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Nanoparticle dynamics impact a wide range of biological transport processes and applications in nanomedicine and natural resource engineering. Differential dynamic microscopy (DDM) was recently developed to quantify the dynamics of submicron particles in solutions from fluctuations of intensity in optical micrographs. Differential dynamic microscopy is well established for monodisperse particle populations, but has not been applied to solutions containing weakly scattering polydisperse biological nanoparticles. Here we use bright-field DDM (BDDM) to measure the dynamics of protein-rich liquid clusters, whose size ranges from tens to hundreds of nanometers and whose total volume fraction is less than 10(-5). With solutions of two proteins, hemoglobin A and lysozyme, we evaluate the cluster diffusion coefficients from the dependence of the diffusive relaxation time on the scattering wave vector. We establish that for weakly scattering populations, an optimal thickness of the sample chamber exists at which the BDDM signal is maximized at the smallest sample volume. The average cluster diffusion coefficient measured using BDDM is consistently lower than that obtained from dynamic light scattering at a scattering angle of 90°. This apparent discrepancy is due to Mie scattering from the polydisperse cluster population, in which larger clusters preferentially scatter more light in the forward direction.

The dynamic behavior of the concentration field in crystallization is investigated by considering the coupling of the bulk concentration field and interfacial kinetics. It is shown that the concentration field may become unstable for perturbations with certain wavelength. When instability occurs, the physical environment in front of the growing interface will fluctuate and the interfacial growth mode will be affected accordingly. We suggest that our analysis can be used to interpret some spatial-temporal instabilities observed in crystallization.

We have expanded our numerical model of coupled bulk transport in solution and interfacial kinetics in crystal growth [Vekilov, Lin, and Rosenberger, Phys. Rev. E 55, 3202 (1997)] by explicitly including adsorption on and desorption from terraces between growth steps, surface diffusion, and incorporation into steps. At the steps, the surface (adsorption layer) concentration ${C}_{s}$ is assumed to be either continuous, i.e., have the same values at the top and bottom of a step, or to be discontinuous, i.e., to take on different, respective terrace-width-dependent values. In order to maximize spatial resolution about individual steps, we use a mesoscale grid at the solution-crystal interface, which moves with the step positions and adjusts to the changing terrace widths during the simulation. This model was evaluated with transport and kinetics parameters characteristic for the growth of lysozyme crystals from aqueous solutions. With continuous ${C}_{s}$ at steps, the simulations reproduced the results of our previous model in which the step supply field overlap was only indirectly accounted for by a step-density-dependent deceleration parameter in the step velocity. When discontinuities in ${C}_{s}$ were allowed, significantly higher bunching instability resulted. More importantly, we found that step bunching may or may not occur, depending on the specific step-density perturbation (magnitude, sign and rate of step-density change). This is why linear stability analyses do not predict the unsteady growth behavior observed in our experiments and obtained in our simulations.

Based on our experimental findings of growth rate fluctuations during the crystallization of the protein lysozym, we have developed a numerical model that combines diffusion in the bulk of a solution with diffusive transport to microscopic growth steps that propagate on a finite crystal facet. Nonlinearities in layer growth kinetics arising from step interaction by bulk and surface diffusion, and from step generation by surface nucleation, are taken into account. On evaluation of the model with properties characteristic for the solute transport, and the generation and propagation of steps in the lysozyme system, growth rate fluctuations of the same magnitude and characteristic time, as in the experiments, are obtained. The fluctuation time scale is large compared to that of step generation. Variations of the governing parameters of the model reveal that both the nonlinearity in step kinetics and mixed transport-kinetics control of the crystallization process are necessary conditions for the fluctuations. On a microscopic scale, the fluctuations are associated with a morphological instability of the vicinal face, in which a step bunch triggers a cascade of new step bunches through the microscopic interfacial supersaturation distribution.

Intrinsic kinetics instabilities in the form of growth step bunching during the crystallization of the protein lysozyme from solution were characterized by in situ high-resolution optical interferometry. Compositional variations (striations) in the crystal, which potentially decrease its utility, e.g., for molecular structure studies by diffraction methods, were visualized by polarized light reflection microscopy. A spatiotemporal correlation was established between the sequence of moving step bunches and the striations.

Recent experiments have revealed several surprising features of the phase equilibria in protein solutions: liquid-liquid phase separation which is, in some cases, metastable with respect to the liquid-solid equilibrium, and in others-unobservable; widely varying crystallization enthalpies, including completely athermal crystallization; the co-existence of several crystalline polymorphs; and others. Other studies have shown that the solvent molecules at the hydrophobic and polar patches on the protein molecular surfaces are structured, introducing repulsive forces at surface separations equal to several water molecule sizes. In search of a causal link between the latter and former findings, we apply Monte Carlo simulation techniques in the investigation of phase diagrams associated with globular biological molecules in solution. We account for the solvent structuring via short-range isotropic two-body intermolecular potentials exhibiting multiple extrema. We show that the introduction of a repulsive maximum or a secondary attractive minimum at separations longer than the primary attractive minimum has dramatic effects on the phase diagram: liquid-liquid separation curves are driven to lower or higher temperatures, the sensitivity of the solubility curve (liquidus) to temperature, i.e., the enthalpy of crystallization, is significantly reduced or enhanced, metastable liquid-liquid separation may become stable and vice versa, and both low- and high-density crystalline phases are observed. The similarity of these features of the simulated phase behavior to those observed experimentally suggests that at least some of the mysteries of the protein phase equilibria may be due to the structuring of the solvent around the protein molecular surfaces. Another conclusion is that at least some of the dense liquids seen in protein solutions may be stable and not metastable with respect to a solid phase.

We employ atomic force microscopy to monitor in situ, in real time, the molecular processes of crystallization of ferritin, a protein that has an inorganic single-crystalline core that can be varied. We determine the statistics of molecular attachment and detachment at the growth sites and find that the ratio of the fluxes in and out of the kinks is significantly lower than expected, assuming direct incorporation of the molecules from the solution. Determinations of the energy barrier for incorporation yield approximately 30 kJ mol(-1), significantly higher than expected for this mechanism. We conclude that attachment of molecules occurs via the surface adsorption layer. The surface coverage resulting from this mechanism is approximately 0.9, suggesting a growth mode different from the classical surface diffusion mechanism.