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(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
Actin polymerizes to double stranded filamentous form (F-actin)
in solutions of physiological ionic strength (2 mM MgCl 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.
where N is the valence of the counterion and 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 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
Human plasma gelsolin was purified by elution from DE52 ion exchange
matrix in 30 mM NaCl, 3 mM CaCl Recombinant chicken gizzard
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
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
Figure 2:
Bundle formation of 0.2 mg/ml F-actin in
150 mM KCl, plus Cu
Figure 7:
Formation of F-actin bundles induced by
MARCKS peptide, in comparison with Lys
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
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 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 an attempt to
distinguish these two components, MgCl 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
Fig. 3b shows that the amount of Lys 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
where V This simple exercise
with the Manning theory further predicts the local ion concentration of
Lys In Fig. 3b the minimal bundling concentration of
Lys
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 Fig. 5a displays the increasing amount of
Co(NH
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 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. ( 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 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 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 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 We assume that
side-by-side aggregates start to appear at a critical concentration of
[Lys In the absence of other ligands, the total concentration of
oligolysine [Lys
where v 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
Volume 271,
Number 15,
Issue of April 12, 1996 pp. 8556-8563
©1996 by The American Society for Biochemistry and Molecular Biology, Inc.
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
APPENDIX
FOOTNOTES
ACKNOWLEDGEMENTS
REFERENCES
)
, 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.
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. 
= 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,
= /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. 
reaches 90%, which requires a valence of
3 or higher.
-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.
Proteins
Monomeric (G-)actin was prepared from
an acetone powder of rabbit skeletal muscle according to Spudich and
Watt(25) . The nonpolymerizing solution contained 4 mM Hepes buffer at pH 7.2, 0.2 mM CaCl, 0.5
mM ATP, and 0.5 mM NaN. The buffer
concentration was sufficient to ensure the stability of pH, since
concentrated reagents were frequently added to actin samples. Actin was
polymerized by 150 mM KCl, unless mentioned otherwise. , 25
mM Tris, pH 7.4, as described by Kurokawa et
al.(26) , rapidly frozen in liquid nitrogen and stored at
-80 °C.-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.Peptides
MARCKS peptide was purchased from Biomol,
supplied as trifluoroacetate salt. A stock solution of 200 µM peptide was prepared in 50 mM Hepes at pH 7.5. Oligomers
of arginine, lysine, histidine, and aspartic acid were synthesized and
purified by Daina Biseniece, Ieva Liepkaula, and Ivars Lipsbergs at the
Latvian Organic Synthesis Institute and were conveyed to us by Rolands
Vegners. Polylysines of degree of polymerization larger than 10 were
purchased from Sigma. All the other common chemicals are of research or
analytical grade.Measurements
90 degree light scattering
measurements were performed using a Perkin-Elmer LS-5B luminescence
spectrometer. Different settings of wavelength, slit combination, and
sample cuvettes of several dimensions and geometries were explored to
find experimental conditions with sufficient signal and minimal
multiple scattering. The instrumental settings altered the magnitude of
the signals but not the concentrations of cations at which scattering
changes were evident. We initially chose 365 nm excitation and 375 nm
emission to avoid reflective signals, and slit widths of either 3 nm (Fig. 1, Fig. 3, and Fig. 6) or 5 nm (Fig. 2, Fig. 7, and Fig. 8) for both beams.
Another frequently used setting was 365 nm/370 nm wavelength and 3 nm/3
nm slit width ( Fig. 4and Fig. 5). High-UV transparent
plastic cuvettes of 10 
5-mm inside dimensions were used for
600-µl samples of low actin concentrations (0.1-1.0 mg/ml).
Smaller glass tubes of 6 mm diameter were used for more concentrated
samples in order to avoid the saturation of light scattering signals (Fig. 3). Square cuvettes (10 10 mm) and a 1200-µl
sample volume were used to generate the data of Fig. 6b. Polycations and nucleoside phosphates were
prepared as stock solutions at neutral pH at least 20 times more
concentrated than required in the final mixtures. Dilution effects
which amounted to less than 5% were ignored.
. 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.
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.
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.
and
Lys
. The scattering intensity readings were roughly 0.07
for the three identical samples, prior to additions of the respective
peptides.
) at four salt
conditions. b, variation of the bundling onset concentrations
of Co(NH) and Mnversus [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.
Bundle Formation by Metal Ions and
Polyamines
The formation of F-actin bundles is conveniently
detected by changes in light scattering. Fig. 1shows the bundle
formation of 0.5 mg/ml F-actin induced by a number of polycations. All
the polyvalent cations were added in the form of concentrated chloride
salts to ensure that the variation among these data was not
attributable to anion species. The concentration of cations needed for
the onset of bundling increases with decreased valence, indicating
weakening ability to bundle. Hexamers of arginine bundle more
efficiently than those of histidine, apparently because they carry a
higher amount of net positive charges. D- and L-lysine isomers had identical effects (data not shown). The
minimal bundling concentration of lysine hexamers (not shown) is almost
the same as that of the arginine, indicating equally complete titration
of one amine per side chain at pH 7.2. An intriguing result is that
oligohistidines are fairly efficient actin bundlers at neutral pH,
although the pK value for its side chain amine is as low as
6.5 and hence most of the side chains should be neutral. These
oligomers of histidine either have more specific binding to F-actin or
else they form small aggregates capable of bundling actin. 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.
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) .Unique Effects of Specific Cu
Deviations from the predictions of counterion
condensation reveal specific binding of cationic ligands. Bundling of
F-actin by Cu Binding is not consistent with purely
electrostatic binding. Fig. 2a shows the light
scattering measurements after sequential additions of Cu to 0.2 mg/ml F-actin in 150 mM KCl, without and with 20
mM MgCl. For this set of experiments, we used a
modified actin buffer containing 2 mM Tris at pH 7.5, 0.5
mM ATP, and 0.2 mM CaCl. This change was
necessary since Cu forms insoluble precipitates with
Hepes. It may also interact with dithiothreitol and NaN. In
the absence of MgCl, large F-actin bundles start forming at
0.4 mM Cu, a much lower value than required
for other divalent cations shown in Fig. 1. This observation may
be explained by specific binding of Cu to the C
terminus of actin with high affinity(28, 29) , causing
a reduction in the surface charge of F-actin. Although binding between
Cu and the actin C terminus is of micromolar
affinity, 0.4 mM Cu is required to form
actin bundles because an additional fraction of the charge must be
neutralized by lower affinity interactions. 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. 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.Dependence on F-actin Concentration
The amount of
polycation required to bundle different concentrations of
polyelectrolyte provides information about the affinity of the
interaction and the degree of binding required for the bundling
transition. Fig. 3a shows the increase of light
scattering when actin bundling occurs with sequential addition of
18-mers of lysine Lys to various concentrations of
F-actin. The dotted lines indicate where the scattering
signals increase steeply at low concentrations, or roughly double at
high actin concentrations. This point is selected as the concentration
of Lys required for paracrystal formation. At high actin
concentrations, the scattering intensity is relatively high prior to
any bundling activity, and the increase in scattering at the onset of
bundle formation is blunted by multiple scattering. 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.
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,
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. 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. 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%.Effects of Filament Length
Although the original
counterion condensation theory assumes filaments to be infinitely long,
we have made no attempt to conduct our measurements with extremely long
actin filament. On the contrary, small quantities (1:500 molar ratio)
of gelsolin, an actin severing protein were generally added to F-actin
in order to reduce the filament length to an average of 1.6 micron and
thereby reduce solution viscosity(30) . A systematic test of a
possible length dependence for bundling of actin by polycations was
made by varying the gelsolin:actin ratio. Fig. 4shows the light
scattering increases caused by adding Lys to 0.2 mg/ml
F-actin solution containing various amounts of gelsolin. The onset
bundling profile varies very little until the filaments contain 50
monomers (140 nm) on average. This result implies that the basic
prediction of charge condensation is applicable to cylindrical
filaments of sufficiently large aspect ratios (>20:1).Effects of Ionic Strength
A direct consequence of
the Manning theory is that the association constant, K, is a
function of the solution ionic strength, c, as shown below,
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. ) 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.Dissociation by Nucleotides and Other
Polyanions
Addition of millimolar ATP has been reported to
dissolve actin bundles formed by spermine and spermidine(4) ,
and some actin cross-linking or bundling
proteins(31, 32, 33) . A very similar
reversibility was found to apply to actin bundles formed by several of
the polycations tested. A typical example is shown in Fig. 6a for actin bundles formed by Lys.
Millimolar concentrations of nucleoside triphosphates such as ATP, CTP,
and GTP are equally efficient in dissociating actin bundles. This
reversal is consistent with competitive binding between polyanionic
nucleotides and the polycations that cause actin bundling, and does not
imply a specific binding of nucleotides to the actin filaments.
Therefore, the process may be purely electrostatic and hence
structurally nonspecific. The dependence of this effect on
electrostatic charge rather than on specific structures of nucleotides
is confirmed by the data of Fig. 6b showing that the
ability to dissolve actin bundles decreases with the number of
phosphates, and therefore the anionic charge, in adenine nucleotides.
Di(adenosine-5`)pentaphosphate and hexamers of aspartic acid dissolved
the actin bundles at even lower concentrations, due to higher anionic
valence (not shown).Bundling by MARCKS Peptide
To extend the
applicability of counterion effects to other agents that may function in vivo, experiments similar to those shown in Fig. 1were done with the actin-binding domain of the
myristoylated, alanine-rich C kinase substrate (MARCKS), a
physiologically regulated actin binding protein implicated in
cytoskeletal reorganization(34) . A peptide based on the
sequence of this domain, KKKKKRFSFKKSFKLSGFSFKKNKK, bundles F-actin,
and the bundling activity is lost upon phosphorylation or binding to
Ca/ calmodulin(34) . . 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.Bundling by Smooth Muscle Calponin
Bundling of
actin by intact proteins can also follow the predictions of counterion
condensation. The smooth muscle isoform of calponin is highly basic,
with roughly 8 net positive charges at neutral pH. It binds F-actin
with high affinity, and the binding is reversed by phosphorylation (35) . Fig. 8a shows the bundling of F-actin by
calponin at 30, 50, and 75 mM KCl. An identical experiment
with 150 mM KCl did not show a sharp increase in the light
scattering at up to 6 µM calponin. These data demonstrate
features qualitatively similar to those of cobalt hexamine shown in Fig. 5. Fig. 8b shows that the dissociation of
calponin/F-actin bundles by millimolar concentrations of ATP, ADP, and
AMP is nearly identical to the dissolution of actin-lysine bundles (Fig. 6b). The bundling of actin by the basic isoform
of smooth muscle calponin is consistent with an electrostatic mechanism
like that of other polycations.)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) .
fragments bind and bundle
F-actin(45, 46) , as well as microtubules. 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.
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.
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.]. 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. ]
is an appropriate
summation of [Lys] and
[Lys] as shown in the following
equation,
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. 
] 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.
))
We thank Dr. Terrence Tao of the Boston Biomedical
Research Institute for the gift of recombinant smooth muscle calponin,
and Rolands Vegners for the oligomers of lysine, arginine, histidine,
and aspartic acid. We also thank David J. Kwiatkowski and Thomas P.
Stossel for their critical readings.
©1996 by The American Society for Biochemistry and Molecular Biology, Inc.
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