Chapter 8: Proteins
Many transcripts encode proteins, which are sequences of amino acids that fold into specific structures that determine their functions. To a great extent, the sequence of the protein determines its structure, which in turn determines its function. Therefore, identifying similar protein sequences can suggest structures and functions. The field of protein bioinformatics is certainly extensive, and we will only be able to cover a small portion to introduce some concepts that may be useful.
To go from mRNA to protein, we need an open reading frame (ORF) defined by a start codon in frame with a stop codon. Typical mRNAs have many possible ORFs, with other signals, such as the Kozak sequence, determining which ORF is used. In most cases, the longest ORF is the coding DNA sequence (CDS), or the region that is actually translated. In general it is important to distinguish ORFs, which are quite common, from the CDS.
Once we have the CDS sequence, it is easy to compute the corresponding peptide sequence with Biopython, as we have seen in section 1.2.2.
8.1 Protein Alignment
Our previous discussion of alignment applies to proteins as well as nucleic acid sequences. However, with 20 amino acids, our scoring system can be updated to account for chemical similarity, and the fact that some amino acids are more likely to mutated to others.
Typically, when aligning two sequences, the assumption is that the two sequences have a common evolutionary origin, and the association between single characters in the alignment correspond to the evolutionary history of those characters. In order to optimize such an alignment, we need to define a scoring system used to compare two characters.
Let’s define some probabilistic models of sequence alignments so that we can describe the scoring system with such a formalism. Much of what we will describe here was developed for protein sequences, but the formalism could be used more generally. First, let’s formulate the probability of the two sequences given a random model. That is, the two sequences are just two random strings of characters that have been independently generated from a generative probabilistic model.
Consider an ungapped alignment of the sequences [latex]x[/latex] and [latex]y[/latex]:
x[1]x[2]x[3]x[4] ... x[n]
| | | | |
y[1]y[2]y[3]y[4] ... y[n]
Let’s work out a scoring system for this, and then later introduce gaps.
For a random model, each of the characters [latex]x[i][/latex] and [latex]y[i][/latex] at each position [latex]i[/latex] is just randomly selected according to their frequency in the database
[latex]P(x,y|Random) = \prod_{i=1}^n p_{x[i]} p_{y[I]}[/latex]
Alternatively, if the sequences have a common ancestor, we could also define a probability [latex]q_{a,b}[/latex] as describing the frequency of occurrence of substitutions in the database between two characters [latex]a[/latex] and [latex]b[/latex].
[latex]P(x,y|Ancestor) = \prod_{i=1}^n q_{x[i],y[I]}[/latex]
If we combine our two