Entropic depletion of macromolecular solutes induces symmetry-breaking surface wrinkling in myelin figures

Abstract

Smectic liquid crystals, including multilamellar stacked lipid bilayers, strongly resist compression along the normal layer but bend readily. When mechanically stressed—such as by dehydration, osmotic stress, physical confinement, or even electric fields—they release elastic compressive energy by buckling into undulatory surface patterns reminiscent of the well-known Helfrich-Hurault instability. Although documented extensively for lamellar liquid crystals, observations of the Helfrich-Hurault instability in cylindrical smectic liquid crystals are scant. Here, we investigate the behavior of myelin figures—cylindrical smectic-A liquid crystals consisting of thousands of concentric amphiphilic bilayer lamellae separated by aqueous channels—when subjected to mechanical compression by the hyperosmotic stress from the osmolyte-laden surrounding bath. We find that the colligative ideal osmotic pressure exerted by small molecular osmolytes alone is insufficient to induce long-lived, surface instabilities. Using real-time optical and confocal fluorescence microscopy, we show that exposure to hypertonic solutions of low-molecular-weight osmolytes (e.g., sucrose and glycerol) leaves myelin surfaces largely smooth, even at elevated osmotic pressures. By contrast, solutions containing macromolecular osmolytes such as polyethylene glycol and dextran trigger pronounced symmetry-breaking surface instabilities in bundles of juxtaposed myelins. These instabilities manifest as long-wavelength, quasi-sinusoidal corrugations that propagate axially and preferentially localize at inter-myelin interfaces. Quantitative analysis reveals that the wavelength and amplitude of the corrugations depend on osmolyte size, even at nominally identical osmotic pressures, further implicating excluded-volume effects. Fluorescently labeled osmolytes are excluded from corrugated interfacial regions, supporting a depletion-driven mechanism. We propose that macromolecular osmolytes generate colligatively non-ideal osmotic stresses and entropic depletion forces that stabilize interlocking surface undulations by increasing the free volume available to the depletants. These findings identify solute entropy and excluded-volume interactions as key drivers that stabilize Helfrich-Hurault-type undulatory instabilities in cylindrical smectics. They further suggest a general physical mechanism by which macromolecular crowding can induce large-scale structural remodeling in soft, multilamellar systems relevant to both synthetic materials and biological assemblies.

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Introduction

Compress a soft, thin-walled tubule radially and it lengthens.¹ This familiar behavior—arising from volume conservation and the Poisson effect—is universal for a broad class of soft, essentially incompressible, tubular materials, including tubular lipid bilayers, hydrogels, and elastomeric tubes.^2–4 Now compress a thick-walled, multilamellar smectic-A liquid-crystalline tube, and it responds very differently.⁵ This is because, in multilamellar, cylindrical smectics—three-dimensional samples with one-dimensional inter-layer periodicity—mechanics are governed by a complex interplay of competing interactions. Forces resisting radial compression originate from the bending rigidity of individual layers, the interlayer compression modulus, and in-plane area elasticity. Opposing axial deformation, however, is the end-cap energy, which penalizes changes in tube length.⁶

Because these energetic contributions cannot all be simultaneously minimized, the tube is unable to relax its interaction energy fully: The interlayer separation (a) remains larger than that expected for the compressed myelin at the new equilibrium (a₀). The stack is therefore effectively hyper-swollen – a seemingly counterintuitive outcome since the tube is under mechanical compression.⁶ This situation is phenomenologically comparable to a swollen stack of planar, lamellar smectic liquid crystals, in which mechanically stressed lamellar stacks—including those obtained through compression—relieve the compression energy by undulating and buckling to maintain their preferred interlamellar spacing^7–9 through the Helfrich-Hurault instability.^10–12

For lamellar smectics, this phenomenology of mechanical instability is well described by continuum elasticity theory.¹³ The same framework extends naturally to cylindrical geometry.^5,13 In this description, the layer displacement, δR, can be decomposed into two contributions: (i) a radially uniform shrinkage, δR̄, which is constant along the cylinder axis, and (ii) a sinusoidally varying component, δR′(r,z) ∝ cos(qz), where k and q are the radial and axial wavevectors of the undulation modes, respectively.

The energy density (energy per unit volume) corresponding to such a deformation takes the form

where B_A represents the in-plane membrane area compression modulus (energy per membrane area), B is the smectic inter-layer compression modulus (energy per unit volume), K (energy per unit length) captures the bulk bending modulus of the multilayer tube, and h is the repeat distance of the layer prior to the osmotic or dehydration perturbation.

Chen and co-workers demonstrate that for a trial deformation δR = ā(r,z) + a′(r)cos(qz), which penetrates to a finite depth d₀ from the outer surface of the myelin, the minima of the total free energy per unit length yield an optimal wavenumber: . At the onset of the instability, where the minimized free energy vanishes at the critical radial deformation, , the corresponding wavelength of the axially propagating instability is where is the standard smectic penetration depth.¹⁴ For a typical phospholipid bilayer, , is on the order of 10 nm. Thus, the wavelength of undulations, λ, is on the order of micrometers if d₀ is several micrometers deep.^13,14

A variety of real-life condensed-phase systems that exhibit smectic-like lamellar morphologies and cylindrical organization display comparable surface instabilities.² In a range of scenarios involving externally applied or internally generated stresses, these liquid-crystalline systems experience geometric frustration that impedes complete relaxation.¹⁵ Consider, for example, the tubular organs of animals such as the esophagus and pulmonary airways.^16,17 Here, the outer layer (the muscle) is much stiffer than the inner layer (the mucosa). This stiffness mismatch creates a geometric incompatibility. During tissue growth, the stress generated is unable to relax, resulting in an instability that produces wrinkling, creasing, and folding of the inner surface of the mucosal layer.¹⁸ Other biological examples include the lipid layers of stratum corneum (skin)¹⁹ and cortical folding in the human brain.²⁰ In all of these cases, differential growth or external strains can give rise to instabilities through geometric frustrations. Synthetic soft matter systems, including smectic liquid crystals, elastomers in the smectic liquid-crystalline phase, and diblock copolymers^21,22 are susceptible to similar instabilities.

In the work reported here, we consider a class of smectic-A cylindrical liquid crystals known as myelin figures. First reported by Virchow,^23,24 now more than 150 years ago, myelin figures form during the dissolution of many common amphiphiles, including surfactants,²⁵ lipids,²⁶ and amphiphilic block polymers.^27,28 They form at the amphiphile-water boundary as ensembles of finger-like tubular protrusions, tens of micrometers wide, and hundreds of micrometers long, when a dry mass of nearly insoluble (∼10⁻¹⁰ M) amphiphiles encounters water.

Molecular organization of myelin figures resembles that of a lyotropic smectic liquid crystals in cylindrical geometry:^26,29–31 concentric arrays of discrete tubules consisting of thousands of cylindrically stacked alternating lamellae of lipid bilayers and aqueous channels wrapping a central (∼100–200 nm) aqueous core (Fig. 1). Individual lamellae, comprising single fluid bilayers, allow for in-plane lateral diffusion, but the spatial confinement due to neighboring layers suppresses the thermally excited out-of-plane undulation fluctuations. The corresponding entropy loss gives rise to the inter-lamellar repulsive interactions (Helfrich repulsion), which stabilize the one-dimensional smectic order in myelins³² and inhibit molecular exchanges between individual lamellae.

Fig. 1 Hydration-induced formation of myelin figures: (a) schematic illustration of a single myelin figure highlighting the multilamellar molecular organization in the cylindrical smectic-A phase (Adapted with permission from Ho et al. 2022²⁹). (b) Histogram depicting the distribution of myelin diameters for a representative experiment (same experiment as Fig. 1d) where the average diameter is 10.69 ± 0.92 µm (n = 32 tubes). Further details on how measurements were made are found in the Methods section. (c) and (d) A montage of a selection time-lapse images from movies (Videos S1 and S2) showing the formation of myelin figures upon hydration. The sample compositions: (c) 100% POPC lipids, brightfield microscopy and (d) 99.9% POPC and 0.1% Rhodamine-PE. All timestamps are shown in mm:ss. (Scale bar = 25 µm).

As soft multilamellar smectic tubes, are myelins susceptible to compression-induced Helfrich-Hurault type interfacial instability? To our knowledge, there is one previous study,¹³ which explores this question. In that study, Chen, Schmidt, Olmsted, and Mackintosh subject isolated myelin figures to macroscopic dehydration.¹³ The accompanying compressive stress, they find, transforms the smooth surface of single, isolated myelin figures into an undulatory one displaying periodic “bumps.” The bumps, they observe, are spatially periodic and appear to grow into longer “arms” before the myelins lose their cylindrical structure and become an amorphous mosaic. The authors argue that the observed initial instability arises from hypertonic osmotic stress induced by dehydration. They propose that as the bulk water evaporates, the concentration of impurities in the water rises, which, in turn, produces hypertonic stress on the myelins. This then triggers the flow of water from the outer layers of myelin figures to the impurity-laden bath, compressing the myelin. Adapting the formulation of Helfrich-Hurault type mechanical instability of smectics,^10–12 the authors provide a theoretical description of how the relief of accumulated intra- and interlayer compression energies through the bending of lamellae can lead to an instability of surface undulations beyond a threshold compression. However, the presumed correspondence between dehydration and osmotic stress, and the causal link between the two that drives surface instability at the myelin surface, has not been experimentally verified.

In the work reported here, we monitor the real-time deformation of myelin figures under osmotic stress. We find that exposing pre-formed myelin figures to hypertonic aqueous solutions containing low-molecular-weight, colligatively ideal, osmotically active solutes (e.g. glycerol, ∼92 g mol⁻¹; sucrose, ∼342 g mol⁻¹) does not induce undulatory instability. Remarkably, however, myelin figures exposed to larger macromolecular osmolytes (i.e., polyethylene glycol (PEG) and dextran (DEX), molecular weights 2000–10 000 g mol⁻¹) exhibit striking undulatory instability in bundles of myelin figures. Individual myelin figures undergo spontaneous chiral symmetry breaking and stabilize an axial pattern of interlocking topographic corrugations or wrinkles, which extend over the entire length of the myelin. The corrugations are almost exclusively localized at the surfaces where neighboring myelin figures (or loops of single myelins) are in direct juxtaposition. Our results suggest that this qualitatively significant difference, dependent solely on the size of the osmolytes, originates from the colligatively non-ideal, differential contribution of depletion interactions³³ to the osmotic pressure in macromolecular solutions.^34,35 More generally, these observations suggest a heretofore underappreciated role of solute entropy in inducing morphological transitions in soft and cylindrical smectic tubules, pervasive in man-made and biological systems.

Results & discussion

We begin by preparing myelin figures under standard isotonic conditions by hydrating a dried mass of fluid-phase phospholipids with deionized water. Adapting previous protocols,^29,36–38 we first prepare a dry plaque of lipid (e.g., 1-palmitoyl-2-oleoyl-glycero-3-phosphocholine (POPC)) with some fluorescent label (e.g., 1,2-dioleoyl-sn-glycero-3-phosphoethanolamine-N-(lissamine rhodamine B sulfonyl) (ammonium salt) (Liss-Rho-PE)) if needed. This is achieved by drying a droplet (4 µL, ≈100 µg) of a chloroform solution containing desired lipids at high concentrations (≥25mg mL⁻¹) onto a planar cover glass (SI). Subsequent hydration with deionized water roughens the edges of the lipid mass, producing a dense tangle of rapidly growing tubular protrusions, or myelin figures.

Monitoring these formation dynamics in real time using brightfield optical and fluorescence microscopy (epi- and confocal) (Videos S1 and S2) confirms the established features of myelin figures. A selection of still micrographs extracted from the video during the first ∼180 s is shown in Fig. 1. The images reveal that the tubes grow sinuously, branch occasionally into secondary myelins, and juxtapose almost invariably into closely spaced myelin bundles. After the rapid growth during the first 100 s, myelins reach their quasi-steady state lengths, and the rafts of myelin exhibit slow, cooperative movements.

Individual myelin figures in single experiments are essentially monodispersed. Measuring the sizes of several tubules in multiple different experiments reveals a strikingly uniform average size. Analyzing 32 myelin tubes in a single representative experiment (the same experiment seen in Fig. 1d, we estimate a mean myelin diameter of 10.69 ± 0.96 µm Assuming that a single POPC bilayer is roughly 4 nm,³⁹ an average inter-layer separation of ∼1–2 nm,^40–42 and the central aqueous core of ∼100 nm,^43–45 we estimate that each myelin is made of roughly one thousand (∼940) bilayers. These preliminary findings are in excellent agreement with those reported previously in the literature.³⁶ While Fig. 1b illustrates the mean diameter for a representative trial (10.69 ± 0.96 µm), similar narrow distributions were consistently observed across various independent experiments. This indicates that while the absolute mean may vary between experiments, the formation of these myelin figures remain consistently monodisperse.

Next, we subject the well-formed myelin populations to a bulk dehydration.¹³ Images shown in Fig. 2a reveal striking remodeling of the myelinic surface, characterized by interdigitated corrugations, similar to those reported previously.¹³ Unlike the previous findings, which reported corrugations of isolated single myelins, we find that the bundles of myelins corrugate asymmetrically: the surface undulations are most pronounced at the juxtaposed myelin–myelin interface; those at the free myelin surfaces are far less prominent, bulge-like protrusions.

Fig. 2 Undulatory surface instability of myelin figures under dehydration stress: (a) a representative confocal fluorescence microscopy image of a well-formed myelin bundle in the fully hydrated state (top) and upon ambient dehydration (bottom). The quasi-periodic undulations are most pronounced at the inter-myelin boundaries with less conspicuous bulging at the free surfaces. Composition: 99.9% POPC doped with 0.1 mol% of Liss-Rho-PE (scalebar = 25 µm). (b) and (c) A selection of frames from a video of time-lapse brightfield microscopy images for 100% POPC myelins (b) and confocal fluorescence microscopy images for myelins consisting of 99.9% POPC and 0.1 mol% of Liss-Rho-PE (c). (scalebar = 25 µm). (Videos S3 and S4). The images reveal the localized appearance followed by a rapid axial propagation of the surface undulations along the lengths of the myelin figures.

The time-lapse movies of brightfield and fluorescence microscopy data shown in Fig. 2b and c, respectively, capture the formation of the corrugations in real-time. These observations reveal that the undulations initiate stochastically, couple across the inter-myelin surface, subsequently propagating along the length of the myelins, effectively transforming the entire bundle into a remarkable pattern characterized by a strikingly corrugated surface.

The previous study by Chen et al.,⁴⁶ which reported observations of the appearance of periodic bumps with the wavelengths on the order of a 0.9 µm but did not examine the formation dynamics, proposed that dehydration-induced wrinkling arises from hypertonic stresses generated by increased impurity concentrations in the aqueous bulk surrounding the myelins. This hypothesis, however, has not been experimentally tested. To address this gap and to determine whether the undulatory profiles observed upon dehydration can be attributed solely to osmotic stress, we subjected pre-formed myelin figures to externally imposed osmotic stresses under controlled conditions by using a seconadry hydration step in which we had a omsolyte-laden solution to the preformed myelin figures. Specifically, we replaced the aqueous bath surrounding the freshly formed myelins with a hypertonic aqueous solution containing several pre-determined concentrations of bilayer-impermeable sucrose (M.W. ∼342 g mol⁻¹) as well as glycerol (M.W. ∼92 g mol⁻¹) (see Videos S5 and S6). Here, the strength of the applied osmotic stress is determined by the van’t Hoff equation:⁴⁷Π = cRT, where Π is the osmotic pressure (Pa), R is the universal gas constant (8.314 m³ Pa mol⁻¹ K⁻¹), T is temperature (K), and c is the osmolyte concentration (mol m⁻³). Strikingly, we find little or no surface undulations even after extended incubation (∼25 minutes). One possible explanation for the absence of myelin responsiveness to the introduction of solutes in the external bath is that small-molecule solutes permeate into the myelin structure, thereby eliminating any osmotic gradient across the lamellae. However, this possibility can be safely ruled out. Experiments using labeled sucrose confirm that no detectable exchange of solute occurs between the interior of the myelin and the surrounding bath. These observations suggest that the osmotic stresses generated by colligatively ideal solutions of low–molecular-weight solutes are generally insufficient to drive the surface instabilities observed during dehydration (see Supplementary Files 7a and b).

These observations raise a fundamental question: Does bulk dehydration produce a separate effect that is not accounted for by the increased concentration of small solutes and the subsequent change in osmotic pressure? It is well known that macromolecular and colloidal impurities, whose larger sizes exclude volume, produce colligatively non-ideal contributions⁴⁷ to osmotic stresses during dehydration. Recall that, unlike colligatively ideal solutions containing typically low-molecular-weight solutes, large macromolecules and/or colloidal solutes generate non-ideal aqueous solutions which have non-negligible solute–solite interactions, causing deviation from the behaviour predicted by the ideal solutions.^48,49 Therefore, for aqueous solutions containing larger macromolecular solutes, osmotic pressure varies non-linearly with concentration: where M_w is the molecular weight, R is the gas constant, c is the mass density of the polymer solution and A₂ [mol mL g⁻²] represents the second virial coefficient (see SI).^50,51 For low-molecular-weight solutes, deviations from ideal osmotic behavior are minimal at millimolar concentrations⁵² and the standard van’t Hoff expression is valid where the osmotic pressure is primarily a function of concentration. In contrast, for moderate- to high-molecular-weight solutes, the nonlinear contribution involving the second virial coefficient A₂ becomes substantial and the colligative non-ideality due to the solute–solute and solute–solvent interactions cannot be ignored. As molecular weight increases, so does the solute's effective size, amplifying excluded-volume interactions that restrict the configurational degrees of freedom available to each solute. This reduction in entropy increases the osmotic pressure non-linearly with concentration, increasing far above that predicted by the van’t Hoff equation. For further details, see SI.

To test whether excluded-volume effects contribute to undulatory instability, we next subject pre-formed myelins to aqueous solutions containing macromolecular solutes, namely poly(ethylene) glycol (PEG 8000, M.W., 8000 g mol⁻¹, hydrodynamic radius, R_H = 2.45 nm⁵³). In the representative experiments shown in Fig. 3a, we exposed pre-formed myelins to an aqueous solution containing PEG 8000 (12.7 mM, osmotic pressure, ∼0.26 MPa). Within seconds of exposure, the myelin figures undergo a striking morphological remodeling commences. (Video S8 and Fig. 3a). The most pronounced change is the emergence of a mesoscopic undulatory surface profile, most pronounced at the interfaces between myelins. In the case highlighted in Fig. 3a, wrinkling begins at a bend in a folded myelin. The initial local wrinkle propagates (over ∼30 s) down the length of the myelin, producing a global undulatory myelin–myelin interface with a quasi-sinusoidal profile. Although less conspicuous, the outer free surface of the myelin figure also exhibits the appearance of long-wavelength, low-amplitude bulges, like that observed under global dehydration (see Fig. 2) and which reflects the expected area conservation across tubular topology.

Fig. 3 Undulatory surface instability of myelin figures bathing in aqueous solutions containing macromolecules: (a) a montage [mm:ss] of time-lapse brightfield microscopy images revealing the initial seed and the propagation of the undulatory surface profile. Sample: Pre-formed POPC myelin figures upon exposure to an aqueous solution containing 12.7 mM PEG 8000, Scalebar = 25 µm) (b) and (c) montages [mm:ss] of time-lapse confocal fluorescence microscopy images revealing undulatory surface profiles when pre-formed myelins were exposed to (b) 37.5 mM PEG 8000 and (d) 55.6 mM DEX 10 000 (scalebar = 25 µm) (d) a Z-stack slice montage of the experiment in (c) (scalebar = 10 µm). (Videos S8–S10)

Analyzing the undulations at the inter-myelin junctions, we estimate the average wavelength of the quasi-sinusoidal, wrinkled myelin to be ∼12.2 (± 2.3 S.D) µm with the average amplitude of 3.8 (± 0.7 S.D) µm (n = 2 measurements, m = 28 inter-myelin junctions). The long-wavelength undulations at the free surfaces have a much longer apparent average wavelength of (∼21 µm). Qualitative features of the appearance of undulatory surface profiles and their growth trajectories are fully reproducible for several different myelin compositions tested (i.e., POPC and POPC/Cholesterol mixtures). (For details, see Videos S11–S16)

To test whether the observed instabilities are unique to PEG, we compared the myelin response to perturbations induced by another common macromolecular solute, distinctly different from PEG. We used high-molecular-weight (M.W., 10 000 g mol⁻¹) dextran, a branched polysaccharide composed of glucose monomers linked together by glycosidic bonds. For our study, 37.5 mM (∼30 weight%) PEG 8000 and 55.6 mM DEX 10 000 were the concentrations chosen to generate comparable osmotic stress (2.15 MPa or 21.2 atm in the present case).^54,55 Images shown in Fig. 3b and c, with the corresponding time-lapse movies (Videos S9 and S10), establish unambiguously that PEG and dextran produce comparable patterns of surface wrinkling, thus suggesting that the response is independent of the chemical identity of the macromolecular osmolytes. Even if the chemical identity does not have a dependent response on the surface wrinkling patterns, PEG 8000 and DEX 10 000 have a size based difference reflected in their in their hydrodynamic radii R_h, which are 2.45 nm⁵³ for PEG 8000 and 1.85–3.24 nm⁵⁶ for DEX 10 000 respectievly. Considering that sucrose has a R_h = 0.52 nm⁵⁷ and no surface undulations were observed after extended incubation, the effect of osmolyte size on surface wrinkling patterns is experimentally tested.

To explore the effect of molecular sizes of the polymeric osmolytes, we next used a self-consistent series of polyethylene glycol solutions (molecular weights [g mol⁻¹], 600, 2000, and 8000) under comparable osmotic pressures. This is achieved by subjecting freshly formed myelins to polymer solutions containing 400 mM for PEG 600, 182 mM for PEG 2000, and 37.5 mM for PEG 8000, all of which have an identical osmotic pressure (Π = 2.15 MPa).

The results summarized in Fig. 4 confirm the size dependence. The larger osmolyte (PEG 8000) produced the most well-defined corrugations with weaker, bulge-like corrugations produced by the shortest PEG 600 osmolyte. These observations are consistent with our proposition that the non-ideal contribution to osmotic pressure from large macromolecular osmolytes is critical for the surface instabilities in myelin figures.

Fig. 4 Comparison of osmolyte size on myelin wrinkling: the average wavelengths and amplitudes of the surface undulations produced in myelin figures upon exposure to aqueous solutions containing three different PEG osmolytes (PEG 600, PEG 2000, and PEG 8000) at nominally identical osmotic pressures (See text for details). Statistics: PEG 600 (n = 76), PEG 2000 (n = 81), and PEG 8000 (n = 137). All scale bars are 10 µm.

The corrugated myelins are in close juxtaposition. Are macromolecular osmolytes present in the narrow space between the roughened myelins? To address this question, we exposed preformed myelin figures to a 55.6 mM dextran mixture containing a small concentration (0.1 mol%) of fluorescently labeled dextran of comparable molecular weight (∼10 000 Da). Confocal fluorescence microscopy images shown in Fig. 5a documents the experiment. The images shown in Fig. 5a (top panel) correspond to the formation of myelin figures, which follow the expected trajectory (See Fig. 1). Upon exposure to the exterior bath containing fluorescently labeled dextran, the pre-formed myelin figures exhibit secondary shape changes. A selection of these images is shown in the Bottom Panel of Fig. 5a. Here, t = 0 is arbitrary, chosen to reflect the time point at which labeled dextran becomes visible in the field of view. The images reveal three noteworthy features. First, the myelins in dextran-laden exterior are bundled closer together. This bundling is not unexpected because of the depletion forces arising from macromolecular crowding⁵⁸ in the solution surrounding the myelin figures. Second, the sequence of images reveals the appearance and propagation of the surface wrinkling, consistent with the experiments reported in Fig. 3 and 4.

Fig. 5 Exclusion of macromolecular osmolytes from the inter-myelin interfaces (a) monitoring the formation of POPC myelin figures upon primary hydration with 30 µL deionized water (a, first column), followed by secondary hydration with 30 µL Dextran 10,000 Da containing 0.1% fluorescently labeled dextran (55.6 mM; 1000 : 1 unlabeled:FITC-labeled dextran) (a, second column). Scale bar: 25 µm. (b) Time-dependent changes in the gap-to-bulk FITC-dextran fluorescence intensity ratio (d) during the corrugation process. (c) Schematic depiction of the depletion forces exerted by exclusion of macromolecular osmolytes on neighboring myelin figures, stabilizing surface undulations. λ denotes the corrugation wavelength and 2A denotes double the transverse inter myelin distance, where A is the plotted amplitude. (Videos S17 and S18).

Third, by monitoring the fluorescence intensity due to FITC-dextran in the bulk relative to that between the myelin we can assess how dextran dissolved in the bath is distributed relative to the bundled myelins. This is shown as gap-to-bulk intensity fluorescence ratio for the FITC-Dextran 10K as a function of time in Fig. 5b. Here, the gap refers to the narrow aqueous space between adjacent myelin figures, and the bulk refers to the surrounding aqueous free dextran solution far from the myelin interface. This ratio is therefore a direct measure of the relative dextran concentration in the confined inter-myelin space compared to the surrounding solution. (A ratio of 1.0 would indicate uniform dextran permeation in the gap; a ratio ≪1.0 confirms depletion of the macromolecular osmolyte within the inter-myelin gap). The measured values fall between 0.03–0.07, well below 1.0, indicating that dextran is excluded from the inter-myelin space.

Taken together, the results presented here establish that the concentration imbalance due to low-molecular-weight osmolytes (e.g., glycerol ∼92 g mol⁻¹, sucrose, ∼342 g mol⁻¹) – those that produce colligatively ideal osmotic pressure difference–is insufficient to induce the surface wrinkling in myelin figures. By contrast, when myelins are exposed to solutions containing macromolecular osmolytes (i.e., polyethylene glycol and dextran, molecular weights 2000–10 000 g mol⁻¹), they break symmetry, generate chirality, and stabilize an axial pattern of interlocking topographic corrugations or wrinkles, which extend over the entire length of the myelin. Furthermore, it is notable that the corrugations are almost exclusively localized at the surfaces where neighboring myelin figures (or loops of single myelins) are in direct apposition, and they produce near-perfect interdigitation at the inter-myelin junctions.

We propose that the extended surface wrinkling we observe in myelins exposed to macromolecular solutes can be understood in terms of synergistic effects from three factors. These include: (1) elevated osmotic stress due to the colligative non-ideality of the macromolecular solutes; (2) macromolecular crowding; and (3) depletion interactions arising from the excluded volume effects – a consequence of the translational entropy of polymeric osmolytes (Fig. 5c). First, the osmotic stress due to the macromolecular solutes (i.e., PEG or dextran) in the bath expels water from the myelins, prompting Helfrich Hurault type instability, as described previously by Chan et al. Second, the macromolecular crowding from the bath bundles myelins closer together. This then sets the stage for short-range depletion interactions to stabilize the wrinkled topography of myelin figures. This is depicted in Fig. 5c.

Consider large macromolecular osmolytes as particles of radius R_p. The center-of-mass of smaller particles cannot approach the myelin figures beyond R_p, developing a corona of the solute-inaccessible excluded-volume that surrounds the myelin figures. Thus, when closely spaced myelins roughen and interdigitate, their excluded-volume coronas overlap, effectively increasing the total space accessible to the center-of-mass of the depletant particle. Consequently, the entropy of the polymeric depletants increases, and the overall free energy of the system decreases. The magnitude of the free energy change can be approximated as ΔF_depletion ≈ −nk_BTΔV, where n is the number density of the polymeric osmolytes, ΔV represents the overlap volume, k_B is the Boltzmann constant, and T is the temperature. The net result then is an osmotic pressure imbalance (ΔΠ = nk_BT) arising from the local difference in the concentration of polymeric depletants between the interdigitating myelins and the surrounding bulk. This then acts as a depletion force stabilizing the surface instability in juxtaposed myelin figures. This scenario then suggests a heretofore underappreciated role of solute entropy in inducing large-scale morphological transitions in soft and cylindrical smectics, which are pervasive in man-made and biological systems.

It is important to recall here that depletion interactions are intrinsically short ranged. In the presence of macromolecular solutes, myelin figures—like other filamentous assemblies—can experience crowding-induced bundling, which brings myelins closer together.⁵⁸ Moreover, myelins are highly dynamic structures. These properties allow segments of large, bundled myelins to spatiotemporally localize in close juxtaposition. These effects can give rise to transient regions of significantly reduced separation, within which macromolecular exclusion becomes appreciable. Under such conditions, depletion interactions can couple with osmotically induced Helfrich-Hurault instability thereby stabilizing wrinkled surface topographies. A quantitative assessment of this mechanism will require further investigation and is beyond the scope of the present study.

More broadly, our finding suggests that myelin wrinkling in macromolecular solutions arises from the cooperative yet distinct roles of Helfrich-Hurault-type elastic instability and depletion-mediated interactions. In multilamellar cylindrical smectics, radial compression frustrates the preferred interlamellar spacing, rendering uniform relaxation energetically unfavorable and predisposing the system toward undulatory deformation modes characteristic of the Helfrich–Hurault instability. However, in contrast to planar lamellar systems subjected to uniform compression, the instability in myelin figures emerges in a spatially heterogeneous environment shaped by bundle geometry and interfacial confinement. Macromolecular osmolytes introduce a non-uniform osmotic pressure landscape through excluded-volume effects: depletion of polymeric solutes from narrow inter-myelin gaps generates a local osmotic pressure imbalance that stabilizes corrugated interfaces by increasing the configurational entropy of the depletants. In this framework, Helfrich-Hurault elasticity defines the accessible deformation modes and characteristic length scales, while depletion forces selectively stabilize interfacial, long-wavelength undulations and lock in their axial propagation and handedness. The resulting morphology thus reflects an interplay between elastic frustration intrinsic to cylindrical smectics and entropic forces arising from macromolecular crowding, providing a general mechanism for symmetry breaking and large-scale structural remodeling in soft multilamellar assemblies.

Materials & methods

Materials

1-Palmitoyl-2-oleoyl-glycero-3-phosphocholine (POPC), cholesterol (Ch),1,2-dipalmitoyl-sn-glycero-3-phosphoethanolamine-N-(7-nitro-2-1,3-benzoxadiazol-4-yl) (ammonium salt) (NBD-PE) and 1,2-dipalmitoyl-sn-glycero-3-phosphoethanolamine-N-(lissamine rhodamine B sulfonyl)(ammonium salt) (Rho-DOPE) were purchased from Avanti Polar Lipids (Alabaster, AL). Sucrose, poly(ethylene glycol)(BioUltra, Molecular weights 300, 600, 2000, 8000), Dextran from Leuconostoc mesenteroides (average molecular weight 9000–11 000), and chloroform were purchased from Sigma Aldrich (St. Louis, MO). Slides (22 × 50 × 0.5 mm and 22 × 50 × 1 mm) were purchased from Corning Incorporated. All the depletant solutions were prepared in deionized water (DI) (Millipore, Sigma, St. Louis, MO) for experimentation.

Formation of metastable myelin figures

Lipid solutions were prepared with a desired concentration of 25 mg mL⁻¹ in chloroform, using either 99.9% of lipid stock with 0.1 mol% Liss-Rho-DOPE or using 100 mol% lipid. From the prepared solutions, 4 µL was placed onto clean slide (22 × 50 × 0.5 mm) which was desiccated for at least 15 minutes under vacuum prior to usage. This slide was then sandwiched with a clean base slide (22 × 50 × 1 mm) and introduced to the microscope where deionized water is introduced at the edge of the cover slip. Capillary action pulls the water into the sandwich from the air–glass interface and flows toward the dried lipid cluster to produce metastable myelin figures.

Introduction of depletants via secondary hydration

30 µL of depletant-rich solution at the appropriate concentration was introduced into the existing pool of deionized water at the edge of the sandwich. It interacted with myelin figures via diffusion-mediated uptake and subsequent capillary action into the sandwich. The corresponding interactions of the new solution to those of the myelin colonies were captured by optical microscopy.

Sample imaging

Myelin figures were monitored in real time using a brightfield microscope and a fluorescence microscope equipped with a spinning disk confocal configuration using a Nikon Ti2 microscope. Real time image sequences were recorded in confocal mode, with a Yokogawa X1 spinning disc and a Hamamatsu Flash 4 SCMOS camera operated through Nikon Elements V 4.0. For visual inspections, long working distance dry objectives were used, for the confocal image acquisition either a 20× NA 0.75 Plan Apo or 60× NA 1.4 Plan Apo objective was used. Intensities of the Toptica iChrome MLE 4 color laser engine were set to 10% for the 488 nm and 561 laser lines, with exposure times to reduce photobleaching. Rho-DOPE (Ex/Em; 560/583) was exposed with a 50 mW 561 laser line and NBD-PE (Ex/Em; 460/535) was exposed with a 50 mW 488 laser line. Images were acquired by Hamamatsu ORCA-Fusion Digital CMOS camera (model #C14440-20UP) that collected images (2304 × 2304 pixels) and was controlled using Nikon NIS-Elements Advanced Research software. Rho-DOPE (Ex/Em; 560/583) was exposed with a 100 mW 561 laser line and NBD-PE (Ex/Em; 460/535) was exposed with a 100 mW 488 laser line.

Image processing

Microscopy images were collected using NIS Elements software (Nikon Instruments). They were further processed using Fiji^59,60 and various Python modules to quantify surface topographies of myelin figures. Myelin figure diameters were measured from line intensity profiles drawn manually in Fiji across individual tubes. The resulting gray value versus distance data were exported and processed in Python. The raw intensity profiles were smoothed using a Savitzky Golay filter (second-order polynomial, 7-point window) to reduce the high frequency noise while greatly preserving the shape of the intensity curve. The tube edges appear as local minima in fluorescent intensity and a peak-finding algorithm will detect the troughs. Tube diameter was calculated as distance between adjacent detected troughs and pooled across all line profiles for a single experiment. Measurements falling outside ±2 standard deviations from the mean were excluded. Final diameter distributions were reported as mean ± standard deviation.

Observed wrinkled surface profiles had quasi-sinusoidal patterns and corresponding wavelengths and amplitudes were measured using a manual approach in Fiji. Frames of interest were isolated and individual tubes displaying surface corrugations were straightened using Fiji's straightening tool. For each wrinkled tube, noise was reduced, contrast enhanced, and the straightened fluorescent image was binarized to facility wrinkle detection. The wavelengths and amplitude were then manually measured on this processed image. Due to the morphological complexity and variability of the wrinkled structures, a manual approach was favored over automated analysis as it provided more consistent and reliable results without the extensive parameter tuning required by algorithmic methods. An average of 10 edges (n = 10) were selected at each time point, with each experiment conducted in triplicate.

Conflicts of interest

The authors declare no competing interests.

Data availability

The data supporting this article has been provided as a part of the supplementary information (SI). Supplementary information: Videos S1–S17, experimental setup, determining osmotic pressure via modified van’t Hoff equation, determining the second virial coefficients, and sample osmotic pressure calculations. See DOI: https://doi.org/10.1039/d6sm00044d.

Acknowledgements

We thank Zhongrui Liu, Robert Golinski, David Sich, Francine Yu, Dr Daniel Speer, Dr Wan-Chih Su, and Dr James C. S. Ho for their productive conversations and experimental assistance. We thank the MCB Light Microscopy Imaging Facility, which is a UC-Davis Campus Core Research Facility, for the use of the spinning disc confocal fluorescence microscope. We thank Dr Thomas Wilkop for training support at the MCB Light Microscopy Imaging Facility. P.D.S. acknowledges additional support through UC-National Laboratory In-Residence Graduate Fellowship (L22GF4492). This work is supported by the Divisions of Materials Research and Physics, National Science Foundation, through the awards DMR-2022385 and DMR-1810540).

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