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 << kl) the filament grows
unidirectionally.
(ii) Head to tail polymerization
The model t h a t is set up for a polymerization which includes the splitting of AT1a
resembles a reaction scheme t h a t has been proposed b y Asakura & Oosawa (1960)
(see Fig. 2). I t is extended b y taking into consideration the structural polarity of
actin filaments (Huxley, 1963). Eight rate constants are introduced to describe the
rate of growth of actin filaments. The various rate constants are defined in Figure 2.
The equilibrium constants for the association of actin monomers with bound A D P
(K2) or with bound A T P (K1), respectively, are related to the rate constants in the
following way:
k21
k2~
kii
kii
ki2
ki2
K2 = -7- = --7--,
k21
k22
(4a)
K~ = -7- = -7-.
(4b)
It is probably not realistic to assume that the association of ATP-actin m o n o m e r s to
form a filament and splitting of A T P is a one-step reaction. However, the kinetics of
association can be described by this simplified mechanism if A T P splitting is fast
compared with the association of a subunit to the polymer. The scheme contains a
i~.."
.~'.".
]',~"'..
t9
A D P ~
ADP
K2
~ADP
-ATP
K3
ADP
P f4
k12
/(2
ADP
AOP
ADP-~X~I
~176176176
~176
_.
.." ..~
&
Fro. 2. Reaction scheme of actin polymerization. The chevron symbol stands for a subunit
with bound ATP or A D P . / 1 and f~ represent the 2 ends of actin filaments. P is inorganic phosphate.
HEAD TO TAIL P O L Y M E R I Z A T I O N OF ACTIN
143
reaction which has not been observed in solutions of polymeric actin, namely the
dissociation of a subunit accompanied by a phosphorylation of ADP to yield A T P
(Straub & Feuer, 1950). Although this reaction may be negligible, it has been taken
into consideration in order to obtain a scheme of reversible reactions. The rates of
growth of the ends of the filaments are given by the following equations
dn~
- - = k11 9 [g-ATP] - - / ~ 9 [P] q- k2~ x [g-ADP] -- k~1
dt
(5a)
dn2
-- k~2" [g-ATP] --/~2 • [P] q-/~22 X [g-ADP] -- k'22~
dt
(5b)
-
-
-
-
where [g-ATP] and [g-ADP] are the concentrations of monomeric actin with bound
ATP or ADP and [P] is the concentration of inorganic phosphate. It is a reasonable
assumption that ATP-actin and ADP-actin are in equilibrium, since the exchange
of the nucleotide is known to be fast (Martonosi et al., 1960; Waechter & Engel, 1975).
[g-ATPJ. [ADP]
[g-ADP]. [ATP]
--
K 3,
(6)
where [ADP] and [ATP] are the concentrations of A D P and ATP.
Combining equations (4), (5) and (6) it is possible to express the rates of growth
in the following way
dnldt = kll " ([g-ATP] -- [P]/K1) -t-/c21 " [g-ATP] " [ATP]. Ka
/~s ,
(7a)
__
(
[ADP]
dn2dt----k12" ([g-ATP] -- [P]/KI) q- k29." [g-ATP] 9 [ATP] 9K3
I)
/~2. .
(7b)
All kinetic parameters and equilibrium constants in equations (7a) and (7b) are
independent.
The interesting conclusion which follows from equations (7a) and (7b) is that the
rates of growth at the two ends can have different signs, in contrast to unidirectional
or bidirectional polymerization. This difference results from the polymerization cycles
of actin. The association is not necessarily the reverse reaction of the dissociation.
Actin monomers with bound A T P associate with filaments, whereas a subunit
dissociated from the filament binds ADP. This type of polymerization is called
head to tail polymerization.
(b) Exchange of monomers and polymer subunits
In the following the time needed for an exchange of all subunits of a filament with
the monomers in solution is calculated for unidirectional or bidirectional polymerization and for head to tail polymerization. This calculation shows to what extent
measurements of the exchange of monomers and polymer subunits allow these
polymerization mechanisms to be distinguished.
Equations (7a) and (7b) derived for the rate of growth in the case of head to taft
polymerization can be reduced to a simpler form. The dissociation of monomeric
actin connected with the synthesis of ATP is negligible (Straub & Feuer, 1950).
The association of actin monomers with bound ADP is omitted, since in a solution
144
A. W E G N E R
c o n t a i n i n g 5 • 10 -4 M-ATP n e a r l y all a c t i n m o n o m e r s b i n d A T P (Martonosi et al.,
1960; Seidel et al., 1967). E q u a t i o n s (7a) a n d (7b) now r e a d :
dnl
d-T - - k11" [g-ATP] - - k 2 1 / K 2 = k l i • c l - - k'21
dn2
dt
- - k12. [g-ATP] - - k 2 2 / K 2 = k 1 2 . c l - - k'22,
where [g-ATP] = cl.
T h e r a t e of g r o w t h of t h e entire filament d n / d t
a t b o t h ends o f t h e filament
(8a)
(8b)
is t h e s u m of t h e r a t e s o f g r o w t h
dn
d--/---- (kll ~- k12) "cl - - (k~l + k~2).
(9)
T h e a v e r a g e length of t h e filament r e m a i n s c o n s t a n t (dn/dt = 0), as soon as t h e
m o n o m e r c o n c e n t r a t i o n has r e a c h e d a s t e a d y - s t a t e v a l u e 51 (critical m o n o m e r
concentration)
k~l + k~2
cl - - k,1 -t- k12"
(10)
U n d e r this c o n d i t i o n t h e f i l a m e n t is lengthened, on average, b y as m a n y s u b u n i t s a t
one end (e.g. end 1) as it is s h o r t e n e d a t t h e o t h e r (end 2). E n d 1 will be called t h e
growing end, a n d end 2 t h e d e g r a d i n g end. This c h a r a c t e r i z a t i o n reflects t h e n e t
result of association a n d dissociation steps which can t a k e place a t b o t h ends.
N e a r t h e critical m o n o m e r c o n c e n t r a t i o n a f i l a m e n t which c o n t a i n s n s u b u n i t s
releases all subullits b y s h o r t e n i n g of t h e f i l a m e n t a t t h e d e g r a d i n g end w i t h i n t h e
t i m e i n t e r v a l A t ( n ) (see Fig. 3)
At(n)--
,
=
k22 - - /c12 9 5,
k l l 9 51 - - k~l"
(ll)
(o)
i
k22
kl2"E I
k 21
(b)
r
(c)
FIG. 3. Head to tail polymerization. Exchange of subunits. Radioactively labelled subunits
are drawn in black.
(a) State of a filament at time to.
(b) State of a filament at a time t where to < t ~ to ~ nl(k11"cl -- k~l).
(e) State of a filament at time t o -~ n/(lcll "~l -- k'.).l).
H E A D TO T A I L : P O L Y M E R I Z A T I O N OF A C T I N
145
I f n is large, deviations from the average value At(n) are relatively small (0osawa,
1970).
An estimation of the time needed for an exchange of all subunits in the ease of
unidirectional polymerization (k2 = 0, k~ = 0) has been given b y Kasai & Oosawa
(1969). I f the monomer concentration is near the critical monomer concentration
(cl = K - 1 ) the average time, t(n), required for the exchange of the n subunit from
end 1 of the polymer is approximately
i(n) = n2/kl.
(12)
I f the frequency of association and dissociation steps is the same for unidirectional
polymerization and head to tail polymerization (k~ : k~l ~ k~.2) the time intervals
differ b y a factor of
At(n)
= n.
k~l + k~2
-- n . s ,
(13)
where
s -
k l l " ~1 - - k ~ l
k~l +
k~2
(14)
Exchange of subunits in the case of bidirectional polymerization can be taken in
an approximation as two unidirectional exchange processes at the ends of filaments.
The time of exchange is therefore expected to be of the same order of magnitude as
for unidirectional polymerization.
Unidirectional and bidirectional growth lead to a time-course of exchange which
depends much more on the length of the filaments t h a n does head to tail polymerization. I n a limiting case of head to tail polymerization association of monomers occurs
solely at end 1 of the filament (k12 ---- 0) and dissociation only at the other (k~l = 0).
I n this case s is equal to 1. I f the rates of association and dissociation at each end are
similar, s approaches zero. The bulk of the actin filaments, on the other hand, contains
more t h a n 100 subunits ( K a w a m u r a & Maruyama, 1970; Wegner & Engel, 1975;
A_risaka et al., 1975). E v e n if the rate of shortening or lengthening is the result of a
small difference between the rate of association of monomers and dissociation of
subunits (e.g. s = 0.1), a great acceleration of subunit exchange is to be expected for
head to tail polymerization compared with unidirectional growth.
(c) Correlation between the kinetids of the monomer concentration and the rate of
exchange of labelled protomers in the case of head to tail polymerization
The average number of subunits n which are incorporated into a filament (see
eqn (8)) which started to form at a time tN amounts at a time to, when the monomer
concentration has reached its steady-state value ~1, to
n -----ft~162
Jts
-~- ]~12) 9 Cl - - (k21 -q- k22)] dr.
(15)
I f n is large, deviations from the average value n are relatively small (Oosawa, 1970).
Combining equations (10), (11), (14) and (15) yields a correlation between the time
needed for a complete exchange of polymer subunits At(n) and the time necessary
for building up the polymer:
At(n) =
/f,0 (c11~1 -- 1) dt.
8 Jts
10
(16)
146
A. WEGNER
At time t o when a trace of labelled monomeric actin is added to the solution,
filaments start to incorporate labelled subunits. The probability p(t) t h a t an incorporated subunit is labelled is equal to the fraction of monomers which are labelled.
The probability p(t) depends on the time, since the relative concentration of labelled
monomers is changed b y the incorporation into and release from filaments. During
the time interval A t ( n ) the subunits which are released b y shortening of the degrading
end are not labelled; after this time interval labelled subunits appear at the degrading
end (see Fig. 3). The probability t h a t these subunits are labelled amounts to
p ( t - - A t ( n ) ) , since these subunits were incorporated at the growing end at the time
t - - A t ( n ) (see Fig. 3). The change of the concentration of labelled monomers c*
which are exchanged by polymers (concentration %) is given by
dc*
dt --
p ( t ) . (kl~ . ~ - - k'21) " % f o r to < t < t o + -
1 I t~
( c J ~ x - - 1) dt
(17a)
8 ,Jtx
-
[p(t)
-
p(t
-
s
-
1)
dr)]-
--
%
for t > 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.