Kinetic Study of Association Processes between Polymer Latex Particles

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Chapter 17

Kinetic Study of Association Processes between Polymer Latex Particles Hiromi Kitano and Norio Ise Department of Polymer Chemistry, Kyoto University, Kyoto, Japan The association processes between polymer latex particles were studied. Advantage was taken of latex particles being large enough to be seen under an ultramicroscope connected to an image-processing system. The kinetic laws were examined directly by visual imagery. The forward rate constants (kf) of the association of oppositely charged latex particles obtained were unexpectedly close to, although slightly smaller than, the theoretical values for the diffusion-controlled association process of neutral species. The kf values of the association of antigen- and antibody-carrying latex particles were evaluated to be several times larger than that of the free antigen-antibody association system. The introduction of a fluorescence dye into the latex particles enabled us to confirm that the association took place specifically between different kinds of latex particles. The k i n e t i c studies o f chemical r e a c t i o n s i n general have been p e r f o r m e d by m e a s u r i n g t h e t i m e changes o f parameters a s s o c i a t e d w i t h the r e a c t i o n . I t would be q u i t e i n t e r e s t i n g t o s t u d y k i n e t i c laws without introducing the assumption that t h e absorbance i n spectrophotometry i s s t r i c t l y proportional t o the concentration of the s p e c i e s i n c o n s i d e r a t i o n . This study a l s o has a n o t h e r s i g n i f i c a n c e i n c o l l o i d science. Polymer latices have been w i d e l y used i n t h e d i a g n o s i s of various kinds o f diseases A g g l u t i n a t i o n methods can be used t o r e c o g n i z e and e s t i m a t e s p e c i f i c compounds i n b i o l o g i c a l samples i n t h e a c t u a l diagnosis o f d i s e a s e s . A g g l u t i n a t i o n o f l a t e x p a r t i c l e s by t h e increase i n ionic s t r e n g t h has been studied extensively (.2/3^ · However, t h e b a s i c nature o f the a s s o c i a t i o n o f latex p a r t i c l e s ( c o l l o i d a l p a r t i c l e s i n g e n e r a l ) , and hence t h e r a t e c o n s t a n t o f t h e association a t t h e very initial stage, has n o t been studied rigorously. I t i s o f course d e s i r a b l e t o determine the a s s o c i a t i o n r a t e a t a much e a r l i e r stage t o examine p r e c i s e l y t h e k i n e t i c e q u a t i o n o f

0097-6156/89/0384-0284$06.00/0 • 1989 American Chemical Society

El-Nokaly; Polymer Association Structures ACS Symposium Series; American Chemical Society: Washington, DC, 1989.

17. KITANO&ISE

Kinetics ofAssociation between Polymer Latex Particles 28 1

c o a g u l a t i o n , f o r example, Smolukowski s e q u a t i o n , s i n c e t h i s e q u a t i o n i s d e r i v e d f o r " b i n a r y " c o l l i s i o n . H e r e i n , we r e p o r t t h e i n i t i a l r a t e o f a s s o c i a t i o n o f polymer l a t e x p a r t i c l e s by c o u n t i n g dimer p a r t i c l e s (4-6). Expérimentais Materials E l e c t r i c a l l y Charged L a t e x

Particles

T h r e e k i n d s o f a n i o n i c l a t e x p a r t i c l e s were p u r c h a s e d from t h e Japan Synthetic Rubber Co., Tokyo (Immutex G-5301) and t h e S e k i s u i Chemicals, Osaka (N-200 and N-700), r e s p e c t i v e l y . The o t h e r a n i o n i c latices SS-30 and SS-40 were p r e p a r e d by e m u l s i o n p o l y m e r i z a t i o n o f potassium p - s t y r e n e s u l f o n a t e and s t y r e n e using potassium peroxydisulfate as an i n i t i a t o r . A c a t i o n i c polymer latex MATA-2 was prepared by e m u l s i o n p o l y m e r i z a t i o n o f 3-methacryloxylaminopropyltrimethylammonium chloride and s t y r e n e u s i n g a c a t i o n i c initiator 2-azobis(2-methylpropamidinium) dichloride. Fluorescent latex particles such a s SMC-3 and SSH-10 were p r e p a r e d by m i x i n g fluorescent dyes such as coumarin-6 and H o s t a l u x KCB w i t h styrene before the emulsion polymerization. The a n i o n i c l a t i c e s were converted t o t h e H form u s i n g a mixed-bed ion-exchange resin, Amberlite MB-3. The c a t i o n i c l a t i c e s were p u r i f i e d by r e p e a t e d washings w i t h pure water u s i n g an Amicon u l t r a f i l t r a t i o n apparatus. T a b l e I shows t h e d i a m e t e r o f t h e s e l a t i c e s e s t i m a t e d from electron micrographs u s i n g a JEM-100U TEM (Nihon D e n s h i , Tokyo, J a p a n ) , and the charge number on t h e s u r f a c e o f t h e polymer l a t i c e s . The charge density o f t h e l a t e x p a r t i c l e s remains c o n s t a n t a t t h e n e u t r a l pH examined h e r e , because s u l f o n a t e and q u a t e r n a r y ammonium groups on the l a t e x s u r f a c e s a r e h i g h l y i o n i z a b l e . +

Latex P a r t i c l e s F o r Immobilization o f Antibody

and A n t i g e n

Acrolein-containing latex p a r t i c l e s were used f o r i m m o b i l i z a t i o n o f proteins. The l a t e x particles were p r e p a r e d by e m u l s i f i e r - f r e e polymerization o f a c r o l e i n and s t y r e n e ( T a b l e I ) . F l u o r e s c e n t latex particles were p r e p a r e d by m i x i n g f l u o r e s c e n t dyes such as H o s t a l u x KCB (Hoechst) o r coumarin-6 into styrene before t h e emulsion polymerization ( T a b l e I ) . To i n c r e a s e t h e immunological sensitivity of the protein-conjugated latex particles, a hexyl group was introduced between t h e l a t e x p a r t i c l e and t h e p r o t e i n (Proteins p a c e r - l a t e x ) . P r o t e i n s such a s human serum albumin (HSA), anti-human serum albumin ( a n t i - H S A - I g G ) , and a fragmented antibody (anti-HSAIgG-Fiab ^ were immobilized onto the spacer-containing latex p a r t i c l e s u s i n g a w a t e r - s o l u b l e c a r b o d i i m i d e . The numbers o f p r o t e i n immobilized onto the latex p a r t i c l e were 16,000(HSA-spacer-AL-2), 16,000(anti-HSA-IgG-spacer-AL-2), 2 2 , 0 0 0 ( a n t i - H S A - I g G - F ( a b ) - s p a c e r AL-3), and 19,000 (HSA-spacer-AL-4). The l a t e x particles modified were p u r i f i e d by r e p e a t e d washing w i t h d i s t i l l e d water u s i n g an Amicon u l t r a f i l t r a t i o n a p p a r a t u s w i t h a M i l l i p o r e membrane. 1

1

Methods Microscopic The

Observation

association

p r o c e s s was d i r e c t l y o b s e r v e d

using

a

Carl


Zeiss

POLYMER ASSOCIATION STRUCTURES

286

m i c r o s c o p e (Axiomat) o r a f l u o r e s c e n c e m i c r o s c o p e (DIAPHOT-EF, N i k o n , Tokyo) c o n n e c t e d t o a C a r l Z e i s s image p r o c e s s i n g system (IBAS)(7). The m i c r o s c o p i c o b s e r v a t i o n was s t a r t e d j u s t a f t e r t h e a d d i t i o n of the latex suspension t o another k i n d of l a t e x suspension in the observation cell using a small polyethylene mixing rod. The suspensions were mixed slowly in a c o n s t a n t manner t o a v o i d t h e enhancement o f t h e a s s o c i a t i o n by the v i g o r o u s m i x i n g . The p r o g r e s s of t h e p r o c e s s was r e c o r d e d on v i d e o t a p e . By r e p l a y i n g t h e tape the number o f dimeric p a r t i c l e s i n the v i s u a l field was counted at appropriate i n t e r v a l s u n t i l i t l e v e l l e d o f f . The p e r c e n t of dimers was estimated by assuming t h e u n i f o r m d i s t r i b u t i o n o f the dimeric and monomeric p a r t i c l e s t h r o u g h o u t t h e s u s p e n s i o n . The number of particles used f o r t h e c a l c u l a t i o n was 200-300 a t one t i m e , and the u n c e r t a i n t y was w i t h i n 10 %. Spectrophotometric

Measurements

The a s s o c i a t i o n between d i f f e r e n t k i n d s o f polymer latex particles was a l s o s t u d i e d s p e c t r o p h o t o m e t r i c a l l y by t h e absorbance change at 800 nm using a h i g h - s e n s i t i v i t y spectrophotometer (SM-401, Union Engineering, Hirakata, Japan). R e s u l t s and D i s c u s s i o n A s s o c i a t i o n P r o c e s s e s Between O p p o s i t e l y Charged L a t e x

Particles

The association in water was t o o r a p i d for visual observation. T h e r e f o r e , t h e m i c r o s c o p i c o b s e r v a t i o n was c a r r i e d o u t i n a 30(w/v)% aqueous s u c r o s e s o l u t i o n a t 25°C, i n which t h e a s s o c i a t i o n was slowed down because o f t h e enhanced v i s c o s i t y . The r e s u l t s a r e as ôwn in Figure 1, where a 1 M l a t e x suspension denotes 6.02x10 latex p a r t i c l e s i n 1 1 o f t h e s u s p e n s i o n . The r e c i p r o c a l o f t h e ^ r e l a x a t i o n time of the a s s o c i a t i o n of latex particles (9.1x10 s ) was obtained from the semilogarithmic p l o t s of the concentration of dimeric particles i n t h e s u s p e n s i o n c o n v e r t e d from t h e percent of dimers i n the v i s u a l f i e l d a g a i n s t time. Clear curves with a single relaxation time could also be observed s p e c t r o p h o t o m e t r i c a l l y by m i x i n g t h e a n i o n i c l a t e x w i t h an excess amount o f c a t i o n i c l a t e x . The reciprocal relaxation time measured s p e c t r o p h o t o m e t r i c a j . l y under t h e same e x p e r i m e n t a l c o n d i t i o n as i n Figure 1 (0.0094 s ) i s ^ i n good agreement w i t h the value o b t a i n e d by m i c r o s c o p y (0.0091 s ). T h i s shows t h a t t h e relaxation phenomena o b s e r v e d s p e c t r o p h o t o m e t r i c a l l y c o r r e s p o n d t o the binary association of particles of opposite charges provided that the s p e c t r o p h o t o m e t r y can be c a r r i e d out a t t h e v e r y i n i t i a l s t a g e . Long after the s t a r t of the a s s o c i a t i o n , f u r t h e r a s s o c i a t i o n of d i m e r i c p a r t i c l e s w i t h o t h e r p a r t i c l e s t o form t r i m e r s , tetramers and so on, was confirmed by the microscopic observation. The absorbance c u r v e changed i n a c o m p l i c a t e d manner. Thus, the kinetic data o b t a i n e d l o n g a f t e r t h e o n s e t o f t h e a s s o c i a t i o n s h o u l d not be c o n s i d e r e d as r e p r e s e n t i n g t h e b i n a r y a s s o c i a t i o n . We could o b t a i n the f i r s t - o r d e r r a t e constant k , (=1/τ) a t ODS . various concentrations of the c a t i o n i c l a t e x by the first-order analysis. We will subsequently d i s c u s s the a s s o c i a t i o n process between o p p o s i t e l y - c h a r g e d l a t e x p a r t i c l e s u s i n g spectrophotometric data obtained i n w a t e r . The s e c o n d - o r d e r r a t e c o n s t a n t k _ f o r the


17. KITANO&ISE

Kinetics ofAssociation between Polymer Latex Particles

T a b l e I . P r o p e r t i e s o f t h e Polymer L a t i c e s Latex

Diameter (A)

Charge Number (per p a r t i c l e )

MATA-2 3000 7.2x10^ G-5301 3700 2.7x10^ SS-40 3000 2.0x10^ SS-30 1250 2.3x10 N-300 3000 2.3x10^ N-700 7000 4.0x10^ SMC-3 6100 3.3x10^ SSH-10 6000 1.7x10 AL-2^ 3750 AL-3 ' 5000 AL-4 ' 4100 (a) Coumarin-6 i s c o n t a i n e d . (b) H o s t a l u x KCB i s c o n t a i n e d . (c) A c r o l e i n - c o n t a i n i n g l a t e x p a r t i c l e . a

b

C

a

C

Charge D e n s i t y (pC/cm ) +4.0 -10 -11 -7.6 -1.3 -4.2 +4.7 -2.3

-

F i g u r e 1. Time dependence o f p e r c e n t o f d i m e r i c l a t e x p a r t i c l e s i n 30 (w/v)% s u c r o s e - w a t e r a t 25°C. [MATA-2]=81 pM, [G-5301]=8.1 pM. Reproduced from R e f . 4. C o p y r i g h t 1987 American C h e m i c a l S o c i e t y


2


288

association of the c a t i o n i c l a t e x w i t h the a n i o n i c l a t e x could be e s t i m a t e d from t h e s l o p e o f t h e p l o t s o f l/τ v s . c o n c e n t r a t i o n o f the c a t i o n i c l a t e x . We c o u l d not e s t i m a t e from the Y - i n t e r c e p t o f the p l o t s , and we can o n l y say t h a t k^ i s v e r y s m a l l . T a b l e I I shows the k and k v a l u e s o b t a i n e d . The table shows the t h e o r e t i c a l rate constants f o r d i f f u s i o n - c o n t r o l l e d association r e a c t i o n s between n e u t r a l p a r t i c l e s o f the same s i z e s as t h o s e o f the l a t e x p a r t i c l e s c a l c u l a t e d by e q u a t i o n s (1 ) - ( 4 ) ( 8 - 1 0 ) . fe

f

=

6TTTIR

(1)

D = kT/f

(2)

k. = 4UN (D +a )R ,/ΙΟΟΟ f A a b ab

(3)

k. = 3(D +D, )/R . b a b ab

2

(4)

where f , η, R, D^, k, Τ, Ν and are the f r i c t i o n c o e f f i c i e n t (in g/s), the v i s c o s i t y o f t h e s o l v e n t (g/cm.s), t h e radius of the particle s p e c i f i e d by the s u b s c r i p t (cm), the d i f f u s i o n coefficient of the p a r t i c l e s p e c i f i e d (cm / s ) , the Boltzmann constant, the absolute temperature, the Avogadro number, and the distance of c l o s e s t approach between p a r t i c l e s "a" and b " (=R +R i n the c a s e o f rigid particles. R and R a r e the r a d i i o f p a r t i c l e s "a" and "b" (cm)), r e s p e c t i v e l y . Note t h a t the t h e o r e t i c a l and e x p e r i m e n t a l k ' s a r e u n e x p e c t e d l y i n t h e same o r d e r o f magnitude. As mentioned above the i n c r e a s e i n the v i s c o s i t y o f the r e a c t i o n suspension r e d u c e d the a s s o c i a t i o n r a t e c o n s t a n t ( F i g u r e 2), which suggests that the association process observed here is mostly d i f fusion-controlled· If we e v a l u a t e the i n f l u e n c e o f the electrostatic interaction between particles by e q u a t i o n s ( 5 ) - ( 7 ) (11,12 ) the theoretical k valine, _lpecomes much larger than the experimental value (3.3x10 M s was o b t a i n e d f o r the t h e o r e t i c a l v a l u e o f k^ i n the c a s e o f a s s o c i a t i o n o f MATA-2 w i t h G-5301). M

fa

f

k

f

f e

« l

f

k

( 5 )

el fo

= Z/[exp(Z)-l]

(6)

2

Ζ = Ζ Zê /eR kT a b ab

(7)

where f _, k_ , Ζ, Ζ , Z, and ε denote the e l e c t r o s t a t i c f a c t o r , the el fo a b , reaction rate constant without electrostatic effects, Z=U/kT (U;potential e n e r g y ) , t o t a l a n a l y t i c a l c h a r g e s o f p a r t i c l e s "a" and "b" and the d i e l e c t r i c c o n s t a n t o f the medium, r e s p e c t i v e l y . Recent transference experiments showed t h a t the so-called counterion association by l a t e x p a r t i c l e s was surprisingly much l a r g e r t h a n t h a t by l i n e a r m a c r o i o n s ; i n o t h e r words, the net charge number i s much s m a l l e r t h a n the a n a l y t i c a l number(13) 0 n l y eight p e r c e n t s o f the t o t a l a n a l y t i c a l number o f c o u n t e r i o n s (H ) were f r e e for l a t i c e s h a v i n g about the same a n a l y t i c a l s u r f a c e charge density as one o f our l a t i c e s , G-5301. T a k i n g t h i s e x p e r i m e n t a l fact into c o n s i d e r a t i o n , and by assuming t h a t the f r a c t i o n o f f r e e counterions is 0.08, Z^ and Z o f the G-5301 - MATA-2 system were assumed t o be +

fa


KITANO & ISE

Kinetics ofAssociation between Polymer Latex Particles 2

T a b l e I I . Rate C o n s t a n t s a t Temp. (°C)

10

_ MATA-2 +_ί3S-40 _ xk (M s ) k. (s D

(5.6) 2

0 (82)

b

4

· h ·° h (7.4) (6.5)

25

o

3

b

h (7.5)

0 (79)

,

b

9

b

-

0 . (60) 0 (68)

1

h

b

h

(6.5)

0 (108)°

-

x

o

f

1 , 4 b

a

_ MATA-2 +_C3-5301 ) k. (s ) xk (M s 1.2 (5.7)

b

( 9 5 )h

b

b

30

) 10

f

15 20

V a r i o u s Temperatures i n Water

2

5

' h (8.5) b

b b

b b

0 . (89) b

a. s p e c t r o p h o t o m e t r i c method b . t h e o r e t i c a l v a l u e s f o r a s s o c i a t i o n o f neu.tral s p e c i e s

Glycerol (ν/ν)·/β 30 20 10 1

1

1

0 Γ

2 -

I

I ι

Ν

1

1 0

0.5

1.0

F i g u r e 2. E f f e c t o f v i s c o s i t y on Ι/τ o f t h e a s s o c i a t i o n process o f SMC-3 w i t h SSH-10 a t 25°C. [SMC-3]=0.18 pM, [SSH-10]=5.8 pM.



290

about 22,000 and 5,700, r e s p e c t i v e l y . T h e r e f o r e , the t h e o r e t i c a l value of k was estimated to be 2x10 M s , which i s s t i l l much larger than the experimental r e s u l t . This i s probably because the point charge model assumed i n the t h e o r e t i c a l consideration i s far from r e a l i t y for latex p a r t i c l e s . The number of e f f e c t i v e charges responsible for the attractive interaction between the latex p a r t i c l e s may even be much less than the number of net charges the latex p a r t i c l e s have. One of the simplest interpretations i s that, i n the association processes, only the charges i n the r e l a t i v e l y narrow surfaces near the c o l l i s i o n center play a decisive r o l e ; the charges on the surfaces diametrically opposite from the c o l l i s i o n center may not be i n f l u e n t i a l because of the r e l a t i v e l y large dimension of the latices. Table III shows the e f f e c t s of charge density and the diameter of the anionic p a r t i c l e s on the forward rate constants (k ) of the association with MATA-2· The charge density on the latex surface c l e a r l y a f f e c t s the k^ values, which supports the importance of the e l e c t r o s t a t i c i n t e r a c t i o n on the association of oppositely charged latex p a r t i c l e s . The claim, that the observed rate constant and the t h e o r e t i c a l rate constant calculated for neutral p a r t i c l e s (by equations ( l ) - ( 4 ) ) agreed, would not be physically sound. Figure 3 shows the influence of sodium chloride on the 1/τ(=k [Cationic latexj+k^). Judging from the figure, we can claim that the i o n i c strength does not have a substantial e f f e c t on the association of latex p a r t i c l e s , because the latex has a large diameter and the number of i t s e f f e c t i v e charges i s much smaller than that of net charges. Harding reported a similar retardation e f f e c t of the increase i n i o n i c strength on the agglutination of AL Ο with SiO^ when the two c o l l o i d a l p a r t i c l e s are oppositely^chargedf14). We could estimate the a c t i v a t i o n parameters, AG , AS and ΔΗ , which are l i s t e d i n Table IV from the temperature dependence of k^. Theoretical values calculated for the d i f f u s i o n - c o n t r o l l e d redaction are also shown i n the t a b l e . In the case of AG , the experimental r e s u l t s are ί η good agreement with the t h e o r e t i c a l values. As for AH and AS , however, the experimental values are larger than the t h e o r e t i c a l values. The AH value i s larger because there i s a rate-determining factor which needs a large a c t i v a t i o n energy i n the association reaction. Dehydration of latex p a r t i c l e s i n the association process as suggested by previous authors (15,16) and conformational changes of charged side chains on the latex surface a r | possible reasons for the larger experimental values of AH and AS . A s i m i l a r e f f e c t was observed for the salt-induced coagulation of highly charged latex p a r t i c l e s using the microscopic measurements (17). Figure 4 shows the time dependences of monomer, dimer and trimer p a r t i c l e s of N-700 at the very i n i t i a l stage of the salt-induced coagulation i n a 1 M NaCl solution at 25 · The binary association constant of the latex p a r t i c l e s was evaluated to be 2.8x10 cm .p~ .s (1.7x10 M s ). From the plots of salt concentration vs. i n i t i a l t u r b i d i t y change, the experimental value obtained was concluded to correspond to the rapid coagulation rate constant of the latex p a r t i c l e s . The experimental value i s , however, much smaller than the t h e o r e t i c a l value evaluated for a diffusioçcogtrojled^ binary âssociation by the equation (3) (12.3x10 cm .p .s , 7.4x10 M s ). Such a slow binary association can also f

f

f

φ

φ


KITANO&ISE

KineticsofAssociation between Polymer Latex Particles

T a b l e I I I . Rate C o n s t a n t s o f A s s o c i a t i o n P r o c e s s o f MATA-2 o a w i t h V a r i o u s A n i o n i c L a t i c e s a t 25 C

d)

Charge D e n s i t y (pC/cm )

(10 xS s )

3700 3000 1250 3000

10 11 7.6 1.3

1.9 3.0 1.0 0.62

Diameter

Latex

G-5301 SS-40 SS-30 N-300 a. i n H_0

9

1

X

txro-

0

10~

2

10'

1

(NQCU

1

10

(mM)

F i g u r e 3. I n f l u e n c e o f [NaCl] on l/τ a t 25 ° C . [MATA3=8.0 pM, [G-5301]=0.80 pM. I n H O . Reproduced from R e f . 5. C o p y r i g h t 1987 American Chemical S o c i e t y


2

292


T a b l e IV· A c t i v a t i o n Parameters o f A s s o c i a t i o n P r o c e s s e s Between L a t e x P a r t i c l e s Φ A

G

(kcal.mol 4.8

MATA-2 w i t h G-5301

Antibody-Latex with Antigen-Latex Theoretical values f o r diffusion-controlled association

0

-1

)

Φ ΔΗ _ (kcal.mol ) 7.4 λ

φ AS (eu) 9

7.7

9.3

5

3.9

4.4

1.5

2.5 5.0 Time (min)

7.5

F i g u r e 4. Time dependence o f monomer(o), dimer(#) and t r i m e r ( • ) o f N-700 l a t e x p a r t i c l e s a t 25°C. [ N a C l ] = l M.


17.

Kinetics ofAssociation between Polymer Latex Particles

KITANO&ISE

be attributed t o the d e h y d r a t i o n and t h e c o n f o r m a t i o n a l change o f charged s i d e c h a i n s on t h e l a t e x s u r f a c e i n t h e a s s o c i a t i o n p r o c e s s . Association Particles

P r o c e s s e s Between A n t i g e n - and A n t i b o d y - C a r r y i n g

Latex

The i n t e r p a r t i c l e r e a c t i o n between t h e A n t i - H S A - I g G - s p a c e r - l a t e x and t h e H S A - s p a c e r - l a t e x was a l s o examined by d i r e c t v i s u a l observation of latex particles u s i n g an u l t r a m i c r o s c o p e ( 2 ) · The p e r c e n t o f monomeric l a t e x p a r t i c l e s i n t h e v i s u a l f i e l d was d e t e r m i n e d w i t h t h e lapse o f time. At time=0, o n l y monomeric p a r t i c l e s of the anti-HSAIgG-spacer-AL-2 were found t o be p r e s e n t i n t h e v i s u a l field and by t h e a d d i t i o n o f a s m a l l amount o f HSA-spacer-AL-2 suspension into the observation c e l l , the number o f monomeric particles d e c r e a s e d w i t h time and almost l e v e l l e d o f f ( F i g u r e 5 ) . A l t h o u g h n o t shown i n t h e f i g u r e , t h e number o f d i m e r i c p a r t i c l e s i n t h e v i s u a l field i n c r e a s e d w i t h time c o r r e s p o n d i n g l y t o t h e decrease i n the number o f monomeric p a r t i c l e s . The o b s e r v e d r e a c t i o n r a t e c o n s t a n t (k ) for the association of l a t e x p a r t i c l e s c o u l d be e s t i m a t e d by p l o t t i n g l o g [dimer] versus time by t h e m i c r o s c o p i c measurements. The s e c o n d - o r d e r r a t e c o n s t a n t , k^, f o r t h e a s s o c i a t i o n o f l a t e x p a r t i c l e s m o d i f i e d w i t h a n t i g e n s and antibodies by e q u a t i o n ( 8 ) , c o u l d be o b t a i n e d from t h e s l o p e o f t h e plots of ^ versus [Anti-HSA-IgG-spacer-AL-2]. o

k

obs

=

k

b

f

s

C

A

n

t

i

b

o

d

y ~

l

a

t

e

x

l

+

k

( 8 b

7

1

>

1

The k v a l u e o b t a i n e d i s 1 . 3 x l 0 M s a t pH 9.2 and 25°C, and i t i s much s m a l l e r t h a n t h e v a l u e o b t a i n e d f o r t h e d i m e r i c association o f oppositely charged latex particles (1.9x10 M s f o r the a s s o c i a t i o n o f G-5301 w i t h MATA-2). The r a t e c o n s t a n t o f t h e f o r w a r d r e a c t i o n o b t a i n e d here i s a l i t t l e l a r g e r than t h e v a l u e o b s e r v e d f o r the association o f t h e anti-HSA-IgG and t h e HSA^ d e j e c j e d by t h e conductance stopped-flow-technique (18)(k =l.9x10 M s a t pH 8.0 and 25 C ) , because t h e l o c a l c o n c e n t r a t i o n o f t h e r e a c t a n t s i s much higher f o r t h e l a t e x - b o u n d case than f o r t h e f r e e systems. The e x p e r i m e n t a l v a l u e f o r t h e f r e e HSA - anti-HSA-IgG system i s i n good agreement w i t h t h e v a l u e s r e p o r t e d f o r o t h e r immunological systems (1.0x10 M s (25°C) and 1.0x10 M s (20°C) f o r o v a l b u m i n i n a n t i - o v a l b u m i n ( 1 9 ) and cytochrome C - a n t i - c y t o c h r o m e C systems(20), respectively). f

2

On t h e anti-HSA-IgG-spacer-AL-2 l a t e x , 16,000 a n t i b o d i e s were a t t a c h e d . The f o r w a r d r a t e c o n s t a n t reduced f o r one a n t i b o d y m o l e c u l e (k^ k^/numbçr o f a n t i b o d i e s on t h e l a t e x s u r f a c e ) was e s t i m a t e d t o be 810 M s , which i s much s m a l l e r t h a n the o b s e r v e d r e a c t i o n rate c o n s t a n t f o r t h e a n t i g e n - a n t i b o d y r e a c t i o n i n t h e homogeneous system. W o l f f e t a l . r e p o r t e d t h a t 1.3 m o l e c u l e s o f IgG p e r v e s i c l e i s enough f o r i n t e r a c t i o n o f the v e s i c l e with a n t i g e n - c a r r y i n g c e l l s (21). We a l s o i m m o b i l i z e d a fragmented a n t i b o d y ( F ( a b ' ) # an a n t i b o d y w i t h o u t a F c h a i n ) , onto t h e f l u o r e s c e n t l a t e x p a r t i c l e (22). Using a f l u o r e s c e n c e m i s c r o s c o p e , we c o u l d c o n f i r m t h a t t h e a s s o c i a t i o n took p l a c e o n l y between a n t i g e n - and fragmented antibody-carrying latex particles, and c o u l d r u l e o u t any p o s s i b i l i t y of self a s s o c i a t i o n . The a s s o c i a t i o n r a t e c o n s t a n t o f t h e ^ f r a j m e n t e d antibody-latex - a n t i g e n l a t e x system was 6.0x10 M s , which i s ,=

9


294


β*

ë 95 90 ο c ο 2

Ο οο ο ο ο ο ο 85 500 Time

1000

1500

(s)

F i g u r e 5. Time dependence o f t h e p e r c e n t o f monomeric l a t e x p a r t i c l e s a t 25°C. pH 8.7. [anti-HSA-IgG-spacer-AL-2]=360 pM. [HSA-spacer-AL-2]=40 pM. Reproduced from R e f . 6. C o p y r i g h t 1987 American C h e m i c a l S o c i e t y


17. KITANO & ISE

Kinetics ofAssociation between Polymer Latex Particles 29

much larger than t h a t f o r an a n t i b o d y - l a t e x system. However t h e reduced k v a l u e was s t i l l much s m a l l e r t h a n that f o r the free a n t i g e n - f r e e a n t i b o d y system. These r e s u l t s s u g g e s t t h a t t h e d i s a d v a n t a g e o u s o r i e n t a t i o n o f the a n t i g e n and t h e a n t i b o d y bound o n t o t h e l a t e x s u r f a c e , and t h e r e s t r i c t i o n o f c o n f o r m a t i o n a l changes o f t h e i m m o b i l i z e d p r o t e i n s (23,24) f o r t h e i r a s s o c i a t i o n largely diminish the binding a b i l i t y of the antibody (25). The t e n d e n c i e s o f t h e a c t i v a t i o n parameters o f t h e i n t e r - l a t e x reaction examined h e r e ( T a b l e IV) a r e s l i g h t l y d i f f e r e n t from those o f t h e a s s o c i a t i o n o f o p p o s i t e l y charged polymer l a t e x p a r t i c l e s , and g r e a t l y d i f f e r e n t from t h o s e c a l c u l a t e d f o r t h e d i f f u s i o n - c o n t r o l l e d association o f l a t e x p a r t i c l e s , which suggests t h a t t h e r e must be rate-determining f a c t o r s such a s (1) t h e c o n f o r m a t i o n a l changes o f the c h a r g e d s i d e c h a i n s n e a r t h e i m m o b i l i z e d p r o t e i n s on t h e l a t e x surface, and (2) t h e conformational changes o f t h e p r o t e i n s t h e m s e l v e s accompanying t h e a s s o c i a t i o n o f t h e l a t e x p a r t i c l e s . f

Acknowledgments This work was s u p p o r t e d by t h e M i n i s t r y o f E d u c a t i o n , Science Culture ( G r a n t - i n - A i d f o r S p e c i a l l y Promoted R e s e a r c h , 59065004 63060003).

and and

Literature Cited 1. Rembaum, Α.; Yen, S.P.S.; Cheong, E.; Wallace, S.; Molday, R.S.; Gordon, I.L.; Dreyer, W.J. Macromolecules 1976,9,328-336. 2. Ottewill, R.H.; Shaw, J.N. Disc.Faraday Soc. 1966,42,154-163. 3. Watillon, Α.; Joseph-Petit, A.M. Disc.Faraday Soc.1966,42, 143-153. 4. Kitano, H.; Iwai, S.; Ise, N. J.Am.Chem.Soc. 1987,109,1867-1868. 5. Kitano, H.; Iwai, S.; Ise, N.; Okubo, T. J.Am.Chem.Soc. 1987,109,6641-6644. 6. Kitano, H.; Iwai, S.; Okubo, T.; Ise, N. J.Am.Chem.Soc. 1987,109,7608-7612. 7. Ito, K.; Nakamura, H.; Ise, N. J.Chem.Phys. 1986,85,6136-6142, ibid. 1986,85, 6143-6146. 8. Bird, R.B.; Stewart, W.B.; Lightfoot, E.N. Transport Phenomena; Wiley: New York, 1960;p780. 9. Einstein, A. Ann.d.Phys. 1905,17,549. 10. Eigen, M. Quantum Statistical Mechanics in the Natural Science; Plenum: New York, 1974. 11. Debye, P. Trans.Electrochem.Soc. 1942,82, 265-272. 12. Alberty, R.A.; Hammes, G.G. J.Phys.Chem. 1958,62, 154-159. 13. Ito, K.; Ise, N.; Okubo, T. J.Chem.Phys. 1985, 82,5732-5736. 14. Harding, H. J.Colloid Interface Sci. 1972,40,164-173. 15. Johnston, G.A.; Lecchini, A.M.Α.; Smith, E.G.; Clifford, J.; Pethica, B.A. Disc.Faraday Soc. 1966,42, 120-133. 16. Lichtenbelt, J.W.T.; Pathmamanoharan, C.; Wieserma, P.H. J.Colloid Interface Sci. 1974,49,281-285. 17. Ono, T.; Ito, K.; Kitano, H.; Ise, N. unpublished results. 18. Okubo, T.; Ishiwatari, T.; Kitano, H.; Ise, N. Proc.Roy.Soc.Lod. 1979,A366,81-90.


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19. Levison, S.A.; Jancsi, A.N.; Dandliker, W.B. Biochem.Biophys. Res.Commun.1968,33,942. 20. Noble, R.W.; Reichlin, M.; Gibson, Q.H. J.Biol.Chem. 1969,244, 2403-2407. 21. Wolff, B.; Gregoriadis, G. Biochim.Biophys.Acta 1984,802,259-263. 22. Kitano, H.; Yan, C.-H.; Maeda, Y.; Ise, N. Biopolymers in press 23. Goldstein, L. Methods Enzymol. 1976,44,435. 24. Kitano, H.; Nakamura, K.; Ise, N. J.Appl.Biochem. 1982,4,34-40. 25. Nakamura, H.; Sugiura, T. In Methods in Immunological Biochemistry; Osawa T.; Nagai, K. Eds.; Tokyo Kagaku Dojin: Tokyo, 1986; pp 126-129. RECEIVED August 10, 1988


Kinetic Study of Association Processes between Polymer Latex Particles

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