eee) TL ts See
fee Sr SSS ee Age os eres
London ners

       
 
   

  

DOr tt Rote ra

  

typewriteen copy of it. This wes SM De Ke ae sO
dogize thut it is not relicble, Tae cigebre Wus OVer wis neud >:
énd ae misread some of your iormilis. 1 ucve caugut sowe o1

tuese dus probi.ol, not ali. a

Pe RO SO Pa rr eT eC a ttre ee POET nee 17 oe

   

(Your wunyseript ug bepn-resa by “urir, Lersue,, ind seves -
rel others ena I weve « talk about it nere lust wees walca wis
ablenced by tose wae took the phege course this yearcnd by
ERS MEET): le (oa oT aR people to whom elgebre is more coo re att ¢

an Te (se OME by © cy -1- 05 7

iim alse enclusing u reprint of ea Littie note on this
problem wuich I published in the J. of tie Term. Acé&d. OL SCe,
Whica has not yet found, io my knowledge, :. sympetnetic rezaer.

I ative a few comments on your 2aper ano will erriunge taese

=s footnotes to the type writcen copy waicn is murkea corres-
pondingly.

i. fhen we eetimetesa tne mutation rate from tue ween number
of mutzents we toux us the tueoretical mezcn not tue true wean
ef an infinite series o: tests but the disely wean to ve ex-

‘ pected in a limitea number of tests. Tne aiscrepencies betwe n

the two metnods of estim.téon of tac Mutution rate @esn not
be expluined in tue wu, you SUcceSte

Cee OL Lee Ve ee bata 2d 2

a ee (142g (2-2g)n72, 0.4)

3e I @B think think tois recurrence formu&e does not cuces
Withn tae preceding Line. 1 obtain instead

eile Tee Mee ne 7) EY
Thais leeds to a value ot

Un = é Fey} | teoee
  
   
      
  
 
 

 
 
  
  

eee eee ect
PCA Cet DES CST ee
mest \ Sa

arate rte CCR Cre ae On
pre acca ac nti sc ar

e to the different ways in wuich mute tior
Ds ceteetl aE 30 Sea cae eee tn be
are equivalent. Botn give ON as tie ween

 

       

Peer eer eC eee

ee ae a ee your method and ours for tue culculetion»
of the memente sre essentially tne same. You compare tiie woments
for n and for n+l generations and te BPE CM cE ee a SE
PE en a by -recurrence formulze, while we superimpose the voisson-Gistri-
rn eC ae ee ei aoe tO eh PSEA Chole MN Yse Ie TAME Ot: Cn
pes ae or eek Me Te CC eo to eliminate tue jackpots.

5. Tnis whole ergument was very enligntenin,, to me. 1 aad
CET TM TCM TE hee em eee lo I ba ht sl aed
MCMC Oct St. SMe CM ee Ca ERM oro D NS S
bias ot tne distrabutton in fevor of powers of two. From your
eye ae ECL RO Lhd only partially,
since only the leck of synchronésm in the terminal sections of
the pedigrees matters. I am not clear in ny mind as whet tue
distribution would be if one retains perfect PME see PP eT Mee
the bacterial divisions but allows mutetions to occur during
eny stoge of the division cycle. Even if the Butctions aid |
POT SET CRTC Te SC) Meee CC Se ME CMC CM Oe
eppeerance of resistence migut occur at any stage during tue
division cycle. I tnink this question of whether the distribu-
tion is or is not biased in favor of powers of two is worta
while following up theoretically and experimenteliy.

6. I do not understand the orizin of tue Lector in front of
tne exponential 1n tuis equation. also 1 aw douotful whetuer tue
result can be correct. Your argument, as I understand it, runs”
TT Oe a ae ee CCL ed
a eee Mee) Pes CORP eC PC we aR MR ee Ly

en LT
2(l-n)N/(2=h) (1-2h)
- eC CROCS Ra tm corresponding number in tne
PPT COC Pe CUCL me De a eT te
tion than in the stendard case. Consequently Po is smxd.ser tain
7
” ae Oe a TM Se ON se a eee ee Er ee oe Lok talgepedieeciteths oy ia ae
 

 

ts parcrentte Ets roe ome ti a ; :
Meee tse lL te Long as as the. Ro cd occur. crear ae 7 ee for bth
ae ea Ac Er ae Se oe,

     

 

- f sm. ae a? ca ere race 80 ee writing tats cert eae
‘and a.ve been Rol Sy CL Ro) oa mnUseripte waen i cane By rea Rit): ae
wes here first tue sywposiun and tnen a phcge course lor tured
bee tees neituer left PUPS Se CPC Lae Che ba mee etre a ete symyposiun — i
was wery “exciting, cia cel Me Came cee ese os WD eee ee people Perr} 7
tney aad indicetions of sex Lite in bacteria. If. bacteri: uave
sex it is entirely Peer ae thet it snaould be CECT aera) now

Oe tS mest) Bae) ee ToL) Se Rae eee Meer eney a: Bs at) doing experigents wits
 eneticully warked strains. Tue most exciting Ese Seb ee Tae

some done at Yale in ere leboratory by a Rh fellow Leder-
“berg. He first secured two double mutints of a strzin of boa cro P|
(X-ray induced). Eaca of the double mut.nts nam had two srowta
factor deficiencies. Gne wutanis was dcficient for a. ned BR, BLy,

-and the other for ¢ and D. Taen he grew these two mut nts to-

getner an broth. Then he pleted the mixture Gut on basal mediun

end obtsinec a few "prototrophs" i.e. colonies o: becteris re-
quiring no growtn fuctor. Hxesx He seendd to tuve ao:.¢ Osi OL

tne obvious control experiments. Le nas since triea to ao tue

same thing wita our strain "BE". He aid secure two doubic ae-

ficient mutents, but dia not ye. any prototropus wnen rowing
tnem togetuer.

pAS pap Rome clad me L-T-7 Ve a BEES to uo a similer experinent witu Te
tents of the phege resistence typo. He tuxes, sey, b/if/2 ana
B/3/4 .cna grows tiem together ana tucn tests to see wnetner ue
has eny B/1/2/3/4. So far no Luck.
With best regerds '

sincerely yours

Kie Delbriick

¥ ; ,
ane Cree Pe