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Table 6 Algorithmic Protocol

From: Robust computational reconstitution – a new method for the comparative analysis of gene expression in tissues and isolated cell fractions

1) calculate the means and standard deviations of the computed mRNA proportions as a function of the number of included genes:
□ increase the number of included genes k
   • generate l random starting values { p j 0 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaaieWacqWFWbaCdaqhaaWcbaGaemOAaOgabaGaeGimaadaaaaa@3095@ } j = 1,..., l, in which p j 0 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaaieWacqWFWbaCdaqhaaWcbaGaemOAaOgabaGaeGimaadaaaaa@3095@ = ( p M j 0 , p F j 0 , p N j 0 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGWbaCdaqhaaWcbaGaemyta0KaemOAaOgabaGaeGimaadaaOGaeiilaWIaemiCaa3aa0baaSqaaiabdAeagjabdQgaQbqaaiabicdaWaaakiabcYcaSiabdchaWnaaDaaaleaacqWGobGtcqWGQbGAaeaacqaIWaamaaaaaa@3D80@ )
determine p j = (p Mj , p Fj , p Nj ) by minimizing the objective function D s ( k ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGebardaqhaaWcbaGaem4CamhabaGaeiikaGIaem4AaSMaeiykaKcaaaaa@326A@ starting from p j 0 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaaieWacqWFWbaCdaqhaaWcbaGaemOAaOgabaGaeGimaadaaaaa@3095@
store p j
   • calculate the mean and standard deviation of {p j }j = 1,...,l for the current value of k
2) determine the means of the computed mRNA proportions at the smallest number of included genes, for which the standard deviations approach zero.