YALE UNIVERSITY oe on
OSBORN BOTANICAL LABORATORY CET ts |
NEW HAVEN, CONNECTICUT _

Marine Biological Lab.,
Woods Hole, Mass.,
August 29, 1947.

Dear Dr. Mather, .

You would, I think, have been not a little amused could you
have observed my mental gyrations during the past few days over
the question of two- and four- strand crossing-over. You have
been, of course, entirely correct in asserting that there should
be no difference . Myf allacy consisted of attending entirely to
the distribution of breaks on the chromatids in the,tetrad, which
one might suppose to show interactions in the four-strand case.If
one considers the distribution of breaks on the strands recovered,
one realizes that it makes no difference what combinations of cos
led to them, they will still be distributed on the strands Poisson-
Wise. It was the identity ofJsinh x/ eX = 1 - e-2* that led to this
realization, the first term having come from my 2-3; the second
from my four- strand analysis. So, you were not quite right in
remarking that I had engtered into crossing-over theory "truly and
well", considering this inexcusable blunder. Please accept my thanks
for having helped me out of it. The formulae of the two strand
case are, of course, essentially the same as Haldane's x,5 = +
Xg -2X)X0, as cah be shown from the addition formula for €anh (x14X2) «
The specific problem becomes very much exa easier to handle,
since the crossovers in each segment will be distributed Poissonwise
with a mean proportional to the length of the segment. In the
case at hand, the ratio of triple-types to total prototrophs will
be: (1 = e728X)(1 - e~2bxX)(1- e-cCX) where a,b,c are the propor-

L ~ e “2x :

tions of the segments, and x the map distance.

 

You are quite right also about the futility of this type of de-
tailed analysis in view of the approximations that must be made of
no inter€#rence. A priori, however, I had absolutely no conception
of the final estimate of the map distance, md if it had proven to
be much greater than it was, some sort of correction for multiple
crossovers would have to be made. Amuxktxk=xxmkkexxxzx This was par-
ticularly cegent since I was using the miltiple-crossover frequency
itself to measure the distance! Inere does not seem to be anything
that can be done about ghxmamsmm chasema interf@rence, but it may
cancel itself out- although it will bas the single- as against
multiple break chromatids, it will also tend to even out the distri-
bution of such multiple breaks as do occur and make them more effec-
tive in producing the "triple" types. I am not sure that chromatid
interBérence would have any effect; complete interference would be
equivalent simply to juxtaposing two two-strand dyads, and would
have no effect. .

 
YALE UNIVERSITY
OSBORN BOTANICAL LABORATORY
NEW HAVEN, CONNECTICUT

When referring to zygotes previously, I had in mind the fact
that the combining cultures are mixed just before being poured
into hardening agar. The gametes produced by a single zygote
should therefore be kept in one place, and under certain circun-
stances give rise to mixed colonies. ’

The crossover algebra has not been as useful in my own work
as I had hoped. It is of course applicable under any restraints
one cares to formulate: non-sister strand c.o., chromafid or
chromosome interference, competitive pairing in multisomics, etc.
One nedd merely place the appropriate restrictions on the sub-
scripts of adjecent crossover-symbols. Zt would be mostvuseful
probably in such a system as Lindegren's analysis of interference

in Neurospora.

I shall be leaving Yale this Fall, and am taking a post as
Asst. Prof. in Genetics at the University of Wisconsin, Madison,
Wisc., stusting im the middle of September. very satisfactory con-
ditions for a program of research in micrworganisms are being
established there, and there is a rapidly growing interest in such
departments as biochemistry and bacteriology in the implications of
genetic research for their work. The prospects for fruitful collabo-
rations there look very good, and were the main reason for my going

out there.

The linkage work has been writteh up and sent to Genetics, where
it should appear in the September issue. Your enmouragement and
assistance have been invaluable- and I hope, fruitful.

With best regards from ny wife,

Yours sincerely,
Joshua Lederberg.

IC TRANS SR THEE EE

 

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