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This paper reports experimental results and modelling on the crystallisation processes induced by counter diffusion method of a precipitant agent in a lysozyme protein solution. Comparison between experimental observations and numerical simulations in the presence of convection and sedimentation and without them (suppressed using gel) provides a validation of the model. Different values of the initial protein concentration are used, in order to investigate the effects of supersaturation conditions on the process, and in particular on nucleation. The model and the experimental approach may represent a useful methodology for the determination of the parameters and conditions that may lead to protein crystallisation. A Mach-Zehnder interferometer is used to monitor the transport dynamics in situ in the fluid phase by observing the compositional field. The effect of the solute transport gives rise to a "nucleation front" that propagates inside the protein solution. The crystal formation, caused by progressing of the front, results in a modulation in time and in space (similar to Liesegang patterns), due to the non-linear interplay among transport, crystal nucleation and growth. Both experimental observation and numerical modelling show spatial and size distributions of crystals that demonstrate comparable evidences of the phenomena.
research papers
Diffusion has a central role in protein crystal growth both in microgravity conditions and on ground. Recently several reports have been focused on the importance to use the generalized Fick's equations in n-component systems where crystals grow. In these equations the total flux of each component is produced by the own concentration gradient (main flow) and by the concentration gradient of the other components (cross-flow) present in the system. However in literature the latter effect is often neglected, and the so-called pseudo-binary approximation is used. Lin et al. (1995) proposed a mathematical model to evaluate the concentration profile of the species present around a growing protein crystal. Although the model is reliable, it suffers of the pseudo-binary approximation (neglecting cross term diffusion coefficients and using binary diffusion coefficients), probably because of the lack of multicomponent diffusion data. The present model is based on the experimental set-up proposed by Lin et al. (1995). Nevertheless we have included the coupled diffusion effects, according to the correct description of the matter transport through the generalized Fick's equations. The crystal growth rate is calculated for different gravity levels. The model has been applied to the ternary lysozyme-NaCl-water and quaternary lysozyme-poly(ethylene glycol) (PEG)-NaCl-water systems using recent diffusion data.
research papers
Mach-Zehnder interferometry is applied to quantitatively characterize growth of lysozyme crystals in microgravity. Experiments were performed by the Free Interface Diffusion technique into APCF FID reactors using large seeds. Tracking of the experiments using interferometry allowed to monitor the onset of supersaturation and the seed growth. A large and stable concentration depletion zone around the growing crystal developed, whose time evolution was analyzed. The interferograms were analyzed taking into account finite thickness of the cell by integrating the concentration over the straight lines through the optical path. It was concluded that there may be a quasi-steady state growth mode at the stage when the spacial concentration distribution did not change but its absolute value over all the cell was slowly diminishing. From this portion of the data, an estimate was made of the dimensionless parameter βR/D where β is the face kinetic coefficient, R is the effective crystal size and D is the lysozyme diffusivity in solution, as followed from the steady state model. For the assumed quasi steady state data portion, the parameter varies between 0.7 and 0.9 suggesting mixed diffusion-interface kinetic controlled growth.
