The Influence of Changes in Conformation of a Macromolecule on

32 The Influence of Changes in Conformation of a Macromolecule on Reaction Rates

Downloaded by UNIV LAVAL on December 15, 2015 | http://pubs.acs.org Publication Date: January 1, 1968 | doi: 10.1021/ba-1968-0081.ch032

REINIER BRAAMS Physics Laboratory, Utrecht University, Bijlhouwerstraat 6, Utrecht, the Netherlands MICHAEL EBERT Radiation Chemistry Department, Paterson Laboratories, Christie Hospital and Holt Radium Institute, Manchester 20, England

The change in the rate constants with temperature for the reactions of ribonuclease (RNase) with hydrated electrons and O H radicals was measured. The RNase molecule un folds reversibly at elevated temperatures exposing sites particularly reactive towards hydrated electrons. The theo retical treatment leads to an estimate of the encounter frequencies for differently shaped macromolecules with small radiolytically produced solvent radicals. The derived encounter frequencies are compared with experimentally determined rate constants. Values as high as 10 M sec. are understandable. 13

-1

-1

T n recent experiments ( 3 ) w e h a v e f o u n d that t h e v a l u e of rate constants f o r reactions b e t w e e n e~

m

nuclease

(RNase)

a n d c e r t a i n p r o t e i n m o l e c u l e s s u c h as r i b o

d e p e n d s o n the c o n f o r m a t i o n of t h e m o l e c u l e . F o r

r i b o n u c l e a s e i t w a s f o u n d that t h e rate constant increases u p o n u n f o l d i n g of t h e m o l e c u l e . T h i s increase c a n p a r t l y b e a s c r i b e d to exposure of t h e h i d d e n d i s u l f i d e b r i d g e s b u t c o u l d also p a r t l y b e c a u s e d b y a n increase i n encounter

f r e q u e n c y of t h e h y d r a t e d e l e c t r o n w i t h

the u n f o l d e d

molecule. T h e expression d e r i v e d b y D e b y e f o r the encounter f r e q u e n c y i n reactions b e t w e e n s p h e r i c a l reactants c a n n o t b e a p p l i e d to m o l e c u l e s that differ m a r k e d l y f r o m s p h e r i c a l shape, s u c h as t h e r o d s h a p e d c o l l a g e n . I n this p a p e r the t h e o r y a p p l i e d b y D e b y e has b e e n e x t e n d e d to reactions between a small spherical molecule a n d a cylindrical macromolecule. 464 In Radiation Chemistry; Hart, E.; Advances in Chemistry; American Chemical Society: Washington, DC, 1968.

32.

BRAAMS A N D EBERT

Conformation

of a

465

Macromolecule

T h e results o b t a i n e d w i t h t h e extended D e b y e t h e o r y h a v e b e e n c o m p a r e d w i t h r e p o r t e d d a t a f o r reactions

between

s m a l l reactants a n d

b i o m a c r o m o l e c u l e s a n d g o o d agreement has b e e n f o u n d . T h e e x t e n d e d t h e o r y has t h e n b e e n u s e d t o a n a l y z e the d a t a o n r i b o n u c l e a s e . I t is c o n c l u d e d that t h e exposure of d i s u l f i d e bridges contributes s u b s t a n t i a l l y to the increase of t h e rate constant u p o n u n f o l d i n g . Material Ribonuclease

(RNase)

is a c o m p a c t l y f o l d e d p r o t e i n m o l e c u l e of


a p p r o x i m a t e l y s p h e r i c a l shape. It consists of o n e p e p t i d e c h a i n w i t h f o u r i n t r a m o l e c u l a r d i s u l f i d e cross-links. I n R N a s e t h e p r o t o n a t e d h i s t i d y l residues a n d t h e c y s t y l residues are a p p a r e n t l y the most reactive sites i n reactions w i t h t h e h y d r a t e d electron. T h i s w a s c o n c l u d e d f r o m measurements of t h e absolute r e a c t i o n rates o f a m i n o acids, peptides, a n d proteins (1, 2) a n d f r o m a n analysis of t h e r e a c t i v i t y of proteins i n terms of t h e reactivities of t h e i n d i v i d u a l a m i n o acids. A t a p H of a b o u t 9 t h e h i s t i d y l residues are d i s s o c i a t e d a n d h a v e a l o w r e a c t i v i t y . T h e absolute r e a c t i o n rate constant of R N a s e at this p H is 5 X 10° M " sec." 1

1

(2) a n d c a n o n l y b e e x p l a i n e d o n t h e a s s u m p t i o n

that t h e f o u r d i s u l f i d e b r i d g e s i n s i d e t h e p r o t e i n m o l e c u l e c o n t r i b u t e t o its r e a c t i v i t y . T h i s c o n t r i b u t i o n , h o w e v e r , is less t h a n w o u l d b e e x p e c t e d for c y s t y l residues w h i c h s h o w a rate constant of a b o u t K e

M

1

a q

= 2 X 10

1 0

sec." . T h e l a c k o f a f u l l c o n t r i b u t i o n f r o m t h e d i s u l f i d e b o n d s w a s 1

a s c r i b e d to t h e s h i e l d i n g of these reactive groups b y t h e u n r e a c t i v e p e p t i d e chains. A t e l e v a t e d temperatures t h e R N a s e m o l e c u l e undergoes a t r a n s i t i o n f r o m a f o l d e d to a n u n f o l d e d state ( 5 ) . T h i s c a n b e s h o w n b y o p t i c a l a n d v i s c o s i t y measurements. a n d i o n i c strength.

T h e transition temperature depends o n p H

A b o v e this t e m p e r a t u r e

t h e t e r t i a r y structure is

d e s t r o y e d b u t t h e c o v a l e n t d i s u l f i d e b o n d s r e m a i n intact. T h e u n f o l d i n g is r e v e r s i b l e since o n l o w e r i n g t h e t e m p e r a t u r e t h e n a t i v e c o n f o r m a t i o n is r e g a i n e d . Experimental T h e properties of t h e R N a s e m o l e c u l e are u s e f u l f o r i n v e s t i g a t i n g the s h i e l d i n g of r e a c t i v e groups b y t h e t e r t i a r y structure. P u l s e - r a d i o l y s i s t e c h n i q u e s ( 6 ) w e r e u s e d f o r measurements of t h e r e a c t i o n rate of R N a s e w i t h t h e h y d r a t e d electron i n b u f f e r e d solutions b e l o w a n d a b o v e t h e t r a n s i t i o n t e m p e r a t u r e . A n llyM s o l u t i o n of R N a s e i n 0 . 6 7 m M p h o s p h a t e buffer ( p H 6.8) a n d 0 . 0 1 M K C 1 w a s c o n t i n u o u s l y b u b b l e d w i t h a r g o n gas to r e m o v e o x y g e n , h e a t e d s l o w l y f r o m 2 0 ° C . to 7 0 ° C . a n d a l l o w e d to c o o l a g a i n . A t different temperatures some s o l u t i o n w a s flushed i n t o a t e m p e r a t u r e c o n t r o l l e d s p i r a l r a d i a t i o n c e l l a n d p u l s e - r a d i o l y z e d . T h e rate

In Radiation Chemistry; Hart, E.; Advances in Chemistry; American Chemical Society: Washington, DC, 1968.

466

RADIATION CHEMISTRY

1

constant for the d i s a p p e a r a n c e of the o p t i c a l a b s o r p t i o n of the h y d r a t e d e l e c t r o n w a s m e a s u r e d a n d thus the rate constant f o r the r e a c t i o n R N a s e + e~ d e r i v e d . I n F i g u r e 1 the rate constants o b t a i n e d i n a t y p i c a l e x p e r i m e n t are p l o t t e d against t e m p e r a t u r e , after c o r r e c t i o n for reactions of t h e h y d r a t e d electron w i t h the buffer s o l u t i o n at the different temperatures. B e t w e e n 2 0 ° C . a n d 40 ° C . the r e a c t i o n rate increases s l o w l y , b u t at temperatures at w h i c h the m o l e c u l a r t r a n s i t i o n f r o m the f o l d e d to the u n f o l d e d f o r m o c c u r r e d the r e a c t i o n rate rises s h a r p l y . I n other experiments at s t i l l h i g h e r temperatures it was f o u n d that after the t r a n s i t i o n is c o m p l e t e d the r e a c t i o n rate rises o n l y s l i g h t l y w i t h temperature. U p o n c o o l i n g , the r e a c t i o n rate decreases s h a r p l y a g a i n a n d attains values l o w e r b u t close to those o b s e r v e d o n h e a t i n g . T h i s difference is a n e x p e r i m e n t a l artifact a n d c a n b e a s c r i b e d to a p a r t i a l d e n a t u r a t i o n of the p r o t e i n i n s o l u t i o n at the highest temperatures caused b y the gas b u b b l e s a n d is d i f f i c u l t to avoid.


m

E x p e r i m e n t s to establish the rate constant of the O H r a d i c a l w i t h the R N a s e m o l e c u l e at different temperatures w e r e also c a r r i e d out. 32/xM R N a s e a n d 100/xM K C N S w e r e a l l o w e d to c o m p e t e f o r the O H r a d i c a l s . W i t h i n the e x p e r i m e n t a l error n o s u d d e n increase of the rate constant f o r the r e a c t i o n of O H w i t h R N a s e w a s o b s e r v e d at the t r a n s i t i o n t e m p e r a t u r e . T h e rate constant increased f r o m 2.6 X 1 0 M " sec." at 2 0 ° C . to 5.2 X 1 0 M ^ s e c . " at 6 0 ° C . 10

1 0

1

1

1

Discussion A n e x p l a n a t i o n of these results w i l l b e a t t e m p t e d b y first d e a l i n g w i t h the p r o b l e m of encounter f r e q u e n c y of reactants i n g e n e r a l a n d t h e n discussing the s p e c i a l case of R N a s e . T h e f r e q u e n c y of encounters b e t w e e n s p h e r i c a l particles of different size has b e e n treated b y D e b y e ( 4 ) , f o l l o w i n g a m e t h o d first u s e d b y S m o l u c h o w s k i (10).

T h e n u m b e r of collisions is o b t a i n e d f r o m the d i f

f u s i o n e q u a t i o n f o r particles d i f f u s i n g steadily i n t o a hole s u r r o u n d i n g the p a r t i c l e i n q u e s t i o n .

F o r s p h e r i c a l particles the e q u a t i o n c a n

be

s o l v e d a n d the w e l l k n o w n E x p r e s s i o n 1 is f o u n d . v = 4TT(RI + R ) (D 2

t

+ D )N 2

• 10-3 i

H e r e v is the encounter f r e q u e n c y , R i a n d R

2

different r e a c t i n g particles i n c m . , D

x

and D

2

i t e r

m o

i -i e

s e c

.-i

(i)

are the r a d i i of the t w o are the d i f f u s i o n constants

f o r the t w o different m o l e c u l e s i n c m . sec." a n d N is A v o g a d r o ' s n u m b e r . 2

1

T h i s expression cannot b e a p p l i e d to m a c r o m o l e c u l e s

w h i c h are

not

s p h e r i c a l i n shape. T h e e q u a t i o n can also b e s o l v e d for s p h e r i c a l particles d i f f u s i n g i n t o a h o l e w h i c h has the shape of a n e l l i p s o i d of r o t a t i o n b u t for most other shapes no exact s o l u t i o n is a v a i l a b l e . T h e d i f f e r e n t i a l e q u a t i o n f o r spheres of r a d i u s R d i f f u s i n g i n t o a h o l e of a n y g i v e n shape is the same as f o r the e l e c t r i c a l c a p a c i t y C of a c l o s e d surface e n c l o s i n g the h o l e at a distance R.



32.

BRAAMS AND EBERT

Conformation

of a

467

Macromolecule

Figure 1. Rate constants for the reaction between the hydrated electron and RNase at different temperatures. The upper curve (%) is for increasing temperatures. The lower curve (O) is obtained after cooling the heated solution

I n o r d e r to o b t a i n t h e c o l l i s i o n f r e q u e n c y t h e t e r m ( R

x

+

R ) in 2

E x p r e s s i o n 1 has to b e r e p l a c e d b y t h e c a p a c i t y C of the c l o s e d surface. E x p r e s s i o n s f o r the c a p a c i t y of some s i m p l e surfaces c a n b e f o u n d i n textbooks o n electricity.

F o r other a n d m o r e c o m p l e x shapes t h e v a l u e

c a n b e o b t a i n e d f r o m a measurement of t h e e l e c t r i c a l c a p a c i t y of a m o d e l surface. T h e encounter f r e q u e n c y c a n n o w b e expressed as: v

= 4 C(D 7r

1

+ D ) N • 10" M " sec. 2

3

1

-1

(2)

F o r a p r o l a t e e l l i p s o i d of r o t a t i o n w i t h t h e axis a ^ b = c t h e e l e c t r i c a l capacity C is: (3)


468

RADIATION CHEMISTRY

1

F o r a long cylinder the capacity can be derived from Expression 3 b y extrapolation: C = -

L

cm.

T

(4)

21n — r i n w h i c h L is the l e n g t h of t h e c y l i n d e r i n c m . a n d r is t h e r a d i u s o f r o t a t i o n o f the c y l i n d e r i n c m . F o r m a c r o m o l e c u l e s of c y l i n d r i c a l shape, C c a n b e d e r i v e d f r o m E x p r e s s i o n 4 u s i n g t h e d i m e n s i o n s of t h e m o l e c u l e .

W i t h t h e a i d of


E x p r e s s i o n 2 t h e encounter f r e q u e n c y a n d therefore t h e m a x i m u m rate constant f o r reactions b e t w e e n s p h e r i c a l reactants a n d s p h e r i c a l o r c y l i n d r i c a l m a c r o m o l e c u l e s c a n b e estimated. I n Tables I a n d I I data f o r the hydrated electron a n d O H radicals r e s p e c t i v e l y are g i v e n . Table I. Calculated Encounter Frequencies and Experimentally D e termined Rate Constants for Reactions of Hydrated Electrons with Macromolecules of Different Size and Shape, Using D - = 4.75 X 1Q"° cm. s e c . (8) and R - = 3 A . for the Hydrated Electron" (

2

Substance RNase RNase

1

r

Molecular Weight

Conformation

13,683 compact sphere 13,683 linear extended chain 360,000 rigid r o d

collagen spherical protein 360,000 compact sphere gelatin 120,000 extended gelatin 120,000 helix gelatin 120,000 random coil gelatin 120,000 compact sphere DNA 5 X 1 0 double helix amino acid 90 sphere nucleotide 350 sphere 6

aq

a q

Capacity C Encounter Rate Constant in Frequency in in 10~ cm. 10 M' sec.' 10 M " seer s

10

1

19

7

81 266

29 94

51 360 322 55 36 5550 6.2 11

18 130 117 20 13 2000 2 4

1

10

1

1

0.5

6

5

h

^10 max. 2 ^1

3

c

d

c

° The diffusion constant of RNase was taken as 10" cm. sec." , for larger macromole cules the diffusion constant is so small that their diffusion can be neglected. Ref. 2. Ref. 9. Ref. 1. 6

2

1

6

c

d

F r o m the d a t a p r e s e n t e d i n T a b l e I i t c a n b e seen that t h e c o l l i s i o n f r e q u e n c y d e p e n d s o n t h e shape of t h e m a c r o m o l e c u l e a n d is l o w e s t w h e n t h e m o l e c u l e is f o l d e d i n t o a c o m p a c t sphere.

M o l e c u l e s s u c h as


32.

BRAAMS A N D EBERT

Conformation

of a

469

Macromolecule

c o l l a g e n a n d D N A are k n o w n t o d e v i a t e strongly f r o m t h e c o m p a c t f o l d e d f o r m . T h e c o l l a g e n m o l e c u l e is a r i g i d r o d a b o u t 3000 A . l o n g c o m p o s e d of three i n t e r t w i n e d single p e p t i d e chains.

D N A consists o f t w o single

p o l y m e r i c chains that f o r m a d o u b l e helix. I t was treated as a n e x t e n d e d molecule.

F o r t h e c a l c u l a t i o n of t h e encounter f r e q u e n c y i t has b e e n

assumed that t h e y h a v e a c y l i n d r i c a l shape.

T h e calculated diffusion

c o n t r o l l e d r e a c t i o n rates f o r c o l l a g e n a n d D N A c o n s i d e r a b l y exceed t h e values u s u a l l y f o u n d f o r s m a l l reactants ( a p p r o x . 1 0

1 0

M " sec." ). F o r a 1

1

d o u b l e s t r a n d e d D N A m o l e c u l e of M W 5 X 1 0 t h e absolute rate constant 6

for r e a c t i o n w i t h a s m a l l species c o u l d b e as h i g h as 2 X 1 0 Downloaded by UNIV LAVAL on December 15, 2015 | http://pubs.acs.org Publication Date: January 1, 1968 | doi: 10.1021/ba-1968-0081.ch032

S u c h h i g h values h a v e b e e n r e p o r t e d b y Scholes

1 3

M' sec." . 1

1

(9) for the hydrated

electron a n d b y K r a l j i c (7) f o r t h e h y d r o x y l r a d i c a l . Since t h e v a l u e of t h e d i f f u s i o n constant o f O H is less t h a n h a l f t h e v a l u e f o r e~ t h e encounter frequencies t a b u l a t e d i n T a b l e I I f o r O H aq

are l o w e r t h a n those g i v e n i n T a b l e I. T h e m e a s u r e d rate constants i n the last c o l u m n of T a b l e I I agree w e l l w i t h t h e c a l c u l a t e d frequencies.

encounter

F o r proteins this m u s t b e a s c r i b e d t o t h e h i g h r e a c t i v i t y of

O H f o r several a m i n o a c i d side chains a n d f o r t h e p e p t i d e g r o u p , l i n k i n g the a m i n o a c i d residues together.

F o r D N A this c a n b e a s c r i b e d to t h e

r e a c t i v i t y of n u c l e o t i d e s . Table II. Calculated Encounter Frequencies and Experimentally Determined Rate Constants for Reactions of H y d r o x y l Radicals with a Few of the Molecules Listed in Table I, Assuming D O H = 2 X 10 c m . sec." and R = 2.2 A . 5

1

Substance RNase

8

13,683 compact sphere

collagen

O H

Capacity C Encounter in Frequency in Conformation 10~ cm. 10 Mr sec.'

Molecular Weight

360,000 rigid r o d

18.2 260

gelatin

100,000 random coil

52

DNA

5 X 1 0 double helix

5500

a b

6

2

10

1

1

Rate Constant in 10 M' seer 10

1

2.6

3.0

40

39

a

9.1°

8.4 830

1

^

1000

h

Ref. 11. Ref. 7. S i n c e t h e h y d r a t e d electron is reactive w i t h o n l y a f e w a m i n o a c i d

residues t h e m e a s u r e d rate constant for proteins is less t h a n t h e c a l c u l a t e d d i f f u s i o n c o n t r o l l e d r e a c t i o n rate. I n t h e s p e c i a l case of t h e R N a s e m o l e c u l e , some geometric i n f o r m a t i o n is a v a i l a b l e f r o m v i s c o s i t y d a t a i n s o l u t i o n . It has t o b e k e p t i n m i n d that t h e t e m p e r a t u r e i n d u c e d r e v e r s i b l e u n f o l d i n g of R N a s e is i n c o m p l e t e , since t h e f o u r d i s u l f i d e b r i d g e s r e m a i n intact.

T h e relation between the


470

RADIATION CHEMISTRY

i n t r i n s i c viscosity rj a n d t h e r a d i u s o f g y r a t i o n R

is g i v e n b y r;

s

^j^-

R

g

3

1

=

w h e r e N is A v o g a d r o ' s n u m b e r a n d M t h e m o l e c u l a r w e i g h t of

the m o l e c u l e (12).

F o r t h e f o l d e d R N a s e rj =

19 A . F o r the u n f o l d e d R N a s e

v

3.3 m l . / g . a n d R

s

=

= 7 m l . / g . (13) a n d R = 25 A . g

Since i t is difficult to calculate t h e encounter f r e q u e n c y of t h e h y d r a t e d electron w i t h t h e u n f o l d e d m o l e c u l e i t is h e l p f u l to consider i t as a r a n d o m c o i l l o c a t e d i n a sphere w i t h t h e r a d i u s R .

T h e increase i n

g

R

g

f r o m 19 A . t o 25 A . w i t h i n c r e a s i n g t e m p e r a t u r e c a n o n l y a c c o u n t f o r

a n increase of t h e encounter f r e q u e n c y of less t h a n 5 0 % .

W e , however,


find a factor of f o u r i n rate constants. T h e r e f o r e , t h e increase i n absolute rate constant f o r the r e a c t i o n of the h y d r a t e d electron w i t h the m o l e c u l e u p o n u n f o l d i n g is either because of a n increase i n r e a c t i v i t y of t h e reactive sites or to a better exposure of a v a i l a b l e reactive sites. T h e r e is n o e v i d e n c e for a substantial increase i n r e a c t i v i t y of a m i n o a c i d residues w i t h a change i n c o n f o r m a t i o n of t h e p r o t e i n . T h e exposure of reactive sites m u s t b e t h e m a i n reason f o r t h e increased r e a c t i v i t y . T h i s confirms o u r p r e v i o u s conclusions

(3).

A n o t h e r i m p o r t a n t p o i n t i n t h e a b o v e a r g u m e n t is that t h e d r a m a t i c increase i n the rate for the r e a c t i o n of the h y d r a t e d electron is not p a r a l l e l e d f o r t h e O H r a d i c a l reaction.

T h i s demonstrates

c l e a r l y a specific

increase for the r e a c t i v i t y t o w a r d s the electron i n contrast to the b e h a v i o r towards the O H radical. W e w o u l d l i k e to c o n c l u d e that t h e r e a c t i v i t y o f a m a c r o m o l e c u l e is c e r t a i n l y not a linear f u n c t i o n of t h e n u m b e r of m o n o m e r units, a n d that it d e p e n d s c r i t i c a l l y o n the size a n d t h e shape of t h e m o l e c u l e . T h e m i s l e a d i n g c u s t o m of q u o t i n g rate constants of m a c r o m o l e c u l e s o n t h e basis o f the c o n c e n t r a t i o n of m o n o m e r units s h o u l d b e d i s c o n t i n u e d . Acknowledgments It is a pleasure to a c k n o w l e d g e g r a t e f u l l y the interest B . U . F e l d e r h o f of U t r e c h t U n i v e r s i t y has t a k e n i n t h e p r o b l e m a n d t o t h a n k h i m f o r t h e t h e o r e t i c a l f o u n d a t i o n o f this p a p e r .

This collaboration was supported

b y a t r a v e l grant f r o m N A T O .

Literature Cited (1) Braams, R., Radiation Res. 27, 319 (1966). (2) Ibid., 31,8(1967). (3) Braams, R., Ebert, M., Intern. J. Radiation Biol. 13, 195 (1967). (4) Debye, P., Trans. Electrochem. Soc. 82, 265 (1942). (5) Hermans, J., Scherega, H. A., J. Am. Chem. Soc. 83, 3283 (1961). (6) Keene, J., "Pulse Radiolysis," Ebert et al., eds., p. 1, Academic Press, London and New York, 1965.


32.

(7)

(8) (9) (10) (11) (12)


(13)

BRAAMS AND EBERT

Conformation

of a

Macromolecule

471

Kraljic, I., "The Chemistry of Ionization and Excitation," G. R. A. Johnson, G. Scholes, eds., p. 303-309, Taylor and Francis Ltd., London, England, 1967. Schmidt, K. H . , Buck, W. L., Science 151, 70 (1966). Scholes, G., Shaw, P., Willson, R. L . , Ebert M . , "Pulse Radiolysis," Ebert et al., eds., p. 151, Academic Press, London and New York, 1965. Smoluchowski, M . S., Z. Physik. Chem. 92, 129 (1918). Southern, E . M., Davies, J. V. (in preparation). Tanford, C., "Physical Chemistry of Macromolecules," I. Wiley and Sons, New York, 1961. Weber, R. E . , Unpublished data, referred to in "Physical Chemistry of Macromolecules," Charles Tanford, ed., p. 516, J. Wiley and Sons, New York, 1961.

R E C E I V E D January 17,

1968.


The Influence of Changes in Conformation of a Macromolecule on

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