Statistical-thermodynamic model for light scattering from eye lens protein mixtures.
We model light-scattering cross sections of concentrated aqueous mixtures of the bovine eye lens proteins γB- and α-crystallin by adapting a statistical-thermodynamic model of mixtures of spheres with short-range attractions. The model reproduces measured static light scattering cross sections, or Rayleigh ratios, of γB-α mixtures from dilute concentrations where light scattering intensity depends on molecular weights and virial coefficients, to realistically high concentration protein mixtures like those of the lens. The model relates γB-γB and γB-α attraction strengths and the γB-α size ratio to the free energy curvatures that set light scattering efficiency in tandem with protein refractive index increments. The model includes (i) hard-sphere α-α interactions, which create short-range order and transparency at high protein concentrations, (ii) short-range attractive plus hard-core γ-γ interactions, which produce intense light scattering and liquid-liquid phase separation in aqueous γ-crystallin solutions, and (iii) short-range attractive plus hard-core γ-α interactions, which strongly influence highly non-additive light scattering and phase separation in concentrated γ-α mixtures. The model reveals a new lens transparency mechanism, that prominent equilibrium composition fluctuations can be perpendicular to the refractive index gradient. The model reproduces the concave-up dependence of the Rayleigh ratio on α/γ composition at high concentrations, its concave-down nature at intermediate concentrations, non-monotonic dependence of light scattering on γ-α attraction strength, and more intricate, temperature-dependent features. We analytically compute the mixed virial series for light scattering efficiency through third order for the sticky-sphere mixture, and find that the full model represents the available light scattering data at concentrations several times those where the second and third mixed virial contributions fail. The model indicates that increased γ-γ attraction can raise γ-α mixture light scattering far more than it does for solutions of γ-crystallin alone, and can produce marked turbidity tens of degrees celsius above liquid-liquid separation.
School of Mathematical Sciences, Rochester Institute of Technology, Rochester, New York 14623, USA.
Michael M
MM
Bell
School of Mathematical Sciences, Rochester Institute of Technology, Rochester, New York 14623, USA.
David S
DS
Ross
School of Mathematical Sciences, Rochester Institute of Technology, Rochester, New York 14623, USA.
Maurino P
MP
Bautista
School of Mathematical Sciences, Rochester Institute of Technology, Rochester, New York 14623, USA.
Hossein
H
Shahmohamad
School of Chemistry and Materials Science, Rochester Institute of Technology, Rochester, New York 14623, USA.
Andreas
A
Langner
School of Mathematical Sciences, Rochester Institute of Technology, Rochester, New York 14623, USA.
John F
JF
Hamilton
School of Mathematical Sciences, Rochester Institute of Technology, Rochester, New York 14623, USA.
Carrie N
CN
Lahnovych
School of Physics and Astronomy, Rochester Institute of Technology, Rochester, New York 14623, USA.
George M
GM
Thurston
D000818:Animals; D002417:Cattle; D007908:Lens, Crystalline / Q000737:chemistry*; D008954:Models, Biological; D015233:Models, Statistical; D012542:Scattering, Radiation; D013816:Thermodynamics; D038201:alpha-Crystallins / Q000032:analysis*; D038222:gamma-Crystallins / Q000032:analysis*
D038201:alpha-Crystallins; D038222:gamma-Crystallins