A general model of cooperativity and its application to DPG inhibition of hemoglobin oxygenation.

A GENERAL MODEL OF COOPERATIVITY AND ITS A P P L I C A T I O N TO DPG INHIBITION OF HEMOGLOBIN OXYGENATION Judith Herz fe ld + and H. Eugene Stanley* +Depa r tmen t of C h e m i s t r y , " D e p a r t m e n t of P h y s i c s , and +*Center for Ma te r i a l s Science and Eng inee r ing M a s s a c h u s e t t s Inst i tute of Technology, Cambr idge , M a s s a c h u s e t t s 02139 Received April 6, I972 S u m m a r y : A gene ra l mode l of coope ra t i v i t y has been developed that combines the concep ts of p r e f e r e n t i a l binding, t e r t i a r y subunit in te rac t ion , and q u a t e r n a r y cons t ra in t . The mode l s of Monod, Wyman and Changeux, and of Koshland et al. , a r e l imi t ing c a s e s of this gene ra l theory. Ano the r spec ia l case of the gene ra l model , app rox ima t ing the P e r u t z de sc r ip t i on of hemoglobin, f i ts monoand b i -phas i c hemoglobin oxygenat ion data, o v e r a wide range of 2-3 Diphosphog lycera te (DPG) concen t r a t i ons , with a total of five adjus table p a r a m e t e r s , and p red i c t s that the change f r o m deoxy to oxy q u a t e r n a r y s t r u c t u r e o c c u r s just be fo re o r just a f t e r the third heine is oxygenated, depending on the DPG level. 1 The a l l o s t e r i c mode l of Monod, Wyman, and Changeux (MWC) explains coope ra t i v i t y in t e r m s of p r e f e r en t i a l binding of subs t r a t e to d i f ferent m o l e c u l a r c o n f o r m a t i o n s , and q u a t e r n a r y c o n s t r a i n t s which main ta in m o l e c u l a r s y m m e t r y . Coope ra t i v t t y has a lso been explained by Koshland, Nemethy and F i l m e r 2, in t e r m s of induced-f i t binding of subs t r a t e and in t e rac t ions be tween subunits in d i f ferent t e r t i a r y confo rma t ions . Both t heo r i e s explain posi t ive coopera t iv i ty . However , only the coope ra t ive m e c h a n i s m of Koshland, et al. explains negat ive coopera t iv i ty , and only the coopera t ive m e c h a n i s m of MWC explains c o o p e r a t i v i t y when s t r u c t u r a l change does not coincide with subs t r a te binding. The coope ra t ive m e c h a n i s m s of both t heo r i e s have been combined in a 3 ,4 single mode l which is d e s c r i b e d in g r e a t e r detail e l s ewhe re ; the MWC and Koshland theo r i e s a re spec ia l c a s e s of this gene ra l mode l (see Table I). Ano the r spec ia l case is p a r t i c u l a r l y appl icable to hemoglobin: P e r u t 2 has sugges ted that c o o p e r a t i v i t y a r i s e s f r o m the combina t ion of induced-f i t binding of oxygen, as hypothes ized by Koshland, and q u a t e r n a r y c o n s t r a i n t s , as hypothes ized by MWC (see Table I). The gene ra l mode l a lso i n c o r p o r a t e s two m e c h a n i s m s for e f f ec to r act ion: (1) E f f ec to r mo lecu l e s m a y in te rac t d i r e c t l y (' d i r ec t e f f e c t o r s ' ) with bound