Frédéric Cardinaux

Equilibrium cluster formation in concentrated protein solutions and colloids.

Controlling interparticle interactions, aggregation and cluster formation is of central importance in a number of areas, ranging from cluster formation in various disease processes to protein crystallography and the production of photonic crystals. Recent developments in the description of the interaction of colloidal particles with short-range attractive potentials have led to interesting findings including metastable liquid–liquid phase separation and the formation of dynamically arrested states (such as the existence of attractive and repulsive glasses, and transient gels). The emerging glass paradigm has been successfully applied to complex soft-matter systems, such as colloid–polymer systems and concentrated protein solutions. However, intriguing problems like the frequent occurrence of cluster phases remain. Here we report small-angle scattering and confocal microscopy investigations of two model systems: protein solutions and colloid–polymer mixtures. We demonstrate that in both systems, a combination of short-range attraction and long-range repulsion results in the formation of small equilibrium clusters. We discuss the relevance of this finding for nucleation processes during protein crystallization, protein or DNA self-assembly and the previously observed formation of cluster and gel phases in colloidal suspensions.

Interplay between Spinodal Decomposition and Glass Formation in Proteins Exhibiting Short-Range Attractions

We investigate the competition between spinodal decomposition and dynamical arrest using aqueous solutions of the globular protein lysozyme as a model system for colloids with short-range attractions. We show that quenches below a temperature Ta lead to gel formation as a result of a local arrest of the protein-dense phase during spinodal decomposition. The rheological properties of these gels allow us to use centrifugation experiments to determine the local densities of both phases and to precisely locate the gel boundary and the attractive glass line close to and within the unstable region of the phase diagram.

Modeling equilibrium clusters in lysozyme solutions

We present a combined experimental and numerical study of the equilibrium cluster formation in globular-protein solutions under no-added salt conditions. We show that a cluster phase emerges as a result of a competition between a long-range screened Coulomb repulsion and a short-range attraction. A simple effective potential, in which electrostatic repulsion is fixed by experimental conditions and attraction is modeled with a generalized Lennard-Jones potential, accounts in a remarkable way for the wavevector dependence of the X-ray scattering structure factor.

Multispeckle diffusing-wave spectroscopy with a single-mode detection scheme

We present a detection scheme for diffusing-wave spectroscopy (DWS) based on a two-cell geometry that allows efficient ensemble averaging. This is achieved by putting a fast rotating diffuser in the optical path between laser and sample. We show that the recorded (multispeckle) correlation echoes provide an ensemble averaged signal that does not require additional time averaging. Furthermore, combined with traditional two-cell DWS, the full intensity autocorrelation function can be measured with a single experimental setup. The scheme provides access to a large range of correlation times thus opening an experimental window for the study of slowly relaxing and arrested systems, such as viscoelastic complex fluids, colloidal glasses, and gels.

Linear and nonlinear rheology of dense emulsions across the glass and the jamming regimes

We discuss the linear and nonlinear rheology of concentrated microscale emulsions, amorphous disordered solids composed of repulsive and deformable soft colloidal spheres. Based on recent results from simulation and theory, we derive quantitative predictions for the dependences of the elastic shear modulus and the yield stress on the droplet volume fraction. The remarkable agreement with experiments we observe supports the scenario that the repulsive glass and the jammed state can be clearly identified in the rheology of soft spheres at finite temperature while crossing continuously from a liquid to a highly compressed yet disordered solid.

Effect of glycerol and dimethyl sulfoxide on the phase behavior of lysozyme: theory and experiments.

Salt, glycerol, and dimethyl sulfoxide (DMSO) are used to modify the properties of protein solutions. We experimentally determined the effect of these additives on the phase behavior of lysozyme solutions. 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 experimentally observed trends are consistent with our theoretical predictions based on the thermodynamic perturbation theory and the Derjaguin-Landau-Verwey-Overbeek model for the lysozyme-lysozyme pair interactions. The values of the parameters describing the interactions, namely the refractive indices, dielectric constants, Hamaker constant and cut-off length, are extracted from literature or are experimentally determined by independent experiments, including static light scattering, to determine the second virial coefficient. We observe that both, glycerol and DMSO, render the potential more repulsive, while sodium chloride reduces the repulsion.

Note: Quasi-real-time analysis of dynamic near field scattering data using a graphics processing unit

We present an implementation of the analysis of dynamic near field scattering (NFS) data using a graphics processing unit. We introduce an optimized data management scheme thereby limiting the number of operations required. Overall, we reduce the processing time from hours to minutes, for typical experimental conditions. Previously the limiting step in such experiments, the processing time is now comparable to the data acquisition time. Our approach is applicable to various dynamic NFS methods, including shadowgraph, Schlieren and differential dynamic microscopy.

Do equilibrium clusters exist in concentrated lysozyme solutions

In contrast to our previous findings (1), Shukla et al. (2) claim the absence of clusters in concentrated lysozyme solutions. This claim is based on scattering data that show no significant differences from our data, where conditions are similar. Our sample preparation and measurements are thus comparable and both our conclusions based on virtually identical data. Nevertheless, the existence of clusters is refuted because, first, “the interference peak … displays a clear trend toward higher q-values with increasing protein concentration” and, second, “is adequately and consistently described by the form and structure factors of individual lysozyme particles using an interaction potential involving short-range attraction and long-range repulsion” (conclusions in ref. 2). However, we both observe the usual shift in peak position at low concentrations, where the well separated molecules experience the long-range repulsion, and, crucially, we both also find an essentially concentration-independent position for concentrated solutions (1, 2) where the closer molecules overcome the repulsive barrier and the short-range attraction induces clusters. [Note that they do not compare data from concentrated solutions in their article (2) but only in supporting information (SI) Fig. S9.] Furthermore, fits of form and structure factors result in values for the pair potential but cannot provide direct information on the presence of monomers and/or clusters. Nonetheless, for a potential with similar values as determined by Shukla et al. (2), MD simulations have confirmed the presence of clusters (3). Therefore, their data (2) actually confirm our earlier data and interpretation (1) that the peak position is concentration-independent and clusters are present in lysozyme solutions, which, as stated in both of our titles, are concentrated.

Structure of marginally jammed polydisperse packings of frictionless spheres.

We model the packing structure of a marginally jammed bulk ensemble of polydisperse spheres. To this end we expand on the granocentric model [Clusel et al., Nature (London) 460, 611 (2009)], explicitly taking into account rattlers. This leads to a relationship between the characteristic parameters of the packing, such as the mean number of neighbors and the fraction of rattlers, and the radial distribution function g(r). We find excellent agreement between the model predictions for g(r) and packing simulations, as well as experiments on jammed emulsion droplets. The observed quantitative agreement opens the path towards a full structural characterization of jammed particle systems for imaging and scattering experiments.

Accounting for inertia effects to access the high-frequency microrheology of viscoelastic fluids

We study the Brownian motion of microbeads immersed in water and in a viscoelastic wormlike micelles solution by optical trapping interferometry and diffusing wave spectroscopy. Through the mean-square displacement obtained from both techniques, we deduce the mechanical properties of the fluids at high frequencies by explicitly accounting for inertia effects of the particle and the surrounding fluid at short time scales. For wormlike micelle solutions, we recover the 3/4 scaling exponent for the loss modulus over two decades in frequency as predicted by the theory for semiflexible polymers.