<s>
In	O
bioinformatics	O
,	O
a	O
spaced	B-Algorithm
seed	I-Algorithm
is	O
a	O
pattern	O
of	O
relevant	O
and	O
irrelevant	O
positions	O
in	O
a	O
biosequence	O
and	O
a	O
method	O
of	O
approximate	B-Algorithm
string	I-Algorithm
matching	I-Algorithm
that	O
allows	O
for	O
substitutions	O
.	O
</s>
<s>
They	O
are	O
a	O
straightforward	O
modification	O
to	O
the	O
earliest	O
heuristic-based	O
alignment	B-Algorithm
efforts	O
that	O
allow	O
for	O
minor	O
differences	O
between	O
the	O
sequences	O
of	O
interest	O
.	O
</s>
<s>
Spaced	B-Algorithm
seeds	I-Algorithm
have	O
been	O
used	O
in	O
homology	O
search.	O
,	O
alignment	B-Algorithm
,	O
assembly	O
,	O
and	O
metagenomics	O
.	O
</s>
<s>
Some	O
visual	O
representations	O
use	O
pound	O
signs	O
for	O
relevant	O
and	O
dashes	B-Protocol
or	O
asterisks	B-Language
for	O
irrelevant	O
positions	O
.	O
</s>
<s>
Spaced	B-Algorithm
seeds	I-Algorithm
allow	O
for	O
even	O
more	O
permissive	O
local	O
matching	O
by	O
allowing	O
certain	O
base	O
pairs	O
(	O
defined	O
by	O
the	O
pattern	O
of	O
the	O
specific	O
spaced	B-Algorithm
seed	I-Algorithm
)	O
to	O
mismatch	O
without	O
penalty	O
,	O
thus	O
allowing	O
algorithms	O
that	O
use	O
the	O
general	O
"	O
hit-extend	O
"	O
strategy	O
of	O
alignment	B-Algorithm
to	O
explore	O
additional	O
potential	O
matches	O
that	O
would	O
be	O
otherwise	O
ignored	O
.	O
</s>
<s>
But	O
a	O
spaced	B-Algorithm
seed	I-Algorithm
of	O
could	O
be	O
used	O
to	O
effectively	O
zero-weighting	O
the	O
mismatch	O
sites	O
,	O
treating	O
the	O
sequences	O
as	O
same	O
for	O
the	O
purposes	O
of	O
hit	O
identification	O
.	O
</s>
<s>
In	O
reality	O
,	O
of	O
course	O
,	O
we	O
do	O
n't	O
know	O
the	O
relative	O
positioning	O
of	O
the	O
"	O
true	O
"	O
mismatches	O
,	O
so	O
there	O
can	O
be	O
different	O
spaced	B-Algorithm
seed	I-Algorithm
patterns	O
depending	O
on	O
where	O
the	O
mismatches	O
are	O
anticipated	O
.	O
</s>
<s>
The	O
concept	O
of	O
spaced	B-Algorithm
seeds	I-Algorithm
has	O
been	O
explored	O
in	O
literature	O
under	O
different	O
names	O
.	O
</s>
<s>
In	O
1995	O
,	O
a	O
similar	O
concept	O
was	O
used	O
in	O
approximate	B-Algorithm
string	I-Algorithm
matching	I-Algorithm
where	O
"	O
gapped	O
tuples	B-Application
"	O
of	O
positions	O
in	O
a	O
sequence	O
were	O
explored	O
to	O
identify	O
common	O
substrings	O
between	O
a	O
large	O
text	O
and	O
a	O
query	O
.	O
</s>
<s>
The	O
term	O
"	O
shape	O
"	O
was	O
used	O
in	O
a	O
2001	O
paper	O
to	O
describe	O
gapped	O
q-grams	B-Language
where	O
it	O
refers	O
to	O
a	O
set	O
of	O
relevant	O
positions	O
in	O
a	O
substring	O
and	O
soon	O
after	O
in	O
2002	O
,	O
PatternHunter	B-Application
introduced	O
"	O
spaced	O
model	O
"	O
which	O
was	O
proposed	O
as	O
an	O
improvement	O
upon	O
the	O
consecutive	O
seeds	O
used	O
in	O
BLAST	B-Application
,	O
which	O
was	O
ultimately	O
adopted	O
by	O
newer	O
versions	O
of	O
it	O
.	O
</s>
<s>
Popular	O
alignment	B-Algorithm
algorithms	O
such	O
as	O
BLAST	B-Application
and	O
MegaBLAST	O
use	O
a	O
non-spaced	O
model	O
,	O
where	O
the	O
entire	O
length	O
of	O
the	O
seed	O
is	O
made	O
of	O
exact	O
matches	O
.	O
</s>
<s>
In	O
a	O
spaced	O
model	O
(	O
such	O
as	O
PatternHunter	B-Application
)	O
,	O
the	O
matches	O
are	O
not	O
necessarily	O
consecutive	O
.	O
</s>
<s>
More	O
formally	O
,	O
the	O
difference	O
in	O
a	O
spaced	B-Algorithm
seed	I-Algorithm
model	O
as	O
compared	O
to	O
a	O
non-spaced	O
model	O
is	O
the	O
relative	O
positioning	O
(	O
otherwise	O
known	O
as	O
weight	O
,	O
)	O
of	O
the	O
matched	O
bases	O
.	O
</s>
<s>
Therefore	O
,	O
a	O
spaced	B-Algorithm
seed	I-Algorithm
model	O
may	O
be	O
longer	O
than	O
a	O
non-spaced	O
seed	O
model	O
but	O
have	O
the	O
same	O
weight	O
.	O
</s>
<s>
The	O
predicted	O
number	O
of	O
hits	O
can	O
be	O
calculated	O
from	O
PatternHunter	B-Application
using	O
the	O
following	O
lemma	O
:	O
</s>
<s>
The	O
type	O
of	O
seed	O
model	O
used	O
for	O
sequence	B-Algorithm
alignment	I-Algorithm
can	O
affect	O
the	O
processing	O
time	O
and	O
memory	O
usage	O
when	O
doing	O
large-scale	O
homology	O
searches	O
–	O
two	O
considerations	O
that	O
have	O
been	O
central	O
in	O
the	O
development	O
of	O
modern	O
homology	O
search	O
algorithms	O
.	O
</s>
<s>
Using	O
spaced	B-Algorithm
seed	I-Algorithm
models	O
has	O
been	O
demonstrated	O
to	O
allow	O
for	O
faster	O
homology	O
searches	O
as	O
seen	O
with	O
PatternHunter	B-Application
wherein	O
homology	O
searches	O
were	O
twenty	O
times	O
faster	O
and	O
used	O
less	O
memory	O
than	O
BLASTn	B-Application
(	O
using	O
a	O
non-spaced	O
model	O
)	O
.	O
</s>
<s>
Most	O
aligners	O
first	O
find	O
candidate	O
locations	O
(	O
or	O
seeds	O
)	O
in	O
the	O
target	O
sequence	O
and	O
then	O
inspect	O
those	O
more	O
closely	O
to	O
verify	O
the	O
alignment	B-Algorithm
.	O
</s>
<s>
Ideally	O
,	O
this	O
first	O
step	O
would	O
find	O
all	O
relevant	O
locations	O
in	O
the	O
target	O
so	O
sensitivity	O
is	O
prioritized	O
but	O
due	O
to	O
computational	O
intensity	O
,	O
many	O
popular	O
algorithms	O
(	O
such	O
as	O
the	O
earlier	O
implementations	O
of	O
BLAST	B-Application
and	O
FASTA	B-Application
)	O
use	O
heuristics	B-Algorithm
to	O
"	O
short-cut	O
"	O
exploring	O
all	O
locations	O
,	O
ultimately	O
missing	O
many	O
but	O
running	O
relatively	O
quickly	O
.	O
</s>
<s>
One	O
possible	O
way	O
to	O
increase	O
sensitivity	O
,	O
as	O
done	O
in	O
the	O
SHRiMP2	O
algorithm	O
,	O
is	O
to	O
use	O
spaced	B-Algorithm
seeds	I-Algorithm
to	O
allow	O
for	O
small	O
differences	O
between	O
the	O
query	O
and	O
the	O
candidate	O
locations	O
so	O
that	O
somewhat	O
more	O
locations	O
are	O
identified	O
as	O
candidates	O
.	O
</s>
<s>
SHRiMP2	O
specifically	O
uses	O
multiple	O
spaced	B-Algorithm
seeds	I-Algorithm
for	O
this	O
and	O
requires	O
multiple	O
matches	O
,	O
increasing	O
sensitivity	O
as	O
it	O
allows	O
different	O
possible	O
combinations	O
of	O
differences	O
while	O
maintaining	O
speed	O
comparable	O
to	O
original	O
methods	O
.	O
</s>
<s>
A	O
variation	O
of	O
spaced	B-Algorithm
seeds	I-Algorithm
with	O
a	O
single	O
contiguous	O
gap	O
has	O
been	O
used	O
in	O
de	O
novo	O
sequence	O
assembly	O
.	O
</s>
<s>
This	O
approach	O
has	O
the	O
additional	O
advantage	O
,	O
as	O
in	O
other	O
uses	O
of	O
spaced	B-Algorithm
seeds	I-Algorithm
,	O
of	O
taking	O
into	O
account	O
any	O
sequencing	O
errors	O
that	O
may	O
have	O
occurred	O
in	O
the	O
gap	O
area	O
.	O
</s>
<s>
Spaced	B-Algorithm
seeds	I-Algorithm
have	O
been	O
successfully	O
utilized	O
for	O
this	O
purpose	O
by	O
finding	O
how	O
many	O
k-mers	O
are	O
found	O
in	O
each	O
genome	O
(	O
hit	O
number	O
)	O
and	O
the	O
total	O
number	O
of	O
positions	O
these	O
k-mers	O
cover	O
(	O
coverage	O
)	O
.	O
</s>
<s>
An	O
improvement	O
to	O
(	O
single	O
)	O
spaced	B-Algorithm
seeds	I-Algorithm
was	O
first	O
demonstrated	O
by	O
PatternHunter	B-Application
in	O
2002	O
where	O
a	O
set	O
of	O
spaced	B-Algorithm
seeds	I-Algorithm
were	O
used	O
,	O
in	O
which	O
a	O
"	O
hit	O
"	O
was	O
called	O
whenever	O
one	O
of	O
the	O
set	O
matched	O
.	O
</s>
<s>
PatternHunter	B-Application
II	O
,	O
in	O
2003	O
,	O
demonstrated	O
that	O
this	O
approach	O
could	O
offer	O
higher	O
sensitivity	O
than	O
BLAST	B-Application
while	O
maintaining	O
similar	O
speed	O
.	O
</s>
<s>
Identifying	O
an	O
optimal	O
set	O
of	O
spaced	B-Algorithm
seeds	I-Algorithm
is	O
an	O
NP-hard	O
problem	O
,	O
however	O
,	O
even	O
finding	O
a	O
"	O
good	O
"	O
set	O
of	O
spaced	B-Algorithm
seeds	I-Algorithm
remains	O
difficult	O
,	O
although	O
several	O
attempts	O
have	O
been	O
made	O
to	O
computationally	O
identify	O
them	O
.	O
</s>
<s>
Since	O
the	O
speed	O
of	O
the	O
algorithm	O
must	O
decrease	O
with	O
an	O
increasing	O
number	O
of	O
spaced	B-Algorithm
seeds	I-Algorithm
,	O
it	O
makes	O
sense	O
to	O
only	O
consider	O
multiple	O
seeds	O
when	O
all	O
offer	O
some	O
useful	O
contribution	O
.	O
</s>
<s>
There	O
is	O
ongoing	O
research	O
on	O
how	O
to	O
quickly	O
calculate	O
good	O
multiple	O
spaced	B-Algorithm
seeds	I-Algorithm
,	O
as	O
previous	O
homology	O
search	O
software	O
calculated	O
and	O
hard-coded	O
their	O
seeds	O
–	O
it	O
would	O
be	O
advantageous	O
to	O
be	O
able	O
to	O
calculate	O
purpose-driven	O
multiple	O
spaced	B-Algorithm
seeds	I-Algorithm
instead	O
.	O
</s>
