Cifrarel
Marine Biological Laboratory t

WOODS HOLE. MASSACHUSETTS t Vo

Dear Josh:

T am sending under separate cover a vrovisicnal ccov
of the paper which Amos Norman and I weuld like to send to
PNAS via Delbruck.

Note that the nkit theory (equation 2) is the same
as the one you arrived at and as far as 7 can see it cannot
be made less cumbersome except where terms of tre order of

can be ignored. This theory in its cumbersome form is
the one on which practically all of the multi-hit work in the
literature has been interpreted. As you will see, I don't
think it is the correct theory to use in interpreting survival
curves anvway.
-kD

The eqwaticn q=e attributed to Delbruck is
given without derivation and I am not certain what his
starting premises were, i.e. whether the Poisson is that due
to phare absorbtion in which case the proporticn of infective
centers when no dose is delivered is l-e-", or whether it is
due to the randorizine effect of radiation, where the exvoressicn
holds only at high dose. Jn other words, it is net clear
whether the expression is intended to aovly to exverimentea
with freshlv absorbed nhace. or following intracellular erowth,
In the former case it 18 erronecus because multinlicity
reactivation can take pvlace.(Comrvare our equaticns 17 and 23).
™ anv case, if Delbruck's eonaticon means the sare thing as
our ecustion 16, then vou are ccrrect in ssvine that the niect
nf Yoastrel/n versus TP wilt not remein JTineer 311 the wav te
the D2 interrert: in fart it becomes infinite at D=0.

Note that the wev we heve handled this ts to use the
deviaticr frem linearity of thia niet in the low dose réenec
te indicate the tyne of dictrimiticn cf the sensitive unites
vertatinine at D=%. Alec rote that the secend derivative of
this rlot can never chenee sien if aa’l-e  }\. Therefore,
an inflerticn noint in the vlot is an indéicaticn that the
data are best described bv ennation 21 or °C. ‘Tmless yor
think the n-hit theorv is still defensible}.

T am indebted te veu for tireine me to read Turia
and Dulbecec's March renetics naper because it made evident.
the need for ceneralizing the rulti-vrocess case as we have
done tn equation 21. Their equations are correct and their
Aeriveticn is very neat if yeu alreadv krow what thev are Grivice
at, but there is considerable confusicn in the tert due to the
inconsistent usace of the terms ‘effective hit' and 'lethel
mutation’, neither of wnich are actvally intended by the
svmbol r. If r is taken to mean the dese ccrresocndine te a
hy-cthetical number of effective hits. re-' cf which are actuelly
Marine Biological Laboratory

WOODS HOLE, MASSACHUSETTS

effective, everything cores out right. A very minor flaw is

the failure to exclude the singly infected bacteria which yield
plaques from the numerator of the experimental value w, when

it is so excluded in the calculation of the thebretical value ye
This leads to a maxirum error of about 4% at low dose and low
multiplicity, in the experiments revorted. The thine that bothers
me mest is that they don't recognize the importance of the effect
that unequal sensitivity of the units will have on the apparent
value of y. Cn o. 113, next to last Pere ee ca ppebends glossed
over. Actually, unequal sensitivity will cause t e,value of

m to become a function of both dose and multiplicity, since

the less sensitive units will contribute neglicably toward
decreasing the probability of reactivation at low dose and high
multiplicity, but will greatly lower this probability at high
dose and low multiplicity. However, the relative effect* of
increasing dose will be creater at hirh multiplicities. TI

think that this may account for much of the discrevancy between
wand y in fies. 2&4. I don't think I've made this clear,

but mavbe you can fieure it out.

The interpretation of the Neurospora data given in
the ms. has some testable consequences, one of which is that
the frequency of allelism among non-dissociating components
Should be very high.

TI hope you have some comments to make on the ms.
(which there is no need to return as I have other copies.)
Also, I would like your prognosis on our chances of having it
published via Delbruck. I'm not worried about that Yule ref.
but will trv to find it in the lib. here. 83v the way, now
what do tou make of Witkin's case in the light of our analvses?

Sincerely,

Kim

P.S. I like your idea for successive appreximaticn, but
shouldn't your equation (5) read: loglog(l-e"")/a,= los n - ad ?
Let me know how you make out irradiating diploid K-12.

*relative to y computed on the basis of equal sensitivity.