January 1938 - Linus Pauling Day-by-Day

January 6, 1939

Dear Linus,

I would like to know your views on certain questions concerning protein denaturation.

(1) When a protein spreads to form a film it unfolds. At the same time it becomes insoluble and its SH groups become available. We would say that it is denatured. And yet it has certain important properties of the native protein. Gorter has studied the enzymatic activity of trypsin after spreading. The interpretation of his observations is, however, ambiguous. Langmuir's exp[eriments] on urease seem pretty clear. While spread out as a film, this protein acts as an enzyme. In this sense it is not denatured. We regard unfolding as taking place in denaturation and yet here is a case of unfolding without loss of a certain configuration. I feel the explanation of the apparent contradiction is as follows: when a protein spreads unfolding takes place in a very orderly manner. Langmuir came over here on day and demonstrated some of his exp[eriments]. As a protein spreads it forms certain visible patterns. The same protein always forms the same pattern; each protein forms a different and characteristic pattern. The whole film forms a continuum, bonds holding everything in one piece. When a protein unfolds at a surface it seems possible for it to do so without passing into a multitude of random configurations. The configuration of the protein in the film may in certain respects be very similar to that of the original native protein. It may therefore still act as an enzyme. At the same time it is insoluble and has its SH groups available. It has some of the properties of native protein and some properties of denatured. The controversy about whether or not it is denatured is in a certain sense surely verbal. What do you think of this?

(2) Another point about configuration and specific properties. When the layers of a protein fall apart from each other to assume random relations to each other, certain specific properties of proteins are lost - as mentioned in our paper. Other properties distinguishing one protein from another will remain. The amino acid contents of proteins vary and the sequence of amino acids in the chains vary from one protein to another. Even after unfolding these differences will persist and manifest themselves in certain properties. There is good evidence that antibodies are proteins. These proteins lose the power to act as antibodies on denaturation in the same way that Hb and the enzymes lose their properties on denaturation. Unfolding (with subsequent random arrangements) is enough to denature antibodies, Hb and enzymes. An antigen is a foreign protein which when injected into an animal gives rise to antibodies. There is some evidence (by no means conclusive) that when an antigenic protein is denatured in the same way as Hb, enzymes etc. are it loses some of its specific properties, but not all of them. It certainly is possible on our views that certain properties of a specific nature would remain after denaturation and there is experimental evidence that this is so. In a certain sense, denaturation will be complete only when the protein is finally resolved into its constituent amino acids. There do, however, appear to be certain definite steps in the loss of specific configurations and our paper was concerned with one of the first and apparently most definite steps.

(3) Have you seen the paper by LaMer in Science of Dec. 31st? Please let me know what you think of this. It seems to me that LaMer does not consider the view that denaturation takes place only after many bonds are broken - after a considerable number of steps (and one after the other) have been taken, so to speak. What do you think of Eyring's views? What about the meaning of S, the steric factor, in the velocity equation? What about the role of collisions in denaturation?

(4) I have made some progress in understanding the coagulation of myosin in muscle. You may remember I told you about comparing the effect of heat on the contraction of muscle (in which myosin coagulates) and on the coagulation of isolated myosin. Frog muscle is caused to contract by raising the temperature to 37 degrees and isolated frog myosin coagulates at 37 degrees. But the rate of this latter process is very slow. I now find that if myosin is treated by NH₄Cl or LiCl (and the excess or free salt carefully washed away) that the myosin has become sensitized. It is now exceedingly unstable. At 37 degrees it is coagulated with very great speed. Heretofore I have prepared myosin by using KCl. After treating myosin with LiCl or NH₄Cl the ppt. of myosin can be washed for at least 10 hours with constantly renewed dilute KCl and still this myosin appears sensitized when compared with myosin that has never been treated with anything but KCl. How much LiCl or NH₄Cl remains attached to the myosin I do not yet know. The instability of the myosin shows itself in other ways too. If ordinary (KCl) myosin is dried it also loses its solubility - it cannot be redissolved. If a surfusion of this myosin is frozen at -10 C it slowly in the course of weeks loses its solubility. It is presumably being dried by freezing away its water. Myosin that has been treated with NH₄Cl loses its solubility after it has been frozen for several hours. The possible bearings of all this on muscle - In the muscle fibre K is the common cation and it is located in the same place in the fibre as is myosin. During contraction K leaves the fibre, passing into the blood, and returning during rest. At the same time (approx) myosin becomes insoluble. Also at the same time the fibre becomes opaque. If gels (the myosin in both are still soluble) of myosin of the same concentration are compared (one of the gels having previously been treated by NH₄Cl) it is striking how much more opaque the NH₄Cl treated myosin is than ordinary KCl myosin. It looks as if K stabilizes myosin in the muscle fibre and that in activity NH₄ or something like it comes in contact with myosin and sensitizes it. All this is quite new and incomplete, but the observations I have just described to you are, I believe, probably sound. Perhaps this has been too incompletely described to be comprehensible.

If you still are in the East, it would be the greatest pleasure for me to see you again. I would be quite willing to travel a bit for a talk with you.

In the meantime, yours as ever,

Alfred Mirsky

O, by the way, I was talking with Gasser about you the other day. He referred to you as a "wizard." I hope you don't find being one a burden.

THE ELEMENTS OF QUANTUM MECHANICS AND THE PRINCIPLE OF INDETERMINACY

By Linus Pauling

Cornell Philosophy Club, Thursday, January 20, 1938.

Introduction. - In speaking before this organization I feel guilty of unintended misrepresentation. I am not a philosopher nor a theoretical physicist, nor, indeed, am I especially interested in philosophy and physics - instead, I am a chemist who finds quantum mechanics a useful aid in the study of chemical problems. Having, however, made the mistake of coming here tonight, I shall try to present my own simple point of view, trusting that the sophisticated auditor will be kind enough to excuse its naiveté.

Classical Mechanics.- In the treatment of a system by the methods of classical mechanics, as developed 300 years ago by Newton and refined by Lagrange, Hamilton, Jacobi, etc. so far as the mathematical technique is concerned (and by Einstein in a more significant way), an instantaneous configuration is defined by three Cartesian coordinates x_iy_iz_i for each particle. [Drawing of two points with the Cartesian coordinates x_iy_iz_i and x₂y₂z₂, respectively.] The problem is to find how the configuration changes with time. The equations of motion are such that a knowledge of the coordinates x_iy_iz_i and the velocities x´_iy´_iz´_{(or the equivalent momenta p_xi=m_ix´_i etc.) at the time t = t₀ permits the prediction of the state of the isolated system at any later time. It is interesting that x_i and p_xi is enough - nature was that kind to us, since she might have included [See drawing] also.}

It is the possibility of this prediction in classical mechanics which underlies the doctrine of classical determinism - that, if the present state of an isolated system (eventually the universe) were known, a sufficiently clever and energetic mathematician could foretell exactly the future behavior of the system. Quantum mechanics differs on this point.

History of Quantum Mechanics. - Planck - 1900 - black-body radiation. k = 6.547 · 10^-27 eng sec. Einstein 1905 - light quantum. Bohr - 1913. Modern physics is a difficult subject partially because it is so extensive - because a multitude of facts is known and must be understood by the student.

The old quantum theory was not a theory - nothing could be said about fundamental questions with use of it, because it was incomplete - a patched-up classical mechanics, representing a first effort to formulate a mechanics of atoms. Then de Broglie, Heisenberg, Schrödinger, Dirac, Born, Jordan etc. set up the quantum mechanics. It is interesting that these men were mostly young - Heisenberg 24 in 1925.

Nature of Quantum Mechanics. - QM permits the formulation of a function Ψ which is compatible with the results of experimental observation of the system at t = t_o and permits predictions to be made regarding results of observations at a later time t = t₁, the system remaining isolated in between. [Drawing of an observer and system.] In general a statistical prediction, given by a probability distribution function. Let us as an example discuss the hydrogen atom. If we know the atom to have energy -e²/2a_o = -13.53 e.v. (normal state) at t = t₀, we know that at t = t₁ it will still have this energy, providing that it remain undisturbed. But for x we can predict only a statistical electron distribution, and for p_x another, with no correlation between them. [Drawings of electron distribution graphs.]

It might be asked if more could not be learned about the state of the atom than its energy - could we not know W and x both, and refine Ψ? The answer is no - that the methods of observation are such that W alone is a maximal observation.

The Uncertainty Principle. - Heisenberg in 1926 formulated this; it is ΔxΔp_x ≥ h/4π. This holds for q_i p_i in general.

For mass 1g. this has no importance: Δx = 10^-13cm for Δp_x = 10^-13 or Δv' = 10^-13cm per sec. But for electron with m = 9.038·10^-28 or ≈10^-27, it gives Δx = 10^-8 for Δx' = 10⁸; i.e., compete lack of x, p_x correlation in normal state (which has x' ≈ 10⁸cm·sec^-1).

QM thus prevents the deterministic point of view from being adopted - by denying that x_i and p_xi can ever be known accurately at t = t₀ ! Heisenberg and Bohr have discussed various experiments to see why this is so, and found that every known method of observation is compatible with this idea. [Drawing of x-ray diffraction.] For example, if x-radiation is used to locate the electron, Compton-effect recoil may change the momentum and energy so that it is no longer known that the atom is in its normal state. Nor can bombardment by particles, such as other electrons, be used, because of their wave character, which leads to diffraction effects.

What About It. - There are several comments that can be made about the uncertainty principle and determinism.

1. Perhaps there really is a deterministic mechanics underlying QM, and perhaps a new physical discovery - such as classical undulatory radiation or real particles - will be made which will permit x and p_x to be measured simultaneously. I don't think that this possibility can be ruled out, but until the discovery is made there is no use to talk about it.

2. In a sense we can still say that there is determinism in the universe. If Ψ is known at t = t₀ for an isolated system, it is known forever after - so long as the system remains isolated. The universe as a whole is an isolated system, and we may thus say that with changing time the Ψ of the universe is changing in the manner prescribed by the Schrödinger wave equation for the universe.

3. These are, however, just words - a possibly more significant question is the following: in a living system is there the possibility that reaction under certain conditions can be varied through the operation of freedom of will, selection being made of one or another of the alternatives provided by the QM wave function? I do not know whether this question has meaning or not - but I think that it hasn't.

The action of will might be of either of the two following kinds: a. In a large assemblage of identical living systems, individual choices are such that the prob. dist. fn. is retained for the assemblage. b. The prob. dist. fn. is not retained - instead, every system selects the good alternative (let us say).

Kind a could not be looked for experimentally. Could kind b? I think not - I am afraid that the limits of our experimental technique is such that the uncertainties in determination of the initial state are infinite very much greater than uncertainties due to Heisenberg's principle. These latter are of magnitude ≥h/4π for every degree of freedom. This is comparable to difference between normal and first-excited state for each degree of freedom. But how determine these experimentally?

Actually, for most interatomic interactions of the type of significance in physiology the ΔxΔp_x uncertainty in the normal H or other atom has no bearing on the question - the atomic functions Ψ determines the interaction potential. I don't see where free will has a chance to say anything - indeed, it hasn't until an observer comes along to make an objective experiment - if it has anything to say even then.

To support my contention that biological systems are too complex for Heisenberg's h/4π to have experimental significance I might mention ice and water. [Drawing of water molecules.] In ice atom absolute zero there are still (3/2)^N configurations. This is 10²³ for N = 0.606 x 10²⁴! Even for one microgram of ice there are 10^{10,000,000,000,000,000} configurations! This perhaps has something to do with the variety in snow-flake crystals as photographed by Mr. Bentley. We see that in tissues - nerve, for example - the structural possibilities are myriad.