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Entanglement Coupling in Porcine Stomach Mucin† T. A. Waigh,*,‡ A. Papagiannopoulos,§ A. Voice,‡ R. Bansil,| A. P. Unwin‡ C. D. Dewhurst,⊥ B. Turner,∇ and N. Afdhal∇ Polymers and Complex Fluids, Department of Physics and Astronomy, University of Leeds, Leeds, LS2 9JT, U.K., Department of Physics, University of Patras, GR 26500, Greece, Department of Physics, Boston University, Boston, Massachusetts 02215, Institute Laue´ Langevin, BP 220, Grenoble, F-38043, France, and Department of Gastroenterology, Beth Israel Deaconess Medical Center, Harvard Medical School, Boston, Massachusetts 02215 Received January 9, 2002. In Final Form: May 21, 2002 We present data from small angle neutron scattering (SANS) on the polyelectrolyte side chain liquid crystalline phases of porcine stomach mucin. There is a polydomain nematic phase at concentrations above the point of brush overlap. Also, the proteoglycans were seen to orient under the influence of a magnetic field at concentrations below which the brushes do not extensively overlap. The field can be used to investigate the nature of the entanglement coupling between the molecules. The structure factor peak scales as c1/3 across the complete concentration range, implying liquidlike behavior (0.4-680 mg/mL). The rheological data present evidence for shear thinning with four regimes: dilute, semidilute, entangled polydomain liquid crystalline, and entangled liquid crystalline. The length and cross-sectional radius of the polymeric brushes could be measured with SANS. Static light scattering and SANS provide evidence for the changes in osmotic compressibility between dilute, semidilute, and entangled brush phases.
Introduction Proteoglycans remain a poorly understood area of molecular biology. They are noncrystalline, which makes structural studies with X-ray and neutron diffraction very difficult. Also, the biochemistry of the samples is varied and complex, making the exact position and conformation of the side chains difficult to elucidate. Furthermore, the peptide units are formed into both the backbone of the glycosylated regions and flexible linkers, the latter of which allows associations between the individual bottle brush subunits and leads to additional structural complications. An understanding of the functioning and misfunctioning of proteoglycans is important for the development of treatments for a number of diseases such as cystic fibrosis (bronchial mucin),1 arthritis (hyaluronates associated with chondroitin sulfate),2 and stomach ulcers (stomach mucin).3,4 Bottle brush structures are a common structural motif in all these biologically important polyelectrolytes, but it is not understood how this relates physically to their function.5 Stomach mucins are also of interest to the † This article is part of the special issue of Langmuir devoted to the emerging field of self-assembled fibrillar networks. * To whom correspondence should be addressed. Telephone: +44 (0) 113 233 3849. Fax: +44(0) 113 233 3846. E-mail: t.a.waigh@ leeds.ac.uk. ‡ University of Leeds. § University of Patras. | Boston University. ⊥ Institute Laue ´ Langevin. ∇ Harvard Medical School.
(1) McCullagh, C. M.; Jamieson, A. M.; Blackwell, J.; Gupta, R. Biopolymers 1995, 35, 149-159. (2) Jin, M.; Grodzinsky, A. J. Macromolecules 2001, 34, 8330-8339. (3) Bansil, R.; Stanley, E.; LaMont, J. T. Annu. Rev. Physiol. 1995, 57, 635-57. (4) (a) Cao, X.; Bansil, R.; Bhaskar, K. R.; Turner, B. S.; LaMont, J. T.; Niu, N.; Afdhal, N. H. Biophys. J. 1999, 76, 1250-1258. (b) Bhaskar, K. R.; Gong, D.; Bansil, R.; Pajevic, S.; Hamilton, J. A.; Turner, B. S.; LaMont, J. T. Am. J. Physiol. 1991, 24, 827-832. (5) Waigh, T. A.; Lisa Kato, K.; Donald, A. M.; Gidley, M. J.; Clarke, C. J.; Riekel, C. Starch 2000, 52, 450-460.
pharmaceutical industry, since they form a barrier toward drug adsorption and will be examined in the present study.6,7 The structure and rheology of synthetic polyelectrolytes has recently made some progress.8,9 Scaling theories can qualitatively explain many parts of the rheology, osmotic pressure, and small angle X-ray/neutron scattering data from linear synthetic polyelectrolytes as a function of concentration in dilute, semidilute, and concentrated regimes.8-10 Mucins are flexible or semiflexible polyelectrolytes depending on the pH and are thought to be formed in bottle brush type structures with highly charged carbohydrate side chains emanating from a semiflexible protein backbone.3,6 The exact size and chemistry of the side chains and backbone depends on the source of the samples.6 Molecular weights from 2 × 105 to 1.6 × 107 Da have been reported for stomach mucins. The structure of porcine stomach mucins relates to their function as a barrier material used to protect the lining of the epithelium from the hostile environment of the lumen. They do this through their ability to form dense viscoelastic gels when the pH is switched to low values (pH 2).4 Rheological studies point to the importance of side chain interdigitation in providing a gelled network.11 A study of canine submaxillary mucin shows that native samples are viscoelastic gels (G′ ∼ c3), but if noncovalent interactions are suppressed they form viscoelastic sols.12 An interesting new development with respect to the physical chemistry of mucins relates to their ability to (6) Allen, A. Physiology of the Gastrointestinal Tract; Johnson, L. R., Ed.; Raven Press: New York, 1981; pp 617-639. (7) Kocevar-Nared, J.; Kristl, J.; Smid-Korbar, J. Biomaterials 1997, 18, 677-681. (8) Dobrynin, A. V.; Colby, R. H.; Rubinstein, M. Macromolecules 1995, 28, 1859-1871. (9) Rubinstein, M.; Colby, R. H.; Dobrynin, A. V. Phys. Rev. Lett. 1994, 73 (20), 2776-2779. (10) Boris, D. H.; Colby, R. H. Macromolecules 1998, 31, 5746-5755. (11) Sellers, L. A.; Allen, A.; Morris, E. R.; Ross-Murphy, S. B. Carbohydr. Res. 1988, 178, 93-110. (12) McCullagh, C. M.; Gupta, R.; Jamieson, A. M.; Blackwell, J. Int. J. Biol. Macromol. 1996, 18, 247-253.
10.1021/la025515d CCC: $22.00 © 2002 American Chemical Society Published on Web 07/16/2002
Entanglement Coupling in Porcine Stomach Mucin
form liquid crystalline phases.4,5,13,14 Viney et al. have found liquid crystalline textures with optical microscopy in mucins from the porcine stomach and slugs’ feet.13,14 They mapped out the phase diagram of porcine stomach mucin with respect to concentration and temperature using differential scanning calorimetry (DSC) and optical microscopy.14 These authors find evidence for a nematic phase of commercially available mucins at high concentrations (>300 mg/mL). Additional evidence is sited by Bansil et al. for more carefully purified porcine stomach mucin molecules where dendritic fingers are associated with particle anisotropy and liquid crystallinity.3,4 It is possible that many naturally occurring proteoglycans will profit from the analogy with polyelectrolyte side chain liquid crystalline polymers (PESCLCP).5 This follows on from a previous study where some of the physical properties of starch, a naturally occurring plant polysaccharide, could be explained in terms of a side chain liquid crystalline polymeric model; i.e., the connection is made between the synthetic and naturally occurring biopolymer architectures and the effect of the side chains on the mesophase formation is stressed.15 The PESCLCP model could be considered to be a description of a general structural motif observed in these biological bottle brush molecules.5 The proteoglycan structures are tailor-made for a specified rheological behavior in these charged liquid crystalline biopolymers. They are ideal boundary lubricants, because they have high viscosities and are both electrostatically and sterically stabilized, reducing the possibility for bridging mechanisms.16 The intrinsic diamagnetic anisotropy of proteins has been extensively examined in both structural studies17 and as a probe of the thermodynamics of liquid crystalline phases.18,19 For example, Welsh et al.17 used a magnetic field to improve the resolution of layer lines from fd Inovirus by inducing tilted smectic structures and Fraden et al.19 used a magnetic field to induce a prenematic phase change in tobacco mosaic virus (TMV). In the present article porcine stomach mucin is examined with respect to the PESCLP model using four separate experimental techniques: small angle neutron scattering (SANS), static light scattering (SLS), dynamic light scattering (DLS), and rheology. Using these methods, our aim is to establish the structure, dynamics, and mesophase formation for this solution-state proteoglycan system. Experimental Section Materials. Type III partially purified porcine stomach mucin was purchased from Sigma Biochemicals and used without further treatment.14 It is known to consist of partially degraded subunits formed from a glycosylated protein region and two terminal peptide segments.14 For rheological experiments the samples were dialyzed with Millipure water to investigate the behavior in limiting salt concentrations. Furthermore, their rheology was investigated in excess salt conditions of 1 M NaCl. The concentration of the Sigma mucin molecules was calibrated as per the method of Viney et al. for the inclusion of a reduced solubility component in the commercial mixtures.14 At high (13) Viney, C.; Huber, A. E.; Verdugo, P. Macromolecules 1993, 26 (4), 852. (14) Davies, J. M.; Viney, C. Thermochim. Acta 1998, 315, 39-49. (15) Waigh, T. A.; Perry, P.; Riekel, C.; Gidley, M. J.; Donald, A. M. Macromolecules 1998, 31 (22), 7980-7984. (16) Persson, B. N. J. Sliding Friction; Springer: New York, 1998. (17) Welsh, L. C.; Symmons, M. F.; Nave, C.; Perham, R. N.; Merseglia, E. A.; Morris, D. A. Macromolecules 1996, 29 (22), 7075-7083. (18) Olgenbourg, R.; Wen, X.; Meyer, R. B.; Caspar, D. L. D. Phys. Rev. Lett. 1988, 61, 1851. (19) Fraden, S.; Maret, G.; Caspar, D. C. D.; Meyer, R. B. Phys. Rev. Lett. 1989, 63, 2068.
Langmuir, Vol. 18, No. 19, 2002 7189 concentrations samples were also recalibrated for the specific volume of mucin of 0.6 mL/g.20 Samples for the neutron experiments were prepared in both 100% D2O and 100% H2O.21 The samples were left for 1 day to ensure complete exchange of the labile hydrogens.21 A small amount of intact porcine stomach molecules was prepared using the method of Cao et al.4 An important difference between the purified samples and those purchased from Sigma Biochemicals was that the purified samples were able to form strong viscoelastic gels when the pH was reduced to strongly acidic conditions (pH 2). No such gelation phenomenon was observed with the Sigma samples, probably because the purified mucin consists of subunits linked via disulfide interactions of the nonglycosylated part of the mucin molecules, whereas in the Sigma mucin the S-S interactions are inhibited leading to unlinked subunits.11 Previous studies of the purified mucin have shown that the gelation at low pH does not occur for mucin which is treated to reduce the S-S bonds or enzymatically digested to break the linkages between subunits.4 The samples were unbuffered and above the pH where a gelation transition is seen to take place for intact porcine stomach mucin molecules in all the experiments.4 In agreement with the conclusions of Bansil et al.,3,4 we note that the carbohydrate side chains are acidic and will become less charged on a reduction in pH. This can be motivated by reference to the HendersonHasslebach equation.22 Reduction of the pH below the pKa value of the side chains will cause association of hydrogen ions with the acidic groups, reducing the charge fraction. The pKa values of the dominant proteins in the protein backbone are around 3.9 and 4.1,6 but this is only 30% of the proteoglycan weight. The other strongly contributing factor will be sialic acid groups (pKa 2.6), sulfated glucosamine (pKa ∼ 1), and galactoamines (pKa ∼ 1) associated with the carbohydrate side chains. The Debye screening length, a measure of the electrostatic repulsion between the side chains, will also be reduced for these polymers as the acidic buffer is introduced. We thus deduce that strong gelation of the proteoglycans is driven by hydrophobicity or disulfide bonds linking the subunits4,11 when the charge on the side chains is reduced at low pHs. Light Scattering. Dynamic light scattering measurements were performed on an ALV 5000 goniometer using the fast multi τ digital correlator providing correlation times in the range 10-7-103 s. The light source was a 5 W Spectra Physics argon ion laser 2016 Stabilite operating at 488 nm and 140 mW. Toluene was used to calibrate the Rayleigh ratio as per standard procedure for static light scattering. The goniometer was accurate to (0.1 °C operating in the range 30-140 °C. Samples were prepared in standard 1 cm diameter Helma quartz cells. Measurements were made on samples prepared in the concentration range 0.5-10 mg/mL. They were filtered through 0.4 µm PTFE syringe filters. The forward scattering32 was obtained from Guinier extrapolation to zero q; i.e., ln intensity was plotted against q2.2,7 Small Angle Neutron Scattering (SANS). Small angle neutron scattering experiments were made on the D11 beam line at the Institute Laue´ Langevin.23 This is a high-flux beam line (∼3 × 107 n cm-2 s-1) with a wide range of possible camera lengths allowing a large q range to be studied. The camera lengths used were 2, 8, and 25 m to ensure overlap between the three separate measurements. Momentum transfers (q ) (4π/λ) sin θ/2) could be accessed in the range 2.5 × 10-3 to 2 × 10-1 Å-1, θ is the scattered angle, and λ is the wavelength. This access to very low q allowed accurate extrapolation to be made to zero q to calculate the forward scattering. The electromagnetic field applied perpendicular to the sample was calibrated using a Gauss meter and could be varied in the range 0-1.48 T. The temperature was maintained in situ by a custom-built heating stage with a thermocouple placed in the sample holder. Temperatures in the range 25-85 °C were available. Strong SANS signals could be found for proteoglycan concentrations greater than 0.4 mg/mL. (20) Harding, S. E. Adv. Carbohydr. Chem. Biochem. 1989, 4, 345380. (21) Jacrot, B. Rep. Prog. Phys. 1976, 39, 911-953. (22) Stryer, L. Biochemistry; W. H. Freeman: New York, 1995. (23) Lindner, P.; May, R. P.; Timmins, P. A. Physica B 1992, 180, 967-972.
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Figure 1. Two-dimensional SANS data for two concentrations of commercial mucin with and without the application of a magnetic field at concentrations (a), (b) 21 mg/mL and (c), (d) 480 mg/mL. Continuous lines indicate the sense of the orientation of the long axes of the molecules. The B field is horizontal and indicated by dotted arrows. The software package Grasp was used with the MATHLAB 5.1 software package to analyze the anisotropic SANS data.24 This allowed rapid GUI analysis of detector anisotropy, which was important for the weakly scattering oriented samples. The flat field correction was taken from a 1 mm H2O sample. The empty cell background was subtracted, the beam center was calibrated with respect to the direct beam, and absolute normalization was achieved relative to the water standard. Samples prepared in H2O had extremely low contrast and were not examined further. The samples in D2O were prepared in flat Helma cells with a 2 mm thickness of specimen to provide the optimal path length. Commercial mucins were studied in the concentration range 0.5-680 mg/mL. Purified samples were only available in sufficient quantities at low concentrations of 0.5-10 mg/mL. Rheology. The sample viscosity was measured on a Bohlin CVO constant stress rheometer in both constant shear rate and oscillatory modes. A Couette cell geometry was employed in all experiments where the bob length and radius were 12.9 and 12.5 mm, respectively, with a cone angle of 1.8° and cup radius of 12.95 mm. A circulating water bath around the cup was used for temperature control, and experiments were performed at 32.0 ( 0.1 °C except for temperature ramps (480 mg/mL). Approximately 700 µL of sample was loaded into the cup using a syringe, after which the bob was lowered to a predetermined level and any excess sample was removed. The fluid rheometer was calibrated with respect to water and silicone oil. Nonlinear (24) Freeware Web page www.ill.fr/lss/grasp/grasp_main.html.
rheological data were taken between 0.1 and 2000 s-1 to find the shear rate dependent viscosity η(γ˙ ) (0.81-680 mg/mL). Error bars on the data for the viscosities were calculated from repeat measurements on the same samples. Viscosity measurements were taken at steady-state values, i.e., when consecutive time steps provided identical measurements of the viscosity, which was a particular problem at low mucin concentrations.
Results and Discussion SANS. Figure 1 shows how the degree of orientation in SANS is affected in the Sigma mucins at 37 °C by the application of a 1.48 T magnetic field. The orientation of the long axes of the molecules is shown by a straight line, and the magnetic field is shown by the arrow. At low and medium concentrations, 0.81-65 mg/mL, the SANS patterns are unoriented (Figure 1a). On application of the magnetic field the long axis of the molecules orient in the direction of the field (Figure 1b). At high concentrations (Figure 1c) we see that the SANS patterns are already anisotropic, indicating orientation of the mucins and a nematic order parameter. When the magnetic field is applied, no change is observed with the SANS patterns at high concentrations, which maintain their orientation at an angle to the magnetic field (Figure 1d). Radial integration of the anisotropic patterns clearly shows a degree of orientation. Thus, at concentrations as high as
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Figure 2. Powder averaged SANS as a function of concentration for commercial samples in the range 0.81-290 mg/mL.
480 mg/mL, we observe no effect of the magnetic field, but the samples are already oriented in a nematic liquid crystalline phase, Figure 1c,d. At 37 °C the peptide chains were found to line up in the magnetic field with their long axes parallel to the field direction in the concentration range 0.81-64.6 mg/mL. Weak anisotropy was often seen at concentrations above 21 mg/mL with no magnetic field, strongly indicating an ambient polydomain nematic structure of the mucin samples with measurements depending on shear alignment during sample loading. Powder averaged curves for Sigma mucins are shown in Figure 2 made using the MATHLAB software from curves such as those shown in Figure 1. An interparticle structure factor peak is seen with both types of sample, which moves to smaller length scales at higher concentrations. Weak oscillations for the form factor were observed in the purified samples below the overlap concentration, 1 mg/mL. To model the SANS data from the proteoglycans at low concentrations (1 mg/mL), we approximate their scattering length density to a homogeneous cylinder and use the Guinier expression for the cross section and radius of gyration of cylindrical molecules (eq 1) and (eq 2).25 The radius of gyration of the cylinder is related to its length and cross-sectional radius (eq 3).
qI(q) ) n∆F2πLVe-q Rc /2
(1)
I(q) ) n∆F2V2e-Rg q /3
(2)
Rg2 ) (L2 + 2Rc2)/12
(3)
2
2 2
2
Here n is the number density of the molecules, ∆F is the difference in scattering length densities between a molecule and the solvent, V is the volume of the molecule, Rg is the radius of gyration, Rc is the cross-sectional radius of gyration (radius of a cylinder), and L is the length of the rod. We find that Rc, Rg are 24 ( 1, 34 ( 2 nm and 23 ( 1, 29 ( 2 nm for the commercial and purified samples, respectively. These results are in fair agreement with the conclusions of Bansil and Fiebrig from TEM and AFM measurements.26,27 A previous calculation using the bond length (0.5 nm) and polymerization degree (30) of the extended side chains gives Rc as 15 nm.14 This is again in fair agreement with the SANS measurements. Taking the ratio of the zero q intercepts of eqs 1 and 2, we find (25) Mortensen, K.; Bauer, R.; Larsson, U. Biological and Synthetic Polymer Networks; Kramer, O., Ed.; Elsevier Applied Science: New York, 1990; pp 76-85. (26) Jumel, K.; Friebig, I.; Harding, S. E. Int. J. Biol. Macromol. 1996, 18, 133. (27) Bansil, R.; et al. Unpublished AFM results.
Figure 3. Magnetically induced Legendre polynomial P2(cos θ) as a function of concentration for commercial samples in a 1.48 T field, 37 °C.
relationship 4, which has a much improved accuracy for the determination of L than eq 3.
|
IGuinier Iqrod
)
q)0
L π
(4)
A separate measure of the proteoglycan length is given from the zero q intercepts, and we find L is 96 ( 8 and 97 ( 8 nm for the purified and commercial samples, respectively. The similar lengths measured for both commerical and purified samples indicate that the differences between them with respect to gelation are due to variations in the nonglycosylated regions and not the size of the carbohydrate brushes. We calculate the Legendre order parameter (3/2〈cos2 θ〉 - 1/2)28 to quantify the orientation of the mucin chains in a magnetic field using standard methods from data such as that shown in Figure 1. The order parameter P2 as a function of concentration is shown in the range 0.465 mg/mL (Figure 3). The magnetic field induced orientation increases slowly with concentration peaking at 42 mg/mL and then suffers a rapid loss in intensity with the high viscosity samples (>88 mg/mL). Thus, we see that the magnetically induced nematic phase (1.48 T) as measured using SANS occurs below the point of extensive brush overlap concentration of the molecules (88 mg/mL, Figure 3). Relaxation of the ordering of the nematic gels evidenced by anisotropic SANS occurred slowly above 4.9 mg/mL with only a small change observed over a period of 1/2 h. The scattering patterns remained anisotropic even at these low semidilute concentrations after the application of the magnetic field. The peak position of the first structure factor peak was plotted as a function of concentration (Figure 4) for both Sigma and purified samples. There is fair agreement between the scaling of the structure factor peak (q*) for both types of sample; see Figure 4. There is a cube root power dependence found for q* on concentration (c).
q* ) Rcβ
(5)
We find R (β) is 0.071 (0.32 ( 0.01) for the commercial samples. No evidence was found for a smectic phase with these samples i.e., sharp lamellar peaks (Figure 2). Only broad liquidlike scaling for the interparticle spacing could be found. Smecticity may be unstable with respect to both main chain and side chain polydispersity. The position of the broad maximum in linear hydrophilic polyelectrolytes is known to follow a c1/2 dependence in semidilute solutions.8 The c1/3 dependence observed with the mucins is in complete contrast to the studies of linear hydrophilic (28) Windle, A. H. In Developments in Crystal Polymers; Ward, I. M., Ed.; Applied Science Publishers: New York, 1982; Vol. I.
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Figure 4. Scaling of the structure factor peak with concentration for porcine stomach mucin. The diamonds are commercial samples, and the squares are the purified samples. The fit is shown for the commercial samples.
c1/3
charged polymers. However, this scaling of the peak position throughout the four polymer concentration regimes is in agreement with the liquidlike scattering expected from charged colloids and previous studies of proteoglycan monomers from cartilage.29 A similar scaling behavior has previously been found for proteoglycan monomers at low concentrations with light scattering.29 This liquidlike scaling with concentration is also consistent with that expected for a spherically symmetric sterically stabilized micellar system.30 The scaling of the neutron data allows the calculation of the mucins’ molecular mass (eq 6).29
[
]
NA M
q* (Å-1) ) 2π10-8 c (g/cm3)
1/3
(6)
Here q* is the peak position, c is the concentration, NA is Avogadro’s number, and M is the molecular weight in daltons. We thus calculate that M is 0.42 ( 0.01 MDa for the commercial samples. It can be compared with the value of 0.5 MDa previously calculated for the partially degraded specimens.14,26 It was found that the magnetic induced ordering in the nematic phase as calculated using P2 is peaked at physiological temperatures. The ordering increases from 25 to 35 °C and then decreases monotonically to 85 °C. The measurements were made on 42 mg/mL unpurified samples at the point where orientation is maximized as a function of concentration; see Figure 3. The structure factor peak experiences only a small change in position with temperature as it moves to larger q values at high temperatures. However, there is a sharp change in the form of the structure factor peak at 65 °C, possibly corresponding to phase separation or denaturation. Figure 5 shows the dependence of the scattering intensity from SANS calculated at zero q using Guinier extrapolations8 of ln intensity against q2. These plots of the forward scattering are particularly useful in this case, since we have access to the very low q data on D11 (>2.5 × 10-3 Å-1). The osmotic compressibility (∂c/∂π) is directly related to the forward scattering through eq 7.
I(0) ) cv2b2kT
∂c ∂π
(7)
Here I(0) is the scattered intensity at zero q, v is the specific volume, b is the contrast factor per unit volume, c is the (29) Reed, W. F. J. Chem. Phys. 1994, 100 (10), 7825-7827. (30) Robert, A.; Grubel, G.; Williams, C. E.; Waigh, T. A. Manuscript in preparation.
Figure 5. Forward scattering from static light scattering and SANS with commercial porcine stomach mucin molecules. SANS results are shown as crosses. SLS measurements are indicated by open squares. Power-law fits are shown as straight lines. The behavior changes at c* and cb.
polymer concentration, and kT is the thermal energy.31 The crossover concentration deduced from the compressibility between dilute and semidilute phases occurs at 1.6 ((0.5) mg/mL with the commercial samples measured using neutron scattering (c*). There is a second discontinuity observable in the osmotic compressibility at still higher concentrations with the commercial samples (42 ((5) mg/mL, cb); the power-law fit changes from I(0) ) 99c1.01(0.04 to I(0) ) 813c0.55(0.07 at cb. The compressibility measured with SANS for the purified samples was significantly lower than those of the commercial mucins. There are three regimes discernible for the osmotic compressibility of the commercial samples: dilute, semidilute, and interpenetrated brush (Figure 5). The discontinuity in the compressibility at the dilute to semidilute regime has been observed before for gelling carbohydrates, c*.32 The discontinuity in the osmotic compressibility at the point of brush compression is in qualitative agreement with theory, cb.33,34 The elastic energy stored in the stretched chains is converted to an interproteoglycan force at the point of overlap, making the samples less compressible.33 In the interpenetrated brush regime the osmotic compressibility follows I(0) ∼ c0.55 behavior. The semidilute phase has I(0) ∼ c1.01. This is close to the value predicted for linear polyelectrolytes,8 S(0) ∼ c0, and thus I(0) ∼ c1 from constructive interference on liquidlike scatterers. The compressibility is significantly less with the purified samples, which is thought to be due to residual salt existing in the commercial samples facilitating thermal density fluctuations.8,14 The energy stored in a magnetic field by diamagnetic molecules follows the square of the magnetic field strength,18 and the maximum field intensity available was used throughout the experiments to optimize orientation (1.48 T, Figure 3). The purified samples do not line up in a magnetic field at the low concentrations available (0.510 mg/mL). We conclude that it is due to the counterion pressure resisting the reorientation, i.e., the longitudinal modulus of the samples and viscosity increases in the semidilute gel phase of the purified sample over the unpurified samples. Light Scattering. The scattering ratio at zero q (Figure 5) was calculated with Guinier extrapolations in a way similar to that for SANS. There is a large increase in intensity between 0.8 and 2.4 mg/mL for the commercial samples in agreement with SANS experiments. An (31) Higgins, J. S.; Benoit, H. C. Polymers and Neutron Scattering; Oxford University Press: New York, 1994; p 197. (32) Esquenet, C.; Buhler, E. Macromolecules 2001, 34 (15), 52875294. (33) Pincus, P. Macromolecules 1991, 24, 2912-2919. (34) Zhulina, E. B.; Borisov, O. V. Macromolecules 1996, 29, 26182626.
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Figure 6. Viscosity as a function of shear rate for the commercial samples at a series of different concentrations (0.81-680 mg/mL).
expression for the osmotic compressibility analogous to eq 7 holds for light scattering. The proportionality of the Rayleigh ratio (R(0)) to c ∂π/∂c is noted. The discontinuity in the osmotic compressibility (Figure 5) from dilute to semidilute solution has been observed previously upon the gelation of associating polyelectrolyte solutions with light scattering.31 Nonassociating linear polyelectrolytes have no such behavior as they enter the semidilute phase8-10. It is in agreement with the results from SANS (1.6 ( 0.5 mg/mL). The semidilute concentration (c*) for the commercial samples corresponds to a distance of 88 nm between the molecules, approximately the length of the glycosylated region (96 nm). Laplace transformation of the correlation functions gives the relaxation rates of the proteoglycan motion in dilute and semidilute solutions. The observed modes are in agreement with previous measurements of Cao et al.4 However, we attribute the fast mode to internal dynamics of the polyelectrolytes and not after pulsing of the detector due to the superior quality of the ALV detection system. The relaxation rates of the dominant translational mode were plotted against q2 to calculate the diffusion coefficients of the mucins. If the proteoglycan is modeled as a rigid rod, we can use the approximation36
kT 6πηRh
(8)
L 2 ln L/d
(9)
D0 ) Rh ≈
D0 is the measured diffusion coefficient extrapolated to zero mucin concentration, kT is the thermal energy, η is the viscosity of water, Rh is the hydrodynamic radius, L is the proteoglycan length, and d is the proteoglycan diameter. From the neutron scattering measurements of L and d, we find Rh is predicted to be 65 nm, compared to the experimentally determined value of 30 ( 1 nm. The literature value for the hydrodynamic radius of the purified samples is 40 nm.4 The difference between theory and experiment is probably due to the increased flexibility of the samples and the ability of the fluid to drain through the carbohydrate brushes. The occurrence of nematic phases in these non-rodlike molecules should be noted. Rheology. The nonlinear shear viscosity of the samples as a function of shear rate is shown in Figure 6 for concentrations in the range 0.81-680 mg/mL. The data are shear thinning with power-law dependence of the (35) Sedlak, M. Langmuir 1999, 15, 4045-4051. (36) Riseman, J.; Kirkwood, J. G. J. Chem. Phys 1950, 18, 512-516.
Figure 7. Viscosity as a function of proteoglycan concentration for commercial mucins. Four rheological regimes are shown: dilute (cII). Error bars indicate the range of results from repeat measurements. The lowest shear rate (0.15 s-1) is the uppermost curve, and the highest shear rate (2000 s-1) is the lowest curve.
viscosity on the shear rate (η ∼ γ˘ r), with exponents (R) in the range -0.4 to -0.74. A Newtonian plateau can be observed at high shear rates with low concentrations.12 This has been previously observed with human trachebronchial mucin.1 At the point of brush interdigitation (29 mg/mL), the nonlinear rheology follows the predictions for a nematic liquid crystalline polymer; i.e., the viscosity depends on the shear rate to the 0.5 power due to reorganization of the liquid crystalline texture;37 see Figure 6. This has been recently demonstrated for the nonlinear rheology of rigid peptide fibers.38 The data are plotted as a function of concentration showing four distinct regions (Figure 7). There is a decrease in the viscosity at 3.25 mg/mL. This we identify with c*. The viscosity then increases again, experiencing a further local decrease at 33.5 mg/mL (cb). The data then have a sharp increase in viscosity, η ∼ c3.4(0.3, between cb and cII, reaching a plateau at high concentrations in agreement with the previous study of Kocevar7 (cII). The dialyzed commercial samples had a rheology similar to those that were not dialyzed. Inclusion of 1 M NaCl salt has only a small effect on the absolute value of the viscosity. However, c* moved to higher concentrations, whereas cb remains unchanged. cII could not be measured at high salt concentrations due to the reduced solubility of the mucins. At 88 mg/mL the structure factor peak is found at 19 nm (Figure 4), which is significantly less than the radius of the molecules (23 nm) calculated from SANS, implying that the side chains have interdigitated and are compressed. The rheology would thus be expected to be that for entangled polymers as observed in experiments;8,11 see Figure 7. There are four clearly discernible concentration regimes for the viscosity (Figure 7): dilute, semidilute, entangled polydomain liquid crystalline, and entangled liquid crystalline. For normal linear polyelectrolytes at high concentration we would expect a transition to the neutral polymer scaling, i.e., η ∼ c3.5.8 The saturation of the viscosity at 479 mg/mL (η ∼ c0) is thus deduced to be due to mesophase formation, since neutral polymer dynamics (37) Larson, R. G. The Structure and Dynamics of Complex Fluids; Oxford University Press: New York, 1999. (38) Mawer, P.; Waigh, T. A.; Harding, R.; McLeish, T. C. B.; King, S. M.; Bell, M. P.; Boden, N. Submitted for publication in Langmuir.
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would predict a monotonic increase. The SANS measurements indicate the existence of strongly compressed interdigitated brushes at these concentrations; see Figure 4. There is no obvious microphase separation or paste formation, and the samples are taken to be weak homogeneous gels (479-680 mg/mL) as observed previously.7 We conclude that it is the crossover between steric osmotic brush and collapsed brush (cII) we are observing at the highest concentrations (479 mg/mL), which causes the change in interproteoglycan potential and thus the change in particle dynamics. The reduction in the viscosity at 33 mg/mL (interparticle distance 26 nm (eq 5)) corresponds to the size of the side chains on the polymer, i.e., 23 nm (Figure 7). We thus conclude that the overlap and compression of the carbohydrate brushes alters the viscosity at >33 mg/mL. Furthermore, the maximum in magnetically induced orientation occurs in SANS at 29-42 mg/mL (Figure 3), the same point as the viscosity decrease in the rheology curves (Figure 7). The maximum orientation with respect to temperature occurs at physiological temperatures (37 °C), which indicates a minimum in the interparticle potential opposing alignment; see Figure 3. The interparticle potential between colloids sterically stabilized with polyelectrolytes is predicted to increase monotonically with temperature by scaling theories which could explain the decrease in orientation above 37 °C.33,34 The maximum at 37 °C could thus be due to the interplay of the glass transition of the side chains arresting the dynamics at low temperatures and the steric forces at higher temperatures opposing orientation.39 The effect of the glass transition is deduced from rheological measurements on 479 mg/mL in the range 20-35 °C corrected for the temperature dependence of the viscosity of water, which indicate a sharp increase in the viscosity at lower temperatures. No distinct phase change of the viscosity was observed through the isotropic/nematic phase boundary, in contrast to the behavior previously observed with lyotropic main chain liquid crystalline polymers.40 The glassy dynamics of the side chains39 could be dominating the temperature dependence of the viscoelasticity masking this phase change. Changing the length of the side chains could be used for adapting the glass transition of the polymer to give the required viscoelastic properties.39 The application of a magnetic field has proven to be a sensitive measure of the entanglement coupling between mucin molecules. The structural arrest at 88 mg/mL is in direct agreement with rheology experiments, where the viscosity experiences a rapid increase (Figures 3 and 7). There are no published studies of the rheology of synthetic lyotropic polyelectrolyte side chain liquid crystalline polymers (SCLCPs), but there has been some work with thermotropic SCLCPs.41 It is interesting to note that the sudden reduction in viscosity at the point of brush overlap corresponds to in vivo concentration (29 mg/mL, Figure 7). This decrease in viscosity with concentration is a feature of lyotropic liquid crystalline phases as observed previously with main chain liquid crystalline polymers.40 The Onsager prediction for liquid crystallinity is Lφ/D ) 3.45 (φ is the volume fraction), and thus for measured mucin aspect ratios it predicts the phase transition to occur at a point above the brush overlap concentration (φ ) 1.65).14,42 A more detailed theory of the (39) Ferry, J. D. Viscoelastic Properties of Polymers, 3rd ed.; Wiley: New York, 1980. (40) Berea, M.; Navard, P. Macromolecules 2000, 33, 6011-6016. (41) Colby, R. H.; Gillmour, J. R.; Galli, G.; Laus, M.; Ober, C. K.; Hall, E. Liq. Cryst. 1993, 13 (2), 233-245. (42) Onsager, L. Ann. N. Y. Acad. Sci. 1949, 51, 627.
Waigh et al.
phase behavior is required to predict the phenomena involved with these proteoglycans. It would need to include the effect on the interparticle potential of the tethered polyelectrolyte chains and the flexibility of the molecules demonstrated with dynamic light scattering. The sharp increase in viscosity above 88 mg/mL is consistent with neutral entangled polymer dynamics. The charged interaction has been screened and the brushes are strongly interdigitated. A similar step increase is observed with the viscosity of cellulose whiskers as a function of concentration, although there was no plateau at high concentrations as observed with the mucins (>479 mg/ mL, Figure 7).40 It is possible that the large interproteoglycan force of the compressed side chains induces rigidity in the backbone at these high concentrations, altering the dynamics. The addition of 1 M NaCl salt on the sample was found to have a small effect on the position of cb, but the range of the semidilute regime was reduced (c*, 8.2 mg/mL). The dilute/semidilute crossover is thought to be a fairly sensitive measure of the electrostatics in agreement with these experiments; i.e., screening the electrostatics moves c* to higher volume fractions. The insensitivity of the interparticle potential defining the brush overlap concentration (cb) is what is expected for polyelectrolyte stabilized colloidal particles.33,34 Only a small effect is observed as cb moves to lower concentrations by 0.4 mg/ mL with the addition of 1 M NaCl salt. The stability of the glycosylated regions to changes in ionic strength has a distinct advantage in maintaining the physical properties in vivo. A time of 100 s was necessary for the assumption of the steady-state viscosity with the commercial mucin samples and is a typical time scale for polymer solutions.39 No stress overshoot was found for 479 mg/mL, which is sometimes observed with liquid crystalline polymers.37 There is a distinct lag period for the resumption of the low shear rate viscosity upon the cessation of shear at 479 mg/mL. We take this to be the rate for the disruption of the flow-aligned structure35 and is in agreement with the long relaxation times observed with magnetically induced orientation (greater than 0.5 h). Oscillatory experiments indicate the weak gel status of these materials.7 The onset of gellike behavior (G′ > G′′) moves to lower frequencies at higher concentrations. The scaling of the G′ samples at low concentrations implies we are observing viscoelastic sols according to the nomenclature of Sellers et al.11,12 We should differentiate between the weak gels characterized in the present samples and the strong viscoelastic gels produced at low pHs with purified samples.4 The appearance of weak gelation phenomena allows us to investigate the steric properties of porcine mucin,12 since rearrangement of the proteoglycans is not completely inhibited. General Discussion The semidilute overlap concentration (c*) is defined as8
c* )
mfib (4/3)π(L/2)3
(10)
We take the mass of a fiber (mfib) as 4.2 × 105 Da and L (length of the cylinder) as 96 nm from the SANS measurements, which gives c* ) 1.5 mg/mL. This is in fair agreement with static light scattering and neutron measurements of the osmotic compressibility (1.6 mg/mL, Figure 5).
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Figure 8. Phase diagram for the commercial samples as a function of concentration and temperature adapted from Davies et al.14
We define a further concentration when the brushes begin to interpenetrate as cb.
cb )
mfib πr2L
(11)
We find that cb is 4.4 mg/mL using r (radius of cylindrical bottle brush) as 23 nm from SANS measurements, and for interdigitated brushes we find 18 mg/mL (r is 12 nm). A separate calculation using eq 5 for the interproteoglycan distance gives the brush overlap at 7.1 mg/mL (q* ) π/r) and gives 57 mg/mL for brush interdigitation (q* ) 2π/r). This second value is on the order of the position of change in osmotic compressibility measured with SANS (cb, 42 mg/mL). The calculations are also in fair agreement with the prediction for the point of appearance of the liquid crystalline phase in the rheology (29 mg/mL); see Figure 7. The phase diagram deduced from SANS, SLS, DLS, and rheology measurements is shown in Figure 8 to aid discussion of the results. Loading-dependent anisotropy calculated with SANS occurs at concentrations above 21 mg/mL, indicating that a liquid crystalline polydomain structure occurs at concentrations far below those observed by Viney et al. (280 mg/mL) with optical microscopy.14 Note cII is a dynamic phase transition and is thus limited by the glass transition. We have presented evidence for the formation of a nematic phase in porcine stomach mucin at concentrations above 21 mg/mL.14 A monodomain nematic can be induced by a magnetic field in the semidilute phase (0.81-88 mg/ mL) and used to explore entanglement coupling between the molecules. The side chains are shown to be important for defining this behavior and make the material phase behavior less sensitive to the molecular weight of the samples. For synthetic colloid stabilization tethered polyelectrolyte chains are used, since they are water soluble, but there is a weak dependence of the interparticle potential on the salt concentration.33,34 This could be one of the roles played by the carbohydrate side chains of the proteoglycans in vivo. Strong gelation is only induced in intact mucin molecules once the charge is lost on the side chains at low pHs and attractive interactions occur between unglycosylated regions of the peptide backbone.4,11
The nematic phase at high concentrations (cII, 479 mg/ mL) with altered dynamics may be related to the in vivo functioning when the polymer is synthesized in granules. These deposits contain compact arrangements of proteoglycan molecules arranged side by side and the nematic phase offers both efficient packing and sufficient fluidity to enable transport to the region of use.3 It is interesting to compare the results with the case of peptide fibers presented by Mawer et al.38 Here the fibers readily formed nematic phases at room temperature (2-10 mg/mL) and are transformed into nematic gels as the pH is lowered; i.e., they are also pH switchable gels. In comparison to this example, the mucin side chains sterically stabilize the fluid phases and gelation is only observed when naked peptide is present.38 There is still much that we do not understand on the phase behavior of these bottle brush molecules, and further experiments are required to understand the interplay between entanglements and the rigidity of the peptide units. It would be also useful to quantitatively study the strength of the induced orientation by varying the magnitude of the magnetic field.18 Interestingly, more information is available from neutron scattering in samples in which gelation is inhibited, since orientation is maximized. It would be useful to study whether the brush overlap concentration (cb) is an important quantity in other proteoglycans. The interplay between liquid crystallinity, conformation, and dynamics of the polyelectrolyte brushes needs to be developed theoretically in more detail.34,42 Synthetic polyelectrolyte side chain polymers have been synthesized, and they could provide model systems to study the structure and dynamics of proteoglycans.43,44 Conclusion There is a polydomain nematic phase in porcine stomach mucin at concentrations above 21 mg/mL. A nematic phase monodomain is induced in the mucin when a 1.48 T magnetic field is applied below the concentration of the strongly entangled regime (0.5-88 mg/mL). At the concentration of brush overlap, there is a maximum in the degree of induced orientation (33 mg/mL). Guinier plots give the length of the cylindrical glycosylated regions of purified (commercial) samples to be 96 ( 8 nm (97 ( 8 nm) with a radius of 23 ( 1 nm (24 ( 1 nm), in fair agreement with electron microscopy and atomic force microscopy measurements from similar samples.26,27 Rheology, SANS, and SLS data give evidence for four distinct regimes for the phase behavior as a function of concentration: dilute, semidilute, entangled polydomain liquid crystalline, and entangled liquid crystalline. The rheological data indicate that entanglements of the polymer bottle brushes provides the weak gel behavior of the samples. The brush overlap concentration has a distinct rheological signature indicating liquid crystallinity. Acknowledgment. Many thanks to D. Bowyer for constructing the temperature cell, C. J. Whiting for demonstrating the pH meter, P. Mawer for help with the Bohlin rheometer, and P. Olmsted for points relating to the theory. A.P. was supported by a Marie-Curie fellowship. LA025515D (43) Nieuwkerk, A. C.; Marcelis, A. T. M.; Sudholter, E. J. R. Macromolecules 1995, 28, 4986-4990. (44) Berlinova, I. V.; Dimitrov, I. V.; Vladimirov, N. G. Polymer 2000, 41, 6431-6438.
