To determine the total number of different polypeptide products that a gene with four exons and three introns could code for, we need to understand the process of gene expression and alternative splicing.
During gene expression, the exons (coding regions) of the gene are transcribed and eventually translated into polypeptides, which are the building blocks of proteins. The introns (non-coding regions) are typically removed from the RNA molecule through a process called splicing.
In alternative splicing, different combinations of exons can be spliced together, resulting in different mRNA molecules. These alternative splicing events can lead to the production of multiple polypeptide products from a single gene.
In this case, since the gene has four exons and three introns, the number of possible combinations of exons is determined by the number of ways we can select different subsets of exons for splicing.
To calculate this, we use the formula for the number of combinations: nCr = n! / (r!(n-r)!), where n is the total number of items and r is the number of items being selected.
For the gene with four exons, we can select various combinations of exons as follows:
Selecting all four exons: 1 combination
Selecting three exons: 4 combinations (C(4,3) = 4)
Selecting two exons: 6 combinations (C(4,2) = 6)
Selecting one exon: 4 combinations (C(4,1) = 4)
Summing up these combinations gives us a total of 1 + 4 + 6 + 4 = 15 possible combinations of exons that can be spliced together.
Therefore, the gene could code for a total of 15 different polypeptide products, each resulting from a different combination of exons through alternative splicing.