THEORY OF LENS TRANSPARENCY Although the lens is comprised of very high concentrations of protein approaching about 37% wet weight in the nucleus of an adult human lens

THEORY OF LENS TRANSPARENCY Although the lens is comprised of very high concentrations of protein approaching about 37% wet weight in the nucleus of an adult human lens [1], it remains relatively transparent throughout most of an individual’s adult life. The original explanation for transparency involved an ordered array of proteins, resulting in periodic destructive interference leading to transparency [2]. However, predictions by Benedek [3], and subsequent studies by Delaye and Tardieu [4] and Bettelheim and Siew [5], showed that a periodic (i.e., crystallin) array of proteins was not necessary for transparency. In their classic study, Delaye and Tardieu [4] showed, as expected, that the scattering of both X-ray and visible light by a lens-protein solution is proportional to the concentration up to approximately 120 mg/ml, then actually decreased with increasing protein concentration. In addition, Bettelheim and Siew [5] showed that a model system of spheres dissolved in a medium of different refractive index with no long-range periodicity had a concentration-dependent light scattering that closely mimicked the experimental scattering curves obtained by Delaye and Tardieu [4]. Both groups found that the intensity of the scattered light increased with solute concentration (be it lens protein or model spheres) up to a volume fraction of 13%, then decreased thereafter in a manner such that by a concentration of 60% the scattering was roughly equal to that of a 1% solution. Both groups successfully explained their measurements as due to short-range order induced by simple hard sphere interactions (Figure 1). It is important to stress that this is simply packing of hard spheres under the obvious constraint that two spheres cannot overlap. It causes a negative correlation of particle positions when the center-to-center distances would be less than one sphere diameter. This negative correlation is what these authors mean when they write “short range order”, and results in a destructive interference of the scattered light, hence a reduction in the scattered light. Fourier transform analysis of the X-ray data by Delaye and Tardieu [4] showed the presence of this short-range order, but a lack of long-range periodicity. Together, the results demonstrated that lens transparency is due to a uniform short-range order of macromolecules induced by hard sphere interactions when present in high concentrations. These results are consistent with the following simple physical picture; molecules scatter light but the total scattering of an ensemble of molecules depends on the spatial arrangement of the molecules. The key quality of the spatial arrangement that allows for large ensemble scattering is random spatial variation, or in the terminology of light scattering, fluctuations in the density of the molecules. These couple directly into index of refraction fluctuations. In a dilute system of randomly placed molecules, where “dilute” means an average nearest neighbor separation large compared to the molecule size, the fluctuations are the molecules themselves with refractive index contrast relative to the background solvent. Thus the total scattering is directly proportional to the number of molecules. In the other extreme of very concentrated molecules touching other molecules, the system is essentially uniformly dense so there are few fluctuations and little scattered light. Examples of this are the transparencies seen in dense liquids and glass. Such is the situation in the normal eye lens in which the cytoplasm is a condensed protein solution which limits the dimensions of the density fluctuations and light scattering. In between these two limits the dimensions of the density fluctuations are larger, hence the scattering must be increased. This explains the nonmonotonic behavior of the scattered intensity versus concentration seen by both groups. Con©2006 Molecular Vision