Hard sphere-like glass transition in eye lens α-crystallin solutions

Abstract

We study the equilibrium liquid structure and dynamics of dilute and concentrated bovine eye lens α-crystallin solutions, using small-angle X-ray scattering, static and dynamic light scattering, viscometry, molecular dynamics simulations, and mode-coupling theory. We find that a polydisperse Percus-Yevick hard-sphere liquid-structure model accurately reproduces both static light scattering data and small-angle X-ray scattering liquid structure data from α-crystallin solutions over an extended range of protein concentrations up to 290 mg/mL or 49% vol fraction and up to ca. 330 mg/mL for static light scattering. The measured dynamic light scattering and viscosity properties are also consistent with those of hard-sphere colloids and show power laws characteristic of an approach toward a glass transition at α-crystallin volume fractions near 58%. Dynamic light scattering at a volume fraction beyond the glass transition indicates formation of an arrested state. We further perform event-driven molecular dynamics simulations of polydisperse hard-sphere systems and use mode-coupling theory to compare the measured dynamic power laws with those of hard-sphere models. The static and dynamic data, simulations, and analysis show that aqueous eye lens α-crystallin solutions exhibit a glass transition at high concentrations that is similar to those found in hard-sphere colloidal systems. The α-crystallin glass transition could have implications for the molecular basis of presbyopia and the kinetics of molecular change during cataractogenesis.

Keywords: alpha crystallin; glass transition; mode-coupling theory; molecular dynamics; scattering.

Fig. 1.

(Top) Structure factors $S_M\left(q\right)$ deduced from the SAXS $I\left(q\right)$ data, using the 5-mg/mL data for the measured form factor $P_M\left(q\right)$. (Bottom) $S_M\left(q\to 0\right)$ vs. ϕ from both SLS and SAXS agree with hard-sphere models, but do not distinguish the polydisperse PY, Schulz-distributed mixture model with $p=0.20$ (black) from either the monodisperse PY (green) or the Carnahan–Starling (red) models.

Fig. 2.

(Top) α-Crystallin solution low shear rate relative viscosity ${\eta }_r={\eta }_0/{\eta }_s$ vs. α-crystallin volume fraction ϕ, using $v=1.7\hspace{0.17em}\text{mL}/\text{g}$ consistent with SAXS and SLS (see text). (Middle) Normalized diffusivities $\left(D/D_0\right)\left(\varphi \right)$, from second-order cumulant fits to the DLS-measured ISF $f\left(q,t\right)$. $D_0=2.2\times {10}^{-11}$ m²/s is the free-particle diffusion coefficient as ϕ approaches 0. Dashed line: the HS theory $D/D_0=1+1.45\varphi$. (Bottom) DLS $f\left(q,t\right)$ vs. delay time t; q = 0.023 nm⁻¹. Progressively slower $f\left(q,t\right)$ decays with increasing ϕ are qualitatively similar to those from MD simulations (Fig. S4, Top). Slow relaxation times ${\tau }_q$ for which $f\left(q,\tau \right)=0.25$ (dashed line) are shown in Fig. 5 (Left).

Fig. 3.

Comparison of experimental structure factors $S_M\left(q\right)$ for α-crystallin solutions with polydisperse hard-sphere Percus–Yevick liquid-structure models, showing the basis for the parameter values $p=0.20$ and $d=15$ nm used in the present work. (Top) SAXS $S_M\left(q\right)$ for $c=290$ mg/mL, corresponding to a deduced $\varphi =0.49$. Percus–Yevick predictions are shown for three polydispersity parameters: $p=0$ (monodisperse, thin gray line), $p=0.1$ (dotted-dashed red line), and $p=0.20$ (thick black line). $p=0.20$ closely reproduces the measured $S_M\left(q\right)$, whereas the less polydisperse and monodisperse models do not match the data. (Bottom) Over the entire range of lower α-crystallin concentrations measured, the same polydisperse Percus–Yevick $S_M\left(q\right)$ with $p=0.20$ (solid lines) closely reproduces the experimental $S_M\left(q\right)$.

Fig. 4.

(Top, Inset) Schematic of idealized hard-sphere relaxation modes near dynamical arrest: fast motion within cages of caged neighbors (β-relaxation) and slow exchange between cages (α-relaxation). The plateau value, $f_q$, and approach and departure power-law exponents a and b (Eqs. 6 and 7) are shown. ${\tau }_q$ is the slow relaxation time, defined as in Fig. 2. (Top plot) Comparison of the experimentally determined ISF $f\left(q,t\right)$ at c = 340 mg/mL $\left(\varphi =0.58\right)$ with the theoretical predictions for the approach to and from the plateau value $f_q$. (Bottom) Rectification plot (32) of power-law fits to find a and b from ISF plateau approach and departure (text). $f_c=0.863$.

Fig. 5.

(Left) The slow relaxation time ${\tau }_q$ at which $f\left(q,{\tau }_q\right)=0.25$, defined as in Fig. 2, for the MD-simulated ISF (solid circles) and the DLS ISF (Fig. 2, Bottom) (open circles). (Right) Replotted data from Left, showing power-law dependence of ${\tau }_q$ on ${\varphi }_c-\varphi$, using $\gamma =2.8$ and the ${\varphi }_c^{\text{sim}}$ (MD) and ${\varphi }_c^{\text{exp}}$ (DLS) values reported in the text.