Dynamic light scattering study on phase separation of a protein-water mixture: Application on cold cataract development in the ocular lens

We present a detailed dynamic light scattering study of the phase separation in the ocular lens emerging during cold cataract development. Cold cataract is a phase separation effect that proceeds via spinodal decomposition of the lens cytoplasm with cooling. The intensity autocorrelation functions of the lens protein content are analyzed with the aid of two methods, providing information on the populations and dynamics of the scattering elements associated with cold cataract. It is found that the temperature dependence of many measurable parameters changes appreciably at the characteristic temperature $\sim 16\pm 1°\text{C}$ which is associated with the onset of cold cataract. By extending the temperature range of this work to previously inaccessible regimes, i.e., well below the phase separation or coexistence curve at $T_{cc}$, we have been able to accurately determine the temperature dependence of the collective and self-diffusion coefficients of proteins near the spinodal. The analysis showed that the dynamics of proteins bears some resemblance to the dynamics of structural glasses, where the apparent activation energy for particle diffusion increases below $T_{cc}$, indicating a highly cooperative motion. Application of ideas developed for studying the critical dynamics of binary protein-solvent mixtures, as well as the use of a modified Arrhenius equation, enabled us to estimate the spinodal temperature $T_{\text{sp}}$ of the lens nucleus. The applicability of dynamic light scattering as a noninvasive, early-diagnostic tool for ocular diseases is also demonstrated in light of the findings of the present paper.

Figure 1

(Color online) Normalized intensity autocorrelation functions of porcine lenses 1 (a) and 3 (b) for various temperatures as shown in the legend. The vertical dashed lines designate the fast, slow, and ultraslow components revealed by the SE exponential analysis as described in the text. The correlation functions labeled 37b correspond to those measured after warming the lens to the physiological temperature after the cooling step. The inset shows the normalized intensity autocorrelation functions of the three lenses studied in this work at the physiological temperature $\left(37°\text{C}\right)$.

Figure 2

Temperature dependence of the average scattered intensity. Solid lines are drawn as guides to the eye to emphasize the two different scattering regimes crossing at $\sim 16°\text{C}$. At the lowest temperature, lens turbidity causes a decrease in the light transmitted through the opaque lens to the detector. The inset shows the intensity traces (time dependence of the scattered intensity) at selected temperatures.

Figure 3

Representative fitting examples of the electric-field time correlation function $g^{\left(2\right)}\left(t\right)$ for lens 1 at various temperatures. Open symbols: experimental data. Solid line: best-fit curve with the aid of Eqs. (2, 3a, 3b) (best fits with the two equations were indistinguishable). Dashed lines: distribution of relaxation times obtained with the aid of the ILT analysis (Eq. (3a, 3b)) using the CONTIN code.

Figure 4

(a) Typical example of the SE analysis of the electric-field time correlation function at $37°\text{C}$ where the three components of $g^{\left(1\right)}\left(t\right)$, i.e., f, sl, and usl, are shown. For comparison, the dashed line corresponds to the correlation function of the calf lens at $14°\text{C}$ arbitrarily scaled [taken from Ref. [6](a)]. (b) Fit residuals for the SE and ILT analysis methods.

Figure 5

Temperature dependence of the stretching exponents of the three relaxation modes obtained by the SE analysis. Lines are used as guides to the eye. The vertical dashed line is used to indicate a change in the temperature dependence of ${\beta }_{\text{f}}$ and ${\beta }_{\text{sl}}$; ${\beta }_{\text{usl}}$ is practically temperature insensitive.

Figure 6

(a) Temperature dependence of the amplitude ratios of the fast $\left(A_{\text{f}}\right)$ over the sum $\left(A_{\text{tot}}\right)$ of the relaxation modes obtained by the SE and ILT analysis methods. (b) Temperature dependence of the amplitude ratios $A_{\text{sl}}/A_{\text{f}}$ and $A_{\text{sl}}/A_{\text{tot}}$ obtained by the SE analysis. The lines through the data points are used as guides to the eye.

Figure 7

Arrhenius-type diagrams of the temperature dependence of the relaxation times of the fast (a) and slow (b) processes obtained by the SE and ILT analyses for lenses 1 and 3. Dashed lines represent best linear fits to the experimental data. The insets show the temperature dependence of the relaxation times in linear temperature scale. Closed circles correspond to the measurements taken during the first cooling cycle of the experiment, while open circles represent the characteristic times obtained during the second cooling cycle for lens 1.

Figure 8

Temperature dependence of the hydrodynamic radii $R_h$ and correlation lengths $\xi$ for the small (a) and large (b) scattering elements. The vertical dashed line denotes $T_{cc}$. The open circles represent the corresponding data of the bovine intact lens nucleus from Ref. [6a]. The inset in (a) illustrates the ratio of the relaxation times related to small and large particles; see text for details.

Figure 9

Temperature dependence of the diffusion coefficients for the fast (a) and slow (b) modes for lens 1. The solid lines represent fits with the aid of Eq. (8). The insets show the Arrhenius-type plots of the fast and slow modes fitted with the aid of the VFT relation [Eq. (9)].