A Lateral Diffusion Study - American Chemical Society

Oct 31, 2014 - Department of Chemistry, University of Basel, Klingelbergstrasse 80, 4056 ... Biozentrum, University of Basel, Mattenstrasse 26, 4058 B...
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Molecular Organization and Dynamics in Polymersome Membranes: A Lateral Diffusion Study Fabian Itel,† Mohamed Chami,‡ Adrian Najer,† Samuel Lörcher,† Dalin Wu,† Ionel A. Dinu,† and Wolfgang Meier*,† †

Department of Chemistry, University of Basel, Klingelbergstrasse 80, 4056 Basel, Switzerland Center for Cellular Imaging and Nanoanalytics (C-CINA), Biozentrum, University of Basel, Mattenstrasse 26, 4058 Basel, Switzerland

‡

S Supporting Information *

ABSTRACT: Amphiphilic block copolymers self-assemble into artificial membranes of enhanced strength and stability compared to lipid membranes and are still able to incorporate biological membrane proteins. Membrane fluidity is a key parameter for retaining function of incorporated proteins. In this study, lateral diffusion properties of membranes of diblock and triblock copolymers based on poly(2-methyl-2-oxazoline) and poly(dimethylsiloxane), with thicknesses between 6 and 21 nm, were systematically investigated. Z-scan fluorescence correlation spectroscopy was used to obtain highly accurate diffusion coefficients. The lateral diffusion coefficients (D) scale with the molecular weight of the hydrophobic block (Mh) for both diblock and triblock configurations as D ∝ Mh−1.25. A significant diffusion increase of diblocks compared to triblocks revealed that diffusion is primarily related to the different structural conformation of the macromolecules assembled in the membrane. Moreover, hindered diffusion for higher molecular weight copolymers was observed, indicating formation of domains due to interdigitation and entanglement, whereas free 2-D diffusion was detected for low molecular weight copolymers. These results represent a further step to understand structure-related membrane properties, i.e., density, stability, fluidity, permeability, etc. Additionally, the tracking of labeled membrane constituents embedded in artificial membranes offers crucial information about the desired functionality of bio-inspired supramolecular 3-D nanoassemblies.

1. INTRODUCTION

factor determined from lateral diffusion coefficients of membrane components.8 According to the fluid mosaic model proposed by Singer and Nicholson,9 the membrane constituents can diffuse freely in a 2-D membrane. Lateral diffusion measurements of cell membranes and artificial membranes showed that supramolecular clusters, called rafts, form functional domains, which are important to maintain cellular functions.10 The experimentally observed fluidity in such membranes is described by different diffusion effects induced by three types of membrane organizations: (i) free diffusion without any hindrance, (ii) hindered-diffusion caused by (micro)domains, and (iii) impeding diffusion caused by a meshwork.11 For this purpose, the lateral mobility and deduced membrane organizations reveal insight into structural aspects at the molecular level. Lipids, due to their low molecular weight, possess a “soft” property within the separated bilayer due to its high fluidity.12 In contrast, amphiphilic block copolymers usually have high molecular weights and thus behave as bulky and coiled macromolecules within the membrane. Regarded from a

Membranes provide barriers to protect and store active entities in a confined space for proper function. Artificial polymeric membranes offer several advantages over biological lipid bilayers including better chemical and mechanical stability as well as lower permeability for water and solutes.1,2 Even though polymeric membranes are up to 5 times thicker than lipid bilayers, membrane proteins were successfully incorporated into them to tune the membrane for specific functions.3,4 By combining amphiphilic block copolymers and proteins, the generation of nanoreactors, or even artificial organelles, was achieved.5 The broad range of possibilities to chemically design polymers, and their increased robustness compared to lipids, makes them more favorable for applications in biomedicine and engineering.4,6 The increased complexity of functionalized nanoreactors necessitates robust methods to analyze their structural properties. Therefore, the interaction of membranes with their associated molecules and proteins is of fundamental importance and is a parameter to deduce information about the activity/function of the artificial system. In order to be fully functional, membrane proteins depend on the flexible environment provided by natural lipid bilayers.7 This can be assured by the fluidity of the membrane, which is an important structural © XXXX American Chemical Society

Received: July 28, 2014 Revised: October 17, 2014

A

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Table 1. Characteristics of Amphiphilic Triblock and Diblock Copolymers and Corresponding Membrane Properties (Membrane Thickness d, Diffusion Coefficient D)

a

molecular compositiona

Mw [kg/mol]

MPDMS [kg/mol]

db [nm]

triblock

A3B19A3 A6B34A6 A6B44A6 A7B49A7 A12B63A12 A12B87A12

2.1 3.8 4.5 5.1 6.9 8.7

1.5 2.6 3.3 3.7 4.7 6.5

32 32 25 27 32 25

6.0 9.2 10.7 12.1 13.4 16.2

± ± ± ± ± ±

0.5 0.5 0.7 1.0 0.9 1.4

4.36 2.35 1.89 1.41 1.02 0.60

± ± ± ± ± ±

0.65 0.15 0.17 0.04 0.04 0.08

diblock

A6B22 A9B31 A8B39 A14B65

2.5 3.3 3.8 6.2

1.7 2.4 3.0 4.9

28 28 22 21

10.9 14.3 16.0 21.3

± ± ± ±

0.7 1.1 1.1 1.2

5.97 4.59 2.97 1.77

± ± ± ±

0.41 0.18 0.29 0.21

lipids

POPCd

0.77

∼35

4.0e

f hydrophilic [%]

Db,c [μm2/s]

12.5 ± 0.5

Determined by H NMR. Mean value ± SD. Z-scan FCS at 20 ± 0.5 °C. Rhod-PE in a POPC bilayer. From ref 36. 1

b

c

d

e

troscopy (FCS) was used to determine lateral diffusion coefficients on the membranes of giant unilamellar vesicles (GUVs) and to retrieve information about the existence of rafts and domain structures below the refraction limit of the laser beam.21,22 Cryogenic transmission electron microscopy (CryoTEM) was performed to determine membrane thicknesses of self-assembled polymersomes in order to deduce the chain conformation of the polymer molecules within the membrane.23

structural point of view, amphiphilic block copolymers within a self-assembled membrane adopt much more complex structures. This results in slow diffusion properties.13 Diblock and triblock copolymers are two of the most commonly synthesized block arrangements in the field of self-assembling polymers for the generation of artificial membranes. Diblock copolymers can form structures similar to lipid bilayers, but due to interdigitation and entanglement of the chains, the layers are not fully separated.14 Triblock copolymer chains having an ABA arrangement (hydrophilic−hydrophobic−hydrophilic) can adapt two possible conformations inside the self-assembled membrane: the I-shape, where the hydrophobic block forms a stretched/elongated chain resulting in a monolayer-like membrane structure, and alternatively a U-shape, where the hydrophobic block forms a loop resulting in a bilayer-like structure.15,16 It is believed that a triblock membrane is composed of a mixture of both chain conformations.15 In addition, by increasing the molecular weight of the polymer, the entropic energy contribution increases, leading to an increased number of possible conformations of the polymer chains, i.e., stronger interdigitation and entanglement of the chains within the membrane.14,17 It was described that the conformation of the polymer molecules changes with the molecular weight due to the strong segregation limit (SSL) at the block interface. The repulsion between the hydrophilic and the hydrophobic block causes a more stretched chain conformation.18 This results in a lower density of the hydrophobic membrane layer for low molecular weight polymers (similar to lipids, ∼1000 g/mol). In contrast, higher molecular weight copolymers form larger membrane thicknesses and therefore experience less segregation force due to an increase in chain flexibility. This leads to more coiled and denser structures, which is reflected in interdigitation of the leaflets. In this respect, we present membrane properties such as lateral diffusion coefficients, domain formation, membrane thickness, and membrane viscosity of artificial membranes based on the diblock (AxBy) and triblock (AxByAx) copolymers containing poly(2-methyl-2-oxazoline) (PMOXA) and poly(dimethylsiloxane) (PDMS) known to form polymersomes in aqueous solution and incorporate membrane proteins.3,19,20 In order to determine lateral diffusion coefficients and to investigate the membrane structure, a large library of diblock and triblock copolymers with different molecular weights was synthesized (Table 1). Z-scan fluorescence correlation spec-

2. EXPERIMENTAL SECTION Materials. Reagents and materials were of the highest commercially available grade and used without further purification, unless indicated. Monofunctional carbinol-terminated poly(dimethylsiloxane) (PDMS-OH) was purchased from ABCR GmbH (AB146681, degree of polymerization (DP) = 65 from NMR). Bifunctional carbinolterminated poly(dimethylsiloxane)s (HO-PDMS-OH) were purchased from Dow Croning (5562 carbinol fluid, DP = 22 from NMR), ShinEtsu (KF-6002, DP = 40 from NMR), and ABCR GmbH (AB 116675, DP = 61 from NMR). 1,3-Bis(hydroxybutyl)tetramethyldisiloxane and dimethyldimethoxysilane were purchased from ABCR GmbH, Germany. 2-Methyl-2-oxazoline, triethylamine, trifluoromethanesulfonic anhydride, sulforhodamine B acid chloride, and all solvents were purchased from Sigma-Aldrich. Synthesis of Diblock Copolymers. PDMS-OH with molecular weights of 3.0 kDa (DP = 39), 2.4 kDa (DP = 31), and 1.7 kDa (DP = 22) were synthesized by anionic ring-opening polymerization.20 The polydispersity indices (PDI) of PDMS-OH were determined in THF on a Viscotek GPC max system (RI detector calibrated against polystyrene standards, Agilent PL gel columns) and were all around 1.10. The poly(dimethylsiloxane)-block-poly(2-methyl-2-oxazoline)s (PDMS-b-PMOXA)s were synthesized according to a previously reported procedure.20,24 Synthesis of Triblock Copolymers. HO-PDMS-OH with molecular weights of 4.5 kDa (PDI = 1.8) and 2.5 kDa (PDI = 1.9) were synthesized by acid-catalyzed polycondensation of dimethyldimethoxysilane in the presence of water and end-capper and purified as described elsewhere.25 The syntheses of amphiphilic triblock copolymers (PMOXA-b-PDMS-b-PMOXA) were performed as published earlier with slight modifications.3 Briefly, the hydroxylterminated bifunctional PDMS was reacted (below −10 °C) with trifluoromethanesulfonic anhydride in dry hexane, resulting in bitriflate-activated PDMS macroinitiator. The reaction mixture was filtered under argon through a G4 frit. The hexane was evaporated and dry ethyl acetate was added, in which the macroinitiator was reacted with dry 2-methyl-2-oxazoline (MOXA) in a symmetric cationic ringopening polymerization. The polymerization reaction was quenched using triethylamine:water (1:4 v/v). The crude product was purified by B

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⎡ ⎛ ⎞⎢ 1 Ttrip 1 − τ τ / G(τ ) = 1 + ⎜⎜1 + e trip⎟⎟⎢ 1 − Ttrip ⎝ ⎠⎢ N 1 + τ τD ⎣

ultrafiltration (MWCO 5000, 3000, or 1000 g/mol based on polymer weight) in water:ethanol (1:1 v/v) to remove low molecular weight impurities, yielding bihydroxyl-terminated triblock copolymer. SRB Labeling of Block Copolymers. Four polymers (A12B63A12, A6B44A6, A14B65, A9B31) were labeled with sulforhodamine B (SRB) acid chloride (Sigma-Aldrich) by esterification according to a previously published method.26 Nonreacted free dye was removed on an organic size exclusion column (Sephadex LH-20, GE Healthcare) in ethanol. Preparation of Giant Unilamellar Vesicles. Giant unilamellar vesicles (GUVs) were prepared according to the standard electroformation method,27 using a Nanion Vesicle Prep Pro setup (Nanion Technologies, Munich, Germany). In short, 50 μL of 4 mg/mL (w/v) polymer solution in ethanol was spread on an ITO-coated glass slide, and the solvent was evaporated in a vacuum chamber for at least 1 h. For FCS studies, the polymer solution was mixed with the corresponding SRB-labeld polymer at a concentration between 0.005 and 0.01% (w/w) in order to yield the best signal-to-noise ratio.28 A chamber was formed by using an O-ring, filled with 100 mM sucrose solution and closed with a second glass plate with the ITO-coated side facing down. The chamber, set to 25 °C, was exposed to a 2.5 V ac current at a frequency of 3.0 Hz for 3 h. The GUV solution was then transferred to a tube and stored at 4 °C before use for FCS experiments. Cryogenic Transmission Electron Microscopy. Polymer suspensions in buffer (20 mM Hepes, pH 7.4, 50 mM NaCl) at high concentrations (5 mg/mL) were deposited on glow-discharged holey carbon grids (Quantifoil, Germany) and blotted before quickfreezing in liquid ethane using a Vitribot plunge-freezing device (FEI Co.). The grids were stored in liquid nitrogen before transferring them into a cryo-holder (Gatan). Imaging was performed on a Philips CM200 FEG TEM at 200 kV accelerating voltage in low-dose mode with a defocus value of about −4 μm and a defocus of −2 μm for membrane thickness measurements. Membrane thicknesses were calculated as mean values ± SD from at least 100 different places on membranes of each polymer type.29 In addition, images were corrected for the contrast transfer function (CTF), and no significant difference of the membrane thickness before and after CFT correction was observed. Furthermore, membranes of liposomes were used as control with known membrane thickness. Z-Scan Fluorescence Correlation Spectroscopy. LSM and FCS measurements were performed on a confocal laser scanning microscope (Zeiss LSM 510-META/Confocor2, Carl Zeiss, Jena, Germany). SRB-labeled GUVs were transferred to freshly plasmacleaned microscopy chamber (Nunc Lab-Tek Chamber Slide System, Thermo Fisher Scientific) filled with 200 μL of buffer (20 mM Hepes, 50 mM NaCl, pH 7.4). A He−Ne laser (λ = 543 nm) was used as the excitation source. The excitation power was 1 mW, and the excitation transmission was set to 10% for FCS and 30% for LSM mode. The light passed a dichroic beam splitter (DBS HFT 543) and was focused onto the sample through a C-Apochromat 40× water immersion objective (NA = 1.2). The fluorescence signal was collected through the same objective and passed through a band-pass BP 560−615 nm filter followed by a pinhole (diameter of 78 μm) onto an avalanche photodiode (APD). The pinhole position was calibrated to maximum count rate with a 10 nM SRB solution in the same buffer. LSM mode was used to find nonmoving, stable GUVs (15−30 μm diameter) at the bottom of the glass surface, and then the laser beam was focused on the top membrane of the GUV. Afterward, a z-stack of 30 LSM images with a distance of 100 nm was performed covering the area of −1.4 to 1.4 μm. The center of the confocal volume was determined by vertical positioning of the focus to the maximum count rate. From there, around 10 FCS autocorrelation curves were recorded for 30 s in steps of 200 nm. Autocorrelation curves G(τ) were fitted with FFS Data Processor 2.3 (SSTC, Minsk Belarus) by using the anomalous 2-D diffusion fitting model for anomalous Brownian motion in a Gaussian volume element (eq 1):

⎤ ⎥ α⎥ ⎥ ⎦

( )

(1)

The first term corrects for intersystem crossing (molecules in triplet state), where Ttrip is the fraction of fluorophores in the triplet state, and τtrip is the corresponding triplet time and was fixed at 3.0 μs. The second term reflects the 2-D diffusion, where N is the average particle number in the focal volume, τD is the diffusion time, and α is the exponential term for anomalous diffusion. The exponent α can vary between 0 and 1 and is necessary to describe hindered diffusion.30 The diffusion coefficient D was calculated from the z-dependence of the beam waist ω0,31 by fitting the obtained diffusion times or particle number at different z-positions, τD(Δz) or N(Δz) (eqs 2 and 3):

τD(Δz) =

ω0 2 ⎛ λ 2Δz 2 ⎞ ⎜1 + 20 2 4 ⎟ 4D ⎝ π n ω0 ⎠

⎛ λ 2Δz 2 ⎞ N (Δz) = N0⎜1 + 20 2 4 ⎟ π n ω0 ⎠ ⎝

(2)

(3)

λ0 is the wavelength of the excitation source, n is the refractive index of water (1.33), and N0 is the number of particles at the beam radius minimum ω0. The advantage of z-scan FCS is that ω0 can be obtained independent of an extrinsic calibration.21 Nevertheless, ω0 was determined during the calibration of the pinhole and compared to the ω0 obtained by fitting eqs 2 and 3. In addition, z-scan FCS reveals structural information about membrane inhomogeneities according to the FCS diffusion law:8,22

τD = t0 +

ω2 4Deff

(4)

where ω is the beam area at the measuring plane of diffusion, Deff is the effective diffusion coefficient, and t0 is the intercept representing the diffusion behavior within the membrane. t0 = 0 corresponds to free Brownian diffusion, whereas hindered diffusion corresponds to t0 > 0. For each polymer sample, the diffusion time was determined for at least 15 different GUVs from two independently, freshly prepared samples. The mean value of all diffusion coefficients for each polymer sample was calculated, and error bars represent the corresponding standard deviation. All measurements were performed at 20.0 ± 0.5 °C. The membrane viscosity ηm is calculated from the diffusion coefficient with the Saffman−Delbrück equation (5).32 The diffusing molecules have to be simplified to cylinders with radius R:

D=

⎤ kBT ⎡⎢ ⎛ ηmd ⎞ ⎟⎟ − γ ⎥ ln⎜⎜ 4πdηm ⎢⎣ ⎝ ηsR ⎠ ⎦⎥

(5)

where kB is Boltzmann’s constant, T is the absolute temperature, d is the membrane thickness, R is the radius of the molecule, ηs is the viscosity of the surrounding media, and γ = 0.5772 is Euler’s constant. ηs (20 mM Hepes, 50 mM NaCl, pH 7.4) was set to 0.001 Pa·s.33 For the lipid bilayer system, the parameters were ηs = 0.001 Pa·s, d = 4.0 nm, R = 0.45 nm, and T = 20 °C. The viscosity of the A6B22 and A3B19A3 block copolymer membranes was determined as a coarse approximation, particularly, to be compared with the values of lipid membranes.

3. RESULTS AND DISCUSSION Lateral diffusion measurements were performed on model membranes of giant unilamellar vesicles (GUVs). The GUVs were assembled from a library of ten different polymers: six were synthesized in triblock and four in diblock configurations (Table 1). The block copolymers are composed of PMOXAx-bPDMSy-(b-PMOXAx) (Scheme S1), further referred to as AxByAx (triblocks) and as AxBy (diblocks), where the subscripts C

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Figure 1. Imaging and FCS data processing of giant unilamellar vesicles. (A) SRB-labeled polymer GUVs adsorbed to a glass surface forming stable half-spheres, optimal for performing z-scan FCS. GUVs were visualized by LSM (laser scanning microscopy). (B) Autocorrelation curves of a full set of z-scans with the corresponding fits for A12B87A12 triblock copolymer. The parabolic z-dependency of the lateral diffusion time τD and number of particles N for (C) A12B87A12 triblock and (D) A6B22 diblock copolymer GUVs is depicted as recorded by z-scan FCS. Error bars represent standard deviations (±SD, n = 10).

always between 0.8 and 1.0. This parameter flattens the autocorrelation curve. For our system we propose that the parameter α indicates the distribution of the diffusion times around a mean value. There were several reasons for this distribution of the diffusion times in these block copolymer membranes. First, the polydispersity (PDI) in molecular weight is intrinsic to polymer amphiphiles37 and broadens from diblocks20 to triblocks3 as displayed in Table S1. Variation in the molecular weight, represented by the PDI, leads to a slight distribution of diffusion times. Second, for triblock copolymers, two different conformations of the ABA copolymer in a membrane have been suggested, influencing the lateral diffusion properties due to the stretched form being represented as Ishape and the curved form as U-shape.15 In addition, the synthesis of triblock copolymers results in a small fraction of diblock copolymers, which are irremovable in the following purification. Thus, triblock copolymers may be blended with a minority of diblock copolymers, a fact that cannot be proven or quantified by standard analytical methods, i.e., NMR or GPC. Third, labeling of triblock copolymers with a fluorescent dye is not quantitative, and therefore polymer molecules with two SRB (one at each end) or with only one SRB are present in the final assembly. These three factors demand this parameter α to explain anomalous diffusion in a polymeric membrane system. Molecular Weight Dependency of Lateral Diffusion. Diffusion times (τD) and number of particles (N) were calculated and plotted against the z-axis (Figure 1C,D, Figures S3 and S4). The minimum diffusion time was obtained by shifting the z-axis to yield the best fit. The waist ω0 of the laser beam (λ = 543 nm) was fitted with eqs 2 and 3 and was

x and y denote the degree of polymerization as determined by 1 H NMR. The polymers, known to have high PDIs (Table S1), differ only in their block lengths and molecular weights. The calculated hydrophilic weight fractions ( f hydrophilic = MPMOXA/ Mw) range from 21 to 32%, similar to the hydrophilic weight fraction of lipids ( f lipids ≈ 35 ± 10%), suggesting these amphiphiles possess the ability to form vesicular structures in aqueous solutions (Figures S1 and S2).34 These block copolymers were able to form GUVs required for z-scan FCS, a single-molecule detection method used to determine the lateral diffusion of single molecules in free-standing membranes. This method also requires that the free-standing membranes are stable and nonmoving.35 Sucrose-filled GUVs sink to the hydrophilic plasma-treated glass surface in a non-sucrose-containing buffer (20 mM Hepes, 50 mM NaCl). Due to hydrophilic forces, they adhere tightly as hemispheres at the bottom without rupturing (Figure 1A). Isosmotic conditions are required to prevent membrane stress, which can affect the measurements. Z-scan FCS measurements were performed on the top of these stable hemispheres. The fluorescently labeled polymer fraction (labeled with sulforhodamine B, SRB, Scheme S1) was homogeneously distributed within the membrane, and no domains or separations were observed at the optical resolution. The z-scan autocorrelation curves were recorded in steps of 200 nm (Figure 1B) on 10 different GUVs from at least two different sample preparations. Autocorrelation curves were fitted with the 2-D anomalous diffusion model (eq 1, see Experimental Section), containing exponent α, which was D

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± 0.6 μm2/s by 2-focus FCS),41 which further underlines the accuracy of the z-scan FCS method. The diffusion coefficients of our block copolymer membranes showed mobilities that were 2−20 times slower than the diffusion coefficients of unsaturated phospholipids. Mobilities reported for other block copolymer membranes, measured by fluorescence recovery after photobleaching (FRAP) experiments, were roughly 10 times slower than in our case. Membranes composed of EO37b-EE40 (poly(ethylene oxide)−poly(ethylethylene)) and EO80b-BD130 (poly(ethylene oxide)−poly(butadiene)) showed diffusion coefficients of 0.12 and 0.0024 μm2/s, respectively.13 In that study, GUVs were pulled into a glass micropipet and FRAP was performed within the micropipet. Therefore, the membrane can interact with the glass wall influencing the measured diffusion, reflected in the low diffusion coefficient for their lipid bilayer system (DSOPC = 3.8 μm2/s). It is also known from other measurement techniques that lipid interaction with surfaces strongly influences the lateral mobility.42,39 Nevertheless, we can conclude that the fluidity within the EO37-bEE40 diblock copolymer membrane is lower than the one of a PMOXA-b-PDMS diblock copolymer membrane with a similar molecular weight of the amphiphiles. Figure 2 represents the dependence of the lateral diffusion coefficients on molecular weight and membrane thickness. The lateral diffusion scales with the molecular weight in a power law dependency: DABA ∝ M−1.32±0.09 (R2 = 0.98) and DAB ∝ PDMS 2 −1.19±0.12 (R = 0.98) (Figure 2A), and the same exponents MPDMS were calculated from the degree of polymerization (Figure S6). Owing to nonsignificant linear fits of the log−log plots in Figure 2A (p = 0.40/p > 0.05), the scaling of diblock and triblock copolymers, consisting of PMOXA-b-PDMS-(bPMOXA), can be generally formulated as D ∝ M−1.25 PDMS and D ∝ N−1.25. The difference between diblocks and triblocks mainly results from structural differences in the conformational organization of the polymer chains in the self-assembled membrane. While diblock copolymers introduce stronger in-plane diffusion within the (interdigitated) block copolymer membrane, triblock copolymers form membranes composed of polymer chains in the stretched I-shape and the bent U-shape conformation, which reduces the mobility of the polymer chains. Although the slopes in Figure 2A are not significantly different, the more negative slope of triblocks compared to diblock copolymers (−1.32 ± 0.09 vs −1.19 ± 0.12) underlines the stronger reduction in lateral diffusion of triblock copolymers with respect to the molecular weight. This indicates the influence of I-shaped triblock chains on the lateral mobility within the membrane and represents the strength of entanglement of the polymer chains, which is more pronounced at higher membrane thicknesses and higher molecular weights, respectively. Similar trends were observed when plotting the lateral diffusion versus the membrane thickness (Figure 2B). The difference is more distinct because the diblock copolymers showed almost pure bilayers with only weak interdigitation. In the present study, the membranes assembled from diblock copolymers are roughly twice as thick as the ones observed for triblock copolymer membranes with comparable PDMS block lengths (Figure S7). For example, by comparing the autocorrelation curves at minimum τD of the diblock polymer, A6B22, and the triblock polymer, A6B44A6, the diffusion time of the triblock was significantly shifted to higher diffusion times compared to the diblock, although both possess the same membrane thickness (Figure S8). A part of the triblock

between 260 and 300 nm for all polymer samples, which is close to the value obtained from external calibration with free SRB dye in buffer (ω0,ext = 260 nm, DSRB = 4.14 ×10−6 cm2/ s).38 The relative errors obtained from the diffusion coefficients were all between 5 and 15%, which is the error range usually obtained with z-scan FCS.21 Diffusion coefficients for all polymers listed in Table 1 were calculated based on eq 2. The lateral diffusion decreases with increasing molecular weight for both block copolymer compositions (diblock and triblock). The difference in the diffusion characteristics between diblock and triblock copolymers is represented as a significant shift of the triblocks toward longer diffusion times (τD) or higher diffusion coefficients (D) compared to diblocks (Figure 2 and Figure S6). Triblock copolymers showed lateral mobility

Figure 2. Log−log plots of diffusion coefficients D versus molecular weight of PDMS MPDMS (A) and membrane thickness d (B). The polymeric membranes are composed of different molecular weight polymers and different block architecture (triblock and diblock). Membrane thicknesses were determined from cryo-TEM images. In addition, the diffusion coefficient of a fluorescently labeled lipid (Rhod-PE) within a POPC bilayer is shown for comparison. Dashed lines represent linear fits; error bars represent standard deviations (±SD).

values, ranging from 4.4 to 0.6 μm2/s for molecular weights from 2100 to 8700 g/mol, almost a 10-fold decrease within the triblock copolymers tested. For diblock copolymers, the trend resembles but the lateral diffusion coefficients shift to higher values compared to triblocks, ranging from 6.0 to 1.8 μm2/s (2500−6200 g/mol). We also determined the diffusion coefficient of an unsaturated lipid (Rhod-PE) within a POPC bilayer by using the same method applied for block copolymer membranes, revealing a value of 12.5 ± 0.6 μm2/s (Figure S5). This value is in good agreement with values reported for freestanding lipid bilayers (10.0 ± 0.7 μm2/s by z-scan FCS39 and 12.9 ± 1.2 μm2/s by FRAP40) or black lipid membranes (11.6 E

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Figure 3. Experimental FCS diffusion laws obtained for diblock and triblock copolymers show a trend toward hindered diffusion (t0 > 0) with increasing molecular weight. (A) Diblock copolymers show t0 values ranging from 1.0 up to 10 ms. (B) Triblock copolymers show t0 values ranging from 0 to 20 ms. (C) t0 values of all triblock and diblock copolymers plotted against the hydrophobic molecular weight MPDMS. Lines represent linear fits; error bars represent standard deviations (±SD).

diffusion within the bilayer due to weak interdigitation of the two layers. Even weak interdigitation causes that no clear bilayer structures could be observed in cryo-TEM images, with the exception of one image of the A9B31 diblock copolymer, where the membrane stands perpendicular to the projection plane (Figure S11). In this image, the membrane reveals a clear bilayer structure. However, the observation of domains with increasing molecular weight also indicates entanglement of the diblock copolymer chains. Effect of Molecular Weight on the Membrane Thickness. The membrane thickness of amphiphilic block copolymer membranes depends on the molecular weight of the hydrophobic block.16,18 Systematic studies on the membrane thickness of hydrophobic blocks composed of poly(butadiene) (PBD)23 and poly(ethylethylene) (PEE)43 revealed that the membrane thickness d scales with the molecular weight of the hydrophobic block (Mh) in the following way:

copolymer macromolecules arrange in the I-shape, affecting the membrane structure and therefore reducing the fluidity of the overall membrane. On the other hand, the diffusion coefficients of the smallest diblock copolymer studied are close to the diffusion coefficients of phospholipids in free-standing lipid bilayers. This suggests these polymersomes have a similar structural organization as lipid bilayers, i.e., bilayer formation without entanglement and very low interdigitation of the PDMS chains. The viscosity of PDMS plays a crucial role in the fluidic characteristic of these polymeric membranes. In this respect, the molecular weight (Mh) of the hydrophobic block is the main contributor to lateral diffusion because the PDMS viscosity is dependent on the block length while the hydrophilic PMOXA block does not or only slightly contribute to the viscosity. Existence of Membrane Inhomogeneities. In addition to the obtained diffusion coefficients, z-scan FCS provides information on membrane inhomogeneities by the FCS diffusion law.8,22 In the case of hindered diffusion, the diffusion time is not proportional to the illuminated area (represented by the relative number of particles, N/N0) and extrapolation of the diffusion time to zero beam waist (y-axis intersection) results in a positive value (t0 > 0). A linear dependency is shown in Figure 3A,B for selected block copolymers and for all block copolymers in Figure S9. Applying this approach to our different polymer membranes, t0 was always positive (Figure 3C). However, the smallest diblock and triblock copolymers (A6B22, A3B19A3) showed free-diffusion properties (t0 ∼ 0) as sole exceptions with membrane thicknesses of 10.9 and 6.0 nm, respectively. Negative t0 values represent a meshwork character and were not observed. In general, t0 steadily increased proportionally to the molecular weight for both block copolymer architectures (triblock and diblock). In the case of triblocks, it means that small copolymer chains are assembled in a more stretched conformation (strong segregation limit, SSL). They are organized similar to alkyl chains of lipids in a lipid bilayer. A stretched structure provides a higher freedom of diffusion, and the polymer chains are less prone to interlinking/entanglement as observed by the free diffusion of the smallest triblock copolymer. For long polymer chains, on the other hand, the possibility of entanglement increases, and therefore domains can form, reducing the overall mobility significantly. For diblock copolymers, the freedom of diffusion is greatly increased compared to triblocks because of the in-plane

d ∝ Mh a

(6)

The exponent a provides information about the polymer structure23,44 and was calculated for both diblock and triblock copolymers (Figure 4). As shown in Figure 5, the membrane thickness increases with the number of PDMS units (block B). The analysis of the membrane thickness (Figure 4) results in similar values for the exponent a of 0.67 (triblock) and 0.62 (diblock) for both polymer typesvalues that show a chain conformation according to the strong segregation theory (SSL:

Figure 4. Power law dependence of the membrane thickness on the hydrophobic molecular weight of the PDMS block (MPDMS) with the corresponding calculation of the slope (exponent a). The slope provides information about the chain conformation of the macromolecules. Lines represent linear fits; error bars represent standard deviations (±SD). F

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Figure 5. Systematic view of diblock (upper panel) and triblock (lower panel) copolymer membranes arranged with increasing membrane thickness (from left to right). A-block: PMOXA; B-block: PDMS. Images were generated by the cryo-TEM technique.

a = 0.66). Furthermore, the data points cannot be represented exactly by eq 6; the exponent a is increasing with decreasing MPDMS and vice versa (Figure S10) as reported previously.18 Figure S10 shows the change of the slope when the fit is based on the upper and lower data points. For both block architectures, if the PDMS molecular weight is below 2500 g/mol, the chains are more stretched (a ≈ 0.70−0.74), leading to more ordered chain configurations within the membrane. On the other hand, with increasing molecular weight (MPDMS > 4000 g/mol) the exponent a decreases toward values below 0.6 (a ≈ 0.55−0.59), reflecting a larger number of coiled polymer chains and thereby increasing interdigitation.18 For example, the theoretical maximal PDMS length using the segment length of PDMS (0.311 nm) according to the Si−O bond distance (0.164 nm) and the Si−O−Si angle (θ = 143°)45 of the smallest triblock copolymer used in this study (A3B19A3) was equal to the mean value of the membrane thickness determined by cryo-TEM (experimental membrane thickness: 6.0 ± 0.5 nm versus maximal stretched PDMS chain: 5.9 nm). This clearly demonstrates to which extent the macromolecules stretch. However, the smoothness of the membrane decreased (Figure S1 for A3B19A3), which might lead to lower membrane stability. On the other hand, the maximal PDMS chain length of the largest triblock copolymer (A12B87A12) is 66% longer (+10.7 nm) than the measured membrane thickness. Moreover, the membranes appear more smooth (Figure S1 for A6B34A6− A12B87A12). In the case of diblocks, all block copolymers have a smaller membrane thickness than the maximum theoretical PDMS chain lengths, ranging from 25% (A8B22) to 90% (A14B65). Similar to the trend observed for triblocks, exponent a is decreasing with increasing PDMS molecular weight. In the coarse-grain molecular dynamics simulation study of diblock copolymers the same behavior was predicted.43 Small molecular weight polymers with membrane thicknesses smaller than 7 nm were shown to have exponents a of about 0.8, while large molecular weight polymers revealed exponents a toward values about 0.5 (pure random coil). The bilayer-like structure of our membranes with only weak interdigitation (Figures S7 and S11) is in contrast to previously reported PEO-b-PBO block copolymer membranes.14 Although we used different chemical composition of block copolymers, we question their model of strongly interdigitated polymer membranes. This conclusion is based on not only the lateral diffusion measurements but also the cryo-TEM images showing

polymersomes with specifiable membrane thicknesses. We did not determine membrane thicknesses from TEM with negative staining because the image contrast originates from the stain around the vesicles. In cryo-TEM imaging, it has to be noted that a high defocus increases the effect of the contrast transfer function (CTF), leading to high errors for distance measurements. We corrected images for the CTF; however, for images with a low defocus we did not observe a significant difference before and after CTF correction. Additionally, thin membranes from self-assembled block copolymers following the strong segregation limit, as stated by the molecular simulation study,43 must have stretched polymer chains. Consequently, thicker membranes will reflect coiled chains together with interdigitation. In this respect, fully interdigitated membranes made of diblock copolymers are questioned and were never observed herein. In our case, even the lateral diffusion results of the diblock copolymers predicted a strong in-plane diffusion supporting bilayer formation. The main concern toward exponential eq 6 is that the exponent a lacks information about the strength of interdigitation and describes only a mean value for the exponent within broad ranges of different molecular weight polymers. A precise conclusion can only be drawn when at least one structure of the data set is known exactly. Besides cryoTEM imaging of polymersome membranes, we have an additional, experimentally obtained, hint from the lateral diffusion study to conclude more details about the membrane structure. Block Copolymer Membrane Viscosity. The membrane viscosity provides another measure to compare artificial membranes made of block copolymers to natural phospholipid bilayers. Since the lateral mobility, reflected by the diffusion coefficient, depends on several factors, such as the membrane fluidity, the size of the diffusing object, and crowding and formation of domains and clusters,46 the calculation of the membrane viscosity is difficult to assess. Saffman and Delbrück proposed a simple model, where the membrane is treated as a 2-D sheet of a viscous fluid with thickness d surrounded by a fluid with a much lower viscosity (usually water).32 This model does not take into account the membrane structure and assumes a perfect fluid continuum. Nevertheless, we provide membrane viscosities of artificial block copolymer membranes in order to compare them to the calculated membrane viscosities of lipid bilayers.41,46,47 Because of the observed membrane inhomogeneities (interdigitation and entanglement) G

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the fluidity of natural membranes due to their low viscosity and low glass transition temperature (Tg ≈ −123 °C).52

of the higher molecular weight block copolymers, we only provide values of membrane viscosities for the polymer membranes composed of the smallest triblock and diblock copolymers (A6B22 and A3B19A3), which showed almost freediffusion properties. The membrane viscosity ηm was determined using the Saffman−Delbrück equation (5).32 The values (Table S1) were calculated based on the lateral diffusion coefficients D, the membrane thicknesses d, and the area occupied by a single polymer chain represented as the radius R of a cylinder diffusing in the membrane.32 As a close approximation, the single polymer molecule radius was calculated according to the radius of gyration using Rg = Na(b/6),48 where N represents the number of siloxane units of the PDMS, b the segment length (b = 0.311 nm), and a the exponent (calculated from Figure 4). Langmuir monolayer studies (data not shown) revealed areas per molecule values that were in good agreement with the calculated values of R, shown here, as well as to values reported from molecular dynamics simulation.43 We obtained Rdiblock being 0.37 nm (43 Å2) and Rtriblock being 0.38 nm (45 Å2), similar to the values reported for lipids (Rlipid = 0.45 nm, 64 Å2),36,41 which was expected due to similar sizes of these two short copolymers and lipids. In the calculations, we used ηs = 0.001 Pa·s and T = 293 K as the fixed parameters. For the triblock copolymer we used h = 6.0 nm (Table 1 and Figure 5) and R = 0.38 nm, which resulted in a membrane viscosity of ηm,A3B19A3 = 0.081 Pa·s. The membrane viscosity of the smallest diblock copolymer membrane was roughly 3 times smaller with a value of ηm,A6B22 = 0.031 Pa·s, using h = 10.9 nm and R = 0.37 nm. The membrane viscosity of the POPC bilayer is ηm,POPC = 0.033 Pa·s (h = 4.0 nm and R = 0.45 nm), which resembles roughly the same viscosity as the artificial diblock copolymer membrane. It is remarkable that the membrane viscosity is similar, although the membrane thickness of the diblock copolymer membrane is roughly 2.5 times thicker and the diffusion coefficient is 2 times lower than the lipid bilayer. Reported membrane viscosity values for a free-standing POPE/POPC (3:2) lipid bilayer (0.039 Pa·s)41 and DMPC (dimyristoylphosphatidylcholine) GUVs (0.06−0.08 Pa·s)49 support the viscosity values found for our POPC lipid membrane. Within lipid bilayers, the viscosity is also affected by hydrogen bonding between the lipid head groups,50 while the hydrocarbon chains might have a similar viscosity as the viscosity of the corresponding liquid alkane.51 Therefore, we expect to have polymeric membrane diffusivities governed mainly by the viscosity of the hydrophobic PDMS layer because we assume to have no molecular interaction between the hydrophilic PMOXA chains. The PDMS viscosities of PDMS22 and PDMS19 are 0.034 and 0.028 Pa·s, respectively (Gelest, Inc., Morrisville, PA)values that are very close to the calculated membrane viscosity of the diblock copolymer. Consequently, the membrane viscosity of a diblock membrane is primarily explained by the viscosity of pure PDMS and changes with respect to the block length. In the case of triblock copolymer membranes, the membrane viscosity is higher, attributed mainly due to the stretched chain (I-shape) fraction in the membrane. In this respect, we assume that increasing the molecular weight of the PDMS block would result in higher membrane viscosity. Hence, the here presented membrane viscosities of artificial polymeric membranes highlight the advantage of PDMS containing block copolymers, which mimic

4. CONCLUSIONS Lateral diffusion coefficients were determined based on a large library of different molecular weight amphiphilic block copolymers with triblock and diblock configuration that are able to self-assemble into vesicular structures. Membrane dynamics of PMOXA-b-PDMS-(b-PMOXA) block copolymers revealed factors of 2−20 times lower diffusion coefficients compared to phospholipids within lipid bilayer membranes. We demonstrated that the lateral diffusion D follows a power law dependency according to the molecular weight of the hydrophobic block MPDMS scaling with D ∝ M−1.25 PDMS. Diblock copolymers showed diffusivities higher than triblock copolymers, which can be explained by the different chain conformation within the self-assembled membrane. Triblock copolymers adapt a mixed conformation of the bent U-shape and the stretched I-shape reducing the lateral mobility. On the other hand, diblock copolymers build a bilayer-like structure with only slight interdigitation and entanglement and, therefore, have more freedom of diffusion than triblock copolymer macromolecules. Interdigitation and entanglement of the polymer chains induce the formation of membrane inhomogeneities and domains. As a consequence, the mobility revealed a hindered diffusion property at molecular weights above 2000 g/ mol, while only low molecular weight polymers (