J. Mol. Biol. (1976) 108, 139-150

Head to Tail Polymerization o f Actin ALBRECHT WEGNER

Department of Biophysical Chemistry, Biozentrum Klingelbergstrasse 70, CH-4056 Basel, Switzerland (Received 14 July 1976) The exchange of subunits at the ends of actin filaments was followed after addition of radioactively labelled actin monomers to solutions of polymeric actin. The incoqooration and release of subunits can be explained by a polymerization mechanism in which the filaments grow at one end and shorten simultaneously at the other (head to tail polymerization). It is found that the net result of four association and four dissociation steps is a lengthening of the filament by one protorner at one end and a corresponding shortening at the other. The head to tail polymerization is made possible by the irreversible ATP dephosphorylation which is connected with the polymerization cycles of actin. This eliminates the restriction which is valid for a completely reversible association mechanism where the direction of growth is either outwards from or inwards to the centre at both ends of the aggregate.

1. Introduction The association of monomeric actin to form filaments is one of the assembly processes which are thought to play an important role in the organization of contractile structures. Straub & Feuer (1950) were the first to point out that this process is connected with dephosphorylation of ATP. They showed that monomeric actin binds A T P firmly and that the A D P resulting from this hydrolysis is incorporated into the filament. Furthermore, they demonstrated that the dissociation of a subunit from the filament is not accompanied by resynthesis of ATP, so that depolymerization of actin is not the reverse reaction "of actin association. Hayashi & Rosenbluth (1960) reported that monomeric actin ~ith bound A D P can also aggregate to form filaments but at a slower rate, and that the polymer is stable even without bound ADP. I t has been shown that polymerization still occurs when the nueleotide is replaced by an A T P analogue (adenylyl imide diphosphate) which cannot be dephosphorylated by actin (Cooke & Murdoeh, 1973; Mannherz et a/., 1975). Since the dephosphorylation of the nucleotide is not required to bring about the aggregation of actin, it was speculated that the nucleotide might play a role in the interaction of actin with one of the proteins to which it is bound (Cooke, 1975). I n this paper the aggregation of actin connected with nueleotide hydrolysis is compared to a polymerization mechanism in which association and dissociation are reverse reactions. I t is demonstrated that actin polymerization is less restricted in the sense that the irreversible dephosphorylation of A T P makes it possible t h a t actin 139

140

A. W E G N E R

filaments can l e n g t h e n a t one end a n d s h o r t e n s i m u l t a n e o u s l y a t t h e other. I n co n t r ast , t h e d i rect i o n of g r o w t h is e i t h e r o u t w a r d s f r o m or i n w ar d s to t h e centre a t b o t h ends o f a linear aggregate, if association is t h e reverse r e a c t i o n of dissociation. K i n e t i c e q u a t i o n s are d e r i v e d w h i c h allow co r r el at i o n b e t w e e n t h e t i m e - c o u r s e o f t h e m o n o m e r c o n c e n t r a t i o n a n d t h e i n c o r p o r a t i o n o f r a d i o a c t i v e l y labelled subu n i t s i n t o t h e filament. T h e m o n o m e r c o n c e n t r a t i o n was d e t e r m i n e d e x p e r i m e n t a l l y b y l i g h t - s c a t t e r i n g m e a s u r e m e n t s . T h e i n c o r p o r a t i o n of s u b u n i t s i n t o t h e f i l a m e n t was followed after a d d i t i o n of a t r a c e of a c t i n m o n o m e r s modified w i t h N-[~4C]e t h y l m a l e i m i d e by d e t e r m i n a t i o n of t h e t i m e - c o u r s e o f t h e d i s a p p e a r a n c e o f m o n o meric-labelled a c t in molecules.

2. Materials and Methods (a) Preparation of actin Actin was prepared according to the m e t h o d of Rees & Young (1967) with the following alterations. The protein was ehromatographed on BioGel P150 and protected against oxidation by modification with N-ethylmaleimide (Lusty & Fasold, 1969). A small a m o u n t of aetin was modified with N-[14C]ethylmaleimide (purchased from CEA-France). Actin concentrations were measured using the Biuret m e t h o d (Wegner & Engel, 1975) or by u.v. absorption at 290 nm (r = 24-9x 10a M-1 cm-1). (b) Experimental procedure The polymerization of monomeric actin was initiated by a sudden increase in salt concentration. The time-course of polymerization was measured by light-scattering. At a time (to) at which the monomer concentration had reached a constant final value a trace of radioactively labelled monomeric actin was added. The incorporation of labelled protomers was followed by separating monomerie and polymeric actin by means of centrifugation and determining the distribution of the labelled material. (c) Light-scattering The solutions of monomeric actin contained 5 x 10 -4 M-ATP, 2 x 10 -s M-MgC12, and 200 mg NAN3/1 to hinder bacterial growth, and were buffered with 5 x 10 -3 M-triethanolamine.HC1 (pH 7-5). All solutions were centrifuged at 100,000 g for 2 h to remove dust and polymers. I n order to initiate aggregation, 2 parts of actin solution and 1 part of buffer were mixed, the latter solution containing sufficient MgC12 to give a final Mg 2+ concentration of 5 x 10 -4 M. The 90 ~ scattering intensity was measured with a fiuorimeter (Farrand MK1) at a wavelength 2 of 546 nm. The instrument was calibrated by measuring the scattering intensity of solutions of aetin polymers of known weight concentration. F o r a solution of polydisperse long, thin rods, such as actin filaments, it has been shown (Casassa, 1955; Wegner & Engel, 1975) t h a t the reduced scattering intensity R is proportional to the concentration of subunits incorporated into filaments Cw R = eonst. Cw.

(1)

This equation can be applied if the length of the actin rods is greater t h a n h* and the diameter is small compared with ~*, where ~* is h/(4n.n-sin(0/2)), n is the refractive index and 0 is the observation angle. (d) Determination of radioactively labelled monomeric actin The monomeric aetin was separated from the polymers by eentrifugation at 200,000 g for 40 rain in a preparative centrifuge. The 2 components are separated q u a n t i t a t i v e l y by this procedure, since the sedimentation coefficient of monomeric aetin is 3 S, whereas t h a t of polymeric actin is about 50 S. The monomer concentration in the supernatant was

HEAD TO T A I L P O L Y M E R I Z A T I O N OF ACTIN

141

measured photometrically. The number of radioactively labelled monomers was determined in a scintillation counter (Packard model 3320/3330) using Insta-Gel (Packard) as scintillation liquid. 3. T h e o r y (a) Mechanisms of linear aggregation (i) Unidirectional and bidirectional polymerization I n polar linear aggregates both ends can serve as centres of elongation (Asakura, 1968) (see Fig. 1). The equilibrium constant (K) for the association of a monomer with a polymer is the same for both ends, since addition of a monomer at either end leads to the same polymer. The rate constants for the association (k~ < k2) or dissociation k~ < k~) need not be equal, since the transition states of the binding reaction k

Fro. 1. R e a c t i o n s c h e m e of bidirectional g r o w t h . T h e c h e v r o n s y m b o l s t a n d s for a p r o t o m e r .

m a y be different for both ends. The only restriction for the rate constants is that their ratios be equal kl k2 K . . t. . (2) kl k~" The rates of growth at the ends of a particular filament, defined as the time derivatives of the number of subunits (n~, n2 for end 1 or 2, respectively) added to or released from the ends, are given by the following equations: dn I

dt dn 2 -=

kl "cl -- k~ ~ kl (cl -- K -1)

(3a)

k 2 " c l - - k~. =

(3b)

k 2 (c~ - - K - 1 ) ,

dt where cl is the monomer concentration. I t follows from equations (3a) and (3b) that the direction of growth depends on whether or not the monomer concentration exceeds K - ! . The direction of growth is either outwards from or inwards to the centre at both ends of an aggregate. This restriction is a consequence of the polymerization mechanism in which the dissociation

142

A. W E G N E R

is the reverse reaction of association. In a limiting case (k2 to q- -l i t ~

(c~/~1

--

1) dt.

(17b)

8 ~t~

The rate of consumption and production of monomers at any time t" is given b y the product of the rate of grouch of a single filament d n / d t and the concentration of all polymers Cp

de1 d t t=t"

= - - [(kn -4- k12) " cl (t") - - (k~x -4- k~2)] " %.

(18)

Combining equations (17), (18), (10) and (14) yields a correlation between the kinetics of the monomer concentration at a time t", and the rate of exchange of labelled monomers at a time t'. d c *l d t t=t'

= s. p(t')"

1 cx(t")[~x - -

1

d t lt=t

for to < t' < to + -

l fO 8

dc* d t t=t'

= s . [p(t') - - p ( t ' - - -

( c l / ~ - - 1)dt

1

1 I t~

S Jr., ( c ~ / ~ - - 1)dt)] 9 c ~ ( t " ) / ~

fort'>t0

(19a)

t.~

q- 1 I t~

de1 -- 1 x

d t t=r'

( c ~ / ~ l - - 1 ) dt 8its

(19b)

where dp(t) 1 dc* at = ~ d---t-"

(20)

These equations hold for a seeds polymerization, where at time t N a fixed n u m b e r of nuclei are added to a solution of monomeric actin to form long polymers and where no further polymers start to form. However, in an actin solution nucleation occurs continuously. The correlation between the kinetics of the monomer concentration and the exchange of protomers can be extended to the case of continuous nucleation.

HEAD TO TAIL P O L Y M E R I Z A T I O N OF ACTIN

147

The concentration of polymers which start to form in a small interval of time

At is, according to equation (18),

d% t= d(i d-7 - - d-~

kll

1

~ - k12 ) 9 c I - - (k~. 1 -~- k9.2) " dt

]" At.

(21)

Summing the contributions of all filaments which start to form in the time between the beginning of the polymerization (t ---- O) and the addition of labelled monomers (t : to), we obtain the following relation for the exchange of labelled protomers. dc__~ =

dt It=t,

Jt~ (.

sJt

ft'~IP d(i dcl/dt )] -f- (k~ 9 ~1 -- k'21) 9 (t') . ~ k~l -4- k~2).c~ -- (k'2~ -+- k'22) dt, to

(22)

where tk is given by 1/'t0

t' -- to -= sJt, (c~/~ -- 1)dr.

(23)

The first term in equation (22) represents the contribution of the small polymers which incorporate and release labelled protomers (see eqn (17)) and the second term includes the long polymers. The time derivative of the monomer concentration at the beginning of the polymerization (t = 0) is zero, since no polymer is present at that time. Using this relation, and combining equations (10), (14) and (22), we obtain finally a correlation between the rate of exchange of labelled protomers and the kinetics of the monomer concentration in the case of continuous nucleation:

dc* =s.ft~176 dt t=t" jt~ [

l d_~)}dt ~tt cl/~ 1 "-- 1

8,] t

1

. d~

,

(24)

+ s'p(t') cl(t'~)/5l -- 1 dt t=t; where p(t) is given by equation (20) and tN by equation (23). B y means of this correlation the parameter s can be evaluated from a measurement of the kinetics of the monomer concentration and of the exchange of labelled protomers. 4. R e s u l t s

(a) Monomer concentration The monomer concentration was evaluated as the difference between the total concentration Ctot and the weight concentration of polymers cw, which was measured by light scattering. Figure 4 shows a plot of the time dependence of the monomer concentration. The total concentration was 21.5• 10 -6 M. The critical monomer concentration 51 was determined at the final stage of polymerization by separating the monomers from the polymers by centrifugation and measuring the optical density at 290 nm. ~1 was found to be 6.3 • 10- 6 M.

148

A. WEGNER 25

20

15 :k

I0

T

5-

i

0

i

I

I

I

I

6 x I0 3

3 x I03

,i

9 x I0 3

t(s) F i e . 4. T i m e - c o u r s e of t h e m o n o m e r c o n c e n t r a t i o n cl. T h e final v a l u e is t h e c r i t i c a l m o n o m e r c o n c e n t r a t i o n ~1.

(b) Rate of exchange of monomers and polymer subunits Labelled actin monomers were added after a polymerization time of 120 minutes. The time-course of the fraction of labelled actin monomers p(t) -= c*/El is shown in Figure 5. As the sedimentation of the polymers took about 20 minutes, the values of p(t) are represented as bars whose length corresponds to t h a t time interval. The fraction of labelled monomers is normalized b y the value at to. To fit these data the time-course of the exchange, which follows from the kinetics of the monomer concentration, was calculated for different values of s according to equations (20), (23) and (24). The integrals were evaluated by inserting cl and dcl/dt at intervals of 240 seconds. A good fit was achieved for s = (kll 9 cl k21)/(k'21 + k'22) = 0"25. -

-

5. Discussion The time-course of the exchange of subunits can be explained by the mechanism of the head to tail polymerization. The value found for s (s = 0.25) indicates t h a t four association and four dissociation steps on the average lead to a lengthening of the filament by one subunit at the growing end and to a shortening b y one subunit at the degrading end. I t cannot be determined from the experimental data to what extent dissociation reactions occur at the growing end and association reactions at the degrading end. For the case of unidirectional or bidirectional growth a considerably slower exchange is to be expected, since actin filaments contain several hundreds of subunits (Kawamura & Maruyama, 1970; Wegner & Engel, 1975; Arisaka et al., 1975). An exchange of the major part of subunits would take about 100 times longer (see eqn (13)). A basic assumption of the proposed model is t h a t filaments are built up solely b y sequential binding and release of protomers. I t cannot be excluded t h a t other processes, such as breaks within polymers or association of polymers, m a y occur and

HEAD

TO TAIL

POLYMERIZATION

OF ACTIN

149

I

0.8

0-4

0"2

~/C,o, i

0

I

4

x I0 3

i

I 8 x I0 3

i

I

~

12 x I0 3

i 16 x tO 3

t-to(S} FIG. 5. Time-course of the exhange of subunits. Dots. Measured time.course of the fraction of labelled monomers normalized by the value at to (p(t)lp(to)). Continuous l i n e . Time-course of e x c h a n g e calculated f r o m the kinetics of the m o n o m e r conc e n t r a t i o n w i t h the a s s u m p t i o n t h a t s = ( k z l 9 51 - - k'.,.1)/(k',.~ + k,'.,o.) = 0.25. T h e equilibritma value of ( p ( t ) l ~ o / p ( t o ) = ~l/Cto~ is d r a w n on the r i g h t side.

have an influence on the kinetics of the monomer concentration and the exchange of subunits. Several studies have been performed on the direction of actin polymerization (Hayashi & Ip, 1974; Woodrum et al., 1975). As a marker for the polarity of actin filaments, heavy meromyosin has been bound to the filaments to form "arrow heads" ("decoration"). Short pieces of arrow heads have been used as nuclei for the formation of long filaments. On addition of monomeric actin to solutions of arrow heads, growth has been observed at the barbed ends of the arrow heads. As far as it m a y be assumed that binding of heavy maromyosin has no effect on the association of subunits, it m a y be concluded that the growing end (end 1) is the barbed end and that the degrading end (end 2) is the pointed end. Woodrum et al. (1975) have re~orted that they have observed short extensions of aetin filaments also at the pointed ends of arrow heads, apart from long extensions at the barbed ends, if the concentration of the added monomeric actin is high. At low concentrations of monomeric actin no extensions at the pointed end have been found, but long extensions at the other end have. This result cannot be explained by bidirectional growth, since for bidirectional growth it is to be expected that the ratio of the extensions at both ends of the arrow heads (kl/k2) does not depend on the monomer concentration. Within the concepts of the model of head to tail polymerization these observations m a y be interpreted in the following way. At high monomer concentration the association rate prevails over the depolymerization rate at both ends of the filament: kll 9cl > k~l and k12 " cz > k~.2. At lower monomer concentration near the critical concentration a different direction of growth is to be expected for both ends, since kll 9c~ -- k;~ = -- (k~2 9~ -- k~2), and this results in extensions at the growing end. Shortening of an end cannot be detected b y binding of heavy

150

A. W E G N E R

meromyosin, since an end to which heavy meromyosin is attached remains decorated after dissociation of a subunit. The head to tail polymerization of actin m a y have great significance in the processes in which actin association is thought to be involved, like the formation and length determination of thin filaments, translocation of actin filaments or shape determination of cells (Lazarides & Weber, 1974). Our present insight however is not sufficient to assign a specific role in these processes to the head to tail polymerization. Detailed knowledge about the interaction of other components with actin is necessary for an understanding of the role of the head to tail polymerization. Further experiments in this direction are investigations on the influence of actinin, myosin, tropomyosin and troponin on the head to tail polymerization. The author expresses his thanl~s to Professor J. Engel for stimulating discussions. This work was supported by research grant 3.183-0.73 from the Schweizerischer Nationalfonds zur Foerderung der wissenschaftlichen Forschung. REFERENCES

Arisaka, F., Noda, H. & Maruyama, K. (1975). Biochim. Biophys. Acta, 40O, 263-274. Asakura, S. (1968). J. Mol. Biol. 35, 237-239. Asakura, S. & Oosawa, F. (1960). Arch. Biochem. Biophys. 87, 273-280. Casassa, E. F. (1955). J. Chem. Phys. 23, 596-597. Cooke, R. (1975). Biochemistry, 14, 3250-3256. Cooke, R. & Murdoch, L. (1973). Biochemistry, 12, 3927-3932. Kasai, M. & Oosawa, F. (1969). Biochim. Biophys. Acta, 172, 300-310. Hayashi, T. & Ip, W. (1974). J. Gen. Physiol, 64, 9a. Hayashi, T. & Rosenbluth, R. (1960). Biol. Bull. 119, 290. Huxley, H. (1963). J. Mol. Biol. 7, 281-308. Kawamura, M. & Maruyama, K. (1970). J. Biochem. 67, 437-457. Lazarides, E. & Weber, K. (1974). Proc. Nat. Acad. Sci., U.S.A. 71, 2268-2272. Lusty, C. J. & Fasold, H. (1969). Biochemiztry, 8, 2933-2939. Mannherz, H. G., Brehme, H. & Lamp, U. (1975). Eur. J. Biochem. 60, 109-116. Martonosi, A., Gouvea, M. & Gergely, J. (1960). J. Biol. Chem. 235, 1700-1703. Oosawa, F. (1970). J. Theoret. Biol. 27, 69-86. Rees, M. & Yore]g, M. (1967). J. Biol. Chem. 242, 4449-4458. Seidel, I)., Chak, D. & Weber, H. (1967). Biochim. Biophys. Acta, 140, 93-108. Straub, F. B. & Feuer, G. (1950). Biochim. Biophys. Acta, 4, 455-470. Waeehter, F. & Engel, J. (1975). Eur. J. Biochem. 57, 453-459. W%mer, A. & Engel, J. (1975). Biophys. Chem. 3, 215-225. Woodrtun, D. T., Rich, S. A. & Pollard, T. D. (1975). J. Cell Biol. 67, 231-237.