(Received for publication, November 10, 1995)
From the
Polymerized (F-)actin is induced to form bundles by a number of
polycations including divalent metal ions,
Co(NH)
, and basic
polypeptides. The general features of bundle formation are largely
independent of the specific structure of the bundling agent used. A
threshold concentration of polycation is required to form lateral
aggregates of actin filaments. The threshold concentration varies
strongly with the valence of the cation and increases with the ionic
strength of the solution. Polyanions such as nucleoside phosphates or
oligomers of acidic amino acids disaggregate actin bundles into single
filaments. These features are similar to the phenomenon of DNA
condensation and can be explained analogously by polyelectrolyte
theories. Similar results were found when F-actin was bundled by the
peptide corresponding to the actin binding site of myristoylated
alanine-rich protein kinase C substrate protein (MARCKS) or by smooth
muscle calponin, suggesting that a broad class of actin bundling
factors may function in a common manner. Physiologic concentrations of
both small ions and large proteins can induce actin interfilament
association independent of a requirement for specific binding sites.
Actin polymerizes to double stranded filamentous form (F-actin)
in solutions of physiological ionic strength (2 mM MgCl and 100 mM KCl). At relatively high (>10 mM)
concentrations of divalent cations such as Mg
,
F-actin forms aggregates of various forms, characterized as types I,
II, and III paracrystals(1) . Stable Type III paracrystals
appear as large and compact side-by-side aggregates, with additional
morphological variations identified by analyzing electron micrographs
(EM)(2, 3, 4, 5, 6) . An EM
specimen typically manifests several morphologies, for which no
difference in experimental conditions can be assigned. The co-existence
of these morphological states implies that the total free energies of
the various bundle forms are similar, provided that an overall
attractive interaction exists in order to bring the filaments together.
Chemicals that cause F-actin to form paracrystalline bundles, such as divalent cations at high concentrations (order of 10 mM) (4) , trivalent cations (mM range)(7) , and polyamines (3, 4) are similar to those which cause DNA condensation(8, 9) , except that the latter effect requires consistently higher concentrations of polycations. Both effects also occur at low pH (<5.5), and at high osmotic pressure (by addition of polyethylene glycol, for example) (10) . It is the goal of this paper to demonstrate that the mechanism of F-actin bundle formation is analogous to that established for DNA condensation.
The phenomenon of DNA condensation has been successfully treated by
the theory of linear
polyelectrolytes(11, 12, 13, 14) . A
double stranded DNA at neutral pH has a linear charge spacing b = 1.7 Å, much less than the Bjerrum length, the
distance between elementary charges at which the electrostatic
interaction energy equals the thermal energy kT, i.e. = e
/4
kT. In
water, for example, the dielectric constant
= 80 at 20
°C and
= 7.1 Å. According to the
Manning counterion condensation theory(12) , a consequence of
DNA's high charge density is that a certain fraction of its
charge is neutralized due to the territorial binding of counterions in
the immediate environment (so-called condensed counterions which are
free to diffuse along the polymer axis, but inhibited from diffusing
away). The fraction of polyelectrolyte charge compensated by the
condensed counterions is determined as the following equation,
where N is the valence of the counterion and
=
/b = 4.2. In monovalent
electrolytes,
is calculated to be 76%. It may reach 88% in the
presence of sufficient divalent cations. Hence the predicted
delocalized binding is stronger for counterions of higher valence, in
which case the charged polymer is neutralized to a higher degree.
The residual electrostatic repulsion between polyelectrolytes of
like charge tends to keep them apart. This repulsive force decreases
with the presence of polyvalent counterions, due to the enhanced charge
condensation. In addition to the weakened electrostatic repulsion
between charged polymers due to counterions, an attractive interaction
can also be induced by two polymers sharing counterions. The
fluctuation (15) and lateral redistribution (14) of
counterions have each been shown theoretically to cause an attractive
interaction between polyelectrolytes. At appropriate ionic conditions,
a balance between attractive and repulsive forces occurs so that the
filaments in suspension form aggregates. This aggregation may also
involve other interactions such as hydration and van der Waals
forces(11, 13) . It has been estimated that DNA
condensation occurs as reaches 90%, which requires a valence of
3 or higher.
Counterion condensation theory has been applied to other polyelectrolytes such as polystyrene sulfonate and heparinate(16, 17) . Justification for applying this theory has come from several different treatments. For example, analytical solutions to the nonlinear Poisson-Boltzmann equation for a cylindrical polyelectrolyte(18, 19) provide a model generally consistent with that of the earlier counterion condensation theory. Similar predictions were also obtained by Monte Carlo simulations(20, 21) . Alternatively, an interesting ligand binding model of counterion condensation was proposed(22) , with an assumption analogous to the territorial binding in the Manning theory. In this paper, the simplified predictions from the original Manning theory are used to explain the phenomenon of bundle formation by F-actin. Different results and interpretations from alternative approaches have been discussed more recently (19, 23).
An actin filament has a lower linear charge
density than DNA. Using the amino acid sequence of -skeletal
muscle actin, one residue of 3-methylhistidine, an acetylated N
terminus and one molecule each of tightly bound divalent cation and
ATP(24) , each subunit of an actin filament bears 14 excess
negative charges. In addition, roughly three histidines per monomer are
likely to be protonated at pH 7.2. Based on 370 monomers per micron
contour length, the linear charge density is approximately 4 e/nm. This value has two implications: the average charge
spacing along the filament axis is sufficiently small compared to the
Bjerrum length to make the counterion condensation theory relevant
(
=
/b > 1); but
is less
than that of DNA, suggesting that a smaller percentage of charge needs
to be neutralized for condensation to occur (). Therefore,
one expects actin bundles to form at similar, but consistently lower,
concentrations of cations compared to DNA. This prediction is tested by
analysis of the effects of a variety of inorganic and organic cations,
including the actin binding domain of MARCKS (
)protein and
the smooth muscle actin binding protein calponin.
Human plasma gelsolin was purified by elution from DE52 ion exchange
matrix in 30 mM NaCl, 3 mM CaCl, 25
mM Tris, pH 7.4, as described by Kurokawa et
al.(26) , rapidly frozen in liquid nitrogen and stored at
-80 °C.
Recombinant chicken gizzard -calponin was
produced as described in Gong et al.(51) and was a
kind gift of T. Tao(27) . The lyophilized power was dissolved
in 3 M KCl and dialyzed against 50 mM Hepes, 5 mM dithiothreitol, and 0.1 M KCl at pH 7.5. A concentrated
stock solution of up to 100 µM was prepared, and the
protein concentration was determined by spectrophotometry, assuming a
specific absorbance of 0.74 (mg/ml)
cm
at 280 nm.
Figure 1: Light scattering signal of F-actin as a function of concentration of various cations. Each sample contained initially 0.5 mg/ml F-actin at pH 7.2, followed by sequential additions of concentrated cations. The scattering was measured at 90 degrees, with 365 nm/370 nm wavelength and 3 nm/3 nm slit width (details under ``Materials and Methods'').
Figure 3:
Effects of F-actin concentration on the
bundle formation induced by Lys. a, bundle
formation by Lys
of F-actin in 150 mM KCl at 3
representative concentrations: 0.1, 2.0, and 6.0 mg/ml. The dotted
vertical lines indicate onset bundle formations determined as
described in the text. b, the onset concentration of
Lys
as a function of F-actin concentration. All six
experimental points were obtained as illustrated in a, and a
linear fit was applied.
Figure 6:
Millimolar concentrations of nucleotides
reverse the formation of actin bundles. a, dissociation of
highly scattering bundles of 0.5 mg/ml F-actin plus 100 µM Lys following the sequential additions of ATP, CTP,
and GTP, respectively. b, dissociation of bundles of 0.3 mg/ml
F-actin plus 50 µM Lys
by ATP, ADP, and
AMP.
Figure 2:
Bundle formation of 0.2 mg/ml F-actin in
150 mM KCl, plus Cu and/or
Mg
. a, Cu
was sequentially
added to F-actin solution, without (open circles) and with (solid circles) 20 mM MgCl
. b,
MgCl
induced bundle formation of F-actin which was
preincubated for roughly 5 min with 0, 10, 50, and 100 µM CuCl
.
Figure 7:
Formation of F-actin bundles induced by
MARCKS peptide, in comparison with Lys and
Lys
. The scattering intensity readings were roughly 0.07
for the three identical samples, prior to additions of the respective
peptides.
Figure 8: Reversible bundling activity of calponin. a, effect of calponin on bundle formation by F-actin in solutions with 30, 50, and 75 mM KCl. b, disassembly of calponin-actin bundles by ATP, ADP, and AMP. 3 µM calponin was added to 2.5 µM F-actin with 50 mM KCl and mixed approximately 10 min prior to additions of the adenine nucleotides.
Figure 4: Comparison of bundle formation by F-actin of various lengths. Actin concentration is 0.2 mg/ml for all the samples, with different gelsolin:actin ratios as noted in the figure. The average filament length is 1.35 µm at 1:500 molar ratio of gelsolin (gel) to actin.
Figure 5:
Effect of ionic strength on bundle
formation. a, formation of F-actin bundles by
Co(NH)
at four salt
conditions. b, variation of the bundling onset concentrations
of Co(NH
)
and Mn
versus [KCl], which gives roughly the initial
ionic strength. In the case of
Co(NH
)
, different types of hollow symbols represent measurements with actin from three
independent preparations. A power law fit was applied to a total of 12
data points for Co(NH
)
and 4
data points for Mn
.
In order to confirm that an increase in light scattering corresponds to bundling, F-actin samples at different light scattering levels due to additions of polycations were examined by electron microscopy (EM), using the negative staining technique. When light scattering signals remained at low levels, actin filaments appeared disperse or intertwined in loose isotropic networks. In contrast, large lateral aggregates were always seen by EM at high light scattering levels.
The bundling efficiency of different divalent metal ions increases
with their atomic number. Co bundles F-actin at 5.5
mM, Mn
at 7 mM, in comparison with
Ca
at 20 mM and Mg
at 27
mM. This variation from 5.5 to 27 mM may correlate
with ionic radius and extent of hydration. Such cation-specific effects
cannot be explained by the Manning theory.
The general behavior
shown in Fig. 1can be qualitatively explained by the
predictions of the polyelectrolyte theory. Assuming an average linear
charge density of 4 e/nm and applying the counterion
condensation theory of Manning, a layer of condensed counterions is
predicted near the F-actin surface. With 150 mM KCl and no
polyvalent cations, the most simplified Manning model estimates
K in this layer to be about 60% () of the
total net surface charge of F-actin. If divalent cations are abundant
in solution, the percentage is estimated to be 82% ().
F-actin forms stable bundles at 150 mM KCl with order of 10
mM divalent cations, suggesting that approximately 80%
neutralization of the surface charge is required for bundle formation.
This is a less stringent condition than that for DNA, in which case 90%
of the charge needs to be neutralized for the transition to occur. The
increased bundle formation by
Co(NH
)
and polyamines
compared with divalent cations is due to the higher apparent binding
constants at higher valence, as predicted in the Manning
theory(12) .
In an attempt to
distinguish these two components, MgCl was first added to
the F-actin solution to 20 mM, in which condition the surface
charge of F-actin should be neutralized to a large extent, but not
enough to form bundles. A slight, yet reproducible increase in the
light scattering signal was measured following addition of MgCl
to 20 mM, which may correspond to some other forms of
aggregation, such as the fishnet-like paracrystalline structures (types
I and II) characterized by a previous EM study(1) . Addition of
as little as 25 µM Cu
causes a
significant increase in light scattering, and the high level scattering
at 50 µM Cu
indicates extensive bundle
formation.
A complementary set of measurements is shown in Fig. 2b, in which 0.2 mg/ml F-actin was first treated
with various amounts of Cu and its effect on bundling
was compared with sequential addition of MgCl
. While 10
µM Cu
does not affect the onset of
bundling by MgCl
, 50 µM Cu
facilitates bundle formation with only 15 mM MgCl
as opposed to about 30 mM required without
Cu
. The decreased amount of Mg
required for bundling is due to the reduction of surface charge
on F-actin caused by the tight specific binding of
Cu
.
Fig. 3b shows that the amount of Lys required to bundle actin increases approximately linearly with
the actin concentration. The intercept of the vertical axis from a
linear fit, c
= 19.4 µM, is the
concentration of free Lys
necessary to induce bundling.
The slope of 0.26 Lys
per actin monomer determines the
molar ratio of Lys
to actin in the bundled state. Assuming
that each actin monomer carries 11 e of negative charge in the
polymerized form, the number of bound polylysine per charge on the
actin filament is
= 0.26/11 = 0.024.
This number implies that about 40% (
18) of
the actin surface charge is neutralized by the lysine residues at the
onset of bundling. Consistent with the Manning theory, an additional
40% or so is neutralized by the excess K
to make up to
80% as the criterion for bundling to occur.
In order to explain the
linear relationship measured in Fig. 3, it is helpful to first
elucidate the concept of condensation zone, and how its volume is
related to the molar concentration of actin. Manning introduced V as the volume of condensation per molar charge
of the polyelectrolyte, within which counterions are bound (12) . At excess univalent electrolyte, V
can be calculated as the following,
where V has the units of cm
/mol
if b is expressed in Å. For F-actin, since b = 2.5 Å and
= 7.1/b =
2.8, we estimate V
to be 1.2
10
cm
/mol, or equivalently 1.2 M
. The constant value for V
implies that the total volume of condensation zone is directly
proportional to the molar concentration of actin. Based on this
property, a brief derivation in the appendix predicts a behavior which
is consistent with Fig. 3b.
This simple exercise
with the Manning theory further predicts the local ion concentration of
Lys as c
=
/V
= 0.02 M.
The association constant, defined as the ratio of concentrations of
localized to free counterions, K =
c
/c
, is therefore on the order of 20
mM/20 µM = 10
for the case of
Lys
with 150 mM KCl in solution.
In Fig. 3b the minimal bundling concentration of
Lys is in the micromolar range, comparable to the range of
F-actin concentration. In the case of divalent and trivalent cations,
millimolar concentrations of free cations are required for bundle
formation, and the amount sequestered by actin filaments is negligible.
Measurements similar to those of Fig. 3using
Co(NH
)
showed no apparent
dependence of the minimal bundling concentration on actin concentration
from 0.1 to 5.0 mg/ml within our experimental error of approximately
10%.
where N is the valence of the small cation. This
dependence is only correct for a trace amount of polyvalent counterions
in the presence of excess monovalent counterions. Otherwise, the
Manning one variable approach predicts a similar power law dependence
with a slope varying between 1 and N in the log-log plot,
which approaches 1 with increased concentration of the polyvalent
counterion. In addition, such dependence is expected to hold only at c < 0.1 M. In practice, testing the ionic strength
dependence for F-actin bundles is limited to high ionic strength (order
of 100 mM KCl), or with 2 mM MgCl in
solution in order to keep actin polymerized prior to adding
polycations. 0.2 mM Ca
and 0.5 mM ATP are also present in the usual buffer solutions. Nevertheless,
one should still expect a marked effect of ionic strength on the
minimal concentrations of polycation needed to induce bundling.
Fig. 5a displays the increasing amount of
Co(NH)
required to form actin
bundles in solutions of increasing KCl concentration. Fig. 5b shows the functional dependence between
[Co(NH
)
] and
[KCl]. Assuming that the concentration of
Co(NH
)
ions in the
condensation layer reaches a fixed value of
[Co(NH
)
]
at the onset of bundle formation, the relation K =
[Co(NH
)
]
/[Co(NH
)
]
and the Manning theory predicts a linear dependence between
log[Co(NH
)
] and
log[KCl] with a slope between 1 and 3. However, a linear fit
to the data of Fig. 5b gives a slope of roughly 0.74. A
similar experiment using Mn
instead of
Co(NH
)
gave a slope value as
small as 0.20 (Fig. 5b). These values of less than one
may be partially attributed to the complication in ionic conditions as
addressed above, and to a number of oversimplified assumptions in the
simplest Manning treatment. For instance, at the onset bundling
condition the concentration of
Co(NH
)
in the condensed layer
may depend on the solution ionic strength. In addition, the assumption
of a charged line for F-actin is apparently oversimplified.
Nevertheless, the qualitative prediction of the polyelectrolyte
treatment is confirmed.
Fig. 7compares the bundling effect of MARCKS peptide with
those of lysine 18-mers and 42-mers. The dose-response curves are
similar, but the MARCKS peptide is effective at 1 order of magnitude
lower concentration than the more highly charged Lys. In
all three cases the preformed bundles dissolved after addition of
millimolar ATP (not shown). It is therefore likely that the MARCKS
peptide bundles actin as a consequence of its binding to the negatively
charged actin surface, thereby neutralizing its electrostatic charge.
In addition, cross-bridging of F-actin by long peptides may enhance
bundling efficiency and possibly account for the finding that the
MARCKS peptide of 14 net positive charges bundles actin more
efficiently than 18-mers of lysine, since the charges on the MARCKS
peptide are mainly distributed at both ends of a longer sequence. It is
also possible that the MARCKS peptide self-associates into dimers or
trimers and hence becomes more efficient in bundling F-actin.
In addition to the light scattering
experiments, analysis of co-sedimentation of calponin with F-actin
revealed that in equimolar mixture (roughly 4 µM of each
protein) the amount of calponin bound to F-actin decreased continuously
with increasing ionic strength. ()This result is consistent
with an electrostatic model of binding, and the behavior at least
partially accounts for the conflicting reports in literature of the
binding stoichiometry between calponin and
F-actin(32, 35, 36, 37) .
Theories for counterion condensation by linear polyelectrolytes can explain the formation of actin bundles by agents as diverse as metal ions, inorganic polycations, polyamines, homopolymers of basic amino acids, peptides identified as specific actin binding sites, and intact actin binding proteins. These theories have many implications for actin structure and function, and possibly for other cytoskeletal biopolymers.
The most direct implication is that proteins with sufficient numbers of positive charges, exposed appropriately on their surface, will inevitably bind to actin filaments even in solutions of physiologic ionic strength and often with relatively high (µM) affinity. It has been noted that there are surprisingly many F-actin binding proteins, but no obvious consensus F-actin binding site has been identified(38, 39, 40) . Given the strong electrostatic effects between polyelectrolytes and their counterions, the binding of some proteins to F-actin may be largely independent of unique tertiary structures that form tight specific binding interfaces typical of the protein/protein bonds that have been identified for several G-actin binding proteins. The relatively nonspecific nature of the electrostatic forces by which some proteins may bind F-actin does not necessarily mean that these interactions have no relevance in vivo. On the contrary, the filament density in cells is high compared to what can be achieved in vitro, and ionic fluxes are both common and poorly understood. The results of this work suggest that proteins that interact primarily or exclusively by electrostatic interactions can cause bundling of F-actin when present at micromolar concentrations, and such bundles can be dissolved by increasing ionic strength, protein phosphorylation, or by changes in nucleotide concentrations in the millimolar range.
The effects of polycations on F-actin show that cross-linking is not always required for bundle formation, and neutralization of sufficient surface charge on F-actin can directly induce bundling. Many actin binding domains are rich in positive charge, and long range electrostatic interaction may dominate their binding to F-actin. In this interpretation, an actin bundling protein need not contain two distinct actin binding domains, nor is dimerization required. Cross-links between parallel filaments shown in electron microscopy in some cases are perhaps merely the result of steric hindrance, and their locations are often of a stochastic nature. In the case of lateral aggregation, there is no absolute requirement for locking the filaments at the opposite sites of actin bundling proteins, although the presence of such links caused by specific actin bundling proteins, such as the acidic proteins fimbrin or villin, can modulate the structure of such bundles(39) .
The analogy
between bundling F-actin and DNA condensation should also be applicable
to other charged biopolymers such as microtubules, intermediate
filaments, filamentous bacteriophage fd, and tobacco mosaic virus. The
electrostatic features such as the requirement of polycationic protein
domains and the extreme sensitivity to ionic strength have been
examined for lateral association of microtubules (41, 42) . Parallel experiments to those reported in
this paper have been extended to fd and tobacco mosaic virus
suspensions(43) . The nonspecific electrostatic model also
explains the co-bundling of different filament types such as actin and
microtubules(44) , and the finding that microtubule associated
proteins MAP2 and fragments bind and bundle
F-actin(45, 46) , as well as microtubules.
In addition to the formation of supermolecular aggregates, the structural dynamics of single actin filament can also be altered by the ions surrounding it, even if these ions do not have specific binding sites on the protein. Polymerization and depolymerization are extremely sensitive to the ionic conditions in solution. Many actin bundling factors accelerate actin polymerization even at lower concentrations than required for inducing the lateral aggregation of F-actin(47) .
Since the condensed counterions on the surface
of either F-actin or microtubules move freely along the filament axis,
cells may transport metal ions such as Ca preferentially along these filaments. This so-called cable-like
property has been reported for F-actin(48) , and the role of
microtubules in intracellular transport may also relate to the similar
polyelectrolyte nature.
Charge differences in actin subunits often
occur and can accordingly alter the structure of the filament or its
ability to interact with other proteins electrostatically. For example,
when P is released from actin filament following hydrolysis
of the actin-bound ATP to ADP-P
, the surface charge density
of the filament falls approximately 9% (1/11). An opposite effect would
occur if actin rebound P
or became phosphorylated.
Similarly,
and
nonmuscle actin isoforms have one or two
fewer net negative charges than
-actin according to their amino
acid sequence. Filaments formed by these isoforms might be more
susceptible to bundling at borderline conditions, and such differences
may relate to the partitioning of actin isoforms into specific
structures within a cell. In a similar vein, mutations which reduce the
net negative charge of actin have reportedly caused the mutant actin
filaments to spontaneously bundle (49, 50) . These
observations provide additional evidence for the polyelectrolyte nature
of F-actin and its related properties.
Applying the electrostatic model to the association between F-actin and actin binding proteins does not alter the importance of additional binding forces due to the large size and the structural variations of intact proteins. This model does not exclude the dominant effects of specific actin binding sites. Although the specific binding site may be closely related to the distribution of charged residues, the individual tertiary structures and regions of compatible hydrophobicity must also contribute to the overall association. Therefore, the sole consideration of polyelectrolyte properties of F-actin should not be exaggerated in an attempt to explain every aspect of F-actin related associations. On the other hand in those cases where tight and specific actin binding sites cannot be identified, these electrostatic interactions can lead to bindings that are remarkably efficient and regulated by physiologic signals.
We provide here a simple derivation following a chemical
binding model as elucidated by Manning(12) . Assuming 18-mers
of lysine, Lys binds to F-actin with an apparent affinity k =
[Lys
]
/[Lys
]
,
where [Lys
]
is the concentration of
free lysine in solution and [Lys
]
is
the local concentration of lysine in the condensed region surrounding
F-actin. Both k and [Lys
]
are functions of the ionic strength of the excess monovalent salt
and are independent of F-actin concentration.
We assume that
side-by-side aggregates start to appear at a critical concentration of
[Lys]
. This corresponds to an
undetermined, but fixed total fraction of charge neutralization of
F-actin
, which can be obtained if a Scatchard plot is provided.
In the absence of other ligands, the total concentration of
oligolysine [Lys]
is an appropriate
summation of [Lys
]
and
[Lys
]
as shown in the following
equation,
where v 1 is the volume fraction of the
condensation zone surrounding F-actin in solution, and is proportional
to actin concentration at a given ionic strength. Note that the volume
fraction which F-actin occupies is neglected in the above expression.
Experimentally, since there is usually 0.5 mM ATP in F-actin buffer, possible formation of lysine-ATP complex should be taken into account. The complete expression based on Eq. 4 is shown below.
In the above formula, the linear dependence of
[Lys]
on F-actin concentration is
preserved in v, in spite of the complication due to the
presence of ATP, an interacting polyion of the opposite charge.