Unexpected Like-Charge Self-Assembly of a Biguanide-

based Antimicrobial Polyelectrolyte

Afroditi Maria Zaki, Alessandro Troisi and Paola Carbone*

School of Chemical Engineering and Analytical Science, University of Manchester, Oxford Road,

Manchester M13 9PL, UK.

Department of Chemistry and Centre for Scientific Computing, University of Warwick, Coventry CV4

7AL, UK.

AUTHOR INFORMATION

Corresponding Author: paola.carbone@manchester.ac.uk

Abstract: Polyelectrolyte chains dissolved in good solvent are expected to collapse in compact

configurations in the presence of multivalent ions. Here, we show that a weakly charged, hydrophilic

polyelectrolyte containing biguanide groups self-assembles in water also in the presence of monovalent

counterions, even at low salt concentrations. The polymer assembles in a compact, ordered, hairpin-like

shape that, with increasing the ionic strength of the solution, can collapse further in three- or five-folded

structures. Neither water nor ions mediate the self-assembly which, instead, is driven by the like-charge

pairing of the biguanide units. The thermodynamics of the self-assembly show that the self-association

is enthalpically driven, isodesmic (at least at low aggregation number), and is favored by increasing salt

concentration. This unique self-assembly behavior may be linked to the well-known polymer’s

antimicrobial properties and could help in rationalizing its biological activity.

TOC GRAPHICS

Keywords: PHMB, Like-charge ion pairing, polyelectrolytes, folding, antibacterial

Polyelectrolytes (PEs) are macromolecules containing electrolyte groups that dissociate in aqueous

solutions and, releasing ions, make the polymer chain charged. Examples of such polymers include

synthetic and biological molecules (DNA or peptides) and their behavior is dominated by inter- and

intra-chain electrostatic interactions. Polyelectrolytes can assume a large variety of conformations as a

function of the solvent polarity, chain charge density and rigidity, salt concentration, temperature and

valency of the counterions.1-3 This rich conformational phase diagram is the result of the balance

between short range (Van der Waals) and long range (Coulomb) interactions between the polymer and

the counterions. Specifically, salt-induced polymer condensation is the transition from an extended

structure of the chain to a compact, ordered one that occurs upon addition of multivalent ions into the

solution. This effect is well known for DNA strands which despite being highly negatively charged,

show aggregation in the presence of multivalent ions,4, 5 but it is also common to other polyelectrolytes.6,

7 The degree of order of the compact structure depends on the degree of rigidity of the chain with toroid

or folded conformations shown by polymer with rigid or semi-flexible backbone.8 Counterion

condensation around the charged groups of the polymer backbone is often invoked to justify like-charge

aggregation and the majority of the theoretical derivations focus on the assembly of rigid highly charged

polyelectrolyte chains seen as proxy for DNA strands.9 While the inter- and intra-chain attraction

induced by multivalent ions is well documented experimentally,6, 10, 11 computationally12-14 and

theoretically,15, 16 more controversial is the effect that monovalent ions have on the chain association.9, 17-

21 Different mechanisms including depletion attractions, polymer entanglements or entropic effect of the

ions have been proposed to explain those experiments and simulations showing like-charge pairing in

presence of monovalent ions.9 In all cases, only in PEs characterized by high charge density (i.e. with a

Manning parameter ξ = λB)/b, where λB is the Bjerrum length, in water, at room temperature λB 0.7 nm,

and b is the distance between neighbouring charged monomers larger than 1)22 ion condensation, and

therefore like-charge attraction, is possible and with monovalent ions Tom et al.13 recently suggested

that ξ must exceed the value of 8 when the total charge of the monomer is 1.

In this paper we show, by means of atomistic molecular dynamics simulations, that the salt-induced

condensation can also occur in polyelectrolyte chains with low charge density (ξ 0.53) and in the

absence of multivalent ions if the monomer interactions allow for strong like-charge association. It is

important to notice here that amphiphilic polyelectrolytes (APEs)23 containing both hydrophilic and

hydrophobic blocks, constitute a different category of polymers as their self-assembly is driven by

unfavorable polymer-solvent interactions.

The polymer investigated here is polyhexamethylene biguanide (PHMB), a biguanide derivative

where each biguanide group along the chain is separated by six methyl groups (Figure 1). Such polymer

is known to possess antimicrobial activity against a wide variety of bacteria and is present in a large

group of formulated commercial products,24, 25 but the mechanism of its biocidal action is not known. In

what follows, we show that polymer chains containing biguanide groups self-assemble in ordered

compact structures even at low concentration of monovalent ions and -among other ordered

conformations- they predominantly form hairpin-like structures similar to that typical of biological

polyelectrolytes. Our simulation results are in agreement with recent dynamic light scattering

experiments showing that PHMB indeed aggregates in solution26, but propose a different self-assembly

mechanism than that of micelle formation. This aggregation behavior could be linked to the

antimicrobial activity that PHMB shows against a surprisingly wide variety of species27 and could

support a proposed recently alternative mechanism to its bactericidal properties that involves a direct

condensation with the bacterial chromosome28 rather than the most common and so far accepted

hypothesis that the polymer interacts only with the bacterial cell membrane.29

Figure 1. Chemical structure of one of the possible tautomers of a PHMB dimer.

Single chain structure and energetics. In all the simulations, the polyelectrolyte chains display a

counterintuitive behavior, as they self-assemble into ordered folded structures with the positively

charged groups facing each other. The collapse of the chains, described by the change in their radius of

gyration (Rg), occurs within a few nanoseconds after the beginning of the simulations (Figure 2). Within

few nanoseconds, the –initially extended– pentamer chain folds in a “hairpin-like” structure typical of

RNA30 or globular proteins31 and its Rg decreases from approximately 1.5 nm to 0.9 nm. The dodecamer,

can reach a similar configuration with a drop of its Rg from 2.7-3 nm to 2 nm (in agreement with the

only previous computational work reported in the literature32), but at high concentration of salt it can

further collapse reducing the Rg to around 1.0-1.6 nm with the chain forming a “three-folded” or even a

“five-folded” structure.

(a)

(b)

(c)

(d)

(a) (b)

(c) (d)

Figure 2. Top: Time evolution of the radius of gyration (Rg) of the pentamer (up) and the dodecamer

(down), at Cs = 225 mM (similar results are obtained at other salt concentrations see Figure S3). Bottom:

Selected folded and unfolded configurations of the chains.

The intra-chain (and we will see later inter-chain as well) association observed in the PHMB chain

can be related to the remarkable like-charge pairing properties demonstrated for free guanidinium ions

in previous experimental and computational studies.33-37 According to these studies, the association of

the like-charged cations stems from hydrophobic attraction which overcomes the electrostatic repulsion.

In particular, it was shown that hydrogen bonds are formed between the oxygen atoms of the water

molecules and the nitrogen atoms of the ions but not between the water and the carbon atoms (despite

their relative high charge) and therefore the cations (which have a planar symmetry) behave as

hydrophobic surfaces.35 In order to examine whether this is the case also in the present polymeric

system, the distribution of the hydrogen bonds (HBs) formed between water and the polymer chain was

investigated. To identify a HB, we used a geometrical criterion similar to that employed by Karimi et

al.38 which includes the distance between the water oxygen atom (acceptor) and a hydrogen of the

biguanide group (dH···O) and the value of the donor-hydrogen-acceptor planar angle (N−H∙∙∙O). This

calculation has been repeated for both the biguanide groups (Bgd+) in the unfolded chain and those

paired in a folded one to see whether the HBs’ arrangement is visibly affected by the intra-chain

association (Figure 3). The densely populated cluster of data points at short dH···O distance (smaller than

0.2 nm) and angles (ϕ) larger than 150˚ satisfies the typical requirements of HB formation,38 verifying

the presence of a HB network around the Bgd+ group of the polyelectrolyte and is in agreement with

similar geometrical values that have been found for the HBs formed by the guanidinium ions in aqueous

solution.35 The points in the plot that correspond to smaller angles and larger distances represent the

water molecules that are in the vicinity of the biguanide groups, but are not hydrogen-bonded to them.

The two plots of Figure 3a show that the structure of the hydrogen-bonded water molecules is not

affected by the folding of the chain since the two scattered plots are almost identical. Indeed, our

simulations show that neither water molecules nor ions are present between the paired cationic groups

and that the hydrogen-bonded water molecules are organized in the same plane of the biguanide groups

and therefore their arrangement is not affected by the folding. Figure 3b reports the distribution of the

cosine of the angle (ϕ) formed by the vectors connecting the centers of mass of two paired biguanide

groups with either the oxygen of the water molecules or a Cl- counterion. In the calculations only water

molecules and counterions closer than the distance corresponding to the second minimum of their RDFs

(0.52 nm for the water molecules and 0.56 nm for the Cl -, see Figure S4) to the center of mass of at least

one biguanide group (Bgd+CoM) are included. Figure 3c shows the dihedral angle distribution for the N-

C-N-C and the N-C-N-H backbone dihedrals of the biguanide, as well as the distribution of the C-N-

H···O dihedral angles for all the water molecules that form HBs with the Bgds+.

(a) (b) (c)

Figure 3. (a) the N-H∙∙∙O angles against the H∙∙∙O distance for all the water oxygen atoms. Calculations

performed on a folded (top) and an unfolded (bottom) dodecamer chain at Cs = 150 mM; (b)

distributions of the cosine of the angle (ϕ) calculated between the centers of mass of the paired

biguanides dBgd+

CoM and the oxygen atoms of the water molecules (solid black line) and the Cl- ions (red

dashed line), where dBgd+

CoM−Owater < 0.52 nm and dBgd+

CoM-Cl- < 0.56 nm, at Cs = 150 mM; (c) probability

distribution of the N-C-N-C and the N-C-N-H dihedral angles of the Bgd+ and the C-N-H···O dihedral

angles for all the hydrogen-bonded water molecules.

The plots show that the biguanide group is planar and that the highest probability of finding a water

molecule in its proximity is in the equatorial region (ϕ between 90˚ and 70˚) of the biguanide plane.

Calculating the number of HBs in both the folded and unfolded state for the pentamer and the

dodecamer chains (Table 1), we find that, on average, around 4.5 water molecules are hydrogen-bonded

to each biguanide group irrespectively to whether the chain is folded and to the salt concentration. This

indicates that not all the six hydrogen atoms of the Bgd+ form separate hydrogen bonds with the water.

Indeed as Figure 3b and 3c show, the counterions condense on the same plane occupied by the water

molecules and therefore compete with them to form a HB with the Bgd+ hydrogen atoms available (in

agreement with what has been observed for the guanidinium solutions35). It is important to note here that

the fact that the number of HB does not change upon folding implies that PHMB is soluble in water and

that the self-assembly is not driven by poor solubility (i.e. water is a good solvent at this temperature as

shown experimentally26).

The folding of the polyelectrolyte chain and the pairing of the biguanide groups is driven by the

“hydrophobicity” of the carbon surface of the biguanide groups, as the hydrophilic (i.e. carrying positive

partial charges) carbon atoms do not form hydrogen bonds with the water and therefore assume a

hydrophobic behavior (water cannot wet the molecule surface). Figure 4 shows how when the transition

from the extended to the folded state takes place (for example at 20 and 50 ns, see for the structural

changes at these times in Figure 2), as expected the polymer-polymer electrostatic energy component

increases of approximately 60 kJ·mol-1, but at the same time the Lennard-Jones (LJ) polymer-polymer

energy component decreases of around 180 kJ·mol-1. The plots of Figure 4 refer to the pentamer and the

dodecamer in a specific salt concentration (225 mM), but similar results are obtained for any other ion

concentration.

Table 1. Number of hydrogen bonds per Bgd+ calculated for the pentamer and the dodecamer

considering dHO 0.2 nm and ϕ 150˚ (see text). Values have been averaged over 3 ns and include

different folded structures.

Cs [mM] folded structure unfolded structurePentamer

0 4.9 0.5 5.2 0.575 4.6 0.4 5.0 0.4150 4.7 0.4 5.2 0.5225 4.2 0.4 4.9 0.5300 4.7 0.5 4.7 0.4

Dodecamer

0 4.5 0.6 4.0 0.775 4.6 0.6 4.2 0.7

150 4.0 0.6 4.2 0.7225 3.6 0.6 4.4 0.7300 4.1 0.6 4.8 0.7

A better understanding of the amount of energy gained per biguanide group during the folding can be

estimated using the simulations performed on the pentamer where, due to the short chain length, the

polymer folds only in hairpin-like structures. In this case, the chain contains only five biguanide groups

and only two like-charge pairings can be formed. Monitoring the short-range polymer-polymer LJ and

Coulomb interactions it is possible to observe the respective variations when the chain folds. The

folding reduces the LJ interactions by around 50-60 kJ·mol-1 and increases the electrostatic interactions

by around 12-19 kJ·mol-1. Since in the pentamer only two pairs can be formed and in the dodecamer six

are allowed, we can estimate that the gain in the LJ energy and the increase in the Coulomb one when

two biguanide groups pair are approximately −25 kJ·mol-1 and 10 kJ·mol-1, respectively.

Figure 4. Time evolution of the Lennard-Jones (upper panel) and the Coulomb (lower panel) energy

components for the polymer-polymer interaction calculated for the PHMB pentamer (left) and the

PHMB dodecamer (right) at Cs = 225 mM. In grey the instantaneous values saved every 20 ps, in red

(LJ) and cyan (Coulomb) the running averages with an average length of 150 data points.

Free energy of association. The effect of the ion concentration on the chain folding mechanism can be

quantified calculating the free energy of association (ΔG) of two separate dimers. The free energy

profile presented in Figure 5 shows that the ion concentration slightly increases the free energy barrier

for dissociation (see Table 2). This result agrees with the fact that at high ionic strength the chain can

fold in very compact shape and folding seems to be irreversible (in the time scale of our simulations). 39

Again when the oligomers are associated no water molecules or ions could be found in between the pair.

Table 2. Free energy of association, enthalpy (internal energy) and entropy (multiplied by the

temperature, 293 K) calculated for 1+1 PHMB dimers and for 2+1 PHMB dimers at different salt

concentrations.

Cs [mM] ΔG [kJˑmol-1] ΔH [kJˑmol-1] −¿TΔS [kJˑmol-1]Two dimers (1+1)

0 −¿4.9 0.5 −¿35.3 25.5 30.4150 −¿7.0 1.2 −¿36.3 25.4 29.3300 −¿8.2 1.1 −¿39.9 25.9 31.7

Three dimers (2+1)0 −¿5.0 0.9 −¿36.6 11.1 31.6

150 −¿5.9 0.9 −¿33.3 11.3 27.4300 −¿7.8 0.9 −¿36.3 11.3 28.5

Looking at the various interactions that contribute to the chains’ association (Figure S5), we notice

again that upon association the polymer-polymer Coulomb potential increases of an amount (+20

kJ·mol-1 ca.) that is almost independent of the ion concentration. Similar increase is shown by the LJ

potential calculated between the polymer and the water molecules. The polymer-polymer LJ potential

(−50 kJ·mol-1) together with the Coulomb one calculated between the polymer and counterions (−30

kJ·mol-1) are the interactions responsible for the drop in free energy when the chains associate. In

particular the latter contribution is higher for high ion concentrations. This indicates that an increase in

the ionic strength of the solution increases the number of counterions around the polymer and, screening

the polymer charge groups, favors chain association. This can be also observed from the calculation of

the chloride-carbon RDF that shows that ion condensation occurs at high ionic strength and that the

number of counterions condensing around the biguanide groups is higher in the folding state than in the

unfolded one (Figure S6 and S7). This latter observation shows also that, probably due to the

localization of the polymer charges, folding favors ion condensation.

Figure 5 also indicates that the chain association, at least at low aggregation number, is an isodesmic

process40 where the ΔG values, within their errors, show the same increment regardless of the number of

PHMB oligomers that associate. Calculating the enthalpy (ΔH) (assumed to be equal to the total internal

energy) and the entropy (ΔS) of association from the PMF profile, we see that the self-assembly

mechanism is enthalpically driven and that with increasing the ion concentration, while the (positive)

entropic contribution to the free energy does not change, the enthalpy increases. This is another feature

that differentiates the physics of association in these polyelectrolytes from multivalent-salt induced

condensation where upon association (and ion concentration) the entropy of water and ions increases.2, 41

0.5nm

2nm

0.25nm

2nm

Figure 5. Free energy of association (PMF) calculated for 1+1 PHMB dimers (top) and for 2+1 PHMB

dimers (bottom), at different ion concentrations.

Multiple chains association. Polyelectrolyte aggregates in 1:1 salt solutions have been reported

experimentally. In these studies, however, the ratio of assembled to non-assembled chains is very small

and the aggregates disappear in the presence of excess salt.42 The simulations performed on multiple-

chain systems here reveal simultaneous intra- and inter-chain association, which, contrary to what seen

in experiments with other PEs, is enhanced by high ionic strength, as this behavior is the most

predominant in the systems with Cs = 300 mM, with three out of four chains forming a cluster, in the

time scale of the simulation (Figure S8).

In summary, we have found that the very widely used and commercially available biocide PHMB is

the first example of loosely charged polyelectrolyte that self assembles in a good solvent in the presence

of monovalent ions. The self-assembly leads to ordered structures where the charged biguanide groups

almost face each other and which resemble the intermediate conformations shown by proteins in the

early stages of fibrils formation.31 The self-assembly is enthalpically driven and the underlying

mechanism appears to be isodesmic, indicating that large aggregates could be formed. The resulting

clusters become more stable at high salt concentrations and are soluble in water at least as much as the

unfolded chains (they present the same number of HBs and both Coulomb and Lennard-Jones polymer-

water energy components remain negative) and therefore phase separation should not occur upon

folding. This unique behavior is due to the experimentally known like-charge association of the

guanidinium in water solution and could provide a mechanistic explanation for the antibacterial activity

shown by PHMB against an unusual wide variety of bacteria. Indeed recent experimental data28 shows

that unlike other antimicrobial polycations that kill bacteria by disrupting their membrane after binding

to it, PHMB crosses the microbial (as well as mammalian) cellular membrane and condenses with the

bacterial chromosome. Since our simulations show that PHMB forms in water a compact, regular, stable

and water/ion impermeable nano-object we can hypothesize that its mechanism of interaction with the

lipid membrane is similar to that observed for positively charged nanoparticles or cell penetrating

peptides.43-45 Further simulations and experiments are needed to confirm this hypothesis. It is also worth

noting that it is not guaranteed that all the biguanide-based polymers show this peculiar behavior, as it is

possible that an optimal distance between the charged biguanide groups along the chain is needed to

allow for self-assembly. These results open up the possibility of using PHMB also for applications other

than antimicrobial solutions, such as structural materials or for nanopattering of surfaces.

Supporting Information

Computational details on the model employed for the polyelectrolyte and the simulations performed

as well as additional supporting figures.

Notes

The authors declare no competing financial interest.

Acknowledgements

The authors thank Professor Steve Yeates for providing the initial experimental data and Professor

Andrew Masters for useful discussion on the fundamental nature of the polyelectrolytes. We thank the

Computational Shared Facility (CSF) of the University of Manchester as well as the N8 HPC Centre of

Excellence, coordinated by the Universities of Leeds and Manchester for the computing time. This work

has been sponsored by the Leverhulme grant number RPG-2013-246.

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