Do protein crystals nucleate within dense liquid clusters?

Protein-dense liquid clusters are regions of high protein concentration that have been observed in solutions of several proteins. The typical cluster size varies from several tens to several hundreds of nanometres and their volume fraction remains below 10(-3) of the solution. According to the two-step mechanism of nucleation, the protein-rich clusters serve as locations for and precursors to the nucleation of protein crystals. While the two-step mechanism explained several unusual features of protein crystal nucleation kinetics, a direct observation of its validity for protein crystals has been lacking. Here, two independent observations of crystal nucleation with the proteins lysozyme and glucose isomerase are discussed. Firstly, the evolutions of the protein-rich clusters and nucleating crystals were characterized simultaneously by dynamic light scattering (DLS) and confocal depolarized dynamic light scattering (cDDLS), respectively. It is demonstrated that protein crystals appear following a significant delay after cluster formation. The cDDLS correlation functions follow a Gaussian decay, indicative of nondiffusive motion. A possible explanation is that the crystals are contained inside large clusters and are driven by the elasticity of the cluster surface. Secondly, depolarized oblique illumination dark-field microscopy reveals the evolution from liquid clusters without crystals to newly nucleated crystals contained in the clusters to grown crystals freely diffusing in the solution. Collectively, the observations indicate that the protein-rich clusters in lysozyme and glucose isomerase solutions are locations for crystal nucleation.

Thermal fluctuations in a layer of liquid CS2 subjected to temperature gradients with and without the influence of gravity.

We report data for nonequilibrium density fluctuations in a layer of liquid CS(2) subjected to temperature gradients on Earth and in a satellite. The structure factor S(q) was measured using a calibrated shadowgraph. Upon removing gravity, S(q) increased dramatically at small wave vector, until the fluctuations generated by thermal noise were limited only by the 3 mm sample thickness. The results agree with theory to within a few percent on Earth and are ∼14% below theory in microgravity, demonstrating that the use of equilibrium Langevin forces is appropriate in this nonequilibrium situation.

Fractal fronts of diffusion in microgravity.

Spatial scale invariance represents a remarkable feature of natural phenomena. A ubiquitous example is represented by miscible liquid phases undergoing diffusion. Theory and simulations predict that in the absence of gravity diffusion is characterized by long-ranged algebraic correlations. Experimental evidence of scale invariance generated by diffusion has been limited, because on Earth the development of long-range correlations is suppressed by gravity. Here we report experimental results obtained in microgravity during the flight of the FOTON M3 satellite. We find that during a diffusion process a dilute polymer solution exhibits scale-invariant concentration fluctuations with sizes ranging up to millimetres, and relaxation times as large as 1,000 s. The scale invariance is limited only by the finite size of the sample, in agreement with recent theoretical predictions. The presence of such fluctuations could possibly impact the growth of materials in microgravity.

Mutual Voronoi tessellation in spoke pattern convection.

Planar cellular networks are made of polygonal cells usually having an average of six sides and trivalent vertices. We analyze the topological properties of spoke patterns observed in the convection of highly viscous fluids. The competition between ascending and descending columns of fluid generates dual networks where on average cells are four sided and vertices tetravalent. This observation identifies a new class of dual networks satisfying a mutual Voronoi relation. The metric of the pattern is dominated by the distance between nearest neighbors vertices of opposite species.

Nondiffusive decay of gradient-driven fluctuations in a free-diffusion process.

We report the results of an experimental study of the static and dynamic properties of long wavelength concentration fluctuations in a mixture of glycerol and water undergoing free diffusion. The shadowgraph method was used to measure both the mean-squared amplitude and the temporal correlation function of the fluctuations for wave vectors so small as to be inaccessible to dynamic light scattering. For a fluid with a stabilizing vertical concentration gradient, the fluctuations are predicted to have a decay rate that increases with decreasing wave vector q , for wave vectors below a cutoff wave vector qC, determined by gravity and the fluid properties. This behavior is caused by buoyant forces acting on the fluctuations. We find that for wave vectors above approximately qC, the decay rate does vary in the normal diffusive manner as Dq2, where D is the mass diffusion coefficient. Furthermore, for q approximately less than qC we find that longer wavelength fluctuations decay more rapidly than do shorter wavelength fluctuations, i.e., the behavior is nondiffusive, as predicted.

Fluctuations in diffusion processes in microgravity.

It has been shown recently that diffusion processes exhibit giant nonequilibrium fluctuations (NEFs). That is, the diffusing fronts display corrugations whose length scale ranges from the molecular to the macroscopic one. The amplitude of the NEF diverges following a power law behavior proportional to q(-4) (where q is the wave vector). However, fluctuations of wave number smaller than a critical "rolloff" wave vector are quenched by the presence of gravity. It is therefore expected that in microgravity conditions, the amplitude of the NEF should be boosted by the absence of the buoyancy-driven restoring force. This may affect any diffusion process performed in microgravity, such as the crystallization of a protein solution induced by the diffusion of a salt buffer. The aim of GRADFLEX (GRAdient-Driven FLuctuation EXperiment), a joint project of ESA and NASA, is to investigate the presence of NEFs arising in a diffusion process under microgravity conditions. The project consists of two experiments. One is carried out by UNIMI (University of Milan) and INFM (Istituto Nazionale per la Fisica della Materia) and is focused on NEF in a concentration diffusion process. The other experiment is performed by UCSB (University of California at Santa Barbara) concerning temperature NEF in a simple fluid. In the UNIMI part of the GRADFLEX experimental setup, NEFs are induced in a binary mixture by means of the Soret effect. The diagnostic method is an all-optical quantitative shadowgraph technique. The power spectrum of the induced NEFs is obtained by the processing of the shadowgraph images. A detailed description of the experimental apparatus as well as the ground-based experimental results is presented here for the UNIMI-INFM experiment. The GRADFLEX payload is scheduled to fly on the FOTON M3 capsule in April 2007.

Effect of gravity on the dynamics of nonequilibrium fluctuations in a free-diffusion experiment.

Diffusion is commonly believed to be a homogeneous process at the mesoscopic scale, being driven only by the random walk of fluid molecules. On the contrary, very large amplitude, long wavelength fluctuations always accompany diffusive processes. In the presence of gravity, fluctuations in a fluid containing a stabilizing gradient are affected by two different processes: diffusion, which relaxes them, and the buoyancy force, which quenches them. These phenomena affect both the overall amplitude of fluctuations and their time dependence. For the case of free diffusion, the time-correlation function of the concentration fluctuations is predicted to exhibit an exponential decay with correlation time depending on the wave vector q. For large wave vector fluctuations, diffusion dominates, and the correlation time is predicted to be 1 / (Dq2). For small wave vector fluctuations, gravitational forces have time to play a significant role, and the correlation time is predicted to be proportional to q2. The effects of gravity and diffusion are comparable for a critical wave vector q(c) determined by fluid properties and gravity. We have utilized a quantitative dynamic shadowgraph technique to obtain the temporal correlation function of a mixture of LUDOX(R) TMA and water undergoing free diffusion. This technique allows one to simultaneously measure correlation functions achieving good statistics for a number of different wave vectors in a single measurement. Wave vectors as small as 70 cm(-1) have been investigated, which is very difficult to achieve with ordinary dynamic light-scattering techniques. We present results on the transition from the diffusive decay of fluctuations to the regime in which gravity is dominant.

Gradient-driven fluctuations experiment: fluid fluctuations in microgravity.

We describe an experimental breadboard developed for the investigation of nonequilibrium fluctuations induced by macroscopic temperature and concentration gradients under microgravity conditions. Under these conditions the amplitude of the fluctuations diverges strongly for long wavelengths. The setup was developed at the University of Milan and at the University of California at Santa Barbara within the gradient-driven fluctuations experiment (GRADFLEX) project of the European Space Agency, in collaboration with the National Aeronautics and Space Administration. The apparatus uses a quantitative shadowgraph technique for characterization of the static power spectrum of the fluctuations S(q) and the measurement of their dynamics. We present preliminary experimental results for S(q) obtained in the presence of gravity for gradient-driven fluctuations for two cases, those induced in a liquid mixture with a concentration gradient produced by the Soret effect and those induced in a single-component fluid by a temperature gradient.

Use of dynamic schlieren interferometry to study fluctuations during free diffusion.

We used a form of schlieren interferometry to measure the mean-squared amplitude and temporal autocorrelation function of concentration fluctuations driven by the presence of a gradient during the free diffusion of a urea solution into water. By taking and processing sequences of images separated in time by less than the shortest correlation time of interest, we were able to simultaneously measure dynamics at a number of different wave vectors. The technique is conceptually similar to the shadowgraph method, which has been used to make similar measurements, but the schlieren method has the advantage that the transfer function is wave-vector independent rather than oscillatory.

Scaling behavior for the onset of convection in a colloidal suspension.

We investigate the early stages of mass convection in a colloidal suspension at high solutal Rayleigh number Ras. From the time evolution of shadowgraph images and by assuming a diffusive growth of the boundary layers we obtain an indirect measurement of the concentration boundary layer thickness delta* at the onset of convection. We show that the dimensionless boundary layer thickness delta=delta*/d scales as Ra-ps, where Ras=Rasdelta is a modified solutal Rayleigh number for convection which accounts for the actual density unbalance and d is the thickness of the sample layer. This scaling behavior is analogous to that reported at steady state for turbulent convection in simple fluids. We find p=0.35, a value compatible with the exponent 1/3, reported for turbulent heat convection in simple fluids at steady state.

Soret driven convection in a colloidal solution heated from above at very large solutal Rayleigh number.

Convection in a colloidal suspension with a large negative separation ratio psi is studied experimentally by heating from above. Shadowgraph observations at very large solutal Rayleigh numbers Rtilde; are reported as a function of time. Fast relaxation oscillations are reported for the root mean square value of the shadowgraph intensity. While pure fluids exhibit a transition to turbulent convection for Rayleigh number R approximately 10(6), stable spoke-pattern planform with up and down columnar flows are observed up to Rtilde; approximately 1.9 x 10(9). It is suggested that the surprising stability of the planform against turbulence is due to nonlinear focusing arising from the concentration dependence of the diffusion coefficient.