Molecular Dynamics Simulations of Polyelectrolyte-Polyampholyte Complexes. Effect of
Solvent Quality and Salt Concentration
Junhwan Jeon† and Andrey V. Dobrynin*,‡,§
Department of Chemical Engineering, Vanderbilt UniVersity, NashVille, Tennessee 37235, and Department of
Physics and Polymer Program, Institute of Materials Science, UniVersity of Connecticut,
Storrs, Connecticut 06269-3136
ReceiVed: July 7, 2006; In Final Form: September 25, 2006
Complexation between polyelectrolyte and polyampholyte chains in poor solvent conditions for the
polyelectrolyte backbone has been studied by molecular dynamics simulations. In a poor solvent a
polyelectrolyte forms a necklace-like structure consisting of polymeric globules (beads) connected by strings
of monomers. The simulation results can be explained by assuming the existence of two different mechanisms
leading to the necklace formation. In the case of weak electrostatic interactions, the necklace formation is
driven by optimization of short-range monomer-monomer attraction and electrostatic repulsion between
charged monomers on the polymer backbone. In the case of strong electrostatic interactions, the necklace
structure appears as a result of counterion condensation. While the short-range attractions between monomers
are still important, the correlation-induced attraction between condensed counterions and charged monomers
and electrostatic repulsion between uncompensated charges provide significant contribution to optimization
of the necklace structure. Upon forming a complex with both random and diblock polyampholytes, a
polyelectrolyte chain changes its necklace conformation by forming one huge bead. The collapse of the
polyelectrolyte chain occurs due to the neutralization of the polyelectrolyte charge by polyampholytes. In the
case of the random polyampholyte, the more positively charged sections of the chain mix with negatively
charged polyelectrolyte forming the globular bead while more negatively charged chain sections form loops
surrounding the collapsed core of the aggregate. In the case of diblock polyampholyte, the positively charged
block, a part of the negatively charged block, and a polyelectrolyte chain form a core of the aggregate with
a substantial section of the negatively charged block sticking out from the collapsed core of the aggregate. In
both cases the core of the aggregate has a layered structure that is characterized by the variations in the
excess of concentration of monomers belonging to polyampholyte and polyelectrolyte chains throughout the
core radius. These structures appear as a result of optimization of the net electrostatic energy of the complex
and short-range attractive interactions between monomers of the polyelectrolyte chain.
1. Introduction
Electrostatic interactions control molecular process in different
areas of natural sciences ranging form biophysics to materials
science.1-5 For example, electrostatic attractions between
negatively charged DNA and net positively charged histones
are responsible for the packaging of DNA into chromosomes.2,6-8
The complexation of DNA with positively charged polyelec-
trolytes, dendrimers, colloidal particles, and liposomes facilitates
the uptake of the DNA through the cell membrane and is utilized
for gene therapy.4 Electrostatic interactions between multivalent
ions and DNA molecules, actin filaments, and tobacco mosaic
viruses are the driving forces behind their assembly into compact
bundle structures.7,9-21
Electrostatic attraction between oppositely charged macro-
molecules is a foundation of the electrostatic assembly technique
that allows fabrication of multilayer films from synthetic
polyelectrolytes, proteins, DNA, nanoparticles, etc.5,22,23 A
typical experimental procedure involves exposure of a solid
substrate to dilute solutions of positively or negatively charged
species for a period of time optimized for their adsorption
followed by a rinsing step to remove all loosely adsorbed
material. Further film growth is achieved by alternating deposi-
tion of polyanions and polycations from their solutions. Inside
the film oppositely charged molecules form complex-like
multichain aggregates.5
The electrostatic driven complexation between oppositely
charged macromolecules in solutions is utilized for protein
separation.3,4,8,24 In this case, flexible synthetic polyelectrolytes
are added to aqueous protein solutions. Polyelectrolytes form
complexes with proteins, which then precipitate from the
solution. The binding between polyelectrolytes and proteins
occurs in such a way that oppositely charged amino acids on
the protein are close to the polyelectrolyte backbone, causing
an electrostatic attraction between the two and resulting in the
so-called polarization induced attraction mechanism for complex
formation.25 The electrostatic nature of association between
polyelectrolytes and proteins is supported by the strong effect
of pH and salt concentration on the complex stoichiometry and
structure.3,4,8 Another factor that can influence the affinity
between proteins and polyelectrolytes is the counterion release
* Address correspondence to this author. E-mail: avd@ims.uconn.edu.
† Vanderbilt University.
‡ Department of Physics, University of Connecticut.
§ Polymer Program, University of Connecticut.
24652 J. Phys. Chem. B 2006, 110, 24652-24665
10.1021/jp064288b CCC: $33.50 © 2006 American Chemical Society
Published on Web 11/10/2006

from the polyelectrolytes. For example, if net positively charged
proteins with an excess of the positively charged amino acid
groups over negatively charged ones bind to anionic polyelec-
trolytes, the positively charged groups of the protein partially
neutralize the polyelectrolyte charge allowing the release of
counterions that reduce the charge of the polyelectrolytes in
the absence of the proteins.3,4 Substitution of the counterions
by positively charged groups of the protein provides an
additional entropic contribution to complex binding free energy.
Over the years molecular simulations of polyelectrolyte-
protein (polyampholyte) mixtures were very helpful in elucidat-
ing factors controlling complex formation.25-31 However,
previous molecular simulations have ignored the effect of the
solvent quality for the polyelectrolyte backbone on the com-
plexation between polyampholyte and polyelectrolyte chains.
Solvent quality for the polymer backbone plays an important
role in determining the structure of a polyelectrolyte chain in
solution. Polyelectrolytes in a poor solvent form a necklace-
like structure of beads connected by strings of monomers.32-41
This structure optimizes contributions of the short-range mono-
mer-monomer and electrostatic interactions. As polymer
concentration increases, the fraction of the condensed counter-
ions on the chain increases and the chain shrinks by decreasing
the length of the strings and number of beads per chain.39-41
Thus, condensed counterions reduce effective charge on the
polyelectrolyte chain altering its conformation. A similar effect
on chain conformation can be achieved either by changing the
salt concentration or by adding polyampholyte chains to the
solution. In the former case, the increase of the salt concentration
lowers the entropic penalty for counterion localization near the
polyelectrolyte backbone. In the later case, complexation of the
polyampholyte chain with a polyelectrolyte leads to neutraliza-
tion of the polyelectrolyte charge. In both cases, the reduction
of polyelectrolyte charge triggers conformational transformations
in the polyelectrolyte chain. In this paper we use molecular
dynamics simulations to study the effect of the salt concentration
and the strength of the electrostatic interactions on conformations
of a polyelectrolyte chain in poor solvent conditions for the
polymer backbone and its complexation with symmetric polyam-
pholytes of net zero charge.
2. Model and Simulation Details
We performed molecular dynamics simulations of complex-
ation between hydrophobic polyelectrolyte (PE) and polyam-
pholyte (PA) chains. Both chains are modeled as bead-spring
chains of charged Lennard-Jones particles with diameter ó and
consisting of NPE ) 187 and NPA ) 186 beads. Every third
bead on the polyelectrolyte chain is carrying a negative
elementary charge, -e. This corresponds to the fraction of
charged monomers, f, on the polymer backbone equal to f )
1/3. All beads of polyampholyte are positively or negatively
charged with the net polymeric charge being equal to zero. We
studied polyampholytes with random (RPA) and diblock charge
sequences along the polymer backbone.
The connectivity of beads into polymer chains is maintained
by the finite extension nonlinear elastic (FENE) potential
where kspring is the spring constant set to be kspring ) 7kBT/ó2
and the maximum bond length is Rmax ) 2ó, kB is the Boltzmann
constant, and T is the absolute temperature.
Electrostatic interaction between any two charged particles
bearing the charge valences qi and qj, and separated by a distance
rij, is given by the Coulomb potential
The strength of the electrostatic interactions is determined by
the value of the Bjerrum length lB ) e2/kBT, which is defined
as the length scale at which the Coulomb interaction between
two elementary charges e in a dielectric medium with the
dielectric constant  equal to the thermal energy kBT. For
example, the Bjerrum length is about 7 Å in water at room
temperature, 298 K. In our simulations, the value of the Bjerrum
length lB is equal to 1ó, 2ó, and 3ó. The system electroneutrality
is maintained by adding monomer-like counterions to compen-
sate for each charge on the polyampholyte and polyelectrolyte
chains. In addition to counterions we have also added salt ions
with concentration varying between 0 and (1.25  10-3)ó-3.
Zero salt concentration means that there are only counterions
in the systems. All charged particles in our simulations are
monovalent ions with valence qi ) (1.
In addition to electrostatic interactions both charged and
uncharged particles in the system interact through the truncated-
shifted Lennard-Jones potential
where rij is the distance between two interacting ith and jth
beads, ó is the bead diameter, which is chosen to be the same
regardless of the type of beads, and rcut is a cutoff distance
beyond which the interactions are ignored. The interaction
parameters for LJ interactions are summarized in Table 1. The
choice of the LJ parameters for the polyelectrolyte and polyam-
pholyte chains corresponds to poor and ı solvent conditions
for the polyelectrolyte and polyampholyte backbones, respec-
tively.
Simulations are carried out in a constant number of particles,
constant volume, and constant temperature (NVT) ensemble
with periodic boundary conditions and simulation box size
L ) 123.2ó. This corresponds to a polyelectrolyte concentration
c ) 10-4ó-3. The electrostatic interactions in our simulations
are calculated by the Particle-Particle Particle-Mesh (P3M)
method42-44 implemented in LAMMPS,45 which takes into
account electrostatic interactions with all periodic images of the
system.
The constant temperature is maintained by coupling the
system to the Langevin thermostat.45 In this case, the motion
of beads in the system is described by the following equation
UFENE(r) ) -0.5kspringRmax2 ln(1 - r2Rmax2) (1)
TABLE 1: Interaction Parameters Used in Simulations
pairs LJ (kBT) rcut (ó)
PE monomer-PE monomer 1.5 2.5
PA monomer-PA monomer 0.35 2.5
PE monomer-PA monomer
x
(1.5  0.35) 2.5
PE monomer-counterion 1.0
x
6 2
PA monomer-counterion 1.0
x
6 2
counterion-counterion 1.0
x
6 2
UCoul(rij) ) kBT
lBqiqj
rij
(2)
ULJ(rij) ) {4LJ[(órij)12 - (órij)6 - ( órcut)12 + ( órcut)6] r e rcut0 r > rcut
(3)
m
dVbi(t)
dt ) FBi(t) - ŒVbi(t) + FBi
R(t) (4)
Polyelectrolyte-Polyampholyte Complexes J. Phys. Chem. B, Vol. 110, No. 48, 2006 24653