Mathematical analysis of cake layer formation in an ultrafiltration membrane of a phycobiliprotein-containing solution extracted from Nostoc commune

Phycobiliproteins have been used as a natural dye, an analytical probe for fluorescence studies, and a chemical for medicinal use. An ultrafiltration membrane is useful for the purification of phycobiliproteins. This study addressed the purification of a phycobiliprotein-containing solution, extracted from Nostoc commune, which was individually performed by two kinds of ultrafiltration membrane (MWCO 150 kDa and 10 kDa) in cross-flow. Three proteins were mainly included in the extractant and analyzed by gel permeation chromatography. Molecular weight of included proteins were 60 kDa, 20 kDa, and 200 Da. The formation of a cake layer was analyzed mathematically by solving ordinary differential equation to fit the experimental data and obtain the 5 parameters needed to mechanistically predict cake-formation. The obtained packed coefficient (K4) and permeation coefficient of protein (K5) demonstrated that the proteins of the phycobiliprotein-containing solution were filtered by the formation of a cake layer in the 150-kDa membrane, while the proteins filtered by the 10-kDa membrane resulted in the clogging of the membrane pores. Transport coefficient of each protein through 10 kDa- and 150 kDa-ultrafiltration membrane showed 0.40 and 0.94 of phycobiliprotein, respectively, demonstrating that 10 kDa-ultrafiltration membrane had the ability for separation of 60 kDa and 10 kDa proteins. The 10-kDa ultrafiltration membrane showed the sensitive purification performance of phycobiliprotein, having the potential for scale-up modules.