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Amine Initiated Copolymerization of N-Carboxy-a-amino Acid Anhydrides1 B Y YECHIELSHALITIN~ AND EPHRAILI KATCIL~LSKI RECEIVEDM A Y 14, 1959
Kinetic data have been obtained for the diethylamine initiated lioriio~iolynierizati(~t~s c i f e,S-carbobenzoxy-c,S-carboxyL-lysine anhydride (L) and y-beiizyl-N-carboxy-~-glutan~ate anhydride (G) in dimethylformamide ( D M F ) . On copolymerizing these monomers i t was found t h a t the conversion rate in copolymerization is practically the surrl of the conversion rates of the individual monomers when polymerized singly, using tile same amount5 of solvent and initiator. Coinpositional analysis shows t h a t the more reactive monomer, G, is incorporated into the growing peptide chains about 2 . 5 times more rapidly than the other monomer, L. From these results i t is cmclutled t h a t i n tlie bimolecular propagation reaction only the monomer, and not the nature of the active end of the groiviiig chain, determines the copolymerization rate. Other pairs of N-carboxy-or-amino acid anhydrides were found to copolymerize in a mechanism similar t o t h a t described for L and G. Based on these findings the chain length distribution a r i u the compositional distribution of the copolymers were calculated,
The synthesis of a considerable number --L-glutamate anhydride, G, in the polymerization mixture, while X ' c gives the molar fraction of the glutamic acid residue in the initial copolyrner formed. c [GIo/[L]o gives the initial ratio between the corresponding monomers, while [Glu]/ [Lys] gives the ratio between the corresponding residues in the intial copolymer formed. 0.3
.1
0.25
0.67
0 .3 3 , 00
April 5, 1960
COPOLYMERIZATION OF N-CARBOXY-a-AMINO ACIDANHYDRIDES
1633
ported demonstrate t h a t the ratio between the glutamic acid to lysine residues in all the copolymers investigated is approximately 2 to 2.5 times greater than the molar ratio between [GIo and [Ll0in the initial copolymerization mixture. These findings demonstrate clearly t h a t a t equal molar concentrations the probability of G t o react with a growing chain is about 2.5 times greater than that of L. The composition of the copolymers obtained after 20y0 conversion as a function of initial monomer ratio is represented graphically in Fig. 5.
0.2
!
;/i 0.2
0.4
0.6
0.8
J
X G.
Fig. ,i.--RIolar fraction of glutamic acid residucs ill glutamic acid-lysine copolymers, S ' a , obtained after 2OY0 conversion, as a function of molar fraction of glutamate component in initial monomer mixture, XG. The conditions of copolymerization are specified in Table 11. The full curve gives the values of X'G calculated according t o eq. 8.
Change in Composition of the Glutamic AcidLysine Copolymer during Polymerization.-As G reacts with the growing peptide chains considerably faster than L, the relative amount of the free lysine monomer will increase during the copolymerization. It could therefore be expected that the relative amount of the lysine residues in the GluLys copolymer formed will also increase with time. Such an increase was demonstrated experimentally in three copolymers derived from diff ercnt initial [GIo/[L]omixtures (see Table 111). TABLE I11 MOLARRATIOOF GLUTAMIC ACID T O LYSIKE RESIDUES OI? cOPOLY?dERS ISOLATED FROM THE POLYhlERIZATIOX h I I X -
TURE AT
DIFFERESTTIMEISTERVALS
0.77 1.41 1.16 1.56 1.50 0.67 1.66 2.50 2.40 3.00 1.50 3.12 4.30 G.66 5.00 7.70 4,O 9.00 Crrpol!-inerizations were performed in IO n i l . o f DJIP a t 25'. The reaction mixtures cuntaincd 3 X IO-j niolc o f diethylnniirie, and a total amount o f mule of monomer.
The significant difference in composition of copolymers derived from L and G copolymerization a t the beginning and toward the end of the
Fig. 6 -Electrophorograrn of the initial and final glutamic acid-lysine copolymer: 1, copolymer obtained after 20% conversion; 2, copolymer obtained after complete reaction; 3, glutamic acid, 4, lysine. For details see text.
Additional proof for the change in composition of the polypeptides was given by the estimation of
their N-terminal glutamic acid and lysine residues by the dinitrophenylation method described in the Experimental part. Copolymers isolated at 25, 3.0 and 93'/c conversion from a polymerization mixture which contained initially 5 X mole of G, 5 X l o p 4 mole of L and 2 X mole of diethylamine in 10 nil. of D X F , possessed N-terminal glutamic acid and lysine residues in a molar ratio of 3.0, 1.3 and 0.22, respectively. Copolymerizaiion of Other Pairs of N-Carboxya-amino Acid Anhydrides.-Copolymerization experiments performed with L-phenylalanine-NCA and ~,N-cbzo-~-lysine-SCX, L-phenylalanine-XCA and y-benzyl-L-glutamate-NCA, glycine-NCh and e,N-cbzo-L-lysitie-NCB,e,N-cbzo-r--lysine-NCAand DL - alanine - NCA, or y - benzyl - L - glutamateNCA and m-alanine-NCX, in dimethylformainide using diethylamine as initiator revealed that the course of copolymerization of these monomer pairs was similar to the copolymerization of e,?J-cbzolysine-NCX and y-benzyl-L-glutamate-NCA. The rate of copolymerization in all cases equalled the sum of the rates of homopolymerization of the corresponding, individual monomers (see Table IV). I n copolymerization experiments performed in 10 ml. of DMF a t 25' with glycine-NCA (4 X mole, k = 40 l.mole-linin-l) and y-benzyl-Lglutamate-NCX (G X 10F4 mole, k = 10 l.mole-l mole, K = 7 xiiin,-l) or sarcosine-NCX ( 3 x l.molc-lniin.-l) :mcl y-benzyl-L-glutamate-Tu'CX mole), using diethylamine (5 X (5 X mole), as initiator, it was noticed, however, that the copolynierization proceeds in the later stages of the reaction a t a considerably lower rate than
1634 TABLE
I\'
SPECIFIC RATECONSTANTS OF ~IOMOPOLUMERIZATION ASD COPOLYMERIZATION OF PAIRS OF KCAs ( A A N D U )" k.1,
IAIa,
XCA of:
mole I .
1. mole-1 -1
11:
h-CA of
min. - 2
0.05 11.5 e-cbzo-L-lysine .05 11.5 r-benzyl-L-glutamate .33 40 e-cbzo-L-lysine .05 6 e-cbzo-t-lysine .05 6 y-benz yl-L-glu tamatc All t h e polymerizations were initiated with 0.004 A4 diethylatniiie aiid copolymerization constants were derived from eq. 4. L-Phenylalaninc L-Phenylalanine Glycine DL- Alanine DL- Alanine
t h a t expected from the sum of the homopolynierization rates (see Fig. 7). Discussion Analysis of the Kinetics of Copolymerization.As stated above, the data on the hornopolymerizations of G and I, may be represented by eq. 2 which was derived for a NCh-polymerization devoid of a termination reactioii when the specific rate of propagation equals that of initiation. l6
fieon. I 5 . 0 , I . mole-1mrn.-l Exptl. Calcd.0
kH,
lo,
mule 1.
:
1. mule-'
min. - 1
-1
3.5 10 4
0 , 05
8 7.5 10.5 11.2 ,067 16 16 .05 4 5.5 5 .u5 11 0 8.5 perfornicd in DMI: at 25". * T h e calculated
.05
instant is given by the sun1 of the propagation rates of the individual monomers when polymerized at the corresponding monomer and initiator concentrations. The rate of consumption of the individual monomers in the copolynierization reaction may therefore be represented by -d[Glidt = KG[I]O[GI,[GI = [Glo exp(-kkc, [Ilut) (6) -d[Llldt
=
~ L [ I ] O [ LIL] I;
[LIo exp( - k ~ [ I l o t )
=
Formulas 6 are similar to those describing the respective honiopolynierir,ation re?' C t'1011s. Copolymerization reactions are generally goverried by the four different propagation constants k l l , k ~ k z ,l arid K?s
I' ' I
I
I
' 1
-A ki? *-A t B --+w B
I
0
I
v H
0" V
--u
k + A -+ --h
0.4
),
fu
20
40 GO Time minutes. Fig. 7.-Carbon dioxide evolution as EL functioii of time for the diethylamine initiated polymerization of the followglycine-XCX ( 4 X ing N-Chs in DMF a t 25': mole); 0-0, r-benzyl-L-glutaiiiate-XC.~ (6 X 1I)P mole); A-A, glyciiie-NCX ( 4 X mole) mid -,,-benzylL-glutamate-NCX ( 6 X l o u 4 mole). T h e dotted curve is the sum of curves a -m and 0-0. All the polymerizntion reactioiis were carried out in 10 ml. of DMF, using 5 X 10-6 mole of initiator.
.-.,
The values found for the specific rate constants of homopolymerization of the various NCAs tested are given in Table I. A comparison of the course of copolymerization of G and L with that of the corresponding homopolymerization reactions (see Figs. 1 arid 2 ) shows that the rate of copolymerization, -d[G+L],/dt, may be represented to a good approximation, by -d[G
or
T A -----f
t
0
ki I
.-A
4-L l l d t
+
-d[G Ll/dl where the coeiscient
kc[I]o[G]
+ k~[Ilo[Ll
kw,,[lIo[G
(5)
+ Ll
111 eq. 5 it is assumed, in agreement with experiment, that the rate of copolymerization a t any
k.. -+MI13
deterniiiiiug the rates of the different reactions given above, where -A andmB denote propagating chains with terniinal -4 or B residues. Two specific rate constants ( k L and k G ) , however, suffice to describe the copolymerization of L and G. The kinetics of this copolymerization may therefore be described by the assumption that k11 = k,, = kr, and k,, = k l z = k G . The rate of propagation in the copolymerization reaction seems there fore to be determined mainly by the cheniical nature of the reacting XCA4and not by the nature of the terminal amino acid residue, bearing the reacting free a-amino group, of the growing peptide chain. The rate of reaction between NCAs and primary or secondary aniines is usually determined by the basicity of the amine and by the cllemical structure of the S C X . The basicity of the terminal a-amino groups of the growing peptide chains does not vary significantly with the chain length or with the character of the N-terminal amino acid residue. On the other halid, Gallard and Bamford17 have shown that substitution at the a-carbon of the KC.1 may influence the reactivity of the 5carbonyl of the oxazolidine-2,~-dione. The over-all specific rate constant of the copolymerization reaction at the early stages of the reaction, is given by eq. 4 as ey .? a t t+O reduces to
Ii - d[G - - ~+_L11 _ dt \ (17) D . G. H (1958).
= i+o
Hallard a n d C . H
Uamford, J . Chem. Scc., 355
April 5 , 1960
C O P O L Y M E R I Z A T I O N OF ~ - C A R € 3 O X Y - a - 4 M I i Y O h C I D . & N I I Y D R I D E S
Since k G is larger than k L , G is consumed faster than L during the copolymerization. The reaction mixture toward the end of the copolymerization will therefore contain only traces of G and a relatively large quantity of L, if these were initially present in equal amounts. The value of kcop a t this stage of the reaction will be given by kcop = k L . t-
- --- - _- - - - - _ _ _
m
The assumptions made concerning the mechanism of copolymerization permit the calculation of the composition of copolymers obtained a t low conversion. At the initial stages of the copolymerization the ratio between the amounts AG' and AL' incorporated into the polymeric fraction
where a = k G / k L , and [GIo and [LIDdenote the initial concentrations of the monomers. The factor a thus designates the relative enrichment of the polymeric fraction with respect to the more reactive monomer. Equation 7 may readily be transformed to where X G denotes the molar fraction of the G monomer in the initial polymerization mixture, while Xi:gives the molar fraction of the G residues in the copolymer obtained a t the initial stages of the copolymerization. Figure 5 gives the theoretical curve derived from eq. 8 assuming a = 2.5. The experimental data (see Table 11) concerning the composition of the copolymers formed in the early stages closely fit those expected. In the type of copolymerization here considered the composition of the copolymers formed varies with time. The ratio [G]'j[L]' between the Glu and the Lys residues of the copolymer as a function of time and initial monomer composition is given in eq. 9 as derived from the equations 6.
I40
120 200 280 Time, minutes. Fig. 8.-The composition [G]'/ [L]' of the copolymer formed as a function of copolymerization time. Initial monomer mixture contained e,N-cbzo-L-lysine-iKA (6 X mole) and y-benzyl-~-glutamate-n'C.4 (4 X lo-* mole) in 10 ml. of D M F . T h e polymerization was initiated by diethylamine (2 X 10" mole) and performed at 25'. T h e circles give the experimental findings, while the dashed curve represents the expected values according to eq. 9 assuming kc = 10 1. mole-' min.-' and k L = 3.5 1. mole I min.-'.
where kdv = kc[G]dt
or
+ k~[Lldt
-d[Il/dt
= [I1 (kc[Gl
+ k~[Ll)
(10)
[I] = [I]ge+"
(12)
The concentration [Nj] of growing chains composed of j amino acid residues varies with time according to eq. 13 d [ N , ] / d t = kc[Nj-i][G] 4- k ~ [ N j - i ] [ L ] ~ G [ N [GI II
- ~ L [ N ,[LI I
(13)
which on introduction of eq. 11 gives
- k[S,]
(14)
This procedure is justified in the present case since the specific initiation rate constant is close to that of propagation (see above). Successive solution of the last set of equations gives
The last equation shows that the chain length distribution of the polymer formed is Poissonian, and thus resembles the distribution obtained in a homopolymerization of NCAs, in the absence of a termination reaction. '6 A similar conclusion was derived by Gold. From eq. 15 it follows that the number average degree of polymerization, DP,, approximately equals the weight average degree of polymerization, DP,, and is given by eq. 16.16 DP, = DP, = k v (16) Compositional Distribution.-By a statistical calculation analogous to that of Katchalski, et a1.19 (18) L. Gold J Chem. Phys., 21, 1190 (1953). (19) E Katchalski, M Gehatia and M. Sela, TAWJOURNAL, 77,
may be rewritten in the form -d[I]/'dv
(11)
Integration of (loa) gives
d[N,]/dv = k[h'j-i]
The expected change with time in the composition of a growing copolymer derived from an initial [GIo/[L], = 0.67 monomer mixture, assuming for k~ and k L the values 10 1. mole-lmin.-l and 4 1. mole-lmin.-l, respectively, is given in Fig. 8. The experimental data obtained fit closely those calculated. Molecular Weight Distribution.-In a previous paper16 i t was demonstrated that when the polymerization of NCAs is initiated by primary or secondary amines and no termination reaction takes place, polymers with a Poissonian chain length distribution are obtained. Below, it will be shown that a similar chain length distribution is to be expected in amino acid copolymers derived from a reaction mixture in which the rate of propagation is determined by the specific rate constants k G and k L defined previously. Equation 10, describing the rate of initiator consumption
1G33
k[I]
(loa)
6175 (1955),
XNNE BUZZELL
1GBG
Vol. 8,"
T h e expression obtained for N L may , ~ also be d e rived by successive solution of the following set o f kinetic equations tlescribing tlic rate of formation of peptide chains composed i i f I lysin? residues :md g glutaiiiic acid residues
t'[NI'l = tlt
f i r IV(i
1)
][I,] ki
+ ki,[R;l
[GI
[xi 1 ILI - ~
-
L [ ,IS[GI
(15)
The total concentratioii [N, ] of copolymer chains composed of j amino acid residues may be derived from eq. (17) on summation over 1 values from 0 to j , for the c a s e j = Z+g. The expression thus obtained is identical with that given in eq. 15. T h e concentration [XI] of molecules containing I residues of amino acid L, irrespective of the number of residues of amino acid G , is given by [Si]=
2
[Yl
,= 0
)]
=
(y
[I]"
c
-'I
"1
(19)
Equation 19 shows t h a t the Poisson distribution of Nl is the same as that of the corresponding homoIO
30 50 1. Fig. 9.-The relative number of chains containing 1 lysine residues and g glutamate residues [ N ~ , , ] / [ I ] o( I -k g = GO), in copolyiners obtained by the copolymerization of L and G a t a monomer to initiator ratio ( [LID [GIG),' [I10 = GO. The given curves were calciilntcd according to eq. 17 for k1.w = IO, 20 and 30.
+
(see their eqs. 1 to 9) for the molecular weight distribution of homopolyamino acids, it can readily be shown that the concentration [ N L . of ~ ]copolymer molecules composed of I residues of the amino acid L and g residues of the amino acid G is given by [ N 1 , , ]= [ I I o @Lvl:i l!
' 1-2-2 k r v r l exp( -kI,vL g!
-kc,vi:)
(17)
where = j [ I . , c l t anc1 v(: = 0
j-,G] v I , / k G v G The formulas given above for the molecular weight distribution and the compositional distribution derived for the Lys-Glu copolymers obviously apply to the copolymers derived from the other pairs of NCAs which undergo copolymerization a t a rate which equals t h e sum of t h e rates of the homopolymerization of the corresponding component monomers under similar conditions. Acknowledgment.-This investigation was supported by a research qrant (PHS H-2279) from U S A. National Institutes of Health, Public Health Service REHOVOI'II, ISRAI7
0
BY ANNE BUZZELL RECEIVED AUGUST7 , 1959 Six molar urea at 0' degrades tobacco mosaic virus within 20 minutes into app:irent!y intact RXA having sedimentation constant, &w, 30 and into the smallest subunit of protein with .S20u about 2. Intact monomer virus is less stable than fragments. T h e monomer is degraded in 2 minutes to rods, measured in electron microgmphs, ranging from 2/3 t o '/2 the original length. After 6 minutes these stable intermcdintes begin t o degrade further. Fragments do not degrade appreciably in 6 minutes b u t are mainly gone in 20.
Introduction virus is destroved by whereas infectivity R S X is not.4 The other of phenol extracted The nlechanism of urea action on tobacco Inosaic virus (Thf[T) has appeared paradoxical in two paradox is that the virus protein appeared to be respects. One paradox is that infectivity of the ( 2 ) m.n . ~Stanley a n d M. A. ~ a u f i e r .,\ ; a t w e , 89, 345 (1089). ( 1 ) Publicntion No, 60 of t h e D e p a r t m e n t of Biophysics. T h i s research was supported b y contract nu. AT(30-1)913, Atomic E n e m y Commission.
( 3 ) 11. A . 1 , n ~ l f f e r a n d TT
11 Stanley, A u c h . Biorhrln., 2, ,413
(1043).
(1)F. C Tl:iwvllen a n d N . \T I'irie, J . C i w .Mir~obiol , 17, 80 (1057).
