Computer Modeling of Carbohydrate Molecules - American Chemical

Chapter 23

Lysozyme Hydrolysis of β-Glycosides A Consensus Between Binding Interactions and Mechanism 1,3,4

2

3

Carol Beth Post , Christopher M. Dobson , and Martin Karplus 1

Department of Biological Sciences, Purdue University, West Lafayette, IN 47907 Inorganic Chemistry Laboratory, Oxford University, OX1 3QR, England Chemistry Department, Harvard University, Cambridge, MA 02138

Downloaded by MIT on May 21, 2013 | http://pubs.acs.org Publication Date: July 6, 1990 | doi: 10.1021/bk-1990-0430.ch023

2

3

Analysis of a molecular dynamics trajectory of the enzyme-substrate complex chicken lysozyme and (GlcNAc) provides insight into the mechanism of polysaccharide hydrolysis by lysozyme. An alternative mechanism, which involves endocyclic bond cleavage and no ring distortion was formulated. Binding interactions stabilize a conformation of the glycosidic linkage to be hydrolyzed which is optimum for catalysis by the alternative mechanism. In contrast, the other linkages of (GlcNAc) have a cellulose-like conformation. The energy of the average structure and the dynamically averaged energy calculated for residues in each of the six (GlcNAc) binding sites vary due to differences in intermolecular nonbond contributions; the configurational and intramolecular nonbond energies are similar for all sites. The relative energies are consistent with the experimental observation that the E-F dimer product dissociates more rapidly than the A-D tetramer product. Atomic fluctuation cross-correlations between enzyme and substrate reveal that correlations are not uniform throughout the binding cleft. 6

6

In this paper we describe energetic and dynamic properties of the enzyme-substrate interactions in the complex of chicken lysozyme and hexa-(N-acetylglucosamine), (GlcNAc)6, as obtained from a molecular dynamics (MD) simulation (1). Lysozyme was the f i r s t enzyme to have its three-dimensional structure determined by X-ray crystallography (2.), yet the details of the catalytic mechanism remain elusive. Although experiments have played an essential role in determining certain features of the enzymic reaction, the information that they provide is limited. The kinetics and thermodynamics of species along the reaction pathway have been measured Q and references cited therein), evidence for certain chemical transformations has been obtained from isotope effects (4.5) and the importance of functionalities has been demonstrated by studying different 4

Current address: Department of Medicinal Chemistry, Purdue University, West Lafayette, IN 47907 0097-6156/90/0430-0377$06.00/0 © 1990 American Chemical Society

In Computer Modeling of Carbohydrate Molecules; French, A., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1990.


378

COMPUTER MODELING OF CARBOHYDRATE MOLECULES

s u b s t r a t e s o r modified enzymes (6.7) . However, i n t h i s c a s e , as i n o t h e r s , s u p p l e m e n t a r y i n f o r m a t i o n s u p p l i e d b y MD o r r e l a t e d t e c h n i q u e s i s e s s e n t i a l f o r a f u l l u n d e r s t a n d i n g o f t h e mechanism a t the atomic l e v e l . One r e s u l t from t h e a n a l y s i s o f t h e MD s i m u l a t i o n was t h e p r o p o s a l o f a new enzymic pathway f o r h y d r o l y s i s by lysozyme. We b e g i n w i t h a d e s c r i p t i o n o f t h e a l t e r n a t i v e mechanism, and t h e b a s i s on which i t was p r o p o s e d . The e n e r g e t i c s o f t h e i n d i v i d u a l GlcNAc u n i t s i n t h e lysozyme c l e f t a r e t h e n p r e s e n t e d , f o l l o w e d b y a g r a p h i c a l r e p r e s e n t a t i o n o f t h e c o r r e l a t i o n between t h e a t o m i c f l u c t u a t i o n s o f t h e s u b s t r a t e and t h o s e o f t h e enzyme. Of p a r t i c u l a r i n t e r e s t i s the fact that the binding i n t e r a c t i o n s s t a b i l i z e a bound s t a t e c o n f o r m a t i o n f o r t h e two g l y c o s i d e s i n v o l v e d i n h y d r o l y s i s t h a t i s optimum f o r c a t a l y s i s by t h e a l t e r n a t i v e mechanism and which d i f f e r s from t h e c o n f o r m a t i o n s o f t h e o t h e r glycosides. These c o n f o r m a t i o n a l f e a t u r e s a r e d e s c r i b e d i n t h e f i n a l two s e c t i o n s .

Mechanism A pathway (Scheme I) (8 9) f o r t h e h y d r o l y s i s o f o l i g o g l y c o s i d e s by lysozyme t h a t d i f f e r s from t h e p r e v i o u s l y a c c e p t e d mechanism (Scheme I I ) (3.10-12) i s d e s c r i b e d i n t h i s s e c t i o n . The a l t e r n a t i v e pathway, s u g g e s t e d by r e s u l t s o f a 55-ps MD s i m u l a t i o n o f t h e lysozyme*(GlcNAc)6 complex (1), i s c o n s i s t e n t w i t h t h e a v a i l a b l e e x p e r i m e n t a l d a t a and w i t h s t e r e o e l e c t r o n i c c o n s i d e r a t i o n s . E x p e r i m e n t a l d a t a have d e m o n s t r a t e d t h a t G l u 35 and Asp 52 a r e e s s e n t i a l , as shown by r e c e n t s i t e - d i r e c t e d m u t a g e n e s i s r e s u l t s (13.) which c o r r o b o r a t e c h e m i c a l m o d i f i c a t i o n s t u d i e s ( 3 1 4 and r e f e r e n c e s c i t e d t h e r e i n ) , and t h a t t h e r e a c t i o n p r o c e e d s w i t h r e t e n t i o n o f c o n f i g u r a t i o n a t C i Q and r e f e r e n c e s c i t e d t h e r e i n ) . A fundamental f e a t u r e o f t h e a l t e r n a t i v e pathway i s t h a t an e n d o c y c l i c bond i s b r o k e n i n t h e i n i t i a l s t e p , i n c o n t r a s t t o t h e e x o c y c l i c bond c l e a v a g e i n t h e a c c e p t e d mechanism. f

r

The MD s i m u l a t i o n employed an i n i t i a l s t r u c t u r e w i t h (GlcNAc)s b u i l t i n t o t h e a c t i v e s i t e by use o f t h e c r y s t a l l o g r a p h i c c o o r d i n a t e s o f a lysozyme-(GlcNAc)3 complex; d e t a i l s have been r e p o r t e d (1). In t h e c r y s t a l l o g r a p h i c s t r u c t u r e , (GlcNAc)3 o c c u p i e s s i t e s A, Β and C i n t h e a c t i v e s i t e c l e f t . To d e t e r m i n e c o o r d i n a t e s f o r t h e s u g a r m o l e c u l e s i n s i t e s D, Ε and F, a GlcNAc monomer was b u i l t i n t o each s i t e u s i n g a computer g r a p h i c s system. Starting i n s i t e D, a GlcNAc monomer i n a r e g u l a r c h a i n c o n f o r m a t i o n was added w i t h a j3-linkage t o t h e t e r m i n a l oxygen atom o f t h e s u g a r i n s i t e C. The bonds o f t h e g l y c o s i d i c l i n k a g e were r o t a t e d u n t i l t h e s u g a r f i t t e d the s i t e without unreasonably c l o s e contacts with the protein. F u r t h e r f i t t i n g was done by r o t a t i n g t h e h y d r o x y l and a c e t a m i d e s i d e - g r o u p s o f t h e sugar t o o p t i m i z e hydrogen-bond formation. The s u g a r s i n s i t e s Ε and F were b u i l t s e q u e n t i a l l y from s i t e D i n a similar fashion. Removal o f b a d c o n t a c t s i n some c a s e s i n v o l v e d r o t a t i o n o f amino a c i d s i d e - c h a i n s ; no r o t a t i o n s o f backbone d i h e d r a l a n g l e s were r e q u i r e d . Favorable binding of the N - a c e t y l g l u c o s a m i n e r e s i d u e t o s i t e D was f o u n d w i t h o u t d i s t o r t i n g t h e r i n g . The model was c o n s t r u c t e d t o maximize i n t e r m o l e c u l a r c o n t a c t and t o a v o i d s h o r t i n t e r a t o m i c d i s t a n c e s . During the s i m u l a t i o n , t h e c h a i r form o f t h e p y r a n o s e r i n g i n s i t e D remained unperturbed. The motions o f t h e c a r b o x y l group o f G l u 35 l e d t o hydrogen bonds w i t h t h e e n d o c y c l i c oxygen O5 and t h e h y d r o x y m e t h y l oxygen Oç b u t n o t w i t h t h e e x o c y c l i c oxygen 04'.


Lysozyme Hydrolysis of β-Glycosides


23. POST ET AL.


379


380


The s t a n d a r d mechanism f o r lysozyme (Scheme II) was p r o p o s e d by P h i l l i p s and co-workers (1Û) on t h e b a s i s o f model b u i l d i n g and d a t a f o r t h e nonenzymatic h y d r o l y s i s o f g l y c o s i d e s . An e s s e n t i a l element o f t h i s p r o p o s a l i s t h e d i s t o r t i o n o f t h e GlcNAc r e s i d u e i n s i t e D. The r e s u l t i n g t w i s t - b o a t c o n f o r m a t i o n makes i t p o s s i b l e t o t a k e advantage o f s t e r e o e l e c t r o n i c a s s i s t a n c e (15-17) from t h e r i n g oxygen O5 i n t h e t r a n s i t i o n s t a t e l e a d i n g t o c l e a v a g e o f t h e e x o c y c l i c C1-O4' bond. Scheme I I a l s o i n v o l v e s p r o t o n a t i o n o f O4' by G l u 35 and y i e l d s t h e c y c l i c oxocarbonium i o n which c a n be s t a b i l i z e d by t h e c a r b o x y l a t e group o f Asp 52. The i n i t i a l s t e p i n t h e a l t e r n a t i v e h y d r o l y s i s mechanism i s p r o t o n a t i o n o f t h e r i n g Οχ b y G l u 35 (Scheme I ) . C l e a v a g e o f t h e e n d o c y c l i c C1-O5 bond forms t h e a c y c l i c oxocarbonium i o n i n t e r m e d i a t e , which i s s t a b i l i z e d by Asp 52. A t t a c k by water, c l e a v a g e o f t h e C1-O4' bond, and r i n g c l o s u r e t h e n l e a d t o t h e observed products. E x i s t i n g e x p e r i m e n t a l d a t a on lysozyme h y d r o l y s i s a r e c o n s i s t e n t w i t h Scheme I (see r e f e r e n c e s i n P o s t and K a r p l u s (.2.) ) . Moreover, d i s t o r t i o n o f t h e r i n g i n s i t e D i s n o t r e q u i r e d and t h e a n t i p e r i p l a n a r o r i e n t a t i o n o f an e x o c y c l i c 04' l o n e p a i r o r b i t a l r e l a t i v e t o t h e c l e a v e d C1-O5 bond f o u n d i n t h e s i m u l a t i o n (see s e c t i o n on "Enhancement o f a S u b s t r a t e C o n f o r m a t i o n Optimum f o r C a t a l y s i s " ) i s i n a c c o r d w i t h s t e r e o e l e c t r o n i c r e q u i r e m e n t s (UL) . In Scheme I, a r o l e o f t h e enzyme i s t o c a t a l y z e t h e r e a c t i o n by means o f o r i e n t a t i o n a l ( e n t r o p i e ) c o n t r i b u t i o n s , i n s t e a d o f t h e d i s t o r t i o n a l ( e n t h a l p i c ) s t a b i l i z a t i o n assumed i n t h e s t a n d a r d mechanism (Scheme I I ) . I n p a r t i c u l a r , t h e i n t e r m o l e c u l a r i n t e r a c t i o n s c o u l d s e r v e t o r e s t r i c t o s c i l l a t i o n about t h e d i h e d r a l a n g l e φ (Os-Ci-04'-C4') and t o a i d i n m a i n t a i n i n g t h e p r o p e r geometry f o r r e c l o s i n g t h e r i n g . The MD r e s u l t s a r e o n l y s u g g e s t i v e , a n d n o t h i n g i n t h e p r e s e n t a n a l y s i s would r e q u i r e t h a t t h e same mechanism be found i n a l l j3-glycosidases.

Energy p f GlcNAc

Sites

An a n a l y s i s o f t h e p o t e n t i a l energy o f t h e i n d i v i d u a l GlcNAc u n i t s was p e r f o r m e d t o o b t a i n i n f o r m a t i o n c o n c e r n i n g t h e d e g r e e o f i n t e r a c t i o n a t each s i t e o f t h e b i n d i n g c l e f t o f lysozyme, as w e l l as t o a s s e s s t h e f i t a c h i e v e d by model b u i l d i n g . The p o t e n t i a l e n e r g y c o m p r i s e s t h e configurâtional terms f o r bonds, a n g l e s and d i h e d r a l a n g l e s a n d nonbond terms f o r v a n d e r Waals, e l e c t r o s t a t i c s , and hydrogen bonds (lfi.) . C o o r d i n a t e s from t h e i n i t i a l c r y s t a l l o g r a p h i c / m o d e l - b u i l t s t r u c t u r e and t h e a v e r a g e dynamics s t r u c t u r e , b o t h o p t i m i z e d by e n e r g y m i n i m i z a t i o n , were u s e d t o evaluate the energies. The e n e r g y c o r r e s p o n d o n g t o i n d i v i d u a l c o o r d i n a t e s e t s from t h e t r a j e c t o r y was a l s o c a l c u l a t e d t o o b t a i n t h e a v e r a g e e n e r g y a t each s i t e o v e r t h e 55 p s o f t h e s i m u l a t i o n . T h i s p r o c e d u r e p r o v i d e s t h e average p o t e n t i a l energy, , the p h y s i c a l l y r e l e v a n t q u a n t i t y , which c a n be compared t o t h e e n e r g y o f t h e average s t r u c t u r e , E ( < r > ) . (The p o t e n t i a l e n e r g y f u n c t i o n i s e x p r e s s e d i n terms o f a t o m i c p o s i t i o n s , r . ) E v a l u a t i n g E()d is c o m p u t a t i o n a l l y more e f f i c i e n t and c o r r e s p o n d s most c l o s e l y t o t h e use o f an X - r a y s t r u c t u r e t o e s t i m a t e i n t e r a c t i o n s . However, t h e a v e r a g e s t r u c t u r e may have a r t i f a c t s i n t r o d u c e d b y a v e r a g i n g a t o m i c p o s i t i o n s which c o u l d l e a d t o s i g n i f i c a n t d e v i a t i o n s f r o m t h e a v e r a g e e n e r g y . Such d y n a m i c a l a v e r a g i n g e f f e c t s a r e e v i d e n t when d e v i a t e s from E ( < r > ) . I n c o n t r a s t , d e v i a t i o n s between and E() t h e energy o f t h e X-ray/model b u i l t s t r u c t u r e , d y n

yn

d y n

i n i t r


23. POST ET A L

can a r i s e f r o m e i t h e r dynamic e f f e c t s o r d i f f e r e n c e s i n t h e a v e r a g e structure (ii). E() , E() and a r e p l o t t e d i n F i g u r e l a f o r r e s i d u e s i n s i t e s A t h r o u g h F o f t h e b i n d i n g c l e f t as l a b e l e d a l o n g the a b c i s s a . The c o n t r i b u t i o n s f r o m t h e c o n f i g u r a t i o n a l , t h e s u b s t r a t e - s u b s t r a t e nonbond and s u b s t r a t e - p r o t e i n nonbond terms t o E() i n i t r £()dyn and a r e p l o t t e d i n F i g u r e s l b t h r o u g h I d , r e s p e c t i v e l y , and l i s t e d i n T a b l e I . D e c o m p o s i t i o n o f t h e t o t a l p o t e n t i a l energy p e r r e s i d u e p r o v i d e s i n s i g h t i n t o t h e nature o f t h e enzyme-substrate i n t e r a c t i o n . From F i g u r e l a i t i s s e e n t h a t relative to E() ( A ) and E ( < r > ) (•), t h e a v e r a g e e n e r g y < E ( r ) > (·) i s h i g h e r o v e r a l l due t o t h e p r e s e n c e o f k i n e t i c e n e r g y i n t h e 304 Κ s i m u l a t i o n , which a l l o w s d e v i a t i o n f r o m t h e e n e r g y minimum. The i n c r e a s e d e n e r g y r e s i d e s p r i m a r i l y i n t h e c o n f i g u r a t i o n a l terms, as shown by t h e upward s h i f t i n t h e d o t t e d curve o f Figure Id. The m i d d l e GlcNAc r e s i d u e s have a lower p o t e n t i a l e n e r g y t h a n the t e r m i n a l r e s i d u e s f o r a l l curves i n F i g u r e l a . Indeed s i t e s C and D have t h e l o w e s t e n e r g i e s o f t h e h e x a s a c c h a r i d e . T h i s a s p e c t c o n t r a s t s with t h e poor s t e r i c c o n t a c t s expected i n s i t e D i f t h e r e were s t r a i n i n t h e r i n g bound a t t h i s s i t e ( 2 0 ) . The v a r i a t i o n o f t h e p o t e n t i a l e n e r g y among t h e s i t e s r e s u l t s p r i m a r i l y from s u b s t r a t e - p r o t e i n i n t e r a c t i o n s ; examination o f F i g u r e s l b , l c and I d shows t h a t t h e i n t e r m o l e c u l a r nonbond e n e r g y v a r i e s a l o n g t h e c l e f t (dot-dash curves) w h i l e t h e i n t r a m o l e c u l a r nonbond (dash c u r v e s ) and c o n f i g u r a t i o n a l (dot c u r v e s ) terms a r e nearly equal at a l l s i t e s . Thus t h e g e o m e t r i e s o f t h e monomers a r e e n e r g e t i c a l l y e q u i v a l e n t , w i t h no s t r u c t u r a l s t r a i n i n d u c e d i n f a v o r o f i n t e r m o l e c u l a r nonbond i n t e r a c t i o n s . E() i i and E ( < r > ) a r e v e r y s i m i l a r e x c e p t f o r s i t e s A and B. In t h e i n i t i a l s t r u c t u r e , t h e energy E ( < r > ) i i f o r Β i s h i g h e r t h a n t h a t o f any o t h e r s i t e , w h i l e t h e a v e r a g e s t r u c t u r e e n e r g y E() o f s i t e Β i s lower t h a n t h a t o f A, Ε and F. E ( < r > ) of s i t e Β i s d e c r e a s e d because o f t h e more f a v o r a b l e i n t e r m o l e c u l a r nonbond e n e r g y o b t a i n e d i n t h e dynamic c a l c u l a t i o n (compare F i g u r e s l b and l c ) . The d e v i a t i o n i n t h e s u b s t r a t e e n e r g y a t s i t e A between E ( < r > ) i i and E ( < r > ) i s t h e r e s u l t o f dynamic a v e r a g i n g . To demonstrate t h i s p o i n t , the r e l a t i v e s i t e e n e r g i e s f o r t h e averages E() and a r e compared. The s i t e dependence f o r t h e a v e r a g e e n e r g y and t h e e n e r g y o f t h e a v e r a g e dynamics structure E() i s s i m i l a r e x c e p t a t s i t e A; s i t e A has t h e h i g h e s t p o t e n t i a l e n e r g y when E ( < r > ) i s e v a l u a t e d , y e t i t s energy i s l o w e r t h a n t h a t o f Ε and F when i s e v a l u a t e d . The l a r g e E() v a l u e i s due t o u n f a v o r a b l e i n t r a m o l e c u l a r nonbond e n e r g y (see F i g u r e l c and T a b l e I ) ; c l o s e van d e r Waals c o n t a c t s r e s u l t when t h e c o o r d i n a t e s a r e a v e r a g e d o v e r t h e t r a j e c t o r y and a r e n o t removed by e n e r g y m i n i m i z a t i o n . I n t h e i n d i v i d u a l dynamics s t r u c t u r e s , t h e c o n t a c t s a r e l o n g e r so t h a t t h e r e l a t i v e e n e r g y o f s i t e A i s l o w e r when i s e v a l u a t e d . i n i t

d y n

i n i t


381


n

d y n

t

d y n

n

t

d y n

n

d y n

t

d y n

d y n

d y n

d y n

d y n

There i s an asymmetry w i t h r e s p e c t t o t h e m i d d l e o f (GlcNAc)6 i n t h e e n e r g y p r o f i l e ; s i t e Ε has h i g h e r e n e r g y t h a n s i t e Β ( F i g u r e s l a and I d ) . Compared w i t h t h e o t h e r GlcNAc s i t e s , t h e r e a r e fewer c o n t a c t s between t h e s u b s t r a t e and t h e enzyme a t s i t e E . In p a r t i c u l a r , t h e i n t e r m o l e c u l a r hydrogen bond e n e r g y i s 1/3 t o 1/2 that f o r the other residues. This lack of i n t e r a c t i o n i s consistent w i t h r e s u l t s o f t r a n s g l y c o s y l a t i o n e x p e r i m e n t s which i n d i c a t e t h a t s i t e Ε has a low s u b s t r a t e s p e c i f i c i t y Q ) . The a c e t a m i d o group o f


382


Λ


V

Λ

A B C D E F

A B C D E F

Figure 1. S i t e e n e r g i e s (kcal/mole) o f ( G l c N A c ) bound t o lysozyme. The t o t a l p o t e n t i a l e n e r g y p e r s i t e f o r r e s i d u e s A t h r o u g h F o f (GlcNAc)6 was c a l c u l a t e d f o r t h e i n i t i a l s t r u c t u r e from X - r a y and model b u i l d i n g , E() i i t r (^) f o r t h e average dynamic s t r u c t u r e , E ( < r > ) d (•) / and t h e e n e r g y a v e r a g e d o v e r 5 5 ps o f dynamics s t r u c t u r e s , (·) ( a ) . The c o n t r i b u t i o n s f r o m c o n f i g u r a t i o n a l terms (bonds, a n g l e s , d i h e d r a l s ) ( d o t ) , i n t r a m o l e c u l a r (dash) and i n t e r m o l e c u l a r (dot-dash) nonbond terms (van d e r Waals, e l e c t r o s t a t i c , hydrogen bond) t o E() 6

n

yn

i n i t f

E«r»

dyn and KE(r)"> respectively.

a r e p l o t t e d i n p a n e l b, c and d,


23. POST ET AL.

383

Lysozyme Hydrolysis ofβ-Glycosides

GlcNAc i s one f u n c t i o n a l i t y which does c o n f e r some s p e c i f i c i t y , and t h i s s i d e c h a i n makes one o f t h e two i m p o r t a n t hydrogen bonds f o r t h i s residue i n the simulation. During c a t a l y s i s , the small i n t e r m o l e c u l a r e n e r g y a t s i t e Ε c o u l d enhance p r o d u c t r e l e a s e o f t h e E,F d i m e r m o i e t y , which i s known t o be f a s t r e l a t i v e t o r e l e a s e o f t h e t e t r a m e r A-D (21) . Table

I.

Energy o f GlcNAc R e s i d u e s i n t h e L y s o z y m e - S u b s t r a t e Complex 3

Site

Nonbond* Tntftmolecular Intramolecular Confiourat iona1 optimized i n i t i a l coordinates, E ( < r > ) i i n

A


Β C D Ε F

7 .8 6 .4 7 .6 6 .1 10 .7 8 .6

-31.0 -18.0 -46.4 -49.4 -33.8 -26.2

Β C D Ε F

-28.4 -33.3 -42.4 -44.4 -25.3 -22.7

20 .3 20 .8 19 .9 18 .2 20 .8 20 .3

B C D E

F

4 .0 6 .7 5 .6 5 .1 5 .6 5 .3

-16.2 -8.7 -34.3 -38.1 -16.4 -15.9

0.3 -10.8 -18.9 -19.6 3.2 0.7

8.4 1.7 3.6 6.6 7.7 3.1

o p t i m i z e d dynamics c o o r d i n a t e s , A

t

7.0 2.9 4.5 5.2 6.7 1.7

i n d i v i d u a l dynamics c o o r d i n a t e s , A

Total

a

-30.9 -36.3 -49.5 -50.1 -31.7 -30.9

E()d

yn

20.2 6.3 5.8 8.8 13.8 7.5

-6.7 -23.3 -38.1 -36.2 -12.3 -18.1

a

Sum o f bond, a n g l e and d i h e d r a l a n g l e e n e r g y t e r m s . ^Sum o f van d e r Waals, e l e c t r o s t a t i c and hydrogen bond e n e r g y terms.

Substrate-Enzyme F l u c t u a t i o n C o r r e l a t i o n s N o r m a l i z e d c r o s s - c o r r e l a t i o n s i n t h e a t o m i c f l u c t u a t i o n s between s u b s t r a t e and lysozyme atoms were c a l c u l a t e d from -

< Arj » A r j >

* " < Ar* >

1/2

< Ar| >

1/2

where A r s t a n d s f o r ( r - ). C r o s s - c o r r e l a t i o n c o e f f i c i e n t s a r e a measure o f t h e i n t e r d e p e n d e n c e o f t h e motions o f atoms, and c a n r e v e a l i n t e r a c t i o n s which a r e n o t a p p a r e n t from t h e s t a t i c p i c t u r e p r o v i d e d by an a v e r a g e d s t r u c t u r e . The r e s i d u e s w i t h atoms h a v i n g m o t i o n s c o r r e l a t e d w i t h a s u b s t r a t e atom a r e shown i n F i g u r e 2. C o r r e l a t i o n s w i t h v a l u e s g r e a t e r t h a n 0.3 a r e shown i n t h i c k l i n e s . As i s e v i d e n t from t h e f i g u r e , c o r r e l a t e d m o t i o n s o f t h e s u b s t r a t e and enzyme i n v o l v e p r o t e i n atoms i n t h e b i n d i n g c l e f t and p r i m a r i l y on t h e r i g h t - s i d e as shown i n t h e lower view o f F i g u r e 2. There i s no c o r r e s p o n d e n c e between h i g h c o r r e l a t i o n i n f l u c t u a t i o n s and hydrogen bond; i . e . , n o t a l l r e s i d u e s which hydrogen bond t o (GlcNAc)6 have h i g h c o r r e l a t i o n c o e f f i c i e n t s , and some h i g h l y


384


c o r r e l a t e d r e s i d u e s do not hydrogen bond t o (GlcNAc)6Although i t has been d e m o n s t r a t e d t h a t s o l v e n t a l t e r s c o r r e l a t i o n s c a l c u l a t e d f r o m MD t r a j e c t o r i e s (22-25) t h e r e s u l t s f o r lysozyme»(GlcNAc)6 s h o u l d not be g r e a t l y a f f e c t e d by t h e l a c k o f s o l v e n t because t h e r e a r e no waters m e d i a t i n g t h e i n t e r m o l e c u l a r c o n t a c t s . f

Hydrogen bond o f G l u 35


The n a t u r e o f t h e i n t e r a c t i o n s o f t h e c a t a l y t i c a l l y e s s e n t i a l r e s i d u e G l u 35 (13.14) was i n v e s t i g a t e d by an a n a l y s i s o f t h e s i d e c h a i n hydrogen bond. One-ps average s t r u c t u r e s were u s e d t o f i n d t h e t i m e dependence o f t h e e n e r g y f o r t h e hydrogen bonds i n v o l v i n g t h e two t e r m i n a l c a r b o x y l a t e atoms Hgi and 0ε2· The hydrogen bond p o t e n t i a l and parameters i n c l u d e b o t h a r a d i a l dependence between t h e a c c e p t o r and donor as w e l l as a n g u l a r dependences as p r e v i o u s l y d e s c r i b e d (1).

>Wd=

( j t - j i - ) λ

r

r

ad

ad

U*ia-3-H ) e

'

The hydrogen bonds o f t h e G l u 35 s i d e c h a i n a r e shown i n F i g u r e 3. Two a s p e c t s o f t h e t i m e dependence o f t h e hydrogen bond are of i n t e r e s t . In t h e c a s e o f t h e p r o t o n a t e d c a r b o x y l i c oxygen, m o t i o n o f t h e h y d r o x y l p r o t o n a l l o w s two hydrogen bond a c c e p t o r s s u c h t h a t Hgi s w i t c h e s between t h e e n d o c y c l i c oxygen O5 and t h e h y d r o x y m e t h y l oxygen Oç o f t h e r e s i d u e i n s i t e D. A hydrogen bond i s always p r e s e n t i n v o l v i n g one o r t h e o t h e r a c c e p t o r ( F i g u r e 4 a ) . The s e c o n d p a t t e r n i s from t h e u n p r o t o n a t e d oxygen, 0^2r and i s a b i f u r c a t e d hydrogen bond i n which t h e oxygen s i m u l t a n e o u s l y i n t e r a c t s w i t h two donors, t h e m a i n c h a i n amide H o f lysozyme r e s i d u e s 109 and 110 ( F i g u r e 4 b ) . Some m o d u l a t i o n o f t h e 0^2 hydrogen bonds can be seen; t h e bond t o 110 i s s t r o n g e r i n i t i a l l y and t h e n t h e two e n e r g i e s become n e a r l y e q u a l f r o m 15 t o 35 p s , p o s s i b l y c o r r e l a t e d w i t h a s w i t c h i n t h e Ηει bond toward Οβ. The t h r e e hydrogen bonds t o G l u 35 s t a b i l i z e t h e o b s e r v e d c o n f o r m a t i o n i n which H£i i n t e r a c t s w i t h t h e e n d o c y c l i c oxygen and has l i t t l e c o n t a c t w i t h t h e g l y c o s i d i c oxygen, O4'. Enhancement o f a S u b s t r a t e C o n f o r m a t i o n Optimum f o r C a t a l y s i s In t h e bound s t a t e , t h e c o n f o r m a t i o n o f t h e c a r b o x y m e t h y l s i d e c h a i n i n s i t e D and t h e g l y c o s i d i c d i h e d r a l a n g l e s l i n k i n g r e s i d u e s i n s i t e s D and Ε d i f f e r from t h o s e o f t h e o t h e r (GlcNAc)g r e s i d u e s and o f c e l l u l o s e (2£). As i l l u s t r a t e d w i t h t h e r e s i d u e s from s i t e s A and Β i n F i g u r e 5, t h e c e l l u l o s e - l i k e c o n f o r m a t i o n i n v o l v e s i n t e r r e s i d u e hydrogen bonds (22) between t h e e n d o c y c l i c oxygen O5 o f one r e s i d u e and H3 o f t h e next r e s i d u e , and between Hg and O3 o f t h e same two r e s i d u e s , r e s p e c t i v e l y . These hydrogen bonds p r o d u c e a h e l i c a l t w i s t t o t h e c h a i n such t h a t t h e v a l u e f o r t h e g l y c o s i d i c d i h e d r a l φ ( 0 - C i - 0 - C ) i s -86°, s i m i l a r t o t h a t o f c e l l u l o s e , -98° (2£) . The unbound s t a t e o f (GlcNAc) s would be presumed t o have t h e c e l l u l o s e - l i k e d i h e d r a l a n g l e s . W h i l e t h e l i n k a g e s between GlcNAc r e s i d u e s i n s i t e s A, B, C and D m a i n t a i n t h e c e l l u l o s e c o n f o r m a t i o n , t h e l i n k a g e between D and Ε d i f f e r s i n a way which promotes c a t a l y s i s by Scheme I . /

5

4

/

4



23. POST ET XL

Lysozyme Hydrolysis ofβ-Glycosides

385

F i g u r e 2. C r o s s - c o r r e l a t i o n s i n lysozyme and (GlcNAc)6 fluctuations. P r o t e i n m a i n c h a i n atoms drawn i n t h i c k l i n e s c o r r e s p o n d t o p o s i t i v e c o r r e l a t i o n s > 0.3. These lysozyme r e s i d u e s a r e 35, 42, 44, 52, 57, 63, 73-76, 94-104, 106-110, 112 and 113. A l l ( G l c N A c ) atoms a r e drawn i n t h i n l i n e s . The two s t e r e o views a r e r e l a t e d by two a p p r o x i m a t e l y 90° r o t a t i o n s . 6

F i g u r e 3. S t e r e o view o f t h e a c t i v e s i t e c l e f t o f lysozyme n e a r s i t e D. Hydrogen bonds o f t h e G l u 35 s i d e c h a i n a r e shown i n dotted l i n e s . The s i d e c h a i n atom Η χ o f G l u 35 i s shown. ε



386


0.

10.

20. 30. 40. Time (ps)

50.

F i g u r e 4. Time s e r i e s o f t h e hydrogen bond e n e r g y f o r t h e f o u r hydrogen bonds o f G l u 35: (Α) Η ι t o t h e r i n g 0 ( A ) and 0 (·) o f s i t e D; (Β) Ο t o HN o f r e s i d u e 110 ( A ) and 109 (·) . ε

5

6

ε 2

F i g u r e 5. I n t e r s a c c h a r i d e hydrogen bonds ( d o t t e d l i n e s ) and t h e g l y c o s i d i c a n g l e φ ( 0 - C - 0 4 - C 0 between s i t e A and B. These hydrogen bonds and φ (= -86°) a r e s i m i l a r t o t h o s e f o u n d f o r cellulose. /

5

1

4


23.

POST ET XL


387

By t h e a l t e r n a t i v e mechanism, G l u 35 p r o t o n a t e s t h e r i n g oxygen of D. F u r t h e r m o r e , optimum s t e r e o e l e c t r i c a s s i s t a n c e f o r r i n g o p e n i n g i s a c h i e v e d when φ i s -60°. These two a s p e c t s a r e not c o n s i s t e n t with a c e l l u l o s e - l i k e conformation: (i) the i n t e r s a c c h a r i d e hydrogen bond o f Hg t o O3 would s t e r i c a l l y i n t e r f e r e w i t h G l u 35 p r o t o n a t i o n o f t h e r i n g oxygen and ( i i ) φ would d i f f e r by 38°. (For t h e o t h e r i n t e r s a c c h a r i d e l i n k a g e s , t h e H -» 0 hydrogen bond does e x i s t and φ v a r i e s f r o m a p p r o x i m a t e l y -86 t o 6

3

-75°.)


B i n d i n g t o lysozyme s t a b i l i z e s a c o n f o r m a t i o n i n s i t e D c o m p a t i b l e w i t h t h e a l t e r n a t i v e mechanism. ( i ) Hg o f r e s i d u e D does not i n t e r a c t w i t h r e s i d u e Ε but forms a s t r o n g hydrogen bond t o t h e m a i n c h a i n Ο o f r e s i d u e 57, a r e s i d u e i n v o l v e d w i t h t h e u n u s u a l b u r i e d β t u r n i n lysozyme. ( i i ) The v a l u e o f φ between D and E, which was -54° i n t h e i n i t i a l s t r u c t u r e , s t a b i l i z e d a t -62°, n e a r the optimum o f -60° f o r s t e r e o e l e c t r o n i c a s s i s t a n c e .

Conclusions MD s i m u l a t i o n s can a i d i n t h e u n d e r s t a n d i n g o f enzymic r e a c t i o n s by p r o v i d i n g new i n s i g h t s i n t o t h e s t r u c t u r e s and i n t e r m o l e c u l a r i n t e r a c t i o n s fundamental t o t h e c h e m i c a l c a t a l y s i s . By s t u d y i n g t h e s t r u c t u r e s from t h e s i m u l a t i o n o f t h e l y s o z y m e - ( G l c N A c ) g complex, we have p r o p o s e d an a l t e r n a t i v e t o t h e a c c e p t e d mechanism which a c c o u n t s f o r t h e a v a i l a b l e e x p e r i m e n t a l o b s e r v a t i o n s . The p r o p o s a l of t h i s lysozyme mechanism i l l u s t r a t e s one way i n which s i m u l a t i o n s can s e r v e t o g e n e r a t e new i d e a s which can be e x p l o r e d by e x p e r i m e n t and c o m p u t a t i o n . The i n f o r m a t i o n o b t a i n e d from t h e s i m u l a t i o n i n c l u d e d an e x p l a n a t i o n from the e n e r g e t i c s f o r the l a c k of s p e c i f i c i t y i n s i t e Ε and a p o s s i b l e d r i v i n g f o r c e f o r p r o d u c t r e l e a s e , as w e l l as a d e s c r i p t i o n o f how t h e hydrogen bond i n t e r a c t i o n s and g l y c o s i d i c d i h e d r a l a n g l e o f t h e GlcNAc r e s i d u e i n s i t e D c o u l d promote c a t a l y s i s v i a t h e a l t e r n a t i v e mechanism. Since the a l t e r n a t i v e mechanism was s u g g e s t e d by e x a m i n i n g t h e r e s u l t s o f t h e s i m u l a t i o n , t h e r e was no b i a s i n t h e i n i t i a l model b u i l d i n g o f t h e s u b s t r a t e (see a b o v e ) . As such, t h e s u p p o r t o f t h e a l t e r n a t i v e mechanism by the n a t u r e o f t h e hydrogen bond p a i r s , t h e r e l a t i v e s i t e e n e r g i e s and t h e g l y c o s i d i c φ a n g l e i s a consequence o f t h e s i m u l a t i o n . The dynamics a l s o improved t h e i n i t i a l model b u i l t complex i n t h a t t h e s u b s t r a t e - e n z y m e i n t e r a c t i o n e n e r g y was l o w e r e d i n s i t e B. A d d i t i o n a l s t u d i e s of the enzyme-substrate complementarity i n o t h e r complexes a l o n g t h e r e a c t i o n p a t h a r e under way. Since the i n i t i a l r e p o r t o f an a l t e r n a t i v e pathway f o r lysozyme h y d r o l y s i s (8 9 28) work on t h e s o l u t i o n h y d r o l y s i s o f g l u c o s i d e s has d e m o n s t r a t e d t h e e x i s t e n c e o f a r i n g o p e n i n g mechanism (29 30) . I t i s hoped t h a t t h e a n a l y s i s and r e s u l t s r e p o r t e d h e r e w i l l s t i m u l a t e new e x p e r i m e n t s on t h e lysozyme mechanism. r

f

f

Literature Cited 1. Post, C. B.; Brooks, B. R.; Karplus, M.; Dobson, C. M.; Artymiuk, P. J.; Cheetham, J. C.; Phillips, D. C. J. Mol. Biol. 1986, 190, 455. 2. Blake, C. C. F.; Koenig, D. F.; Mair, G. Α.; North, A. C. T.;. Phillips, D. C.; Sarma, V. R. Nature 1965, 206, 757. 3. Imoto, T.; Johnson, L. M.; North, A. C. T.; Phillips, D. C.; Rupley, J. A. In The Enzymes; Boyer, P. D., Ed.; Academic: New York, 1972; ρ 665.



388


4. Smith, L. E. H.; Mohr, L. H.; Raftery, M. A. J. Am. Chem. Soc. 1973, 95, 7497. 5. Rosenberg, S.; Kirsch, J. F. Biochemistry 1981, 20, 3196. 6. Pollock, J. J.; Sharon, N. Biochemistry 1970, 9, 3913. 7. Rupley, J. Α.; Gates, V. Proc. Natl. Acad. Sci. 1967,57,496. 8. Post, C. B.; Karplus, M. In Mechanisms of Enzymatic Reactions: Stereochemistry, Steenbock Symp. 1985; Frey, P. Α., Ed.; Elsevier: New York, 1985; ρ 345. 9. Post, C. B.; Karplus, M. J. Am. Chem. Soc. 1986, 108, 1317. 10. Blake, C. C. F.; Mair, G. Α.; North, A. C. T.; Phillips, D. C.; Sarma, V. R. Proc. Roy. Soc. London. Series No. B167; 1967; ρ 365. 11. Vernon, C. A. Proc. Roy. Soc. London, Series No. B67; 1967; ρ 378. 12. Walsh, C. Enzymatic Reaction Mechanisms, 1979; W. H. Freeman: San Francisco. 13. Malcolm, Β. Α.; Rosenberg, S.; Corey, M. J.; Allen, J. S.; Baetselier, Α.; Kirsch, J. F. Proc. Natl. Acad. Sci. 1989, 86, 133. 14. Kuroki, R.; Yamada, H.; Moriyama, T.; Imoto, T. J. Biol. Chem. 1986 261, 13571. 15. Gorenstein, D. G.; Findley, J. N.; Luxon, Β. Α.; Kar, D. J. Am. Chem. Soc. 1977, 99, 3473. 16. Kirby, A. Acc. Chem. Res. 1984, 17, 305. 17. Kirby, A. CRC Crit. Rev. Biochem. 1987, 22, 282. 18. Brooks, B. R.; Bruccoleri, R. E.; Olafson, B. D.; States, D. J.; Swaminathan, S.; Karplus, M. J. Comput. Chem. 1983, 4, 187. 19. Dobson, C. M.; Karplus, M. Meth. Enzym. 1986,131,362. 20. The experimental data which have been used to suggest ring distortion in site D may not be relevant. The interpretation of data on the energetics of binding is complicated when it i s unknown what group on the ring gives rise to poor contacts (Schindler, M.; Assaf, Y.; Sharon, N.; Chipman, D. M. Biochemistry 1977, 16, 423), whether the bound conformation i s analogous to that of the natural substrate, and what is the contribution from the release of bound water (9). In addition, structural results on complexes with synthetic substrates are not important i f the complex is not homologous to a reaction intermediate (Ford, L. O.; Johnson, L. N.; Machin, P. Α.; Phillips, D. C.; Tjian, R. J. Mol. Biol. 1974,88,349). 21. Chipman, D. M.; Pollock, J. J.; Sharon, N. J. Biol. Chem. 1968, 243, 487. 22. Ahlstrom, P.; Teleman, O.; Jonsson, B.; Forsen, S. J. Am. Chem. Soc. 1987, 109, 1541. 23. Brooks, C. L.,III;Karplus, M.; Pettitt, Β. M. Adv. Chem. Phys. 1988, 71, ρ 1. 24. Chen, L. X. Q.; Engh, R. Α.; Brunger, A. T.; Nguyen, D. T.; Karplus, M.; Fleming, G. R. Biochemistry 1988, 27, 6908. 25. van Gunsteren, W. F.; Karplus, M. Biochemistry 1982, 21, 2259. 26. Gardner, Κ. H.; Blackwell, J. Biopolymers 1974, 12, 1975. 27. Ham, J. T.; Williams, D. G. Acta Crystallogr. 1977, B26, 1373. 28. Fleet, G. W. J. Tetrahedron Lett. 1985, 26, 5073. 29. Guindon, Y.; Anderson, P. C. Tetrahedron Lett. 1987, 28, 2485. 30. Guindon, Y.; Bernstein, Μ. Α.; Anderson, P. C. Tetrahedron Lett. 1987, 28, 2225. RECEIVED Februaiy 13, 1990


Computer Modeling of Carbohydrate Molecules - American Chemical

Recommend Documents