Moss - What genes cant do - 2003 (522929), страница 16
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But positive? Why?Schrödinger’s central concern is with that most perennial (and perennially elusive) topic of those who would presume to “explain” life—56Chapter 2i.e., the acquisition, retention, and propagation of organized form.Schrödinger has set himself the task of showing that there has been acertain special problem and that now the problem can be solved. Theproblem for Schrödinger is that statistical physics cannot account for thestability which genetics has shown must be invested in only a single orperhaps two copies per cell capable of stability over numerous generations.
His favorite example is the “Hapsburg lip,” a Mendelian trait(autosomal dominant) observed to be faithfully reproduced in its passagethrough many generations of Hapsburgs. Schrödinger’s solution to thisproblem is to be found in the new explanatory insights into the stability of the solid state which quantum mechanics claims to provide and inthe specific form of the 1926–1927 Heitler-London theory of the chemical bond.
Schrödinger begins by presupposing the kind of “constitutive”genetic preformationism I have already attempted to criticize. What heproceeds to do is to make the question of inheritance interesting tophysicists by recouching it in terms of the physics of stability andpredictability. He follows Delbrück in uniting the idea of genetictransmission with that of information given a physical meaning byquantum mechanics. The product of this marriage is the concept of the“hereditary code-script.”Although he begins with an uncritical acceptance of genetic reductionism, Schrödinger proceeds to offer an independent argument for theneed for a genetic code-script.
It is this argument which has a specialappeal to physical scientists. Schrödinger’s case for the hereditary codescript is based on distinguishing between “order-from-disorder” and“order-from-order,” with the former being the predominant legacy ofstatistical physics and the latter the result of new insights from quantumtheory that could meet the challenges to biology which the former framework could not. Schrödinger begins with a naive notion (but perhapsjustifiable for his time) of the cell as a disorganized bag of atoms andargues his way to the need for a solid-state “aperiodic crystal” to serveas that bedrock of order, continuity, and heroic resistance to entropywhich makes life possible.
Those who have come since and who continue to sing the praises of the hereditary code-script have failed toexamine these accompanying presuppositions in light of the empiricalfindings that have since accrued.The Rhetoric of Life and the Life of Rhetoric57Schrödinger tells us that natural order, as hitherto described by physical laws, was based on atomic statistics and so only approximate.Lawful precision—as demonstrated by the examples of paramagnetism,Brownian motion, and diffusion, is predicated on large numbers of interacting atoms. The relationship of the number of units in the system tothe predictability of the system is given by the “square root of n rule,”with n equal to the number of interacting units in the system:The laws of physics and chemistry are inaccurate within a probable relative error–of the order of 1/÷n, where n is the number of molecules that co-operate to bringabout that law—to produce its validity within such regions of space or time (orboth) that matter, for some considerations or for some particular experiment(Schrödinger, p.
19).A system with only 100 molecules would see a relative error of 0.1 whilea system of 1 million molecules would see only a relative error of 0.001.Schrödinger then goes on to draw upon the evidence of classical genetics in order to argue that the stability in living systems entails thestability of small numbers of units. A gene, for example, appears to becomposed of approximately 1000 atoms, as was estimated by Delbrück,using x-ray induced mutation data. The overriding point is that biological stability simply cannot be accounted for on the basis of those lawswhich statistical physics has to offer for explaining the stability ofmolecular systems.Having established the problem, Schrödinger offers to provide thesolution.
The solution, he believes, is to be found in quantum mechanics, and in particular in the 1926–1927 Heitler-London theory of thechemical bond. First and foremost for Schrödinger, quantum mechanismintroduced a break with the ontology of continuity:The great revelation of quantum theory was that features of discreteness werediscovered in the Book of Nature, in a context in which anything other than continuity seemed to be absurd according to the views held until then (p.
51).Why this should be important is not hard to imagine. In a world ofunbroken continuities, predictability will vary along a continuum as–described by the 1/÷n law. Configurations consisting of small numbersof atoms will always be relatively unstable. In a world of discontinuities,however, critical thresholds can emerge which can account for the preservation of stability within some sub-threshold regime.58Chapter 2Atomic configurations, as described by quantum mechanics, do notvary along a continuum but rather are limited to some set of allowedstates. And of the allowed states there may be a lowest energy or moststable configuration. Such a configuration will then be separated fromthe next most stable configuration by a discrete difference in energy thatwould be required for a transition of states to occur.
Now if all configurations were “allowed,” then energy differences would presumably runalong a continuum and fluctuations would be ongoing. But with allowedconfigurations being constrained at the most fundamental level, discretedifferences in the energy of allowed states can constitute relative barriers and thus provide for relative stability.Following Delbrück, Schrödinger formalizes this relationship asfollows. If W is the energy difference between two (allowed) molecularconfigurations, then stability will be a measure of the ratio of W to theaverage heat energy of the system, which is given by kT, where k isknown as Boltzmann’s constant and derived from the average kineticenergy of a gas atom at room temperature, and T is the absolute temperature.
The “time of expectation” for a transition of states to occur,represented by t, which is a measure of the probability of enough energygathering by chance in one part of a system to effect a transition, is givenas an exponential function of the ratio of W : kT and is thus highly sensitive to changes in this ratio. With t representing the time in secondsfor a molecular vibration (10-13 or 10-14 s) to occur, the full expressionis t = teW/kT.
The sensitivity of this equation to changes in the ratioof W : kT is such that while the time of expectation for a transition tooccur with a ratio of W = 30 kT is only one-tenth of a second, t goesup to 16 months when W = 50 ¥ kT and up to 30,000 years whenW = 60 ¥ kT. To this picture Schrödinger added two amendments, whichwill be familiar to anyone acquainted with contemporary chemistry.The first is that the next highest energy level does not actually entailmolecular rearrangements:The lowest level is followed by a crowded series of levels which do not involveany appreciable change in the configuration as whole, but only corresponds tothose small vibrations among the atoms which we have mentioned (p. 56).These vibrational states are also quantized (and any given molecular configuration will be compatible with some range of vibrational states).
TheThe Rhetoric of Life and the Life of Rhetoric59next amendment pertains to the atomic mechanisms involved in an actualmutational event. A mutation, caused perhaps by radiation, may entaila rearrangement of the molecular configuration such as to produce anisomer. “Isomers” are molecules that are described by the same chemical formula but have different spatial arrangments. Now two isomersmay be fairly close with respect to their lowest energy state, and yet thetransition from one to another may still be highly constrained. Thereason for this constraint is that the mechanism used in getting from oneisomer to another is an intermediate configuration which is of a muchhigher energy level than either of the isomers.
In other words there is nota direct mechanical path from one isomer to another but only a paththat entails an intermediate state which is at a significantly higher energythan either of the two stable isomers. There is typically thus a significant“energy of activation” which intervenes between two otherwise fairlystable, low-energy configurations.The physics of the chemical bond described by the Heitler-Londontheory pertains equally to molecules, solids, and crystals. From thequantum-mechanical point of view these terms all represent one and thesame state of matter.
The notion of Schrödinger’s celebrated aperiodiccrystal is simply that of a molecule which enjoys this stability and is sufficiently lengthy and sufficiently heterogeneous in its composition to bethe putative bearer of coded information which allows for the sustenanceand reproduction of organized life-forms. Why organized life-forms mustbe dependent upon coded information is never explicitly addressed butcan be inferred from Schrödinger’s reasoning.
His view requires, amongother things, the assumption that no other aspects of the cell are capableof ‘standing on their own’ with respect to preserving high levels of order.If the bulk of the cell is not based on some form of solid-state organization and yet is dependent on it, then that order retained in a relativelyinert solid-state form—being at a kind of remove from the dynamics ofmetabolizing life processes—must exist as something like a representation of those dynamics, embedded perhaps, in some form of code.Schrödinger approaches this kind of vision in the following sentence:An organism’s astonishing gift of concentrating a “stream of order” on itselfand thus escaping the decay into atomic chaos—of “drinking orderliness” froma suitable environment—seems to be connected with the presence of the60Chapter 2“aperiodic solids,” the chromosome molecules, which doubtless represent thehighest degree of well-ordered atomic association we know of—much higherthan the ordinary periodic crystal—in virtue of the individual role every atomand every radical is playing here (p.
82).Schrödinger did not attempt to adumbrate any of the laws or mechanisms by means of which the order of chromosomes serves to dictate anddirect the dynamics of an organism. Rather he holds this out for futurebiochemical physiologists to work through. But it is the very idea thatthere are such new laws to be found which Schrödinger asserts is theprincipal motivation for writing his book What Is Life?What is novel for the physicist about the living organism is thatits exquisite stability and predictability is the result of an “order-fromorder” process. This new order-from-order is not being put forwardas evidence for new fundamental laws of physics nor is it seen to contravene any of the established laws.
Rather, Schrödinger foresees thefinding of new higher-level laws or principles that explain the abilityof living systems to parlay high levels of order between the chemicallystable but metabolically inert aperiodic crystal and the growing andmetabolizing, but entropically vulnerable, apparatus of the cell andorganism. He likens this to the example of the spring-based clock. Theclock is made of real physical stuff and so cannot in principle escape thepossible consequences of thermal fluctuations.
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