Design of chimaeric polymersomes

Abstract

We discuss the development of hierarchical polymer particles, or variegated polymersome composites, in which at least two different components are phase separated within one polymersome chimaera. We briefly discuss the present status in experimental polymersome research, and then discuss a speculative design strategy, based on mesoscopic simulations with a dynamical variant of polymer self-consistent field theory (Mesodyn). The main conclusion is that the counter-intuitive co-assembly of demixing block copolymers is the key in controlling hierarchical structures on a mesoscopic scale. This is the classical paradox of a chimaera: the constituents live in the same scaffold, but apart. Block copolymers beyond a certain length will always split the assembly, and without further precautions, polymer based chimaerae are intrinsically unstable. To this end, we propose the application of a branched block copolymer as composite compatibilizer, glueing the separate domains together, and thereby stabilizing the chimaeric polymersome.

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Introduction

The formation of vesicles is a well-established and familiar property of phospholipids. Such hollow structures have been applied in a variety of techniques in drug release or as micro-reactors. In recent years, it was shown various amphiphilic block copolymers also form vesicles, the so-called polymersomes. Polymersomes have been prepared of biodegradable,¹ thermal tunable,² conducting³ or polyelectrolyte materials.⁴ A number of papers, especially from the Eisenberg group, describe an entire ‘Wonderland’ of more complex polymersome architectures.^5–15 For example, vesicles with hollow rods running inside and parallel to the surface of the walls, or vesicular structures with protrusions or holes. Döbereiner and coworkers¹⁶ published the properties of giant polymersomes (>10 μm) with a wall formed either by a double-layer, which is connected by a lattice of passages, or a tubular network with hexagonal symmetry. In all cases the polymer is impure, sometimes deliberately so, and the structures are discovered by trial and error. ‘Peptosomes’, that is, polymersomes—or more general various tubes, micelles etc.—based on (conjugated) block polypeptides, were demonstrated very recently.^17–22 Assembling random peptides have in fact a much longer history. In the origin of life area, proteineous microspheres had been prepared already a few decades ago by Fox,^23,24 by simply baking amino acids, and exposing the residue to water. These structures lacked precisely defined compositions.

Polymersome research exploded following the publication of a few high-profile papers on the general principles²⁵ and detailed physical chemical characterization.^26,27 The interest is understandable from a technological point of view, since polymeric vesicles have many advantages over low-molecular weight vesicles, such as enhanced stability and flexibility in chemical modification.

The formation of one-component hollow polymersomes of low complexity is well understood by the formation of polymeric bilayers, guided by mixing and demixing rules set forth by standard Flory–Huggins theory. Also for amphiphile packing the theory seems straightforward. The essential ingredients are not so much different from lipid bilayers. The molecule comprises a hydrophilic ‘head’ and a hydrophobic ‘tail’. The packing factor, derived from the sizes of head and tail, determines whether the amphiphile aggregates in spheres, cylinders or lamellae (bilayers). The only difference between polymersomes and lipid vesicles is the molecular conformation: random in the case of flexible polymers and more narrowly distributed in the case of the packed lipids. Simple concepts are adequate to design single-component polymersomes, but they need extension in designing compound aggregates.

We foresee the design of organelle mimicking phases, or the design of reactive genetic assemblies in which in situ polymer synthesis is coupled to a genetic coding string by self-assembly. These polymersome chimaerae would be much more complex than the spheres, cylinders or hollow sacs one observes with single-component polymersomes. Our envisioned chimaeric particles have three geometrical characteristics which set them aside: (1) they are not hollow, but filled with a microstructure (which, when continued, leads to a hierarchy of embedded structures), (2) they have a means to interact with the environment through protrusions, ‘legs’, or invaginations, ‘holes’, etc. and (3), when the polymers are produced in situ, the geometry is dynamical, dissipative and may grow and fission and potentially obey evolutionary rules.

Chimaeric complexity obviously offers enormous potential for the design of “intelligent” self-assembled structures, but at the same time the challenge for keeping control also increases. The apt question is: How to construct a plastic mitochondrion? Or an artificial de novo macromolecular chloroplast? Construction implies rational design, not just trial and error. And clearly, the ‘trial-and error’ approach, which has led to the plethora of complex polymersomes structures so far, is inadequate and unsatisfactory from an intellectual point of view. What we need is, in the clearest terms possible, general rules by which one can design a desired hierarchical polymersome structure from block polymer mixtures and possibly from biological components. This is nothing less than the ambitious development of a theory for abiotic proto-cells. But even a superficial comparison between an in vivo biological organelle and a current state-of-the-art in vitro polymer assembly teaches us humility. It makes us realize that chemical science is a very, very long way from attaining such goals. Here is where we start: the real, living, biological organelles serve as beacons, posing a distant goal. We will concentrate on a very basic subtask: design of a polymersome with two polymers, co-assembling in different domains within one vesicular body.

Theory and simulation

The computations require the repeated simulation of polymer vesicle formation and stability, given a certain mixture of block copolymers, so as to generate a microphase diagram of polymersome morphologies. The rules are based on Flory–Huggins χ-parameters to account for block demixing, and size ratios of the blocks for the induction of bilayer curvature. In previous work we studied the formation of single component polymersomes, demonstrating the delicate influence of soft confinement on the classical microphase structures.²⁸ Here, following the same simulation method, we study two-component polymersome chimaerae, a mixture of two diblock polymers, where the two hydrophobic blocks become demixed, and the hydrophilic blocks having different curvature preference. In this way, unstable domains or rafts are formed, which then lead to protrusions and invaginations.

In our calculations, we generate structures by quenching a homogeneous vesicular droplet of polymer surfactant in an aqueous bath. The vesicle relaxes by a non-linear diffusion process:

[small rho, Greek, dot above]_I = D_I∇²(ρ_sI − f_I)

where f_I is the density functional of the polymer (or solvent) molecule, with the mean-field chemical potentials as variable (details of the model are in ref. 28; see the Appendix for the explicit formula of f_I).

It can be shown that the non-linear diffusion equations have the same kinetic coefficients as in collective Rouse dynamics, which is correct for the spinodal-like microphase separation internal to the vesicular structures. The simulation parameters are for diblock polymer surfactants in strongly selective solvent and strong segregation. They are: the architecture of the two polymers A13H7 and B13H17, where each chain is a necklace of “beads”, and Flory–Huggins parameters χ_HS = 0.5 (theta solvent for the hydrophilic blocks), Nχ_AH = 40, Nχ_BH = 60 (strong segregation within one polymer, N the polymer length), χ_AS = χ_BS = 2.0, (strongly hydrophobic blocks with respect to solvent) and χ_AB = 0.5 (weakly mutually phase separating hydrophobic blocks of the two polymers).

One should realize that in the mean-field model any polymer surfactant solution, with the same properly scaled interaction parameters, behaves in the same way. Taking into account that each bead or statistical unit represents at least three or four monomers, a possible system with the given parameters values would be a mixture of polybutadiene–polyethylene oxide, and polypropyleneoxide–polyethyleneoxide diblocks, with number of monomers each O(100). The dimensionless time indicated in Figs. 1–4 is τ = Dt/a²; where a is the bead size. The diffusion coefficient of all components is identical in all simulations. The typical real time scale of the polymer composite phase separation is on a mesoscopic scale (seconds–hours)—depending on realistic values for the bead size and diffusion coefficient. Both polymer architectures affect the intrinsic stability of the assembly structure curvatures differently: the larger polymer (B13H17) is asymmetric, promotes high curvature and destabilizes the vesicle wall, the smaller polymer (A13H7) is more symmetric and forms stable vesicles (data not shown).

The free energy model is that for an nVT ensemble, and consequently we do not calculate the global equilibrium of an open system, but rather the local equilibrium morphology of an isolated vesicular structure. The situation is analogous to that of classic studies of the shape of isolated lipid vesicles, when interactions between vesicles are less relevant. With the selected values of the Flory–Huggins parameters and length of the polymers the polymers molecules are all insoluble, hence deformations of the vesicles occur at constant mass of polymer.

The simulations proceed by a sudden quench of a vesicle in a solvent bath. Following the quench, the assembly takes up or releases additional solvent locally and globally, depending on the particular morphology being formed. The unimer polymer concentration is zero, and this remains so during adaptations in morphology. We have found it advantageous to add white noise to the mean-field chemical potentials. The uncorrelated noise does not obey the fluctuation-dissipation theorem, but it helps to cross barriers in the free energy landscape. The vesicles are placed in the center of the box with sufficient space, N/2 cells, between the vesicular surface and the boundaries of the computational box, thereby avoiding artifacts resulting from the periodic boundary conditions. In all cases the droplets develop a fuzzy outer layer of solvophilic blocks. Since the confinement of the polymers is not restricted, the vesicular surface is not necessarily spherical, nor is the topology constant.

The results (see Figs. 1 and 2) clearly demonstrate demixing of the two block copolymers. In related simulations (data not shown) we decreased the chemical incompatibility between the two hydrophobic blocks slightly (by a few tenths of a kT unit to χ_AB = 0.25) and observed no phase separation. Here, with slightly larger incompatibility, we observe phase separation into rafts, but the phase separation is already so strong the two polymers further demix into separate assemblies entirely, depending on the relative composition. This can be seen very clearly in Fig. 1a and 1b.

Fig. 1 Two-component polymersome chimaera, simulated with a dynamical variant of self-consistent field theory (Mesodyn), shapshots at τ = 5000. Fractional composition x = 0.25/0.50/0.75 (left to right), x(A13H7) + (1 − x)(B13H17) (rightmost image is 75% composition, but in open view). Architectures of Gaussian chains (A and B, hydrophobic and H hydrophilic bead types):

Fig. 2 illustrates the time evolution of the domains for one composition ratio (50%). Here, we also observe the disappearance of separate smaller domains, and the growth of larger domains (Ostwald ripening), but there is a peculiar topological alteration too: a small domain pinches off as a micelle, while the larger domains respond by buckling (τ = 4500). Phase separation also depends on the initial composition ratio of the two polymers. In Fig. 1a, the majority phase is the asymmetric polymer, and the vesicles bursts apart, completely disrupting the assembly structure into separate islands. In Fig. 1c, however, the more symmetric polymer is the majority phase, the vesicle is stable, with at the end one domain of the minority phase. From the theory of membrane fluid–fluid coexistence,²⁹ it is known that in such a case budding will occur when the domain of the minority phase is above a certain critical size. We would therefore expect that a larger vesicle (not yet accessible to simulation at present), of same initial composition as in Fig. 1c would split apart too.

Fig. 2 Formation dynamics of 50% polymersome chimaera (Fig. 1b). Snapshots at (from left to right) τ = 500, 1000, 2500, 3000, 3500, 4000, 4500 (5000 in Fig. 1b).

Demixing vesicles, even if the topology does not change, do not maintain a perfect smooth spherical structure. Rather, the domain-domain interface, here a line, has a reduced bilayer thickness. This is easy to understand: since when the two polymers demix, the contact between domains must be as small as possible, hence the evolution to a few large domains, and the decrease in domain-domain interface perpendicular to the membrane.

A theoretical description of fluid-fluid coexistence in multi-component (lipid) vesicular membranes has been the subject of intensive research for over ten years,^29,30 and was recently observed aslo in mixed lipid vesicles by advanced light microscopy.³¹ Phenomenological approaches of different degree of sophistication have been applied to two types of complex membranes: lipid membranes anchored by macromolecules (e.g. proteins or synthetic flexible polymers), and domain-induced budding of lipid membranes.

The starting point of the theoretical analysis is usually a Helfrich Hamiltonian of a membrane or a membrane patch. Such an analysis is useful if the topology is constant. In addition to the analytical theory, membrane-budding was extensively studied by Monte Carlo simulation.²⁹ The evolution of a multi-component lipid membrane experiences the following distinct time regimes during the phase separation process: (1) formation and growth of intramembrane domains, (2) multiple bud formation, and (3) coalescence of small buds into larger ones. Although both the time and size scales of the polymersome chimaerae are different from lipid systems, our field simulation qualitatively agrees with this scenario. We observe both the in-plane phase separation of different types of block copolymers, as well as the escape of one of the components into the third dimension due to membrane flexibility. Coarse graining of the resulting aggregates is a natural consequence of the demixing process.

Another comparable system is a concentrated solution containing a mixture of block copolymers, microphase separated in co-micelles. In principle, such micelles may also be multi-component chimaerae, just as the polymersomes we described above, and so similar rules for mixing and demixing will apply. One may distinguish here between (1) the co-micellisation of block polymers of same chemical composition, but of different block lengths (such co-micellisation is usually accidental following the application of heterodisperse polymer samples and not further discussed here), and (2) the mixing of block copolymers, where either the core forming, or corona forming blocks are different. The case where the corona forming blocks are incompatible is less interesting for forming chimaerae micelles, since the law of demixing according to Flory–Huggins theory dictates that in solvent rich environments, such as a micelle corona, the block-block interaction is reduced, in proportion to the solvent concentration. Hence, even if two corona forming blocks are chemically incompatible, their phase separation will be diminished accordingly, and two such blocks may well be accommodated within one single micelle, without internal microphase separation.

The case of demixing core-forming blocks is very similar to our scenario.^32,33 Here, since the cores are dense, demixing again follows the strong phase separation principle we discussed before. When the core-forming blocks demix, the micelles will split into two, when the core-forming blocks mix, the micelles will house the two blocks together. But the internal mixing will then be homogeneous, without forming chimaeric micelles! Hence, such a system is either bimodal in micelle distribution, or unimodal, but rarely microphase separated within each individual micelle. The situation is clarified by considering the stability of three phases: chimaeric micelles, a mixture of micelles and homogeneous micelles. When we increase the interactions, the phase boundary is crossed between the homogeneous state and the mixed micelles state, and the chimaeric state is never reached. Essentially the same conclusion was reached for co-micellisation in block copolymer blends.³³

Our simulations, applied to 70% polymer solutions (Fig. 3) precisely follow the proposed rule. The pure block copolymer solutions (0% or 100% of each polymer), are micellar, the mixed copolymer solution (50% of each) is completely demixed in micelles composition. Notice that the separate micellar fractions do not macrophase separate (as discussed in ref. 33), since the hydrophilic coronas of identical chemical nature ensure good mixing of the dissimilar micelles (this is not a general conclusion for all co-micelles but applies here due to the particular choice of the corona blocks under consideration).

Fig. 3 Pure and mixed micelles at polymer fraction x = 0/0.50/1.00 (Fig. 1) at 70% total polymer concentration. Chimaeric phase is unstable.

Discussion

The simulations so far indicate that a design rule based on simply mixing diblock copolymers in one assembly, is inadequate to predict the formation of stable chimaeric polymersomes. When one mixes two block polymers, of same hydrophobic block, and same hydrophilic block, but different chain lengths, the polymer with the longer hydrophilic block accumulates in regions of higher curvature (this is already known from the Eisenberg experiments; for a discussion of the effect of polymer dispersity see for example ref. 34). When the two hydrophilic blocks have different chemical composition, lateral phase separation leads to the formation of raft structures.

For our purpose of designing polymersome chimaerae, the most favorable situation is when the two hydrophobic blocks have different chemical composition, so that the polymers phase separate, and in addition the hydrophilic blocks must be of dissimilar length, so that planar rafts are unstable and open. This is due to the fact that both the chemical composition (Flory–Huggins parameters χ) and block length (entropic effect) contribute to the effective bending moduli of structures. This seems an attractive scenario, because of its simplicity, but we believe the practical range of chemical incompatibility is too narrow. When the phase separation is too strong, the two polymers will pinch off and individually form assemblies. When the phase-separation is too weak, the hydrophilic blocks will not be forced to accumulate into rafts, the longer hydrophilic block remains dispersed homogeneously, and the wall is not destabilized. There may be a value range in parameter space 0 < χ_AB < χ^c where the chemical incompatibilities between the hydrophobic blocks is strong enough for phase separation, but not yet strong enough for splitting the assembly. But arguably, such region will be very small. Since we are dealing with polymers, not with low molecular weight surfactants or lipids, even a small discrepancy in chemical compatibility on a monomer scale, is amplified at the polymer level. The relevant interaction parameter is Nχ_AB, not χ_AB, and χ^c = O(1/N). Therefore, given a certain chemical composition of the monomers, χ^c → 0 as the block length increases, and long block copolymers, trapped in a bilayer, will either mix homogeneously, or the assembly splits. There is no intermediate outcome: without further precautions chimaerae are intrinsically unstable.

Robust rules for polymersome composite design must somehow counteract the fission of the vesicle due to the built-in phase separation, that is, the polymers must separate individually to form hierarchical structures, but without splitting the overall assembly structure. This is the classical paradox of a chimaera: the polymers must “live in the same house, but apart”. The biological strategy for dealing with the paradox is manifold, for example, (1) by generating the amphiphiles in situ (for example, specifically inside an assembly), in such a way that on the biological life-span, the transport is too limited by barriers for the assembly to fall apart, or, (2) by maintaining a dissipative process for the integrity of the assembly structure (that is, the assembly is far out of equilibrium), or (3) by the incorporation of additional networking or skeleton molecules for spanning and cross-linking the membrane. Except for covalent cross-linking, in man-made polymersome composites such strategies cannot be employed. Also, in a practical approach we are limited to rather crude macroscopic assembly techniques, such as by quench, film de-stabilization or sonication. These methods lack the inherent fine-graded ‘nanoscopic’ instrumentation by which biological entities can shape and mold individual assembly structures. The challenge is therefore reduced to the development of additional block copolymers, capable of spontaneously glueing and stitching together the phase separated domains within each single polymersome. We have speculated that multi-arm block copolymers may be useful for such purpose, but any experimental evidence is lacking at present. Fig. 4 displays a cartoon of the four-arm copolymer glue in action: a planar block copolymer bilayer is separated into two different domains, each pure in one block copolymer. The compatibilizer has four arms, two branches similar to the two hydrophobic blocks, and two branches similar to the hydrophilic blocks. In this way, the branched polymer stabilizes the in-plane domain–domain interface of the polymersome chimaerae, similar in action to diblock compatibilizers stabilizing mixed polymer phases in bulk industrial systems, on a much larger scale. In our naïve design, branches of identical composition and length act as the separate blocks of the constituting di-block copolymers. Perhaps, rather than two hydrophilic blocks, one bigger hydrophilic block may suffice: this would be a minimal three-arm compatibilizer. It may be interesting to test our hypothesis experimentally, while we calculate the phase diagram theoretically.

Fig. 4 Four-arm in-plane compatibilizer.

Appendix

The expanded formula for the density functional is:²⁸

μ^MF_I(r) = ∑_J∫dr′ ε_IJK(r − r′)ρ_J(r′) + κνρ_J(r)

where Z is a normalization constant (∫dr f_I = ∫dr ρ_I), θ_Is is 1 when bead s is of type I and 0 otherwise, H is the ideal Gaussian chain Hamiltonian, μ^MF_s is the mean-field chemical potential, the Flory–Huggins parameter is χ_IJ = ν⁻¹β(ε_IJ + ε_JI − ε_II − ε_JJ), ν is the bead volume and κ the Helfand compressibility parameter.

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