1. Expressions are derived for the distribution at density-gradient equilibrium of macromolecules whose densities are (a) close to the values characterizing the solution limits or (b) outside the span of the gradient. 2. Density-distribution predicted by the expressions agree with those obtained by rigorous methods. 3. The distribution equations are applied to hypothetical mixtures of proteins and glycoproteins in commonly used density-gradient media to simulate separation and fractionation conditions. 4. It is shown that CsBr, although less efficient than CsCl for fractionation, is nevertheless adequate for most purposes; in analytical experiments it may often have advantages over CsCl. Limitations on the use of LiBr are explored. 5. An expression is derived which allows the variance of the partial specific volume of the macromolecular component to be determined from the variance of the buoyant density. It is shown that the relative resolving powers of different salts is expressed by their values of the quantity (formula: see text). 6. The equations are applied to a well-characterized glycoprotein preparation at equilibrium in CsCl and in Cs2SO4:it is shown that the much wider distribution in CsCl than in Cs2SO4 is explicable in terms of the variance in buoyant density and the solvation properties of the salts. 7. Limitations of the expressions arise when dispersity in density is represented by a low apparent molecular weight; realistic simulations can then only be obtained when the component is fully banded.

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