Human IgM monoclonal antibody is secreted into the culture medium by hybridoma cells in a stirred fermenter, at a concentration of 200 mg/L, after cell removal. The product is concentrated by precipitation, and the yield of antibody recovered is determined as a percentage of the initial mass of antibody present in the broth. The precipitate purity (percentage of the precipitate weight that is IgM) is also measured. Various precipitation methods are tested, and the following results are obtained.

a) Explain the result with ethanol as precipitant (last row).

b) Explain the change of antibody yield and purity precipitated with 8% and 12% polyethylene glycol.

c) Using % w/v as the unit for salt concentration and mg/L of broth as the unit for protein solubility, derive an empirical equation for IgM solubility as a function of (NH4)2SO4 concentration (broth density 1 kg/L).

d) What is the yield of recovery if 33% w/v (NH4)2SO4 is used to treat 100 L broth? e) The residual solution after salting-out with 33% w/v (NH4)2SO4 is treated for second-stage precipitation using more (NH4)2SO4 and it is found that the amount of antibody contained in the precipitate is somewhat more than expected. What possible reasons can you give for this?

\begin{tabular}{lllll} \hline & ConcentrationofPrecipitant(%w/v) & pH & AntibodyYield(%) & PrecipitatePurity(%w/w) \\ \hline Precipitant & 18 & 7.2 & 0.0 & - \\ Ammonium sulphate & 24 & 7.2 & 49 & 90 \\ & 29 & 7.2 & 75 & 51 \\ Polyethylene glycol & 81 & 7.2 & 83 & 18 \\ & 12 & 5.5 & 75 & 95 \\ Ethanol & 51.5 & 96 & 60 \\ \hline \end{tabular}