LEVlTZKl
m;inuacript R c fe re n ccs 13arnes. :E M., Jr., and Kaback, H. R. (1971), J . Biol. (‘howl. 246, 5518. ox. G . R., Newton, N . A., Gibson, F., Snoswell, A. M . , ,ind Hamilton, J. A. (1970), Biochem. J . 117, 551. Davis. B. D., and Mingioli, E. S. (1950), J . Bacteriol. 60, 17 Flcctr. S . , Zakim, D., and Vessey, D. A. (1973), J . Mol. H i o l . 78, 351. tiong. K.. and Hubbell, W. L. (1972), Proc. Nut. Acad. .Yc.i. L’. S . 6 9 , 2617. flubbcll. W. l.., and McConnell, H . M. (1971), J . Amer. C ~ h P U I S. O C ~ .Y3, 3 14. l m t . P C., Capeldil, R. A,, Vanderkooi, G., and Griffith, 0 , I { . ( 1973), J . Supramol. Struct. I , 269. kaback, H . R . (1971), Methods Enzymol. 22, 99. Kuback, k l . R . (1972), Biochim. Biophys. Acta 265, 367. Kaback. tl. R . ( 1 974), Science (in press). K;ib;ick. t i . R . , and Barnes, E. M . , Jr. (1971), J . Biol.
AND SCHLESSINGER
Chem. 246, 5523. Kaback, H. R., and Hong, J. (l973), C R C Critical Reviews in Microbiology, Vol. 2, Laskin, A. I., and Lechevalier, H . , Ed., Cleveland, Ohio, Chemical Rubber Co. Keith, A,, Sharnoff, M., and Cohn, G. E. (1973), Biochim. Biophys. Acta 300, 379. Kohn, L. D., and Kaback, H . R. (1973), J . B i d . Chem. 248, 7012. Lombardi, F. J., and Kaback, H. R. ( 1 972), J . Biol. Chem. 247, 7844. McConnell, H. M., and McFarland, B. G . (1970), Quart. Rev. Biophys. 3, 91. Morrisett, J. D., and Drott, H. R. (l969), J . Biol. Chem. 244, 5083. Rottem, S . , and Samuni, A. (1973), Biochim. Biophy.r. Acta 298, 32. Schuldiner, S., Kerwar, G. K., Weil, R., and Kaback, 1H. R. (1974), J . Biol. Chem. (in press). Seelig, J . (1971), J . Amer. Chem. Soc. 93, 5017. Yu. K., Baldassare, J. J.. and Ho, C. (1974), Biorhemistry 13, 4375.
Cooperativity in Associating Proteins. Monomer-Dimer Equilibrium Coupled to Ligand Binding? .4lexander Levitzki* and Joseph Schlessinger
,\I COOPERATIVITY IN ASSOCIATING
PROTEINS
LE+,] = K,[ES]' = K,Kz2[E]2[S]2 (8 1 It is apparent that the total enzyme concentration [E]T is LEI77 [ E ] 4 2[E,1 + [ESJ + 2[EzSI + 2(E,Sz] (9) By inserting eq 5 , 6, 7, and 8 into eq 9 one obtains
LEIT = [El +
+
Kz[EI[SI
2KpT,[E]2[S]
+
+
2K&z?l E]'[S]"
(10)
-440 -280
-120
-440 - 2 8 0 LOG
Rewriting eq 10 one obtains
- 4 4 0 -280
-I20
-120
[SI
V' ' " K ,'
2(1(, + K 2 K 3 [ S ]+ K,K,2[S12)[E]2 +
2 40- K , : I O ~
-1
(1 + K2(S])[E] - [E]T = 0 (11) Solving the quadratic equation one obtains an expression for the free enzyme concentration [E] -(1 - K 2 [ S ] )+ {(l + K , [ S ] ) ? + 8 ( K ,
+ LOG [SI
F I G b R E 1:
tration =
The saturation function, 1 -4 i s
p, for
Cases with no dimer species formed. Total enzyme concenM . Other details are given in the text.
the system described in eq
When K I = IO6, K2 = IO3, and K3,K4 = 1 , saturation begins only a t high ligand concentrations. From the above considerations one concludes that in order for a dimerizing Therefore monomer to bind substrate, one of the following two conditions must be fulfilled: ( I ) a moderate affinity of the monoI~ +_ lE2SI + _~LEzSZI _ _ _ _ IESI (14) ~mer toward the ligand or (2) very high dimerization constants ( K 3 and K 4 ) when the monomer affinity is low. 1-r[El 2LE21 + LEzSI At high K2 values ( K 2 > lo4) the main binding process Inserting eq 5-8 into eq 14 one obtains occurring will be to the monomeric form and the main I' K21S] + KzIC31E][S] + 21 K2 and K3 > K4 as in Figure 4G. However, under these conditions the enzyme is largely a dimer in the absence of ligand. It can be seen that this case is an example of negative cooperativity in the transformation: E2 2 s 2ES. Effect of Protein Concentration, The calculations described were performed, assuming an enzyme concentration of 10- M. The concentration is within the range of values chosen for 1 / K l , 1/K2, 1/K3, and 1/K4. Under most conditions chosen no dimer is found in the absence of ligand since the aim of this study is to explore the transformation of monomer to dimer as a function of ligands bound. Upon increasing enzyme concentrations enzyme dimer may form in the absence of ligand. If the enzyme concentration tested is within the range of 1/Kl significant dimer concentrations may exist in the absence of added ligand. The change in cooperativity of ligand binding as a function of protein concentration will depend on the relative values of K I l K 2 , K3, and K4. In the extreme case where [enzymeItotal > l / K l , the enzyme will be exclusively in the dimeric form prior to ligand binding. Under these conditions the cooperativity in binding will depend on the ratios K4K2/K3, namely on the ratio of ligand affinity toward E2S to that toward E2. This case. therefore, represents the study of ligand binding to a dimer where the dimeric form is preserved as a function of ligand concentration. It is clear that the value of this ratio determines the type of cooperativity observed (Levitzki, 1974) and this cooperativity is exclusively due to the subunit interactions within the dimer. Some examples as to the dependence of the Hill coefficient
-
+
-1.20
.240[-1 320
,
,
,
l
-440 -280
, -120
LOG [SI
FIGURE 4: The formation of E2S. Total enzyme concentration = IOw5 M. The relative amounts of ES, E2S, and E& at the end of the titra-
tion are shown on the figure. Other details are given in the text.
on protein concentration for different sets of K values are summarized in Table 111. In general, for the same set of K values the cooperativity will either remain unchanged, or decrease as a function of protein concentration. One can in fact prove (see Appendix) that the effect of increasing protein concentration is to diminish the cooperativity. Discussion In a system where a monomer to dimer transformation coupled to ligand binding the two types of cooperativity, positive and negative, can be generated. The basic rules which govern the system can be summariled as follows (see Table IV). (a) At any protein concentration used, in order for ligand binding to occur a t all, the monomer form must have finite affinity toward the ligand. If the monomer-ligand dissociation constant ( 1 / K z ) is one or two orders of magnitude higher than total enzyme concentration, positive cooperativity can be generated a t fairly low ligand concentrations. If the monomer-ligand dissociation constant is within the range of enzyme concentration ES will form and the cooperativity in ligand binding will decrease. (b) The
Behavior of the Dimerizing System as a Function of the Characteristic Parameters. ~~_________ __ Predominant Species Parameter Range of Other Parameters during Titration
TABLE I V :
-~
I _ . -
_ _ ~ _ _ _ _ _ ~
K?
=
1
K? = 103
K~IK > ~103 K I ~ K > ~IO6
Ka = lo6 K4/Ka = 1 KS = lo6 K I I K ~< 1
____
1-10', a 11 combinations K ~ K$ ~ K~ , = 1-103, all combinations K~ = 103, K~ = 1-103, all combinations K.? = 103, K, = 1-103, all combinations K? = 103, K~ = 1-103 K~ = 103, K~ = 1-103
Ki?Ka, K.j
=
____
_ _ . _ I . _ . .
.___
Type of Cooperativity (Max. Hill CoefT.)
____
__
N o binding
N o binding
E, ES
E, E2S2
N o cooperativity (nH = 1) Positive (~ZH= 1 . 5 )
E, E&
(nII =
E, E2S, E2S, E&
Negative (nit < 1 .O)
E, ES, E2S
Negative
BIOCHEMJSTRY, VOL.
2 0)
(nH
< 1,O)
13, NO. 25, 1 9 7 4
5217
LEVlTZKl + I L L PLOT5 FOR D LACTATE
€NZYHE
7
'
'
'
i
f
n,
40
-
DEHYDROGENASE AT DIFFERENT
CONCENTRATIONS
, , , I ,
,
I
, , I
,
a log
" 1 ' 8
.-.
I-
__
00025pMenrlm;
enzyme concentration than a t low enzyme concentration for each set of association constants. Since B[E]/J[S] is a negative number, the term 2K2Kl [SI2(a[E]/a[S]), in the nominator in eq 16, will become more negative as [E]T increases. The net result is, therefore, that n decreases with increasing [E]T (Table 111). That this is indeed the case in real systems is seen in Figure 5 , where the effect of protein concentration on the cooperative response of D-lactate dehydrogenase toward pyruvate was studied. Although the data presented in Figure 5 are based on saturation kinetics rather than on binding studies, in every regulatory enzyme thus far studied the assumption that p = v/V,,, was found to be valid. General Significance. Equations 12- 16 can be used to fit ligand binding data and obtain the values for K1 through K 4 . If experiments are conducted at different total protein concentrations, [E]T, the quality of the fitting can be analyzed. Biological Significance. The response of a protein to a ligand in a situation where the protein associates or dissociates upon ligand binding offers a means of controlling the response, by the change in the total concentration of the protein. This device can be extremely efficient especiallj when a large difference in ligand affinity exists between the dissociated and the aggregated species of the protein. I t is interesting that in very cooperative proteins where the Hill coefficient measured approaches the total number of binding sjtes, it is found that the protein represents an aggregating system in which the aggregation process is tightly coupled to ligand bindings (Table V). It may be suggested that whenever high degrees of cooperativity had to be attained
A--b.O025uMcnrrme
F I G U R E 5: Hill plots for D-lactate dehydrogenase from Aerobacter aerogenes. The Hill plots were constructed from the data published by Sawula and Suzuki (1970). The plots demonstrate the characteristic features of cooperativity in aggregating systems. The system is highly cooperative at low enzyme concentrations. The Hill coefficient of 1 .O at high enzyme concentration indicates the existence of aggregated species exclu_sively, throughout the titration range. In this study it is assumed that Y = v/V,,,.
degree of positive and negative cooperativity strongly depends on the ratio K 4 / K 3 . (c) Negative cooperativity becomes more pronounced as the ratio K 4 / K 3 decreases. When the ratios K 4 / K 3 become very low, no E& is formed and E2S is converted to ES during the titration (Figure 4G). (d) Increasing protein concentration generally decreases cooperativity (Figure 5 ) . Effect of Total Enzyme Concentration. When [E]T is increased the cooperativity in the system decreases for each set of K 1. K2. K 3 , and K4 (Table 111). This effect is seen in the expression (eq 16) which describes the dependence of the Hill coefficient (see also the Appendix). If one selects certain [S] values for different [E]T values and investigates the value of n as a function of increasing [E]T, the following picture emerges. As [E]T goes up, [E] also will go up, and the rate of change of 4K2 [E] [SI and 2K2K 1 [E] [SI is identical. However, upon increasing [E]T, the value a[E]/a[S] also increases. This is true since more protein will bind ligand for every increment of substrate a t high total
TABLE v :
High Hill Coefficients in Aggregating Enzymes.
Enzyme
No. of Subunits in Dissociated Aggregated Species Species
Ligand Promoting Assn
Highest Hill Coefficient Obsd
D-Lactate dehydrogenase
1
4
Pyruvate
4
N *0-Formyltetrahydrofolate synthetase Phosphofructokinase
1
4
NH4'
4
2
2n
Fructose
3 4
CTP synthetase
2
4
UTP
4'
ATP
4''
a
In the presence of subsaturating ATP. In the presence of subsaturating UTP.
5218
A h D SCHLESSINGER
BIOCHEMISTRY. VOL. 13, hO.
2 5 , 1974
Ref Sawula and Suzuki (1970) McKenzie and Rabinowitz (1971) Froede et a / . (1968); Mansour and Ahlfors (1968) Long and Pardee (1967) Levitzki and Koshland (1972)
COOPERATIVITY
IN ASSOCIATING
PROTEINS
strong subunit interactions had to evolve in the protein. The largest change in subunit interactions expected upon ligand binding would indeed be when the subunits are physically separated when unliganded and tightly associated when liganded. Similarly, high cooperativities can be generated when the nonliganded subunits are strongly aggregated in an oligomeric structure and dissociate upon ligand binding.
SO one
Appendix A relatively simple analytical expression for the Hill coefficient in a dimerizing system can be arrived at for a case in which the species E2S and E2 never accumulate to a significant extent. The cases which qualify to this restriction actually are the cases where the highest cooperativity is seen. With these restrictions eq 14 simplifies to
Cassman, M., and King, R. C. (1972), Biochemistry 11, 4937. Duncan, B. K., Diamond, G. R., and Bessman, M. J. (1972), J . Biol. Chem. 247, 8136. Froede, H . C., Geraci, G., and Mansour, T. E. (1968), J . Biol. Chem. 243, 602 1. Klotz, I. M., Langerman, N. R., and Darnall, 0. W. (1 970), Annu. Rev.Biochem. 39, 25. Koshland, D. E., Nemethy, G., and Filmer, D. (1966), Biochemistry 5, 365. Levitzki, A. (1 974), in Subunit Structure and Interactions of Proteins, Ebner, K. E., Ed., New York, N.Y., Marcel Dekker, in press. Levitzki, A., and Koshland, D. E. (1969), Proc. Nut. Acud. Sci. U. S. 62, 1121. Levitzki, A., and Koshland, D. E. (1972), Biochemistry ZI, 247. Long, C. W., and Pardee, A. B. (1967), J . Biol. Chem. 242, 4715. Mansour, T. E., and Ahlfors, C. E. (1968), J . Biol. Chem. 243, 2523. McKenzie, R. E., and Rabinowitz, J. C. (1971), J . Biol. Chem. 246, 3731. Monod, J., Wyman, J., and Changeux, J. P. (1 9 6 9 , J . Mol. Biol. 12, 88. Sawula, R . V., and Suzuki, I. (1970), Biochem. Biophys. Res. Commun. 40, 1096.
(17)
namely
1 - r
or
[El
-
Y= K,[S]
1 - Y Therefore
+
(18)
-
Y log -1 - Y
= log (Kl[S]
-
but
a log n =
X&z2[E][S]2
a
I’ ~
+
U ( , K Z ~ [ E ] [ S ] ~ )(19)
-
-
1 - Y log [sq-
-
Y a log [SI a[s]
(20)
obtains
References
BIOCHEMISTRY, VOL.
13,
NO.
25, 1974
5219
