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Cyclic nucleotide phosphodiesterases of the superior cervical ganglion Boudreau, Robert James 1975

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CYCLIC NUCLEOTIDE PHOSPHODIESTERASES OF THE SUPERIOR CERVICAL GANGLION Rohert James Boudreau B.Sc.(Hons.), U n i v e r s i t y of Saskatchewan, 1972 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of Pharmacology We accept t h i s t h e s i s as conforming to the requir e d , standard THE UNIVERSITY OF BRITISH COLUMBIA J u l y , 1975 In presenting th i s thesis in pa r t i a l fu l f i lment of the requirements for an advanced degree at the Univers i ty of B r i t i s h Columbia, I agree that the L ibrary shal l make it f ree ly ava i l ab le for reference and study. I fur ther agree that permission for extensive copying of th i s thes i s fo r scho lar ly purposes may be granted by the Head of my Department or by his representat ives. It is understood that copying or pub l i ca t i on of th i s thes is fo r f i nanc ia l gain sha l l not be allowed without my writ ten permission. Department of The Univers i ty of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 ( i ) ABSTRACT A m o d i f i c a t i o n of the assay of c y c l i c n u c l e o t i d e phosphodiesterase i n v o l v i n g batch use of Dowex 1 anion exchange r e s i n was developed. This assay produced q u a n t i t a t i v e r e c o v e r i e s of adenosine, guanosine, and t h e i r metabolites from the r e s i n s l u r r y . The assay was s u i t a b l e f o r use i n crude preparations c o n t a i n i n g purine c a t a b o l i z i n g enzymes. C y c l i c n u c l e o t i d e phosphodiesterase was examined i n canine and bovine s u p e r i o r c e r v i c a l g a n g l i a . A c t i v i t y i n crude supernatant f r a c t i o n s was only s l i g h t l y s t i m u l a t e d by C a + + despite the presence of p r o t e i n a c t i v a t i n g f a c t o r . Three forms of phosphodiesterase were resolved from bovine g a n g l i a supernatant e x t r a c t s by chromatography on DEAE-cellulose. The f i r s t enzyme elu t e d (Dj) was completely s p e c i f i c f o r c y c l i c GMP, while the other two ( D -J-J and D J J J ) hydrolyzed both c y c l i c AMP and c y c l i c GMP ; a l l were f r e e of heat s t a b l e p r o t e i n a c t i v a t o r . Each enzyme was i n h i b i t e d by low concentrations of Ca++ i n the assay medium. I n h i b i t i o n by C a + + was reversed by the a d d i t i o n of p r o t e i n a c t i v a t o r but a c t i v i t y d i d not increase above the c o n t r o l l e v e l . C y c l i c AMP h y d r o l y s i s by D^j was s t i m u l a t e d by micromolar concentrations of c y c l i c GMP. This s t i m u l a t i o n was reduced by C a + + unless p r o t e i n a c t i v a t o r was present. The k i n e t i c s of c y c l i c n u c l e o t i d e h y d r o l y s i s by each of the three enzymes were examined. A l l enzyme species d i s p l a y e d n o n l i n e a r double r e c i p r o c a l p l o t s of s u b s t r a t e h y d r o l y s i s . Through the use of r e v e r s i b l e i n h i b i t i o n k i n e t i c s and n o n l i n e a r l e a s t squares f i t t i n g , r ate equations to describe the data were ( i i ) evaluated. Apparent n e g a t i v e l y cooperative "behaviour was observed f o r the h y d r o l y s i s of c y c l i c GMP by the f i r s t peak eluted (K^ < K 2 and V± < V g ) . The two c y c l i c AMP-cyclic GMP h y d r o l y z i n g enzymes d i s p l a y e d apparent p o s i t i v e c o o p e r a t i v i t y f o r c y c l i c GMP h y d r o l y s i s (K^ > and >^2^' an<^ n e S a ^ ^ v e c o o p e r a t i v i t y f o r c y c l i c AMP h y d r o l y s i s (K^ < K^ , and < Vg). The k i n e t i c behaviour d i s p l a y e d by a l l three enzyme species could be explained u s i n g v a r i a t i o n s of a model c o n s i s t i n g of an enzyme wit h two i n i t i a l l y equivalent i n t e r a c t i n g s i t e s . ( i i i ) TABLE OF CONTENTS Page I . INTRODUCTION 1 I I . EXPERIMENTAL PROCEDURE 15 A. M a t e r i a l s 15 B. Methods 15 1. P r e p a r a t i o n of reagents 15 2. P r e p a r a t i o n of heart e x t r a c t s 16 3. P r e p a r a t i o n of s u p e r i o r c e r v i c a l ganglion e x t r a c t s 16 4-. P r e p a r a t i o n of other enzymes 17 5. DEAE-cellulose chromatography 17 6. Phosphodiesterase assay 18 C. D e r i v a t i o n of Rate Equations and A n a l y s i s of Data 19 1. I t e r a t i v e cross c o r r e c t i o n of v e l o c i t i e s 19 2. Rate equations f o r the two s i t e d enzyme model 20 3. S t a t i s t i c a l a n a l y s i s 27 I I I . RESULTS 28 A. Phosphodiesterase Assay 28 B. Phosphodiesterases of the S u p e r i o r C e r v i c a l Ganglion 4-3 1. E f f e c t of Ca++ and p r o t e i n a c t i v a t o r on the crude supernatant 4-3 2. K i n e t i c a n a l y s i s of the crude supernatant f r a c t i o n 4-9 3- ".DEAE-cellulose chromatography of "bovine s u p e r i o r c e r v i c a l ganglion e x t r a c t 57 4- . P r o p e r t i e s of the DEAE-cellulose r e s o l v e d enzymes 63 IV. DISCUSSION 84-A. The Assay of Phosphodiesterase 84-B. Phosphodiesterases of the S u p e r i o r C e r v i c a l Ganglion 87 V. REFERENCES 94-VI. APPENDIX 100 ( i v ) LIST OF TABLES No. Page I K i n e t i c parameters of c y c l i c AMP h y d r o l y s i s "by heart supernatant f r a c t i o n s . 41 I I E f f e c t of Ca++ on crude supernatant f r a c t i o n s of s u p e r i o r c e r v i c a l g a n g l i a . 4-4-I I I E f f e c t of Ca++ on i s o l a t e d enzyme s p e c i e s . 64-IV Variances. 79 V Parameters derived from l e a s t squares f i t t i n g . 81 (v) LIST OF FIGURES No. Page 1. General model f o r the r e v e r s i b l e i n h i b i t i o n of an enzyme wi t h two i n t e r a c t i n g s i t e s . 22 2. General model f o r the r e v e r s i b l e i n h i b i t i o n of an enzyme w i t h two i n i t i a l l y e q u i v a l e n t i n t e r a c t i n g s i t e s . 2k 3- Recovery of u n l a b e l l e d purines from phosphodiest-erase assay. 31 k. C y c l i c AMP h y d r o l y s i s by r a b b i t heart homogenate. 35 5- K i n e t i c s of c y c l i c AMP h y d r o l y s i s by r a b b i t heart supernatant. 37 6. K i n e t i c s of c y c l i c AMP h y d r o l y s i s by r a t heart supernatant. kO 7. A c t i v a t o r p r o t e i n of s u p e r i o r c e r v i c a l ganglion crude supernatant. 4-7 8. E f f e c t of c y c l i c GMP on the k i n e t i c s of c y c l i c AMP h y d r o l y s i s by bovine ganglion crude supernatant. 51 9. K i n e t i c s of c y c l i c GMP h y d r o l y s i s by bovine ganglion crude supernatant. v 5^  10. E f f e c t of c y c l i c AMP on the k i n e t i c s of c y c l i c GMP h y d r o l y s i s by bovine ganglion crude supernatant. 56 11. DEAE-cellulose e l u t i o n p r o f i l e of phosphodiesterase a c t i v i t y from a bovine s u p e r i o r c e r v i c a l ganglion crude supernatant f r a c t i o n . 60 12. Rechromatography of t r a i l i n g a c t i v i t y from f i r s t DEAE-cellulose column. 62 13. E f f e c t of Ca++ on phosphodiesterase D j j • 67 14-. E f f e c t of Ca++ on the k i n e t i c s of c y c l i c AMP h y d r o l y s i s by enzyme D j j • 70 15. K i n e t i c s of c y c l i c GMP h y d r o l y s i s by enzyme species D r 72 16. K i n e t i c s of c y c l i c n u c l e o t i d e h y d r o l y s i s by enzyme species D-^ . 75 17. K i n e t i c s of c y c l i c n u c l e o t i d e h y d r o l y s i s by enzyme species D J J J • 77 ( v i ) ABBREVIATIONS ATP adenosine 5'-triphosphate c y c l i c AMP adenosine 3 ' : 5 ' - c y c l i c phosphate c y c l i c GMP guanosine 3' 5 ' - c y c l i c phosphate 2' O ' - c y c l i c GMP guanosine 2' : 3 ' - c y c l i c phosphate c y c l i c XMP xanthosine 3 ' : 5 ' - c y c l i c phosphate DBcGMP N - 2 ' 0-dibutyryl-guanosine 3 ' : 5 ' - c y c l i c phosphate DTE d i t h i o e r y t h r i t o l EGTA ' e t h y l e n e g l y c o l - b i s - ( ^ - a m i n o e t h y l ether) N,N'-tetraacetate GTP guanosine 5'-triphosphate I m o d i f i e r c o n c e n t r a t i o n K d i s s o c i a t i o n constant : K m M i c h a e l i s constant a s s o c i a t i o n constant k r a t e constant MIX l-methyl - 3-isobutylxanthine MOPS morpholinopropane s u l f o n i c a c i d m m i l l i n nano P product p p i c o phosphodiesterase 3 , 5 5 ' - c y c l i c AMP phosphodiesterase (E.C. 3-1.4-.17) S substrate c o n c e n t r a t i o n T r i s tris(hydroxymethyl)aminomethane u micro ( v i i ) g gram; a c c e l e r a t i o n due to g r a v i t y p i pH a t i s o e l e c t r i c p o i n t of p r o t e i n v v e l o c i t y V maximal v e l o c i t y , product of the t o t a l enzyme concent r a t i o n and the r e s p e c t i v e rate constant, k v o l volume(s) ( v i i i ) ACKNOWLEDGEMENTS The author wishes to thank Dr. George Drummond f o r h i s a i d and guidance d u r i n g the course of t h i s work. The k i n e t i c a n a l y s i s was aided by s e v e r a l h e l p f u l d i s c u s s i o n s w i t h Drs. Robert Wickson, Gene Huber, and Dave Godin. The c o n t i n u i n g support and encouragement provided by my w i f e , Yvonne, i s duely acknowledged a t t h i s time. I would a l s o l i k e to thank her f o r t a k i n g time from a h e c t i c schedule to type t h i s t h e s i s . The f i n a n c i a l support of the Medical Research C o u n c i l of Canada i s g r a t e f u l l y acknowledged. - 1 -INTRODUCTION Sutherland and h i s a s s o c i a t e s , u s i n g l i v e r p a r t i c u l a t e p r e p a r a t i o n s , f i r s t observed the production of a heat s t a b l e r i b o n u c l e o t i d e which was shown to mediate glucagon and epinephrine induced increases inphosphorylase a c t i v i t y . This r i b o n u c l e o t i d e , i d e n t i f i e d as c y c l i c AMP, was shown to be degraded by t i s s u e e x t r a c t s by an enzyme which was l a t e r termed phosphodiesterase. This enzyme hydrolyzes the 3 ' : 5'-phosphodiester bond of c y c l i c n u c l e o t i d e s a t the 3' p o s i t i o n to form a 5'-nucleotide (1,2). C y c l i c AMP was formed by t i s s u e p a r t i c l e s i n the presence of Mg++ and ATP (3) by an enzyme which i s now known as adenylate c y c l a s e . Subsequent i n v e s t i g a t i o n s revealed that the i n t r a c e l l u l a r concentrations of c y c l i c AMP were increased d u r i n g epinephrine induced a c t i v a t i o n of gly c o g e n o l y s i s i n heart and s k e l e t a l muscle (4-,5)- The a d d i t i o n a l discovery of l i p o l y t i c hormone induced increases i n c y c l i c AMP i n f a t c e l l s (6,7) l e d to the proposal of the "second messenger" concept. B a s i c a l l y t h i s concept i n v o l v e s the t r a n s d u c t i o n of an e x t r a c e l l u l a r hormonal b i n d i n g ( f i r s t messenger) i n t o an i n t r a c e l l u l a r biochemical message. The message was proposed to be an increase i n the l e v e l s of c y c l i c AMP (second messenger) which was brought about by hormonal s t i m u l a t i o n of adenylate c y c l a s e . The increased l e v e l s of c y c l i c AMP would then produce an a l t e r e d s t a t e i n the c e l l (8,9»10)« The mechanism through which an increase i n c y c l i c AMP could d r a m a t i c a l l y a l t e r the metabolic s t a t e of the c e l l was el u c i d a t e d by Krebs and h i s a s s o c i a t e s i n an i n v e s t i g a t i o n of the mechanism of r e g u l a t i o n of gl y c o g e n o l y s i s i n s k e l e t a l muscle - 2 -(11). C y c l i c AMP was found to st i m u l a t e the a c t i v i t y of an ATP dependent p r o t e i n phosphorylating enzyme ( l a t e r termed p r o t e i n kinase) which a c t i v a t e d phosphorylase b kinase v i a phosphorylation. A c t i v a t e d phophorylase b kinase then c a t a l y s e d the conversion of phosphorylase b to phosphorylase a r e s u l t i n g i n increased glycogen "breakdown. The a c t i v a t i o n of p r o t e i n kinase "by c y c l i c AMP was shown to be a consequence of bi n d i n g of the c y c l i c n u c l e o t i d e to a r e g u l a t o r y subunit of the enzyme which caused the release of an a c t i v e c a t a l y t i c subunit (12-15)- P r o t e i n kinases have since been shown to phosphorylate a v a r i e t y of p r o t e i n substrates i n s e v e r a l t i s s u e s (16-20). C y c l i c AMP i s not the only n a t u r a l l y occuring c y c l i c n u c l e o t i d e . F o l l o w i n g the i s o l a t i o n of c y c l i c GMP from r a t urine (21), there have been many i n v e s t i g a t i o n s i n t o i t s p o s s i b l e r o l e as a r e g u l a t o r of c e l l processes. The enzyme re s p o n s i b l e f o r the synthe s i s of c y c l i c GMP from GTP, guanylate c y c l a s e , has now been i d e n t i f i e d i n a v a r i e t y of mammalian t i s s u e s (22). C y c l i c GMP can a c t i v a t e p r o t e i n kinases (I5»l6) and there appear to be mammalian p r o t e i n kinases which c o n t a i n a r e g u l a t o r y subunit s p e c i f i c f o r c y c l i c GMP (23,24-). Phosphodiesterases which are r e l a t i v e l y s p e c i f i c f o r c y c l i c GMP h y d r o l y s i s have a l s o been reported (25). I n t r a c e l l u l a r l e v e l s of c y c l i c GMP increase i n response to a c e t y l c h o l i n e and muscarinic agonists i n heart (26), o x y t o c i n i n the uterus (27), oxotremorine i n the b r a i n (28), d e p o l a r i z i n g agents i n the cerebellum (29), and a c e t y l c h o l i n e or muscarinic agents i n the s u p e r i o r c e r v i c a l ganglion (3°). A ra t h e r a t t r a c t i v e proposal that c y c l i c AMP and c y c l i c GMP may act as opposing forces i n the c o n t r o l -of c e l l u l a r f u n c t i o n , the - 3 -Y i n Yang hypothesis of " b i o l o g i c a l c o n t r o l , has been suggested (27, 31)• A r a t h e r elegant example of the opposing r o l e s of c y c l i c AMP and c y c l i c GMP has been elaborated by Greengard and h i s a s s o c i a t e s f o r the modulation of neurohormone mediated e l e c t r i c a l t r a n s m i s s i o n through the s u p e r i o r c e r v i c a l ganglion (30,32). I n t h i s t i s s u e n i c o t i n i c c h o l i n e r g i c s t i m u l a t i o n of the p o s t g a n g l i o n i c neuron i s thought to produce the f a s t e x c i t a t o r y " p o s t s y n a p t i c p o t e n t i a l . The r e s t i n g membrane p o t e n t i a l of the p o s t g a n g l i o n i c neuron i s thought to be regulated by the l e v e l s of c y c l i c AMP and c y c l i c GMP. Muscarinic c h o l i n e r g i c s t i m u l a t i o n of the p o s t g a n g l i o n i c neuron caus-es an increase i n the l e v e l s of c y c l i c GMP, which then gives r i s e to a slow e x c i t a t o r y postsynaptic p o t e n t i a l (s-EPSP). Dopaminergic s t i m u l a t i o n of the p o s t g a n g l i o n i c neuron, brought about through p r e g a n g l i o n i c s t i m u l a t i o n of a dopaminergic interneuron (S.I.F. c e l l ) , causes increased l e v e l s of c y c l i c AMP i n the p o s t g a n g l i o n i c neuron. The increased l e v e l s of c y c l i c AMP then produce a slow i n h i b i t o r y p o s t s y n a p t i c p o t e n t i a l (s-IPSP). This model i s f e a s i b l e i n that the time course of s-EPSP and s-IPSP are c o n s i s t e n t w i t h the p o s s i b i l i t y of an enzymatic c o n t r o l mechanism. There i s no longer any serio u s doubt that the c y c l i c n u c l e o t i d e s p l a y a key r o l e i n the r e g u l a t i o n of c e l l u l a r f u n c t i o n . As w i t h any r e g u l a t o r y system there must be a way to terminate the e f f e c t s of the c y c l i c n u c l e o t i d e s once formed. As p r e v i o u s l y mentioned, t h i s f u n c t i o n i s performed s o l e l y by a c l a s s of enzymes termed phosphodiesterases. F o l l o w i n g the i n i t i a l d i s covery of phosphodiesterase a c t i v i t y i n l i v e r p a r t i c u l a t e preparations (2), i t was l a t e r shown that the enzyme occurred - 4- -i n a l l mammalian t i s s u e s i n v e s t i g a t e d (33,3k). The d i s t r i b u t i o n of a c t i v i t y was not uniform however, w i t h a c t i v i t y i n the c e r e b r a l cortex being the highest (33,3k,35)• The erroneous c l a i m that phosphodiesterase a c t i v i t y i n every t i s s u e i n v e s t i g a t e d was 10 to 100 f o l d g r e a t e r than the a c t i v i t y of adenylate cyclase (35.36,37) was based on the use of s a t u r a t i n g concentrations of substrate f o r phosphodiesterase determinations (mM in s t e a d of uM) and p h y s i o l o g i c a l concentrations of substrate f o r the adenylate cyclase assays. The r e j e c t i o n of t h i s hypothesis and concurrent work r e v e a l i n g the complex k i n e t i c and chromatographic behaviour e x h i b i t e d by the enzyme, heralded the r e c o g n i t i o n of phosphodiesterase as a key re g u l a t o r y enzyme i n c y c l i c n u c l e o t i d e metabolism. Indeed, much of the impetus f o r the e a r l y work on phosphodiesterase stemmed from i t s contamination of adenylate cyclase preparations and subsequent i n t e r f e r e n c e w i t h the assay of c y c l i c AMP production. The p r o p e r t i e s , assay, and p u r i f i c a t i o n of phosphodiesterase have been the subject of s e v e r a l review a r t i c l e s (38-4-6) and the reader i s r e f e r r e d to these f o r an exhaustive coverage of the l i t e r a t u r e i n t h i s f i e l d . The number of review a r t i c l e s c i t e d i s ample evidence of the mushrooming number of i n v e s t i g a t i o n s being c a r r i e d out on phosphodiesterases. From a survey of the l i t e r a t u r e to date i t i s c l e a r that phosphodiesterase i s a complex enzyme having s e v e r a l i n t e r e s t i n g p r o p e r t i e s , each of which w i l l be d e a l t with s e p a r a t e l y . C y c l i c n u c l e o t i d e phosphodiesterase has not as yet been e x t e n s i v e l y p u r i f i e d and most i n v e s t i g a t i o n s have been c a r r i e d out on r e l a t i v e l y impure pr e p a r a t i o n s . The enzyme r e q u i r e s a d i v a l e n t c a t i o n , Mg++ or Mn++, f o r f u T l a c t i v i t y (33,34-). The l o c a l i z a t i o n of the enzyme has been i n v e s t i g a t e d i n r a b b i t b r a i n s e c t i o n s (4-7)-- 5 -Phosphodiesterase was found to occur i n low l e v e l s i n myelinated c e l l processes ( o p t i c nerve, white matter of cerebellum, and do r s a l columns of s p i n a l r oot) or dense c e l l u l a r areas ( r e t i n a and v e n t r a l columns of s p i n a l cord). F u r t h e r i n v e s t i g a t i o n s revealed t h a t phosphodiesterase a c t i v i t y was not a s s o c i a t e d w i t h catecholamine c o n t a i n i n g s t r u c t u r e s and that there was no general c o r r e l a t i o n of phosphodiesterase and adenylate cyclase a c t i v i t i e s i n the t i s s u e s s t u d i e d (4-7). Florendo et a l . , (48) and Greengard et a l . , (4-9) using lead phosphate p r e c i p i t a t i o n to cytochemically l o c a l i z e phosphodiesterase a c t i v i t y , concluded that the enzyme was l o c a t e d almost s o l e l y i n postsynaptic nerve endings. Other i n v e s t i g a t o r s have reported s i m i l i a r f i n d i n g s based on c e l l u l a r f r a c t i o n a t i o n techniques (36.5°)• A considerable p o r t i o n (30-100$) of the phosphodiesterase a c t i v i t y of a t i s s u e homogenate i s u s u a l l y recovered i n the so l u b l e supernatant f r a c t i o n (33.4-3,4-5, 50). Whether t h i s s o l u b l e p o r t i o n of a c t i v i t y represents true cytoplasmic a c t i v i t y or e a s i l y s o l u b i l i z e d p a r t i c u l a t e m a t e r i a l i s u n c e r t a i n . Large unexplained l o s s e s i n a c t i v i t y encountered i n e a r l y attempts to p u r i f y phosphodiesterase (33.51) have now been shown to be a t l e a s t p a r t l y due to the removal, by DEAE-cellulose or g e l f i l t r a t i o n chromatography, of a heat s t a b l e p r o t e i n a c t i v a t i n g f a c t o r (52). The discovery by Cheung of t h i s a c t i v a t i n g factor-i n i t i a t e d numerous i n v e s t i g a t i o n s . The a c t i v a t o r has now been p u r i f i e d to homogeneity from bovine heart (53). r a t b r a i n (54-), bovine b r a i n (55). and porcine b r a i n (56). The p r o t e i n a c t i v a t o r from porcine b r a i n i s h i g h l y a c i d i c , has a molecular weight of 11,500 daltons (as determined by u l t r a c e n t r i f u g a t i o n ) , contains - 6 -10 moles of phosphate per mole of p r o t e i n , and tends to aggregate i n the presence of C a + + (56). The p h y s i c a l p r o p e r t i e s of the p r o t e i n a c t i v a t o r from "bovine heart have been i n v e s t i g a t e d and i t appears to be a g l o b u l a r p r o t e i n of molecular weight 19.200 daltons (53)' Bovine b r a i n contains a s i m i l a r p r o t e i n a c t i v a t o r of molecular weight 15.000 d a l t o n s ; i t contains a c i d i c amino acid s and has a p i of 4-.3 (55) • The p r o t e i n a c t i v a t o r i s not i n d e n t i c a l with e i t h e r r a b b i t muscle tro p o n i n or p i g b r a i n SI00 p r o t e i n (56). K a k i u c h i and Yamazaki (57) f i r s t reported that phosphodiesterase obtained from d i a l y z e d r a t b r a i n supernates was sti m u l a t e d by low concentrations of C a + + i n the presence of a t l e a s t 1 mM Mg++. The presence of EGTA (0.1 to 0.3 mM) reduced enzymatic a c t i v i t y by 65$, and the presence of trac e amounts of Ca++ i n excess of the EGTA re s t o r e d a c t i v i t y . L a t e r they independently i s o l a t e d a p r o t e i n f a c t o r which enhanced s t i m u l a t i o n of the enzyme by Ca++. When t h i s p r o t e i n a c t i v a t i n g f a c t o r was present', the enzyme was sti m u l a t e d by lower concentrations of Ca++ than i t was i n the absence of the f a c t o r (58,59)- The r e l a t i o n s h i p between Ca ++ ions and the a c t i v a t i n g f a c t o r has now c l a r i f i e d and i t appears th a t there i s an absolute co-requirement f o r Ca++ i n any p r o t e i n a c t i v a t o r mediated event (60,61,62). The exact mechanism through which C a + + i n t e r a c t s w i t h the enzyme and p r o t e i n a c t i v a t o r to increase phosphodiesterase a c t i v i t y i s s t i l l u n s e t t l e d . Using e i t h e r p u r i f i e d bovine heart (60) or bovine b r a i n (55) preparations of p r o t e i n a c t i v a t o r i t has been shown that i t " b i n d s Ca ++ with a d i s s o c i a t i o n constant of 3 uM. I t has a l s o been shown, by gel f i l t r a t i o n , t h a t Ca++ i s r e q u i r e d i n order f o r the enzyme to bind s i g n i f i c a n t amounts of p r o t e i n " - 7 -a c t i v a t o r ( 5 4 - ) . Based on the a v a i l a b l e evidence s e v e r a l authors ( 5 4 - , 5 5 . 60,63) have proposed that the mechanism of a c t i v a t i o n of phosphodiesterase by p r o t e i n a c t i v a t o r and Ca++ proceeds v i a the formation of a Ca+ + ,Ap complex which then binds to the enzyme. This proposal has been questioned (62) on the ba s i s of a d e t a i l e d k i n e t i c a n a l y s i s of bovine cortex phosphodiesterase, which revealed that the most l i k e l y model was one i n which C a + + , E , Ca++"Ap, Ap-E, and Ca+ + ,Ap-E complexes can a l l occur. The a c t i v i t y of the enzyme would only be a l t e r e d with the formation of the l a t t e r complex. I n t h i s model the b i n d i n g of Ca++ or p r o t e i n a c t i v a t o r to the enzyme would produce p o s i t i v e h e t e r o t r o p i c c o o p e r a t i v i t y w i t h respect to the b i n d i n g of the other l i g a n d . This proposal i s supported by other i n v e s t i g a t i o n s i n which the K f o r p r o t e i n a c t i v a t o r i s reduced i n the presence of Ca++ and v i c e versa (59-63)- I t has r e c e n t l y been shown that Ca++ and p r o t e i n a c t i v a t o r increase the a c t i v i t y of c y c l i c GMP h y d r o l y s i s more so than c y c l i c AMP h y d r o l y s i s , and that a c t i v a t i o n i s reduced i f h i g h , r a t h e r than Low-', concentrations of substrate are used (61,63 ,64). K a k i u c h i et a l . , ( 6 4 - ) , u s i n g g e l f i l t r a t i o n , have separated m u l t i p l e molecular forms of phosphodiesterase from a v a r i e t y of r a t t i s s u e s . I n view of evidence that the primary enzyme species which i s a c t i v a t e d by Ca++ and a c t i v a t o r p r o t e i n p r e f e r e n t i a l l y hydrolyzes c y c l i c GMP (at s u b s a t u r a t i n g substrate concentrations) these authors have proposed that Ca++ dependent a c t i v a t i o n i s p r i m a r i l y a c y c l i c GMP phosphodiesterase phenomenon. The existence of mutiple molecular forms of phosphodiesterase w i t h i n a v a r i e t y of t i s s u e s has been demonstrated repeatedly. F o l l o w i n g the i n t r o d u c t i o n of s e n s i t i v e r a d i o i s o t o p i c assays of phosphodiesterase - 8 -a c t i v i t y by Brookes, et a l . , (65) i t was revealed t h a t the b r a i n enzyme had K m values f o r c y c l i c AMP h y d r o l y s i s l / l O to l/50 those o r i g i n a l l y reported. I t appeared that there were two values observable of 1 u l and 150 uM i n d i c a t i n g the p o s s i b l i t y of two separate enzymatic e n t i t i e s . Subsequent i n v e s t i g a t i o n s revealed the presence of chromatographically separable forms of the enzyme i n a v a r i e t y of t i s s u e s (4-3,4-5.4-6). S u r p r i s i n g l y , even upon se p a r a t i o n , the i s o l a t e d enzymes do not obey-Michaelis-Menten * k i n e t i c s - i n " several' i n s t a nces. Thompson and Appleman (66), u s i n g agarose g e l f i l t r a t i o n , i d e n t i f i e d a t l e a s t two forms of a c t i v i t y from the supernatants of sonicated homogenates of r a t b r a i n , kidney, adipose t i s s u e , heart muscle, s k e l e t a l muscle, and erythrocyte ghosts. A k i n e t i c a n a l y s i s of the i s o l a t e d enzymes revealed t h a t the low molecular weight enzyme d i s p l a y e d anomalous k i n e t i c s w i t h c y c l i c AMP and was i n a c t i v e w i t h c y c l i c GMP as su b s t r a t e . The higher molecular weight species d i s p l a y e d apparent Michaelis-Menten k i n e t i c s and hydroyzed both c y c l i c AMP and c y c l i c GMP. R u s s e l l et a l . , (67), u s i n g computer modeling s t u d i e s , revealed t h a t contamination of the low molecular weight f r a c t i o n by the high molecular weight species was i n s u f f i c i e n t to account f o r the observed k i n e t i c s and therefore the most l i k e l y model was one of a n e g a t i v e l y cooperative enzyme. These observations have been extended by the above authors to a sonicated l i v e r p r e p a r a t i o n (25)- Using DEAE-cellulose chromatography, three forms of the enzyme were r e s o l v e d , namely DI to D i l i i n order of t h e i r e l u t i o n from the column. DI was s p e c i f i c f o r c y c l i c GMP h y d r o l y s i s , e x h i b i t e d l i n e a r k i n e t i c s , and the h y d r o l y s i s of c y c l i c GMP by t h i s species was not a f f e c t e d by^the - 9 -presence of c y c l i c AMP (concentrations used were not given) . DII hydrolyzed both c y c l i c n u c l e o t i d e s and e x h i b i t e d n e g a t i v e l y cooperative behaviour f o r c y c l i c AMP h y d r o l y s i s and p o s i t i v e c o o p e r a t i v i t y f o r c y c l i c GMP h y d r o l y s i s . The c o o p e r a t i v i t y of c y c l i c GMP h y d r o l y s i s was observable a t pH 7-4- but not a t pH 8.0. C y c l i c GMP markedly s t i m u l a t e d c y c l i c AMP h y d r o l y s i s i f low concentrations of both substrate ( c y c l i c AMP) and m o d i f i e r ( c y c l i c GMP) were used. At higher concentrations both c y c l i c n u c l e o t i d e s were non-competitive i n h i b i t o r s of each others h y d r o l y s i s . F r a c t i o n D i l i was a p a r t i c u l a t e enzyme which hydrolyzed c y c l i c AMP i n a n e g a t i v e l y cooperative manner. C y c l i c GMP i n h i b i t e d c y c l i c AMP h y d r o l y s i s i n a proposed h y p e r b o l i c manner. The co n c l u s i o n of n e g a t i v e l y cooperative behaviour was based on c a l c u l a t i o n s i n d i c a t i n g i n s u f f i c i e n t contamination of D i l i by DII to e x p l a i n the k i n e t i c behaviour. The observation that c y c l i c GMP could a c t i v a t e c y c l i c AMP h y d r o l y s i s had been reported (68-71) although the more common observation was that c y c l i c GMP i n h i b i t e d the h y d r o l y s i s of c y c l i c AMP (4-5). E x i s t e n c e of substrate analog a c t i v a t i o n i s strong evidence i n favour of a cooperative enzyme system. Bevers et a l . , (71) u s i n g g e l f i l t r a t i o n , have observed that r a t l i v e r contains three c y c l i c AMP h y d r o l y z i n g enzymes. The highest and lowest molecular weight species were i n a c t i v a t e d by heat treatment at 5°°. The heat s t a b l e form of intermediate molecular weight' had a r e l a t i v e l y high K m f o r c y c l i c AMP and dis p l a y e d substrate c o o p e r a t i v i t y ( H i l l c o e f i c i e n t of 1.9)- C y c l i c GMP (2 uM) a c t i v a t e d the h y d r o l y s i s of c y c l i c AMP and supressed c o o p e r a t i v i t y ( H i l l c o e f i c i e n t of 1.0). These r e s u l t s were i n t e r p r e t e d as being c o n s i s t e n t w i t h the heat s t a b l e ' h i g h K form - 10 -of the enzyme being an a l i o s t e r i c p r o t e i n . Uzunov and Weiss (72) have resolved s i x forms of phosphodiesterase from r a t c e r e b e l l a r homogenates on a pr e p a r a t i v e polyacrylamide g e l e l e c t r o p h o r e s i s column. These observations have been extended by Pledger et a l . , u s i n g i s o e l e c t r i c f o c u s i n g techniques (73) • Again s i x enzyme forms were resolved and f i v e of the s i x enzyme species d i s p l a y e d n o n l i n e a r k i n e t i c s approximating the k i n e t i c s observed i n the crude homogenate. Three of the s i x enzyme forms showed l i t t l e c y c l i c GMP h y d r o l y z i n g a c t i v i t y . The use of a t i s s u e with such a complex c e l l u l a r s t r u c t u r e does not lend i t s e l f p a r t i c u l a r l y w e l l to p r o v i d i n g evidence f o r m u l t i p l e molecular forms of the enzyme w i t h i n a c e l l l i n e . A case i n p o i n t i s the l a t e r examination by Uzunov e_t a l . , of m u l t i p l e forms of a c t i v i t y i n r a t cerebrum and cloned astrocytoma or neuroblastoma c e l l s (74-). Rat cerebrum contained f o u r peaks of phosphodiesterase a c t i v i t y while the astrocytoma, Cg astrocytoma, and neuroblastoma c e l l l i n e s , r e s p e c t i v e l y , c o n t a i n e d only three, two, and one peaks of a c t i v i t y . As with t h e i r previous i n v e s t i g a t i o n s (72), various i n h i b i t o r s a l t e r e d the a c t i v i t i e s of the i s o l a t e d enzyme species to d i f f e r e n t degrees (74-,75)-I t should be noted that some authors have n o t i c e d a p o s s i b l e i n t e r c o n v e r s i o n of enzyme forms. For example R u s s e l l et a l . , (25) observed l i n e a r k i n e t i c s of c y c l i c AMP h y d r o l y s i s a t pH 8.0 i n a f r e s h l y sonicated e x t r a c t of r a t l i v e r . F o l l o w i n g storage a t 4-° f o r 24 hours or t r y p t i c d i g e s t f o r 12 minutes the n o n l i n e a r k i n e t i c s suggestive of m u l t i p l e enzyme species or negative c o o p e r a t i v i t y appeared. They a l s o observed that f o l l o w i n g agarose g e l chromatography of a sonicated r a t l i v e r homogenate"The - 11 -intermediate molecular weight f r a c t i o n d i s p l a y e d l i n e a r k i n e t i c s w i t h a high f o r c y c l i c AMP (66). However, a 0.6 M sodium acetate cut of t h i s a c t i v i t y from a DEAE-cellulose column, e x h i b i t e d downward c u r v i n g double r e c i p r o c a l p l o t s of substrate h y d r o l y s i s (25). Schroeder and Rickenberg u s i n g bovine l i v e r homogenates (76) and Wickson (77) u s i n g bovine cortex homogenates, have reported a decrease i n the apparent molecular weight of phosphodiesterase when ge l f i l t r a t i o n was conducted i n the presence of Mg++. Wickson (77) a l s o observed a f u r t h e r decrease i n molecular weight i f Ca++ was included as w e l l as Mg++ i n the g e l f i l t r a t i o n e l u t i n g b u f f e r . Schroeder (76) has proposed that the two c y c l i c AMP h y d r o l y z i n g forms of the enzyme i s o l a t e d by g e l f i l t r a t i o n of bovine l i v e r p r e p a r a t i o n s , represent i n t e r c o n v e r t i b l e forms of a high and low K m a c t i v i t y . High NaCl or Mg++ concentrations lead to a preponderance of the low K m form (120,000 dalton) while high c y c l i c AMP or c y c l i c GMP concentrations or low Mg++ concentrations favour the formation of the high K m (24-0,000 dalton) form. I t thus appears that the r e s o l u t i o n of m u l t i p l e molecular forms of the enzyme i s a complex problem and i s o l a t i o n ; ' a r t i f a c t s , p a r t i c u l a r l y when u s i n g g e l f i l t r a t i o n , may be obtained. The i n h i b i t i o n of phosphodiesterase by a myriad of exogenous and endogenous compounds has been the subject of the m a j o r i t y of the papers i n t h i s f i e l d . I n view of the p r e v i o u s l y mentioned com p l e x i t i e s of the enzyme i t i s perhaps superfluous- to caution that many of these e f f e c t s may be only q u a l i t a t i v e evaluations w i t h l i t t l e p h y s i o l o g i c a l s i g n i f i c a n c e . The reader i s r e f e r r e d to a comprehensive recent review on the subject of phosphodiesterase i n h i b i t i o n by Amer and Kreighbaum (4-5). Twenty-one lengthy t a b l e s of phosphodiesterase i n h i b i t o r s are presented. A c l e a r s t r u c t u r e - a c t i v i t y r e l a t i o n s h i p could not be e s t a b l i s h e d although c e r t a i n s t r u c t u r a l m o i e t i e s , i n c l u d i n g amidine (N-C(=N)~N), amidrazone (N-N-C=N), and 3,4--d i s u b s t i t u t e d phenylethylamine were common to a la r g e percentage of the phosphodiesterase i n h i b i t o r s (45)- These s t r u c t u r e s a l s o tend to appear r a t h e r f r e q u e n t l y i n u s e f u l drug e n t i t i e s . I n view of the complex behaviour e x h i b i t e d by phosphodiesterase, the assay of t h i s enzyme i n v o l v e s the use-of substrate concentrations v a r y i n g over a 2000 f o l d range and r e s u l t s i n g r e a t l y d i v e r s e r e a c t i o n v e l o c i t i e s . Because of t h i s , and since most assays are performed on r e l a t i v e l y crude preparations i n which purine m e t a b o l i z i n g enzymes are present, any assay of phosphodiesterase must a l l o w f o r recovery of product or product c a t a b o l i t e i n high y i e l d . A t present there are s e v e r a l assays a v a i l a b l e f o r c y c l i c n u c l e o t i d e phosphodiesterase, the advantages and disadvantages of each have been discussed ( 7 8 , 7 9 , 8 0 ) . G e n e r a l l y speaking the r a d i o i s o t o p e assays provide maximum s e n s i t i v i t y and permit the use of sub-micromolar concentrations of su b s t r a t e . Most of these assays i n v o l v e the use of a l a b e l l e d c y c l i c n u c l e o t i d e ; the immediate product, the corresponding 5'-nucleotide, i s converted to a nucleoside by the a d d i t i o n of excess 5'-nucleotidase present i n snake venom. The nucleoside can a l s o be formed and f u r t h e r degraded by purine c a t a b o l i z i n g enzymes present i n the t i s s u e e x t r a c t s . Separation of nucleoside or i t s c a t a b o l i t e , can be accomplished by passage over an alumina column ( 8 0 ) , a Dowex 2 column (81), a Dowex 1 column (82) , by t h i n l a y e r chromatography (83), by paper chromatography (84-), or by batch use of Dowex 1 (6"5,85)- The - 13 -l a t t e r method has been e x t e n s i v e l y used due to i t s t e c h n i c a l • s i m p l i c i t y . Some time ago we began assays of phosphodiesterase according to the procedure of Thompson and Appleman (85) and found that r e c o v e r i e s of nucleosides and bases were inadequate and v a r i a b l e (86). Other r e p o r t s have claimed;, that assays u s i n g Dowex 1 X 2 r e s i n i n both batch and column mode are complicated by u n s a t i s f a c t o r y r e c o v e r i e s of nucleosides and bases (78,87). The assay method was modified to in c l u d e a c i d i f i c a t i o n of the r e s i n s l u r r y p r i o r to i t s a d d i t i o n . This procedure r e s u l t e d i n q u a n t i t a t i v e r e c o v e r i e s of adenosine, guanosine, and t h e i r major c a t a b o l i t e s (86). The assay as described provides a simple and r a p i d method by which c y c l i c AMP or c y c l i c GMP h y d r o l y s i s can be determined w i t h r e l i a b i l i t y , even i n crude p r e p a r a t i o n s . In t h i s t h e s i s the phosphodiesterases'of bovine and canine s u p e r i o r c e r v i c a l g a n g l i a were examined. The s u p e r i o r c e r v i c a l ganglion was chosen as the t i s s u e source due to the proposed r o l e of c y c l i c n u c l e o t i d e s i n r e g u l a t i n g neurohormonal.mediated e l e c t r i c a l t r a n s m i s s i o n through the t i s s u e (30). Despite the importance of c y c l i c n u c l e o t i d e metabolism i n t h i s t i s s u e , there i s a p a u c i t y of inf o r m a t i o n on the p r o p e r t i e s of i t s phosphodiesterases. I t has been reported that phosphodiesterase a c t i v i t y i n s u p e r i o r c e r v i c a l ganglion homogenates i s i n h i b i t e d by t h e o p h y l l i n e but not by dopamine (88). Phosphodiesterase a c t i v i t y has been recovered i n the bathing medium of whole;s up e r r o r c e r v i c a l g a n g l i a . The a c t i v i t y of phosphodiesterase i n the bathing medium was decreased by h i s t a m i n i c s t i m u l a t i o n of the ganglion (89). A d e t a i l e d examination of the - 14- -s u p e r i o r c e r v i c a l ganglion phosphodiesterases, given i n the f o l l o w i n g p r e s e n t a t i o n , revealed s e v e r a l i n t e r e s t i n g p r o p e r t i e s , some of which are p r e v i o u s l y unreported f o r other phosphodiesterase p r e p a r a t i o n s . DEAE-cellulose chromatography of a crude supernatant f r a c t i o n s revealed a t l e a s t three separable forms of the enzyme. The a c t i v i t y of each of these species was r e v e r s i b l y i n h i b i t e d by low concentrations of Ca++. A l l enzymes el u t e d from a DEAE-c e l l u l o s e column e x h i b i t e d cooperative k i n e t i c behaviour. A d e t a i l e d k i n e t i c a n a l y s i s of each of the three enzymes revealed t h a t the general model of an enzyme with two i n i t i a l l y e q uivalent i n t e r a c t i n g s i t e s was s u f f i c i e n t and necessary to describe the • anomalous k i n e t i c behaviour. The s i g n i f i c a n c e of t h i s k i n e t i c behaviour i n the r e g u l a t i o n of c y c l i c n u c l e o t i d e l e v e l s i n the s u p e r i o r c e r v i c a l ganglion i s discussed. - 15 -EXPERIMENTAL PROCEDURE A. M a t e r i a l s Dowex 1 X8 200-4-00 mesh ( C I " form), c y c l i c AMP, c y c l i c GMP, adenosine, hypoxanthine, xanthosine, 5'-nucleotidase (Type I I , 10 units/mg), T r i s base, EGTA, MOPS, DTE, and 2-mercaptoethanol were purchased from Sigma Chemical Company (St. L o u i s , Mo.). Guanosine and i n o s i n e were obtained from Calbiochem (Los Angeles, C a l f . ) ; adenine was purchased from N u t r i t i o n a l Biochemicals Corp. (Cleveland, Ohio). DBcGMP, c y c l i c XMP, and ,2': 3 ' - c y c l i c GMP were obtained from Boehringer Mannheim; DEAE-cellulose was the product of Eastman Kodak. Omnifluor, cyclic'AMP (24- C i / mmole), C^Hj c y c l i c GMP (4-.3 Ci/mmole), and C^ HD guanosine (6.13 Ci/mmole) were purchased from New England Nuclear (Boston,Mass.). [ C] adenosine (32.2 Ci/mmole) was the product of Schwartz Bioresearch (Orangeburg, N.Y.). T r i t o n XI00 was purchased from B r i t i s h Drug Houses. A c i d and neutralV''alumina , Brockman a c t i v i t y I , 80-200 mesh, were obtained from F i s h e r S c i e n t i f i c Co. ( F a i r Lawn, N.J.). B. Methods 1. P r e p a r a t i o n of reagents T r i t i a t e d and u n l a b e l l e d c y c l i c n u c l e o t i d e s were p u r i f i e d p r i o r to use on Dowex 50 c a t i o n exchange columns (90) then d i s s o l v e d i n deionized water and stored at -20°. The Dowex 1 X8 r e s i n was prepared i n a l a r g e chromatography funnel by washing w i t h 0,5 N NaOH (2 1 ) , deionized HgO (4- 1 ) , 0.5 N HCl (2 l ) , and HgO (4- l ) . - 16 -The r e s i n was then suspended i n .3 volumes of 0.1 N NCI and allowed to stand overnight. F o l l o w i n g t h i s the r e s i n was washed e x h a u s t i v e l y w i t h deionized water i n a l a r g e s i n t e r e d glass f u n n e l . The r e s i n was then suspended i n 3 r e s i n v o l of E^O and allowed to stand two days p r i o r to use with d a i l y water changes. The r e s u l t i n g pH of the r e s i n supernatant was 4-.66. 2. P r e p a r a t i o n of heart e x t r a c t s . A New Zealand white r a b b i t was k i l l e d by a blow to the head, the heart was q u i c k l y removed and f r e e d of blood i n i c e c o l d 20 mM T r i s - H C l , pH 7-5- The v e n t r i c l e s were i s o l a t e d , placed i n 10 v o l of the above b u f f e r , and homogenized a t 0° i n a S o r v a l Omnixer set a t maximum speed f o r 3X4-5 sec bursts w i t h 4-5 sec c o o l i n g p e r i o d s . The homogenate was c e n t r i f u g e d a t 37 , P0"0. x^g. f or 20 min; the supernatant r e t a i n e d , and stored a t -20°. The p r e p a r a t i o n of the r a t heart e x t r a c t was the same. 3. P r e p a r a t i o n of s u p e r i o r c e r v i c a l g a n g l i a e x t r a c t s . Bovine s u p e r i o r c e r v i c a l g a n g l i a were removed from f r e s h l y k i l l e d animals immediately f o l l o w i n g exsanguination; they were placed i n 0.9fo NaCl a t 4-° and transported to the l a b o r a t o r y . F o l l o w i n g de.sheathing eand removal of other debris they were stored at -80° u n t i l used. Dog s u p e r i o r c e r v i c a l g a n g l i a were removed s u r g i c a l l y from animals anesthetized w i t h sodium p e n t o b a r b i t a l , and f r o z e n immediately a t -80° u n t i l used. Ganglia were f i n e l y minced wi t h s c i s s o r s and homogenized i n 10 v o l of 10 mM T r i s - H C l , pH 7-5 i n a S o r v a l Omnimixer a t maximum v e l o c i t y ; three 4-5 sec bursts f o l l o w e d by equal c o o l i n g periods were used. The suspension was f u r t h e r dispersed by homogenization - 17 -i n a Potter-Elvehjem glass homogenizer wi t h a t i g h t f i t t i n g p e s t l e . Repeated passes were necessary to completely disperse the m a t e r i a l . The r e s u l t i n g homogenate was c e n t r i f u g e d at 37,000 x g f o r 20 min; the supernatant f l u i d was withdrawn, the p e l l e t was suspended i n 5 v o l of b u f f e r , homogenized again i n a t e f l o n glass homogenizer and c e n t r i f u g e d . The supernatant f l u i d s were combined and s t o r e d a t -20°. This p r e p a r a t i o n was r e f e r r e d to as the crude supernatant f r a c t i o n . k. P r e p a r a t i o n of other enzymes C y c l i c n u c l e o t i d e phosphodiesterase f r e e of p r o t e i n a c t i v a t o r and p r o t e i n a c t i v a t o r f r e e of phosphodiesterase were prepared from bovine c e r e b r a l cortex as p r e v i o u s l y described (62). 5'-Nucleotidase was obtained commercially i n a l y o p h i l i z e d form and was d i s s o l v e d i n deionized water to a c o n c e n t r a t i o n of 1 mg per ml. This p r e p a r a t i o n was stored a t -20° u n t i l used. P r o t e i n was determined by the method of Lowry et a l . , (91) when u s i n g crude preparations. The method of Warburg and C h r i s t i a n (92) was used f o r p r o t e i n determinations w i t h p u r i f i e d p r e p a r a t i o n s . 5- DEAE-cellulose chromatography DEAE-cellulose f r a c t i o n a t i o n of bovine g a n g l i a crude supernatant was performed by the method of R u s s e l l et a l . , (25) w i t h minor m o d i f i c a t i o n s . A 1.5 x 21 cm bed volume column was e q u i l i b r a t e d w i t h 5° mM T r i s - a c e t a t e , pH 6.0 (4-°) c o n t a i n i n g 3-75 mM 2-mercaptoethanol. F r a c t i o n s were c o l l e c t e d a t 7 min i n t e r v a l s i n tubes c o n t a i n i n g 5° u l of a s o l u t i o n c o n s i s t i n g of k mg of egg albumin and k umoles of MgClg. This was r e q u i r e d to s t a b i l i z e the phosphodiesterase. P r i o r to assay, a l i q u o t s (1.5.-ml) - 18 -of i n d i v i d u a l f r a c t i o n s were d i a l y z e d a g i n s t two 8 1 changes of 5 mM T r i s - H C l , pH 7-5- Appropriate f r a c t i o n s were then pooled, and concentrated by u l t r a f i l t r a t i o n u s i n g an Amicon PM30 u l t r a f i l t e r Such concentrates were d i a l y z e d a g a i n s t one l i t e r of 10 mM T r i s -HCl, pH 7.5 c o n t a i n i n g 1 mM MgClg and 0.5 mM DTE. These preparations were s t a b l e when stored a t -80°. 6. Phosphodiesterase assay The standard i n c u b a t i o n mix contained 10 mM T r i s - H C l , pH 7.5. 1 mM MgClg, enzyme s o l u t i o n s , the appropriate u n l a b e l l e d and l a b e l l e d c y c l i c n u c l e o t i d e s (or nucleoside f o r recovery s t u d i e s ) , and water to a f i n a l volume of 200 u l . F o l l o w i n g i n c u b a t i o n a t 3°° f o r heart t i s s u e e x t r a c t s , or 37° for' a l l other t i s s u e p r e p a r a t i o n s , the r e a c t i o n was terminated by p l a c i n g the tubes i n a b o i l i n g water bath f o r 75 sec followed by c h i l l i n g on i c e . F o l l o w i n g r e e q u i l i -b r a t i o n to the i n c u b a t i o n temperature, 5° u l of a 1 mg/ml s o l u t i o n ' of 5 -nuc"lfe-0itidas:e was added. A f t e r a 20. min in'cubation, the r e a c t i o n was terminated by the a d d i t i o n of 1.0 ml of the Dowex 1 X8 r e s i n s l u r r y OHgO:! r e s i n ) . The tubes were allowed to stand at l e a s t 10 min, c e n t r i f u g e d a t 1000 x g f o r 10 min, then 0.5 ml (of ' the 1.25 ml t o t a l assay volume)'was withdrawn and placed i n an 18 ml glass s c i n t i l l a t i o n v i a l . Four ml of T r i t o n XI00-toluene (1:2) s c i n t i l l a t i o n f l u i d c o n t a i n i n g 4- g / l i t e r Omnifluor was added. R a d i o a c t i v i t y was determined i n a Sea r l e Isocap 3°° l i q u i d s c i n t i l l a t i o n spectrometer. E f f i c i e n c y of[^Hl counting was 35% w h i l e [ C]was counted with an e f f i c i e n c y of 80$. For i s o t o p i c recovery s t u d i e s , HgO was s u b s t i t u t e d f o r the enzymes i n the assay. O p t i c a l recovery assays were performed u s i n g a Beckman model DU - 19 -spectrophotometer set at 256 nm. These assays were sc a l e d up by a f a c t o r of two over the r a d i o i s o t o p e assay. Nucleosides or bases were present a t a f i n a l c o n c e n t r a t i o n of 80 uM. The, k i n e t i c assays were performed under the f o l l o w i n g standardized c o n d i t i o n s : ( l ) p r o t e i n c o n c e n t r a t i o n was not v a r i e d w i t h i n a set of v e l o c i t y measurements, (2) c y c l i c n u c l e o t i d e h y d r o l y s i s was kept below 20$ by v a r y i n g the time of i n c u b a t i o n between 5 and 90 min, (3) unless otherwise i n d i c a t e d EGTA (250 uM) was included i n a l l tubes to e l i m i n a t e Ca++ dependent a l t e r a t i o n s of c y c l i c n u c l e o t i d e h y d r o l y s i s , (4-) average substrate d u r i n g the course of the i n c u b a t i o n was determined (93) and used f o r the p l o t t i n g and l e a s t squares f i t t i n g , (5) "the substrate c o n c e n t r a t i o n was v a r i e d between 0.1 uM and the conc e n t r a t i o n at which substrate s a t u r a t i o n occurred (to a maximum of 200 uM). C. D e r i v a t i o n of Rate Equations and A n a l y s i s of Data 1. I t e r a t i v e cross c o r r e c t i o n of v e l o c i t i e s The a n a l y s i s of the heart phosphodiesterase k i n e t i c data was performed u s i n g the i t e r a t i v e cross c o r r e c t i o n of v e l o c i t i e s method (94-). The break o f f p o i n t f o r high and low enzymes was estimated from S/v versus S p l o t s i n i t i a l l y . One cy c l e of cross c o r r e c t i o n was then performed and the data examined. A more accurate determina-t i o n of the c r i t e r i o n f o r the i n c l u s i o n of a data p o i n t i n the c a l c u l a t i o n was chosen as f o l l o w s : a t l e a s t 5°% of the v e l o c i t y measured a t that substrate l e v e l must have been due to the form of the enzyme under l e a s t squares f i t t i n g i n order f o r t h a t p o i n t to be included. I n the l e a s t squares f i t t i n g the f u n c t i o n v = VS/(K m+S) was f i r s t l i n e a r i z e d to the form S/v = ( K m A ) + ( l / v ) - S , (Y = P + PgX) - 2 0 -and the appropriate values of X and Y entered. Weighting f a c t o r s of v /S ( 9 5 ) were used i n the l e a s t squares a n a l y s i s unless otherwise i n d i c a t e d . I f an unweighted f i t i s to be made, the S/v vs S l i n e a r i z a t i o n i s f a r more s t a t i s t i c a l l y r e l i a b l e than the l / v vs l/S method ( 9 5 ) • 2 . Rate equations f o r the two s i t e d enzyme model Harper ( 9 6 , 9 ? ) has derived r a t e equations to describe a two s i t e d enzyme under the i n f l u e n c e of a r e v e r s i b l e m o d i f i e r . However, a d d i t i o n a l r a t e equations were re q u i r e d i n the a n a l y s i s of the data presented h e r e i n . These equations were obtained e i t h e r through a f u r t h e r treatment of the equations given by Harper ( 9 7 )» or derived u s i n g the assumption of r a p i d b i n d i n g e q u i l i b r i a by the method of Cha ( 9 8 ) . The general r e a c t i o n scheme,adapted from ( 9 7 ) , i s shown i n F i g . 1 . The corresponding r a t e equation ( 9 7 ) i s K„ V ' l ' K' V~I (v 9+.v*) + (v: + - ^ — ) + (v 1 K Q I K' I K.K' I I I* S R T T I S K^1Z K-j- K.J K-JK I I ( 1 ) " I I I I f we assume that thie s i t e s on the enzyme are i n i t i a l l y e q uivalent p r i o r to substrate b i n d i n g , we can s i m p l i f y equation 1 and F i g . 1 to give equation 2 and F i g . 2 . This transformation was accomplished by s e t t i n g a l l unprimed symbols equal to a l l primed symbols. The r e s u l t a n t r a t e expression i s given as K 9 V o l V 0 + — ( V 1 + - 2 — ) , 2 S K I I I J 2 K . I K,K 0 2 1 I 2 ( 2 ) ± + (1 + } + _1_Z ( 1 + — + K i n S 2 K x K l K l I - 2 1 -Figure 1 . General model f o r the r e v e r s i b l e i n h i b i t i o n of an enzyme wit h two i n t e r a c t i n g s i t e s . Each s i n g l e headed arrow i n d i c a t e s a r a p i d e q u i l i b r i u m segment wit h the d i s s o c i a t i o n constant i n d i c a t e d . Each double headed arrow i n d i c a t e s an i r r e v e r s i b l e r a t e l i m i t i n g c a t a l y s i s step w i t h the r a t e constant i n d i c a t e d alongside-. - 23 -Figure 2 . General model f o r the r e v e r s i b l e i n h i b i t i o n of an enzyme wi t h two i n i t i a l l y e quivalent i n t e r a c t i n g s i t e s . Each s i n g l e headed arrow i n d i c a t e s a r a p i d e q u i l i b r i u m segment w i t h the d i s s o c i a t i o n constant i n d i c a t e d . Each double headed arrow i n d i c a t e s an i r r e v e r s i b l e r a t e l i m i t i n g c a t a l y s i s step w i t h the rate constant i n d i c a t e d alongside. - 2 4 -- 25 -Equation 1 can a l s o be s i m p l i f i e d by s e t t i n g V ^ = ' = V ^ = 0 to give the r a t e equation f o r a simple a l l o s t e r i c enzyme (one c a t a l y t i c and one r e g u l a t o r y s i t e ) K' V_I V" + — ( V 1 ) b * T I I v = . ( 3 ) K I I K K " I I IT 1 + — (1+ ) + — (1 + )• •+ (1 + — + — + ) S K m S YL^ S 2 K x K' K' K l I Equation 3 can then be modified by s e t t i n g a l l unprimed symbols equal to a l l primed symbols. The r e s u l t i n g expression, d e s c r i b i n g a simple a l l o s t e r i c enzyme with both c a t a l y t i c and r e g u l a t o r y s i t e s i n i t i a l l y e q uivalent i s K V I V . + — (V. + - 2 — ) S K j I I v = ^ (4-) 2K I K K 21 j / 1 + — - (1 + ) + (1 + — + ) S K m S 2 K l K l K l I Two f u r t h e r submodels of equations 1 and 2 can be derived to describe the c o n d i t i o n were there i s no c a t a l y t i c a c t i v i t y u n t i l both the s i t e s are occupied. This d e r i v a t i o n i s obtained by simply s e t t i n g V ^ = V ^ = 0 i n equation 1 and V ^ = 0 i n equation 2 to give equations 5 and 6 r e s p e c t i v e l y . K _ V ' I K ' V „ I ( v 2 + v p + + ( - 2 - ^ - ) S K I I I S K i n V = K I K' I K K' I I I 2 1 + (1 + - ) + (1 + ) + ( 1 + _ + _ + (5) K I I I S K i l l S K I K i K i K I I - 26 -K 9 V „ I 2: ( V 0 + -2-^-) S K I I I v.= 9 (6) 2K 0 I K.K 9 21 \ c 1 + — (1 + ) + (1+ — + ) S K l I I S 2 K l K l K I Z There are a t l e a s t three other submodels of F i g . 2 which i n v o l v e the p o s s i b i l i t y that there i s only one s i t e a v a i l a b l e u n t i l one l i g a n d i s bound. These models represent, t h e r e f o r e , the ordered a d d i t i o n ( r e l e a s e ) of S , I , and P. The s t o i c h i o m e t r y of the r e a c t i o n s are changed by these assumptions and gives the f o l l o w i n g mathematical f o r m u l a t i o n s : S , I , and P ordered „ V 9 S V o l K l ^ 1 K 2 K I I I v = r. (7) K v K K K v K *1 ^2 ^ I I I ^1 ^11 S and P ordered, I random c V 9 S V o l K v 1 K K ' V = (8) 1 + § _ / 1 + S _ _ I ) + I _ / 2 + _ I _ ) K l ( K2 K I I I K I ( K I I I ordered, S and P random 9 C, V 9 S V o l K ^ 1 K K *1 1 2 ^ I I I v = (9) K l ( K 2 K I I I K I K I I The remaining model to be considered i s that of two enzymes a c t i n g on the same substrate under the i n f l u e n c e of a r e v e r s i b l e i n h i b i t o r (97). The ra t e equation can be shown to be - 27 -K' I K I V + VgS (1 + £T) + V + (1 + i r ) v = (10) K" K I K' K ' l S I S \, I* , s . s S SK^-J' u + S SKJ 3. S t a t i s t i c a l a n a l y s i s A l l ten r a t e equations were expanded and then s i m p l i f i e d by d e f i n i n g a l l i n h i b i t o r d i s s o c i a t i o n constants as a s s o c i a t i o n constants, eg. k J J J ^ = l A j j j • The p a r t i a l d e r i v a t i v e s of each expression with respect to each parameter were evaluated. FORTRAN programs were then w r i t t e n to evaluate the value of each of the p a r t i a l d e r i v a t i v e s as w e l l as the value of the f u n c t i o n . This procedure i s o u t l i n e d i n d e t a i l i n the Appendix. The subroutines were then compiled on an IBM 370 computer and l i n k e d to the i t e r a t i v e n o n l i n e a r l e a s t squares r o u t i n e BMDX85 (obtained from the UCLA Health Sciences Computing Center). The r o u t i n e provided the best l e a s t squares f i t to the f u n c t i o n and returned the varian c e , asymptotic standard d e v i a t i o n s of each of the parameter estimates, and the estimates of the parameters. P r e l i m i n a r y estimates of the parameters were obtained by i t e r a t i v e cross c o r r e c t i o n of v e l o c i t i e s , as p r e v i o u s l y o u t l i n e d . - 28 -RESULTS -A. Phosphodiesterase Assay I n e a r l y experiments we assayed phosphodiesterase a c t i v i t y "by the method of Thompson and Appleman (85). As p r e v i o u s l y s t a t e d , t h i s assay i n v o l v e d the use of a l a b e l l e d c y c l i c n u c l e o t i d e which was hydrolyzed to a 5'-nucleotide by phosphodiesterase. F o l l o w i n g conversion of the 5'-nucleotide to a nucleoside by the a d d i t i o n of excess 5'-nucleotidase, s e p a r a t i o n of nucleoside could be' accomplished by the a d d i t i o n of a s l u r r y of Dowex 1 anion exchange r e s i n . Unreacted c y c l i c n u c l e o t i d e was bound by the r e s i n while the nucleoside was proposed to remain i n the r e s i n supernatant (85)-I n i t i a l experiments were conducted to monitor the recovery of f_ Cj adenosine from tubes to which a Dowex 1 X8 r e s i n s l u r r y was added. I t was found that the recovery of adenosine from the r e s i n s l u r r y supernatant was between 4-3 and 73$ and depended on the method of r e s i n p r e p a r a t i o n . The recovery could be increased to 100$ i f u n l a b e l l e d purines ( c y c l i c GMP, 0.2 uMoles;5 *-GMP, 0.2 uMoles; and guanosine, 0.2 uMoles) were added to the recovery assay i n the absence of b u f f e r . However i n the presence of b u f f e r , the a d d i t i o n of the u n l a b e l l e d purines had l i t t l e e f f e c t . T r i s - H C l , pH 7-5. imidazole, pH 7 - 0 . and MOPS, pH 7-5 were a l l t r i e d as b u f f e r s and s i m i l i a r problems of low rec o v e r i e s were encountered. I t was, the r e f o r e , assumed that the low r e c o v e r i e s were due to n o n s p e c i f i c b i n d i n g that was dependent on pH, wit h r e c o v e r i e s being higher a t a lower pH. Various compounds were t e s t e d f o r t h e i r a b i l i t y to 14-increase the recovery of [ ,C] adenosine from the (standard assay mix. These assays included 10 mM T r i s - H C l , pH 7-5, 1 uM MgCl ?, - 29 -and l a b e l l e d nucleoside. H i g h l y a c i d i c compounds such as a c e t i c a c i d , formic a c i d , or HC1 were a l l e f f e c t i v e i n i n c r e a s i n g r e c o v e r i e s . P l o t s of recovery of nucleoside versus a c i d c o n c e n t r a t i o n were hyperbolas. Recoveries were f i r s t increased f o l l o w i n g the a d d i t i o n of l e s s than 10$ of the co n c e n t r a t i o n of a c i d which gave maximal recovery. HC1, although very e f f e c t i v e i n i n c r e a s i n g r e c o v e r i e s , a l s o tended to give high blanks. The blank value was obtained by adding t H] c y c l i c n u c l e o t i d e to an i d e n t i c a l assay mixture and then determining r a d i o a c t i v i t y i n the r e s i n supernatant. For the recovery of adenosine, a c e t i c a c i d (3-0 mM i n the r e s i n s l u r r y ) was found to be the best compromise between high recovery and low blank values. With t h i s amount of a c e t i c a c i d i n the s l u r r y the pH of the r e s i n supernatant p r i o r to a d d i t i o n to the assay was 3-00. S i m i l a r i l y , 115 mM formic a c i d was found to be the best compromise between blanks and r e c o v e r i e s f o r l^E] c y c l i c GMP and [-^ H] guanosine. The pH of the s l u r r y supernatant, c o n t a i n i n g 115-mM formic a c i d was 2.25. In F i g . 3, "the recovery of u n l a b e l l e d purine d e r i v a t i v e s from the r e s i n s l u r r y was determined by measuring absorbance a t 256 nm. I n F i g . 3A, i t i s apparent that the modified assay provided q u a n t i t a t i v e r e c o v e r i e s of adenosine and a l l i t s major c a t a b o l i t e s . The assay as described by Thompson and Appleman (85) provided u n s a t i s f a c t o r y r e c o v e r i e s of adenosine(73$) and i t s c a t a b o l i t e s , i n o s i n e (22$), hypoxanthine (23$), and adenine (37$)• The rec o v e r i e s of adenosine and i n o s i n e are v i r t u a l l y i d e n t i c a l to those published by Rutten et a l . , (78). These authors used Dowex AG1 X2 200-4-00 mesh r e s i n so these low rec o v e r i e s are not l i k e l y due to d i f f e r e n c e s i n r e s i n type or p r e p a r a t i o n (Dowex AG1 r e s i n s are reprocessed Dowex - 30 -F i g u r e 3« Recovery of u n l a b e l l e d purines from the phosphodiesterase assay. The standard assay, c o n t a i n i n g HgO i n place of enzyme s o l u t i o n , was sc a l e d up "by a f a c t o r of two. Resin s l u r r y was then added which contained the required amount of a c i d . C o n t r o l tubes had HgO s u b s t i t u t e d f o r the r e s i n s l u r r y . I f a c i d was present i n the s l u r r y , an equivalent amount of a c i d was inc l u d e d i n the c o n t r o l tubes. F o l l o w i n g e q u i l i b r a t i o n and c e n t r i f u g a t i o n the Ag^£ of the supernatant was measured. Re s u l t s are expressed as a percentage of absorbance of the c o n t r o l tube. S o l i d bars, r e s i n s l u r r y contained 3•0 mM a c e t i c a c i d p r i o r to a d d i t i o n ; open bars, r e s i n s l u r r y w i t h no a d d i t i o n ; cross hatch bars, r e s i n s l u r r y contained 115 mM formic a c i d p r i o r to a d d i t i o n . P l a t e A, adenosine and me t a b o l i t e s ; p l a t e B, guanosine and metabolite. A b r e v i a t i o n s ; A,, adenosine; I , i n o s i n e ; HYPOX, hypoxanthine; ADE, adenine; G, guanosine; X, xanthosine. - 32 -1 r e s i n s c o n t a i n i n g fewer trace metals: and narrower mesh s i z e ) . I n F i g . 3B, the re c o v e r i e s of guanosine and xanthosine are presented. The method of Thompson and Appleman a l s o gave very poor r e c o v e r i e s of these compounds. Mod i f y i n g the assay to in c l u d e a c e t i c a c i d (3 mM) i n the r e s i n s l u r r y . a g a i n d r a m a t i c a l l y increased nucleoside r e c o v e r i e s , however, these w e r e . ; s t i l l low and not uniform. Optimal recovery was obtained by adding 115 mM formic a c i d to the s l u r r y . Although 100$ r e c o v e r i e s could be obtained i f the formic a c i d c o n c e n t r a t i o n was increased beyond 115 mM, rec o v e r i e s of 90$ f o r guanosine and 8.7$ f o r xanthosine were accepted i n order to minimize the blanks. The f i n a l m o d i f i c a t i o n s adopted were, t h e r e f o r e , the i n c l u s i o n of 3.0 mM a c e t i c a c i d i n the r e s i n s l u r r y f o r the assay of c y c l i c AMP h y d r o l y s i s , and the i n c l u s i o n of 115 mM formic a c i d i n the r e s i n s l u r r y f o r the assay of c y c l i c GMP h y d r o l y s i s . The exact amount of a c i d to be added depended on the b u f f e r c o n c e n t r a t i o n used i n the assay. The above values are f o r 10 mM T r i s - H C l , pH 7.5. Other concentrations of T r i s , MOPS, or imidazole were t r i e d and found to r e q u i r e s l i g h t l y d i f f e r e n t amounts of a c e t i c a c i d f o r 100 $ recovery of [ Cj adenosine. The assay should, t h e r e f o r e , be p i l o t e d out on'the p a r t i c u l a r assay mixture used. I t should be noted that the blank values obtained were lower i f MOPS was used to replace T r i s - H C l as the b u f f e r i n g agent. I n order to determine the recovery and blank values i n the presence of v a r y i n g concentrations of nucleoside or c y c l i c n u c l e o t i d e , r a d i o a c t i v e l y l a b e l l e d nucleosides were used. I n these assays a range of nucleoside or c y c l i c n u c l e o t i d e concentrations between 0.1 and 5 0 0 uM was- included i n a s e t of tubes, then the recovery and blank values determined. These values were found not to depend - 33 -on the c o n c e n t r a t i o n of c y c l i c n u c l e o t i d e or nucleoside present. The blank value f o r C H J c y c l i c AMP was found to be 6.7$ of the added c y c l i c AMP w i t h a c o e f f i c i e n t i?8j*^a'riation of 1.2$ while the corresponding value f o r C H2 c y c l i c GMP was 5-7$ w i t h a c o e f f i c i e n t of v a r i a t i o n of 1.6$. While these blank values may be somewhat high, t h e i r e x c e l l e n t r e p r o d u c i b i l i t y allows f o r l i t t l e e r r o r . Since the modified assay produced q u a n t i t a t i v e r e c o v e r i e s of adenosine met a b o l i t e s , an experiment was conducted to compare the l i n e a r i t y w i t h time of both the modified and the o r i g i n a l assays. These data are presented i n F i g . 4. Using a crude homogenate of r a b b i t heart as the enzyme source, i t can be seen that the h y d r o l -y s i s r a t e determined u s i n g the o r i g i n a l assay was not l i n e a r with time and i n a l l cases the measured r e a c t i o n product was l e s s than 73$ of that obtained w i t h the modified assay. The lower r e c o v e r i e s with time i n the o r i g i n a l assay could be a t t r i b u t e d to the formation of the adenosine c a t a b o l i t e s i n o s i n e , hypoxanthine, and adenine (78,83) which are recovered i n very low y i e l d . Experiments were conducted to compare k i n e t i c parameters derived from an assay of heart supernatant u s i n g both the o r i g i n a l and modified assays. Since there i s a v a r i a t i o n i f i the l e v e l s of contaminating purine m e t a b o l i z i n g enzymes between species (83) and a l s o i n the l e v e l s of phosphodiesterase, e x t r a c t s of both r a b b i t and r a t heart were used. I n F i g . 5, the k i n e t i c s of h y d r o l y s i s of c y c l i c AMP by a r a b b i t heart supernatant f r a c t i o n are presented. Unless overlapping occurred, both p o i n t s of a m u l t i p l e de t e r m i n a t i o n are included to i n d i c a t e the r e p r o d u c i b i l i t y - 3k -Figure 4- . C y c l i c AMP h y d r o l y s i s "by ra"b"bit heart homogenate. A standard i n c u b a t i o n mix c o n t a i n i n g 10 mM T r i s - H C l pH 7-5> 250 uM EGTA, 1 mM MgCl 2 and 0 . 4 6 6 mM c y c l i c AMP was sc a l e d up by a f a c t o r of 3°. to 6 . 0 ml. Enzyme (4-.0 ml of a 1:5 d i l u t i o n i n HgO of the homogenate) was added to s t a r t the r e a c t i o n . A t 0 time; and a t 15 minute i n t e r v a l s , 1.0 ml a l i q u o t s were withdrawn and placed i n a tube i n a b o i l i n g water bath. The • tube was c e n t r i f u g e d to remove p r e c i p i t a t e d p r o t e i n and 200 u l a l i q u o t s of the supernatant withdrawn. These a l i q u o t s were then incubated w i t h 5'-nucleotidase and the standard assay continued as o u t l i n e d i n Experimental Procedure. Values are the means of d u p l i c a t e s . Closed c i r c l e s , r e s i n s l u r r y contained 3.0 mM a c e t i c a c i d p r i o r to additon; open c i r c l e s , r e s i n s l u r r y with no a d d i t i o n s . - 35 -- 36 -Figure 5- K i n e t i c s of c y c l i c AMP h y d r o l y s i s "by r a b b i t heart supernatant. Substrate concentrations p l o t t e d are average concentrations present d u r i n g the i n c u b a t i o n . The standard assay contained 250 uM EGTA and 23-5 ug p r o t e i n . P l a t e A, a r e s i n s l u r r y was used which contained 3•0 mM a c e t i c a c i d . P l a t e B, a r e s i n s l u r r y was used without any a d d i t i o n s . - 37 -2 0 . 0 4 0 . 0 6 0 . 0 8 0 . 0 1 0 0 . 0 1 2 0 . 0 1 4 0 . 0 A V E R A G E S U B S T R A T E (juM) - 38 -of the assay. The phosphodiesterase from t h i s t i s s u e e x h i b i t e d n o n l i n e a r S/v vs S p l o t s when assayed both w i t h and without the m o d i f i c a t i o n . The h y d r o l y s i s of c y c l i c AMP by r a t heart supernatant i s p l o t t e d i n F i g . 6. A d e f i n i t e n o n l i n e a r ! t y i s seen once again This type of n o n l i n e a r ! t y has been a t t r i b u t e d to e i t h e r a n e g a t i v e l y cooperative enzyme (67) or a mixture of two enzymes w i t h d i f f e r e n t K values (82). m • I n t h i s p r e l i m i n a r y i n v e s t i g a t i o n , which was p r i m a r i l y concerned w i t h the v a l i d i t y of the assay method, the data were f i t t e d to the model of a mixture of two enzymes both of which obey Michaelis-Menten k i n e t i c s . The data-presented i n F i g . 5 and 6 were analyzed as described i n Experimental Procedure, s e c t i o n C - l , and the r e s u l t s are given i n Table I . The most predominant e f f e c t produced by modifying the assay was an-increase i n V. The K m values were a l s o somewhat lower when determined with the modified assay w i t h the exception of the low K form of r a t heart which was m somewhat higher. The values recorded were obtained by u s i n g the average substrate c o n c e n t r a t i o n during the course of the assay. I f t h i s c o r r e c t i o n i s not a p p l i e d the K values obtained are $-10% r r m higher. The values i n parentheses are those values obtained i f an unweighted l e a s t squares f i t i s performed. As can be seen the a p p l i c a t i o n of s t a t i s t i c a l weights can produce a 10-30$ a l t e r a t i o n i n the value of a parameter. I n d i v i d u a l V values were only s l i g h t l y d i f f e r e n t than the values l i s t e d i f weighting f a c t o r s were omitted. An index of the recovery of the o r i g i n a l assay (85) can be determined from the r a t i o : v o r i g i n a l assay/v modified assay. - 39 -Figure 6. K i n e t i c s of c y c l i c AMP h y d r o l y s i s by r a t heart supernatant. Substrate values p l o t t e d are the average concentrations of c y c l i c AMP present d u r i n g the i n c u b a t i o n . The standard assay used contained 250 uM EGTA and 27-3 ug p r o t e i n . P l a t e A, r e s i n s l u r r y was used which contained 3.0 mM a c e t i c a c i d p r i o r to i t s a d d i t i o n . P l a t e B, r e s i n s l u r r y was used which contained no added a c e t i c a c i d . _ JLJ>0 — AVERAGE SUBSTRATE (/LM) TABLE I : K i n e t i c parameters of c y c l i c AMP h y d r o l y s i s "by heart supernatant f r a c t i o n s The data presented i n i n F i g s . 5 and 6 were analyzed as described i n Experimental Prodedure. The values i n the t a b l e are those determined by using the average substrate c o n c e n t r a t i o n d u r i n g the course of the incubation. M i c h a e l i s constants f o r the high K_ form; K m^, V ^ . M i c h a e l i s constants f o r the low K m form; K ^ , V T . Values i n H parentheses are K estimates obtained using a weighting f a c t o r of 1.0 i n the l e a s t 4 9 squares f i t t i n g . A weighting f a c t o r of v /S was used f o r a l l other c a l c u l a t i o n s Tissue HOAc i n s l u r r y (mM) K mH (uM) V. H (pMoles/min/mg) K (uM) VT (pmoles/min/mg) Rabbit Heart Rabbit Heart 3.0 0.0 44.5(54-.0) 57.0(4-7.4) 4 6 6 269 0 . 3 1 0 ( 0 . 4 - 3 4 ) 0 . 4 1 4 ( 0 . 3 4 3 ) 134 99.5 Rat Heart Rat Heart 3.0 0.0 35-6(39.1) 48.4(52.1) 1 0 8 0 8 8 2 0.195(0.252) 0.158(0.185) 56.0 33-9 - i+2 -Such an a n a l y s i s r e v e a l s t h a t recovery i n the o r i g i n a l assay v a r i e d "between 55 and 7k%. For assays i n v o l v i n g r a b b i t t i s s u e s , the r e c o v e r i e s f l u c t u a t e d throughout the substrate range. For r a t t i s s u e s , however, the r e c o v e r i e s a t higher substrate l e v e l s were s i g n i f i c a n t l y g r e a t e r than those a t lower substrate ranges. This v a r i a t i o n tended to increase the measured w i t h the o r i g i n a l assay and thus minimize the d i f f e r e n c e s i n between the assays f o r t h i s t i s s u e . The assay presented here was a l s o compared w i t h the alumina oxide i s o t o p i c assay f o r c y c l i c AMP h y d r o l y s i s (80). The procedure was modified somewhat from that described by the o r i g i n a l authors. For r o u t i n e use columns were poured from a s l u r r y of a c i d alumina oxide i n 0.1 M ammonium acetate pH 4-.0 r a t h e r than e q u i l i b r a t i n g columns of n e u t r a l alumina to pH k.O w i t h 0.1 M ammonium acetate. Both types of alumina were found to give i d e n t i c a l r e s u l t s . A standard i n c u b a t i o n of r a t heart supernatant (27.3 ug p r o t e i n ) c o n t a i n i n g k.68 uM c y c l i c AMP was performed u s i n g t h i s assay. The nu c l e o t i d a s e i n c u b a t i o n was stopped by the a d d i t i o n of 25 u l df :\l M ammonium acetate pH k.0; 200 u l of the r e a c t i o n mixture was a p p l i e d to a 1.5 g alumina column and eluted w i t h 1.5 ml of the e q u i l i b r a t i n g b u f f e r . R a d i o a c t i v i t y was determined i n the e f f l u e n t i n 12 ml of Tr i t o n - t o l u e n e s c i n t i l l a t i o n f l u i d . A f t e r c o r r e c t i o n of the values obtained f o r an 86% recovery / • r l 4 - 1 \ (obtained from a dummy assay c o n t a i n i n g L CJ adenosine), t h i s assay gave a value l.k-% lower than t h a t obtained by the modified procedure u s i n g Dowex 1. The two assays are,• t h e r e f o r e , i n e x c e l l e n t agreement. - 43 -B. Phosphodiesterase of the Super-ior C e r v i c a l Ganglion As p r e v i o u s l y mentioned, i t has "been proposed that c y c l i c n u c l e o t i d e s may,modulate the s e n s i t i v i t y of the s u p e r i o r c e r v i c a l ganglion to neurohormonal and e l e c t r i c a l s t i m u l a t i o n (30)- Despite the importance of phosphodiesterase i n r e g u l a t i n g c y c l i c n u c l e o t i d e l e v e l s i n most t i s s u e s , there i s almost no i n f o r m a t i o n a v a i l a b l e on i t s p r o p e r t i e s i n the s u p e r i o r c e r v i c a l ganglion. I t , t h e r e f o r e , seemed -essential t o i n v e s t i g a t e the r e g u l a t i o n of phosphodiesterase i n ganglion e x t r a c t s . 1. E f f e c t of Ca++ and p r o t e i n a c t i v a t o r Using the p r e v i o u s l y described assay, the p r o p e r t i e s of phosphodiesterases i n crude t i s s u e preparations could be examined. U n l i k e most t i s s u e s s t u d i e d to date i n which phosphodiesterase i s present i n both the s o l u b l e cytoplasmic f r a c t i o n and i n t i s s u e p a r t i c l e s , the enzyme i n e x t r a c t s of both canine and bovine s u p e r i o r c e r v i c a l g a n g l i a was completely recovered i n the 37,°°0 x g supernatant f l u i d . The a c t i v i t y i n crude supernatant f r a c t i o n s of both canine and bovine g a n g l i a , assayed with two concentrations of c y c l i c AMP and one concent r a t i o n of c y c l i c GMP i s shown i n Table I I . When Ca++ was present a t a concent r a t i o n of 25® uM only modest s t i m u l a t i o n of a c t i v i t y (1.2 to 1.5 f o l d ) occurred. This i s i n marked c o n t r a s t to the 3 to 6 f o l d s t i m u l a t i o n of the bovine c e r e b r a l cortex enzyme produced by Ca ++ under s i m i l a r c o n d i t i o n s . An experiment was then performed to determine whether the p r o t e i n a c t i v a t o r was present i n the ganglion e x t r a c t s . Thus, phosphodiesterase from bovine cortex f r e e of p r o t e i n a c t i v a t o r (62) _ 44 -TABLE I I : E f f e c t of Ca++ on crude supernatant f r a c t i o n s of s u p e r i o r c e r v i c a l g a n g l i a Crude supernatant f r a c t i o n s from e i t h e r a bovine or canine source were assayed a t the concentrations of substrate i n d i c a t e d i n the presence of the standard assay mixture supplemented with e i t h e r 250 uM Ca++ or 250 uM EGTA. Increase i n a c t i v i t y when EGTA was replaced by Ca++ i n the assay mixture i s given i n brackets. V e l o c i t i e s are given i n pmoles of substrate h y d r o l y z e d / min/mg p r o t e i n . Values are the means of d u p l i c a t e experiments. 35 uM cAMP. 0.8 uM cAMP 3 • 9 uM cGMP Enzyme EGTA Ca++ EGTA Ca++ EGTA Ca++ Bovine 384 535 (1.4) 30.3 36.8 (1.2) 279 k06 (1 .5 ) Canine 98 . 6 ' 118 (1.2) 8.11.'. 10.9 (1.3) 35.7 41 .6 (1.2) - 45 -was assayed i n the presence and absence of b o i l e d e x t r a c t of canine s u p e r i o r c e r v i c a l ganglion. I n F i g . 7, histogram A, bar 1 represents the a c t i v i t y of the bovine cortex enzyme assayed i n the presence of 250 uM Ca++. The a d d i t i o n of 10 u l ( 6 4 ug p r o t e i n ) or 25 u l (160 ug p r o t e i n ) of b o i l e d (to destroy the phosphodiesterase) canine ganglion e x t r a c t produced a s i g n i f i c a n t increase i n phosphodiesterase a c t i v i t y (bars 2 and 3 r e s p e c t i v e l y ) i n the presence of 250 uM Ca++, but t h i s s t i m u l a t i o n was completely e l i m i n a t e d when 250 uM EGTA was added (bar 4) . This experiment i n d i c a t e d that the canine e x t r a c t s contained an a c t i v a t i n g f a c t o r which was capable of s t i m u l a t i n g the bovine cortex a c t i v a t o r - f r e e enzyme i n a Ca++ dependent manner. I n an a d d i t i o n a l experiment a crude supernatant f r a c t i o n of bovine cortex ( c o n t a i n i n g p r o t e i n a c t i v a t o r ) was a l s o assayed i n the presence of b o i l e d ganglion e x t r a c t s (histogram B, F i g . 7) . The a c t i v i t y of t h i s p r e p a r a t i o n assayed i n the presence of 2 5 ° uM EGTA i s shown i n bar 1. As had been reported p r e v i o u s l y (62) r e p l a c i n g EGTA wit h 250 uM Ca++ caused an increase i n a c t i v i t y (bar 2) r e s u l t i n g from endogenous p r o t e i n a c t i v a t o r . A d d i t i o n of b o i l e d canine ganglion e x t r a c t (25 u l ) caused a f u r t h e r s t i m u l a t i o n of a c t i v i t y , bar 3, apparently by more f u l l y s a t u r a t i n g the phosphodiesterase w i t h p r o t e i n a c t i v a t o r beyond th a t endogenous to the b r a i n e x t r a c t . I n histogram C, canine s u p e r i o r c e r v i c a l ganglion supernatant was the enzyme source. As noted p r e v i o u s l y Ca ++ s t i m u l a t i o n of phosphodiesterase a c t i v i t y was extremely small (compare bar 3 w i t h bar l ) . Bar 2 represents the a c t i v i t y observed i n the presence of the standard assay mixture c o n t a i n i n g n e i t h e r Ca++ nor EGTA. The p o s s i b i l i t y _ 4.6 -Figure ?• A c t i v a t o r p r o t e i n of s u p e r i o r c e r v i c a l ganglion crude supernatant. S o l i d "bars, standard assay included 250 uM EGTA; open "bars, 250 uM Ca++; crosshatched bars, exogenous p r o t e i n a c t i v a t o r plus Ca++; h o r i a o n t a l l y s t r i p e d bars, no Ca++ or EGTA. The enzyme source f o r each histogram was as f o l l o w s ; A and E, 3-5 and 4 .5 ug DEAE-cellulose p u r i f i e d bovine cortex phosphodiesterase; B, 7-2 ug crude supernatant of bovine c o r t e x ; C, 160 ug crude cannine ganglion phosphodiesterase; D, enzymes of B and C were mixed. P r o t e i n a c t i v a t o r was obtained from b o i l e d crude supernatants of the f o l l o w i n g t i s s u e sources; A2 , 6 4 ug canine ganglion; A3, A4, B3, l6'0 ug canine ganglion; C4 and C5 ,9° and 9 ug bovine cortex; E2, 77 ug bovine ganglion. C y c l i c AMP, 35 uM, was the su b s t r a t e . - w? -10 CVJ 4* o CVJ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ 10 ^ |_ I CVJ QQ (U!ai/d|/\iv OjpAo S9|oaid) A - 4 8 -of contaminating Ca++ being p r e s e n t - i n the assay mixture i s indicated, by t h i s determination having a value intermediate between the EGTA and Ca++ l e v e l s . When the assay was supplemented w i t h Ca++ plus b o i l e d e x t r a c t of bovine b r a i n (25 u l , 90 ug p r o t e i n ; bar 4 , or one-tenth t h i s amount; bar 5) no increase i n phosphodiesterase a c t i v i t y occurred. S i m i l a r l y a p u r i f i e d p r o t e i n a c t i v a t o r p r e p a r a t i o n from bovine b r a i n (2.8 ug p r o t e i n ) f a i l e d to s t i m u l a t e the ganglion enzyme i n the presence of Ca++ (data not shown). Such data i n d i c a t e d t h a t n e i t h e r Ca++, nor Ca++ plus e i t h e r crude or p a r t i a l l y p u r i f i e d p r o t e i n a c t i v a t o r , s i g n i f i c a n t l y a f f e c t e d the canine ganglion phosphodiesterase present i n crude e x t r a c t s . The data would a l s o tend to r u l e out the p o s s i b i l i t y t hat an a d d i t i o n a l h e a t - s t a b l e f a c t o r (e.g. p r o t e i n , l i p i d , carbohydrate or ion) might be absent from the ganglion e x t r a c t s , but present i n the b r a i n p r e p a r a t i o n . Histogram D represents an experiment i n which:a-mix'ture of .'crude supernatant f r a c t i o n s of bovine cortex and canine s u p e r i o r c e r v i c a l g a n g l i a served as the enzyme. Bar 1 represents the a c t i v i t y i n the presence of EGTA. This value i s e x a c t l y t h a t p r e d i c t e d from the sum of the two a c t i v i t i e s , represented as bar 3» the a r i t h m e t i c sum of bars B l and CI. Bar 2 i s the a c t i v i t y obtained when t h i s mixture of the two e x t r a c t s was assayed i n the presence of Ca++. The p r e d i c t e d value of t h i s a c t i v i t y i s shown as bar 4 which i s the a r i t h m e t i c sum of bars B3 and C 4 . This experiment reveals that the l a c k of Ca++ s t i m u l a t i o n of the ganglion phosphodiesterase i s not due to an a d d i t i o n a l heat l a b i l e f a c t o r absent from the ganglion e x t r a c t but present i n the cortex p r e p a r a t i o n . _ 4-9 -I n s i m i l a r e x p e r i m e n t s i t was - r e v e a l e d t h a t p h o s p h o d i e s t e r a s e from b o v i n e s u p e r i o r c e r v i c a l g a n g l i a behaved i d e n t i c a l l y t o the c a n i n e enzyme; n e i t h e r Ca++ a l o n e n o r Ca++ p l u s p r o t e i n a c t i v a t o r produced s i g n i f i c a n t s t i m u l a t i o n of the enzyme. L i k e c a n i n e g a n g l i a , b o v i n e g a n g l i a e x t r a c t s were a good s o u r c e of p r o t e i n a c t i v a t o r . T h i s i s shown i n h i s t o g r a m E ( F i g . 7 ) . I n t h i s e x p e r i m e n t p u r i f i e d b o v i n e c o r t e x p h o s p h o d i e s t e r a s e was a s s a y e d i n the p r e s e n c e of Ca++ ( b a r l ) and i n the p r e s e n c e of Ca++ p l u s b o i l e d b o v i n e g a n g l i o n e x t r a c t (77 ug p r o t e i n ) . The s t i m u l a t o r y e f f e c t of p r o t e i n a c t i v a t o r i n the g a n g l i o n e x t r a c t i s r e a d i l y a p p a r e n t . The above e x p e r i m e n t s i n d i c a t e d t h a t a l t h o u g h s u p e r i o r c e r v i c a l g a n g l i a p r e p a r a t i o n s were a good s o u r c e of p r o t e i n a c t i v a t o r , Ca++ dependent s t i m u l a t i o n of the g a n g l i o n p h o s p h o d i e s t e r a s e c o u l d n o t be demonstrated under any c o n d i t i o n s . P r o t e i n a c t i v a t o r f r o m g a n g l i o n e x t r a c t s , however, r e a d i l y s t i m u l a t e d a c t i v a t o r - f r e e p h o s p h o d i e s t e r a s e from b o v i n e c e r e b r a l c o r t e x when Ca++ was p r e s e n t w h i l e p a r t i a l l y p u r i f i e d p r o t e i n a c t i v a t o r from c o r t e x was w i t h o u t s t i m u l a t o r y a c t i o n on the g a n g l i o n p h o s p h o d i e s t e r a s e . 2. K i n e t i c a n a l y s i s of the crude s u p e r n a t a n t f r a c t i o n The k i n e t i c s of c y c l i c n u c l e o t i d e h y d r o l y s i s were examined i n the b o v i n e s u p e r i o r c e r v i c a l g a n g l i o n crude s u p e r n a t a n t f r a c t i o n . I n F i g . 8 the k i n e t i c s of c y c l i c AMP h y d r o l y s i s a r e p r e s e n t e d as a v e l o c i t y vs l o g g (average s u b s t r a t e c o n c e n t r a t i o n ) p l o t . T h i s p l o t was chosen t o accommodate the l a r g e range of s u b s t r a t e c o n c e n t r a t i o n s u s e d . The i n c l u s i o n of 2 . 5 uM c y c l i c GMP (open t r i a n g l e s ) i n the a s s a y m i x t u r e i n c r e a s e d the h y d r o l y s i s r a t e of the h i g h e r - 50 -Figure 8. E f f e c t of c y c l i c GMP on the k i n e t i c s of c y c l i c AMP h y d r o l y s i s by "bovine ganglion crude supernatant. K i n e t i c assays were performed i n the presence (open t r i a n g l e s ) or absence (open c i r c l e s ) of 2.5 uM c y c l i c GMP. The i n s e r t represents the r a t e of h y d r o l y s i s of 7.8 uM c y c l i c AMP i n the presence of the concentrations of c y c l i c GMP i n d i c a t e d on the a b s c i s s a . ' The assay mixture contained 250 uM EGTA and 77 ug p r o t e i n . - 51 -- 52 -concentrations of c y c l i c AMP. The c y c l i c GMP a c t i v a t i o n of c y c l i c AMP h y d r o l y s i s i s f u r t h e r i l l u s t r a t e d i n the i n s e r t to F i g . 8. A c t i v a t i o n of the h y d r o l y s i s of 7-8 uM c y c l i c AMP was maximal a t 15 uM c y c l i c GMP and h a l f maximal a c t i v a t i o n was obtained a t approximately 2.7 uM c y c l i c GMP. Attempts to f i t the k i n e t i c data of c y c l i c AMP h y d r o l y s i s to the model of a mixture of two simple enzymes, us i n g the i t e r a t i v e cross c o r r e c t i o n of v e l o c i t i e s method, were not s u c e s s f u l . The f i t was poor and an absurdly low estimate f o r the low was obtained. A l s o , the existence of substrate analog a c t i v a t i o n which i s suggestive of cooperative behaviour, tended to preclude t h i s model. Double or s i n g l e r e c i p r o c a l p l o t s of c y c l i c AMP h y d r o l y s i s e x h i b i t e d complex n o n l i n e a r behaviour w i t h the general trend being downward curvature. The existence of more than one enzyme species with a t l e a s t one of these being a cooperative enzyme was suggested by the data obtained. This s u p p o s i t i o n was supported by an a n a l y s i s of the k i n e t i c s of c y c l i c GMP h y d r o l y s i s . I n F i g . 9 the complex double r e c i p r o c a l p l o t of c y c l i c GMP h y d r o l y s i s i n d i c a t e d k i n e t i c behaviour which could not be explained by e i t h e r a n e g a t i v e l y cooperative enzyme or a mixture of two enzymes. The general trend of the curve i s downward but there i s a suggestion of f u r t h e r k i n e t i c c o m p l e x i t i e s i n the intermediate substrate concentrations. The e f f e c t of c y c l i c AMP on c y c l i c GMP h y d r o l y s i s was examined and . i s presented as a Dixon p l o t i n F i g . 10. The s l i g h t a c t i v a t i o n of the h y d r o l y s i s of the higher concentrations of c y c l i c GMP by low concentrations of c y c l i c AMP r e s u l t e d i n upward curvature as the l i n e s of c y c l i c GMP h y d r o l y s i s approach the o r d i n a t e . The h y p e r b o l i c form of the - 53 -Figure 9. K i n e t i c s of c y c l i c GMP- h y d r o l y s i s by bovine ganglion crude supernatant. The assay mixture contained 250 uM EGTA and 77 ug p r o t e i n . - 54 -- 55 -Figure 10. E f f e c t of c y c l i c AMP on the k i n e t i c s of c y c l i c GMP h y d r o l y s i s by "bovine ganglion crude supernatant. Concentrations of c y c l i c GMP used were: 100 uM, (open c i r c l e 50 uM, (open t r i a n g l e s ) ; 16 uM, (open squares); 8 uM, (closed c i r c l e s ) ; 3 .2 uM, (closed t r i a n g l e s ) ; 1.4- uM, (closed squares and 0.28 uM, (closed double t r i a n g l e s ) . C y c l i c AMP was present a t the concentrations i n d i c a t e d on the a b s c i s s a . The assay mixture included 77 ug p r o t e i n and 250 uM EGTA. - 56 -0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0 c y c l i c A M P ( / i M ) - 57 -l i n e s and the substrate analog ac t i - v a t i o n are compatable wi t h the existence of a complex enzyme system. Since i t would be extremely d i f f i c u l t to k i n e t i c a l l y examine an enzyme system composed of a mixture of cooperative enzyme species, attempts were made to determine i f m u l t i p l e molecular forms of the enzyme were present. Should t h i s be the case, the sepa r a t i o n of these enzymes would a l l o w examination of each one i n d i v i d u a l l y and thus ^permit t h e i r k i n e t i c c h a r a c t e r i z a t i o n . I t would a l s o a l l o w a f u r t h e r i n v e s t i g a t i o n of the l a c k of response to Ca++ and p r o t e i n a c t i v a t o r observed i n crude preparations.. Bovine g a n g l i a were used i n these s t u d i e s because of the r e l a t i v e l y l a r g e amounts of t i s s u e a v a i l a b l e . 3. DEAE-cellulose chromatography of bovine s u p e r i o r c e r v i c a l ganglion e x t r a c t The p r e p a r a t i o n of the ganglion e x t r a c t and i t s chromatography on DEAE-cellulose have been p r e v i o u s l y o u t l i n e d i n Experimental Procedure. R o u t i n e l y , 60 ml of e x t r a c t (180 mg p r o t e i n ) , r e p r e s e n t i n g 4 g of t i s s u e was di a l y z e d overnight a g a i n s t the e q u i l i b r a t i n g b u f f e r , then a p p l i e d to the column. The column was washed wi t h s e v e r a l bed volumes of e q u i l i b r a t i n g b u f f e r which eluted a p r o t e i n f r a c t i o n c o n t a i n i n g no detectable phosphodiesterase a c t i v i t y . A l i n e a r gradient from s t a r t i n g b u f f e r to 1 M sodium acetate was then a p p l i e d . The e l u t i o n p r o f i l e produced depended on the t o t a l volume of the gradient. The use of a 3°0 ml gradient, as described by R u s s e l l - e t a l . , (25), produced a p a r t i a l - ' s e p a r a t i o n of a t l e a s t three enzyme speci e s . I n c r e a s i n g the t o t a l gradient volume to 400 ml r e s u l t e d i n the complete s e p a r a t i o n of the i n i t i a l - 58 -peak of a c t i v i t y . However, t h i s increase i n gradient volume reduced the s e p a r a t i o n of the second and t h i r d peaks of a c t i v i t y r e l a t i v e to that obtained u s i n g the 300 ml gradient. I t was subsequently found that the s e q u e n t i a l use of these two gradients provided the best r e s o l u t i o n of a l l enzyme speci e s . I n F i g . 11, a t y p i c a l DEAE-cellulose column e l u t i o n p r o f i l e of-a crude supernatant f r a c t i o n obtained from bovine g a n g l i a . i s presented. The t o t a l gradient volume used was 4-00 ml (200 ml of s t a r t i n g b u f f e r and 200 ml of 1 M sodium a c e t a t e ) . As p r e v i o u s l y s t a t e d , the f i r s t peak of a c t i v i t y was w e l l r e s o l v e d . This enzyme species was r e l a t i v e l y s p e c i f i c f o r the h y d r o l y s i s of " c y c l i c " GMP . - Two p o o r l y r e s o l v e d peaks of a c t i v i t y were e l u t e d l a t e r which hydrolyzed both c y c l i c AMP and c y c l i c GMP. Tubes c o n t a i n i n g the f i r s t peak of a c t i v i t y (20 to 4-0) were pooled, concentrated, and s t o r e d a t -80°. This p r e p a r a t i o n i s r e f e r r e d to as enzyme D-j-. Tubes c o n t a i n i n g the remaining a c t i v i t y (50 through 100) were pooled, concentrated, and then rechromatographed on an i d e n t i c a l DEAE-c e l l u l o s e column w i t h a 300 ml l i n e a r gradient of sodium acetate. This e l u t i o n p r o f i l e i s given i n F i g . 12. Tubes c o n t a i n i n g the f i r s t peak of a c t i v i t y (tubes 34- to 52) and those c o n t a i n i n g the second peak (tubes 57 through 100) were s e p a r a t e l y pooled, .;• concentrated, and s t o r e d . They are r e f e r r e d to as D^ -j- and D-J-J-J-r e s p e c t i v e l y . I t should be mentioned that the mixture of D^ and D J J J from more than one DEAE-cellulose column was a p p l i e d to t h i s second column. The r e l a t i v e peak heights are, t h e r e f o r e , not d i r e c t l y comparable between Fig.11 and F i g . 12. A t o t a l of 23$ of the crude supernatant a c t i v i t y was recovered i n the three - 59 -Figure 11. DEAE-cellulose e l u t i o n p r o f i l e of phosphodiesterase a c t i v i t y from a "bovine s u p e r i o r c e r v i c a l ganglion crude supernatant f r a c t i o n . A 400 ml l i n e a r gradient to 1 M sodium acetate was s t a r t e d a t tube 0 and continued through tube 14-0; (open squares), c y c l i c AMP c o n c e n t r a t i o n was 0.111 uM;(closed ci r c l e s ) ; v c y c l i c GMP c o n c e n t r a t i o n was O.77 uM. EGTA (250 uM) was included i n a l l assay tubes. - 60 -0 20 40 60 80 400 420 440 TUBE NUMBER - 61 -Figure 12. Rechromatography of t r a i l i n g a c t i v i t y from the f i r s t DEAE-cellulose column. A 300 ml l i n e a r gradient to 1 M sodium acetate was a p p l i e d a t tube 0 and continued through tube 100.. (closed t r i a n g l e s ) , f o l d a c t i v a t i o n produced by i n c l u d i n g 7.57 uM u n l a b e l l e d c y c l i c GMP i n an assay of the h y d r o l y s i s r a t e of 2.48 uM c y c l i c AMP. Remaining symbols as f o r F i g . 11. EGTA (250 uM) was i n c l u d e d i n a l l assay tubes. v (p moles cyclic GMP/min./ml x 10) ( • — • ) D ro O J cn (j) -g ~~ 1 1 1 1 1 1 n I I 1 1 I I ' ' I CD oo o r o ^ (J> 00 ro O v (p moles cyclic AMP / min. / ml x 10) (• °) - 63 -concentrated enzyme forms. The e l u t i o n p r o f i l e s presented were h i g h l y r e p r o d u c i b l e . I t w i l l be r e c a l l e d t h a t c y c l i c GMP a c t i v a t e d c y c l i c AMP h y d r o l y s i s i n the crude supernatant f r a c t i o n (see F i g . 8) . The e f f e c t of c y c l i c GMP on c y c l i c AMP h y d r o l y s i s throughout the e l u t i o n p r o f i l e i s a l s o presented i n F i g . 12. I t can be seen that enzyme species D ^ ^ was a c t i v a t e d by c y c l i c GMP whereas enzyme D J J J was s l i g h t l y i n h i b i t e d . k. P r o p e r t i e s of the DEAE-cellulose resolved enzymes I t now became p o s s i b l e to examine the e f f e c t of p r o t e i n a c t i v a t o r and Ca++ on each of the separated enzyme species and a l s o to perform a d e t a i l e d a n a l y s i s of t h e i r k i n e t i c s of c y c l i c n u c l e o t i d e h y d r o l y s i s . E f f e c t of Ca++ and p r o t e i n a c t i v a t o r - Each phosphodiesterase species was elu t e d from the column f r e e of p r o t e i n a c t i v a t o r ; the l a t t e r remaining on the column under the con d i t i o n s used. Thus when b o i l e d e x t r a c t s of a l l three enzymes were added i n the presence of Ca++ to the assay of bovine cortex phosphodiesterase f r e e of p r o t e i n a c t i v a t o r , no increase i n a c t i v i t y occurred. The behaviour of each enzyme species to Ca++ and p r o t e i n a c t i v a t o r (from bovine cortex) i s presented i n Table I I I . S u p r i s i n g l y , each enzyme was markedly i n h i b i t e d by Ca++ (250 uM) i n the absence of p r o t e i n a c t i v a t o r . A d d i t i o n of the p r o t e i n a c t i v a t o r reversed Ca++ i n h i b i t i o n but d i d not s i g n i f i c a n t l y s t i m u l a t e the phosphodiesterase above the c o n t r o l l e v e l s i e . EGTA present. The p o s s i b i l i t y that EGTA a c t i v a t e s the enzyme i s not - 6 4 -TABLE I I I : E f f e c t of @a++ on i s o l a t e d enzyme species Phosphodiesterase a c t i v i t y of each of the DEAE-cellulose r e s o l v e d enzymes was determined at a c y c l i c AMP con c e n t r a t i o n of 5-2 uM or a c y c l i c GMP conc e n t r a t i o n of 0.83 uM. A l l v e l o c i t i e s represent pmoles/min/ml enzyme. V^p' v e l o c i t y i n presence of 2.8 ug p u r i f i e d "bovine cortex p r o t e i n a c t i v a t o r , vgQij^» v e l o c i t y i n presence of 250 uM EGTA; + + f v e l o c i t y i n presence of 250 uM Ca++; Vca+++Ap' v e l o c i t y i n presence of 250 uM Ca++ and 2.8 ug p u r i f i e d bovine cortex p r o t e i n a c t i v a t o r . Values are means of du p l i c a t e determinations and are r e p r e s e n t a t i v e of r e s u l t s obtained w i t h two d i f f e r e n t p r e p a r a t i o n s . Enzyme Substrate V A p "^ EGTA VCa++ VCa+++Ap D j c y c l i c GMP 263 D U c y c l i c GMP 104 D I j j c y c l i c GMP 48.0 D U c y c l i c AMP 776 D T T T c y c l i c AMP 529 270 76.0 363 99.0 0 94.0 43.0 4.7 50.0 666 107 650 510 93.0 4 4 1 - 65 -l i k e l y i n view of. the data i n his-togram C, F i g . 7» The amount of p r o t e i n a c t i v a t o r added (2.8 ug) was s a t u r a t i n g s i n c e no f u r t h e r increase i n a c t i v i t y could be obtained by i n c r e a s i n g i t s concentra-t i o n . However, the a d d i t i o n of l e s s than s a t u r a t i n g amounts of p r o t e i n a c t i v a t o r d i d not f u l l y r e s t o r e the a c t i v i t y to ba s a l l e v e l s (data not shown). These observations on Ca++-activator p r o t e i n s e n s i t i v i t y were f u r t h e r examined u s i n g D-J--J- as the enzyme source. I n F i g . 13, the i n h i b i t o r y e f f e c t of Ca++ i s again c l e a r l y seen (compare open c i r c l e s w i t h open t r i a n g l e s ) . When p r o t e i n a c t i v a t o r was added i n the presence of C a + + (open squares), the a c t i v i t y returned to c o n t r o l l e v e l s (open c i r c l e s ) . Assays were conducted a t s e v e r a l time i n t e r v a l s up to 90 min. I n each case the v e l o c i t y was l i n e a r w i t h respect to time ( w i t h i n the l i m i t a t i o n s of s u b s a t u r a t i n g s u b s t r a t e ) p r o v i d i n g evidence t h a t Ca++ i n h i b i t i o n was not l i k e l y due to a time dependent a l t e r a t i o n of phosphodiesteras f o r example by a Ca+ +-dependent p r o t e o l y t i c enzyme. I n F i g . 13, the s t i m u l a t i o n of c y c l i c AMP h y d r o l y s i s by c y c l i c GMP i s a l s o seen. C y c l i c GMP con s i d e r a b l y s t i m u l a t e d the h y d r o l y s i s of c y c l i c AMP i n the standard assay c o n t a i n i n g 250 uM EGTA (compare open c i r c l e s with'cl'os.ed c i r c l e s ) or i f Ca++ and p r o t e i n a c t i v a t o r were present together (compare open squares w i t h closed squares). S t i m u l a t i o n by c y c l i c GMP was s i g n i f i c a n t l y reduced i f Ca++ was present without p r o t e i n a c t i v a t o r (closed t r i a n g l e s ) . I n c i d e n t a l l y , p r o t e i n a c t i v a t o r had no e f f e c t on any of the three enzyme species when added i n the presence of EGTA. S t i m u l a t i o n of c y c l i c AMP h y d r o l y s i s seemed r e l a t i v e l y s p e c i f i c f o r c y c l i c GMP; 3 ' : 5 ' - c y c l i c XMP, 2 ' : 3 ' - c y c l i c GMP, and DBcGMP a t concentrations from 0.5 to 125 uM - 66 -Figure 13• E f f e c t of Ca++ on phosphodiesterase DJJ_« Assay tubes included e i t h e r 250 uM Ca++ (A) ; 250 uM Ca++ plus 2.6 uM u n l a b e l l e d c y c l i c GMP (A); 250 uM EGTA (•) ; 250 uM Ca++ plus 13 ug p u r i f i e d bovine cortex p r o t e i n a c t i v a t o r (o); 250 uM EGTA plus 2.6 uM c y c l i c GMP (••) ; or 250 uM Ca++ plus 13 ug p r o t e i n a c t i v a t o r plus 2.6 uM c y c l i c GMP (•). The enzyme i n c u b a t i o n volume was scaled up to 1.2 ml, 0.2 ml a l i q u o t s were withdrawn a t the times i n d i c a t e d and the r e a c t i o n stopped by b o i l i n g f o r 75 sec. The remainder of the assay was performed as described i n Experimental Procedure. The substrate was 4.92 uM c y c l i c AMP. - 67 -TIME (Minutes) - 68 -were without e f f e c t . The nature of Ca++ i n h i b i t i o n of enzyme species D-^  i s examined i n F i g . 14. The enzyme i n the absence of Ca++ (open c i r c l e s ) e x h i b i t e d negative c o o p e r a t i v i t y . The presence of 250 uM Ca++ i n the assay produced a complex i n h i b i t i o n c h a r a c t e r i z e d by an apparent change i n both s u b s t r a t e a f f i n i t y and v e l o c i t y constants. I n view of the complex k i n e t i c s of the phosphodiesterase a determination of the d i s s o c i a t i o n constants f o r Ca++ was not attempted. Such a determination w i l l r e q u i r e the complete removal of contaminating Ca++ from the assay components (60). K i n e t i c c h a r a c t e r i z a t i o n of the enzyme species - I n order to determine p o s s i b l e r a t e equations f o r the enzyme s p e c i e s , a k i n e t i c a n a l y s i s , which employed r e v e r s i b l e m o d i f i e r s , was a p p l i e d . P r e l i m i n a r y experiments revealed t h a t i t was s t a t i s t i c a l l y impossible to d i f f e r e n t i a t e between a model of negative c o o p e r a t i v i t y and one based on a mixture of two enzymes us i n g equations d e s c r i b i n g h y d r o l y s i s r a t e s i n the absence of a m o d i f i e r (variances were i d e n t i c a l to f i v e decimal p l a c e s ) . This c o n c l u s i o n can be reached on t h e o r e t i c a l grounds alone (97). Rate equations d e s c r i b i n g the r e v e r s i b l e i n h i b i t i o n of a two s i t e d enzyme have been presented i n Experimental Procedure. P r o p e r t i e s of Dj - Enzyme species D j , which was r e l a t i v e l y s p e c i f i c f o r c y c l i c GMP h y d r o l y s i s , represented 17$ of the t o t a l c y c l i c GMP h y d r o l y z i n g a c t i v i t y e l u t e d from the column. I n F i g . 15A, the k i n e t i c s of c y c l i c GMP h y d r o l y s i s by t h i s enzyme are presented a t s e v e r a l concentrations of the i n h i b i t o r MIX. The i n s e r t s of F i g . 15 are double r e c i p r o c a l p l o t s of the same data - 69 -Figure lk. E f f e c t of Ca++ on the k i n e t i c s of c y c l i c AMP h y d r o l y s i s "by enzyme D J J - C y c l i c AMP h y d r o l y s i s was measured i n the presence of 250 uM EGTA (open c i r c l e s ) or 250 uM Ga++ (closed c i r c l e s ) . - 70 -- 71 -Figure 1$. K i n e t i c s of c y c l i c GMP h y d r o l y s i s "by enzyme species D-j-. Panel A, c y c l i c GMP h y d r o l y s i s was measured i n the presence of the f o l l o w i n g concentrations of the r e v e r s i b l e i n h i b i t o r , MIX; (O), none; (A) , 2 uM; (•) 10 uM; (•) , 20 uM; ( A ) , 30 uM. Panel B, c y c l i c GMP h y d r o l y s i s was measured i n the presence of the f o l l o w i n g concentrations of c y c l i c AMP; (O), none; (•), 33-2 uM; (•) , 87.8 uM; ( 4 ) , 176 uM. I n s e r t i n both panels i l l u s t r a t e double r e c i p r o c a l p l o t s of the same data over a l i m i t e d s ubstrate range. EGTA (250 uM) was included i n a l l assays. L O G e S A V E ( M M) - 73 -over a more l i m i t e d substrate range. The v versus Logg S p l o t i s the only d i s p l a y s u i t a b l e to accommodate the l a r g e range of substrate concentrations used. Even wi t h t h i s p l o t c l u s t e r i n g of poi n t s a t s i m i l i a r i n h i b i t o r concentrations tended to occur. For t h i s reason the data presented i n F i g . 15-17 are only r e p r e s e n t a t i v e of the t o t a l data. The data of F i g . 15A i n d i c a t e the apparent n e g a t i v e l y cooperative behaviour e x h i b i t e d by D-j-. F i g . 1 5 B i s a s i m i l i a r p l o t of the. e f f e c t of u n l a b e l l e d c y c l i c AMP on c y c l i c GMP h y d r o l y s i s by D-j-. C y c l i c AMP can be seen to be a r e l a t i v e l y poor i n h i b i t o r of c y c l i c GMP h y d r o l y s i s . P r o p e r t i e s of D - ^ - I n F i g . l6A the.-hydrolysis of c y c l i c AMP by enzyme species D-j--j- i n the presence of various concentrations of c y c l i c GMP i s presented. C y c l i c GMP s t i m u l a t e d c y c l i c AMP h y d r o l y s i s i n t h i s enzyme p r e p a r a t i o n . The s t i m u l a t i o n was maximal a t 20 uM c y c l i c GMP and f u r t h e r i n c r e a s i n g the c o n c e n t r a t i o n of c y c l i c GMP reduced a c t i v i t y . The c y c l i c AMP h y d r o l y z i n g a c t i v i t y of D-J--J- appears to be n e g a t i v e l y cooperative as w e l l . I n F i g . l6B the k i n e t i c s of c y c l i c GMP h y d r o l y s i s are presented a t various concentrations of u n l a b e l l e d c y c l i c AMP. A p o s s i b l e p o s i t i v e c o o p e r a t i v i t y i s seen f o r the h y d r o l y s i s of c y c l i c GMP. C y c l i c AMP can be seen to be a r e l a t i v e l y potent i n h i b i t o r of c y c l i c GMP h y d r o l y s i s by t h i s enzyme. Enzyme species D - ^ represented 60$ of the c y c l i c GMP and 66$ of the c y c l i c AMP h y d r o l y z i n g a c t i v i t y recovered from the column. P r o p e r t i e s of D J J J - Figure 17A i l l u s t r a t e s the k i n e t i c behaviour of with c y c l i c AMP as the substrate and c y c l i c GMP as the m o d i f i e r . At low concentrations of c y c l i c AMP, c y c l i c GMP was i n h i b i t o r y while a t higher concentrations of c y c l i c AMP - 74 -Figure 16. K i n e t i c s of c y c l i c n u c l e o t i d e h y d r o l y s i s by enzyme species D - J - J* Panel A, c y c l i c AMP h y d r o l y s i s was measured i n the presence of the f o l l o w i n g concentrations of c y c l i c GMP; (O), none; (A), 0.52 uM; (e), 2.1 uM; (•), 20 uM. Panel B, c y c l i c GMP h y d r o l y s i s was measured i n the presence of the f o l l o w i n g concentrations of c y c l i c AMP; (O), none; (A), 33'2 uM; (•) , 87.8 uM; (O), 176 uM. I n s e r t i n both panels represent double r e c i p r o c a l p l o t s of the same data over a l i m i t e d s ubstrate range. A l l assays contained 250 uM EGTA. - 75 -LOGe S A V E (/iM) - 76 -Figure 17 • K i n e t i c s of c y c l i c n u c l e o t i d e h y d r o l y s i s "by enzyme species D j J J • Panel A, c y c l i c AMP h y d r o l y s i s was measured i n the presence of the f o l l o w i n g concentrations of c y c l i c GMP; (O) , none; (A), 12.6 uM; (•), 20.1 uM. Panel B, c y c l i c GMP h y d r o l y s i s was measured i n the presence of the f o l l o w i n g concentrations of c y c l i c AMP; (O), none; (A), 1.0 uM; (•), 6.3 uM; '.(=•), 44 uM; ( A ) , 176 uM. I n s e r t i n both panels represent double r e c i p r o c a l p l o t s of the same data over, a l i m i t e d s ubstrate range. EGTA (250 uM) was inc l u d e d i n a l l assay tubes. L O G e S A V E ( / x M ) - 78 -c y c l i c GMP a c t i v a t e d modestly. At one substrate c o n c e n t r a t i o n ( c y c l i c AMP 4 . 4 8 uM) c y c l i c GMP d i d not a f f e c t c y c l i c AMP h y d r o l y s i s . I t i s r e a d i l y apparent from t h i s f i g u r e t h a t one must use more than one substrate c o n c e n t r a t i o n when examining the e f f e c t of an i n h i b i t o r on a cooperative enzyme. F i g . 17B i l l u s t r a t e s the k i n e t i c s of h y d r o l y s i s of c y c l i c GMP by D J J j • A t high concentrations of c y c l i c GMP, 1 uM c y c l i c AMP modestly increased a c t i v i t y . This behaviour could be demonstrated i n crude supernatant f r a c t i o n s . At higher concentrations of c y c l i c AMP, c y c l i c GMP h y d r o l y s i s was markedly i n h i b i t e d . The double r e c i p r o c a l i n s e r t to F i g . 17B i l l u s t r a t e s upward curvature which i s suggestive of p o s i t i v e c o o p e r a t i v i t y . Enzyme species D J J J represented 23$ of the c y c l i c GMP and 33 $ of the c y c l i c AMP h y d r o l y z i n g a c t i v i t y recovered from the column. L.east squares f i t t i n g - I n order to extend the g r a p h i c a l a n a l y s i s (Figures 15 to 17), the technique of n o n l i n e a r l e a s t squares f i t t i n g was a p p l i e d to p l a u s i b l e r a t e equations to describe the data. The d e r i v a t i o n of these equations was presented i n d e t a i l i n Experimental Procedure. I n Table IV the variances observed on f i t t i n g the data presented i n F i g . 15, 16, 17 to equations 1 to 10 i s shown (supplementary data i s in c l u d e d i n the a n a l y s i s ) . I n a d d i t i o n to the variance, the number of parameters whose 95% confidence i n t e r v a l i n cludes zero must be?considered i n choosing a model to f i t the data. Using D-j. as the enzyme source and e i t h e r MIX or c y c l i c AMP as the i n h i b i t o r , equation 2 and i t s r e l a t e d equations 4 , 7» 8 and 9 r e s u l t i n a f i t w i t h the lowest v a r i a n c e . Equations 4 , 7. 8 and 9 do not improve the f i t or the TABLE IV: Variances The variance obtained from l e a s t squares f i t t i n g to the equations presented i n Experimental Procedure are given. The data was obtained using the enzyme, r a d i o a c t i v e s u b s t r a t e , and un l a b e l l e d m o d i f i e r i n d i c a t e d . L e a s t squares f i t t i n g was performed as described i n Experimental Procedure. The a n a l y s i s i s based on a t o t a l of 480 v e l o c i t y measurements. Variance Obtained with Equation Enz. S Modifier 1 3 2 3 4 5 6 7 8 9 10 DI cGMP MIX 0. .23513 0. 23260 0 .47892 0. 23260 0.72658 0.70312 0.23260 0 .23260 0. 23260 0.24036 DI cGMP cAMP 0. .15536 0. 14325 0 .15536 0. 14325 0.51825 0.47777 0.14325 0, .14534 0. 14325 0.14340-DII cAMP cGMP <1. ,4476a 1. 3508 <5 .56803 4. 4102 1.4678 1.3519 <8.9068a 1, .9260 1. 3616 14.363 DII cGMP cAMP «. ,64438a 0. 52572 1 .0207 0. 52570 0.66687 0.58524 0.52570 0, .78740 0. 52570 1.0511 DIII cAMP cGMP 2. ,1264 1. 3763 1 .5167 1. 3753 2.6996 2.6645 1.3770 1, .5159 1. 3753 2.2090 DIII cGMP cAMP 1. ,0075 <. 933053 5 .7969 0. 84381 1.0086 0.91502 0.86005 0, .85416 <. 79884a 0.91439 aThe process was converging but had not yet converged by 5° i t e r a t i v e c y c l e s , - 80 -s t a t i s t i c a l d e f i n i t i o n of the parameters and f o r t h i s reason are excluded i n favour of the simple s t model, equation 2. This equation i s based on two i n i t i a l l y e q uivalent i n t e r a c t i n g s i t e s on the enzyme. The model d e s c r i b i n g a mixture of two enzymes, equation 10, does not describe the k i n e t i c behaviour of D-j. as w e l l as the p r e v i o u s l y mentioned equations and was, t h e r e f o r e , excluded. Using equation 2 as the model f o r f i t t i n g , Table V, row 1, l i s t s the parameters obtained. Not presented i n Table V f o r enzyme species are the f o l l o w i n g i n h i b i t i o n constants: u s i n g c y c l i c AMP as the i n h i b i t o r , KIA•'.'•= 0.00972*0.004-05 ( K ] ; = 102) and KJ1A = 0.0004-71-0.00385 ( K J I = 2120); u s i n g MIX as the i n h i b i t o r , K J A = 0.325*0.271 (K-j. = 3-07), K J I A = 0.017± 0.04-15 ( K - J - J = 58.8) , K I I I A = 0.0078-0.0066 ( K ^ = 127). The high values of and f o r c y c l i c AMP are c o n s i s t e n t w i t h t h i s compound being a poor substrate f o r enzyme . As w i t h p r e v i o u s l y s t u d i e d phosphodiesterases, MIX was a potent i n h i b i t o r . From the data given, enzyme species D-j. can be c h a r a c t e r i z e d as a n e g a t i v e l y cooperative enzyme (K^< K^, V 1< V 2 ) . The i n h i b i t i o n of c y c l i c GMP h y d r o l y s i s by both c y c l i c AMP and MIX was c h a r a c t e r i z e d by V i n h i b i t i o n (V.^< Vg). With c y c l i c AMP as the i n h i b i t o r , no K i n h i b i t i o n occurred ( K = K 1 K I I I = 1 . 5 u M ^ K . ) while MIX caused J K l a concurrent K i n h i b i t i o n ( K ^ = 56" uM). Using D-J--J- as the enzyme species and c y c l i c AMP and c y c l i c GMP as substrate or m o d i f i e r , the variances observed on f i t t i n g to equations 1-10 are presented i n Table IV. Based on these values there, are only two p o s s i b l e choices f o r the best equations to describe the data, equations 2 and 6. I f we base our choice on TABLE V: Parameters derived from l e a s t squares f i t t i n g The parameters obtained from a l e a s t squares f i t to the equation given i n column two (see Experimental Procedure) are presented. Values are parameters ± asymptotic standard d e v i a t i o n . The value i n brack e t s , f o l l o w i n g the value of K^-^ i s the corresponding d i s s o c i a t i o n constant K - J - J ^ . Values are based on a t o t a l of 4-80 v e l o c i t y determinations. A p r e l i m i n a r y a n a l y s i s (n=170) y i e l d e d s i m i l a r r e s u l t s . E n z . E q n . S M o d i f i e r K 1 ( u M ) K 2 ( u M ) V l p m o l e s / m i n V 2 p m o l e s / m i n V 3 p m o l e s / m i n K H I A ( u M ) D I 2 c G M P c A M P 1 . 3 7 ± 0 . 2 7 2 6 . 8 9 ± 1 . 0 8 7 . 1 6 ± 0 . 8 7 3 1 1 . 9 + 0 . 2 7 9 6 . 6 8 ± 1 . 5 1 0 . 0 0 8 7 2 ± 0 . 0 0 2 1 3 ( 1 1 4 ) D I I 6 c A M P c G M P 1 3 . 9 ± 5 . 7 7 5 5 . U 1 0 . 4 - 4 2 . 9 ± 3 . 8 4 8 1 . 3 ± 2 . 0 5 0 . 7 1 2 ± 0 . 1 5 2 ( 1 . 4 0 ) D I I 6 c G M P c A M P 1 0 . 5 ± 4 . 1 1 1 4 . 8 ± 3 . 3 1 - 2 6 . 5 ± 2 . 3 7 9 . 7 4 ± 2 3 . 5 a 0 . 0 2 5 5 ± 0 . 0 1 4 4 ( 3 9 . 2 ) D I I I 4 c A M P c G M P 1 . 8 7 ± 1 . 2 5 a 2 2 . U 8 . 9 6 1 1 . 4 ± 3 . 6 3 2 7 . 6 ± 2 . 5 8 5 3 . 7 ± 1 . 2 2 1 5 2 . ± 1 0 2 a ( 0 . 6 6 6 x l 0 ~ 2 ) D I I I 4 c G M P c A M P 8 5 . U 3 6 . 4 3 3 . 4 ± 2 1 . 3 5 0 . 4 ± 1 8 . 6 1 9 . 5 ± 4 . 2 2 1 0 " 8 0 . 0 5 0 ± 0 . 0 1 6 ( 2 0 . 0 ) D I I 2 c A M P c G M P 1 . 3 6 ± 4 . 4 1 a 1 0 1 . ± 2 4 . 4 1 . 3 1 ± 2 . 1 7 a 5 7 . 4 ± 7 . 8 6 8 0 . 8 ± 1 . 9 5 0 . 6 6 2 ± 0 . 1 2 2 ( 1 . 5 1 ) D T I 2 c G M P c A M P 1 9 4 . ± 4 1 1 .a 4 . 2 8 ± 6 . 8 6 a 6 5 . 9 ± 1 4 8 . a 1 8 . 1 ± 5 . 4 5 4 . 4 5 ± < f c 2 ' . i a ' : 0 . 0 8 6 H 0 . 1 3 4 3 ( 1 1 . 6 ) ^he 95% confidence i n t e r v a l f o r the parameter included zero. - 82 -"both the s t a t i s t i c a l d e f i n i t i o n of-the parameters and v a r i a n c e , equation 6 i s the "better model. This i s i l l u s t r a t e d i n Table V where the parameters and t h e i r standard d e v i a t i o n s are l i s t e d f o r both models. Since equation 6 r e s u l t e d i n the production of b e t t e r defined parameters, i t i s l i s t e d i n the main body of Table V. The secondary choice, equation 2, which r e s u l t e d i n a f i t w i t h a lower variance but po o r l y defined parameters, i s a l s o l i s t e d a t the bottom of the t a b l e . As described i n Experimental Procedure, equation 6 represents equation 2 wi t h = 0. A p o s s i b l e p h y s i c a l i n t e r p r e t a t i o n of t h i s equation would be that there i s not any ( s t a t i s t i c a l l y s i g n i f i c a n t ) c a t a l y t i c a c t i v i t y u n t i l two s i t e s are occupied. Notice that f o r c y c l i c AMP as the substrate and equation 2 as the model, i s indeed an i n s i g n i f i c a n t component of the t o t a l v e l o c i t y (compare wi t h and V^). The r e s u l t s from e i t h e r equation r e v e a l that the enzyme hydrolyzes c y c l i c AMP i n a n e g a t i v e l y cooperative manner (K^< , V^<Vg) and that c y c l i c GMP a c t i v a t e s the enzyme by combined V a c t i v a t i o n (V„>V p) and K a c t i v a t i o n (K~ = K 1 K I I I = 1 . 8 6 uM.<Kj. The values of K-j... and KJ-J. can be obtained f o r D-^ and D J J J from the corresponding value of and when the m o d i f i e r was used as the su b s t r a t e . For example, f o r c y c l i c AMP h y d r o l y s i s by D-J-J , the values of and f o r c y c l i c GMP can be obtained from the values of and Kg when c y c l i c GMP was used as the s u b s t r a t e . For enzyme species D-^ wi t h c y c l i c GMP as s u b s t r a t e , the observed anomalous k i n e t i c s are due to V a c t i v a t i o n (equation 6 ) or combined K a c t i v a t i o n - V i n h i b i t i o n (equation 2 ) . E i t h e r of these e f f e c t s can r e s u l t i n the observed double r e c i p r o c a l p l o t s of 83 F i g . 16B (96,97). The i n h i b i t i o n - o f - c y c l i c GMP h y d r o l y s i s by c y c l i c AMP i n the enzyme system i s accomplished through V i n h i b i t i o n (^^<^ Z J a n d K i n h i b i t i o n (K^ = 30 uM > K 1 ) . F i n a l l y the k i n e t i c behaviour of DJ-J-J was-examined. The variances i n Table IV r e v e a l t h a t equation 2, 4- and 9 best describe the data. On the basi s of the s t a t i s t i c a l d e f i n i t i o n of the parameters and va r i a n c e , -equation 4-, which represents a simple a l l o s t e r i c enzyme, was chosen. I t should be mentioned that while equation 9 gave a low v a r i a n c e , the parameter estimates obtained f o r c y c l i c GMP h y d r o l y s i s were not reasonable. I n Table V the parameters obtained from a l e a s t squares f i t to equation 4-are l i s t e d . The occurrence of po o r l y defined parameters i s p o s s i b l y a consequence of imperfect r e s o l u t i o n of the two enzyme species D^j and D-^ -^ on the DEAE-cellulose column. However, the r e s u l t s are s u f f i c i e n t l y accurate to r e v e a l the existence of negative c o o p e r a t i v i t y i n the h y d r o l y s i s of c y c l i c AMP by D-J-JJ ( K 1 < K 2 , V 1< V 2 ) . The a c t i v a t i o n of c y c l i c AMP h y d r o l y s i s by c y c l i c GMP (at high c y c l i c AMP concentrations) was a consequence of V a c t i v a t i o n (V^ > > V^). C y c l i c GMP h y d r o l y s i s by t h i s enzyme species d i s p l a y e d p o s i t i v e l y cooperative behaviour (K^> K , V.^>V 2), which i s i n agreement with the g r a p h i c a l a n a l y s i s . C y c l i c AMP was shown i n Table V to produce dramatic V i n h i b i t i o n (V^-0 pmoles/ min) and a l s o K i n h i b i t i o n (K^ = 910 u M » K 1 ) . The r e s u l t s of the n o n l i n e a r l e a s t squares f i t t i n g are, t h e r e f o r e , compatible with the hypothesis that an enzyme with two i n i t i a l l y e q u i v a l e n t i n t e r a c t i n g s i t e s i s s u f f i c i e n t and necessary to describe the k i n e t i c behaviour of the three enzyme species i s o l a t e d . - 84 -DISCUSSION A. The Assay of Phosphodiesterase I n the i n i t i a l p o r t i o n of t h i s work a simple, f a s t and r e l i a b l e assay of c y c l i c n u c l e o t i d e phosphodiesterase s u i t a b l e f o r use i n crude preparations was presented. I n view of the n o n l i n e a r k i n e t i c s e x h i b i t e d by the enzyme, i t i s necessary t h a t one be able to produce l a r g e numbers of data p o i n t s over a great range of i n i t i a l s ubstrate concentrations. Unless v a r i a t i o n s i n r e a c t i o n v e l o c i t i e s a t t r i b u t a b l e to the presence of contaminating enzymes are e l i m i n a t e d , meaningful k i n e t i c r e s u l t s cannot be obtained. The assay methods were f u r t h e r i n v e s t i g a t e d by conducting a p i l o t examination of the k i n e t i c s of c y c l i c AMP h y d r o l y s i s by crude heart p r e p a r a t i o n s . Standardized methods of performing the in c u b a t i o n s , and an a n a l y s i s s u i t a b l e f o r use on enzymes d i s p l a y i n g downward c u r v i n g double or s i n g l e r e c i p r o c a l p l o t s were a l s o presented. Harper (96) has i n d i c a t e d t h a t the e x t r a p o l a t i o n of the two l i n e a r p o r t i o n s of a downward s l o p i n g double r e c i p r o c a l p l o t does not provide the constants of e i t h e r of the enzyme sp e c i e s . This technique of e x t r a p o l a t i o n i s s t i l l used by many i n v e s t i g a t o r s (6l ,73,74,9.9,100).. A much- more.-, s a t i s f a c t o r y method of a n a l y z i n g downward c u r v i n g r e c i p r o c a l p l o t s i s the i t e r a t i v e cross c o r r e c t i o n of v e l o c i t i e s method (78,'82'). This a n a l y s i s invokes the assumption t h a t the model of two enzymes a c t i n g on a common substrate i s adequate to describe the data and i s n o t , ^ t h e r e f o r e , a general method of a n a l y s i s . However, t h i s method does a l l o w the production of comparable and V values - 85 -f o r t h i s model w i t h a minimum of a n a l y s i s . There are other f a c t o r s which can a l t e r the values of k i n e t i c parameters obtained i n an a n a l y s i s of phosphodiesterase. The v a r i a t i o n of p r o t e i n c o n c e n t r a t i o n d u r i n g k i n e t i c determinations can introduce a d d i t i o n a l e r r o r s (81) which are probably due to a v a r i a t i o n "in the c o n c e n t r a t i o n of modifying f a c t o r s present i n the enzyme s o l u t i o n . The use of unweighted l / v vs l/S and to a l e s s e r extent S/v vs S data can , s i m i l a r i l y introduce e r r o r s i n t o the a n a l y s i s (95>10l)- The use of weighting f a c t o r s can serve to minimize t h i s problem. However, i t i s b e t t e r to f i t the data to the n o n l i n e a r form of the k i n e t i c expression under a n a l y s i s , as performed i n the l a t e r examination of the s u p e r i o r c e r v i c a l g a n g l i a phosphodiesterases. The c o m p l e x i t i e s of t h i s method, which i n v o l v e s d e r i v i n g a p p r o p r i a t e r a t e equations, determining t h e i r p a r t i a l d e r i v a t i v e s , and then attempting the n o n l i n e a r l e a s t squares f i t t i n g , have l i m i t e d i t s r o u t i n e us-eA by many i n v e s t i g a t o r s . Indeed, the use of the f a r s i m p l e r i t e r a t i v e cross c o r r e c t i o n of v e l o c i t i e s method has been l i m i t e d as w e l l , presumably due to i t s requirement f o r some computational procedures. An a d d i t i o n a l c o r r e c t i o n a p p l i e d to the data was the use of average r a t h e r than i n i t i a l s ubstrate c o n c e n t r a t i o n (93)- Since the t o t a l h y d r o l y s i s of c y c l i c AMP d u r i n g the assay was kept below 20%, t h i s c o r r e c t i o n produced only moderate changes i n values (Table I ) . I t should be pointed out that the percent h y d r o l y s i s determined by the o r i g i n a l assay method of Thompson and Appleman (85) was always f a l s e l y low. Because of the l o w e r i n g of apparent percentage of h y d r o l y s i s , u s i n g the assay as o r i g i n a l l y - 86 -described one could o b t a i n apparent s u b s t r a t e h y d r o l y s i s of 20$ while i n f a c t 40$ of the substrate had been consumed. Having such a h i g h percentage h y d r o l y s i s would l e a d to i n v a l i d k i n e t i c analyses and f o r t h i s reason the percentage h y d r o l y s i s f i g u r e s quoted always r e f e r r e d to the modified assay. Taking the above standardized procedures i n t o c o n s i d e r a t i o n , i t i s easy to v i s u a l i z e some p o s s i b l e reasons f o r the v a r i a b l e k i n e t i c parameters of c y c l i c AMP h y d r o l y s i s reported i n the l i t e r a t u r e . Of p a r t i c u l a r s i g n i f i c a n c e are the need f o r the c o n t r o l of endogenous f a c t o r s a f f e c t i n g the r e a c t i o n v e l o c i t y and the use of a h i g h l y r e l i a b l e and r e p r o d u c i b l e assay. A d e t a i l e d k i n e t i c a n a l y s i s based on mathematically sound k i n e t i c p r i n c i p l e s must then be a p p l i e d to the data. Since there are no k i n e t i c parameters published f o r heart phosphodiesterase under such c o n d i t i o n s , i t i s very d i f f i c u l t to compare the values obtained here w i t h those c u r r e n t l y i n the l i t e r a t u r e . Two K m's were presented f o r c y c l i c AMP h y d r o l y s i s by the supernatant f r a c t i o n of both r a t and r a b b i t homogenates (Table I ) . These.values are i n reasonably good agreement wi t h K m values reported by Beavo et a l , (81) f o r p a r t i c -u l a t e bovine heart t i s s u e (K m's of 0.8 and 25 uM) and values reported by M i c h a l et a l . , (102) f o r a commercial (Boehringer-Mannheim) bovine heart p r e p a r a t i o n ( K m's of 0.7-1 and 20-30 uM). The values are lower than those obtained by Thompson e_t a l . , (85) f o r two enzyme species resolved by g e l f i l t r a t i o n of r a t supernatant f r a c t i o n s ( K m ' s °^ 3-85 and 86.7 uM). The values obtained u s i n g the unmodified assay of Thompson and Appleman were somewhat higher than those obtained with the modified assay. These values - 87 -are once again lower than those reported by the above authors f o r agarose eluates of r a t heart supernatant. These d i f f e r e n c e s could be a s c r i b e d to the d i f f e r e n t methods of p r e p a r a t i o n and/ or methods of i n c u b a t i o n and a n a l y s i s . B. Phosphodiesterases of S u p e r i o r C e r v i c a l Ganglia Phosphodiesterase a c t i v i t y i n the crude supernatant f r a c t i o n s of s u p e r i o r c e r v i c a l g a n g l i a were r e l a t i v e l y unaffected by Ca++. When the enzymes were freed of p r o t e i n a c t i v a t o r by DEAE-cellulose chromatography, an unsuspected i n h i b i t i o n of a l l three enzyme species by Ca++ was revealed. Moveover, t h i s i n h i b i t i o n was prevented by the presence of p r o t e i n a c t i v a t o r . R e v e r s i b l e Ca++ i n h i b i t i o n of phosphodiesterase has not been p r e v i o u s l y reported although there i s a p o s s i b i l i t y t h a t enzymes i s o l a t e d from other t i s s u e s may be s i m i l a r i l y a f f e c t e d by Ca++. I n t h e i r recent examination of Ca++-Mg++ dependent phosphodiesterases from s e v e r a l t i s s u e s , K a k i u c h i et a l . , ( 6 4 - ) added p r o t e i n a c t i v a t o r to a l l assay tubes when determining the e f f e c t s of Ca++ on the enzymes i s o l a t e d from a g e l e x c l u s i o n column. I t i s p o s s i b l e that Ca++ i n h i b i t i o n could have been e x h i b i t e d by some of the enzyme species examined, but was masked by the presence of p r o t e i n a c t i v a t o r . Bovine cortex phosphodiesterase was not s i g n i f i c a n t l y i n h i b i t e d by low concentrations of Ca++ (62). Thus i t seems that there may be at l e a s t two types of Ca++ r e g u l a t i o n of phosphodiesterase. One in v o l v e s a Ca++ dependent increase i n a c t i v i t y produced by p r o t e i n a c t i v a t o r (54-,56 ,60,62). This form of a c t i v a t i o n may be di s p l a y e d p r i m a r i l y by one form of the enzyme designated as peak I I by - 88 -Kakiuchi et a l . , (64). The other type i n v o l v e s an i n h i b i t o r y e f f e c t of Ca++ which i s reversed by p r o t e i n a c t i v a t o r as described herein. The existence of t h i s Ca++ i n h i b i t i o n lends support to the k i n e t i c model of phosphodiesterase a c t i v a t i o n presented by Wickson et a l . , ( 6 2 ) . I n t h i s model the formation of an enzyme-Ca++ complex was proposed. Since Ca++ i n h i b i t e d the enzymes from su p e r i o r c e r v i c a l g a n g l i a , the formation of t h i s enzyme-Ca++ species i s confirmed i n t h i s t i s s u e . The mechanism through which Ca++ and a c t i v a t o r p r o t e i n may i n t e r a c t to produce a l t e r a t i o n s i n the p r o p e r t i e s of the s u p e r i o r c e r v i c a l g a n g l i o n phosphodiesterases was not examined a t t h i s time. This i n v e s t i g a t i o n w i l l r e q u i r e the use of Ca++ f r e e reagents and w i l l i n v o l v e a complex k i n e t i c experiment i n which Ca++, p r o t e i n a c t i v a t o r , and sub s t r a t e concentration are v a r i e d simultaneously. Since the phosphodiesterases of the s u p e r i o r c e r v i c a l g a n g l i a e x h i b i t cooperative k i n e t i c behaviour, the r a t e equations to describe the process w i l l become qui t e complex. I f one a l s o considers the e f f e c t s of other c y c l i c n u c l e o t i d e m o d i f i e r s on such a system the equations may reach unmanagable p r o p o r t i o n s . An example of such an e f f e c t was the redu c t i o n i n c y c l i c GMP a c t i v a t i o n of c y c l i c AMP h y d r o l y s i s when Ca++ was present i n an assay of D-^  ( F i g . 1 3 ) . The p h y s i o l o g i c a l s i g n i f i c a n c e of the r e v e r s i b l e i n h i b i t i o n of c y c l i c n u c l e o t i d e h y d r o l y s i s by micromolar concentrations of Ca++ cannot be s t a t e d a t t h i s time. Rasmussen et a l . , (103) have proposed that changes i n Ca++ co n c e n t r a t i o n i n the c e l l c y t o s o l are general mechanisms f o r c e l l u l a r a c t i v a t i o n . Some of - 89 -the proposed e f f e c t s of c y c l i c <nucleotides could, t h e r e f o r e , he a r e s u l t of t h e i r a b i l i t y to a l t e r the i n t r a c e l l u l a r f r e e c o n c e n t r a t i o n of C a + + ions (103). Conversely, Ca++ ions can a f f e c t the l e v e l s of c y c l i c n u c l e o t i d e s i n the c e l l "by i n h i b i t i o n of adenylate cyclase (104), by a c t i v a t i o n of guanylate cyclase (105), or by the p r e v i o u s l y mentioned e f f e c t s on phosphodiesterases. The i n h i b i t i o n of phosphodiesterase presented h e r e i n would tend to augment and prolong the e f f e c t s of hormonally induced a l t e r a t i o n s of c y c l i c n u c l e o t i d e l e v e l s a s s o c i a t e d w i t h increased i n t r a c e l l u l a r concentrations of Ca++. The e l u c i d a t i o n of the complex r e l a t i o n -s h i p between c y c l i c n u c l e o t i d e s and Ca++ w i l l g r e a t l y increase our understanding of c e l l u l a r r e g u l a t i o n . Based on e x i s t i n g data, the p o s s i b i l i t y of short term r e g u l a t i o n of phosphodiest-erase a c t i v i t y by Ca++ ions and lon g term r e g u l a t i o n by p r o t e i n a c t i v a t o r , d e f i n i t e l y e x i s t s . As w e l l as Ca++ dependent a l t e r a t i o n s i n a c t i v i t y , the s u p e r i o r c e r v i c a l ganglion enzymes e x h i b i t other r e g u l a t o r y p r o p e r t i e s . The n o n l i n e a r k i n e t i c s e x h i b i t e d by the three forms of the enzyme i n d i c a t e t h a t substrate i t s e l f , or substrate analog, exert r e g u l a t o r y a c t i o n s . The downward s l o p i n g double r e c i p r o c a l p l o t s of substrate h y d r o l y s i s produced by the enzymes are not i n themselves evidence f o r cooperative k i n e t i c behaviour. The problem of g r a p h i c a l l y d i s t i n g u i s h i n g between n e g a t i v e l y cooperative behaviour and a mixture of two enzyme species h y d r o l y z i n g the same substrate has r e c e n t l y been examined (97). This d i f f e r e n t i a t i o n i s not p o s s i b l e on the ba s i s of substrate h y d r o l y s i s k i n e t i c s alone. I n t h i s i n v e s t i g a t i o n the use of r e v e r s i b l e m o d i f i e r s and standard - 90 -l e a s t squares f i t t i n g techniques were proved s u f f i c i e n t to exclude the model based on a mixture of two. enzyme species f o r a l l three enzymes. This d i f f e r e n t i a t i o n could be made on a q u a l i t a t i v e b a s i s f o r enzyme species D-^  and ^-rj_j_ but not . A mixture of two enzyme species cannot e x h i b i t e i t h e r s u b s t r a t e analog a c t i v a t i o n ( F i g . l6A and 17A) or upward c u r v i n g double r e c i p r o c a l p l o t s ( i n s e r t s to F i g . l6B and 17B). Based on the l e a s t squares f i t t i n g and g r a p h i c a l a n a l y s i s we can d e f i n i t e l y s t a t e t h a t the anomalouss Mne-tics-s d i s p l a y e d by the phosphodiesterase species are not a t t r i b u t a b l e to a simple mixture of two enzymes or contamination of one enzyme by another/ Previous attempts to confirm t h i s hypothesis by i n v e s t i g a t o r s u s i n g d i f f e r e n t techniques have not been s u c c e s s f u l . I n f a c t R u s s e l l et a l . , (25,67) i n t h e i r examination of phosphodiesterases from various r a t t i s s u e s obtained a higher e r r o r i n the f i t to a n e g a t i v e l y cooperative model than to the mixture of two enzymes model. The co n c l u s i o n of phosphodiesterase being a n e g a t i v e l y cooperative enzyme was based on the f i n d i n g that there would have to be too l a r g e a degree of contamination from overlapping peaks to e x p l a i n the k i n e t i c s . The p o s s i b i l i t y that e i t h e r peak represented a mixture of two enzyme species was not considered by R u s s e l l et a l . , ( 6 7 0 . Although the p u r i t y of the p r e p a r a t i o n used f o r the a n a l y s i s , l i m i t s the conclusions that could be made, i t i s c l e a r that phosphodiesterase e x h i b i t e d cooperative k i n e t i c behaviour. W i t h i n the s u p e r i o r c e r v i c a l ganglion there were a t l e a s t three enzyme spe c i e s . Enzyme hydrolyzed c y c l i c GMP i n a n e g a t i v e l y cooperative manner and was not comparable w i t h any p r e v i o u s l y reported phosphodiesterase. The c y c l i c GMP s p e c i f i c phosphodiesteras - 91 -i s o l a t e d form r a t l i v e r by R u s s e l l e t - a l . , (25) d i d not e x h i b i t cooperative k i n e t i c behaviour. Enzymes D-^  and D J J J hydrolyzed both c y c l i c AMP and c y c l i c GMP and were s i m i l i a r to enzyme "DIP" i s o l a t e d by R u s s e l l et a l . , (25) from r a t l i v e r . The h y d r o l y s i s of c y c l i c AMP by both DJ-J- and D J J J was n e g a t i v e l y cooperative and i n the case of D J J was uniformly s t i m u l a t e d by c y c l i c GMP. C y c l i c GMP was hydrolyzed by D J J J i n a p o s i t i v e l y cooperative manner while the behaviour of D^.-j- w i t h respect to t h i s s u b s t r a t e was c h a r a c t e r i z e d by e i t h e r V a c t i v a t i o n or p o s i t i v e c o o p e r a t i v i t y . The behaviour e x h i b i t e d by a l l three enzymes can be explained by the model of an enzyme w i t h two i n i t i a l l y e q u i v a l e n t i n t e r a c t i n g s i t e s ( F i g . 2 ) . As i s the case w i t h any k i n e t i c i n v e s t i g a t i o n there could e x i s t other models which were not considered and which could b e t t e r e x p l a i n the data. For example the more complex s t r u c t u r a l k i n e t i c s (106) would not be appropriate to apply to an impure p r e p a r a t i o n i n the absence of .evidence f o r a subunit s t r u c t u r e . F u r t h e r p u r i f i c a t i o n , p r e f e r a b l y to homogeneity w i l l be r e q u i r e d to completely define the behaviour of the enzyme. However, the observation that the k i n e t i c s of a l l enzyme species i s o l a t e d from the s u p e r i o r c e r v i c a l ganglion can be described by v a r i a t i o n s of the model presented i n F i g . 2, i s a f i r s t step toward the complete c h a r a c t e r i z a t i o n of the enzymes. One can speculate on the p o s s i b l e s i g n i f i c a n c e of the observed anomalous k i n e t i c behaviour of the phosphodiesterases. N e g a t i v e l y cooperative behaviour would .tend to a c t as a k i n e t i c b u f f e r of the substrate i n v o l v e d . Increased concentrations of the s u b s t r a t e would be returned to b a s a l l e v e l s a t a reduced r a t e r e l a t i v e to t h a t produced by a Michaelis-Menten enzyme. A p o s i t i v e l y - 92 -cooperative enzyme system can be envisaged as a c t i n g as a k i n e t i c s w i t c h . Increased l e v e l s of substrate would be r a p i d l y returned to ba s a l l e v e l s i n such a system. The proposed e f f e c t of c y c l i c AMP i n the s u p e r i o r c e r v i c a l ganglion i s the generation of a s-IPSP ( 3 0 ) . The h y d r o l y s i s of c y c l i c AMP was shown to proceed i n a n e g a t i v e l y cooperative manner suggestive of a more sustained e f f e c t once formed. Thus c y c l i c AMP could be termed an a t t e n u a t i n g f a c t o r i n the c o n t r o l of s e n s i t i v i t y of the ganglion to s t i m u l a t i o n . Prolonged depression of the ganglion would be prevented by c y c l i c AMP i n h i b i t i n g c y c l i c GMP h y d r o l y s i s thereby r a i s i n g i t s concen-t r a t i o n . C y c l i c GMP has been proposed to produce a s-EPSP i n t h i s t i s s u e (3°)• The h y d r o l y s i s of c y c l i c GMP by enzymes and D - Q J proceeded i n a p o s i t i v e l y cooperative manner. Increased l e v e l s of c y c l i c GMP would be r a p i d l y returned to b a s a l l e v e l s by such a system, presumably to prevent a prolonged d e p o l a r i z a t i o n and subsequent h y p e r s e n s i t i v i t y of the ganglion. This h y p e r s e n s i t i v i t y could be caused both by the increase i n c y c l i c GMP and a l s o by a c y c l i c GMP mediated decrease i n the l e v e l of c y c l i c AMP i e . c y c l i c GMP a c t i v a t i o n of c y c l i c AMP h y d r o l y s i s . The n e g a t i v e l y cooperative behaviour of Dj w i t h c y c l i c GMP as sub s t r a t e i s more d i f f i c u l t to f i t i n t o such a scheme. The p o s s i b i l i t y t h a t t h i s enzyme r e s i d e s i n a d i f f e r e n t i n t r a c e l l u l a r l o c a t i o n or i n a d i f f e r e n t c e l l p o p u l a t i o n could be considered. As evidence f o r the complexity of phosphodiesterase grows, i t s r o l e as a key enzyme i n r e g u l a t i n g i n t r a c e l l u l a r c y c l i c n u c l e o t i d e l e v e l s becomes i n c r e a s i n g l y apparent. 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Biochem., 4 l , 499 (1974). - 100 -APPENDIX This appendix deals w i t h the n o n l i n e a r l e a s t squares f i t t i n g r o u t i n e s used i n the e v a l u a t i o n of s u i t a b l e r a t e equations f o r the data presented i n F i g . 15 to 17. Using equations 1 to 10 of Experimental Procedure, we must f i r s t evaluate the p a r t i a l d e r i v a t i v e s of each f u n c t i o n w i t h respect to each of the parameters. Using the simples t case, equation 10, as an example we define a l l i n h i b i t o r d i s s o c i a t i o n constants as a s s o c i a t i o n constants, eg. K-^ = l/K-j-. We can expand equation 10 i n t o the f o l l o w i n g form S 2V + K'VS + VK'K* I § + S 2 V + V K S + V I K SK T A v = S 2 + K' gS + SK'IK' A + K sS + K'K s + K ^ ' I K ^ + S K s I K I A + K s K s I K I A + K s K s l 2 K i A K I A D e f i n i n g X± = S , X g = I , V± = K g, P g = K^, 7^ = K-^, P^ = K-J A , P^ = V, P^ = V'; we can s u b s t i t u t e i n t o equation 1-A to obta i n X ? P 5 + P 2 X 1 P 5 + W 2 P 5 X 1 + X 1 P 6 + W l + P 6 X 2 P 1 X 1 P 3 (1-A) v = 4 + P 2 X 1 + P 2 X 2 X A + P 1 X 1 + P 2 X 1 + P 1 P 2 X 2 P 4 + P 1 X 2 X 1 P 3 + P 1 P 2 X 2 P 3 + P 1 P 2 X 2 P 4 P 3 (2-A) To determine the p a r t i a l d e r i v a t i v e s of the f u n c t i o n w i t h respect to P^ through P^ we f i r s t define the f u n c t i o n f as being the numerator of equation 2-A, and the f u n c t i o n g as being the denominator. The t o t a l f u n c t i o n , designated as F, can then"be represented as F = f g " 1 and - 101 -i l L _ 3f_ { - h + ( f )  a p n - 9 P n <S ^ Since 3 P n 3g 3 P n 3 P n ^ T i 2 ) we ob t a i n 3 P n a P n 3 p n ^ i 2 ^ I f we define k = f / - ( g ) the expression can be s i m p l i f i e d f u r t h e r to 3 P n 3 ? n ( g ] 3 P n W which can e a s i l y be evaluated f o r any parameter. An example of t h i s i s the f o l l o w i n g e v a l u a t i o n of the p a r t i a l d e r i v a t i v e of F with respect to P^. To a i d i n the computer programming we w i l l designate f = AKK1, g = AKK2, k = AKK3 and, th e r e f o r e , F = A K K l / AKK2. i l l _ 9 AKKl , 1 , + 3 AKK2 (hvvr>) 3 P 1 - 3 P 1 AKK2 5 P 1 ^ A ^ ) 3F _ ( P 6 X 1 * P 6 X 2 X 1 P 3 } 3P, - AKK2 + AKK3 (X± + P 2 + P ^ + P 3 X 2 X l + P 2 X 2 P 3 + P 2 X 2 P 4 P 3 } The d e r i v a t i o n of the p a r t i a l d e r i v a t i v e s w i t h respect to P 2 through P^ i s s i m i l i a r . We can now code the f u n c t i o n F and i t s p a r t i a l d e r i v a t i v e s w i t h respect to P , designated i n the ro u t i n e s as D(n), f o r FORTRAN compi l a t i o n . The compiled subroutines can then be l i n k e d to any n o n l i n e a r l e a s t squares f i t t i n g r o u t i n e . I n t h i s work the program B M D X 8 5 , obtained from the UCLA Health Sciences Computing Center, was used f o r the l e a s t squares a n a l y s i s . A computer l i s t i n g of the subroutines r e q u i r e d to f i t data to equations 1 to 10 of Experimental Procedure f o l l o w s . The l i s t i n g f o r equation 2 includes the JCL and data cards r e q u i r e d f o r subroutine l i n k a g e and data input u s i n g an IBM computer. - 102 -S U B R O U T I N E F U N ( F , D , P , X ) D I M E N S I O N 0 ( l i » ) , P ( l % ) , X ( ? ) E Q U A T I O N i T H I S S U B R O U T I N E E V A L U A T E S T H E V A L U E O F T H E R A T E E Q U A T I O N , F , F O R T H E T W O S I T E D E N Z Y M E M O D E L U N D E R T H E I N F L U E N C E O F A R E V E R S I B L E I N H I B I T O R , X ( 2 ) . T H E R O U T I N E ALSO E V A L U A T E S T H E P A R T I A L Q E R I V A T I V E S , D ( N ) , O F T H E R A T E E X P R E S S I O N W I T H R E S P E C T T O E A C H O F T H E P A R A M E T E R S , P ( N ) , P A P A METERS A * E AS FOLLOWS? P C D = K 1 , P ( 2 ) = < 2 , P ( 3 ) =K" 2 , P ( * f ) = K I A , P ( 5 ) = K I I I A , PC 6 ) = « " I A , P C 7 ) = ,K* I I I A , P 8 = K I I A , P ( 9 ) = V ( 2 > , P ( 10) = V(3) , P ( 11) =V ' i , PC 1 2 ) , V * 2 , P C 13) =V' 3 , P ( 1 « » ) = V 1 V A R I A B L E S ! X C 1 ) = S U S S T R A T E C O N C , X ( 2 ) =1NH I B I T O R CONC. ( M A Y = 0 . ) . E Q U A T I O N S 3 AND 5 T H I S SUBROUTINE WILL BE USED TO F I T TO THE MODEL OF AN A L L O S T E R I C ENYME WITH T « 0 N O N - E Q U I V A L E N T S I T E S . NO CHANGE I N THE S U B R O U T I N E I S R E Q U I R E D . I N THE F I R S T CASE OF AN A L L O S T E R I C ENZYME WE SET V 1 * = V 2 = V 3 " = 0 . FOR THE MODEL OF NO C A T A L Y T I C A C T I V I T Y U N T I L 2 S U B S T R A T E MOLECULES HAVE BEEN BO J ND WE S I M P L Y F I X V i = V f = 0 . . A K K l = C ( P I 9 ) * ( X ( i ) » * 2 ) ) + ( P ( 1 2 ) » ( X ( i ) » * 2 > l + ( P ( 2 ) * ( X ( i ) » P ( l i ) ) + < P ( 2 ) * C ( X ( l ) * ( P [ 1 3 ) * ( X ( 2 ) » P ( 5 ) > ) ) ) * ( P ( 3 ) » ( X ( l ) * P ( m ) ) ) * ( P C 3 ) * { X ( i ) » ( P ( 1 0 ) C * ( X ( 2 ) * P C 7 ) ) ) ) ) ) ) AKK2=( C X ( l > * * 2 ) M P ( 2 ) * X ( l ) ) + ( P ( 2 ) * ( X ( i ) * ( X ( 2 ) * P C 5 ) ) > ) M P C 3 ) * X C i ) ) + C { P C 3 ) * { X ( l ) » ( P { 7 ) * X ( 2 ) ) ) ) - K P ( l ) * P ( 3 ) ) + { P ( i ) » { P ( 3 ) » ( X ( 2 ) » P { * » ) ) > ) « - ( P C ( l ) M P < 3 ) M X ( 2 ) * P ( 6 ) ) ) ) M P ( l > M P ! 3 ) M X ( 2 > M X ( 2 ) » ( P ( 6 > » P { 8 ) > m > ) A K K 3 = ( A K < i / C ( A K K 2 * * 2 ) * ( - 1 ) ) ) AK2=AKK2 AK3=AKK3 F = A K K i / A < K 2 D ( l ) = A K < 3 » f P ( 3 ) + ( P ( 3 ) » ( X ( 2 ) » P ( ^ ) ) ) « - ( P ( 3 ) » ( X ( 2 ) » P ( 6 ) ) ) + ( P t 3 ) » { X ( 2 > * C ( X ( 2 ) * ( P C 6 ) * P ( 8 ) ) ) ) ) ) 0 { 2 > = ( C C X C l ) * P C l i ) ) + C X ( i ) * C P C 1 3 ) * C X ( 2 ) * P ( 5 ) ) ) ) ) / A K K 2 ) + (A KK 3 * ( X ( l ) + C ( X ( i ) » ( X ( 2 ) » P ( 5 ) ) ) ) ) DC3) = ( M « U ) » P ( 1 ^ ) ) + ( X ( D * ( P C 1 0 ) * ( X ( 2 ) » P ( 7 ) ) ) ) ) / A K 2 ) + ( A K 3 » ( X ( l ) + (X C ( l ) » { P ( 7 ) * X ( 2 ) ) ) + P ( l ) « - ( P ( l ) » ( X ( 2 ) * P ( M ) ) + ( « a ( l ) * C X ( 2 ) * ( P ( 6 ) ) ) J + ( P ( i C ) » ( X ( 2 > * f X ( 2 ) » ( P ( 6 ) » P ( 8 ) n m i D ( ! » ) = A K K 3 » ( P ( 1 ) » ( P ( 3 ) » X ( 2 > ) ) D ( 5 ) = ( ( R ( 2 ) * ( X ( 1 ) * ( P ( 1 3 ) * X ( 2 ) ) ) > /A < 2) + (A K K 3 * ( ( P ( 2 ) * < X < 1 > * X (2 ) > ) ) ) D (6) = A K K 3 * ( ( P ( 1 ) * ( P ( 3 ) * X ( 2 ) ) ) + ( P ( 1 ) * ; ( P ( 3 ) * < X ( 2 ) * ( X ( 2 ) * D { 8 ) ) ) ) ) ) O ( 7 ) = C ( ( : M 3 ) * C X C l ) * ( P ( 1 0 ) * X C 2 ) ) ) ) > / A K K 2 > + C A KK3 * ( P ( 3 ) * ( X ( 1 ) * X (2) ) ) ) DCS) = A K K 3 * ( P C I ) * (P ( 3) * CP (6 ) * (X ( 2 ) * * 2 ) ) ) ) D C 9 ) = C X C 1 ) * * 2 ) / A K K 2 O C i O ) = C C ? C 3 ) * ( X ( i ) M X C 2 ) * P C 7 ) } ) ) / A K K 2 l D C l l ) = ( f : » { 2 ) * X C l ) ) / A K K 2 ) D C 1 2 > = ( ( X ( i ) * * 2 ) / A K K 2 ) 0 ( 1 3 ) = C ( : » C 2 ) * ( X ( D * ( X ( 2 ) * P ( 5 ) ) ) ) /fl<K2) DCl<f) = (Pf 3 ) * X C 1 ) ) / A K K 2 RETURN FNO - 103 -'/B021FITC JOB 00381,YVONNE,MSGLEVEL=( 1,1) ,TIM£=15 //STEP1 EXEC F3RTHCL,NAME=BMDX35,CMAP=*NOMAP,SIZE=2D0K' //FORT.SYSIN DO * SUBROUTINE FUN(F,D,P,X) DIMENSIOM X ( 2 ) , D ( 8 ) , P ( B) : EQUATION 2 2 THIS SUBROUTINE EVALUATES THE VALUE OF THE RATE EQUATION F, FOR THE 2 TWO SITED ENZYME MODEL WITH BOTH SITES INITIALLY IDENTICAL.THE RATE 2 EQUATION IS DERIVED WITH THE ENZYME UNDER THE INFLUENCE OF A 2 REVERSIBLE INHIBITOR,X(2). 2 EQUATION 6 2 THIS MODEL REPRESENTS NO CATALYTIC ACTIVITY UNTIL BOTH SITES ARE 2 OCCUPIED AND IS SIMPLY MODEL C WITH Vi=0,(P6=0) 2 PARAMETERS A?E AS FOLLOWS! 2 P(l) =<1,P(2) =<2, P(3) =KIA,P(/»)=<IIAtP{5) =KIIIA,P{6) = V1 , p(7) =V2,P(8)=V 3 C THIS LISTING ALSO INCLUDES THE JCL AND DATA CARDS REQUIRED FOR A 2 NONLINEAR LEAST SQUARES FITTING USING THE UCLA ROUTINE BMDX85. 2 IF MORE THAU ONE SET OF DATA IS TO BE FITTED TO THE SAME SUBROUTINE 2 ONE SIMPLY INSERTS ADDITIONAL PR03LM, FORMAT, DATA, SEND, MAXMUM 2 MIN MUM, AND PARAM CARDS. THE FINISH CARD INDICATES THAT THERE ARE 2 NO MORE DATA SETS TC BE ANALYSED. FOR MORE INFORMATION SEE THE BMD 2 MANUAL IN THE COMPUTER CENTER LIBRARY. "\ AKK1 = (X(t>MX<l)»P(7))) + <P<21»(X(l)»P<6)))+(P<2)*(P(8)MX(2)*<X(i C ) * P { 5 ) ) > ) ) AKK2= ( (0. 5MX ti) **2 ) ) + ( P (2 ) *X(1) ) f ( P (2 )* { X (2) * (X (1) *P( 5 ) ) > ) « - ( P( 1) * C ( P ( ? ) * 0 . i ) ) t ( P ( l ) * ( P ( ? ) * I X ( 2 l * ° l 3 ) ) ) ) + ( P ( l ) » ( P ( 2 } * ( P ! 3 ) * ( P | l t ) ' f I O ^ C*(X(2)**2)) ))))) AKK3=(AK<1/ ( { AKK2**2) * (-1) ) ) AK3=AKK3 F=AKK1/A < K2 D<1) = {flK<3M (P<2 )»0.5) M P ( 2 ) MX ( 2) * (P(3) ) ) ) + (P(2)» ( P (3) • <P («»)»< 0 .5 CMX(2)*»2) )))))) D(2) = ( ( ( X ( i ) » P ( 6 ) ) + (P(8)MX(2)MX(l)*o< 5 H ) ) ) /AKK2) + (AKK3* (X(l)MX C(2 ) * ( X(1)*P | 5 ) ) ) + ( P(1)»0 . 5 I * ( P(1 ) » C P(3)»XC2))) + ( P ( 1 ) » { P ( 3 ) » ( P < M » C(0.5MX<2)**2)) ) ))) ) O(3)=AK3M(P(i)M°(2)*X(2)))*(°(l)MP(2)MP(*f)M0.5MX(2)**2)))))) 0(4)= AKK3MP (1)*(P<2)MP(3)MQ.5 MX(2)**2))))) 0 ( 5 ) = ((P(2)»(P(8)»(X{2)*X(1)))> /AK<2) *(AKK3* <D(2)* (X (2) *X (1) ))) 0(6)=<P(2)*X(1))/AKK2 0(7) =(X(1)**2)/A KK2 0(8) = <P<2) MX (2) MX <1) »P(5) ) )> / AKK2 RETURN END //LKED.BMD DD 3SN=UC.LIB.BMDLOAD,DIS°=SH? //LKED.SYSIN OD * INCLUDE BMD(BMDX85) ENTRY M4IN ft EXEC 8MO,PR35RAM=8MDX85,REGION=104K ttSTEPLI8 DD D3N=*.STEP1.LKE0.SYSLM00,DISP=(0LD,DELETE) 3?O9LMDFP37C00030003 06 8.00001.000050100 (10X,3F10.5) - 1 0 4 -130.5 0000 128. 31778 0.00000 21.8222^ 130.50000 128.29251 0. 00000 22.07*»89 1 30.50000 128. 1^058 2.06000 23.59M5 130.50000 127. 9«»217 5.02500 25.57825 130.50000 128.55962 12.56000 19.^0375 130.50000 127.98303 20.10000 25.16973 BIND • M4XMUM 1000. 13 00. 100 0. 1000. 1000. 1000 . 1000. 1000 . MINMUM 0. 0. 0. 0. 0. 0. 0. 0. 3 A R A H .95829<+<t. 616 . 02*f 03. 0 0^7777. 92^5 . 757 7 27 .6 2526.887 FINISH / f - 105 -SUBROUTINE FUN(F,D,P,X) DIMENSION X(2),D (8) «<M8) EQUATION 4 THIS MODEL REPRESENTS A SIMPLE ALLOSTE^IC ENZYME * THAT IS ONE SITE IS NCN-CATALYTIC BUT INTERACTS WITH THE OTHER SITE. P A P A METERS A*E AS FOLLOWS? P<1) =K1,P(2> = <2 ,P(3) =KIA,P(M =KIIA, 9(5) =KIIIA ,P{6) =V1, P ( 7) =V2, P( 8) =V 3 AKK1 = (X(l)MX(i) * P ( 7 ) ) ) + ( P ( 2 ) * ( X ( i ) * P ( 6 ) ) ) + ( P{2 ) * ( P(8)MX(2)*(X(l C)*P<5) )))) AKK2 =((0. 5*(X(1) »»2))•(P(2)»XCi))*(P(2)MX(2>»<X(i)»P(5)))H-(Pm» C(P(2)*0.5>) + (P(1)*(P(2)*(X(2 ) * P{3})))+(P(1 ) * ( P(2)*(P(3)*(P{4)*(0.5 C*(X(2)**2>>))))) AKK2=AKK2*2 AKK3={AK<i/{fAKK2**2)*(-1))) AKK3=AKK3*2 AK3= AKK3 F=AKK1/A<K2 D{1) = (AK<3*(<P(2)*0.5) + ( P(2)MX(2)MP(3)))) + (P(2)*(P(3)*(P(«»)*C0.5 C*(X( 2) **2) ) ) ) )) ) 0(2) = (((X(i)*P(6))«-(P(3)MX(2)»(X(t)»P(5)>))) /A KK2) + (AKK3* (X(l)« (X C(2)»(XClJ»PI5)))*(PCH»0.51 + (P(l)»{P(3)»XC2))) + (P(l)*(P(3)»(PC«f)» C(0.5»(X(2)»»2))) )))) D(3) = AK3» ((P(1)»(P(2)»X(2))) + (P(1)»(P(2)MP(^)»(0. 5* (X(2)**2 )))))) 0(«*> =AKK3MP(i>* (P(2)*(P(3)*(0.5*(X(2)**2))))) D(5)=((P(2)»(P(8)»(XC2)*X(1))))/AKK2>+(AKK3*(P{2)*(X(2)*X(i)))) 0(6)=(P(2)*XC1)) /AKK2 0(7) = (X(n**2)/AKK2 D(8) = (P(2)»(X{2>MX(n*P(5>m/AKK2 RETURN END - 106 -SUBROUTINE FUN(F,0,PfX) DIMENSION X(2> ,D (8) ,P<8) EQUATION 7 THIS SUBROUTINE EVALUATES THE RATE EQUATION FOR OROEREO ADDITION OF BOTH I AND S TO THE TWO SITED ENZYME MODEL GIVEN IN FUN C. AKK1=(X(l) *(X(1)*P(7) ))*f«M2)»(X(l)»P(6>n+tP(2)»(P(8>»(X(2>MX(i C)*P(5) )))) AKK2=((i. 0MXfl)**2))*(P(2)»X(i) )*(P(2)»(X(2)»(X(i)»P(5)))>+(P(i)* C(P(2)M.I))HP(l)MP(2)M)((?)* o(3))))KP(i)'(P!2)*(PI3)'(P(M » ( 1.0 C M X ( 2 ) * » 2 n > > >)) AKK3=(AK<i/((AKK2**2) *(-1))> AK3=AKK3 F=AKKi/A<<2 D(l)=(AK<3*((P(2)*1.0J-»-(P(2),f(X(2J*(P(3)))) + (P(2)*(P(3)*{P('»)*{l.Q C * (X(2)**2 >)) ) ))) 0(2) = ( ( ( X ( l ) * P ( 6 ) ) + ( P ( 8 ) * ( X ( 2 ) * ( X ( l ) * P ( 5 ) ) ) ) )/AKK2) + (AKK3* (X (1) 4- ( X C(2)»(X(ll»P(5)))+fP(i)»1.0)-KP(l)»(P(3)»XC2))) + (P(l)»(P{3)»(P('j)* C(l.Q*(X(2>**2)> ) ))) ) D(3> = AK3*((P(l)»(P(2)»X(2)+ • ( P ( 2 ) » CPC^ ) * ( 1 .0» ( X C 2 ) * » 2 ) ) ) ) ) ) D(<*)=AKK3* ( P ( D * (P(2)MP<3>Mi .0»(X(2)**2))>>) D(5) = ((P(2)*(P(8)*(X(2)*XU)>n /AK<2)*(AKK3*(PC2)*(X(2)*X(1)))) DC6)=CP(2)»X(1))/AKK2 0(7)=(X(1)**2)/AKK2 D(8) = (P(2)*(X(2)*(X(1)*P(5))))/AK<2 RETURN END - 107 -S U B R O U T I N E F U N ( F , O t P , X ) D I M E N S I O N X ( 2 ) , 0 ( 8 ) , P ( 8 ) E Q U A T I O N 8 T H I S S U B R O U T I N E E V A L U A T E S T H E V A L U E O F T H E R A T E E Q U A T I O N F O R T H E O R D F R E O A D O I T I O N O F S B U T N O T I T O T H E T W O S I T E D ENZYME M O O E L . A K K 1 = ( X C 1 ) » ( X ( I ) » P ( 7 ) ) ) + ( P ( 2 ) » ( X ( 1 ) » * > ( 6 ) ) ) + ( P { 2 ) * ( J > ( 8 ) » ( X ( 2 ) * ( X ( 1 C ) * P ( 5 ) ) ) ) ) A K K 2 = { ( 0 , 5 * ( X ( 1 ) » » 2 ) ) • ( P ( 2 ) » X ( 1 ) ) K P ( 2 ) * ( X ( 2 ) * ( X ( i ) » P { 5 ) ) » ) • ( P ( l ) » C ( P ( 2 ) » 0 . 5 ) ) * ( P ( i ) » ( P ( 2 ) * ( X ( 2 ) * C P ( 3 ) » 0 . 5 ) ) ) ) * ( P ( l ) » ( P ( 2 ) » ( P ( 3 ) » ( P < ^ C > * ( 0 . 5 M K ( 2 ) * * 2 ) ) » ) ) ) ) A K K 3 = ( A K < l / ( C A K K 2 » * 2 ) * ( - 1 ) ) ) A K 3 = A K K 3 F = A K K 1 / A < < 2 D ( 1 ) = ( A K < 3 * ( ( P ( 2 ) * 0 . 5 ) * ( C > ( 2 ) * ( X { 2 > * ( P ( 3 ) * 0 , 5 ) ) ) + ( P ( 2 ) * ( P ( 3 ) * ( P { ^ ) * C < 0 . 5 * < X ( 2 ) » » 2 ) ) I ))) ) D ( 2 ) = ( ( ( X ( i ) » P ( 6 ) > 4 - ( ° m M X ( 2 > M X ( l ) » P < 5 ) > ) ) > / A K K 2 ) • < A K K 3 * ( X ( l ) + ( X C ( 2 ) * ( X ( 1 > » P ( 5 > ) ) + ( P ( 1 ) » 0 . 5 ) * C P ( 1 ) » ( P ( 3 ) » » { X C 2 ) » 0 . 5 ) ) ) * ( P ( 1 ) » ( P ( 3 ) * C C P ( « » ) » C 0 . 5 » ( X ( 2 ) * * 2 ) )) )) ) I D ( 3 ) = A K 3 * < ( P { l ) M P ( 2 ) M X ( 2 ) * 0 . 5 ) ) ) M P ( l ) M P < 2 ) » ( P ( < i } * ( 0 . 5 : M X ( 2 ) » » 2 C ) ) > ) > ) D ( ^ ) = A K K 3 * ( P ( 1 > * ( P ( 2 ) * ( P ( 3 ) * ( 0 . 5 * ( X ( 2 ) * * 2 ) ) ) ) > 0 ( 5 ) = ( ( P ( 2 ) » { P ( 8 ) * ( X ( 2 ) * X ( 1 ) ) ) ) / A « 2 ) * ( A K K 3 * ( P ( 2 ) * ( X ( 2 ) * X ( 1 ) ) ) ) 0 ( 6 ) = ( P ( 2 ) * X ( 1 ) ) / A K K 2 0 ( 7 ) = ( X ( 1 ) * * 2 ) / A K K 2 D ( 8 ) = ( P ( 2 ) * ( X ( 2 ) * ( X ( 1 ) * P ( 5 ) ) ) ) / A K < 2 RETURN E N D - 1 0 8 -SUBROUTINE FUN(F,D,P,X> DIMENSION X(2) ,D(8),P{8) EQUATION 9 THIS SUBROUTINE EVALUATES THE RATE EQUATION FOR THE ORDERED AOOITION OF I BUT RANDOM ADDITION OF S TO A TWO SITED ENZYME. AKK1= (X(l) *<X (1) *P ( 7 ) n M P ( 2)»(X(l)»P ( 6 ) ) ) t(P ( 2)*(P{8)»(X ( 2)MX(l C)»P(5))))) AKK2= ( { l.fl*(X ( l»**2)) + (P(2)*X ( i))*(P(2)*(X(2)*(X ( l)*P(5))))*-(P ( l ) * C ( P(2))) + (2MP(l)*(P<2) , f(X(2)*P(3)}))) + ( P ( i ) * ( P ( 2 ) * ( P ( 3 ) , f ( P ( « » ) * ( i . O C* (X(2)**2)))) ))) AKK3=(A« l / ( ( AKK2**2) ) > AK3=AKK3 F=AKK1/A<K2 O ( l ) = (AK<3*<(P(2)) + (2 * ( P(2)MX(2 ) * ( P(3))))) + (P{2)M D(3)M°(if)*(1.0 C*(X(2>**2>)>)))) 0(2) = !((!!(l)*P(6)) + (O(8)'(X(2]*(X(tPP(5) ) ) ))/A K K 2 ) • (A KK3 * (X (1) + ( X C(2)*(X ( i)*P(5))}+(P< i ) ) + (2*tP { l)M 0(3)*X{2)))) + ( P ( l ) * ( P ( 3 ) * C 0 ( ^ ) * C(1.0*(X(2)**2>>) )))) 0(3)=flKKS»({2»(P(l)MP(2)»X(21) ))KP(l)*(P(2)MP(i>IMX(2)»*2)))l| D(if)=AKK3» (P(i)» <P(2)MP(3>»(1.0»(X<2)**2>>))> D(5) = { ( P(2)*(P(8)MX(2)*XC1)))) / AK< 2 ) • (AKK3 * (P ( 2 ) * (X ( 2 ) *X {1) )) ) D(6)=(P(2)*X(1))/AKK2 0(7) = (X(1)**2)/AKK2 D(8) = (P(2)*(X(2)*(X(1)*P(5) ) )) /AKK2 RETURN END - 109 -SUBROUTINE FUN(F,0 ,P fX) DIMENSION X(2),D (6) ,P(6) EQUATION 10 THIS SUBROUTINE EVALUATES THE VALUE Or THE RATE EQUATION ,F, FOR THE TWO ENZYMES ACTING ON ONE SUBSTRATE MODEL IN THE PRESENCE OF A REVERSIBLE INHIBITOR. PARAMETERS A*E AS FOLLOWS: P ( l ) =KS,P(2) = K* S,P(3 ) = KIfl,°(i»> =K* IA,P(5) =V,P(6) =V* AKK1=((P{5)*(X(1)**2)) + {P(2)*(X(1)*P(5)) ) + (P(2)*(PU)MX(2 ) * ( P(5)* C X ( l ) ) ) M t - ( P ( 6 ) * ( X ( l ) * » 2 ) ) + { P C 6 ) » ( P ( l ) » X ( l ) ) ) * ( 0 ( 6 ) » ( X ( 2 ) * ( P ( l ) » ( X C C1)*P(3)>I ))) A K K 2 = ( ( X ( 1 ) * * 2 ) + ( P ( 2 ) * X ( 1 ) ) * ( P ( 2 ) » ( X ( 2 ) » ( X ( l ) » P ( ^ ) ) ) ) + f P ( i ) » X ( l ) ) + C ( P ( 2 ) » P C 1 ) ) * ( P ( 1 ) » ( P ( 2 ) » ( X ( 2 ) * P ( U ) ) ) ) + ( P ( 1 ) » ( X ( 2 ) * ( X ( 1 ) * P ( 3 ) ) ) ) « - ( P C { l ) » ( P ( 2 ) » ( X ( 2 ) » P ( 3 ) ) ) ) * { P ( l ) » C P ( 2 ) » ( X ( 2 ) » ( X ( 2 ) » ( P ( ^ ) * C P ( 3 ) l ) ) » n ) AKK3=(AK<l/{(AKK2**2>*(-1))) AK3= AKK3 F = AKK1/A< K2 0(1) = (((:»(5)*X(1)) + (P(6)*(X{2)*(X(1)*P(3))}))/AKK2)+{AKK3*(X(1)* CP(2) + (PC2)»(X(2 ) » P ( ^ ) > ) + ( P{3)»(X(2>»X(1)))+(P(2)»(X(2 ) » P(3)1 ) < - C P(2 C>*(P(«0»(P(3)»(X (2)»»2)))))) 0(2) = ( ( ( X ( l ) * P ( 5 ) ) + ( P ( < O * ( X ( 2 ) * ( P ( 5 ) * X ( i ) ) ) ) ) /AKK2) + (A<3* ((X ( l > + (X C(2)* (X<1) *P(<») >)+P (1) + ( P ( D * (X(2)»P (**))) + (P(1 ) » ( X C 2) (3) ) | t ( P ( U * C (P(*f)*(Pf3)*(X(2 )»»2))))))) 0(3) = ( ( ( : > ( 5 ) * ( X ( 2 ) * { o ( l ) * X ( l ) } ) ) )/a«K2) + < AKK3*( ( P (1) *( X { 2) *X (1) ) ) • C(P( i)MPC2)*X(2)n + ( P ( l)*<P(2>*(PU)*(X(2)**2> l ) ) > > O(if) = ( ( (» (2) * <XC2>* (P(5) *X (1 )) ) ) ) / a KK2 ) *• (AKK3* ((R(2)*(X(2)*X(1)))«-C(P(1)*{PC2)*X(2))) + { P(1)*( C ,(2)*{P(3)*(X(2)**2)))))) n(5) = ( { < X ( l ) * * 2 ) + f P ( 2 ) * X ( l ) ) + (P(2)*(P(«*)*(X(2)*X(l)>)))/AKK2) 0(6) = ( ((X (1) **2) + (P(1) *X(1) ) + (X (2) * (P C D * (X (1) » P(3) ) )) ) / AKK2) PETURN ENO 

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