Electrostatic Shape Control of a Charged Molecular Membrane from Ribbon to Scroll

Electrostatic shape control of a charged molecular membrane from ribbon to scroll

Changrui Gaoa,1, Sumit Kewalramania,1, Dulce Maria Valenciaa, Honghao Lia, Joseph M. McCourtb, Monica Olvera de la Cruza,b,c,2, and Michael J. Bedzyka,b,2

aDepartment of Materials Science and Engineering, Northwestern University, Evanston, IL 60208; bDepartment of Physics and Astronomy, Northwestern University, Evanston, IL 60208; and cDepartment of Chemistry, Northwestern University, Evanston, IL 60208

Edited by Lia Addadi, Weizmann Institute of Science, Rehovot, Israel, and approved September 22, 2019 (received for review August 12, 2019) Bilayers of amphiphiles can organize into spherical vesicles, nano- acids, nanoribbons were found to transform into helical ribbons as tubes, planar, undulating, and helical nanoribbons, and scroll-like the PA concentration was reduced (17) and into helical and cochleates. These bilayer-related architectures interconvert under twisted nanoribbons when the amino acid sequence was permuted suitable conditions. Here, a charged, chiral amphiphile (palmitoyl- (18). Helical assemblies have been previously used to template

lysine, C16-K1) is used to elucidate the pathway for planar nano- semiconductor nanohelices (19). Despite the progress, the corre- ribbon to cochleate transition induced by salt (NaCl) concentration. lation between experimental conditions such as molecular design, In situ small- and wide-angle X-ray scattering (SAXS/WAXS), atomic ionic strength, pH, amphiphile concentration, and the attained force and cryogenic transmission electron microscopies (AFM and nanoribbon-related morphology are not fully established. There- cryo-TEM) tracked these transformations over angstrom to microme- fore, precise control of nanoribbon-related architecture requires ter length scales. AFM reveals that the large length (L) to width (W) further understanding of the delicate interplay between intermo- ratio nanoribbons (L/W > 10) convert to sheets (L/W → 1) before lecular interactions and elastic and interfacial energies. rolling into cochleates. A theoretical model based on electrostatic A recent theoretical study showed that for charged molecules, and surface energies shows that the nanoribbons convert to sheets tuning the range of electrostatic interactions could induce tran- via a first-order transition, at a critical Debye length, with 2 shallow sitions between different nanoribbon-related morphologies (20).

minima of the order of thermal energy at L/W >> 1 and at L/W = 1. Specifically, a phase diagram was deduced for a 2D lattice of CHEMISTRY SAXS shows that interbilayer spacing (D) in the cochleates scales charged points, which interacted via long-range repulsive elec- linearly with the Debye length, and ranges from 13 to 35 nm for trostatic interactions and short-range attractive interactions. NaCl concentrations from 100 to 5 mM. Theoretical arguments that Planar nanoribbon to wavy ribbon with periodic undulations to include electrostatic and elastic energies explain the membrane roll- helical ribbon transitions were predicted as the range of the ing and the bilayer separation–Debye length relationship. These electrostatic interactions is increased. This study suggests a facile models suggest that the salt-induced ribbon to cochleate transi- method for accessing distinct nanoribbon architectures by vary- tion should be common to all charged bilayers possessing an ing the ionic strength (μ) of the solution because the range of intrinsic curvature, which in the present case originates from electrostatic interactions as parametrized by Debye length (λd) −1/2 molecular chirality. Our studies show how electrostatic interac- scales as μ . Recent experiments also attest that tuning the tions can be tuned to attain and control cochleate structures, which have potential for encapsulating, and releasing macromol- Significance ecules in a size-selective manner. Controlling the shape and internal architecture of assemblies of bilayer assembly | electrostatics | nanoribbon | cochleate amphiphiles is critical for many technologies. The structure, and thus the function, of these assemblies reconfigures in re- mphiphilic molecules can self-assemble into a variety of 3D, sponse to stimuli, via mechanisms that are often elusive. Here, A2D, and 1D nano- and mesoscale structures. These struc- we observe and explain how molecular reordering driven by tures serve as simplified models for understanding biological variations in electrostatic screening length induce micrometer- assemblies and their functions and have applications in drug scale structural changes in crystalline membranes of charged, delivery (1–5), regenerative medicine (6, 7), biosensing (8), hy- chiral molecules: The transformation of high aspect ratio, pla- drogen production (9, 10), and clean water technologies (11). An nar bilayers into scroll-like cochleates by increasing the solution interesting assembly structure is the nanoribbon, which is a high salt content is described and explained. Our study suggests that aspect ratio (10:1 or greater) bilayer. Nanoribbons are a gateway to this transformation should be general to charged bilayers pos- a number of other morphologies with distinct functionalities. For sessing a spontaneous curvature. example, nanoribbons of a charged chromophore amphiphile can transform to a scroll-like (cochleate) morphology when the solu- Author contributions: S.K., M.O.d.l.C., and M.J.B. designed research; C.G., S.K., D.M.V., H.L., and J.M.M. performed research; C.G., S.K., D.M.V., H.L., J.M.M., M.O.d.l.C., and M.J.B. tion ionic strength is increased (9). These cochleates serve as ef- analyzed data; and C.G., S.K., D.M.V., M.O.d.l.C., and M.J.B. wrote the paper. ficient charge-transfer agents for photocatalysts in hydrogen The authors declare no competing interest. production. Cochleate formation from liposomes of negatively charged phospholipids in the presence of multivalent cations also This article is a PNAS Direct Submission. involves a nanoribbon intermediate (3, 12, 13). Biocompatible Published under the PNAS license. phospholipid cochleates are being explored as drug-delivery agents Data deposition: All the X-ray data shown in the manuscript and the SI Appendix, as well as the code for simulating the WAXS intensity along with the data from theory calcula- because they can trap macromolecules, such as proteins, and tions, have been deposited at Bitbucket (https://bitbucket.org/NUaztec/gao_et_al_pnas_ DNA, and provide protection against degradation due to their 2019_charged_membrane/src/master/). multilayer geometry. Nanoribbons have also been observed in 1C.G. and S.K. contributed equally to this work. peptide amphiphiles (PAs), which consist of a sequence of amino 2To whom correspondence may be addressed. Email: [email protected] or acids covalently linked to an alkyl tail (14, 15). For example, a [email protected]. peptide amphiphile that stimulates collagen production has been This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. found to self-assemble into nanotapes with an internal bilayer 1073/pnas.1913632116/-/DCSupplemental. structure (16). In a PA with alternating charged and neutral amino

www.pnas.org/cgi/doi/10.1073/pnas.1913632116 PNAS Latest Articles | 1of7 Downloaded by guest on October 1, 2021 ionic strength leads to predictable changes in the nanoribbon- Fig. S1). Therefore, under the experimental conditions, nearly all related assembly morphology. For example, the period of the of the C16K1 are expected to be in their +1 ionized state. twists in amyloid fibril aggregates monotonically decreases with The AFM image of C16K1 assemblies at a silica (SiOx)/water decreasing ionic strength (21). interface (Fig. 1B) and other AFM images collected at different In this study, we analyze morphological changes in charged spots on the substrate reveal that in the absence of added salt, W planar nanoribbons as a function of increasing ionic strength. In C16K1 assembles into flat ribbons, with widths ( ) in the range L μ this regime, nanoribbon to cochleate transformations have been of a few hundred nm, lengths ( ) ranging from 2 to 20 m, and L W observed in phospholipids (12) and chromophore amphiphiles (9, aspect ratio ( / ) as high as 30. All of the ribbons exhibit the same thickness of ∼4.0 nm, as shown by a representative AFM 10, 22, 23). However, the generality and the mechanistic details of C this transition are still unknown. In particular, the correlation height scan (Fig. 1 ). This thickness is less than twice the length (5.4 nm) of fully extended C K molecules (Fig. 1A), suggesting between the ionic strength induced changes in the molecular 16 1 that the C K ribbons are bilayers with the alkyl tails of the 2 packing and the mesoscopic morphology transformations are 16 1 leaflets interdigitated. The interdigitated bilayer configuration, elusive. The principal aim of this study is to start with a nano- which has also been observed in C16K2 (24) and other PAs (17), ribbon structure and experimentally trace the micrometer to is expected for molecules with headgroup cross-sectional areas angstrom length-scale transformations in the membrane much larger than that for the alkyl tails. structure as a function of ionic strength by using a combination Screening effects are analyzed in C16K1 dispersions that contain of cryotransmission electron microscopy (cryo-TEM), liquid- NaCl at concentrations (c) ranging from 0 to 100 mM. Fig. 2 A–D atomic force microscopy (liquid-AFM), and in situ small- and show AFM images of C16K1 assemblies at SiOx/NaCl solution in- wide-angle X-ray scattering (SAXS/WAXS). The experiments are terfaces for c = 0, 1, 3, and 5 mM. Peak-force error images are coupled with theoretical models that qualitatively explain the shown as they deliver better 3D representation of the morphol- observed morphological transitions. ogies (26, 27). With increasing NaCl concentration the ribbon We chose a simple peptide amphiphile (PA), C16K1,witha aspect ratio decreases, and at c = 3 mM nearly isotropic sheets of 1 single ionizable amino acid lysine (K) covalently linked to a to 3-μm diameter are observed (Fig. 2C). At or above this c palmitoyl (C16)alkyltail(Fig.1A). This PA was chosen because threshold concentration ( th), the sheets roll into cochleates (Fig. D our recent study (24) on C16K2 found spherical micelle to cylin- 2 ). AFM images depicting semirolled membranes and detailed drical micelle to a mixture of cylindrical micelle and nanoribbon screw-like features of the cochleates are shown in SI Appendix, transformations as the molecular charge was reduced by increasing Figs. S2 and S3. The multilayered nature of the scrolls is also E–H SI Appendix the solution pH. Therefore, we hypothesized that removing one of observed in cryo-TEM images (Fig. 2 and , Fig. S4). Fig. 2 F–H further reveal that the interbilayer spacing (D) the charged lysines from the headgroup could yield a macroscopic c state consisting purely of nanoribbons. Second, the choice of this within the cochleates monotonically decreases with increasing . Overall, AFM and cryo-TEM show that increasing the ionic PA ensures that the interheadgroup interactions are Coulombic, strength even over a narrow range first induces the ribbon to sheet unlike the case of PAs with multiple amino acids, where the as- to cochleate transitions, and thereafter reduces the interlamellar sembly is strongly modulated by intermolecular hydrogen bonding. spacing within the cochleates. We first describe the C16K1 assembly in the absence of added L We obtain ensemble-averaged, quantitative details of the salt. For this, -C16K1 was dispersed in pure water at 4 mM mesoscopic morphology by SAXS and the molecular packing by concentration. Unless otherwise stated, the enantiomeric form of WAXS in the ribbons and the cochleates. Fig. 3 A and B show the the amino acid [left-handed (L)] and the PA concentration background-subtracted SAXS and WAXS data for C16K1 ribbons (4 mM) are the same in all of the samples. The pH of this C16K1 in pure water, as a function of scattering vector magnitude q = dispersion was ∼4.6, which is much lower than the dissociation 4πsin(θ)/λ.Here,λ = 0.827 Å is the X-ray wavelength, and 2θ is the ∼ SI Appendix −1 −2 constant pK 7.4 for C16K1 in their aggregates ( , scattering angle. For q < 0.4 nm (Fig. 3A), the intensity I ∝ q is indicative of structures with extended sizes in 2D, which is consistent with the AFM observation of flat ribbons with length and width both greater than 2π/qmin ∼ 300 nm, where qmin is the minimum accessible q in the measurements. Fig. 3B shows strong Bragg re- − flections in the range 14 < q < 16 nm 1 corresponding to 0.45 > 2π/q > 0.4 nm distances, which are close to the diameter of the alkyl tails. Therefore, within the ribbons, the alkyl tails pack on a crystalline lattice such that the nearest-neighbor distances are commensurate with the tail diameter. A symmetric bilayer model with a hydrophobic tail region sandwiched between 2 hydrophilic head regions is used for fitting theSAXSdata(Fig.3A). The tail region electron density (ED) was − 3 fixed at ρt = 320 e /nm , the value for crystalline, densely packed alkyl tails (28). Setting th ≤ 0.85 nm, based on a molecular dynamics (MD) simulation for a single C16K1 molecule in water (Fig. 1A), the best fit for the SAXS data (black curve, Fig. 3A) was obtained t = +0.5 t = +0.0 with thicknesses t 2.3−0.0 nm and h 0.85−0.45 nm for the tail and ρ = +61 − 3 the head region, respectively, and h 386−0 e /nm for the head region ED. The most robust parameter, the bilayer thickness t + t = +0.0 2 h t 4.0−0.4 nm, is consistent with the AFM measurements (Fig. 1C). Consistent with the interdigitation hypothesis, SAXS Fig. 1. (A) Molecular structure of +1 charged C16K1 with estimates for hydrophobic tail and hydrophilic headgroup lengths. The molecular confor- reveals a much lower thickness of the hydrophobic region (2.3 nm) as compared to the length of 2 fully extended C16 tails (2 × 1.9 nm). mation was derived from an MD simulation for a single C16K1 in water using C the universal force field (25). (B) AFM image from a silica/water interface TheSAXSobservationsaresummarizedinFig.3 . B showing high aspect ratio C16K1 nanoribbons. (C) The height profile across a The WAXS data for ribbons (Fig. 3 ) show 3 strong Bragg −1 C16K1 ribbon (green line in B). peaks at q = 13.9, 15.0, and 16.2 nm ; consistent with crystalline

2of7 | www.pnas.org/cgi/doi/10.1073/pnas.1913632116 Gao et al. Downloaded by guest on October 1, 2021 Fig. 2. (A–D) AFM peakforce error images of drop-cast C16K1 membranes at SiOx/NaCl solution interface. As NaCl concentration increases, structural transformations are observed from nanoribbon to isotropic sheet and to rolled-up cochleates, which exhibit a screw-like pitch. (E–H) Cryogenic TEM images of CHEMISTRY cochleates exhibiting scroll morphology and the internal multilayer features. The interbilayer spacing D within the cochleate structure decreases as NaCl concentration increases.

− packing of the alkyl tails into an oblique unit cell with lattice of the Bragg reflections for q > 10 nm 1 (Fig. 3B, black curve). constants at = 0.49 nm, bt = 0.53 nm, and γt = 127°. To distin- Complementary grazing incidence X-ray scattering (GIXS) guish between the tails from the 2 leaflets, the unit cell is recast measurement on C16K1 ribbons drop-casted onto a Si substrate with a = 0.49 nm, b = 0.85 nm, and γ = 100° (Fig. 3D). In this unit revealed diffraction peaks at qxy positions, which were identical cell, the tails at the vertices and the center belong, respectively, to the q positions of the diffraction peaks observed in solution to the 2 opposing leaflets. By using these 2D unit cell parameters WAXS (SI Appendix, Fig. S5). Here, qxy is the component of the and an untilted parallelepiped to model each tail (SI Appendix, scattering vector in the bilayer plane. The above observation section 2), we are able to simulate the positions and the intensities validates the WAXS-derived oblique lattice (Fig. 3D), and the near-zero tilt of the tails with respect to the bilayer normal. Specifically, GIXS yields the maximum tilt of the alkyl tails ∼6° (SI Appendix,Fig.S5). Line-shape analysis of WAXS peaks (Fig. 3B) reveals an average 2D crystal domain size of ∼15 nm, which is significantly smaller than the ribbon size. This implies that the ribbons are polycrystalline. The SAXS/WAXS data from the ribbons also exhibit weak, but − sharp Bragg reflections for q ≤ 10 nm 1. The most prominent of − these reflections is at q = 2.5 nm 1 (Fig. 3A). A much weaker − reflection is also observed at q = 7.5 nm 1 (Fig. 3B). In fact, GIXS measurements of ribbons revealed qz-extended intensity rods at −1 qxy = 2.5, 5.0, 7.5, and 10.0 nm (SI Appendix,Fig.S6). Here, qz is the scattering vector component along the bilayer normal. Thus GIXS shows that the low-q Bragg reflections originate from an in- plane ordering within the bilayer, which we attribute to a preferred orientational ordering of C16K1 headgroups. This headgroup ordering is commensurate with the alkyl tail lattice, and can be de- fined by a unit cell that is a 1 × 3 supercell of the alkyl tail unit cell in Fig. 3D because the position of the first Bragg reflection (q1 = − 2.5 nm 1) equals one-third of the magnitude of the (0 1) reciprocal Fig. 3. (A) Background-subtracted in situ SAXS intensity profile for C16K1 lattice vector for the alkyl tail lattice [i.e., q1 = b*/3 = 2π /(3b sinγ)]. nanoribbon. The solid black curve is the best fit over the range of 0.1 < q < Perhaps headgroups of neighboring C K along the b axis in each −1 16 1 6nm based on a symmetric bilayer model. (B) Background subtracted in leaflet are rotated 120° clockwise (or anticlockwise) relative to situ WAXS intensity profile of C16K1 nanoribbon shows diffraction peaks − each other about the bilayer normal. However, proving this hy- over the range of 10 < q < 30 nm 1. The solid black curve is a simulation based on a parallelepiped model for alkyl tails and the unit cell in D.(C) The pothesis is beyond the scope of the current work. Overall, the SAXS/WAXS analysis of C K ribbons in pure water proves that interdigitated C16K1 bilayer structure and electron density profile deter- 16 1 mined from analysis of SAXS data. (D) Two-dimensional unit cell and lattice ribbons are bilayers with interdigitated leaflets and that the parameters for alkyl tail packing, derived from WAXS. packing of alkyl tails and headgroups exhibits crystalline ordering.

Gao et al. PNAS Latest Articles | 3of7 Downloaded by guest on October 1, 2021 −1/2 We traced the ribbon to cochleate transformation and the the electrostatic screening length (λd ∝ c ). Thus, the range of changes in cochleates as a function of NaCl concentration via electrostatic interactions also controls the interbilayer spacing. 3) SAXS/WAXS. Fig. 4 A and B show X-ray scattering from 4 mM As noted in the SAXS analysis of ribbons, the broad intensity −1 C16K1 at low (c = 1–5mM)andhigh(c = 5–50 mM) NaCl modulation for 0.8 < q < 3nm is due to an individual C16K1 − concentrations, respectively. Fig. 4A shows that for c ≥ 2 mM and bilayer. Fig. 4A shows that the minimum position at q ∼0.9 nm 1 −1 for q < 0.1 nm , the monotonic fall in intensity (Figs. 3A and 4A, shifts to a lower q when the ribbons are transformed into coch- bottom curve) is replaced by multiple intensity modulations due leates. This shift is observed up to c = 4mM(Fig.4B), and is to cochleates. The SAXS-deduced NaCl concentration of 2 mM consistent with an increase in the bilayer thickness from 4.0 nm for ribbon to cochleate transition is only slightly lower than the (ribbon) to 4.3 nm (cochleate) due to an increase in the thickness threshold cth = 3 mM in AFM experiments. More importantly, cth of the tail region (SI Appendix,Fig.S8). Thus, a curvature-induced is independent of the C16K1 concentration, as indicated by SAXS strain in the cochleates reduces the extent of interdigitation be- experiments on 10 mM C16K1 solutions (SI Appendix,Fig.S7). tween the bilayer leaflets. 4) The curvature also reduces the de- Therefore, rolling of the membrane into cochleates is driven by the gree of order in the packing of C16K1 tails and headgroups. For solution ionic strength; i.e., the range of intermolecular electrostatic the case of 4 mM C16K1, the sharp diffraction peaks corre- interactions controls the ribbon to cochleate transition. sponding to the crystalline ordering smear out for c ≥ 3mM.A A q Fig. 4 shows intensity modulations across the entire range similar behavior is observed for 10 mM C16K1 solutions (SI Ap- − of 0.02–30 nm 1, which are divided into 4 groups, each yielding pendix,Fig.S7). Overall, X-ray scattering analysis reveals that < q < −1 information at a different length scale: 1) the 0.02 0.06 nm above a threshold NaCl concentration of 2–3mM,C16K1 as- modulation (Fig. 4A, left red box) arises from the cross- sembles into cochleates. The interbilayer spacing within these section of the cochleates. If we assume the overall shape of a cochleates depends linearly on the electrostatic screening cochleate is a cylinder of radius R, then the scattering ampli- length, and the curved morphology of the cochleates induces a tude FcylðqÞ ∝ J1ðqRÞ=ðqRÞ where J1 is the first-order Bessel reduction in the interdigitation between the bilayer leaflets and function of the first kind. The first zero of J1ðqRÞ=ðqRÞ occurs the crystallinity in the molecular packing. − at qR = 3.8. Therefore, the minimum at q ∼ 0.022 nm 1 yields We developed simple theoretical models to rationalize the an average cochleate radius R = 3.8/0.022 ∼173 nm, which is observed structural changes. We focused on 3 aspects: 1) The consistent with the TEM image of the cochleates in 5 mM NaCl decrease in the ribbon aspect ratio with increasing salt con- − (Fig. 2D). 2) For 0.1 < q < 1nm 1, the intensity maxima po- centration, 2) The rolling of the membranes, and 3) the linear sitions follow the sequence qmax:2× qmax:3× qmax. Therefore, relationship between the interbilayer separation within the these modulations are Bragg reflections due to periodic la- cochleates and the electrostatic screening length. mella, with a spacing D = 2π/qmax within the cochleates. Based on Wefirstdiscusstheribbontosheet transformation. For this, −1/2 qmax (Fig. 4B) for 0.005 ≤ c ≤ 0.1 M, D (nm) = 6.40 + 2.05 × c we model the membrane as a thin parallelepiped (Fig. 5 A, (Fig. 4C). That is, for the range of NaCl concentration used, Inset)oflengthL,widthW,thicknessδ, and uniform charge the interlamellar spacing could be continuously tuned from density ρ = Q=LW for the top and bottom surfaces. The mem- 13 to 35 nm, and the interlamellar spacing varies linearly with brane energy is formulated as the sum of electrostatic interactions

Fig. 4. (A) Background-subtracted in situ SAXS/WAXS data for 4 mM C16K1 as the NaCl concentration is increased from 1 to 5 mM. The datasets are offset − vertically for clarity. With increasing NaCl concentration, the appearance of multiple intensity modulations for q < 0.1 nm 1 and the smearing of the sharp

WAXS diffraction peaks are connected with the ribbon to cochleate transition. (B) Background-subtracted in situ SAXS data for 4 mM C16K1 as the NaCl concentration is increased from 5 to 50 mM. The datasets are offset vertically for clarity. The position of first-order small-angle diffraction peaks(0.1< q < − 1nm 1) is used to determine the interbilayer spacing D inside the cochleates. (C) SAXS-derived interbilayer spacing in the cochleates varies linearly as a function − − of c 1/2,wherec is NaCl molar concentration. The solid black line is the best fit with equation: D (nm) = 6.40 + 2.05 × c 1/2.

4of7 | www.pnas.org/cgi/doi/10.1073/pnas.1913632116 Gao et al. Downloaded by guest on October 1, 2021 but exhibit a twist with respect to their neighbors. This relative orientation constraint and the constraint of a preferred tilt angle with respect to the bilayer normal can be simultaneously satisfied by shapes exhibiting cylinder-like curvature, such as closed tubes. In qualitative agreement with these theories, SAXS/WAXS measurements show that at high salt concentrations, cochleates are formed for (left-handed) L- and (right-handed) D-C16K1. Under identical conditions, planar bilayers are observed for a racemic mixture (1:1 mixture of L- and D-C16K1)(SI Appendix, Fig. S9). Furthermore, molecular chirality induces chirality in the assemblies at all length scales: At the nanoscale, the 2D lattice for Fig. 5. (A) The membrane energy per molecule (Eq. 1) as a function of the tail packing is oblique (Fig. 3D), and at the mesoscale the coch- inverse of membrane aspect ratio W/L. At low salt concentrations (large Debye leates have a screw-like handedness (Fig. 2D and SI Appendix, Fig. lengths), an elongated ribbon structure is the equilibrium morphology. By – contrast, at very high salt concentrations (small Debye lengths), the membrane S3). For these reasons, we use the Helfrich Prost model (29) to show that the combined effects of molecular chirality and tilt not energy is minimized when L/W = 1. (Inset) Schematic representation of a C16K1 nanoribbon for numerical calculation. (B) The optimal inverse aspect ratio only lead to helical ribbon and cylinder (29–31) morphologies, but (minimum energy) for different Debye lengths. The first-order transition hap- can also stabilize the spiral-helicoidal shape of cochleates. This λ = pens at d 2.96 nm. (Inset) The energy difference between the optimal aspect model also yields insights into the relationship between inter- ratio and the sheet (aspect ratio = 1). The energy difference near the transition bilayer separation in cochleates and salt concentration. point is much smaller than kBT. The scroll morphology (SI Appendix,Fig.S3) resembles a spiral-helicoidal surface (Fig. 6A) that can be parameterized as: Xðθ, zÞ = ðDθ sin θ, Dθ cosθ, pθ + zÞ.Here,D is the sheet sepa- HS, interfacial energy HI, and the edge energy HL that accounts ration in the cochleate, and p is the pitch of the helical windings for the exposure of hydrophobic tails to water on the edge surfaces along the cochleate long axis. The relevant interactions for such a of the membrane, HT = HS + HI + HL: membrane are the elastic energy, the long-range electrostatic interaction, the short-range attractive van der Waals interaction, and ZQ Z Z the short-range hydration repulsion (32). Based on SAXS/WAXS CHEMISTRY D–δ HT = φs q dq+ σ dA + γδ dl. [1] measurements, the aqueous layer thickness ( )variesbetween ∼31 and 9 nm when the salt concentration is varied between 5 and 0 100 mM. This thickness is much larger than the hydration decay length (32). Therefore, the hydration energy term can be neglec- Here, φs is the screened electrostatic potential evaluated on the ted. Besides, in a mean-field description, short-range attractive membrane surface, σ is the interfacial tension, and γ is the energy forces can be neglected (29, 33). Theoretical arguments and ex- density for the membrane edge surfaces. For details, see SI Ap- perimental observations above suggest that lipid tilt and chirality pendix,section3. Short-range interactions, such as the intermolec- are relevant in the membrane description. Thus, the energy for a ular van der Waals are neglected. Furthermore, the second term in cochleate can be written as: HT = HF + HS + HB.Here,HF is the Eq. 1 can be ignored because AFM images (Fig. 2) show 1–5-μm2 Frank interaction describing the increment in the energy due to membranes, independent of the electrolyte concentration. We the molecular reordering and distortions from their uniformly evaluated Eq. 1 numerically for rectangular membranes of a aligned configuration. HS and HB are the electrostatic and the fixed area A that are constituted by a fixed number of charges bending energies, respectively. The electrostatic interactions Hs interacting through the Debye–Hückel potential (Fig. 5A). The renormalize the physical properties of the membrane. In particu- numerical values of parameters ρ, γ, δ,Aare listed in SI Appendix, lar, the membrane bending rigidity changes as: κ = κ0 + κelðλdÞ (34). Table S1. Briefly, at very high salt concentrations (λd → 0), the Here, κ is the intrinsic membrane bending rigidity and κel is an electrostatic interactions are weak, short-ranged, and thus insensi- 0 electric contribution that depends on the membrane geometry and tive to the membrane shape. Here, the interfacial energy domi- the Debye length, λd. This electric contribution to bending has nates and leads to square sheets (Fig. 5A, λd ≤ 2.96 nm), a configuration that minimizes the exposed edge surfaces or the been experimentally verified for some lipid membranes (35). Thus, ratio of perimeter to area for the top and bottom membrane the combined effect ofR bending and electrostatic energies can be 2 2 + θ2 written as Hs + HB ≈ κ dAK .HereK = = is twice the surfaces. For the same reason, in experiments quasicircular sheets Dð1p+ θffiffiffiffiffiffiffiffiffiffiffiffi2Þ3 2 are observed (Fig. 2C). In the very low salt condition, the elec- mean curvature of the cochleate, and dA = D 1 + θ2 is the area trostatic interactions are strong and long-range and HS becomes element. If we assume that the molecules orient uniformly such dominant. This leads to high aspect ratio ribbons (Fig. 5A, λd ≥ 2.97 nm). Fig. 5B shows the optimal membrane aspect ratio for different Debye lengths (salt concentrations) revealing a first- order transition from narrow ribbons to square sheets. The energy difference between the two phases is much lower than kBT (Fig. 5 B, Inset). Therefore, the two phases can coexist near the transition, which is consistent with experimental observation of membranes of varied aspect ratios near the transition (Fig. 2B). We note that λd = 2.97 nm corresponds to ∼10 mM NaCl, which is larger than the experimental 3 mM NaCl for the ribbon to sheet transition. This minor difference may be due to the approximate parameters used for the surface tension and membrane charge density. Next, we consider the cochleate formation. Previous theoretical studies have shown that membranes of chiral molecules will – Fig. 6. (A) The geometry of the cochleates. D is the interbilayer separation. experience an out-of-plane bending force (29 31) if the molecules Arrows represent the projection of the tilt vector in the local tangent plane. are tilted with respect to the bilayer normal. Briefly, because (B) Theoretical prediction showing a roughly linear relationship between of chirality, the molecules do not pack parallel to each other, interbilayer spacing D and c−1/2, where c is NaCl molar concentration.

Gao et al. PNAS Latest Articles | 5of7 Downloaded by guest on October 1, 2021 that the tilt projection m in the local tangent plane forms an angle from L- and D-C16K1 ribbons clearly show sharp diffraction peaks φ m = φ θ^ + φ ^z C SI Appendix 0 with the azimuthal direction, then cos 0 sin 0 ,where indicating crystalline bilayers (Fig. 3 and ,Figs.S5 ^ θ,^z are the unit vectors in the azimuthal and axial directions (Fig. and S9). Second, membrane curvature is expected for cases where 6A). Therefore, the Frank energy takes the simple form the molecules are tilted with respect to the bilayer normal. Our WAXS and GIXS data are currently inconclusive in this regard: In H κ′ the planar ribbon phase, the molecules may have a slight (<6°) tilt. F 2 2 = K cos φ − λHP K sin φ cos φ . [2] W 2 0 0 0 Whether, the molecules in bilayer have a small tilt or the molecules undergo a tilting transition just prior to the sheet to cochleate Here, κ′ is the difference between elastic constants for bend- transformation will be a subject of future studies. ing the membrane in the parallel and perpendicular directions Conclusions to the tilt vector, and λHP measures the strength of the intermolecular chiral interactions (29, 30). The minimization of the We designed a peptide amphiphile C16K1 to investigate the H φ total energy T with respect to 0 predicts a critical tilt angle electrolyte-induced transformation of planar bilayers to scroll- φ = −ð κ + κ′Þ=κ′ sec 2 0 2 . If the energetic costs of bending the mem- like cochleates. We show that with the addition of NaCl, the brane parallel or perpendicular to the tilt direction are almost the high aspect ratio C16K1 ribbons formed in zero salt conditions κ′ ≈ φ ≈ same, (i.e., 0), then 0 45°. This is roughly equal to the angle transform to isotropic sheets, prior to rolling up to form coch- of the helical windings with the cochleate’s principal axis (SI Ap- leates. This ribbon to cochleate transformation also induces a pendix,Fig.S3) suggesting that molecular tilt direction coincides reduction in the crystallinity in the molecular packing. Further with the membrane folding direction. This hypothesis needs fur- addition of salt reduces, within the cochleates, the interbilayer ther exploration. While the molecular tilt orientation is related separation, which scales linearly with the Debye length. A sim- only to the membrane elastic parameters, the interbilayer separa- plified model demonstrates that the ribbon to sheet trans- tion D depends on κ/λHP, i.e., the ratio of the membrane bending formation is a first-order transition induced by the reduction in rigidity and the molecular chiral interaction parameter (SI Appen- the range of electrostatic interactions. Theoretical models show dix,Eq.S16). In particular, D decreases nearly linearly with the that rolling of membranes into cochleates is the combined effect Debye length for R k=λHP,whereR is the cochleate external of molecular chirality and tilt. The linear relationship between radius. Furthermore, a theoretical curve that approximately repro- the interbilayer separation and the screening length in cochleates duces the D vs. λd experimental data (Fig. 6B) yields κ0/λHP ∼ is qualitatively explained by the competition between electro- SI Appendix 200 m. (See , section 3 for details.) The slight quanti- static and the effective elastic interactions that include the in- B tative deviation between the experiment and theory (Fig. 6 )is ternal degrees of freedom of tilt and chirality. These results likely due to neglecting the stretching degrees of freedom and the suggest that the salt-induced structural transitions in the C16K1 thickness of the membrane. Nevertheless, the accuracy of the system should be observed in other charged bilayer mem- qualitative predictions of the model clearly highlights the collec- branes. Our combined experimental and theoretical study tive effect of molecular tilt and chirality in inducing the spontane- yields insight into attaining the cochleate structures and con- ous membrane curvature. This combined with the electrostatic trolling their internal architecture. These results should be effects, which rigidifies the membrane, enable us to deduce qual- useful for optimizing the structure and function of cochleates itatively the key structural features of the cochleates. In particular, in many applications, including drug delivery and photocatalytic this simplified theoretical model suggests that the linear relation- production of hydrogen. ship between the interbilayer separation and the electrostatic screening length is not a result of system-specific design, but of Materials and Methods the interplay between electrostatic energy and the membrane in- Peptides synthesis and SAXS/WAXS, Cryo-TEM, and liquid-AFM measure- ternal degrees of freedom. Therefore, it is not surprising that ments are described in SI Appendix. similar linear relationships have been observed in other charged layered systems, such as clay mineral montmorillonite (36, 37). Data Availability We note that the linear relationship is not valid in the presence All the X-ray data shown in the manuscript and the SI Appendix, multivalent ions. For example, negatively charged phospholipid as well as the code for simulating the WAXS intensity along with cochleates show little or no dependence of interbilayer spacing the data from theory calculations, have been deposited at Bitbucket on the CaCl2 concentration (38). It is possible that the multi- (39). The files are in folders labeled with corresponding figure valent cations are tightly bound to the molecules resulting in numbers. interbilayer electrostatic interactions that cannot be parame- λ terized by the screening length d alone. By contrast, the use of ACKNOWLEDGMENTS. This research was primarily supported by the De- monovalent salts to induce the C16K1 cochleate structure leads partment of Energy (DOE), Office of Basic Energy Sciences under Contract to tunable interbilayer spacing over ∼10–40 nm. This structural DE-FG02-08ER46539. Peptide synthesis was performed in the Peptide feature may have application for controlled encapsulation and Synthesis Core Facility of the Simpson Querrey Institute at Northwestern release of drug particles within a specific size range. University. The SAXS/WAXS experiments were performed at the DuPont- Northwestern-Dow Collaborative Access Team (DND-CAT) located at Sector 5 Finally, we note that while the experimental results for of the Advanced Photon Source (APS) and at APS Sector 12. The APS, an cochleates are in qualitative agreement with the predictions of Office of Science User Facility operated for DOE by Argonne National theoretical models for assembly of chiral molecules, there are still Laboratory, is supported by DOE under Contract DE-AC02-06CH11357. GIXS unresolved questions. First, these continuum models (29–31) are was performed at the XRD Facility and TEM used the EPIC facility at Northwestern University. The authors thank M. Karver for peptide synthesis, strictly applicable to fluid-like membranes or membranes with Dr. Liam Palmer for discussions and for suggesting cryo-TEM, and Drs. S. Weigand hexatic order. That is for cases where there are no long-range (DND-CAT) and B. Lee (APS, sector 12) for the assistance with the X-ray intermolecular positional correlations. However, the WAXS data scattering measurements.

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