Dynamic light-scattering (DLS) studies are reported for lysozyme in aqueous magnesium chloride solutions at ionic strengths 0.6, 0.8, and 1.0 M for a temperature range 10-30 degrees C at pH 4.0. The diffusion coefficient of lysozyme was calculated as a function of protein concentration, salt concentration, temperature, and scattering angle. A Zimm-plot analysis provided the infinitely-dilute diffusion coefficient and the protein-concentration dependence of the diffusion coefficient. The hydrodynamic radius of a lysozyme monomer was obtained from the Stokes-Einstein equation; it is 18.6 +/- 1.0 Angstrom. The difference (1.4 Angstrom) between the hydrodynamic and the crystal-structure radius is attributed to binding of Mg2+ ions to the protein surface and subsequent water structuring. The effect of protein concentration on the diffusion coefficient indicates that attractive interactions increase as the temperature falls at fixed salt concentration. However, when plotted against ionic strength, attractive interactions exhibit a maximum at ionic strength 0.84 M, probably because Mg2+-protein binding and water structuring become increasingly important as the concentration of magnesium ion rises. The present work suggests that inclusion of ion binding and water structuring at the protein surface in a pair-potential model is needed to achieve accurate predictions of protein-solution phase behavior.