The Phase Diagram of Charged Colloidal Lipid A-Diphosphate

Feb 26, 2008 - Chester A. Faunce , Hendrik Reichelt and Henrich H. Paradies. The Journal of Physical Chemistry B 2008 112 (30), 8859-8862. Abstract | ...
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2008, 112, 3290-3293 Published on Web 02/26/2008

The Phase Diagram of Charged Colloidal Lipid A-Diphosphate Dispersions Hendrik Reichelt, Chester A. Faunce, and Henrich H. Paradies* The UniVersity of Salford, Joule Physics Laboratory, Materials Research Institute, Manchester, M5 4WT, United Kingdom ReceiVed: December 13, 2007; In Final Form: February 11, 2008

Small-angle X-ray-scattering, light-scattering, and electron microscope experiments were used to determine the phase transitions of colloidal lipid A-diphosphate aqueous dispersions. The phases detected were a correlated liquid phase, a face-centered cubic (Fd3m) and a body-centered cubic (Im3m) colloidal crystal phase and a new glass phase. These experimentally determined phases were shown to be in accord with theoretically predicted equilibrium phases.

The physical structure of lipid A-diphosphate (Figure 1), the conserved and abundant part of lipopolysaccharides (LPS) of E. coli, is of uppermost importance in a variety of applications, including binding of cationic antimicrobial peptides (CAMPs) and endotoxin inhibitors.1 Lipid A-diphosphate is one of the surface components of many enteric bacteria, as well as being responsible for their virulence. The molecule is also of major interest because it provides the human host with protection against infection from microorganisms; however, it may also give rise to endotoxic shock. Even though these and other activities are known, a phase diagram for this molecule had not previously been attempted. Therefore, the construction of a phase diagram was undertaken to provide greater overall understanding of the molecule. The most compelling observations of the phenomenon of colloidal crystallization are the order-disorder transition at low ionic strengths and the structural transition from a body-centered cubic (bcc) to a face-centered-cubic (fcc) structure2 Computer simulations3 and scaled-particle theories4 show that the range of the attractive part of the intermolecular potential determines whether a material possesses stable liquid-liquid-phase coexistence or a liquid-solid phase separation.5 In colloidal dispersions, it is important to consider the co-occurrences of phase separation and crystalline ordering, for example, fcc, bcc, and simple-cubic (sc) structures. For the material under investigation, simulations6 and experimental studies7 suggest that the crystalline phase is a supercooled liquid phase with some liquid retained in a metastable state for a considerable time, even at φcolloid > 0.58. A decrease in entropy in the colloidal crystals associated with a nonuniform mean density is also recognized. However, a greater local volume that each particle can independently explore compensates for the phenomenon.8 Until recently, it was not possible to prepare stable aqueous colloidal dispersions of lipid A-diphosphate with low polydispersity in shape, size, and charge over a range of volume fractions, φ.9-12 These dispersions are influenced by long-range * To whom correspondence should be addressed. Phone: (+44)-161295-4286 or (+49)-2371-12305. FAX: (+44)-161-295-5575 or (+49)-2371149705. E-mail: [email protected].

10.1021/jp711720j CCC: $40.75

interactions where particles repel one another at large separation distances; thus repulsion increases with decreasing particleparticle separation. The electric double layer surrounding the particles extends to more than a particle diameter beyond the surface of the particle. This being the case, particles may interact at volume fractions from as little as 10-4 and order-disorder transitions may only be observed at very low volume fractions. In this investigation, using small-angle X-ray scattering (SAXS), static-light scattering (LS) and electron microscopy, it was possible to study how charged lipid A-diphosphate nanoparticles10-12 are affected by changes in the volume fraction. Also considered were the effects on the nanoparticles of a range of interactions between the stable fluid (liquid) phases, the bcc phase, and the fcc phase. The experimental results were then compared with theoretical calculations for the orderdisorder and bcc-fcc transitions.13 A newly discovered lipid A-diphosphate glass phase was obtained by an effective “quench” from a solution of φ ) 4.5 × 10-4 at an ionic strength of I ) 1 mM NaCl. An alternative method of obtaining the phase is to very rapidly increase φ from φ ) 2.5 × 10-4 to φ ) 4.5 × 10-4 in the presence of micromolar HCl, which increases the ion density to twice the molecular density. The SAXS and LS results of the noncrystalline phases are influenced by size, shape, and charge polydispersity. An appropriate structure factor Shexp(Q) was extracted from the scattered intensity after subtracting the measured background and dividing by the form factor P(Q) ) |F(Q)2| for polydisperse spheres. Because Shexp(Q) varies in the liquid phases, the radii and polydispersity determine the line shape near the form factor minima P(Q). The polydispersity is represented by a three-component mixture of sizes of a-σ, a, and a-σ with relative number densities 1, 2, and 1. It was found from the calculation of S(Q) that a threecomponent system with F ) 0.052, subcomponent diameters of d ) 70.5, 75.8, and 79.3 nm, and mole fractions of 0.05, 0.90, and 0.05 gave a very good fit in solving the hypernettedchain approximation. This approach gave the correct behavior of the minima in the disordered phases for various volume fractions, φ. Scattering profiles are shown for the four phases in Figure 1 as a function of φ. The colloidal crystalline phases were identified by the presence of resolution-limited Bragg © 2008 American Chemical Society

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Figure 1. Left: scattering profiles of intensity I(Q) vs Q (Q ) (4π/λ)‚sin θ/2). (a) LS-profile (λ ) 637.8 nm from a polarized laser beam (35 mW He-Ne)10 for the liquid phase of a lipid A-diphosphate aqueous dispersion (φ ) 2.0 × 10-4, I ) 0.5 mM, red); drawn curve (black) is the RayleighGans-Debye (RGD) form factor with polydispersity σ ) 5.2% and R ) 35 nm. The pink arrows show the positions of the first and second minima in the RGD approximation. (b) SAXS profile of bcc-(Im3m) type crystals (λ ) 0.154 nm, KR/Kβ filtered CuKR radiation12) with a ) 37.5 nm (φ ) 3.5 × 10-4, I ) 0.5 mM NaCl); (c) SAXS profile for the glass phase (φ ) 4.0 × 10-4, I ) 10 µM HCl); (d) SAXS profile of colloidal fcc (Fd3m) type crystals with a ) 57.5 nm (φ ) 5.0 × 10-4, I ) 0.5 mM NaCl). Right: chemical structure of lipid A-diphosphate.

Figure 2. (A) Lipid A-diphosphate profiles of S(Q) vs Q for the glass phase (3‚‚‚3) and liquid phase (blue),9‚‚9) with φ ) 4.0 × 10-4 and I ) 10.0 µM HCl (20 °C). (B) Pair distribution function g(R) vs R/a with an interparticle spacing of a ) 55.5 nm for the glass phase (black), and for the liquid phase (blue-dotted). Vertical bars indicate positions of the four nearest neighbors in the fcc lattice.

peaks that were indexed according to their structures:14 a bcc (Im3m) lattice (a ) 37.5 ( 2.0 nm) at φ ) 3.5 × 10-4 and an fcc (Fd3m) lattice (a ) 57.5 ( 2.5 nm) at φ ) 5.0 × 10-4 with I ) 5.0 mM NaCl or another fcc (Fm3m) lattice (a ) 55.0 ( 2.5 nm) at φ ) 2.5-4.0 × 10-4 with 1.0-10.0 µM HCl (see Supporting Information). The peak broadening observed in Figure 1a,b indicates a lack of long-range crystalline order and the existence of either a glass phase or a liquid phase. To study the noncrystalline phases in more detail, it was necessary to extract the structure factor S(Q) from the scattered intensities. This was accomplished by taking into account the particle size, charge, and shape polydispersities of the multicomponent system (MCS). Assuming a colloidal lipid A-diphosphate sphere radius of 35.0 nm with a 5.7% Gaussian size polydispersity, the recorded minima and shape of the scattering curves were found to be correct for the disordered phases at φ ) 2.0 × 10-4 (I ) 0.5 mM NaCl). Figure 2 shows S(Q) versus Q for the glass phase obtained from the normalized SAXS and LS profiles. The distinction between the glass and liquid transitions observed in different regions of the phase diagram is made on the basis of the height and width of

the S(Q) peaks. The structure factors of the glass phase, which appear like an “enlarged” fcc structure, display a measured peak width (full widthat half-maximum (fwhm)) for the first peak of Seff(Q), ranging between 0.058 and 0.073 nm-1. The peak width of the liquid phase is greater than 0.013 nm-1 with the glass phase showing a structure factor peak well above the HansenVerlet criteria15 for the volume fraction range 1.5 × 10-4 e φ e 3.5 × 10-4 and 1.0-10.0 µM HCl. Note: The dynamiclight scattering and shear-viscosity results also agreed well with the calculated values obtained from the mode coupling theory.16 Accordingly, a dramatic reduction in the low shear viscosity occurred when the surface charges were neutralized. Also observed for this system was a substantial decrease in stress at the onset of shear thickening.17 The equilibrium phase diagrams shown in Figure 3A,B were constructed according to Robbins et al.13 The particle-surface charge was determined by comparing Seff(0) and Ip(Q) obtained from SAXS or LS with the computed Ip(Q) and S(Q)0).10 Because the Derjaguin-Landau-Verwey-Overbeck (DLVO) expression assumes a linearization of the colloid-ion interactions, it was necessary to use a renormalization charge that is smaller

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Figure 3. (A) Phase diagram for lipid A-diphosphate, kBT/ν‚(F-1/3) vs κ‚F-1/3 as simulated13 for the experimentally obtained data for lipid A-diphosphate dispersions. Open symbols, I ) 0.25 mM; solid symbols, I ) 12 mM. The dispersions show only short-range order (ο-ο), bcc (Im3m) order (9‚9), or fcc (F3dm) order (1‚1). (B) Phase diagram for lipid A-diphosphate as a function of φ and micromolar HCl. 9-9, bcc crystals; 4-4, fcc crystals; 0-0, bcc and fcc coexistence; b-b, glass; and O-O, liquid phases. Solid lines are phase boundaries; dashed line is the theoretical fccliquid-phase boundary. Inset: (A) TEM images of the two lattice types and single particles in the liquid; (B) hexagonal packing of fcc colloidal crystals (4-4).

than the structural charge. We applied the approach of Alexander et al.18 based on the Poisson-Boltzmann cell model, and a calculated effective charge of 430e was determined, a charge that was independent of φ at low ionic strength. The average structural charge was determined to be (780 ( 80)e at 10-4 M and (760 ( 60)e at 10-2 M salt. The values of the surfacecharge density FT ) 0.25 C/m2 and the Stern capacity CS ) 0.70 F/m2 were close to those determined previously.11 Employing the parameters obtained from SAXS and the MCS modeling of the lipid A-diphosphate dilute dispersions, kBT/ν‚F-1/3 was plotted as a function of κ‚F-1/3 (Figure 3). The solid lines in Figure 3 are the theoretical results showing the bcc region whose stability range decreases as κ‚F-1/3 increases, and the dotted lines represent the quasi-harmonic approximation prediction of the bcc-fcc phase boundary. Using the renormalization surface-charge values, the agreement with the theoretical predictions is very good for both phase boundaries. The thermodynamic results found for this system at I ) 5.0 × 10-4 M suggest a transition from the liquid to the fcc (F3dm) phase with no indication of the existence of bcc (Im3m) structures. However, there appears to be a phase situated between the liquid and the fcc phases. Amorphous phases were observed at φ ) 6.0 × 10-4, and all dispersions show shortrange order. After weeks or months, the systems eventually crystallize if a polydispersity of 5.5% in sphere radii or charge exists; however, at high-volume fractions and at a polydispersity of ∼7.5% a glass phase forms. For a system like lipid A-diphosphate, which may contain a single species interacting with a spherical symmetric potential, a glass phase will normally form if quenched at a sufficiently rapid rate. Such a system is strongly dependent on deionization time, requiring several days (or weeks) to form the solid phase from the liquid-stock solution. The fundamental time steps for crystallization of atomic materials are the inverse of the phonon frequency = 10-13 s. For a system where lipid A-diphosphate exhibits a polyball morphology, an interparticle spacing of 55 nm and a StokesEinstein diffusion coefficient D0 ) 4.0 × 10-8 cm2 s-1, the value of a2/D0 = 1.0-1.5 s is calculated for an aqueous solution at 20 °C. Thus, the deionization process on a time scale of 3-4 days is equivalent to a 10-4 s quench from the liquid to the solid phase. Therefore, it becomes much easier to attain a

crystalline state if the liquid-phase boundary is approached by increasing the volume fraction and/or by slowly changing the ionic strength. Phonon frequencies in colloidal systems are much smaller because of the large particle mass and long spacings (0.05-1.5 µm) and scale with m-0.5‚a-1, which is ∼105 times smaller for colloidal crystals than for normal solids. The links of the onset of melting to the thermally driven rms displacements, δr, of particles about their mean positions approach roughly 0.15a when the crystal melts:19 This results in a movement of ∼6.5 nm, a distance considerably less than the spacing between the surfaces of the colloidal spheres and less than the screening length. Figure 3B shows the lipid A-diphosphate phase diagram for volume fraction φ as a function of µM HCl. Only a liquid phase will exist below φ ) 2.5 × 10-4 without the presence of µM HCl. With an increase in φ, corresponding phase transitions were initiated, first a bcc, then an fcc and finally a glass phase. At a fixed moderate volume fraction (φ ) 3.0 × 10-4), if the µM HCl concentration is increased the general progression is from a glass to an fcc solid to a liquid. The bcc phase exists only in a small area; however, an unusual feature of the bcc structure is that it appears at about the same volume fraction at two different ionic strengths, which differ by an order of magnitude. The formation of an fcc-type structure appears to be inhibited by the shape and charge polydispersity, small particle size, and a very low number density (a3 ≡ 1/F with F the particle density and a the interparticle spacing). The system at I ∼ 5.0-7.0 mM NaCl closely resembles a hard-sphere model, which is more sensitive to the degree of polydispersity. Experiments on screened Coulombic potentials show that the interaction strength increases in a progression from the liquid state to the solid state, which is normally bcc for long-range interactions, for example, small ka at low φ. Therefore, an increase in the effective charge of as little as 5% at the same diameter of d ) 75.8 nm leads to a region of instability that would intersect the narrow fcc phase. The presence of a glass phase in the phase diagram was unexpected. In fact, the glass phase may be seen as an array of polyspherical particles, with two or more differently sized or charged species, which form a metastable glass. The freeze transition is mutually entropy driven, and the bcc phase is formed at a high-packing fraction bcc, with I ) 1.0 mM. The disordered fluidlike configurations suggest that the lipid A-

Letters diphosphate assemblies are movable. This type of system is quite different from that of the ordered-crystal phase. The structure of the lipid A-diphosphate glass phase formed in the presence of 100 µM HCl was evaluated using the radial distribution function from a plot of g(R) versus R/a. Here a is the characteristic interparticle spacing. The g(R) was obtained from the Fourier transform of S(Q) - 1. The local fcc-like order gives rise to the g(R) peaks shown in Figure 2B. However, in very dilute dispersions no distinct satellite peaks of g(R) were detected, even at 100 µM HCl (Figure 2A). The splitting of the second g(R) peak is indicative of an Random Close Packing (RCP) lipid A-diphosphate structure found at either 1.0 mM NaCl or 100 µM HCl. Consequently, the splitting of the second peak into two different and distinct peaks is at R1 x3 and 2R1, where R1 is the position of the first peak at nearest-neighbor distance. The additional small peak at R1 x2 in g(R) is also characteristic of an RCP structure, which is normally R1, R1 x3 and 2R1. For fcc (Fm3m)) crystals, the first nearest neighbors are R1, R1 x2, R1 x3, and 2R1. Although the lipid A-diphosphate phases studied are very similar to other well-known systems, they are neither covalently linked polymers20 nor colloidal silica dispersions.21 The observed lipid A-diphosphate vitreous phase could possibly play a crucial role in the preparation of pharmaceuticals, adjuvants, and vaccine formulations. Consequently, preserving a feedstock under extreme conditions such as chronic inflammation and acidic pH could enhance biochemical activity.1c,17 Furthermore, the loss of ergodicity was observed either by increased volume fractions and ionic strength or by addition of HCl at 20 °C. All of these factors hindered particle motion because of cluster formation with neighboring lipid A-diphosphate particles (attractive glass). It is also possible that this system undergoes a reentrant liquid-glass transition at a high-volume fraction (φ = 5.8 × 10-4) and at an increased temperature ∼40 °C. If either of these two conditions occurs independently or simultaneously the system evolves to form a vitreous state known as a repulsive glass.22 Acknowledgment. We thank Professor S. E. Donnelly for support and critical discussions.

J. Phys. Chem. B, Vol. 112, No. 11, 2008 3293 Supporting Information Available: Supporting information available. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) (a) Christ, W. J.; Hawkins, L. D.; Lewis, M. D.; Kishi, Y. In Carbohydrate-based Drug DiscoVery; Wong, C.-H., Ed.; Wiley-VCH Verlag GmbH & Co: Weinheim, Germany, 2003; Vol. 1, pp 341-355. (b) Raetz, C. R.; Whitfield, C. Annu. ReV. Biochem. 2002, 71, 635. (c) Mims, C. A.; Nosh, A.; Stephen, J. Mim’s Pathogenesis of Infectious Disease, 5th Ed.; Academic Press: London, 2001; pp 74-78. (2) Monovoukas, Y.; Gast, A. P. J. Colloid and Interface Sci. 1989, 128, 533. (3) (a) Dijkstra, M.; van Roij, R.; Evans, R. Phys. ReV. Lett. 1998, 81, 2268. (b) Soft and Fragile Matter; Cates, M., Evans, M. R., Eds.; Institute of Physics Publishing: Bristol, U.K., 2000; and ref. therein. (4) Lekkerkerker, H. N. W.; Poon, W. C. K.; Pusey, P. N.; Stroobants, A.; Warren, P. B. Europhys. Lett. 1992, 20, 559. (5) Sear, R. P. Phys. ReV. E 2000, 61, 651. (6) Matuyama, A. J. Phys. Soc. (Japan) 2006, 75, 034604. (7) Pusey, P. N.; van Megen, W.; Bartlett, P.; Ackerson, B. J.; Rarity, J. G.; Underwood, S. M. Phys. ReV. Lett. 1989, 63, 2753. (8) Woodcock, L. V. Nature 1997, 384, 141. (9) Thies, M.; Quitschau, P.; Zimmermann, K.; Rusch, V.; Faunce, C. A.; Paradies, H. H. J. Chem. Phys. 2002, 116, 3471. (10) Faunce, C. A.; Paradies, H. H.; Quitschau, P. J. Phys. Chem. B 2003, 107, 2214. (11) Faunce, C. A.; Reichelt, H.; Paradies, H. H.; Quitschau, P.; Rusch, V.; Zimmermann, K. J. Phys. Chem. B 2003, 107, 9943. (12) Faunce, C. A.; Reichelt, H.; Paradies, H. H.; Quitschau, P.; Zimmermann, K. J. Chem. Phys. 2005, 122, 214727. (13) Robbins, M. O.; Kremer, K.; Grest, G. S. J. Chem. Phys. 1988, 88, 3286. (14) International Tables for X-ray Crystallography; Henry, N. F. M., Lonsdale, K., Eds.; The Kynoch Press: Birmingham, U.K., 1965. (15) (a) Hansen, J. P.; Verlet, L. Phys. ReV. 1969, 184, 151. (b) Verlet, J. Phys. ReV. 1968, 165, 201. (16) Go¨tze, W.; Sjo¨gren Rep. Prog. Phys. 1992, 55, 241. (17) Zimmermann, K.; Paradies, H. H. The University of Salford, Manchester, U.K. Unpublished work, 2004. (18) Alexander, S.; Chaikin, P. M.; Grant, P.; Morales, G. J.; Pincus, P. J. Chem. Phys. 1984, 80, 5776. (19) Lindemann, Z. Phys. 1910, 11, 609. (20) (a) Sirota, E. B.; On-Yang, H. D.; Sinha, S. K.; Chakin, P. M. Phys. ReV. Lett. 1989, 62, 1524. (b) Zon, D. Z.; Sun, L. Q.; Aklonis, J. J.; Salovey, J. J. Polm. Sci. 1992, A30, 1463. (21) (a) Chang, J.; Lesieur, P.; Delsanti, M.; Belloni, L.; Bonnet-Gonnet, C.; Cabane, B. J. Phys. Chem. 1995, 99, 15993. (b) Philipse, A. P.; Vrij, A. J. Chem. Phys. 1988, 88, 6459. (22) Chen, S.-H.; Chen, W.-R.; Mallamace, F. Science 2003, 300, 619.