pubs.acs.org/Langmuir © 2009 American Chemical Society
Polypeptide Nanoribbon Hydrogels Assembled through Multiple Supramolecular Interactions )
Yun Yan,*,†,‡ Arie de Keizer,† Aernout A. Martens,† Cristiano Luis Pinto Oliveira,§ Jan Skov Pedersen,§ Frits A. de Wolf,^ Markus Drechsler, Martien A. Cohen Stuart,*,† and Nicolaas A. M. Besseling#
)
† Laboratory of Physical Chemistry and Colloid Science, Wageningen University, Dreijenplein 6, 6703 HB Wageningen, The Netherlands, ‡Beijing National Laboratory for Molecular Science (State Key Laboratory for Structural Chemistry of Unstable and Stable Species), College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, People’s Republic of China, §Department of Chemistry and NANO Interdisciplinary Nanoscience Center, University of Aarhus, DK-8000 Aarhus C, Denmark, ^Agrotechnology & Food Innovations B.V., Wageningen UR, Bornsesteeg 59, 6708 PD Wageningen, The Netherlands, Makromolekulare Chemie II, University of Bayreuth, 95440 Bayreuth, Germany, and #Nano Structured Materials, Department of Chemical Engineering, Delft University of Technology, Julianalaan 136, 2628 BL Delft, The Netherlands
Received May 26, 2009. Revised Manuscript Received July 29, 2009 We investigated the formation of nanoribbon hydrogels in a mixed system of zinc ions, bis(ligand)s, and triblock peptide copolymers. Using a combination of experimental techniques: dynamic light scattering, cryo-transmission electron microscopy, small-angle X-ray scattering and circular dichroism, we arrived at a model for the formation of nanoribbon hydrogels in which well-defined nanoribbons are formed out of multiple supramolecular interactions: (1) metal coordination that yields supramolecular polyelectrolytes; (2) electrostatic complexation between the supramolecular polyelectrolytes and the oppositely charged blocks of the peptide copolymers; (3) hydrogen bond and (4) hydrophobic interactions that support the secondary and ternary structure of the ribbons; (5) van der Waals interactions that enable bundling of the ribbons.
Introduction Molecular self-assembly has attracted considerable attention in generating new advanced materials.1-3 Molecules that are capable to self-assemble turn out to be manifold. The forces that are involved in self-assembly are usually noncovalent interactions. These interactions include hydrogen bonds,4,5 van der Waals forces,6 hydrophobic interactions,7 electrostatic forces,8,9 metalligand coordination interactions,10,11 dipole-dipole interactions,12 and π-π stacking,13 etc. Often one type of noncovalent interactions is enough to lead to formation of a self-assembled structure. For instance, hydrophobic interaction between the surfactant molecules drives the formation of vesicles and micelles; metalcoordination interaction between metal ions and multitopic ligands *Corresponding authors. E-mail: (Y.Y.)
[email protected]; (M.A.C.S.)
[email protected]. (1) Tang, C. B.; Lennon, E. M.; Fredrickson, G. H.; Kramer, E J.; Hawker Craig, J. Science 2008, 322, 429–432. (2) Warren, S. C.; Messina, L. C.; Slaughter, L. S.; Kamperman, M.; Zhou, Q.; Gruner, S. M.; DiSalvo, F. J.; Wiesner, U. Science 2008, 320, 1748–1752. (3) Segalman, R. A. Science 2008, 321, 919–920. (4) Brinke, G, R. J.; Ikkala, O. Adv. Polym. Sci. 2007, 207, 113–177. (5) Xu, H, S. S.; Rotello, V. A. Adv. Polym. Sci. 2007, 207, 179–198. (6) Botta, B.; Cassani, M.; D’Acquarica, I.; Subissati, D.; Zappia, G.; Delle Monache, G. Curr. Org. Chem. 2005, 9, 1167–1202. (7) Meyer, E. E.; Rosenberg, K. J.; Israelachvili, J. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 15739–15746. (8) Hammond, P. T. Curr. Opin. Colloid Interface Sci. 1999, 4, 430–442. (9) Cohen Stuart, M. A.; Hofs, B.; Voets, I. K.; de Keizer, A. Curr. Opin. Colloid Interface Sci. 2005, 10, 30–36. (10) Burnworth, M.; Knapton, D.; Rowan, S. J.; Weder, C. J. Inorg. Orgmet. Polym. 2007, 17, 91–103. (11) Kurth, D. G.; Higuchi, M. Soft Matter 2006, 2, 915–927. (12) Zhang, H.; Zhang, H.; Edwards, E. W.; Wang, D. Y.; Mohwald, H. Phys. Chem. Chem. Phys. 2006, 8, 3288–3299. (13) Chen, Z. J.; Stepanenko, V.; Dehm, V.; Prins, P.; Siebbeles Laurens, D. A.; Seibt, J.; Marquetand, P.; Engel, V.; Wurthner, F. Chem. Eu. J 2007, 13, 436–449.
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facilitates formation of coordination polymers;10,11 electrostatic complexation between a charge-neutral diblock copolymer and an oppositely charged polyelectrolyte leads to complex coacervate core micelles (C3Ms), also called polyion complex (PIC) micelles.9,14 These simple self-assembled structures are the first stage of the ‘bottom-up’ strategy to develop artificial materials. Hierarchical self-assembled structures can be formed from simple self-assembled structures and further build up advanced materials.15 These may consist of second or even higher ordered assemblies based on a simple self-assembled structure. Recently, we have successfully combined metal-coordination and electrostatic interaction to fabricate such self-assembled hierarchical nanoparticles.16 In this strategy, metal ions and small bis(ligand) molecules 1,11-bis(2,6-dicarboxypyridin-4yloxy)-3,6,9trioxaundecane (L2EO4, Scheme 1a) were mixed at a stoichiometric ratio to form coordination polymers (Scheme 1b).17 These selfassembled coordination polymers are analogues to traditional polyelectrolytes owing to the negative charges at the coordination center (Scheme 1b). Upon combination with oppositely charged species, the local concentration of the coordination polymer is enhanced which leads to an increase of its degree of polymerization. This simultaneously promotes the formation of hierarchical assembly between the coordination polymer and the oppositely charged species via electrostatic interaction. By utilization of this property, we have demonstrated the formation of spherical and (14) Osada, K.; Kataoka, K. Adv. Polym. Sci. 2006, 202, 113–153. (15) Pokroy, B.; Kang, S. H.; Mahadevan, L.; Aizenberg, J. Science 2009, 323, 237. (16) Yan, Y.; Besseling, N. A. M.; de Keizer, A.; Marcelis, A. T. M.; Drechsler, M.; Cohen Stuart, M. A. Angew. Chem., Int. Ed. 2007, 46, 1807–1809. (17) Vermonden, T.; van Steenbergen, M. J.; Besseling, N. A. M.; Marcelis, A. T. M.; Hennink, W. E.; Sudholter, E. J. R.; Cohen Stuart, M. A. J. Am. Chem. Soc. 2004, 126, 15802–15808.
Published on Web 09/08/2009
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Scheme 1. (a) Bis(ligand) L2EO4. (b) Formation of 1:1 Coordination Complexes (Zn-L2EO42-)n between Zn2+ and L2EO4. (c) Amino acid sequence of the peptide triblock copolymer 1 in single-letter amino acid codea
a The middle block [(AlaGly)3HisGly]48 (highlighted in red) can form a β-sheet or β-rolls20 with parallel AlaGly strands and histidines at the edges. Histidine is positively charged at pH < 6, and at higher pH it becomes uncharged.
worm-like micelles in a mixed system of coordination polymers and oppositely charged-neutral diblock copolymers.16,18 Recently, we found that when a special biosynthetic A-B-A type polypeptide polymer 1 (Scheme 1c) is used instead of charged-neutral diblock copolymer, a novel type of nanoribbons can be formed.19 The outer block A of 1 consists of neutral polypeptide which is water-soluble at any pH, whereas the middle block B contains histidine residues at every eighth position which are positively charged at pH < pI =6.86.19 At slightly acidic conditions, the combination of 1 and Zn-L2EO4 coordination polymers leads to well-defined nanoribbons. The formation of nanoribbons involves multiple weak interactions: 1) metal coordination yielding coordination supramolecules; 2) electrostatic interaction leading to folding of the B block in 1; 3) hydrogen bonding that leads to secondary structure of the polypeptide; 4) and hydrophobic interactions resulting the stacking of the folded structures. All these interactions are crucial for the formation of ribbons. This is a new type of self-assembling system which requires cooperation of multiple weak interactions. In our previous communication, we briefly reported the formation of nanoribbons in dilute solutions.19 In the present paper, we present detailed investigations on the formation of hydrogels at higher concentrations by using dynamic light scattering (DLS), cryo-TEM, smallangle X-ray scattering (SAXS), freeze-dried TEM, and circular dichroism (CD). The formation of hydrogels from a combination of polypeptide 1 with coordination polymers is much faster than of those formed from the same polypeptide 1 by addition of a covalent polyelectrolyte and than that formed at high pH. The structure of the gel in the former system is better defined than that in the latter two systems both on the molecular, and hierarchical self-assembly level. These detailed analysis help to build up the fundamental knowledge about the requirements and the driving force for the formation of such an unusual nonribbons. (18) (a) Yan, Y.; Besseling, N. A. M.; de Keizer, A.; Drechsler, M.; Fokkink, R.; Cohen Stuart, M. A. J. Phys. Chem. B 2007, 111, 11662–11669. (b) Yan, Y.; Besseling, N. A. M.; de Keizer, A.; Cohen Stuart, M. A. J. Phys. Chem. B 2007, 111, 5811–5818. (c) Yan, Y.; de Keizer, A.; Cohen Stuart, M. A.; Drechsler, M.; Besseling, N. A. M. Soft Matter 2009, 5, 790–796. (d) Yan, Y.; Harnau, L.; Besseling, N. A. M.; de Keizer, A.; Ballauff, M.; Rosenfeldt, S.; Cohen Stuart, M. A. Soft Matter 2008, 4, 2207–2212. (e) Yan, Y.; Besseling, N. A. M.; de Keizer, A.; Cohen Stuart, M. A. J. Phys. Chem. B 2008, 112, 10908–10974. (19) Yan, Y.; Martens, A. A.; Besseling, N. A. M.; de Wolf, F. A.; de Keizer, A.; Drechsler, M.; Cohen Stuart, M. A. Angew. Chem., Int. Ed. 2008, 47, 4192–4195. (20) Martens, A. A.; Portale, G.; Werten, M. W. T.; de Vries, R. J.; Eggink, G.; Cohen Stuart, M. A.; de Wolf, F. A. Macromolecules 2009, 42, 1002–1009.
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Experimental Section Materials. Preparation of 1. Template DNA of the histidinecontaining chargeable sequence (i.e., the middle block of 1) (GAGAGAGH)2GA was produced by annealing two oligonucleotides and inserting the resulting double-strand DNA into a pMTL23 derived vector.20 This sequence was enlarged to the desired size corresponding to (GAGAGAGH)48GA by recursive directional ligation. This sequence was then combined with that corresponding to the neutral polypeptide blocks (blocks contain 8-16 glutamic acids and 6-12 lysines, depending on the position (end block or mid block, the latter being twice as long as an end block); 28 charges in total in the two outer blocks can be formed under acidic conditions, but they form random coils at all pH) to form the template gene which was transferred to the pPIC9 expression vector. Pichia pastoris transformed with pPIC9 was induced to produce the protein polymer in a fermenter at pH 5, essentially as described by Werten et al.21 The secreted soluble protein was selectively precipitated from the fermentation supernatant by adding 258 g/kg ammonium sulfate (45% saturation), incubating for 30 min at 21 C and centrifugation for 20 min at 8000 rad/min and 4 C (Sorval, SLA1500). The polymer pellet was dissolved in 0.5 L 100 mM acetic acid from which the polymer was selectively precipitated by adding acetone to a final concentration of 50% (v/v). The pellet was dissolved in 300 mL of 10 mM acetic acid and freeze-dried. The salt containing freeze-dried product was resuspended in 100 mL of 50 mM formic acid and dialyzed four times for 18 h against 4 L of 10 mM formic acid, after which the polymers were freezedried again and used for the experiments. The final products were shown to have the expected length by mass spectrometry and N-terminal amino acid sequencing. Using the purified product as a standard, the amount of product present in the original fermentation was determined by optical densitometric analysis of the Coomassie-blue-stained product bands in a polyacrylamide gel. Several dilutions were compared. The centrifuged, cell-free fermentation broth contains 6.1 g/L of 1, which is comparable to the highest yields of secreted heterologous protein published to date.22 Other Materials. The metal-1,11-bis(2,6-dicarboxypyridin4yloxy)-3,6,9-trioxaundecane metallosupramolecular polyelectrolytes (Zn-L2EO4 complex), were prepared according to literature.23 (21) (a) Werten, M. W. T.; de Wolf, F. A. Appl. Environ. Microbiol. 2005, 71, 2310–2317. (b) Werten, M. W. T.; Van den Bosch, T. J.; Wind, R. D.; Mooibroek, H.; De Wolf, F. A. Yeast 1999, 15, 1087–1096. (c) Werten, M. W. T.; Wisselink, W. H.; van den Bosch, T. J. J.; de Bruin, E. C.; de Wolf, F. A. Protein Eng. 2001, 14, 447–454. (22) Cereghino, G. P. L.; Cereghino, J. L.; Ilgen, C.; Cregg, J. M. Curr. Opin. Biotechnol. 2002, 13, 329–332. (23) Vermonden, T.; Branowska, D.; Marcelis, A. T. M.; Sudholter, E. J. R. Tetrahedron 2003, 59, 5039–5045.
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Figure 1. DLS intensity-autocorrelation function g2(τ) - 1 during gelation at T=20 C. Key: (a) mixture of 1/Zn-L2EO4; (b) mixture of 1/PANa; (c) 1/pH=11. In all the three system, [1]=6.95 g/L. The dotted line indicates the shift of the characteristic decay time upon progress of the gelation process. Symbols: black squares: without addition of Zn-L2EO4, PANa, or NaOH, i.e., gelation time is zero; other symbols represent gelation at different times after addition of Zn-L2EO4, PANa, or NaOH to the solution of 1. (d) Photos for the gels in 8 mm (diameter) light scattering cells. From 1 to 3: 1/Zn-L2EO4; 1/PANa; 1 at pH 11. Sodium polyacrylate (PANa48, 48 is the polymerization degree) is prepared from poly(acrylic acid)by neutralizing the acid with sodium hydroxide. Ultra pure water was used throughout the experiments. pH was adjusted by HCl or NaOH. Methods. Dynamic Light Scattering (DLS). Light scattering measurements were performed with an ALV light scatteringapparatus, equipped with a 400 mW argon ion laser operating at a wavelength of 514.5 nm. The standard ALV software (ALVSoftware System Version 3.0.2.5) automatically shifts the correlation functions g2(τ) to put g2(τ) - 1 for large times at level 0. For a gelling system this is unjustified. We corrected this by shifting the initial levels of the correlation functions to be at the same level in order to show the variation of the final level of g2(τ) - 1 between different conditions, and with time during formation of gels. A refractive index matching bath of filtered cis-decalin surrounded the cylindrical scattering cell, and the temperature was controlled at (0.5 C using a Haake C35 thermostat.
Cryogenic Transmission Electron Microscopy (Cryo-TEM). A few microliters of samples were placed on a bare copper TEM grid (Plano, 600 mesh), and the excess liquid was removed with filter paper. This sample was cryo-fixated by rapidly immersing into liquid ethane cooled to -170 to -180 C in a cryo-box (Carl Zeiss NTS GmbH, Oberkochen, Germany). The specimen was inserted into a cryo-transfer holder (CT3500, Gatan, Munich, Germany) and transferred to a Zeiss EM922 EFTEM (Zeiss NTS GmbH). Examinations were carried out at temperatures around -180 C. For freeze-dried TEM imaging, the gel samples were prepared as the same procedure of the cryo-TEM operation except that the sample grid was allowed to dry in vacuum before observation. TEM observation was operated at an acceleration voltage of 200 kV. Zero-loss filtered images were taken under reduced dose conditions (500-2000 e/nm2). All images were recorded digitally by a bottom-mounted CCD camera system Langmuir 2009, 25(22), 12899–12908
(UltraScan 1000, Gatan) and processed with a digital imaging processing system (Digital Micrograph 3.9 for GMS 1.4, Gatan).
Small-Angle X-ray Scattering Measurements (SAXS). SAXS measurements were performed using the pinhole SAXS instrument at the University of Aarhus. The instrument consists of an X-ray camera (NanoSTAR, Bruker SAXS) with a rotating anode X-ray (Cu KR radiation) source, cross-coupled G€ obel mirrors, collimation using three pinholes, an evacuated beam path, and a 2D position-sensitive gas detector (HiSTAR). The setup has been modified and optimized for scattering investigations of solutions as described in detail in ref.24 In the current experiments the sample-to-detector distance was kept at 64.7 cm, and small pinholes were used, giving a range of scattering vectors as 0.0085 e q (A˚-1) e 0.34, where q = (4π/λ) sin(θ/2) is the modulus of the wave vector, θ is the scattering angle, and λ=1.542 A˚ is the X-ray wavelength. Samples were gently transferred into reusable sample holders with glued-in quartz glass mark tubes with an o.d. of about 2.0 mm and a wall thickness of about 0.01 mm (Hilgenberg). The data were corrected for detector efficiency and for spatial distortions, and azimuthally averaged. The scattering from water was measured as background and was subsequently subtracted from scattering spectra recorded for particle dispersions. Water at 20 C was used as a primary standard to normalize the data to absolute scale.24 Circular Dichroism (CD). Samples at pH 5.4 for CD measurements were prepared from stock solutions of mono 1 or a mixture of 1 and Zn-L2EO4. A dilution to 0.1 g/L 1 for all samples was made in 20 mM PIPES buffer. For the measurement at pH 11, a salt-free solution of 1 was prepared, and the solution was adjusted to pH 11 with 0.1 M NaOH, in which the concentration of 1 was also controlled at 0.1 g/L. The above solutions were (24) Pedersen, J. S. J. Appl. Crystallogr. 2004, 37, 369–380.
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permitted to age for more than 72 h in a refrigerator at 4 C before measurement. CD spectra were acquired on a CD Jasco J-715 Spectropolarimeter. Spectra were recorded in the far-UV region (190-260 nm) at 20 C at a speed of 10 nm/min and a sampling interval of 0.2 nm in a quartz cuvette with diameter 0.1 cm. Ten repeating measurements were made for all the samples and the background was subtracted. The raw data φ in millidegrees (mdeg) were converted into ellipticities E (kdegdmol-1cm2) by dividing the raw data by the cuvette path length l and the molar concentration of the amino acids c. E ¼ j=ðlc 104 Þ One polypeptide has 802 amino acids. In our experiments, a concentration of 0.1 g/L of the polypeptide, which has a molecular weight of 66135.3 g/mol, gives an amino acid concentration of 1.210-3 mol/L. The amino acids from the middle block represent a concentration of 5.9 10-4 mol/L, and those from the outer block 6.110-4 mol/L.
Results and Discussion Gelation of 1 Detected by DLS. The triblock polypeptide 1 was disolved in water after two freeze-thaw cycles. At pH 5.4, it is positively charged due to charge-up of the histidine residues in the middle block. In this case, it exists in the form of random polymer coils in aqueous solution and no gels can be formed. However, upon charge neutralization of 1, gelation occurs. Neutralization of 1 can be realized by mixing 1 (1) with negatively charged Zn-L2EO4 coordination polymers, with (2) negatively charged covalent homopolymer PANa48, or (3) increasing the pH to basic conditions. In Figure 1a, we show the evolution of DLS correlation functions g2(τ) - 1 for the charge neutralized mixed system of 1 and Zn-L2EO4. Before mixing, polypeptide 1 alone gives a low scattering intensity and the noisy g2(τ) - 1 function decays very fast. Upon addition of Zn-L2EO4 at charge neutral mixing ratio, the scattered intensity increases more than 10 times, and a smooth g2(τ) - 1 function featured by longer decay time is obtained within 20 s indicating formation of larger objects after the addition of Zn-L2EO4. Meanwhile, the correlation function show a stretched exponential decay leading to a plateau at long decaying time which is a characteristic feature for the formation of gels.25 Usually the g2(τ) - 1 value always starts from unity and decays to zero for freely moving particles, and the characteristic relaxation time τc depends on the size of the particles. However, in a gelling system, the single-particle diffusion can only execute limited motions about their fixed averaged positions so that the correlation function exhibits an arrested decay leading to nonzero values at long times.26 As shown in Figure 1a, a stretched exponential with an arrested decay leading to a plateau shortly after gelation occurs (within 1 min). It appears that the characteristic decay time τc reaches a constant value within 1 h, but the shifting of the plateau continues for at least 8 h. This suggests that the main association process completes within 1 h, but that rearrangements of the gel structure take at least 8 h. The gelation process induced by Zn-L2EO4 is compared with that caused by covalent polyelectrolyte sodium polyacrylate (PANa48), and that by increasing pH to basic condition. The results are shown in Figure 1, parts b and c, respectively. For the (25) Miyazaki, S.; Endo, H.; Karino, T.; Haraguchi, K.; Shibayama, M. Macromolecules 2007, 40, 4287–4295. (26) (a) Romer, S.; Scheffold, F.; Schurtenberger, P. Phys. Rev. Lett. 2000, 85, 4980–4983. (b) Romer, S.; Urban, C.; Lobaskin, V.; Scheffold, F.; Stradner, A.; Kohlbrecher, J.; Schurtenberger, P. J. Appl. Crystallogr. 2003, 36, 1–6.
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Figure 2. (a) Freeze-dried TEM image of the scaffold in the gel of 1/Zn-L2EO4 (6.9 g/L for 1. (b) Cryo-TEM image of the separated ribbons formed in the aqueous solution of 1/Zn-L2EO4 (1 g/L of 1); short and long arrows indicate the face and side view of the ribbons, respectively. (c) Enlarged face view of the ribbons demonstrating the width of the ribbon is about 20 nm. (d) Enlarged side view that shows the thickness of the ribbons is about 4 nm. (e) Selected area to show the overlaying of the ribbons even at this low concentration. (f) Ribbons formed in the 1/PANa aqueous solutions (1 g/L of 1). (g) Rodlike fibrils formed in 1 g/L of 1 at pH 11.
same polymer concentration, gelation induced by PANa48 and pH is much slower than that induced by Zn-L2EO4. On the one hand, the characteristic decay time in the two systems keeps increasing even after 8 h, indicating that the association process is still ongoing. On the other hand, the plateau is much lower for these two systems as compared to the 1/Zn-L2EO4 mixed system, demonstrating that the gelation in the two systems is not as pronounced as what occurs in the 1/Zn-L2EO4 mixed system. Obviously, neutralization of 1 with coordination polymer gels the system most efficiently, whereas gelation induced by increasing pH is the slowest. In fact, when the gels formed in the mixed systems of 1/Zn-L2EO4 and 1/PANa are solidlike, the 1/pH 11 system is still fluidlike. Figure 1d illustrates that the 24 h old gels formed in a solution of 6.95 g/L 1 in the presence of Zn-L2EO4 and PANa48 can support their own weight, but the 1/pH 11 system at the same concentration and same gelling time fail to do so. Gel Structure Detected by TEM. To determine the structure of the gel, we investigated the scaffold of the gel by freeze-dried TEM. As can be seen in Figure 2a, In a 1 g/L 1/Zn-L2EO4 solution, network of ribbons are observed. The width and the thickness of ribbons seem to be very polydisperse, suggesting overlay of the ribbons may occur. We therefore carried out cryoTEM in 1 g/ L solution where no gels are formed to investigate the single ribbons. It is seen in Figure 2b-e that the single ribbon can be longer than 1 μm with bendings. The good contrast allowed us to recognize the characteristic features of the ribbons, that is, broad, low contrast sections (short arrows in Figure 2b) as well as thin, high contrast ones (long arrows in Figure 2b), are clearly visualized. The broad sections are side-views, and they give the width of the ribbons to be about 20 nm (Figure 2c). The thinner sections are from edge-on views, and they give the thickness of the Langmuir 2009, 25(22), 12899–12908
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Figure 3. (a) Comparison of the effects of pH, covalent polyelectrolyte PANa48, and coordination complex Zn-L2EO4 on the CD spectrum of 1. The contribution of the outer blocks was subtracted from all the spectra. (b) Effect of zinc and bis(ligand), respectively, on the CD spectrum of 1 at pH 5.4. The contribution of the outer blocks was not subtracted.
ribbons to be only about 3-4 nm (Figure 2d). In addition, bundling of the ribbons seems to occur even at this concentration, as indicated by arrows in Figure 2e. For comparison, the structures formed in the systems of 1/PANa48 and 1/pH 11 were also analyzed by cryo-TEM (Figure 2, parts f and g). The contrast for the 1/PANa48 system is also good, but for the 1/pH 11 system it is rather poor. The different contrast quality is attributed to the larger density of material in the ribbons formed by 1/PANa48. When neutralizing 1 by charge compensation with PANa48, the PANa48 chains are also involved in the structures. In contrast, when neutralizing 1 by increasing pH, the structures are formed by 1 alone. As a consequence, the amount of solid material in the structures in the pH 11 system is less than in the 1/PANa48 system. The discernible broad and narrow, low and high contrast sections in Figure 2f demonstrate that the structures formed in the 1/PANa48 system are also ribbons. Although the resolution is not high enough to estimate the thickness of the ribbons, the width of these ribbons is assessed around 14 nm, which indicates that the structure of these ribbons is different from those formed in the 1/Zn-L2EO4 system. However, no broad and narrow regions for the structures in the pH 11 system can be recognized, indicating rodlike fibrils rather than flat ribbons are formed. The diameter of the fibrils is about 10 nm, demonstrating the structures are very different from those formed in the 1/Zn-L2EO4 and 1/PANa48 systems. Circular Dichroism Analysis on the Secondary Structure of the Polypeptide. The microstructural differences in the assemblies in the 1/L2EO4, 1/PANa, and 1/pH 11 systems are also reflected in their CD spectra, which reveal the molecular arrangement in these structures. As seen in Figure 3a, the CD spectra for the three mixed systems clearly give different patterns: at basic pH (e.g., pH 11), we obtain a negative minimum around 207 nm and two positive maxima at 200 and 220 nm, respectively. This indicates the contribution from β-turns,20,27 and is almost indiscernible from the CD spectrum of a mutant of 1,20 in which all histidines were replaced by glutamic acid and which most probably assumes a ss-roll conformation in water and a ss-sheet in methanolic solvent mixtures.28 We found that the negatively charged covalent polyelectrolyte sodium polyacrylate (PANa48) was also not capable of inducing predominant β-sheet structures. The CD pattern possibly reflects a mixture of (27) Werten, M. W. T.; Moers, A. P. H. A.; Vong, T.; Zuilhof, H.; van Hest, J. C. M.; de Wolff, F. A. Biomacromolecules 2008, 9, 1705–1711. (28) Schor, M.; Martens, A. A.; Dewolf, F. A.; Cohen Stuart, M. A.; Bolhuis, P. G. Soft Matter 2009, 5, 2658–2665.
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β-turns,29 helices30 (REF X), and probably some amount of β-sheets.30 However, by mixing 1 with Zn-L2EO4, the CD spectrum of the middle block exhibits positive ellipticity at 200 nm and negative minima at 210 and 220 nm (open red triangles). The spectrum can be approximately attributed as the mixture of β-sheet and β-turns,29 where the turns occur at the histidine site of 1. Deconvolution of the spectra by using the Johnson and Hennessey method31 shows that the content of β-sheets and β-turns is about 80% and 20%, respectively. Since at least two amino acid residue is required to form one β-turn, the result suggests that except the histitine residues at the turn position, almost all other amimo acid residues in the sequence have folded into β-sheets. Since the uncharged sequence at pH 11 by itself possibly folds into ss-rolls,28 the formation of β-sheets triggered by discharging the polypeptide with coordination supramolecules must be specifically related to the existence of coordination polymer. To elucidate whether zinc ions and ligand molecules alone affect the secondary conformation of the 1, the CD spectra of 1/Zn and 1/ L2EO4 are compared with that of 1 in acidic solutions. It is clear in Figure 3b that all three sets of spectra exhibit similar pattern with a deep minimum in the 195-200 nm region, which is characteristic for a random coil conformation of the polypeptide. Obviously, zinc and pyridine dicarboxylic acid ligands as single components have little effect on the secondary structure of 1, although zinc ions alone may coordinate with histidine groups. It is also very important to note that the negative charges on the separate ligand molecules do not affect the conformation of 1 although it is oppositely charged with respect to the polypeptide. Therefore, we can unambiguously conclude that it is indeed the Zn-L2EO4 coordination polymer that induces predominant β-sheets in 1. Moreover, the different secondary structure of the folded middle block induced by discharging the system by covalent polyelectrolyte PANa also supports the viewpoint that the presence of reversible coordination bond is very crucial in the predominant β-sheets formation. It should be noted that due to the existence of turns in 1, the characteristic CD spectrum of β-sheets in 1 is probably not be completely the same as that of pure β-sheets which shows a deep minimum of larger than -5 kdegdmol-1 cm2 around (29) Crisma, M.; Fasman, F. D.; Balaram, H.; Balaram, P. Int. J. Peptide Protein Res. 1984, 23, 411–419. (30) Yang, J. T.; Wu, C. S. C.; Martinez, H. M. Meth. Enzymol 1986, 130, 208– 269. (31) Hennessey, J. P.; Johnson, W. C. Biochemistry 1981, 20, 1085–1094.
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Figure 5. Illustration of the model of a rectangular plate surrounded by random-coil polymer chains on the sides. The three dimensions of the rectangular plate are indicated as a, b, and c, for the thickness, width, and length, respectively.
Figure 4. (a) SAXS results (top to bottom) for 1/Zn-L2EO4, 1/PANa and 1 at pH 11. (b) Model fits (solid lines) and SAXS data (points) for 1/Zn-L2EO4 and 1/PANa gel systems using a rectangular-plate model with chains on the sides and for 1 at pH 11 using the model for Gaussian chain (eq 12 in apendix). The experimental data have been shifted upward for clarity. In all systems, the concentration of 1 is 18.6 g/L.
215 nm.32 In addition, the particle flattening effect33 in a long stack of polypeptide molecule also leads to a decrease of the negative magnitude of the characteristic β-sheet band, because the monomers closest to the light source will absorb nearly all the light and cast a molecular shadow on the monomers more distant from the light source but within the same polymer. In view of the β-sheet formation in the 1/Zn-L2EO4 mixed system, we compared the theoretical β-sheet dimension with that from the cryo-TEM observations. The dimension of a single β-sheet is estimated to be about 3 nm23 nm.34 This coincides, within experimental uncertainty, with the thickness and width of the nanoribbons observed in cryo-TEM. The superiority of Zn-L2EO4 coordination polymers in inducing predominant β-sheet conformation and further stacking of them is probably owing to the reversible coordination bonds between zinc ions and the L2EO4 ligands. As was reported in our previous work, the coordination polymer is a dynamic equilibrium system since coordination-bond formation and breaking occurs quickly in solution.23 On the one hand, the labile nature of the bonds enables the polypeptide to adopt energetically optimal conformations when charge neutralization occurs. On the other hand, the presence of the polymeric structures links the neighboring β-turns on one edge of the folded sequence which facilitates formation of hydrogen bonds between the antiparallel strands. Both effects promote the formation of β-sheets and the stacking of them. In contrast, both the PANa48 and pH 11 systems lack one of these two effects: (i) the covalent PANa48 may interfere with the formation of β-sheets by tangling their chains with the polypeptide, so that no well-defined β-sheets can be formed in the system; (ii) the lack of a linking force between two neighboring turns in the pH 11 system apparently favors the formation of a different structure. Obviously, the labile coordination bonds in ZnL2EO4, which allow easy rearrangement of conformations, and avoid kinetically trapped conformations, is the crucial factor that allows formation of well-defined β-sheets. (32) Lednev, I. K.; Ermolenkov, V. V.; Higashiya, S.; Popova, L. A.; Topilina, N. I.; Welch, J. T. Biophys. J. 2006, 91, 3805–3818. (33) Bustamante, C.; Maestre, M. F. Proc. Natl. Acad. Sci. U.S.A. 1988, 85, 8482–8486. (34) Cantor, E. J.; Atkins, E. D. T.; Cooper, S. J.; Fournier, M. J.; Mason, T. L.; Tirrell, D. A. J. Biochem. 1997, 122, 217–225.
12904 DOI: 10.1021/la901834v
Table 1. Results for the Fit Parameters Obtained for a RectangularPlate Model for the Gels Formed in 1/Zn-L2EO4 and 1/PANa Systemsa sample parameter a [nm] b[nm] σa/a σint [nm] c [nm] Rg [nm] D Sc1 (103) 1/Nprim R [nm] νRPA χ2
1/Zn-L2EO4
1/PANa48
1/pH 11
17.6 ( 0.8 25.9 ( 0.7 0.48 ( 0.04 2.3 ( 0.2 >500 3.7 ( 0.4 2.6 ( 0.2 16 ( 2 0.0014 ( 0.0001 0.69 ( 0.07 (1.7 ( 0.2) 10-8 2.0
14 ( 1 19.2 ( 0.5 0.68 ( 0.09 1.3 ( 0.4 >500 4.3 ( 0.4 2.1 ( 0.4 14 ( 4 0.005 ( 0.001 0.78 ( 0.04 (2.4 ( 0.3) 10-8 1.6
10.3 ( 0.5
0.62 ( 0.02 ∼0.003 8.8
a The parameters a, b, and c are the dimensions of the ribbons as illustrated in Figure 5. σa/a is the relative polydispersity of the thickness, σint is the width of the surface of the rectangular cross section, Rg is the radius of gyration of the chains, d is the relative displacement of the chains with respect to the prism surface, Sc1 is a scale factor depending among other parameters on the relative contrast of the core and chains, 1/NChain is the inverse of the number of chains per particle, R is an estimate of the cross-section radius of gyration, νRPA is a concentration parameter, and χ2 is the reduced chi-squared describing the fit quality.
SAXS Results for the Gel. The significant difference both from molecular and macroscopic level between the 1/Zn-L2EO4 system and 1/PANa and 1/pH 5.4 systems motivates us to investigate the in situ gel structure in these three systems. In Figure 4a, we show the SAXS data from the gels of 1/Zn-L2EO4, 1/PANa, and 1/pH 11, respectively. In order to obtain better quality of the SAXS signal, the concentration of 1 in all the gelly systems is fixed at 18.6 g/L. It is clearly indicated in Figure 4a that the scattering pattern for the pH 11 system is completely different from those of either 1/Zn-L2EO4 or 1/PANa48, demonstrating differences in the nanoscale structure which is in line with our cryo-TEM observations. To our surprise, none of the three scattering curves can be fitted by a model for flat nanoribbons, nanofibers, or fibrils (data not shown). Considering the concrete situation of our nanoribbons that are stabilized by a corona of water-soluble polypeptide coils, we modified the normal ribbon model (rectangular plate) into a long rectangular plate model, which on the short sides is surrounded by polymer blobs with a gyration radius Rg, as illustrated in Figure 5 (see details of the model calculation in the Appendix). It should be mentioned that several model approaches were tried, assuming simple shapes and geometries, but none of them was capable to provide a good fit for the scattering data (data not shown). In order to be able to represent all the structural features present in the system a more elaborated model was developed, which corresponds to the Langmuir 2009, 25(22), 12899–12908
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Figure 7. Cross-section structure of the model with definitions of some of the parameters describing the structure.
Figure 6. Illustration of the formation of single ribbons at low concentrations (low C) and overlay of ribbons at high concentrations (high C) in the mixed system of 1/Zn-L2EO4.
structural model given in ref 19. As shown in Figure 4b, both the scattering curves in the 1/Zn-L2EO4, 1/PANa systems can be nicely fitted by this model, showing that the SAXS data is in agreement with the ribbon-like structures recognized by cryoTEM. The model includes several parameters (as described in detail in the Appendix): Among these were two parameters defining the rectangular cross-section, which was fitted, and the length, which had to be fixed to a large value (500 nm) due to the limited resolution of the SAXS data. It is assumed that the ribbons are polydisperse in thickness and that the cross-section of the rectangular rod has graded interfaces. The polymer chains on the sides are described by a radius of gyration and a center of mass position, which defines the average position of the chain with respect to the prism interface. A Gaussian chain model, which includes a description of a finite thickness of chain, had to be used for a proper description of the high-q SAXS data. It was found that this Gaussian chain model alone (eq 12 in the Appendix) could successfully describe the data for the pH11 sample. This indicates that with the resolution of our SAXS experiments, the rodlike component of the scattering data is not observed, and the data is dominated by polymer-like scattering. The fit quality is given by the χ2 parameter and it is together with results for the fit parameters given in Table 1 for the 1/Zn-L2EO4, 1/PANa, and 1 at pH 11 systems. Although it is not possible to discard the possibility of having another models that can also represent the SAXS data, the proposed model included all the known physical properties and assumptions that came from the TEM pictures and the polymer sequences in a closed, compact form, enabling a direct determination of the structural parameters by least-squares fitting. The influence of the structural parameters for the scattering curve is described in the Appendix. Table 1 shows that the fit quality for the two ribbon systems is very good. The radius of gyration Rg of the chains attached to the ribbons is found to be around 4 nm, which is smaller than the value expected for a polypeptide chain for this molecular mass. The thickness of the ribbons in the gel network is about 14-17 nm with a relative polydispersity of 0.5-0.7. The average thickness is about 4-5 times longer than that of the ribbons observed by cryoTEM, showing that the ribbons in the gel form stacks within an average of four to five layers. Since the stacking is an open association, one should expect a relatively large polydispersity, which agrees with the determined values. The width of the ribbons estimated from SAXS is about 20-25 nm, which is in very good agreement with the cryo-TEM results of about 20 nm. The results furthermore show that there is a significant smearing of the prism core surface with a width σint =1.6-2.3 nm. As mentioned above, there is a relatively high polydispersity of 50-70% of the thickness, in agreement with an open association and a dynamic system. It is possible that the overlaying of the ribbons is not very stable since shifting of the ribbons may occur Langmuir 2009, 25(22), 12899–12908
due to the weak interaction forces between two consecutive layers. The overlaying of the ribbons is probably due to attractions or ionic correlation forces and/or weak van der Waals attractions. From the combination of cryo-TEM, CD, and SAXS results, we can propose a complete picture of the formation of nanoribbons in the 1/Zn-L2EO4 mixed system, as illustrated in Figure 6. The length c used in the SAXS fits was 500 nm, which is shorter than the ones seen from the cryo-TEM images. However, as mentioned before, the experimental setup does not allow determination of this dimension. Sizes larger than about 100 nm cannot be resolved in this configuration and therefore we had to fix it and we chose a large value. The structure of the sample at pH 11 is completely different from the two other samples. The form factor of Gaussian chains fits the data well with a radius of gyration of Rg =10.8 ( 0.3 nm. This indicates that at pH 11, the structures do not have a well-defined core but rather consists of weakly associated, very swollen chains.
Conclusion We have investigated the gelation of a biosynthetic triblock copolymer type polypeptide induced by coordination polymers formed out of mixing of metal ions and bis(ligand)s. Multiple weak interactions, including electrostatic, coordinating, hydrogen bonding, hydrophobic, and van der Waals interaction, were involved in the formation of this new type of hydrogel. The labile nature of the coordination bonds in the coordination polymer allows them to take appropriate conformation along the polypeptide so that they do not hinder the folding of the polypeptide. Meanwhile, the polymeric nature of the coordination polymer shortens the distance between the turns. The cooperative interaction results in regular stacking of the β-sheets connected by β-turns, which leads to formation of nanoribbons. Such welldefined nanoribbons cannot be achieved by neutralizing the charges by either increase of pH or with oppositely charged covalent polyelectrolytes. The ribbons can bundle into 4 to 5 layers via van der Waals interaction and gel the aqueous system at concentrations higher than 6.95 g/L. This is an elegant example of hierarchical self-assembling systems facilitated by multiple weak interactions. The principle of the fabrication of such advanced structures is expected to motivate more interesting researches in the field of self-assemblies and material science. Acknowledgment. Financial support is from the EU POLYAMPHI/Marie Curie program (RT6-2002, Proposal 505027) and SONS Eurocores program (Project JA016-SONS-AMPHI). M.D. gratefully acknowledges financial support by the Deutsche Forschungsgemeinschaft (SFB 481).
Appendix Model for Scattering Intensity from Rodlike Nanoribbons. The structure that we consider is shown in Figure 7 and consists of rectagular prism with random walk chains attached on two opposite sides. Some of the parameters of the model are defined graphically in the Fig. 7. The prism has dimensions a, b, and c, where the latter is the length which is much larger than the two other parameters. DOI: 10.1021/la901834v
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The form factor Frib(q) of the model structure contains four different terms: the self-correlation of the core (in our case the rodlike, rectangular shaped prism) FPrism(q), the self-correlation term of the chains FChain(q), the cross-term between the core and the chains SPrism-Chain(q) and the cross term between different chains SChain-Chain(q). The total form factor35 can be written as follows: Frib ðqÞ ¼ ΔFPrism 2 VPrism 2 FPrism ðqÞþNChain ΔFChain 2 VChain 2 FChain ðqÞ þ2NChain ΔFPrism VPrism ΔFPrism VChain SPrism -Chain ðqÞ þNChain ðNChain -1ÞΔFChain 2 VChain 2 SChain -Chain ðqÞ
ð1Þ
NChain is the number of blocks attached to core. ΔFPrism and ΔFChain is the excess scattering length density of the core and a chain, respectively, and VPrism=abc is the total volume of a chain and VChain is the volume of a single chain. As we want to introduce polydispersity of the cross-section dimension a, we separate out the two parameters for the size of the cross section: Frib ðqÞ ¼ ΔFPrism c Æa b FPrism ðqÞæ þ NChain ΔFChain VChain FChain ðqÞ 2 2
2
2 2
2
þ2NChain ΔFPrism cΔFPrism VChain ÆabSPrism -Chain ðqÞæ þNChain ðNChain -1ÞΔFChain 2 VChain 2 SChain -Chain ðqÞ
Frib ðqÞ ¼ ΔFPrism
and36 Fc ðq, cÞ ¼ 2SiðqcÞ=ðqcÞ - 4sin2 ðqc=2Þ=ðq2 c2 Þ Z SiðxÞ ¼
x
t -1 sin t dt
ð7Þ ð8Þ
0
The term exp(-q2σint2/2) smears the interface of the rectangle with a Gaussian of width σint. With the assumption of polydispersity in thickness we have: ÆabArect ðq, RÞæ ¼
da0 a0 bArect ðq, RÞDða, a0 , zÞ R¥ 0 0 0 da Dða, a , zÞ
ð9Þ
da0 a0 2 b2 Arect ðq, RÞ2 Dða, a0 , zÞ R¥ 0 0 0 da Dða, a , zÞ
ð10Þ
0
and R¥ 2
2 2
1/Nchain a b c σa σint Rg vRPA d R Back
scale for the overall intensity scale including ratio between the excess scattering length of the prism core and the chain. inverse of the total number of chains prism thickness prism side prism length (fixed to 500 nm) polydispersity in thickness smearing of the prism interface radius of gyration of the Debye chain RPA concentration parameter relative shift of the Gaussian chain from the prism side estimate of cross-section radius of gyration of chains. constant background
R¥
ΔF VChain c Æa b FPrism ðqÞæ þ NChain Chain 2 2 FChain ðqÞ ΔFPrism c
2 2
Sc Sc1
ð2Þ
and we rewrite the expression as follows: "
Table 2. Summary of All Parameters Included in the Model
2
ΔF VChain ÆabSPrism -Chain ðqÞæ þ NChain ðNChain -1Þ þ2NChain Prism ΔFPrism c ΔFChain 2 VChain 2 S ðqÞ Chain -Chain ΔFPrism 2 c2 1 2 2 Sc1 2 FChain ðqÞ ¼ ΔFPrism c Æa2 b2 FPrism ðqÞæ þ NChain 1 þ2Sc1 ÆabSPrism -Chain ðqÞæ þ 1 Sc1 2 Schain -chain ðqÞ NChain ð3Þ where Sc1 = NChainΔFChainVChain/(ΔFPrism c), which will be a fit parameter together with 1/NChain. Assuming that we have a long prism with length c, we can write Æa2 b2 FPrism ðqÞæ ¼ Æa2 b2 Frect ðqÞæFc ðq, cÞ
ð4Þ
2
Æa b Arect ðq, RÞ æ ¼ 2 2
0
which should be related to (5) when calculating Æa2b2Frect(q)æ. A Schultz-Zimm distribution is used for the size distribution: Dðx0 , x, zÞ ¼
zþ1 x0
zþ1
xz x exp -ðzþ1Þ x0 Γðzþ1Þ
ð11Þ
Here Γ(x) is the real Gamma function, x0 is the center of mass of the distribution and z is related to the relative polydispersity σa/a of the thickness as z = 1/(σa/a)2 - 1. Although we assume a polydispersity in the prism thickness a single value is assumed for 1/NChain, which can be considered as an average number of chains per particle. The form factor37,38 of a single chain with radius of gyration Rg is approximated by: ! R2 q 2 ð12Þ FChain ðq, Rg Þ ¼ PDEB ðqÞ exp 2 PDEB(q) is the Debye expression for Gaussian chains39 given by:
with 1 a2 b2 Frect ðqÞ ¼ 2π
abArect ðq, a, b, RÞ ¼ ab
Z
2π
PDEB ðq, Rg Þ ¼ 2½expð -uÞþu -1=u2 , dR ðabArect ðq, a, b, RÞÞ
ð5Þ
0
sinðqb cos R=2Þ sinðqa sin R=2Þ q2 σ 2 int exp 2 qb cos R=2 qa sin R=2
!
ð6Þ (35) Pedersen, J. S.; Schurtenberger, P. J. Appl. Crystallogr. 1996, 29, 646–661.
12906 DOI: 10.1021/la901834v
u ¼ Rg 2 q2
ð13Þ
We use the term exp(-q2R2/2) for describing the finite cross section of the polypeptide chains,40 where R is an estimate of the cross-section radius of Gyration of the chains. (36) Neugebauer, T. Ann. Phys. 1943, 42, 509–533. (37) Pedersen, J. S.; Gerstenberg, M. C. Macromolecules 1996, 29, 1363–1365. (38) Pedersen, J. S. J. Chem. Phys. 2001, 114, 2839–2846. (39) Debye, P.; Phys, J. Colloid Chem. 1947, 51, 18–32. (40) Fitzkee, N. C.; Rose, G. D. Proc. Natl. Acad. Sci. U.S.A. 2004, 101, 12497– 12502.
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Figure 8. Theoretical calculations for the model. The curves in parts a), b) and c) have been displaced by powers of 10 to allow easier comparisons. In all cases the following parameter values were used: b=25 nm, c=500 nm, Rg=6 nm, Sc1=16000, 1/NChain=0.0015, d=1. (a) Influence of fiber thickness: the thickness a of the fiber is changed from 2 to 25 nm while the other parameters were fixed (σint=1 nm, σa/a= 0.01, νRPA=0). The chain form factor is also plotted to show the contribution from the scattering of the chains. (b) Influence of thickness polydispersity: The polydispersity of the fiber thickness is varied from 5 to 70% while the other parameters were fixed (a=15 nm, σint=1 nm, νRPA=0). (c) Influence of the smearing of the interface: the width of the Gaussian smearing on the rectangle interface is varied from 0 to 2 nm (a=15 nm, σa/a=0.01, νRPA=0). (d) Influence of the interaction parameter: the νRPA is varied from 0 to 10-7 (a=15 nm, σa/a=0.01, σint1 nm).
An estimative for the overall radius of gyration of the Gaussian chains41 can be obtained using the formula: ð14Þ Rg ¼ R0 N ν ˚ where R0=(2.08 ( 0.02) A, ν=0.62 ( 0.01, and N is the number of peptides segments. In our case, one side of the rectangle has 217 peptides attached and the other side, 207. In the fitting an average value of 212 peptides will be assumed, which gives an expected Rg ∼ 60 A˚. This value is also optimized on the model fit. SPrism-Chain(q) is the cross term between the core and the chains; it will be given by " Z 1 2π dR ÆabArect ðqÞæAchain ðqÞ ÆabSPrism -Chain ðqÞæ ¼ 2π 0 cosðqðb þ dRg Þ cos R=2Þ Fc ðq, cÞ ð15Þ (41) Tran, H. T.; Wang, X.; Pappu, R. V. Biochemistry 2005, 44, 11369–11380.
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in which it is assumed that the chains’ center of mass is placed at a distance dRg from the sides of the prism. AChain(q,Rg) is the scattering amplitude of the polymer chain is given by Achain ðq, Rg Þ ¼ ½1 - expð -uÞ=u,
u ¼ Rg 2 q2
ð16Þ
SChain--Chain(q) is the cross term between the polymer chains. Since they are placed along the prism length this term is given by42 "
1 SChain -Chain ðqÞ ¼ 2π
Z
2π
# dR cosðqðb þ dRg Þ cos R=2Þ
2
0
Achain ðq, Rg Þ2 Fc ðq, cÞ
ð17Þ
(42) Pedersen, J. S. J. Appl. Crystallogr. 2000, 33, 637–640.
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The low-q scattering from the sample is affected by the relatively high concentration of the scattering objects. If one does not account for the interference effects related to the concentration, the length of the rods might be underestimated by the fitting procedure. Even in our case, we are not able to resolve the particles length due to limited resolution in the experimental setup, this correction is still needed since the high concentration of the system affected the beginning part of the experimental data, as shown in simulations in Figure 4b. Therefore, the random phase approximation (RPA)43 was used to account for interactions between the rods: Imod ðqÞ ¼
FRib ðqÞ ð1 þ νRPA FRib ðqÞÞ
ð18Þ
where νRPA is an increasing function of the concentration. The fitting procedure is based on the least-squares method.44 The final expression used to fit the experimental data is given by IðqÞ ¼ ScImod ðqÞ þ Back (43) Benoit, H.; Benmouna, M. Polymer 1984, 25, 1059–1067. (44) Pedersen, J. S. Adv. Colloid Interface Sci. 1997, 70, 171–210.
12908 DOI: 10.1021/la901834v
ð19Þ
where Sc is an overall scale factor for the intensity, Back is used to account for a constant background in the fitting procedure.44 The fitting parameters in the model are summarized in Table 1. Simulations. In order to illustrate the influence of the various contributions to the scattering intensity of the various parameters, some examples were calculated. When decreasing the thickness (Figure 8a), the forward scattering at q=0 decreases and the subsidiary maxima and minima in the form factor moves to higher q. The maxima in general become less pronounced for decreasing thickness as the contribution from the chains becomes relatively more important. The decrease is not monotonous since there are contributions from both thickness and width to the maxima and for some combinations, they are added. Increasing the polydispersity of the thickness (Figure 8b), the maxima and minima get smeared out. Increasing the width of the core surface (Figure 8c) leads to a decrease if the amplitude of the maxima, however, the characteristic relatively sharp crossover close to the first minimum to the polymer scattering is still pronounced. Introducing concentration effects in the form factor (Figure 8d) gives rise to a strong decrease of the forward scattering whereas the high-q part of the form factor is barely influenced.
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