Question

A hypothetical family of proteins consists of six similar but different proteins. Each of the six proteins can form transcription factors by forming homo- or heterodimers in combinatorial mixtures, each binding to different regulatory sites. Calculate the number of different dimeric structures that can be formed from the six proteins (and, thus potential number of different regulatory sites that can be bound). Show the calculation.

Answer 1

Since each protein can form a homo and heterodimer:

Thus First  protein has 6 options to combine to form a homo or heterodimer.As it can combine with itself and the 5 other proteins,

Second protein has 5 options since we have taken into account the ccombination of first protein with the second one

Similarly Third protein has 4 options since we have taken into account the ccombination of first protein with the second one and combination of third with second

Similarly fourth would have 3 option ,fifth would have 2 optionand sixth would be leftt with only one option

Thus the proteins would be in total=6+5+4+3+2+1=21 proteins and 21 different regulatory sites.