Phase Behaviour of Lysozyme Solutions
C. Gögelein and G. Nägele
Proteins are typically of nanometric size and anisotropic shape. Amino acid groups, and hydrophilic and hydrophobic subunits are the origin of charge patterns and distributions of hydrophobic patches on their surfaces, giving rise to complex protein interactions. In a first attempt to apply colloid methods to protein solutions, the isotropic Derjaguin-Landau-Verwey-Overbeek pair
potential was used to predict the phase behaviour. In other work, the effect of the anisotropic interactions was modeled by a simple square-well potential, disregarding the electrostatic interactions.
In our work in [1,2] , we use a patchy interaction model which includes the electrostatic repulsion and the anisotropic attraction. The latter is accounted for by an angular-modulated pair potential of Yukawa-type.
Second-order thermodynamic perturbation theory based on a hard-sphere reference system is used to calculate the equilibrium phase diagram.
Our patchy model describes the gas-liquid phase coexistence curves overall quite well (see left figure). In particular, it captures the influence of added salt on the stability of the fluid phase. See here the calculated binodals in the figure on the right- hand side. The range of attraction predicted in our calculations is in good agreement with experimental results by Israelachvili and Pashley [Nature 300, 341 (1982)]. This strongly suggests that the attractive interactions caused by hydrophobic patches on the protein surface dominate the phase behaviour in lysozyme solutions. The good agreement between the calculated and experimental binodal supports the assumption by Hoskins et al. [J. Chem. Soc., Faraday Trans. 92, 4515 (1996)] that the asymmetric distribution of surface charges becomes non-influential for pH-values 2-3units separated from the isoelectric point. As a crucial test of our model, we have calculated the fluid-solid coexistence curve, using interaction parameters obtained from the experimental data at the gas-liquid critical point. We find reasonable good agreement between the experimental curve and our theoretical prediction.
[1] C. Gögelein, “Phase behaviour of proteins and colloid-polymer mixtures”, Ph.D.
thesis, Heinrich-Heine-Universität Düsseldorf, November 2008 (Supervisor: G.
Nägele)
[2] C. Gögelein, G. Nägele, R. Tuinier, T. Gibaud, A. Stradner, and P.
Schurtenberger, “A simple patchy colloidal model for the phase behaviour of lysozyme dispersions“, J. Chem. Phys. 129, 085102 (2008).
Effect of Additives on Phase Behaviour of Lysozyme
C. Gögelein and G. Nägele
Theoretical-experimental collaboration with S.U. Egelhaaf and D. Wagner (both at Heinrich-Heine-Universität Düsseldorf)
In biotechnology, specific additives are often added to protein solutions to modify the protein interaction and the phase behaviour, for example to favour crystallization. By combining theory and experiment, in Ref. [3] we investigate the changes in the phase behaviour of aqueous lysozyme solutions induced by the addition of NaCl, glycerol and dimethyl sulfoxide (DMSO).
Upon the addition of glycerol and DMSO, the fluid-solid transition and the gas-liquid coexistence curve (binodal) shift to lower temperatures, and the gap between them increases. The experimental trends are consistent with our theoretical predictions based on second-order thermodynamic perturbation theory and the Derjaguin- Landau-Verwey-Overbeek (DLVO) model for the lysozyme-lysozyme effective pair interactions. We observe that both glycerol and DMSO render the potential more repulsive, while NaCl reduces the repulsion.
[3] C. Gögelein, D. Wagner, F. Cardinaux, G. Nägele, and S.U. Egelhaaf, “Effect of glycerol and dimethyl sulfoxide on the phase behaviour of lysozyme: Theory and experiment“,
J. Chem. Phys. 136, 015101 (2012).
Depletion-induced Aggregation and Phase Separation in Colloid-Polymer Mixtures
C. Gögelein, G. Nägele, J. Buitenhuis and J. Dhont
A fascinating feature of colloidal dispersion is that the specific pair interactions can be tuned. Repulsive interactions are often caused by surface-released charges. This allows us to vary the range of repulsion by changing the salt content. For significant differences in the colloid and solvent dielectric constants, also the short-range van der Waals attraction plays a role. A depletion-induced longer-ranged attractive interaction can be imposed by adding free polymer chains.
In colloidal systems with competing attractive and repulsive interactions, the phase separation process can interfere with the colloid cluster aggregation process. To study this interference, we have analyzed an aqueous mixture of charged, nanosized silica particles and dextran polymers using photon correlation spectroscopy and visual inspection [4,6]. We have investigated the
effect of salt-induced screening, the influence of increasing the colloid volume fraction, , and the effect of increasing the polymer concentration, c, on the initial cluster growth by measuring the collective diffusion coefficient of the aggregates.
The hydrodynamic radius, R, was determined from the Stokes-Einstein relation. We find that the cluster aggregation process is enhanced with increasing and c, and increasing salt content.
Furthermore, the aggregation time, a, increases with increasing polymer-to-colloid size ratio q. From the exponential time behaviour of R(t), we conclude that the cluster growth is induced by a reaction-limited aggregation process (RLA).
Our experiments can be quantitatively understood by the standard dimer formation theory based on the DLVO pair potential in conjunction with the Asakura-Oosawa-Vrij (AOV) depletion potential.
Deviations from the theoretically predicted aggregation times are observed for c close to the polymer overlap concentration, c*, where non-ideal solution behaviour of dextran is expected.
At higher and c, and lower salt content, the sample becomes turbid right after mixing, with a turbid viscous phase formed at the
sample bottom. By re-diluting the samples within a couple of hours after preparation we find that the colloidal particles do not form larger aggregates. By comparing the experimental non-equilibrium phase diagram to the equilibrium phase diagram obtained from a generalised free-volume theory (GFVT) [5], we find that the experimental phase line observed after two days nearly coincides with the GFVT
spinodal line. We argue that the colloid-polymer mixture undergoes an initial phase separation into a denser and a less dense phase, accompanied by a more slowly
progressing irreversible aggregation process in the denser phase. The formation of a gel-like bottom phase, which cannot be re-diluted, is indicative of an irreversible aggregation process at later times.
[4] C. Gögelein, “Phase behaviour of proteins and colloid-polymer mixtures”, PhD thesis, Heinrich-Heine-Universität Düsseldorf, November 2008 (Supervisor: G.
Nägele).
[5] C. Gögelein, R. Tuinier, “Phase behaviour of a dispersion of charge-stabilised colloidal spheres with added non-adsorbing interacting polymer chains”, Eur. Phys. J.
E 27, 171 (2008).
[6] C. Gögelein, G. Nägele, J. Buitenhuis, R. Tuinier, and J.K.G. Dhont, “Polymer depletion-driven cluster aggregation and initial phase separation in charged nanosized colloids”, under review in J. Chem. Phys. 130, 204905 (2009).
Additionally appeared in: Virtual Journal of Nanoscale Science and Technology, June 8 issue (2009).
