Correspondence (Fuller)

Date:
1975-1978
Reference:
PP/CRI/H/6/12/6
Catalogue details

Licence: In copyright

Credit: Correspondence (Fuller). Source: Wellcome Collection.

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    drift towards each other relatively freely, and when they touch may easily get entangled. This is the common experience with disorderly wads of string in a drawer. Thus one might be led to expect that at equilibrium the entangled states are highly probable. The fallacy here lies in part in the frictional interactions between the strings which we have omitted from our model. Closer analysis shows very clearly that the two coils will have an equally hard time getting entangled as getting dis entangled. The next question would then be again How long will it take the coils to change their state of entanglement in either direction ? and here again I am not prepared to guess an answer. It is likely that the problem of entanglement could be studied experimentally by studying viscosity. Here entanglement between molecules should be a factor of mutual interaction distinct from and additional to the hydrodynamic interactions considered exclusively so far. The entangling interaction should be strongly dependent on the rate of shear and this dependence might serve as an indication of the rate of entanglement. With this last problem, however, we have come a little closer to the realities of life. The nucleic acids, carriers of genetic information, occur in a curious twin- stranded form, the two strands, or chains, being wound around each other in a regular double helix of a thousand turns or more. This double helix form is relatively rigid, it has practically zero entropy. The double helix has to be replicated at each cell division and we believe that this occurs in such a way that the two chains separate from each other, each complementing itself by synthesizing a new opposite number. In other words, an organized disentangling and re-entangling process must occur, and it is essential that this operation should function with great speed and reliability and a minimum of wear and tear on the chain. We know too little as to how this is done in vivo to permit us to set up a reasonable model on which to make calculations. A simpler situation, however, arises in vitro, i.e., in the test tube. Here a variety of conditions causes the chains to fall apart, viz. high temperature, high acidity, or some other chemical interactions. In any one of thèse situations the agent employed serves the purpose of overwhelming weak attractive forces which hold the double helix together in an otherwise improbable configura tion. When these forces are effectively eliminated, then, if the space in which the double helices are embedded is sufficiently large, the chains certainly should and do come apart. Neither experiment nor theory is at present able to cope with the rate problem adequately. Experiment shows that the chains certainly can go quickly into a state of very loose, if any, entanglement. But the evidence presented purporting to show that they disentangle fast is unsatisfactory, and it would be very nice to have at hand a theoretical analysis that would enable one to guess how fast entanglement or disentanglement might proceed. Two theoretical attempts have been published relating to the separation of the two chains (Kuhn, [1]; Longuet-Higgins and Zimm, [2]). Kuhn assumes that the separation occurs in the following manner. At first the double helix is loosened all along its length by untwisting, say, 100 turns of its total of 1000. At this point it is estimated the individual chains have lost their rigidity into which they had been forced by the tight coiling, and they are now free to diffuse away from each other in the longi tudinal direction. In contrast, Longuet-Higgins and Zimm assume that the two chains separate as follows: the bulk of the double helix does not twist, but un ravelling starts at both ends. The unravelled parts form random coils, and these random coils, two at each end, rotate around each other. The driving force for this rotation against the viscous drag is supplied by the gain in free energy. Every link that is unravelled changes from a state of rigidity to one of rather free rotation around several single bonds per link. For reasons too complex to discuss here, it does not seem likely that either of these descriptions of the path of disengagement between the two chains is close to reality. The difficulty in finding the right path is not so much a mathematical as a physical one. What is needed is a knowledge of certain parameters, especially a knowledge of the relative size of the forces tying the chains together crosswise and lengthwise. Once these parameters are better known, the problem will be defined mathematically and then the question of entanglement will play a large role. Neither of the two theoretical treatments cited above considers the problem of entanglement in its generality. Literature cited 1. W. Kuhn, Zeitbedarf der Längsteilung von miteinander verzwirnten Fadenmolekiilen, Experientia 13 (1957), 301-307. 2. M. C. Longuet-Higgins and B. Zimm, Calculation of the rate of uncoiling of the DNA molecule, J. Molec. Biol. 2 (1960), 1-4. California Institute of Technology, Pasadena, California
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