,”Schr¨odinger reveals his hand: “What I wish to make clear in this last chapter is, in short, that from allwe have learnt about the structure of living matter, we must be prepared to find it working in a mannerthat cannot be reduced to the ordinary laws of physics. And that not on the ground that there is any“new force” or what not, directing the behaviour of the single atoms within a living organism, but becausethe construction is different from anything we have yet tested in the physical laboratory.” Indeed, wouldanyone be surprised by the idea that, as we subject new classes of phenomena to quantitative scrutinyin the physical laboratory, yet again, as has been true every century since the days of Tycho Brahe, newconcepts will be demanded of us?Schr¨odinger makes this point beautifully through a colorful analogy for thinking about how the ele-ments of the periodic table can be exploited to totally different ends in living matter. “To put it crudely,an engineer, familiar with heat engines only, will, after inspecting the construction of an electric motor,3be prepared to find it working along principles which he does not yet understand. He finds the copperfamiliar to him in kettles used here in the form of long wires wound in coils; the iron familiar to himin levers and bars and steam cylinders here filling the interior of those coils of copper wire. He will beconvinced that it is the same copper and the same iron, subject to the same laws of Nature, and he isright in that. The difference in construction is enough to prepare him for an entirely different way offunctioning. He will not suspect that an electric motor is driven by a ghost because it is set spinning bythe turn of a switch, without boiler and steam.”Schr¨odinger thus concludes “it needs no poetical imagination but only clear and sober scientific reflec-tion to recognize that we are here obviously faced with events whose regular and lawful unfolding is guidedby a ‘mechanism’ entirely different from the ‘probability mechanism’ of physics.” One category of “newlaws” that might prove particularly potent in biology and that have been given short shrift in the molecu-lar biology era are strictly phenomenological models that make no reference to underlying “mechanism.”These kinds of laws have formed a centerpiece of physics for more than three hundred years in contextsranging from the laws of elasticity to hydrodynamics. Here what I have in mind is a phenomenologicallink in mathematical terms that connects the variables that have emerged from measurements. Both thefamiliar Hooke’s law and ideal gas law originally emerged as highly powerful, and yet, strictly phenomeno-logical reflections of what had been measured in the laboratory. Examples have already started to emergein physical biology as well. Recent high-resolution measurements make it possible to explore the growthof bacteria resulting in a number of propositions for bacterial growth laws [30, 31, 32]. With no referenceto the molecular underpinnings, these phenomenological laws engender corresponding phenomenologicalhypotheses for how populations of bacterial cells maintain a narrow distribution of cell sizes, such asadder and timer models in which the growing cell either waits to divide until it has added a certain fixedquantity of material or until a fixed amount of time has elapsed [33]. Another provocative and beautifulset of phenomenological laws has emerged concerning the character of the entire proteome [34, 35]. Herethe idea is that the growth rate of cells serves as a kind of “state variable” and that depending uponthis growth rate, the fraction of the proteome devoted to protein production (i.e., ribosomes) takes avery specific value. Schr¨odinger’s chapter 6 asks us to think about the emergence of order from order asseen in Figure 4, a topic that has become central to modern physical biology, whether in the context ofbird flocks [36, 37] or cytoskeleton-motor systems such as those that partition chromosomes during celldivision [38, 39, 40, 41]. In all of these cases, phenomenological laws have emerged and we are now in astage of science when the laws are tested and refined, the implications are further examined and effortsare set forth to try and derive those laws from some deeper understanding of the underlying processes.Some of the many other areas in which I suspect we will find “new physics” focus on the ways in whichbiological systems locally defy the tendency towards equilibrium. Examples include a series of problemssuch as the accuracy problem (how biological systems achieve such high fidelity in comparison with what isimplied by the “statistical structure” of classical physics), the adaptation problem (how biological systemschange their physico-chemical behavior in real time in response to environmental cues), the reproducibilityproblem (how living organisms achieve the same outcome such as the human body plan over and overagain in a nearly error-free fashion), the structure problem (how structures such as the outer segmentof photoreceptors are constructed and maintained in the face of the noisy world that surrounds them).I also suspect that there are surprises before us in the unfinished business of dynamics, a subject thatstarted with the great successes of classical mechanics, then to the incomplete promise of thermodynamicsand now the full-fledged challenge of the out-of-equilibrium aspects of biological dynamics, whether theseparation of chromosomes or the origin of species. Of course, these “problems” are offered tentativelyand subjectively since every generation has to decide what are its most pressing problems, but my mainpoint is about the kind of solutions that we should demand in accounting for biological phenomena.4
5. A Manifesto: Schr¨odinger’s Unfinished Business
A perennial question for any scientist is: what to work on? Of course, there is no one right answerand one of my own favorite answers is: whether young or old, scientists should work on whatever they aretruly most curious about understanding from the vast array of mysteries presented by the world aroundus. In academia, much debate and angst are powered by this question in disguise as we ask ourselves,should this person be hired or that grant be funded? One of the ways that people try to sharpen thatquestion is by asking whether we will find new physics or new biology, depending upon within whichdepartment that question is considered. For a very thoughtful modern reflection on the question of newphysics more broadly by a noted physicist who worked in many domains of physics, see “Does AstronomyNeed ‘New Physics’ ?” [42]. Stated most succinctly, Schr¨odinger’s short work ventures the guess thatindeed, by looking at living matter, those who subscribe to the definition of understanding demanded inphysics will find new physics there.As already alluded to throughout the article, the last 30 years have seen enormous progress at theinterface between physics and biology. As for whether or not there is new physics to report, I think itdepends on how we take that question. If we are practicing what Thomas Kuhn referred to as “normalscience,” there is no doubt that there has been an impressive array of results that surely count as newphysics. Examples abound, whether in the context of cellular motility, detection and adaptation in thecontext of chemotaxis [43, 15, 44], or in the analysis of population genetics with its beautiful analogiesbetween the Boltzmann distribution of statistical mechanics and the distribution of allele frequencies [45],or in the surprising new features revealed in the study of active matter [16]. In an excellent series oflectures, John Toner notes: “...the biggest surprise in the entire field of active matter is that a ‘polarordered dry active fluid phase’ is even possible in two dimensions,” technical words behind a fun andinteresting example of the new physics that has emerged in thinking about bird flocks. Yet anotherexample is offered by the phenomenon of cytoplasmic streaming [46], observed before the founding of theUnited States, and yet only in the last decade has the natural language of dimensionless variables allowedus to compare the relative importance of diffusion and flow in transporting materials within large cellsand to compute the kinds of flow patterns that emerge [47, 48, 49, 50]. All of these examples constitutethe activities of normal science and the act of “doing physics” on them has resulted in not only sharpeningour questions, but also in increasing the depth of our understanding. In a playful turn of the millenniumpiece entitled “Molecular Vitalism,” Kirschner, Gerhart, and Mitchison show how many of the issuesraised by Schr¨odinger about what gives living organisms their distinct physicochemical attributes remainas fresh now as they were in the 1940s [51]. “We do not question the importance of genetics, nor disputethe role of DNA as the blueprint for all the components of living systems, but we think it worth asking towhat extent the postgenomic view of modern biology would convince a nineteenth century vitalist thatthe nature of life was now understood.”If we adopt a more sweeping view in which we ask for a revolution in physics that has come on theheels of investigating biological phenomena, we may need to exercise a little more patience. We shouldn’tbe surprised by the glacial pace at which we get our revolutions. There was a century between theinitial discovery of spectral lines and properly “accounting for” them in the series of classic papers bySchr¨odinger [52]. That said, I am wary of the common attitude that, because something has not beendone, or worse yet, because a given commentator themself has not done it, that means that it cannotbe done. I suspect that in the physics pedagogy a hundred years hence (if humans are still teachingeach other important ideas by then), there will be courses whose central ambition will be to explain theharvest of the revolution that resulted from physicists trying to answer the question “what is life?” totheir own satisfaction, in much the same way that we have physics courses dedicated to the question of“what is matter?”Despite both the insight and promise of Schr¨odinger’s thinking in “What is Life?”, not all responsesto his book were positive [2]. Three greatly accomplished scientists who came down on the negative sideof the ledger were famed American geneticist HJ Muller, Caltech chemist and visionary Linus Pauling,5and the structural biologist Max Perutz, Schr¨odinger’s compatriot. Their reactions strike to the veryheart of how different fields view what questions are interesting and what constitutes acceptable answersto those questions [53]. Indeed, as is now clear, a major thrust of this essay has been that in adoptingSchr¨odinger’s physicist definition of understanding, we will see that the study of living matter will demandnew physics. Though differences in philosophy about what it means to understand something explainsome of the negative reaction to Schr¨odinger’s classic, I find a marked lack of generosity given thecircumstances of the book’s origin as a written summary of public lectures.In a centenary volume celebrating Schr¨odinger’s contributions to modern science [54], Pauling wrote“Schr¨odinger’s discussion of thermodynamics is vague and superficial to an extent that should not betolerated even in a popular lecture.” Writing in the same volume, Perutz is even more scathing, makingcomments such as “Sadly, however, a close study of his book and of the related literature has shownme that what was true in his book was not original, and most of what was original was known not tobe true even when the book was written....the apparent contradiction between life and the statisticallaws of physics can be resolved by invoking a science largely ignored by Schr¨odinger. That science ischemistry.” Hence, as did Crick, Perutz takes Schr¨odinger to task for ignoring “chemistry,” which heargues would make the stability of genetic information clear. Here I part ways with Perutz since asour ability to routinely melt DNA in our PCR machines shows, the stability of the genetic material isintimately related to precisely the thermal physics discussed by Schr¨odinger. Understanding the high-fidelity of the processes of the central dogma, to name but one example that falls outside the purview ofboth classical statistical physics and the chemistry of the mid 20 th century, demands much more of usthan Boltzmann distributions and chemical bonding.It is intriguing to explore the claim that if Schr¨odinger had but only appealed to the science ofchemistry, no mysteries would have remained for the classical physicist trying to “account for” the livingorganism. Having spent now nearly a decade trying to come to terms with the field that Perutz wascentral in creating, namely, the subject of allostery, I remain more skeptical than ever of what I will callthe salt-bridge argument [55, 56], an example of the conviction that if we only understand the atomic-levelstructures of the macromolecules of the living world, then “mechanism” and understanding will unfoldbefore our eyes. Really, what we are talking about here is precisely the kind of polarizing debate thatseparates our political lives, what Thomas Sowell christened a “conflict of visions.” Schr¨odinger was notinvalidating or critiquing the world view of chemists or biologists, he was trying to explain what it lookslike for physicists to “account for” a subject. His views are echoed forcefully and eloquently by today’sleading biophysical thinkers [18, 57, 58, 59]. The point of my loving review of Schr¨odinger’s little book“What is Life?” 75 years on is that, to really understand the book’s meaning, we have to remember boththe question being considered and the audience being addressed. In my view, it is a mistake to thinkof his work as a manifesto about biology for biologists. It is a manifesto about the frontiers of physicsand the way that every time physics tackles new classes of phenomena, it requires new concepts andultimately results in the formulation of new laws. It is also a manifesto about the unity of nature. Naturecares not for the names of our subjects. Names such as physics and biology are a strictly human conceitand the understanding of the phenomenon of life might require us to blur the boundaries between thesefields.Sidney Brenner once quipped that, in research, one should either be 6 months ahead of the scientificpack or 30 years behind. There is much to that remark since over and over again, pathbreaking discoveriesare made when new technologies are used to reconsider “old” problems. Nowhere is this more true than inthe case of the hydrogen atom, one of the most remarkable gifts ever given to science [60]. Hydrogen hasserved as the quintessential test case for what it means to “account for” the behavior of atoms (spectrallines), the nucleus (the deuteron), the coupling between radiation and matter, Bose-Einstein condensatesand beyond. Similar case studies are only waiting to be exploited in biology once Schr¨odinger’s notionof what it means to account for a phenomenon is accepted. The study of living matter needs its hy-drogen atoms. Erwin Schr¨odinger’s remarkable ‘What is Life?’ makes it clear that Brenner could have6gone even farther and exhorted us to search 75 years into the past to find an inspiring charge for the future. Acknowledgments
I am especially grateful to David Booth who kindly suggested that I undertake this labor of love, andto Christina Hueschen with whom I have repeatedly discussed Schr¨odinger’s classic book over the lastseveral years. My biggest debt in learning about the confluence of biology and physics is to my bookco-authors Jane Kondev, Julie Theriot, Hernan Garcia, Christina Hueschen, Ron Milo, Wallace Marshalland Thomas Lecuit. In addition, I have learned so much about physics, biology and their intersection froma veritable who’s who of deep thinkers on the state of the art in modern science. For either their direct orindirect help with this article, I want to especially thank Clarice Aiello, Howard Berg, Bill Bialek, CurtCallan, Anders Carlsson, Griffin Chure, Ken Dill, Ethan Garner, Bill Gelbart, Lea Goentoro, Ray Gold-stein, Stephan Grill, Christoph Haselwandter, Hopi Hoekstra, Joe Howard, Tony Hyman, Sri Iyer-Biswas,Quincey Justman, Marc Kirschner, Heun Jin Lee, Jennifer Lippincott-Schwartz, Niko McCarty, MadhavMani, Tim Mitchison, Chris Miller, Andrew Murray, Phil Nelson, Hirosi Ooguri, Mariela Petkova, MollyPhillips, Steve Quake, Manuel Razo, Udo Seifert, Pierre Sens, Lubert Stryer, Mark Uline, Ron Vale,Aleks Walczak, Jon Widom, Chris Wiggins, Ned Wingreen and Carl Zimmer. I am grateful to all ofthese impressive thinkers for useful discussions and/or commenting on the manuscript, though the viewsexpressed here should not be blamed on them. I am also grateful to the NIH for support through awardnumbers DP1OD000217 (Director’s Pioneer Award) and R01 GM085286. The trust and financial supportof this great institution make it possible for today’s scientists to grapple with the endless fascination oftrying to answer Schr¨odinger’s classic question, “What is Life?”7
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