Supramolecular Assemblies of Lipid-Coated Polyelectrolytes

Article pubs.acs.org/Langmuir

Supramolecular Assemblies of Lipid-Coated Polyelectrolytes Guillaume Tresset,*,† Yves Lansac,†,‡ and Guillaume Romet-Lemonne§ †

Laboratoire de Physique des Solides, Université Paris-Sud, CNRS, 91405 Orsay, France GREMAN, Université François-Rabelais, CNRS, 37200 Tours, France § Laboratoire d’Enzymologie et Biochimie Structurales, Centre de Recherche de Gif, CNRS, 91198 Gif-sur-Yvette, France ‡

ABSTRACT: We reveal the existence of a general class of supramolecular assemblies made up of lipid-coated polyelectrolytes including the celebrated lipid−nucleic acid complexes. With the aid of high-resolution cryo-electron microscopy, we unveil the nanoscale internal organization of assemblies generated with a wide range of synthetic and biological polyelectrolytes, several of them being investigated in this context for the first time, namely, poly(styrene sulfonic acid), carboxylmethylcellulose, and filamentous actin. Using an original coarse-grained model representing lipid-coated polyelectrolytes as semiflexible tubes, we thoroughly explored the morphologies resulting from the self-assembly process as a function of tube lengths and rigidities; the computed structures are fully consistent with the experimental observations. In particular, we found a strong extension of the correlation range of the order parameter as the rigidity of the lipid-coated polyelectrolytes increases. Electrostatic interactions provide a stabilizing mechanism leading to finite-size equilibrium assemblies. These assemblies may constitute a generic route for interfacing polyelectrolytes to living cells to perform gene delivery, for instance.

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INTRODUCTION If lipids constitute the building blocks of cell membranes, they are also at the origin of numerous supramolecular assemblies formed in vitro.1 Because of their amphiphilic nature, they hold the remarkable propensity to self-assemble into complex structures in solution. In particular, they can be associated with virtually any organic or inorganic material, provided that either an attractive interactioneven weak in magnitudeor a covalent bonding is involved. In that framework, a number of polymers and nanomaterials have been investigated lately in combination with lipids: carbon nanotubes,2 peptidic nanocrystals,3 actin filaments,4 microtubules,5,6 rodlike polymerized surfactant nanoparticles,7 and, very importantly, nucleic acids.8−12 Apart from the viewpoint of synthesizing novel hierarchical materials, lipids offer the advantage of interfacing molecules and nano-objects to living cells, a special emphasis being given on delivery and labeling applications. For this reason, lipid−nucleic acid complexes are among the most efficient methods to transfer genes into cells via endocytosis.13 Once inside the endosome, complexed lipids are able to fuse with the compartment membrane and release nucleic acids into the cytoplasm.14 A particularly efficient supramolecular structure for transfection purposes is the HIIC phase formed by these complexes:15 nucleic acids are arranged on a hexagonal lattice and are coated by a monolayer of lipids whose alkyl chains are pointing outward. Even though the supramolecular structure is now widely deemed critical for efficient interfacing to cells,13,16,17 very little is known on the three-dimensional morphology of assemblies, and especially those made of lipid-coated nucleic acids. Indeed, the hexagonal arrangement resulting from the close-packing of lipid-coated nucleic acids is generally inferred from X-ray diffraction on high volume fraction samples in order to get a reasonable signal-to-noise ratio. Yet, for delivery purposes, © 2012 American Chemical Society

assemblies have to be small enough to diffuse within tissues or to escape from blood vessels.18 Furthermore, the structural information provided by X-ray diffraction experiments is averaged over all the assembly orientations, preventing from drawing firm conclusions at the level of a single assembly. Monte Carlo and molecular dynamic simulations have enabled to gain a finer insight into the molecular structure and highlighted a certain degree of disorder.9,19,20 Nonetheless, the access to the full three-dimensional morphologies remains impeded by a prohibitive computational cost. In this paper, we show that lipid−nucleic acid complexes in HIIC phase actually belong to a general class of supramolecular assemblies made of lipid-coated polyelectrolytes. For the first time, we have conducted an experimental study with various polyelectrolytes having a wide range of lengths and rigidities, including but not limited to synthetic polymer, polysaccharide, and filamentous actin. High-resolution cryo-electron microscopy reveals the internal structure of the assemblies with an unprecedented level of molecular detail. The three-dimensional morphologies of these assemblies are predicted by an original model of semiflexible self-assembling tubes. This approach allows us to gain a quantitative understanding of the threedimensional structural order and on the role of electrostatics in stabilizing the clusters to finite sizes. We first present high-resolution cryo-electron micrographs of assemblies formed with double-stranded nucleic acids having identical rigidities and charge densities but different lengths. Assemblies formed with two polyelectrolytes much more flexible and one by far stiffer are then detailed. For comparison with the experimental observations, the coarse-grained model Received: October 14, 2011 Revised: March 1, 2012 Published: March 19, 2012 5743

dx.doi.org/10.1021/la2048135 | Langmuir 2012, 28, 5743−5752

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representing a lipid-coated polyelectrolyte as a tube (see Scheme 1) is introduced, and the morphologies of the resulting Scheme 1. Coarse-Grained Model of a Lipid-Coated Polyelectrolytea

a

On the left is a polyelectrolyte (in blue) wrapped into an inverted monolayer of lipids (headgroup in red and tail in gray). On the right is a tube model where the orange part depicts lipidic components and the blue one represents the polyelectrolyte; this distinction is for clarity only, the tube interior does not play any role in practice.

clusters are given as a function of the length and rigidity of the tubes. The crystallization of the tubes and the correlation range of order present in the clusters are investigated before considering the role of electrostatic interactions.

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RESULTS AND DISCUSSION

Figure 1 shows a series of high-resolution cryo-electron micrographs obtained with supramolecular assemblies made of double-stranded DNA. In the entire study herein, lipids consisted of a binary mixture of cationic 1,2-dioleoyl-3trimethylammonium-propane (DOTAP) and zwitterionic 1,2dioleoyl-sn-glycero-3-phosphoethanolamine (DOPE) in a molar ratio of 25/75% known to form a columnar hexagonal HIIC phase upon association with DNA.15 The assemblies were obtained upon mixing lipids in the form of small unilamellar vesicles with DNA in desired lipid-to-DNA charge ratios ρ. Figure 1A gives the electrophoretic mobility of λ-DNA-based assemblies as a function of ρ. For ρ < 1 (excess of DNA), the assemblies had a negative electrophoretic mobility, whereas for ρ > 1 (excess of cationic lipids), the electrophoretic mobility became sharply positive. Around ρ = 1, the solution was turbid indicating the presence of large aggregates hindering any reliable measurement. We chose to work preferentially at 1 ≤ ρ ≤ 3 so that no free polyelectrolyte remained in solution. Figure 1B provides a typical example of a supramolecular assembly made of lipid-coated λ-DNA with a size of about 200−250 nm. The dark spots correspond to the phosphate groups located both on DNA and on lipid headgroups and which are denser to electron than the alkyl chains of lipids. Obviously, the DNA chains surrounded by lipids were fairly ordered and locally formed close-packed hexagonal structures (see magnified view in the inset). The degree of order is even more visible in Figure 1C which was obtained with 146-bp DNA. Note that λ-DNA has 48 502 base pairs and is thereby ∼16 μm long, while 146-bp DNA is much shorter with a length of 52 nm. As in Figure 1B, large areas of hexagonal structures (see upper right panel) corresponding to cross-sectional views of closely packed lipidcoated DNA are present. 2D Fourier transform (see the inset) confirms the hexagonal arrangement and gives a lattice spacing of ∼64 Å, which is consistent with the diameter of a doublestranded DNA rod (∼20 Å) plus the thickness of a lipid bilayer (∼45 Å). At some other locations, striations are visible (see lower right panel). It is the same hexagonal lattice of lipidcoated DNA but seen from the side in such a way that the

Figure 1. Supramolecular assemblies of lipid-coated double-stranded DNA. (A) Electrophoretic mobility of assemblies made of λ-DNA, at various lipid-to-DNA charge ratios ρ. The schematic represents the cross section of a DNA molecule (in green) surrounded by an inverted monolayer of lipids (hydrophilic head in red and hydrophobic tail in gray). (B) Assembly of lipid-coated λ-DNA at ρ = 2.0. (C) Detailed view of an assembly of lipid-coated 146-bp DNA at ρ = 1.0. The inset shows the 2D Fourier transform of the region enclosed in the upper square. The panels on the right are magnified views of the regions enclosed in both squares. (D) Detailed view of another assembly of lipid-coated 146-bp DNA at ρ = 2.0. (E) Large aggregate of lipidcoated λ-DNA at ρ = 1.0. Scale bar is 80 nm. (F) Small assembly of lipid-coated 146-bp-DNA at ρ = 3.0. Scale bar is 50 nm. Unless stated otherwise, scale bars are 60 nm for main panels and 30 nm for magnified views. The microscope defocus is −6.0 μm for all of the micrographs.

spacing corresponds to the distance between planes formed by lipid-coated DNA rods, namely, (√3/2)a where a is the hexagonal lattice spacing. The striations have a consistent spacing of ∼59 Å. It is worth mentioning that no structural differences were observed between assemblies formed with λDNA and 146-bp DNA despite their huge difference in length. Figure 1D illustrates the fact that lipid-coated DNA was often bent over distances shorter than the persistence length of bare double-stranded DNA (∼50 nm). The assemblies are not straight bundles with a hexagonal cross section as sometimes represented in the literature. Instead, they have internal flexibility and therefore multiple orientations which give rise to many structural defects with respect to a perfect hexagonal organization. Figure 1E depicts a large aggregate of lipid-coated DNA that extends over hundreds of nanometers. It was obtained at the isoelectric point, namely, at ρ = 1.0. In contrast, by increasing the lipid-to-DNA charge ratio, assemblies tended 5744


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to be smaller while keeping their internal ordering as shown in Figure 1F with an assembly formed at ρ = 3.0. The high resolution and the sharpness of the details obtained on these micrographs result from a strong defocus and from the numerical correction of the microscope contrast transfer function (CTF). A defocus of −6.0 μm often used in this paper allowed us to enhance the spatial wavelengths in the nanometer range and especially those above 30−50 Å corresponding to the spacings of hexagonal lattices. The CTF correction enabled further contrast on the ordered structures and reduced the background noise.21 We considered the special case of small interfering RNA (siRNA) consisting of a short double-stranded RNA with about 21 base pairs (∼7.1 nm long). siRNA has attracted a lot of attention since the recent discovery that its cytoplasmic delivery induces gene silencing,22,23 which has motivated major efforts to design lipid-based delivery systems as efficient gene silencing vectors.24,25 Because its length is much smaller than its persistence length (∼50 nm), siRNA can be viewed as a short negatively charged rigid rod. Figure 2 displays a few

a size of about 200 nm, which is typical for efficient delivery applications. Quite surprisingly, siRNA can be longitudinally ordered over distances far exceeding its length. The arrow of Figure 2C points out striationscorresponding to the side view of a hexagonal latticethat are more than 100 nm long, that is, at least 15 siRNA molecules are stacked end to end forming straight columns. In the transverse direction, the bundle is about 90 nm. Such long-range order was not observed with long DNA, and it suggests that the shortness and the rigidity of lipid-coated siRNA play a central role in the extent of its organization. To quantify the size of organized domains on a micrograph, we computed the radially averaged and normalized autocorrelation function of an image on which a lot of striations could be identified. Figure 2D shows the autocorrelation over radial distance and compares it to an exponential decay exp(−r/ξ) with ξ the decay length. We found a decay length of 29 nm, which is larger than the decay length for assemblies made of 146-bp DNA (6.2 nm) and λ-DNA (11.2 nm).26 It therefore turns out that short and rigid lipid-coated polelectrolytes can exhibit long-range organization. Notice that the phenomenon is similar to the end-to-end stacking observed with short (≤22 bp) bare DNA and RNA duplexes leading to liquid crystal phases and caused by hydrophobic adhesion at the terminations of the nucleic acids.27,28 We also investigated the case of assemblies obtained with more flexible polyelectrolytes, i.e., whose persistence length was shorter than that of double-stranded nucleic acids. Figure 3A depicts assemblies formed with 3 MDa poly(styrene sulfonic acid) (PSS), which has a persistence length of less than 1 nm (Table 1) while its contour length is ∼4 μm. Organized structures are still present even though the degree of order is slightly weaker than with nucleic acids. The curvatures are higher but we can distinguish regular spacings (∼50 Å) that agree well with a side view of closely packed lipid-coated PSS, PSS having a diameter of 12 Å (Table 1). The effect of polyelectrolyte flexibility is more striking with carboxymethylcellulose (CMC)a polysaccharride commonly used in the food industryas depicted in Figure 3B. Although CMC has a persistence length of 12 nm (Table 1), that is, much longer than that of PSS, and a contour length of ∼400 nm, the internal structures seen within assemblies are by far more disordered. The typical separation between striations (∼60 Å) is in agreement with closely packed lipid-coated CMC chains, namely, 23 Å for CMC (Table 1) plus 45 Å for lipids multiplied by √3/2, but as revealed by the magnified view, order is rather short-ranged compared to that of assemblies obtained with double-stranded nucleic acids. In addition, we hardly observed any hexagonal arrangement probably because the correlation of orientations between monomers was too short-ranged to produce any significant order by projection. It can seem surprising that PSS-based assemblies look more ordered, whereas PSS rigidity is much lower. However, we must note that the key factor is the rigidity of the polyelectrolyte coated with its inverted lipid monolayer. The electrostatic interactions between lipid headgroups and the charges carried by the polyelectrolyte can increase the net elastic energy. Considering PSS and CMC as tubes with circular cross sections, their surface charge densities are 0.88 and 0.34 e−.nm−2, respectively. As a result, we expect stronger interactions between lipids and PSS, which, in turn, will give rise to a higher apparent rigidity of lipid-coated PSS. In the next study, we focused on a long polyelectrolyte having a persistence length much larger than its contour length

Figure 2. Supramolecular assemblies of lipid-coated siRNA at ρ = 1.0. (A) Large assembly. Upper and lower right panels are magnified views of the regions enclosed in squares. (B) Small assembly. (C) Detailed view of the internal structure of an assembly. (D) Normalized autocorrelation function versus distance after radial averaging (black line) of the micrograph in the inset. The red line is a fit by an exponential decay. Scale bars are 80 nm except in the magnified views in (A) where they are 30 nm. Microscope defocus is −6.0 μm.

micrographs showing the structure of assemblies made of lipidcoated siRNA at the isoelectric point. As with 146-bp DNA and λ-DNA, assemblies exhibit a hexagonal arrangement with a lattice spacing close to 66 Å, which is consistent with the close packing of lipid-coated siRNA rods (see Figure 2A upper right panel). Moreover, it can be seen on the lower right panel of Figure 2A that lattices exhibit various orientations in the thickness of the frozen film. Figure 2B shows an assembly with 5745


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into lipidic ribbonlike tubules4 or two-dimensional rafts by multivalent cations,30 and we demonstrate here that it can also make bundles by lipidic coating. Figure 4A depicts the helical

Figure 4. Supramolecular assemblies of lipid-coated F-actin. (A) Schematic of a filamentous actin (F-actin) made of globular actin (Gactin) monomers. (B,C,D) Assemblies obtained at ρ = 1.0. Scale bars are 80 nm. Microscope defocus is −6.0 μm.

Figure 3. Supramolecular assemblies of lipid-coated flexible polyelectrolytes. (A) Assemblies made of 3 MDa poly(styrene sulfonic acid). The chemical formula of a monomer is shown on the left panel and the assemblies on the micrograph are obtained at ρ = 2.0. (B) Assemblies made of 171 kDa carboxymethylcellulose. The chemical formula of two linked monomers is on the upper panel. R = −H or R = −CH2COONa depending on the degree of substitution. The micrographs depict assemblies at ρ = 2.0. The lower right panel is a close-up view of the region enclosed on the left panel. Its scale bar is 30 nm. Unless stated otherwise stated, scale bars are 80 nm. Microscope defocus is −4.0 μm.

structure of filamentous actin resulting from polymerization of globular actin (G-actin). The diameter of F-actin is between 5 and 9 nm and its persistence length is about 18 μm (Table 1). In our experiments, F-actin had an estimated mean contour length of ∼400 nm. Figure 4B shows a ∼200-nm-wide lipidcoated F-actin bundle having a length larger than the length of one filament. In many of our images, we could see a lot of Factin remaining free; it is due to the fact that the lipid-to-F-actin charge ratio was only 1.0, and since the surface charge density of F-actin is low (∼0.18 e−.nm−2), there were not enough lipids available to coat the whole surface of the F-actin present in solution. Figure 4C shows that bundles are not all aligned and can form entangled networks. A closer look at one bundle reveals that lipid-coated F-actins are not perfectly closely packed and that many defects exist (see arrow in Figure 4D). Although moderately long, lipid-coated F-actin misses orientational entropy that could permit it to nicely align into a hexagonal liquid crystalline structure as a consequence of the close-packing condition. The system is then trapped in a metastable state, albeit apparently not far away from equilibrium. We performed Monte Carlo (MC) simulations in order to get a deeper insight into the three-dimensional morphology and the underlying physics of these supramolecular assemblies. Because these systems are very large and involve a huge number of interactions, numerical simulations at the level of individual molecules are out of reach of present-day computers.

so that it can be considered as a long rigid rod. We selected filamentous actin (F-actin) which forms part of the cytoskeleton of all cells and which is a component of muscle fibers essential for contraction.29 F-actin can be nanostructured Table 1. Physical Properties of the Polyelectrolytes Used in This Studya polyelectrolyte

d (nm)

L (nm)

lp (nm)

σ (e−.nm−2)

λ-DNA 146 bp DNA31 siRNA31 3 MDa PSS32 171 kDa CMC33 F-actin34,35

2 2 2 1.2 2.3 5−9

16 500 52 7.1 ∼3800 ∼390 ∼400

50 50 50 0.7 12 ∼18 000

0.94 0.94 0.94 0.88 0.34 0.18

31

a

d is the diameter, L the contour length, lp the persistence length, and σ the surface charge density assuming a circular cross section. The contour lengths of PSS, CMC, and F-actin are approximates due to a slight polydispersity. 5746


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Figure 5. Morphologies of self-assembling semiflexible tubes. MC simulations are performed on M = 40 tubes with varying numbers of nodes N and persistence lengths lp/d. The lower panel shows a cross-sectional view of clusters, while the upper panel shows the entire clusters calculated for a number of nodes N = 30. The figures in green next to the clusters are the reduced RPA correlation lengths ξRPA* (see text for details).

done in polymer simulations. Instead, we adopted a more accurate representation that has been proven efficient to recover the structural motifs of proteins such as α-helices and β-sheets,37 and that has also been used to explore the fundamental properties of helices encountered in biomolecules and polymers.38,39 We therefore introduced the GonzalezMaddocks potential UGM(r1, r2, r3) between three nodes at vector positions r1, r2, and r340

Either the geometry of the system has to be simplified by limiting the degrees of freedom of the polyelectrolytes,9,19,20 or the number of interacting molecules has to be further lowered down by coarse-graining into particles capturing the main features of the system. We chose the latter option, and we modeled the lipid-coated polyelectrolytes as semiflexible tubes with a circular cross section (see Scheme 1) interacting with one another through hydrophobic force and excluded-volume repulsion. Tubes were first assumed electrically neutral, cationic lipids and counterions counterbalancing exactly the charges carried by the core polyelectrolyte; in the last section, we will discuss the case of tubes carrying a residual net charge. MC simulations were performed through the traditional Metropolis algorithm with standard translation, pivot, and crankshaft move sets.36 Tubes were added to a cluster at random position and orientation one by one after an equilibration of 105 MC steps so as to make sure the system remained close to equilibrium. Each tube consists of N nodes separated by a fixed distance δ, and referenced by a vector ri with 1 ≤ i ≤ MN, where M denotes the total number of tubes. The total energy was computed as the sum of the elastic energy Eelastic, the volume exclusion energy Eexclusion, and the shortrange hydrophobic energy Ehydrophobic. The elastic energy is given by Eelastic =

1 kBT 2

M

∑∫ i=1

tube i

⎧ rg > d /2 0 ⎪ UGM(r1, r2, r3) = ⎨ ⎪ +∞ r ≤ d /2 g ⎩

(2)

where d is the tube diameter and rg the global radius of curvature defined as the radius of the circle connecting three nodes rg =

|r1 − r2||r1 − r3||r2 − r3| 4A(r1, r2, r3)

(3)

with A(r1,r2,r3) being the area of the triangle with vertices r1, r2, and r3, and |r1 − r2| the Euclidian distance between nodes r1 and r2. Consequently, the total volume exclusion energy that prevents overlapping tubes is given by the sum of GonzalezMaddocks potentials over all of the existing nodes of every tube MN

κ 2(s) ds

Eexclusion = (1)

∑

UGM(ri, rj, rk)

i≠j≠k

where kB is the Boltzmann constant, T the temperature, lp the persistence length of a tube, κ(s) the local curvature, and s the curvilinear coordinate of tubes. Volume exclusion was not modeled as chains of self-avoiding spherical beads as is usually

(4)

A last energy term was used to mimic the attractive hydrophobic interaction arising from the lipidic alkyl chains pointing outward from the lipid-coated polyelectrolytes. There is no comprehensive theory for the hydrophobic effect, and the 5747


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cluster morphology: the larger the monomer−monomer correlation range, the more ordered and elongated the cluster is. Figure 6A gives the pair-distance distributions for cluster (N; lp/d) = (5; 290). If u is a unit vector tangential to a tube at a

most refined models applied to the hydrophobic collapse of a single chain are extremely time-consuming.41 We therefore adopted a heuristic approach in which nonbonded nodes interact via a pairwise square-well potential of depth −ε within a contact range Dc. Thereby, the short-range hydrophobic energy reads MN − 2 MN

Ehydrophobic = −ε

∑

∑

i=1

j=i+2

Θ(Dc − |ri − rj|) (5)

where the Heaviside function Θ(x) is equal to 1 if x > 0 and 0 otherwise. All the spatial quantitites were normalized to the tube diameter d. All the simulations were carried out with δ/d = 0.59, Dc/d = 0.47, and ε = 2kBT. The choice of Dc resulted from a rough estimate provided by the macroscopic theory of dewetting on a flat surface.42 Figure 5 summarizes the morphologies of self-assembled clusters formed by tubes with a number of nodes N varying from 5 to 30 and with a normalized persistence length lp/d ranging from 0.29 to 7300. It is quite remarkable to notice that the semiflexible tubes can locally crystallize and form a hexagonal arrangement resembling to the internal structure observed experimentally, especially at intermediate lp/d between 7.3 and 290 and for N = 5 and 15. A general trend is that, for a given N, clusters evolve from disordered aggregates to straight bundles via partially organized spooled bundles as lp/ d increases. At weak rigidities (lp/d = 0.29), the cluster morphology does not change with N, clusters are just scaled up. In contrast, at strong rigidities (lp/d = 7300), the cluster morphology varies from a compact globular shape for N = 5 to entangled bundles for N = 30. Also, it seems that short tubes (N = 5) start to locally crystallize from lower lp/d (∼7.3) than long tubes (N = 30). These findings are in qualitative accord with the cryo-electron microscopy observations: the hexagonal structures of the 146-bp DNA case (Figure 1) can be compared to those of cluster (N; lp/d) = (15; 7.3), the disorder of CMCbased assemblies (Figure 3) resembles that of cluster (N; lp/d) = (30; 0.29), and the entangled bundles obtained with F-actin (Figure 4) have similarities to cluster (N; lp/d) = (30; 7300). The degree of order within clusters is closely related to the density fluctuation correlations between monomers. An approximate expression for the monomer−monomer correlation length ξRPA of a semidilute polymer solution is given by the random phase approximation (RPA) theory43 ξRPA ≡

Figure 6. Pair-distance distributions of cluster (N; lp/d) = (5; 290). (A) Pair-distance distribution as a function of longitudinal and transverse distances in logarithmic scale. (B) Longitudinal component of the pair-distance distribution. The schematic represents two adjacent tubes with interacting nodes in red. (C) Transverse component of the pair-distance distribution in the lower panel. The upper panel is the same quantity computed for a hexagonal bundle as a reference. The figures are Miller indices for a hexagonal lattice.

RG

with 2(1 + ρNv) ⎡ ⎛ ⎤ ⎞ 1 L L R G2 = l p2⎢exp⎜⎜ − ⎟⎟ − 1 + ⎥ 3 ⎢⎣ ⎝ l p ⎠ l p ⎥⎦

node ri, and rj another node, then we define the longitudinal and transverse distances as r∥ ≡ |u(ri − rj)| and r⊥ ≡ |u × (ri − rj)|. The longitudinal and transverse distances were populated for every pair of nodes belonging to distinct tubes, and a pairdistance distribution P(r∥, r⊥) was inferred from the resulting histogram. The pair-distance distribution was then averaged over 1000 uncorrelated MC steps after cluster equilibration. Figure 6A exhibits several peaks characteristic of an internal order present in both the longitudinal and the transverse directions. Notice that, for (r∥/d)2 + (r⊥/d)2 < 1, P(r∥, r⊥) = 0 due to the tube avoidance effect. Figure 6B shows the pairdistance distribution averaged over transverse distances, which yields the longitudinal component of the pair-distance distribution ⟨P∥⟩. We can see several maxima regularly spaced by a distance δ/d, the first one being located at r = 1/2(δ/d). As schematized in the inset, this spacing is specific to the tube

(6)

where RG denotes the radius of gyration, ρ the monomer concentration, v the excluded volume parameter proportional to the second virial coefficient, and L ≡ Nδ the contour length. For a given monomer−monomer interaction, and so an excluded volume parameter, the correlation length in the dense regime can be reduced so that ξRPA/d ∝ ξ*RPA ≡ (RG/ (d√N)). At low persistence lengths (L ≫ lp), the reduced RPA correlation length is independent of N, ξ*RPA ≈ [(lp/d)(δ/d)/ 3]1/2, while for rigid tubes (L ≪ lp), it no longer varies with the persistence length, ξ*RPA ≈ (N/6)1/2(δ/d). The values of ξRPA* are reported in Figure 5 and illustrate their relationship with the 5748


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size. The mechanisms are identical to those involved in charged colloids with both short-range attractive and long-range repulsive pair potentials.44 Besides, upon their association with polyelectrolytes, oppositely charged lipids along with the counterions that have not been released tend to neutralize the charges carried by monomers. As a result, the net charge carried by the lipid-coated polyelectrolytes is small enough not to overcome the attractive part of the pair potential over the short range. The short-range attractive potential leads to the aggregation of tubes until the resulting net charge carried by the cluster becomes too high to overcome this electrostatic barrier. It results in a finite-size cluster comprising a number Mmin of tubes. In the absence of a net charge on the tubes, the clusters grow indefinitely (Mmin → ∞) and eventually phaseseparate with the solvent. The process is illustrated on the left panel of Figure 8, which shows the internal energy per tube E/M over MC steps. Each

model: each node tends to maximize the number of neighbors within its attractive range Dc, and a maximum of four neighboring nodes can be achieved by shifting longitudinally adjacent tubes by 1/2(δ/d). Figure 6C gives information about the transverse organization inside the cluster through the transverse component of the pair-distance distribution ⟨P⊥⟩. The upper panel gives ⟨P⊥⟩ for a bundle made of flexible tubes (N; lp/d) = (10; 0.29) initially arranged on a hexagonal lattice and evolving freely over 105 MC steps. The peaks can be indexed on a hexagonal crystal structure. As distance increases, the peaks start to be slightly shifted outward because the attractive potential was a square well and tubes were free to move from each other within the width of the well. Especially, near the edge of the cluster, the tubes are much less forced to be closely packed than at the center because of the weaker osmotic pressure. The lower panel of Figure 6C gives ⟨P⊥⟩ for the cluster of interest. It can be seen that, even if the peaks are less sharp than those in the upper panel owing to a larger disorder, they are nonetheless nicely aligned with the peaks of the reference ⟨P⊥⟩, giving clear evidence of the existence of a local transverse hexagonal arrangement, i.e., close packing. Next, we investigated the spatial range of order as a function of the persistence length of tubes. To do so, we computed the order parameter s(r) 1 s(r ) ≡ ⟨3(n i . n j)2 − 1⟩ (7) 2 between every node i and j belonging to distinct tubes and separated by a distance r = |ri − rj|, with ni and nj being unit vectors tangential to their respective tubes. The order parameter was averaged over 1000 uncorrelated MC steps. A value of 1 indicates a fully oriented system, while a null value corresponds to an isotropic system. s(r) for the set of clusters N = 30 is plotted in Figure 7. The graph shows that s(r) follows

Figure 8. Effects of electrostatics on charged clusters (N; lp/d) = (5; 290). The tubes carry a net charge per node as indicated in the legend of the left panel: no charge (black), 0.6 e− (blue), 1.5 e− (red), 2.0 e− (green), and 2.35 e− (magenta). (Left panel) Energy per tube E/M versus Monte Carlo steps as tubes are added to the clusters. Tubes are introduced every 105 steps so that the final systems are made up of 40 tubes. (Right panel) Transverse component of the pair-distance distribution versus distance for the clusters of the left panel with the number of tubes Mmin that minimizes E/M for each cluster. Mmin = 40 (black), 24 (blue), 17 (red), 14 (green), and 3 (magenta). The distributions are obtained by averaging over 106 Monte Carlo steps after equilibration.

node of the tubes carried a charge q, and a Coulomb interaction term was added to the energy of the system ECoulomb = Figure 7. Order parameter s versus distance for the clusters N = 30 at various lp/d: 0.29 (blue inverted triangles), 7.3 (cyan triangles), 29 (green losanges), 290 (red squares), and 7300 (black circles). Solid lines are exponential fits with decay lengths ζ. The inset summarizes the estimated decay lengths versus the persistence lengths of the tubes.

q2 4πεr ε0

MN − 1 MN

1 |ri − rj| i=1 j=i+1

∑

∑

(8)

where εr = 80 and ε0 denote the dielectric and electric constants, respectively. The tubes were added one by one every 105 steps so that the graph indirectly shows E/M as a function of M. The energy per tube first decreased steadily until a critical number of tubes Mmin was reachedexcept for neutral tubes which corresponded to the maximal size of a cluster for a given charge per tube. Beyond Mmin, additional tubes were not incorporated to the existing cluster yielding a rise of E/M which eventually relaxed to the mean energy of a single isolated tube as M → ∞. Mmin decreased rapidly as the charge per tube increased; clusters are therefore smaller when the tubes are more charged. The clusters kept a hexagonal structure as can be seen in the right panel of Figure 8 as the positions of the peaks of ⟨P⊥⟩ are close to those reported in Figure 6C. The only significant difference arose from the spatial extent of the

an exponential decay, which means that, beyond a certain decay length ζ, the tube orientations become uncorrelated. ζ thereby quantifies the spatial range of order within a cluster. Quite expectedly, ζ increases with the persistence length and supports the general trend that clusters are more ordered as tube rigidity is higher. Finally, the role of electrostatics on the cluster formation was studied. Electrostatics has a stabilizing effect on clusters in the sense that it prevents the addition of tubes beyond a critical 5749


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with Etube = −α + β + γ being the energy of an isolated tube. The branches b′ and b in Figure 9 give a representation of eq 10. Only the branch b is stable. Thus, the combination of the branches a and b provides a rationale of the variations of the energy per tube. If the charge per tube is increased through γ ∝ q2, the equilibrium size of clusters Mmin ∝ 1/γ ∝ 1/q2 is shifted to lower values (see upper curve of Figure 9) the more rapidly as the charge becomes high. These behaviors are in very good agreement with the results presented in Figure 8, which gives us confidence in the validity of the model encompassed by eqs 9 and 10.

distributions, which was directly correlated to the smaller size of the clusters as the charge per tube was higher. The fact that the minimum in E/M coincides with the equilibrium size of a cluster is not fortuitous. A classical result in the theory of self-assembling molecules states that, provided the entropic part of the free energy of clusters is negligible with respect to their (internal) energy, minimizing the free energy becomes equivalent to minimizing E/M.44,45 To better interpret the variations of E/M in the above MC simulations, we performed a dimensional analysis on the various contributions entering the energy. The energy E of a cluster made of M tubes is E = Eelastic + Ehydrophobic + ECoulomb. Eelastic varies as the number of tubes +M and is usually small compared to the other terms. Ehydrophobic comprises an attractive component between pairs of nodes proportional to −M and an interfacial energy penalty arising from the tubes localized at the edge of the cluster and thereby in contact with the solvent. Assuming a spherical cluster, the latter energy varies as R2, where R is the radius of the cluster, and therefore also as +M2/3. The Coulomb energy can be inferred from the self-energy of a uniformly charged sphere, which scales as Q2/R, with Q the total charge carried by the sphere, and yields ECoulomb ∝ + M5/3. Consequently, the energy per tube of a cluster reads E /M = −α + βM −1/3 + γM 2/3

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CONCLUSIONS We have demonstrated the existence of a general class of supramolecular assemblies made of lipid-coated polyelectrolytes. These assemblies exhibit a rich polymorphism parametrized by the rigidity and length of lipid-coated polyelectrolytes. We have unveiled the varying degree of order within assemblies both experimentally by high-resolution cryo-electron microscopy on a variety of flexible and stiff polyelectrolytes having different lengths and numerically by devising a remarkably efficient model of self-assembling semiflexible tubes. The model reproduced well the local hexagonal structures and revealed an increase of the spatial range of order with the rigidity of the lipid-coated polyelectrolytes. The addition of charges in the tubes resulted in equilibrium clusters made of a finite number of tubes inversely proportional to the square of the carried charges per tube. It should be noted that lipids are in liquid state, and as such, they are not strictly confined to the vicinity of polyelectrolytes. They fill the gaps inside assemblies, and they may be able to “jump” from the surroundings of one polyelectrolyte to the surroundings of another one. Therefore, the tube model should be regarded as an effective potential felt by the polyelectrolytes. Moreover, the finite-size clusters calculated by our numerical simulations should be thought of as wrapped into a lipid monolayer so as to protect the outermost alkyl chains from aqueous environment (see Scheme 2). We hope that these findings will help better control the entry and the delivery of a wide range of polyelectrolytes into cells, in particular, for gene expression and silencing applications. We envisage two future directions: the first one concerns the

(9)

with α, β, and γ positive parameters independent of M. Figure 9 depicts the variation of E/M given by eq 9 through the

Scheme 2. Proposed Structure of an Assembly of LipidCoated Polyelectrolytesa Figure 9. Energy per tube E/M as a function of the number of tubes M. The branches a and a′ are computed from eq 9, while the branches b and b′ are given by eq 10. The upper curve is obtained with an electrostatic parameter γ twice as high as that of the lower curve.

branches a and a′. The curve exhibits a minimum (d(E/M)/dM = 0) for a number of tubes given by Mmin = β/2γ corresponding to the equilibrium size of the cluster. In other words, Mmin results from a competition between the interfacial energy penalty (through β) and the electrostatic energy (through γ). Beyond Mmin, eq 9 no longer holds and the branch a′ is unstable. Instead, the internal energy is given by the equilibrium energy of the cluster Emin plus the energy of the isolated tubes in excess, that is E /M = (Emin /M min − E tube)

M min + E tube M

a

(10) 5750

The colors are described in Scheme 1. dx.doi.org/10.1021/la2048135 | Langmuir 2012, 28, 5743−5752

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accurate control of the cluster size by elucidating how polyelectrolytes get associated with lipid vesicles to form assemblies and by further exploiting the residual net charge of the lipid-coated polyelectrolytes in the stabilization of the clusters. The second direction will aim at investigating numerically the fusion process between a cluster and a lipid bilayer, as well as the subsequent mechanisms of polyelectrolyte release.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]; Tel: +33 1 69 15 53 60; Fax: +33 1 69 15 60 86. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Jéril Degrouard, Amélie Leforestier, and Françoise Livolant for their support with cryo-electron microscopy, Anniina Salonen and Didier Poncet for providing them with carboxymethylcellulose and siRNA duplexes, respectively, Marie-France Carlier for valuable advices, Dominique Didry for providing them with proteins related to the F-actin preparation, and Mehdi Zeghal for insightful discussions. The three-dimensional graphics were rendered with the POV-Ray package (www.povray.org). The research was partly funded by Triangle de la Physique contracts 2009014T and 2009-073T, CNRS through the “Interface Physique, Chimie, Biologie” program, the association “Ligue Contre le Cancer”, and the ERC Advanced Grant #249982.

EXPERIMENTAL SECTION

Liposome Preparation. Lipids were purchased from Avanti Polar Lipids (Alabaster, AL) and dissolved in chloroform:methanol 2:1 (v/ v). They were dried by rotary evaporation under vacuum at 40 °C and placed in a vacuum chamber overnight to remove the last traces of organic solvent. Liposomes were formed by addition of sterile water (18.2 MΩ.cm) from a Milli-Q filtration system (Millipore) at a concentration of 0.5 mg.mL−1. After overnight incubation at room temperature, liposomes were tip-sonicated for 10 min and extruded through a 0.2 μm polycarbonate filter. Their mean size measured by dynamic light scattering was smaller than 100 nm. They were subsequently stored at 4 °C and remained stable for months. Polyelectrolyte Preparation. λ-DNA was purchased from Invitrogen and used as received. 146-bp DNA was obtained from calf thymus DNA following a protocol described elsewhere.46 siRNA duplexes (target sequence: CGGGCAGATAATAAATACTTA) were purchased from Qiagen (France) and prepared as recommended by the manufacturer. Absorbance measurement indicated a purity of A260/ A280 = 1.93. Poly(styrene sulfonic acid) (PSS) was prepared by an interfacial reaction of total postsulfonation of polystyrene according to the method of Vink.47 Briefly, about 100 mg of 1.5 MDa polystyrene purchased from Polymer Source (Dorval, Canada) was dissolved in 25 mL of cyclohexane. The dissolved polystyrene was then slowly added to 50 mL of concentrated sulfuric acid and maintained under agitation for 2 h at 50 °C. 150 mL of ice water was then added and the aqueous phase was recovered after decantation. After pH neutralization by sodium hydroxide, the solution was thoroughly dialyzed against pure sterile water, and sulfonated polystyrene was lyophilized. NMR measurements indicated a sulfonation efficiency higher than 95%. Sodium carboxymethylcellulose (CMC) was supplied by Aqualon Hercules with a minimum purity of 99.5%. The degree of substitution was DS = 1.23 and the molecular weight 171 kDa. CMC was buffered in 10 mM MOPS pH 7.0. Actin was purified from rabbit muscle,48 isolated as CaATP-G-actin by size exclusion chromatography on Superdex 200 equilibrated in G buffer (5 mM Tris-HCl, pH 7.8, 200 μM ATP, 100 μM CaCl2, 1 mM DTT, 0.01% NaN3), and stored on ice in this buffer. CaATP-G-actin was converted into MgATP-G-actin and polymerized into filaments by adding 2 mM MgCl2 and 10 mM KCl, in the presence of bacterial recombinant human gelsolin expressed and purified as described elsewhere.49 The actin-to-gelsolin ratio determines the average filament length. Filaments were stabilized by adding 20 μM phalloidin (Sigma). Cryo-Electron Microscopy. Assemblies were prepared by mixing liposomes and polyelectrolytes in desired charge ratios at a final concentration of approximately 0.3 mg.mL−1. The assemblies were left about 5 min to be formed prior to cryo-fixation. Electrophoretic mobility was carried out with a Delsa Nano C zetameter (Beckman Coulter, France) using a flow cell. A Quantifoil carbon grid (Jena, Germany) was ionized by glow discharge and 3 μL of assembly solution was deposited onto it. The grid was then abruptly immersed in liquid ethane via a custom-made cryo-plunger and stored in liquid nitrogen until use. The frozen samples were introduced into a highresolution JEOL 2011 transmission electron microscope via a cryoholder. They were imaged at 200 kV and a magnification of 50 000× using a minimal dose system enabling film exposure while preserving the samples from beam damage. The films were digitalized at 4000 ppi with a Nikon CoolScan scanner and processed with the SPIDER package.50

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