When an equilibrium is reached, a single homogeneous protein distributes exponentially, given by the following equation:
(Subscript[C, r])  =  (Subscript[C, o ])(e^( (M \(\(\((1 - \ v\&_\ ρ)\)\ ω\^2\ \((r\^2 - 
                          r\_m\^2)\)\)\/\(2\ R\ T\)\))))
where (Subscript[C, r]) and (Subscript[C, o]) are the concentrations of the sample at radial position r and at a reference position, taken to be the meniscus, respectively.  M is the sample molecular mass, \(TraditionalForm\`v\&_\) and ρ are the sample partial specific volume and solvent density, ω is the angular velocity, r is the distance from the center of rotation, (Subscript[r, m ])is the radial position of the reference concentration, R is the Universal Gas Constant, and T is the absolute temperature. 
For a simple self-associating system,  monomer + monomer (Overscript[⇌, (Subscript[K, 12])]) dimer, the observed distribution will now be the sum of two exponentials, one for monomer and one for dimer.

(Subscript[C, r])  =  (Subscript[C, o, monomer ])\(TraditionalForm\`e\^\(\(\ \)\((M\ \(\((1 - \ v\&_\ ρ)\)\ ω\^2\ \((r\^2 - r\_m\^2)\)\)\/\(2\ R\ T\))\)\)\) +  \(TraditionalForm\`e\^\(\(\ \)\((2  M\ \(\((1 - \ v\&_\ ρ)\)\ ω\^2\ \((r\^2 - r\_m\^2)\)\)\/\(2\ R\ T\))\)\)\) 
By fitting the measured data to a series of aggregation models, it is therefore possible to determine the degree to which the protein self-associates.