So, this way, basically, we are aligning this A with
A, C with C, C with T, T with C.
Because for this C, there's no letter, we ent, we insert a dash.
So, this is a possible alignment.
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Okay?
Now, if I look at this, what the biologist has told me,
then I can go to a biologist saying, is this an alignment?
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I inserted a dash, but here, between the A and C.
And it does, it does, it looks like an alignment because
it's of the same, both of them are the same length.
And I'm aligning a letter with a letter or a letter with a dash, right?
And biologist say, yes this is an alignment.
And then I say, is this an alignment?
And the biologist say, no
I don't like this because
this is meaningless.
Right?
I'm saying there was a, there was no letter here, no letter here.
And this is unnecessary to add.
So, biologist tells me that no, this is not an alignment.
Okay?
So now I start getting some information about
how to model the structure of an alignment.
So, to model the structure of an alignment, given two
sequences, basically I need to enter dashes in one or two
of the sequences so that I can make them aligned in
terms of, that is, they are both of the same length.
And when I enter these dashes, then I have to make the sequences of the same
length such that either a letter goes with a letter, or a dash with a letter.
But no dash with dash, okay?
So, this is a possible alignment, this is a possible alignment.
And this is the first step in, towards answering
the problem and solving the questions that the biologist is
interested in, which is how do we model an alignment,
what is the actual mathematical object that captures an alignment.
And in this case, it is we can formalize it very cleanly, mathematically by
saying, given two sequences, you can enter dashes in any of them or both.
Such that you make them of the same length.
And such that no dash goes with a dash, either
a letter with a letter or a dash with a letter.
And, of course, you cannot change the order
of the letters in any of the sequences.
So I cannot take ACCT and make it ACTC, for example.
All right?
So now, the first phase of, of modeling here was to get a notion of feasibility.
What is a feasible alignment versus what's not feasible.
This is not allowed.
The biologist doesn't like something like this.
So, now that I understand from a biologist what he or she wants
from me in terms of what is an alignment, I can look at this.
Now we can use mathematical skills to say, okay,
what is the number of such possible feasible alignments?
And I'm not going to show the number here.
But believe me, the number is going to be very large.
Right?
In the sense that if you give me a sequence of length four
and a sequence of length five, there are many, many ways of aligning them.
For example, one that you are not seeing here, is, for is ACCT.