<s>
In	O
bioinformatics	O
and	O
evolutionary	O
biology	O
,	O
a	O
substitution	B-Algorithm
matrix	I-Algorithm
describes	O
the	O
frequency	O
at	O
which	O
a	O
character	O
in	O
a	O
nucleotide	O
sequence	O
or	O
a	O
protein	O
sequence	O
changes	O
to	O
other	O
character	O
states	O
over	O
evolutionary	O
time	O
.	O
</s>
<s>
It	O
is	O
an	O
application	O
of	O
a	O
stochastic	B-Algorithm
matrix	I-Algorithm
.	O
</s>
<s>
Substitution	O
matrices	O
are	O
usually	O
seen	O
in	O
the	O
context	O
of	O
amino	O
acid	O
or	O
DNA	O
sequence	B-Algorithm
alignments	I-Algorithm
,	O
where	O
they	O
are	O
used	O
to	O
calculate	O
similarity	O
scores	O
between	O
the	O
aligned	O
sequences	O
.	O
</s>
<s>
(	O
Here	O
,	O
a	O
residue	O
refers	O
to	O
an	O
amino	O
acid	O
stripped	O
of	O
a	O
hydrogen	O
and/or	O
a	O
hydroxyl	O
group	O
and	O
inserted	O
in	O
the	O
polymeric	B-Language
chain	I-Language
of	O
a	O
protein	O
.	O
)	O
</s>
<s>
If	O
we	O
can	O
line	O
up	O
the	O
two	O
sequences	O
using	O
a	O
sequence	B-Algorithm
alignment	I-Algorithm
algorithm	O
such	O
that	O
the	O
mutations	O
required	O
to	O
transform	O
a	O
hypothetical	O
ancestor	O
sequence	O
into	O
both	O
of	O
the	O
current	O
sequences	O
would	O
be	O
evolutionarily	O
plausible	O
,	O
then	O
we	O
'd	O
like	O
to	O
assign	O
a	O
high	O
score	O
to	O
the	O
comparison	O
of	O
the	O
sequences	O
.	O
</s>
<s>
There	O
are	O
many	O
different	O
ways	O
to	O
construct	O
such	O
a	O
matrix	O
,	O
called	O
a	O
substitution	B-Algorithm
matrix	I-Algorithm
.	O
</s>
<s>
The	O
simplest	O
possible	O
substitution	B-Algorithm
matrix	I-Algorithm
would	O
be	O
one	O
in	O
which	O
each	O
amino	O
acid	O
is	O
considered	O
maximally	O
similar	O
to	O
itself	O
,	O
but	O
not	O
able	O
to	O
transform	O
into	O
any	O
other	O
amino	O
acid	O
.	O
</s>
<s>
This	O
identity	B-Algorithm
matrix	I-Algorithm
will	O
succeed	O
in	O
the	O
alignment	O
of	O
very	O
similar	O
amino	O
acid	O
sequences	O
but	O
will	O
be	O
miserable	O
at	O
aligning	O
two	O
distantly	O
related	O
sequences	O
.	O
</s>
<s>
The	O
base	O
of	O
the	O
logarithm	O
is	O
not	O
important	O
,	O
and	O
the	O
same	O
substitution	B-Algorithm
matrix	I-Algorithm
is	O
often	O
expressed	O
in	O
different	O
bases	O
.	O
</s>
<s>
To	O
create	O
a	O
PAM1	O
substitution	B-Algorithm
matrix	I-Algorithm
,	O
a	O
group	O
of	O
very	O
closely	O
related	O
sequences	O
with	O
mutation	O
frequencies	O
corresponding	O
to	O
one	O
PAM	O
unit	O
is	O
chosen	O
.	O
</s>
<s>
Based	O
on	O
collected	O
mutational	O
data	O
from	O
this	O
group	O
of	O
sequences	O
,	O
a	O
substitution	B-Algorithm
matrix	I-Algorithm
can	O
be	O
derived	O
.	O
</s>
<s>
The	O
BLOSUM	O
(	O
BLOck	O
SUbstitution	B-Algorithm
Matrix	I-Algorithm
)	O
series	O
of	O
matrices	O
rectifies	O
this	O
problem	O
.	O
</s>
<s>
To	O
reduce	O
bias	O
from	O
closely	O
related	O
sequences	O
on	O
substitution	O
rates	O
,	O
segments	O
in	O
a	O
block	O
with	O
a	O
sequence	B-Algorithm
identity	I-Algorithm
above	O
a	O
certain	O
threshold	O
were	O
clustered	O
,	O
reducing	O
the	O
weight	O
of	O
each	O
such	O
cluster	O
(	O
Henikoff	O
and	O
Henikoff	O
)	O
.	O
</s>
<s>
It	O
turns	O
out	O
that	O
the	O
BLOSUM62	O
matrix	O
does	O
an	O
excellent	O
job	O
detecting	O
similarities	O
in	O
distant	O
sequences	O
,	O
and	O
this	O
is	O
the	O
matrix	O
used	O
by	O
default	O
in	O
most	O
recent	O
alignment	O
applications	O
such	O
as	O
BLAST	B-Application
.	O
</s>
<s>
The	O
substitution	O
scores	O
are	O
calculated	O
based	O
on	O
the	O
likelihood	O
of	O
a	O
change	O
considering	O
multiple	O
tree	O
topologies	O
derived	O
using	O
neighbor-joining	B-Algorithm
.	O
</s>
<s>
Using	O
this	O
idea	O
,	O
a	O
context-specific	O
extension	O
of	O
the	O
popular	O
BLAST	B-Application
program	O
has	O
been	O
demonstrated	O
to	O
achieve	O
a	O
twofold	O
sensitivity	O
improvement	O
for	O
remotely	O
related	O
sequences	O
over	O
BLAST	B-Application
at	O
similar	O
speeds	O
(	O
CS-BLAST	B-Application
)	O
.	O
</s>
<s>
Although	O
"	O
transition	B-Algorithm
matrix	I-Algorithm
"	O
is	O
often	O
used	O
interchangeably	O
with	O
"	O
substitution	B-Algorithm
matrix	I-Algorithm
"	O
in	O
fields	O
other	O
than	O
bioinformatics	O
,	O
the	O
former	O
term	O
is	O
problematic	O
in	O
bioinformatics	O
.	O
</s>
