Feature-preserving noise reduction by using time-domain Gaussian-weighted multiple noise reduction filters for real-time bioluminescence measurement


Ishigami, K.; Furukawa, H.

Analytical Biochemistry: -

2018


This paper proposes a time-domain Gaussian-weighted noise reduction filter for bioluminescence measurement with low signal-to-noise ratio through photon counting. The filter was used for estimating the true fold-change signal from noisy gene expression data obtained through real-time dual-color luciferase assay. Furthermore, not only was the higher harmonics noise of the measurement system confirmed to reduce from the gene expression data but rapid and slow changes were also preserved in the estimated signal. In addition, the probability value of Pearson's chi-squared test was improved 257 times at most and 1.5 times on average without impairing the noise reduction ratio.

Analytical
Biochemistry
551
(2018)
1-3
Analytical
Biochemistry
Contents
lists
available
at
ScienceDirect
Analytical
Biochemistry
ELSEV'
journal
homepage:
www.elsevier.com/locate/yabio
Feature-preserving
noise
reduction
by
using
time-domain
Gaussian-
weighted
multiple
noise
reduction
filters
for
real-time
bioluminescence
measurement
Keisuke
Ishigami,
Hiromitsu
Furukawa
Electronics
and
Photonics
Research
Institute,
National
Institute
of
Advanced
Industrial
Science
and
Technology
(AIST),
1-1-1
Higashi
Tsukuba,
Ibaraki,
305-8565,
Japan
ARTICLE INFO
ABSTRACT
Keywords:
Luciferin
Luciferase
Real-time
bioluminescence
measurement
Gene
expression
network
Noise
filter
Low
pass
filter
Time-domain
Gaussian-weighted
Weighted
average
Photomultiplier
tube
PMT
Photon
counting
Signal-to-noise
ratio
SNR
This
paper
proposes
a
time-domain
Gaussian-weighted
noise
reduction
filter
for
bioluminescence
measurement
with
low
signal-to-noise
ratio
through
photon
counting.
The
filter
was
used
for
estimating
the
true
fold-change
signal
from
noisy
gene
expression
data
obtained
through
real-time
dual-color
luciferase
assay.
Furthermore,
not
only
was
the
higher
harmonics
noise
of
the
measurement
system
confirmed
to
reduce
from
the
gene
expression
data
but
rapid
and
slow
changes
were
also
preserved
in
the
estimated
signaL
In
addition,
the
probability
value
of
Pearson's
chi-squared
test
was
improved
257
times
at
most
and
1.5
times
on
average
without
impairing
the
noise
reduction
ratio.
Introduction
The
measurement
of
real-time
bioluminescence
by
using
multiple
luciferase
genes
plays
an
important
role
in
the
analyses
of
a
gene
ex-
pression
network
and
the
stimulation-response
mechanism
[
,
].
The
stimulation-induced
response
element-dependent
gene
expressions
can
be
solved
by
obtaining
the
ratio
between
the
response
element-depen-
dent
gene
expressions
of
the
stimulated
and
reference
cells,
called
as
the
fold
change.
In
this
process,
the
response
element-dependent
gene
ex-
pressions
of
the
stimulated
and
reference
cells
should
be
solved
by
obtaining
the
ratio
between
the
gene
expressions
of
the
experimental
and
internal
control
reporters.
As
the
fold
change
is
the
ratio
of
two
ratios,
the
signal-to-noise
ratio
(SNR)
of
the
fold
change
is
generally
insufficient.
For
example,
even
though
the
original
gene
expressions
of
NF—x13(SLR3)
and
thymidine
kinase
(SLG)
[TK(SLG)]
have
sufficient
SNR
(Fig.
la
and
b),
the
SNR
of
the
fold
change
calculated
from
the
original
gene
expressions
of
reporters
is
low
(Fig.
1d).
This
results
in
the
failure
in
estimating
the
quantitative
peak-position
and
peak-height
of
the
fold
change,
which
are
the
most
significant
factors
in
the
analyses
of
gene
expression
network.
Therefore,
the
designing
of
a
noise
filter
that
can
adaptively
preserve
local
behavior
of
the
gene
expressions
of
the
*
Corresponding
author.
E-mail
address
(FL
Furukawa).
https://doLorg/10.1016/j.ab.2018.04.026
Received
2
January
2018;
Received
in
revised
form
20
April
2018;
Accepted
27
April
2018
Available
online
01
May
2018
0003-2697/
@
2018
Elsevier
Inc.
All
rights
reserved.
reporters
is
necessary
[3].
In
the
current
study,
we
proposed
a
noise
reduction
filter,
which
is
practically
effective
for
the
assay
of
real-time
dual-color
luciferase
by
using
a
photomultiplier
tube
(PMT),
without
assuming
a
true
signal.
The
proposed
filter
was
compared
with
the
conventional
low
pass
filter
(LPF),
and
preserved
the
local
character-
istic
of
gene
expression
data.
In
addition,
the
proposed
filter
was
suf-
ficient
for
estimating
the
fold
change
in
real-time
bioluminescence
measurement.
Methods
Test
data
acquisition
Human
hepatoma
(HepG2)
cells
harboring
the
multi-integrase
mouse
artificial
chromosome
(MI-MAC)
vector
[ ]
were
seeded
in
a
96-
well
clear-bottom
black
plate
(Nunc,
Wiesbaden,
Germany)
at
a
density
of
3
x
10
4
cells
per
well.
The
HepG2
cells
stably
expressed
red-emitting
luciferase
(SLR3)
and
green-emitting
luciferase
(SLG)
under
the
control
of
herpes
simplex
TIC
promoter
and
NF—KB
response
element
[5],
re-
spectively.
The
SLR3
and
SLG
were
used
as
experimental
and
internal
control
reporters,
respectively.
After
overnight
incubation,
the
culture
Ishigami,
H.
Furukawa
Analytical
Biochemistry
551
(2018)
1-3
(a)
(b)
TNFa
10
ng/mL
ORIG
LPF
PPSD
NF—KB—TK—SLR3
TK—SLG
0
10
20
30
40
50
60
70
Time
(h)
TNFa
0
ng/mL
ORIG
LPF
PPSD
NF—KB—TK—SLR3
TK—SLG
600
500
400
300
PI
Z
200
100
l'
I
0
0
10
20
30
40
50
60
70
Time
(h)
(c)
NF-KB-TK-SLR3/TK-SLG
(d)
NF-KB-TK-SLR3+TK-SLG
TNFa
10
ng/mL
o
0
60
70
10
20
30
40
50
Time
(h)
10
Original
Low
pass
filter
Proposed
filter
2
-
10
20
30
40
50
60
70
Time
(h)
ORIG
LPF
PPSD
20
TNFa
10
ng/mL
TNFa
0
ng/mL
10
cC
5
Fig.
1.
Real-time
multicolor
bioluminescence
measurement
of
NF—x13
activation
by
using
TNFa
in
SLR3-and
SLG-expressing
HepG2
cells.
Gene
expressions
of
NF—d3
(SLR3)
and
TK(SLG)
as
a
function
of
time
(a)
with
TNFa
stimulation
and
(b)
without
stimulation.
(c)
TNFa-stimulation
dependence
of
the
NF—xlil-dependent
gene
expressions.
(d)
Fold
change:
TNFa-induced
NF—xlil-dependent
gene
expression.
ORIG:
original
data;
LPF:
the
data
processed
using
low
pass
filter;
PPSD:
the
data
processed
using
proposed
filter.
medium
was
replaced
with
Dulbeccos
modified
Eagle's
medium
without
phenol
red
(Gibco-BRL,
Grand
Island,
NY)
but
supplemented
with
10%
fetal
bovine
serum,
25
mM
HEPES/NaOH
(pH
7.0;
Sigma-Aldrich,
St.
Louis,
MO),
and
0.4
mM
D-Luciferin
potassium
salt
(Resem
B.V.,
LD
Lijnden,
The
Netherlands).
The
HepG2
cells
were
stimulated
using
a
tumor
necrosis
factor
a
(TNFa,
Wako,
Tokyo,
Japan)
of
10
ng/mL.
The
real-time
bioluminescence
intensity
was
measured
using
a
microplate-
type
luminometer
(WSL-1560,
ATTO,
Tokyo,
Japan)
equipped
with
PMT.
The
gene
expressions
of
NF—KB(SLR3)
and
TK(SLG)
were
calcu-
lated
from
the
total
and
transmitted
luminescence
intensities
obtained
through
the
620
nm
long-pass
filter
(R62
filter;
Hoya,
Tokyo,
Japan),
as
described
previously
[6].
The
measurement
period
was
3
days
of
7
min
intervals
with
5
s
integration.
In
that
period,
cells
were
kept
in
a
hu-
midified
atmosphere
containing
5%
CO
2
at
37C.
Noise
reduction
and
its
validity
evaluation
After
LPF-smoothing
by
using
cutoff
frequency
v
c
,
the
gene
expres-
sions
0
(t)
of
the
reporters
was
converted
to
LPF
(0
(t),
v
c
).
Cutoff
fre-
quency
v
c
was
optimized
for
the
rapid
and
slow
changing
parts
and
labeled
as
v
1
and
v
2
,
respectively.
Estimated
signal
S
(t)
is
the
weighted
linear
combination
of
the
LPF-smoothed
gene
expressions
0
(t)
for
the
rapid
and
slow
changing
parts,
and
is
defined
as
S(t)
=
W
(t)LPF(0(t),
v
1
)
+
(1
W(t))LPF(0(t),
v2),
(1)
where
W
(t)
is
the
total
weight
function
for
rapid
changing
parts.
The
full
expression
of
LPF
(0
(t),
vc)
and
derivation
of
W(t)
are
explained
in
the
Supplementary
material
[7].
In
the
time-varying
luminescence
of
luciferase
assay
using
PMT,
the
dominant
noise
was
the
thermal
and
shot
noise.
Since
the
target
system
was
shown
systematic
tendency
against
the
cell
stimulation,
we
as-
sumed
that
the
noise
of
this
system
must
be
Gaussian
weighted.
In
this
case,
the
noise
reduction
validity
can
be
evaluated
by
the
Pearsons
chi-
squared
(PCS)
test.
The
noise
reduction
performance
was
evaluated
based
on
three
aspects:
1)
noise
intensity,
namely,
a
residual
between
the
estimated
signal
and
unprocessed
data;
2)
goodness-of-fit
test
of
a
random
variable,
following
a
theoretically
ideal
distribution
using
Pearson's
chi-squared
(PCS)
test
[8];
and
3)
root
mean
square
of
the
noise
intensity
normalized
by
the
estimated
signal
intensity.
The
sig-
nificance
level
of
the
PCS
test
was
set
to
a
typical
value
of
0.05.
The
ideal
distribution
was
derived
from
the
assumptions
that
the
noise
for
the
gene
expressions
of
the
reporters
follows
a
normal
distribution
and
no
cross-talk
exists
between
the
chemical
excitations
of
the
experi-
mental
and
internal
control
reporters.
In
order
to
compare
the
perfor-
mance
between
conventional
LPF
and
proposed filter,
we
used
same
type
of
conventional
LPF
as
proposed
filter
and
same
cutoff
frequency
for
rapid
changing
part
of
proposed
filter
as
that
of
conventional
LPF.
Results
and
discussion
Fig.
la
and
b
shows
the
gene
expressions
of
NF—KB(SLR3)
and
TK
(SLG)
with
and
without
TNFa
stimulation,
respectively.
The
NF—KB-
dependent
gene
expressions
of
the
stimulated
and
reference
cells
are
shown
in
Fig.
lc
and
were
derived
from
the
ratio
between
the
gene
2000
',7)•
1500
1000
A
,
500
2
Ishigami,
H.
Furukawa
Analytical
Biochemistry
551
(2018)
1-3
Table
1
Hypothesis
of
PCS
test
and
comparison
of
noise
reduction
performance
between
conventional
LPF
and
proposed
filter.
Hypothesis
of
PCS
test
Conventional
LPF
Proposed
filter
Random
variable
Probability
density
function
Probability
value
of
PCS
test
Noise
reduction
ratio
Probability
value
of
PCS
test
Noise
reduction
ratio
TNFa
10
ng/mL
NF-KB-TK-
Noise
Nonnal
0.363
0.041
0.473
0.037
SLR3
TK-SLG
Noise
Nonnal
0.463
0.136
0.864
0.139
SLR3/SLG
Noise
ratio
Cauchy
0.919
0.174
0.822
0.177
TNFa
0
ng/mL
NF-KB-TK-
Noise
Nonnal
0.634
0.127
0.618
0.127
SLR3
TK-SLG
Noise
Nonnal
0.235
0.164
0.350 0.170
SLR3/SLG
Noise
ratio
Cauchy
0.003
0.331
0.772
0.340
Fold
change
Ratio
of
noise
ratios
Equation
S8
0.250
0.325
0.661
0.332
expressions
of
NF—KB(SLR3)
and
TK(SLG).
The
TNFa-induced
NF—KB-
dependent
gene
expression,
that
is,
the
fold
change
is
solved
in
Fig.
1d,
and
is
the
ratio
between
the
NF—KB-dependent
gene
expressions
of
the
stimulated
and
reference
cells.
Although
the
normalization
using
SLG
and
reference
cell
minimizes
systematic
error
originating
from
experimental
variability,
the
peak
position
and
height
of
the
original
fold
change
were
difficult
to
de-
termine.
This
is
attributed
to
the
random
error
originating
from
the
thermal
and
shot
noise
of
PMT
in
the
original
gene
expressions
of
NF—x13
(SLR3)
and
TK(SLG).
The
LPF
was
applied
to
reduce
this
type
of
noise.
For
the
conventional
LPF,
the
cutoff
frequency
was
set
to
not
de-
teriorate
the
peak
position
of
rapid
change.
Owing
to
this
limitation,
the
SNR
of
the
fold
change
was
still
low
in
some
measurement
periods.
In
contrast
to
the
conventional
LPF,
the
proposed
filter
allowed
the
in-
crease
of
SNR,
especially
on
the
slow
changing
parts
of
the
estimated
signal.
Table
1
summarizes
the
noise
reduction
performance
for
each
filter.
In
most
cases,
the
proposed
filter
shows
better
probability
value
than
the
conventional
LPF
without
degrading
noise
reduction
ratio.
Note
that
for
the
conventional
LPF,
the
probability
value
of
the
NF—KB-de-
pendent
gene
expressions
of
the
reference
cell
took
the
smaller
value
of
0.003.
This
is
smaller
than
the
significance
level
of
0.05.
The
ratio
between
normally
distributed
noises
with
zero
mean
should
be
dis-
tributed
through
a
Cauchy
distribution.
This
suggests
that
it
is
unlikely
that
the
noise
ratio
of
the
gene
expressions
of
NF—KB(SLR3)
and
TK
(SLG)
was
distributed
according
to
the
Cauchy
distribution
at
the
5%
level
of
significance.
Contrarily,
the
proposed
filter
increased
the
probability
value
by
257
times
to
0.772,
indicating
that
the
proposed
filter
shows
higher reliability
than
the
conventional
LPF
in
terms
of
noise
distribution.
In
spite
of
excluding
this
extreme
case,
the
prob-
ability
value
was
typically
increased
by
1.5
times
in
this
study.
Conclusion
We
proposed
an
adaptive
noise
filter
for
measuring
ultralow
bio-
luminescence
to
obtain
a
high-SNR
estimated
signal.
The
noise
reduc-
tion
performance
of
the
filter
was
quantitatively
evaluated.
Although
the
conclusive
estimated
signal
is
written
as
a
time-domain
Gaussian-
weighted
linear
combination
of
the
estimated
signals
for
the
rapid
and
slow
changing
parts
obtained
through
the
conventional
LPF
with
opti-
mized
cutoff
frequency,
the
proposed
filter
shows
better
performance
than
the
conventional
LPF.
The
suppressed
rough
changes
reduce
the
uncertainty
of
the
estimated
peak
position
and
height
(Fig.
1d).
More-
over,
the
reasonability
of
the
noise
reduction
was
tested
based
on
the
PMT
noise
model,
following
the
normal
distribution,
by
using
the
PCS
test.
The
test
verified
that
the
extracted
noise,
noise
ratio,
and
ratio
of
the
noise
ratio
were
distributed
according
to
the
theoretically
ideal
distributions
(Table
1).
The
probability
value
of
the
PCS
test
was
im-
proved
257
times
at
most
and
1.5
times
on
average
without
impairing
the
noise
reduction
ratio.
Acknowledgment
We
would
like
to
thank
Yoshihiro
Nakajima
for
offering
experi-
mental
result
of
real-time
multicolor
bioluminescence
measurement
and
for
holding
discussions
that
greatly
improved
the
manuscript.
We
would
also
like
to
thank
Naoko
Ohnishi
for
technical
assistance
in
the
laboratory.
We
are
grateful
to
Dr.
Yasuhiro
Kazuki
of
Tottori
University
for
the
generous
gift
of
HepG2
cells
harboring
the
MI-MAC
vector.
This
work
was
supported
by
the
AI-SHIP
Project
of
the
Ministry
of
Economy,
Trade
and
Industry
(METI),
Japan.
Appendix
A.
Supplementary
data
Supplementary
data
related
to
this
article
can
be
found
at
,
ttp://dx.
doi.org/10.1016/j.ab.2018.04.026.
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