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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