Letter from Max Delbruck, California Institute of Technology to Michael Heidelberger
Description:
In this letter, the prominent biophysicist Max Delbruck asked Heidelberger for reprints of his work on the theory of the precipitin
reaction, and himself proposed a mathematical theory for calculating the rate, or velocity, of antigen-antibody reactions.
Item is handwritten.
Number of Image Pages:
4 (185,177 Bytes)
Date:
1938-03-16 (March 16, 1938)
Creator:
Delbruck, Max
California Institute of Technology. Kerckhoff Laboratories of Biology
Recipient:
Heidelberger, Michael
Rights:
Reproduced with permission of Tobias Delbruck.
Subject:
Medical Subject Headings (MeSH):
Antigen-Antibody Reactions
Precipitins
Exhibit Category:
Antigens and Antibodies: Heidelberger and The Rise of Quantitative Immunochemistry, 1928-1954
Relation:
Letter from Michael Heidelberger to Max Delbruck, California Institute of Technology (March 28, 1938)
Dr. L. Pauling and I are planning to run a research-seminar on Protein structure here next term, in which we want to discuss
in particular the inferences one can draw from the serological reactions and from their specificity. On going through the
literature on the subject we find that we will be rather handicapped by the fact, that most of the immunological journals
are not available here in Pasadena. We would appreciate it therefore very much if we could have reprints of your papers on
the polysaccharide reactions. When I called on you in October last you were kind enough to let me have reprints of four of
your papers from the J. of Exper. Med. (Vol. 65 p. 647 and p. 885, and Vol. 66 p. 229 and p. 251). I wonder whether we could
have some more, in particular the theoretical
[END PAGE ONE]
[BEGIN PAGE TWO]
one from Vol 61 p. 563. I remember that you in October offered this one to me for loan. I looked it up in Cold Spring Harbor
but did not study it sufficiently careful, so I would like to see it again. We will of course send it back when we have it
sufficiently animilated[?].
I have been speculating a little on the theory of the absolute value of the reaction rate of serological reaction and have
arrived at the following formula. Consider the rate of formation of a compound AB from the antigen A and antibody B
A plus B yields AB
In a vessel containing NA particles A and NB particles B. The rate of formation should be dNAB divided by dt equals NA times
NB times (DA plus DB) times (aA plus aB) where DA, DB are the diffusion coefficients and a and b the diameter of A and B respectively.
[END PAGE TWO]
[BEGIN PAGE THREE]
This formula D derived by assuming that every collision between A and B leads to a union. If then D an activation energy,
the reaction will be slower, also if the collision must be one between specifically oriented particles. So far as I could
test the formula it fits at least the order of magnitude of the observed reaction rates. In your experiments you do not observe
this primary reaction but the later stages of formation of the precipitate. One can of course not easily make a theory of
the absolute rate of these collisions, but as you have found they seem to be proportional to the concentrations, so they should
also be bimolecular reaction. In that case their temperature dependence should be only the result of the temperature dependence
of the diffusion coefficients, and this in turn is predominantly determined by the change in viscosity of the solvent, and
therefore equal for all
[END PAGE THREE]
[BEGIN PAGE FOUR]
steps in the precipitate reaction. I should be very thankful if your could let me know whether these considerations have
been worked out long ago by other people (as I suspect) and where I could find their papers. Ordinary physical chemistry
is little concerned with collision numbers in liquids, because the reaction rate on either predominantly determined by activation
energy, and any uncertainty in this makes a closer analysis of the collision rates futile, or, if the collision rate determines
the reaction rate, the reaction goes immeasurably fast. Therefore the physico-chemical literature does not give a good theory
of collision rates.