membranes
ArticleLing’s Adsorption Theory as a Mechanism of
Membrane Potential Generation Observed in Both
Living and Nonliving Systems
Hirohisa Tamagawa 1, *, Makoto Funatani 1 and Kota Ikeda 2
1
2*

Department of Human and Information Systems, Faculty of Engineering, Gifu University, 1-1 Yanagido,
Gifu, Gifu 501-1193, Japan; ship_ship19931125@icloud.com
Graduate School of Advanced Mathematical Sciences, Meiji University, 4-21-1, Nakano, Nakano-ku,
Tokyo 165-8525, Japan; ikeda@meiji.ac.jp
Correspondence: tmgwhrhs@gifu-u.ac.jp; Tel.: +81-58-293-2529

Academic Editor: Spas Kolev
Received: 28 September 2015; Accepted: 21 January 2016; Published: 26 January 2016

Abstract: The potential between two electrolytic solutions separated by a membrane impermeable toions was measured and the generation mechanism of potential measured was investigated. From thephysiological point of view, a nonzero membrane potential or action potential cannot be observed
across the impermeable membrane. However, a nonzero membrane potential including action
potential-like potential was clearly observed. Those observations gave rise to a doubt concerning thevalidity of currently accepted generation mechanism of membrane potential and action potential ofcell. As an alternative theory, we found that the long-forgotten Ling’s adsorption theory was the mostplausible theory. Ling’s adsorption theory suggests that the membrane potential and action potentialof a living cell is due to the adsorption of mobile ions onto the adsorption site of cell, and this theory
is applicable even to nonliving (or non-biological) system as well as living system. Through thispaper, the authors emphasize that it is necessary to reconsider the validity of current membrane
theory and also would like to urge the readers to pay keen attention to the Ling’s adsorption theory
which has for long years been forgotten in the history of physiology.
Keywords: membrane potential; action potential; ion permeation; Goldman-Hodgkin-Katz;
ion adsorption; Ling’s adsorption theory

1. Introduction
A cell generates nonzero potential across the plasma membrane, which is called membranepotential [1–16]. Cell exhibits vehement change of membrane potential in the active state, and such a
potential is called action potential. According to the Goldman-Hodgkin-Katz equation (GHK equation),membrane potential is generated by the mobile ion passage through the plasma membrane [1,7,17,18].
Membrane potential is determined by the ion concentration inside and outside of cell and the ion
flux through the plasma membrane. It is broadly acknowledged that the GHK equation precisely
predicts the actual membrane potential behavior. This successful outcome is interpreted as the ion
passage through the plasma membrane is actually one of the fundamental factors for the nonzero
membrane potential generation of the cell. However, nonzero potential is even generated across anartificial impermeable membrane separating two electrolytic solutions [19–22]. Colacicco’s report isa typical example [19,20]. Colacicco observed the nonzero potential generation across oil membrane
impermeable to ions.
Tamagawa, one of authors of this paper, and Morita also reported that the membrane potential
across the membrane impermeable to ions was virtually identical to the membrane potential acrossMembranes 2016, 6, 11; doi:10.3390/membranes6010011

www.mdpi.com/journal/membranes

Membranes 2016, 6, 11

2 of 14a permeable membrane, and the those experimentally obtained membrane potentials were identicalto the membrane potential theoretically obtained by the use of GHK equation [21,22]. Tamagawa
and Morita basically dispute the currently accepted mechanism of membrane potential generationof cell. They take side with the adsorption theory advocated by Dr. Gilbert Ling [1,7,21,22]. Ling hasemphasized that the membrane potential of cell is basically caused by the adsorption of mobile ions
onto the membrane adsorption sites not by the ion permeation through the membrane. The Ling’s
adsorption theory is applicable to the nonliving system as well as living system. In fact, Ling carriedout some experiments many years ago, and confirmed that his theory is applicable to the nonliving
system [1].
The authors would like to briefly comment on Dr. Ling as a scientist and his accomplishments
a little, since the authors employ his theory in this paper. Ling made a historical accomplishment
in his young days. He perfected a microelectrode technique, which has greatly advanced theelectrophysiology, when he was a Ph.D. candidate in University of Chicago. Later, he advocatedhis own theory of cell metabolic activity. Since his own theory was completely in conflict with theexisting theory, his fame once established in his young days has been declining gradually, and now heis completely left out of science world. Nowadays, nobody knows his accomplishments or people whoknow his accomplishments think that what he has advocated is a silly talk. However, the authors of
this paper do not care about the label put on him and his accomplishments, and the authors employ
his theory throughout this work. The authors had to add some more comments as follows: Basicallythe same idea as the Ling’s adsorption theory was put forth by the late K. L. Cheng independently ofLing, though decades after Ling [23–27]. Cheng was an electrochemist and had studied the electrodemechanism. He reached a conclusion that the potential measured by the electrode is caused by the ion
adsorption onto the electrode surface adsorption sites.
Existing theory of cell biology attributes the action potential induction to the function of ionchannels and pumps embedded in the plasma membrane [1,4,5,7,13–16]. Hence, the induction ofaction potential is one of manifestations of biological activity. Therefore, it is quite natural to believethat the action potential is not observed in the artificial system having neither ion channels nor pumps.
Contrary to such a quite natural thought, action potential-like potential has been repeatedly observedin the artificial systems in which no ion channels or pumps were embedded [28–50].
Proteinoid is a tiny sphere consisting of amino acids. It was first created by Sidney Fox [31,32,34,35,40].
Scientists regard it as a protocell or something similar to the protocell. Although the proteinoid was
artificially created and it did not contain any ion channel or pump, it generated action potential-like
potential [31,32,34,35,40]. Yoshikawa et al. reported a number of even more intriguing observations. They
separated two electrolytic aqueous solutions with an artificially created liquid membrane. The experimental
systems they used did not contain any biological material unlike Fox’s. However, Yoshikawa et al. observed
continuous generation of action potential-like potential [33,34,37–39,41,42], and other research groups also
observed similar phenomena [43–49]. Yoshikawa et al. did not seem to have so strong interest in pursuing
the physiological meaning of their observations. Their interest seemed to primarily lie in the physical andmathematical analysis of their observations. We think that those observations by Yoshikawa et al. imply agrave physiological meaning. That is, generation of membrane potential including action potential may not
be a characteristic particular only to living system, and no ion channel or pumps are needed for generating
action potential. The membrane potential generation of cell may not represent the biological activity,and it may be merely a consequence of physical chemistry-based nature of electrolytic solution systems.
i.e., generation of membrane potential including action potential has nothing to do with life and death.
According the GHK equation, ion transfer through the plasma membrane is essential for the membranepotential and action potential generation [1,7,17,18], but it might be possible to generate them without
ion transfer through the membrane. Therefore, in this work, the authors attempted to achieve membranepotential generation and action potential-like potential generation between two electrolytic solutions
without ion transfer through the membrane, then the authors discussed the physiological implication of
the experimental observations.

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2. Preparation of Membranes and Solutions
2.
Preparationof Membranes
and Solutions
The
authors mademeasurementsof potential between two electrolytic solutions separated by animpermeable
material.
Those
potential
measurements
were categorized
into solutions
two measurements.
The authors made measurements of potential between
two electrolytic
separated byExp. I:
Measurementof potential
betweentwo electrolytic
solutionsseparatedby intoan impermeable
membrane
an impermeable
material.
Those potential
measurements
werecategorized
two measurements.
and Exp.
Measurementof oscillating
potential
betweentwo electrolytic
solutionsseparated byExp. I:II:
Measurementof potential
betweentwo electrolytic
solutionsseparated by
an impermeable
membraneand Exp.
II: Measurementof silver
oscillating
betweentwo iselectrolytic
a silverwire & liquid
membrane,where thewire potential
and liquid
membraneof coursesolutions
impermeable
separatedbyasilverwire&
liquidmembrane,where
thesilverwire
andliquidmembrane
is of
to ions.
course impermeable to ions.

2.1. Fabrication of Impermeable Membrane
2.1. Fabrication of Impermeable Membrane

MG90

Conductive adhesive

MG90

Two types of impermeable solid membranes were employed for carrying out Exp. I. One was
Two types of impermeable solid membranes were employed for carrying out Exp. I. One was aa thin urethane film, MG90 (25 µm thick), manufactured by Takeda Sangyo Co., Ltd. (Tokyo, Japan).
thin urethane film, MG90 (25 μm thick), manufactured by Takeda Sangyo Co., Ltd. (Tokyo, Japan).
Another membrane was fabricated by attaching two sheets of MG90 to each other with an
Another membrane was fabricated by attaching two sheets of MG90 to each other with anelectricallyconductive
adhesive.
TheTheelectricallyconductive
adhesivewas
preparedsimplybyby
mixingelectricallyconductive
adhesive.
electricallyconductive
adhesivewas
preparedsimplycarbon(Ketjenblack)
andepoxy.
This
membranefabricatedishereafter
calledKBMG90.
The
structuremixing carbon (Ketjen black) and epoxy. This membrane fabricated is hereafter called KBMG90.
of KBMG90
is shown
in Figure1.
The structureof KBMG90
is shown
in Figure 1.

Figure1.
1. SideSide view
FigureviewofofKBMG90.
KBMG90.

2.2. Liquid Membrane

2.2. Liquid Membrane

Two types of liquid membranes were prepared for carrying out Exp. I and II. One liquid
Two types ofliquidmembranes
were
preparedfor carrying
Exp.
II. One liquid
membranemembranewaspreparedby mixing
0.086
g of surfactant
SDSoutwith
24 Igand1‐pentanol.
This liquid
was preparedmixing called
0.086 S‐penta.
g of surfactant
SDS with
24 g with
1-pentanol.
This liquid membrane ismembrane byis hereafter
S‐penta looked
saturated
SDS.
one wasS-penta
preparedlookedby mixing
0.11 g withof surfactant
hereafter Anothercalled S-penta.
saturated
SDS. CTAB with 24 g 1‐pentanol. This ishereafter
C‐penta.
Anothercalled
one wasprepared by mixing 0.11 g of surfactant CTAB with 24 g 1-pentanol. This ishereafter called C-penta.

2.3. Electrolytic Solutions

2.3. Electrolytic
VariousSolutions
concentrations of KCl solution were prepared simply by dissolving KCl into deionizedwater, and lower concentration of KCl solutions were prepared by diluting the high concentration
Various concentrations of KCl solution were prepared simply by dissolving KCl into deionized
KCl solution with deionized water. These KCl solution were used for both Exp. I and II.
water, and lower concentration of KCl solutions were prepared by diluting the high concentration KCl
Concentration of those KCl solutions ranged from 0.00001 to 3.4 M.
solution with
deionized
water.
KCl solution
were
used
for both
Exp.
andMII.NaCl
Concentrationof
For Exp.
II, two kindsof These
NaCl aqueous
solutionswereprepared.
One
wasI 0.3
aqueousthosesolution,
KCl solutions
from 0.00001
to 3.4 M.
which ranged
was preparedby dissolving
NaCl into deionized water. Another one was the
For
Exp.
II,
two
kinds
of
NaCl
aqueoussolutionswere
One was0.3by
M dissolving
NaCl aqueous
mixture of 0.3 M NaCl & 1 M ethanol aqueous solution,
andprepared.
it was prepared
simplysolution,which
waspreparedbydissolving
NaCl
into
deionized
water.
Anotheronewasthe mixture
NaCl and ethanol into the deionized water.

of 0.3 M NaCl & 1 M ethanol aqueous solution, and it was prepared simply by dissolving NaCl and3. Potential
ethanol
into theMeasurement
deionized water.
3.1. Exp. IMeasurement
3. Potential
Figure 2 illustrates the setup for the measurement of potential across a membrane of MG90

3.1. Exp.
I with a liquid membrane. Two Ag wires served as Ag/AgCl electrode, and their ends were
coatedFigure 2 illustrates the setup for the measurement of potential across a membrane of MG90 coatedwith a liquid membrane. Two Ag wires served as Ag/AgCl electrode, and their ends were coated withMembranes 2016, 6, 11

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AgCl.coated
Two KCl solutions
were supplied in the left and right compartments, respectively, where these
Two KCl solutions were supplied in the left and right compartments,
Membraneswith
2016, 6,AgCl.
11
4 of 14
KCl concentrations
weredenotedby CL and Cwere
the stablepotential
R , respectively.
respectively, where these
KCl concentrations
denoted by Voltmeter
CL and CR, shows
respectively.
Voltmeter
withina few
minutes,andthat
potential
registered.
shows
the
stablepotential
withina few wasminutes,
andthat potential
coated
with
AgCl.
Two
KCl
solutionswere
suppliedin the wasleftregistered.
and right compartments,
respectively, where these KCl concentrations were denoted by CL and CR, respectively. Voltmeter
voltmetershows the stable potential within a few minutes,
and that potential was registered.
Ag wirevoltmetersalt-bridge
Ag wireAgCl coat

AgCl coatsalt-bridge
AgCl coat

AgCl coat

CL
CL

CR
membraneCR

Figure
2. Experimental
setup
measuringpotentialacrossacrossa amembrane.
membrane. C
CL andCR represent
Figure
2. Experimental
setup
for formeasuringthethepotential
L and CR represent themembrane
the KCl concentration of left and right KCl solutions, respectively.
KCl concentration of left and right KCl solutions, respectively.
Figure 2. Experimental setup for measuring the potential across a membrane. CL and CR represent

Anotherexperimentofwas
carriedusing respectively.
the KBMG90 in place of MG90 coated with athe KCl concentration
left andrightout
KCl bysolutions,
Anotherexperiment
was carriedout byusing the KBMG90
in as
place
of MG
MG90
with
liquid membrane.
Procedureof makinga measurement
was samewhen
90 coated
was used,
buta itliquid
took Anotherlongerforexperiment
the potential
to carriedstabilize.
wasout by usingwas
the same
KBMG90in placeof 90
MG90
membrane.
Procedureof makinga measurement
as whenMG
wascoated
used, with
but ita took
liquidmembrane.
Procedureof making a measurement was same as when MG 90 was used, but it
longerfor thepotential
to stabilize.
3.2.
II for the potential to stabilize.
tookExp.
longer

3.2. Exp. II
Figure 3 illustrates the setup for the measurement of potential across the membrane—a silver
3.2. Exp. II

wire & 3S‐penta—.
and KCl
solutionswere suppliedin the acrossleft andglass tubes,silver
FigureillustratesNaCl
the setup
for themeasurementof potential
theright
membrane—arespectively.
Left
and
right
solutionsweredenoted
by
Sol‐L
and
Sol‐R,
respectively.
Theirsilver
KCl
Figure 3 illustrates the setup for the measurement of potential across the membrane—awire & S-penta—. NaCl and KCl solutions were supplied in the left and right glass tubes, respectively.
concentrations
weredenoted
by
C
L
and
C
R
,
respectively.
Two
Ag
wires
connected
tothevoltmeter
wire & S‐penta—. NaCl and KCl solutions were supplied in the left and right glass tubes,
Left and right solutions were denoted by Sol-L and Sol-R, respectively. Their KCl concentrations wereservedas an Left
Ag/AgCl
electrode,and were
their ends
werewith Sol‐R,
AgCl. respectively.
Voltmeter showedtherespectively.
and right
solutionsdenotedbycoated
Sol‐L and
Their KCldenoted
by
C
and
C
,
respectively.
Two
Ag
wires
connected
tothevoltmeter
servedasan
Ag/AgClL
R
stablepotentialwere
withina few byminutes
completing the
preparationof potential
concentrations
denotedCL andafterCR, respectively.
Two
Ag wires connected
tomeasurement.
the voltmeterelectrode,
and
ends
were
coatedwith
AgCl.
Voltmeter
showedthestablepotential
withinThatpotentialwasregistered.
Sol‐L
andtheir
Sol‐R
wereelectricallyconnected
withthemembraneofaa few
servedas theiran Ag/AgClelectrode,
and
ends
were
coatedwith
AgCl.
Voltmeter
showedtheminutes
aftercompletingthepreparationofpotential
measurement.
Thatpotentialwasregistered.
silver& S‐penta.
ion transfer
never tookthe
place
between of
Sol‐Land Sol‐R.
Anotherstable wirepotential
within However,a few minutes
after completing
preparation
potential
measurement.
carriedout by Sol‐L
using
the C‐penta
in placeof S‐penta.
Sol-Lexperimentand potential
Sol-R was
were
electricallyconnected
withwerethemembraneof a silverwith
wirethe& membrane
S-penta. However,That
wasregistered.
and
Sol‐R
electricallyconnected
of asilver wire
& S‐penta.
However,
ionSol-L
transfer
place between
Sol‐Lwasandcarried
Sol‐R. Anotherion transfer
nevertook place
betweenandnever
Sol-R.took
Anotherexperimentout by using
experiment
was carriedout by using the C‐penta
in place of S‐penta.
the C-penta
in placeof S-penta.
voltmeter
Ag wirevoltmeter
AgCl coat
Ag wireS-penta S-penta

AgCl
coat
Ag wireAg wiresalt-bridge
salt-bridge

Sol-L
Sol-L

CL

Sol-R
CR

Sol-R

CL
CR
Figure 3. Experimental setup for measuring
the potential acrossthe membrane of a silver wire &S‐penta. CL and CR represent the concentration of left NaCl and right KCl solutions, respectively.
The
Ag wire whichwasconnected
to thewascoatedwith
AgCl. of aof
Figure3.ofExperimental
setup
for
measuring
thevoltmeter
potential
acrossthethemembranesilverwire wire&
Figure
3.end
Experimental
setup
for
measuringthepotential
acrossmembranea silver&S‐penta.
CL andR represent the concentration of left NaCl and right KCl solutions, respectively.
S-penta.
CL andCRCrepresent
the concentration of left NaCl and right KCl solutions, respectively.
The end of Ag wire which was connected to the voltmeter was coated with AgCl.
The end of Ag wire which was connected to the voltmeter was coated with AgCl.

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4. Results and Discussion
4. Results
Results andand Discussion
Discussion
4.

4.1. Potential Measurement

4.1. Potential
Potential Measurement
Measurement
4.1.

4.1.1. Exp. I

4.1.1 Exp.
Exp. II
4.1.1

The potential
measurement
described
in theinSection
3.1 was3.1
carriedout.
Membranepreparation
The potential
potential
measurement
described
the Section
Sectionwas carried
carriedout. Membrane
MembraneThemeasurement
described
in the3.1 wasout.
shouldbe finalized
rightbebefore
starting
the measurementby the following
procedure:A
few drops ofpreparation
shouldfinalizedright before
beforestarting thethe measurement
measurementby thethefollowing procedure:
procedure:preparation
shouldbe finalized
rightstartingbyfollowing
the liquid
membraneof
S-pentawas
spreadonbothsurfacesofa
MG90,
resultinginaMG90
coated
A
few
drops
of
the
liquidmembraneof
S‐pentawas
spreadonbothsurfacesofa
MG90,
resultinginA few drops of the liquid membrane of S‐penta was spread on both surfaces of a MG90, resulting inaMG90
coatedwith
S‐penta,andhereaftertheresultantmembraneiscalledSMG90.
Sideviewofwith aS-penta,
and hereafter
the resultant
membraneis called
SMG90. isSide
viewof SMG90
is illustrated
MG90 coatedwith S‐penta,
and hereafter
the resultant
membranecalledSMG90.
Side viewof
SMG90
is illustrated
illustrated
inwereFigure4. Both
Bothwithsurfaceswere covered
coveredwithnegatively
chargedplanes,ofsince
sincein Figure4. Bothsurfacescoverednegatively
chargedplanes,sincecharged
head group
SDS wasSMG90
isin
Figure4.
surfaceswerewithnegatively
planes,head group
groupof SDS
SDS
wasdissociatednegatively charged
chargedinthe dissociateddissociatedstate. A
Ato
SMG90
was mounted
mounted
to
the
head
of
was
negatively
thestate.
SMG90
wasnegatively
chargedin thestate. Ain
SMG90
was mounted
the setup
inFigureto
2.theCR wassetup inin Figure
Figure 2.
2. C
CRR waswas maintained
maintained constantconstant at
at 3.43.4 M
M for
for all
all thethe potential
potential measurements.
measurements. Potential
Potential inin
setup
maintained constant at 3.4 M for all the potential measurements. Potential in the left compartment
the leftleft compartmentcompartment inin reference
reference toto thethe right
right compartmentcompartment was
was measured
measured forfor various
various C
CLL.. Figure
Figure 5a5a
thein reference to the right compartment was measured for various CL . Figure 5a shows potential vs.
showspotential
potentialvs.
vs.–log[C–log[CLL].].Potential
Potentialincreases
increaseswith
withthethedecrease
decreaseof
ofC
CLL..Another
Anotherpotential
potentialmeasurement
measurementshows–log[C
Potential
increaseswiththe decreaseof Cmembranepotential
measurement
wasC‐penta.
carried out
L ]. carried
L . Anotherwasoutusing
usinganother
anothermembrane.
membrane.Another
Another membrane
usedwaswas thetheMG90
MG90coatedcoatedwith
withC‐penta.
wascarried out
usedusingHereafter,
another membrane.
membraneused wasthesurfaces
MG90 coatedwith C-penta.
Hereafter, thethe resultant
resultantAnothermembranecalled CMG90.
CMG90.
Both
were coatedcoatedwith thethe positively
positively
Hereafter, themembraneisis calledBothsurfaces werewithresultantmembraneiscalledCMG90.
Bothsurfaceswerecoatedwiththepositively
chargedplanes,charged planes,
planes, since
since head
head group
group ofof CTABCTAB was
was positively
positively charged
charged inin thethe dissociateddissociated state.
state. Potential
Potential
chargedsincemeasurement
head groupwasof CTABpositively
the dissociatedstate.
Potential
measurement
wascarriedwas
out bybyfollowingcharged
the samesameinprocedureas described
described
above.
Figure measurement
5b shows
showscarriedout
following
theprocedure
as
above.
Figure5bpotentialvs.
–log[CL]. Potential
decreaseswiththedecreaseofC
L.above.
Itisopposite
potential
behavior
to vs.
was carriedoutbyfollowingthesameprocedureas
described
Figure5bshows
potential
potential vs. –log[CL]. Potential decreases with the decrease of CL. It is opposite potential behavior to
Figure5a.
–log[C].
Potential
decreaseswiththedecrease
of
C
.
It
is
opposite
potential
behavior
toFigure5a.
Figure5a.
L
L
S-penta
S-penta
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—

SDS
SDS

S-penta
S-penta

MG90
MG90

1-pentanol
1-pentanol
OO
Na++
Na

—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—

SDS
SDS

1-pentanol
1-pentanol

OO
SS

-O

CH3
CH
3

OO

-O

—
—
Figure.
Sideview
viewofofSMG90
SMG90andandthestructure
ofof
SDS.
Figure4. 4.4.
Sideandthethestructure
structure
SDS.
Figure.
Side
view
of
SMG90
of
SDS.

potential
potential/ /mV
mV

200
200
150
150
100
100
50
50
0
0
-50
-50

(a)
(a)

-1
-1

1
1

0
0

1
1

2
2

3
3

4
4

5
5

2
2

3
3

4
4

5
5

-log[CL]]-log[CL

potential
potential/ /mV
mV

50
50
0
0
-50
-50
-100
-100
-150
-150
-200
-200

0
0

(b)
(b)

-1
-1

-log[CL]]-log[CL

Figure 5. Membrane potential generated across (a) SMG90 and (b) CMG90 against –log[CL].

Figure 5. Membrane potential generated across (a) SMG90 and (b) CMG90 against –log[CL].
Figure5. Membrane potential generated across (a) SMG90 and (b) CMG90 against –log[CL ].

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Both
SMG90
CMG90 are impermeable to ions. However, nonzero potential acrossmembrane(membrane
potential)
It wasin conflictwithnonzero
the basic
conceptacrossof membrane
Both
SMG90 andand
CMG90wasare observed.
impermeable
to ions.
ions.
However,potential
the
Both
SMG90
CMG90
are
impermeable
toHowever,nonzero potential
across thepotential
generation
mechanism[1–22].
More
concretely,itiswidelyacknowledged
thatnonzeromembrane(membrane
potential)
wasobserved.
It
wasinconflict
with
the
basic
conceptofmembrane (membrane potential) was observed. It was in conflict with the basic concept ofmembranepotential
generation
mechanism[1–22].
More
concretely,itiswidelyacknowledgedthatmembranepotentialisgenerated
due
to
the
passageofions
throughthemembraneaccordingmembrane potential generation mechanism [1–22]. More concretely, it is widely acknowledged thatto thenonzeromembranepotentialnonzero
is generated
generated
due totothe passage
passageof ionsions throughthroughthe membrane
membrane
GHKnonzero
equation[1,7]. However,potential
acrossthe impermeable
membrane
was actuallymembranepotential
is
due
the
of
the
according
to
the
GHK
equation[1,7].
However,nonzeropotential
acrosstheimpermeableaccordingto thenonzeropotential
the impermeable
generated
as shown
in GHK
Figureequation
5. Some [1,7].
peopleHowever,
may arguethat both
SMG90acrossand CMG90
had a number
membrane waswas actuallyactually generated
generated as
as shown
shown inin Figure
Figure 5.
5. SomeSome people
people may
may argue
argue that both
both SMG90
SMG90
membraneof pinholes
which wereinvisibly small
but large
enough forion passage.
Hence,that
the authors
carried
and
CMG90
had
a
numberofpinholeswhich
were
invisibly
small
but
large
enoughforionpassage.
and
CMG90
had
a
numberofpinholeswhich
were
invisibly
small
but
large
enoughforionpassage.
out further potential measurements in order to eliminate such a doubt.
Hence, thethe authors
authors carried
carried out
out further
further potential
potential measurements
measurements inin orderorder to eliminate
eliminate such
such aa doubt.
doubt.
Hence,
The
same
potential
measurement
wascarriedout bybythetheuseuseofofa toa membrane
KBMG90,
which
The
same
potential
measurement
wascarriedoutmembrane
KBMG90,which
The same potential measurement was carried out by the use of a membrane KBMG90, which
was completely
impermeable
to
the
ions,
in
place
of
SMG90
and
CMG90.
Bothsurfacesof
KBMG90
was completely
completely impermeable
impermeable toto thethe ions,
ions, inin place
place ofof SMG90
SMG90 andand CMG90.
CMG90. Both
Both surfaces
surfaces ofof KBMG90
KBMG90was
were were
coatedwithwith
S-penta,andthetheresultantmembranewasdenoted
denotedbyby
SKBMG90.
The
structurecoatedS‐penta,andresultantmembranewas
SKBMG90.
The
structureof ofwere coated with S‐penta, and the resultant membrane was denoted by SKBMG90. The structure of
SKBMG90isillustratedin
Figure6.
Bothsurfaceswerecoveredwithnegatively
chargedplanes.
SKBMG90isillustratedin
Figure6.
Bothsurfaceswerecoveredwithnegatively
chargedplanes.
SKBMG90 is illustrated in Figure 6. Both surfaces were covered with negatively charged planes.
Anotherpotential
measurement
wascarriedoutusinganother
membrane.The
Themembrane
membrane used
Anotherpotential
measurement
waswascarriedoutoutusing
another
membrane.
Anotherpotential
measurement
carriedusing
another
membrane.
Themembrane
used
was
the
KBMG90coatedwith
C‐pentainplace
of
S‐penta.
Hereaftertheresultantmembraneiscalled
was theKBMG90coated with
C-pentain place
S-penta.
Hereafter
the resultant
membrane
isis
used
was the KBMG90
coatedwith C‐penta
inof
place
of S‐penta.
Hereafter
the resultant
membranecalledCKBMG90.
Bothsurfaceswerecoveredwith
thepositively
chargedplanes.
Measuredcalled CKBMG90.
Both were
surfaceswere withcoveredthe positively
Measured
CKBMG90.
Both surfaces
coveredthewithpositively
chargedcharged
planes.planes.
Measuredpotential
potential profiles
profiles areare shownshown inin Figure
Figure 7.
7. TheThe potential
potential data
data shown
shown inin Figure
Figure 77 is
is virtually
virtually
potential
profiles are shown in Figure 7. The potential data shown in Figure 7 is virtually quantitatively same
quantitatively same
same asas thatthat inin Figure
Figure 5.
5. Hence,
Hence, it
it is concluded
concluded thatthat even
even thethe useuse ofof impermeable
impermeable
quantitatively
as thatin Figure 5. Hence,
it is concluded
that evenistheuse of impermeable
membraneinduces themembraneinducesthenonzeromembranepotential
againsttheprediction
bytheexisting
theory ofofmembraneinducesthe nonzero
membranepotential againsttheprediction
by theexisting
theorynonzeromembranepotential
againsttheprediction
bytheexisting
theoryofmembranepotential
membranepotential
generation
mechanism.
membrane potential generation mechanism.
generation mechanism.

1-pentanol
1-pentanol

—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—

MG90
MG90

SDS
SDS

MG90
MG90

—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—

conductive
conductiveadhesiveadhesive

KBMG90 S-penta
S-penta KBMG90
S-penta
S-pentaSDS
SDS

1-pentanol
1-pentanol

potential
potential/ /mV
mV

Figure6.
Sideview
viewofofSKBMG90
SKBMG90 coatedcoatedwith
S‐penta.
Figure6. 6.
Sidecoatedwith
with
S-penta.
FigureSide
viewof
SKBMG90
S‐penta.
200
200
150
150
100
100
50
50
00
-50
-50

potential
potential/ /mV
mV

(a)
(a)

(b)
(b)

-1
-1

00

11

22

33

44

55

-1
-1

00

11

22

33

44

55

-log[CL]]-log[C
L

50
50
00
-50
-50
-100
-100
-150
-150
-200
-200

-log[CL]]-log[CL

Figure
7. Membrane
Membranepotential
generatedacrossacross(a)(a) SKBMG90
SKBMG90 andand(b)
CKBMG90
against–log[CL]
Figure
7. Membranepotential
generated
and(b)(b)CKBMG90CKBMG90
against–log[CL ].
Figure7.
potential
generated
across(a)
SKBMG90
against–log[CL]

Membranes 2016, 6, 11

7 of 14

Membranes
Membranes 2016,
2016, 6,
6, 11
11

77 of
of 14
14

4.1.2.
Exp.
II IIII
4.1.2.
Exp.
4.1.2.
Exp.
Potential
measurement
described
inin
theSectionPotential
measurement
described
theSection3.2
wascarriedout.
Thepotential
between
0.3
Potential
measurement
described
intheSection3.2
3.2waswascarried
carriedout.
out.TheThepotential
potentialbetween
between0.3
0.3M
NaCl
and
0.5
M
KCl
solutionsseparatedbyasilverwire&
S-pentawasmeasuredasafunctionoftime.
M
M NaCl
NaCl andand 0.5
0.5 M
M KCl
KCl solutions
solutions separated
separated byby aa silver
silver wire
wire && S‐penta
S‐penta was
was measured
measured as
as aa function
function
Spontaneous
potential oscillation
was observed
as shown
Figureofpotential
was
as
shown
in
Figureof time.
time. Spontaneous
Spontaneous
potential oscillation
oscillation
was observed
observed
asin
shown
in8a.
Figure 8a.
8a.
Potential
oscillation
betweenvarious
two twoelectrolytic
solutionshas been
and analyzed
Potential
oscillation
betweenvariouselectrolytic
solutions
has
been
and
Potential
oscillation
betweenvarious
twoelectrolytic
solutionshas observed
been observed
observed
andofup
oscillation
byanalyzed
a numberbyof aresearch
up to groups
date[33,36–39,41–49].
Although the Althoughoscillation
mechanism
has
analyzedbya numbernumbergroupsof researchresearchgroupsup toto datedate [33,36–39,41–49].
[33,36–39,41–49].
Although thetheoscillation
mechanism
has
not
been
fully
elucidatedyet,theoccurrenceofpotential
oscillation
sometimesisnot beenyet,
fully
yet,
occurrenceof potential
oscillation
sometimes
notmechanism
been fully has
elucidated
theelucidated
occurrence
ofthe
potential
oscillation
sometimes
is attributed
to istheattributedion
betweensolutionsjust
indicatedby
attributed toto thethetransmembrane
ion transfer
transfer
between two
two electrolyticelectrolytic
solutionsjust like
like
indicatedby oftransmembraneiontransmembranetransfer between
twoelectrolytic
solutionsjust likeindicatedby theconcept
theconcept
GHK
IfIf notattributedtotransfer,
itit hasthe equation
concept ofof[33,36–39,41–49].
GHK equation
equation [33,36–39,41–49].
[33,36–39,41–49].
not fully
fully
attributed
to thethe ionionhastransfer,has beenbeen
GHK
If not fully attributed
to theion transfer,itbeen believed
that
believed
that
the
ion
transfer
betweentwoelectrolytic
solutions
plays
a
role
of
potential
oscillation
believed
that
the
ion
transfer
betweentwoelectrolytic
solutions
plays
a
role
of
potential
oscillation
the ion transfer between two electrolytic solutions plays a role of potential oscillation induction to
inductionsomeextent.
setup
illustrated
Figure33 neverallowedionbutinduction
toOur
some
extent. Our
Our experimental
experimental
setupinillustrated
innever
Figureneverionallowedion transfer,transfer,but
someextent.toexperimental
setup illustrated
Figure 3inallowedtransfer,but potential
potential
oscillationwas
induced.
Useofasilverwire&
C‐pentaasaseparator
intervening
0.3
potentialwas
oscillation
wasUseinduced.
Use ofwire
a silverwire & as
C‐penta
as a separator
intervening
0.3 M
M
oscillationinduced.
of a silver& C-penta
a separator
intervening
0.3 M NaCl
and
NaCl
and
0.5
M
KCl
solutionsalso
resultedinthespontaneous
inductionofpotential
oscillation
as
NaCl
and
0.5
M
KCl
solutionsalso
resultedinthespontaneous
inductionofpotential
oscillation
as in
0.5 M KCl solutions also resulted in the spontaneous induction of potential oscillation as shown
shown
shown inin Figure
Figure 8b.
8b.
Figure 8b.
Potential
Potential oscillation
oscillation became
became more
more obvious
obvious byby thethe useuse ofof thethe new
new solution—mixture
solution—mixture ofof NaCl,
NaCl,
Potential oscillation became more obvious by the use of the new solution—mixture of NaCl, EtOH
EtOH
EtOH andand deionizeddeionized water—inwater—in place
place ofof 0.30.3 M
M NaCl,NaCl, where
where thethe concentration
concentration ofof NaCl
NaCl andand EtOH
EtOH ininand deionized water—in place of 0.3 M NaCl, where the concentration of NaCl and EtOH in the newthethe new
new solution
solution was
was 0.3
0.3 M
M andand 11 M,
M, respectively.
respectively. Potential
Potential vs.
vs. timetime between
between thethe new
new solution
solution andandsolution
wasacross
0.3 M andseparator
1 M, respectively.
Potential
vs. time between
the new
solution are
and 0.5 M in
KCl
0.5
0.5 M
M KCl
KCl across thethe separator ofof aa silver
silver wire
wire && S‐penta
S‐penta andand ofof aa silver
silver wire
wire && C‐penta
C‐penta are shown
shown inacrossthe9a,b,separatorof a silver& S-penta
and of abecame
silver wire
& clearly
C-pentaare shown
Figure in
9a,b,Figurerespectively.
As
stated,themoreWe
Figure9a,b,respectively.
Aswirestated,the oscillation
oscillation
becamemore
clearly induced.
induced.
Weinnoticed
noticedinrespectively.
As
stated,theoscillation
becamemore
clearly
induced.
We
noticedinFigures8
andFiguresFigures 88 andand 99 thatthat thethe potential
potential peaks
peaks were
were negative
negative going,
going, when
when aa silver
silver wire
wire && S‐penta
S‐penta was
was 9
that
the potential
peaks
negativea silverwire& S-penta
employed,while
employed,while
thepotential
peaks
were
positivegoing,
when
aa silver
wire
&
was
employed,
while
the werepotential
peaksgoing,
were when
positivegoing,
when
silverwaswire& C‐penta
C‐pentawasthepotential
peaks
were
positivegoing,
whenasilverwire&
C-pentawas
employed.
employed.
employed.

potential // mV
mV
potential

-30
-30
-50
-50
-70
-70
-90
-90
4000
4000 4500
4500 5000
5000 5500
5500 6000
6000

(a)
(a)

time
time//ss

potential // mV
mV
potential

95
95
90
90
85
85
80
80
2500
2500

(b)
(b)

3500
3500

4500
4500

5500
5500

time
time//ss

Figure
8. Membranepotential
generated
across& S‐pentaand (b)a silver wire&
C‐penta.
FigureMembranepotential
potentialgenerated
generatedacrossacross(a)(a) aaasilver
silver wire
wire&&
C‐penta.
Figure8. 8.
Membrane(a)silverwire &&S‐penta
S-pentaandand(b)(b)aasilver
silverwire
wire
C-penta.

potential // mV
mV
potential

-110
-110
-120
-120
-130
-130
-140
-140
-150
-150
2000
2000

(a)
(a)

4000
4000

6000
6000

8000
8000

time
time//ss

potential // mV
mV
potential

120
120
110
110
100
100
90
90

(b)
(b)

00

1000
1000 2000
2000 3000
3000 4000
4000 5000
5000

time
time//ss

Figure9. 9.
Membrane(a)silverwire
wire&&S‐penta
S-pentaandand(b)(b)aaasilver
silverwire
C-penta.
FigureMembranepotential
generatedwire&
C‐penta.
Figure9.
Membranepotential
potentialgenerated
generatedacrossacross(a)(a) aa silverwire&
S‐pentaand(b)silverwire&&
C‐penta.

Membranes 2016, 6, 11

8 of 14

Membranes 2016,11
4.2. Mechanismof 6,Potential
Generation across the Impermeable Membrane

8 of 14The
potential behaviors
Exp. I and
II. Exp
I are discussed
and explained using a proposed model.
4.2. Mechanismof Potential in
Generation
acrossthe Impermeable
Membrane
Experimental results shown in Figures 5 and 7 are all membrane potential across an impermeable
The potential behaviors in Exp. I and II. Exp I are discussed and explained using a proposed
membrane. According to the GHK equation, the nonzero membrane potential is generated only
model. Experimental results shown in Figures 5 and 7 are all membrane potential across an
acrossthe semi-permeable
membrane,
GHK
equationthat membrane
the membranepotentialisimpermeable
membrane.
According since
to thethe
GHK
equation,
thestates
nonzeropotentialisdeterminedbytheconcentrationofindividual
ions
in
the
electrolytic
solutionsandthemembranegenerated only across the semi‐permeable membrane, since the GHK equation states that thepermeability
those ions
[1,7]. Without
theconcentration
membrane permeability
ions,equationmembranetopotential
is determinedby theof individual toions
in thethe GHK
electrolytic
solutionsthe membrane
to those ions
[1,7]. Without
permeability
collapses
andandit implies
that thepermeability
nonzero membranepotential
cannotthebemembrane
generated.
However, theto ions,
the GHKequationcollapses induced
and it implies
that theinnonzero
be thenonzeropotential
wasundoubtedly
as shown
Figuresmembrane
5 and 7. potential
Figure cannot
10 shows
generated.
However,thenonzeropotential
wasundoubtedly
inducedasshown
inFigures5
and7.
experimentally measured membrane potentials shown in Figures 5 and 7 and the membrane potentials
Figure10showstheexperimentallymeasuredmembranepotentials
shownin
Figures
5
and
7
and
the
computed by employing GHK equation by appropriately choosing the membrane permeability of PK
membrane potentials computed by employing GHK equation by appropriately choosing theand PCl , where the GHK equation employed is given by Equation (1). Concerning Equation (1), [K+ ]Lmembranepermeability of PK and PCl, where the GHK equation employed is given by Equation(1).
and [K+ ]R represent K+ concentrationin the left and right solutions, respectively. [Cl´ ]L and [Cl´ ]RConcerning Equation (1), [K+]L and [K+]R represent K+ concentration in the left and right solutions,representCl´ concentration
the left and right solutions, respectively. PK and Prespectively.
Cl represent therespectively.
[Cl−]L and [Cl−]in
R represent Cl− concentration in the left and right solutions,+´membranepermeability
tomembrane
K and Cl
, respectively.
Datashown withDataan shown“ˆ” mark
represents
PK and P
Cl represent thepermeability
to K+ and
Cl−, respectively.
with an“×”the computed
membranepotential.
Figure10 indicatesthatappropriately
choosingchoosing
membranemark represents
the computed
membranepotential.
Figure 10
indicatesthat appropriately
membraneand PCl can
reproducethe experimentallyobtained membrane
permeability
PKpermeability
and PCl canPKreproduce
theexperimentallyobtained membranepotential,potential,
even thougheventhoughthemembrane
actually
used
for
the
experimentis
impermeable
to
ions.
Some
scientists
the membrane actually used for the experiment is impermeable to ions. Some scientists acknowledged
acknowledged
the quantity ofof P
permeabilityof P does notmeannecessarilymean membrane
the actual membranethat thequantity ofthat
permeability
does not necessarily
the actual
permeability
permeability
to
ion
[29],
or
the
quantityofpermeability
of
P
is
not
necessarily
constant
but isto ion [29], or the quantity of permeability of P is not necessarily constant but is dependent
on iondependent on ion concentration [30], but such a treatment for theoretical evaluation of membraneconcentration [30], but such a treatment for theoretical evaluation of membrane potential is sort ofpotential is sort of makeshift evaluation for obtaining the desired theoretical membrane potential
makeshift evaluation for obtaining the desired theoretical membrane potential without any reasonable
without any reasonable justification. Therefore, the authors doubt the validity of GHK equation.
justification.
Therefore,
the authors
theisvalidity
GHK equation.
thus
believe the
The authors
thus believe
the GHKdoubt
equationa wrongof
concept.
Now, theyTheneedauthors
to find out
a theory
GHKalternativeequation isawrong
concept.
Now,
they
need
to
find
out
a
theoryalternative
to
the
GHK
equation.
to the GHK equation.

RT PKP “KK` sL ` PCl
P r ClCl´ sR
RT∆V∆V “ ´ F lnln P “ K`
P r ClCl´ sLF PK K sR ` PCl

(1)

(1)

potential / mV

200
150
100
50
0
-50
-1

0

1

(a)

2

3

4

5

3

4

5

-log[CL]potential / mV

50
0
-50
-100
-150
-200

(b)

-1

0

1

2

-log[CL]

FigureMembranepotential
potential shown
(○ (#
mark)
and and7a (● Figuremark) andcomputed
Figure10. 10.
(a) (a)MembraneshownininFigures
Figure5a5a
mark)
7a the( mark)and the= 0.008mark);(ˆ(b)
membranepotential
based onthe onGHK
assuming
PK = 1 andcomputed
membranepotential
based
theequation
GHK equation
assuming
PK =PCl1 andPCl (×= 0.008mark);
Membranepotential
shownin
Figures
5b
(○
mark)
and
7b
(●
mark)
and
the
computed
membrane(b) Membrane potential shown in Figure 5b (# mark) and Figure 7b ( mark) and the computed
potential
based onbased
the GHKequation
K = 0.008 and PCl = 1 (× mark).
membranepotentialon theGHKassuming
equationPassuming
PK = 0.008 and PCl = 1 (ˆ mark).

One of the authors of this paper, Tamagawa, has studied the membrane potential across theOneof the authorsof forthisthepaper,has studied
the membranepotential
acrossimpermeable
membranepast 10Tamagawa,years. He reached
the conclusionthat the GHK
equation
is a theimpermeable membrane for the past 10 years. He reached the conclusion that the GHK equation is a
wrong concept and the adsorption theory advocated by G. Ling is the right theory as the membraneMembranes 2016, 6, 11

9 of 14

Membranes 2016, 6, 11

9 of 14potential generation mechanism [1,7,21,22]. As described in the introduction, Ling has emphasized thatthe membranepotentialof adsorption
cell is basicallycausedby theofright
mobileionsasonto
the adsorption
wrong concept
and thetheoryadvocatedby adsorption
G. Ling is thetheorythe membranesites ofa cell. The
authors
would liketo propose
mechanism
about
this nonzero
potential
potential
generation
mechanism[1,7,21,22].
As adescribed
in theintroduction,
Ling membrane
has emphasizedthat theacrossmembranepotential of cellis basicallyby theadsorptionof mobile ions
onto thegeneration
the impermeable
membraneby caused
employing
theLing’s adsorption
theory.
adsorption
a cell. Thepotential
authors would
likeshownto propose
a mechanism
about thisbynonzeroFirstof all,sites
the ofmembranebehavior
in Figure5a is explained
employingmembranepotential
generation
acrosstheimpermeable
membranebyemployingthethe Ling’s adsorption theory. The adsorption theory states that the adsorption of mobile Ling’sions in theadsorption
theory.
electrolytic
solutionon the membrane surface causes the nonzero membrane potential [1,7]. Figure 11
First of all, the membrane potential behavior shown in Figure 5a is explained by employing theshows the ion distribution in the two electrolytic solutions separated by SMG90, where the KCl
Ling’s adsorption theory. The adsorption theory states that the adsorption of mobile ions in theconcentration in the right solution is assumed to be higher than that in the left solution in thiselectrolytic solution on the membrane surface causes the nonzero membrane potential [1,7]. Figure
illustration.
K+distribution
concentration
theelectrolytic
right solution
is quitehigh,bymostof thenegativecharge11 showsSince
the ionin theintwo
solutionsseparated
SMG90,
where
the KClof theconcentration
SDS plane (hereafter
R-SDS
plane) atinterface
SMG90
and theinrightin the rightcalled
solutionis assumed
to thebe higher
thanbetween
that in theleft solution
this KCl+ concentration
solutionis neutralized
the adsorptionof right
K+ (seeFigurethemostotherofhand,most ofcharge
the negative
illustration.
Since Kbyin thesolutionis 11).
quiteOnhigh,
the negativeof
theofSDS(hereafter
called R‐SDS
the interface
between SMG90
andthe right
chargetheplane
SDS plane(hereafter
called plane)
R-SDSatplane)at the interface
between
SMG90
andKClthe leftsolution isis notneutralized
by thesinceadsorptionof K+ (see Figure11). solution
On the otherhand,of 11).
theKCl solution
neutralized,
K+ concentrationin the left
is low(see mostFigurenegativecharge
of
the
SDS
plane
(hereafter
calledR‐SDS
plane)
attheinterface
between
SMG90
The mobile ions in the right solution distributes in accordance with the Boltzmann distribution+ concentration in the left solution is low (seeandleft KCl solution
is notneutralized,
since KR-SDS
underthetheinfluenceof slightly
negatively
chargedplane, while the mobile ions in the left
Figure 11).
solution distributes in accordance with the Boltzmann distribution under the influence of greatly
The mobile ions in the right solution distributes in accordance with the Boltzmann distribution
negatively
charged L-SDS plane. Therefore, the potential profile must be given as drawn in Figure 11
under the influence of slightly negatively charged R‐SDS plane, while the mobile ions in the left
with solution
dotted line.
Membranepotential
is experimentallymeasured using
electrodes.
Those two
distributes
in accordancewiththe Boltzmann distribution
under twothe influenceof greatly
electrodes
areinserted
into
the
bulk
phases
of
left
and
right
solutions,
respectively.
Hence,
thepotential
negatively charged L‐SDS plane. Therefore, the potential profile must be given as drawn in Figure
measuredis indicatedbyMembrane“observe potential”
Figure 11, where
the potential
detectedby theThoseelectrode
11 withdotted line.
potential isinexperimentallymeasuredusing twoelectrodes.
+ concentrationelectrodes
areisinserted
into the potential
bulk phases
Hence,
in thetwo
rightsolution
the reference
ofof0 left
mV.andAsright
longsolutions,as the Krespectively.
inthe
the leftpotential
measuredis indicatedby “observe
potential”
in Figure
11, where
the potential
by since
solution
is lowerthan thatin the rightsolution,the observed
potential
is expected
to bedetected
positive,+ concentration
the electrodein the rightinsolution
is the withreference
potentialdistributionof 0 mV. As longas thethe mobileions distribute
accordance
Boltzmann
under
theKinfluenceof greatly
in the left solution is lower than that in the right solution, the observed potential is expected to be
negatively
charged L-SDS plane and slightly negatively charged R-SDS plane. In fact, the potential
positive, since the mobile ions distribute in accordance with Boltzmann distribution under theexperimentally observed was basically positive as shown in Figure 5a. The more negative the charge
influence of greatly negatively charged L‐SDS plane and slightly negatively charged R‐SDS plane.
densityof L-SDS plane becomes, the higher the potential observed is expected to be. The experimental
In fact, the potential experimentally observed was basically positive as shown in Figure 5a. The
resultmore
is innegativeline withexpectation
shownplanein Figure
5a. Just
oppositeis induced,
thethechargedensity asof L‐SDS
becomes,the higher
the phenomenon
potential observediswhenexpected
CMG90towas
usedexperimental
in place of result
SMG90
aslineshown
5b, since
the headchargeCTAB
be. Theis inwith intheFigureexpectation
as shown
in Figure5a. ofJust
is positive.
opposite phenomenon is induced, when CMG90 was used in place of SMG90 as shown in Figure 5b,
since the head charge of CTAB is positive.

+ — + —+—+ + —+ +—+ +——+ — + —
—
— + —
—+
—
—+ +
+ +

—

—

+ +—
—
+ —
+
+ — +—
—
—
+ —
+
+ + —

—

—

+

observed
potential

L-SDS plane

+ K+
— Cl-

R-SDS plane

Figure 11. Ion distribution of two electrolytic solutions separated by a SMG90.

Figure 11. Ion distribution of two electrolytic solutions separated by a SMG90.

Ling’s adsorption theory suggests that the entire structure of membrane is not the primary

Ling’sadsorption
theorysuggeststhat theentire structureof membrane
is notthe primaryfactor in
the nonzero
membranepotential
generation.
Ling’s adsorption
theorysuggeststhat thefactor
ion membraneadsorption on
the membraneadsorption
sites
plays a central
rolesuggests
for the inductionofin themobile
nonzeropotential
generation.
Ling’sadsorption
theorythat the mobile
nonzero membranepotential, i.e.,even thoughtheplaysdifferently
structured
membranes
are usedfor
ion adsorption
on the membraneadsorption
sites
a centralrole forthe inductionof nonzero
separating
two electrolytic
thedifferently
membrane structured
potentials observed
acrossmembranepotential,i.e., evensolutions,though themembranes
arethoseusedmembranes
for separatingmust be the same, as long as the structure of adsorption sites on those membranes are same each
two electrolytic solutions, the membrane potentials observed across those membranes must be theother. The surface structure of SKBMG90 was same as that of SMG90 (see Figures 4 and 6),
same, as long as the structure of adsorption sites on those membranes are same each other. The surface
although the entire structure of SKBMG90 was totally different from that of SMG90. As expected,
structureof SKBMG90 was same as that of SMG90 (see Figures 4 and 6), although the entire structure
following the Ling’s adsorption theory, the actual potential behavior across the SKBMG90 wasof SKBMG90 was totally different from that of SMG90. As expected, following the Ling’s adsorption
theory, the actual potential behavior across the SKBMG90 was virtually same as that across the SMG90

Membranes 2016, 6, 11

10 of 14as shown
in Figure
10a. This concept is also true for the potentials across the CKBMG90 and
Membranes
2016, 6, 11
10 ofCMG90
14
as shown in Figure 10b. However, one may still argue that the GHK equation is applicable only
as that acrossthe SMG90 asmembrane
shown in Figure
This conceptmembraneis also true (SKBMG90
for theto thevirtuallysystemsame
employinga semipermeable
not an10a.
impermeable
potentials across the CKBMG90 and CMG90 as shown in Figure 10b. However, one may still argue
and CKBMG90 are completely impermeable), hence, the argument so far described is meaninglessthat the GHK equation is applicable only to the system employing a semipermeable membrane notfromantheimpermeable
beginning. membrane
However, (SKBMG90
Tamagawaand
andCKBMG90
Morita alreadyclarified that point in their previous
are completely impermeable), hence, thereports[21,22].soThey
found thatthe actual potential
between two
KCl solutions
by theargument
far describedis meaninglessfrom the beginning.
However,Tamagawaseparated
and Morita
impermeable
membranewasvirtually
same
as
the
experimentallymeasuredpotential
separatedalready clarified that point in their previous reports [21,22]. They found that the actual potential by
the semipermeable
membrane.
They confirmedthat the latter
potential(across
thesamesemipermeable
between two KClsolutions separated
by the impermeable
membranewasvirtuallyas theexperimentallymeasured potential
separated by
They confirmed
membrane)was quantitatively
well reproducibleby thethe semipermeable
GHK equation,membrane.
and this confirmationsuggeststhat thepotential(across
the semipermeable
membrane)was quantitatively
well reproduciblethat eventhelatter
formerpotential(across
the impermeable)
is reproducibleby the GHK
equation as well.
the GHK equation,
this confirmationsuggests thatthrougheven thethe
formerpotential(acrosstheThis byconsequence
made usand
wonder
if the ion permeation
membranewasthe primary
impermeable) is reproducible by the GHK equation as well. This consequence made us wonder if
cause of membrane potential generation. Instead, Tamagawa and Morita proposed an alternative
the ion permeation through the membrane was the primary cause of membrane potential
mechanism of potential generation across the impermeable material as well as the semipermeable
generation. Instead, Tamagawa and Morita proposed an alternative mechanism of potential
membrane[21,22]. The mechanism proposed was based on the Ling’s adsorption theory [1,7], and it isgeneration across the impermeable material as well as the semipermeable membrane [21,22]. The
basicallythesametheory was
explained
above
using Figure
11, i.e.,the[1,7],
ion adsorption
on the themembraneismechanismproposed
based onthe Ling’s
adsorption
theoryand it is basicallysame
induced,even
when themembrane
is notbut semipermeable.
Consequently,
it results
theoryexplained
above
using Figure
11, impermeable
i.e., the ion adsorption
on the membrane
is induced, evenin thewhen
nonzeromembranepotential
generation.
This mechanism
was in harmony
withpotential
the membrane
is notimpermeable
but semipermeable.
Consequently,
it results inthe thenonzeromembranepotential
generation.
Thismechanism
was in harmony
behaviorsfor bothimpermeable
andpermeable
membranecases. with the potential behaviors forbothimpermeable
andpermeable
membranecases.
To sum up, there is not a firm reason to justify the GHK equation which states that the membrane
Togenerated
sum up, by
there
notpermeationa firm reason
to justify
the GHK equation
which statesthat potential
thepotential istheisionthroughthe semipermeable
membrane.
Nonzeromembrane potential is generated by the ion permeation through the semipermeable membrane.
is generated even across the impermeable membrane, and even the membrane potential across theNonzero potential is generated even across the impermeable membrane, and even the membrane
semipermeable membrane is explicable by the theory based on the Ling’s adsorption theory instead
potential across the semipermeable membrane is explicable by the theory based on the Ling’sof GHKequation [1,7]. We do not have a decisive reason to rule out Ling’s adsorption theory as aadsorption theory instead of GHK equation [1,7]. We do not have a decisive reason to rule out
membranepotential generation
mechanismat all. generation mechanism at all.
Ling’s adsorption
theory as a membranepotential
4.3. Mechanismof Potential
Oscillation
4.3. Mechanismof Potential
Oscillation

potential / V

Ling’sadsorption
theorycan explain
the potential
oscillation
across acrossthe impermeable
membrane
Ling’sadsorption
theorycan explain
the potential
oscillation
the impermeable
membraneshown
and 9Typicalas well profile[1,7]. Typicalprofile ofpotential
oscillating
potential between
generated0.3 M
shownin Figures
8 andin9Figures
as well8[1,7].
of oscillating
generated
M NaCland 0.5separated
M KCl solutions
separated
byS-penta
a silver iswire& S‐penta
illustrated
NaClbetween
and 0.5 0.3
M KCl
solutionsby a silver
wire &
illustrated
inisthedashed insquarethe dashedsquarein Figure 12,potential
and this oscillating
potential profile
in Figure
12, andthis oscillating
profile is analyzed
here. is analyzed here.

S-penta

④

②
①

③
④

②
①

③

time / stypical oscillating potential profile

Sol-L

①

②

＋

＋ ＋

③

④

＋ ＋ ＋ ＋ ＋

: SDS
＋ : Na +Figure12. Typicalpotential
profileand0.5
0.5MMKCl
KClsolutionsseparateda silverFigure12. Typicalpotential
profilebetween
between 0.3
0.3 M NaCl
NaCl andsolutionsseparatedby a bysilver& S‐penta
is illustrated
dashedsquaresquare andand thethe molecularmechanismof potential
wire wire& S-penta
is illustrated
in in
thethedashedmolecularlevel
level
mechanismof potential
oscillationinducedtheinterface
interface between
andandSol‐Lis illustrated
in dotted
oscillationinducedat at
thebetweenS‐septa
S-septa
Sol-L
is illustrated
in square.
dotted square.

Membranes 2016, 6, 11

11 of 14

It is speculated that the potential oscillation is induced at the interface between S-penta and Sol-L.
Therefore, molecular level electrochemical phenomenon at the interface is discussed. Once S-penta
and Sol-L comes into contact with each other, SDS molecules tend to form a monolayer at the interface
between them, and K+ in Sol-L are adsorbed on the negative head charge of SDS molecule as illustrated
in 1 in the dotted square in Figure 12, i.e., a capacitor is formed at the state 1 . Therefore, thepotential slightly increases as indicated by 1 in the potential profile in the dashed square in Figure 12.
As time goes by, SDS molecules come to form a more densely charged capacitor as illustrated in thedotted square in Figure 12, the state 1 Ñ the state 2 Ñ the state 3 . Consequently, the potential
increases as indicated by 1 Ñ 2 Ñ 3 in the potential profile in the dashed square in Figure 12.
SDS concentration at the interface between S-penta and Sol-L increased further as time went by, andonce SDS concentration reached critical micelle concentration (CMC), the capacitor collapsed and a
micelle formed as illustrated in the state 4 in the dotted square in Figure 12. At the very same moment
when the capacitor collapses, the potential abruptly plunged as indicated by 4 in the potential profile
shown in Figure 12. Since this process (the state 1 through 4 ) repeated, the potential oscillation wasobserved. It is speculated that the potential oscillation, when C-penta was used, is induced basicallyby the same mechanism. Since the sign of head charge of CTAB contained in C-penta is just opposite
to the sign of head charge of SDS, the potential peaks went positive going, while the potential peaks
went negative going, when S-penta was used.
Potential oscillation mechanism we proposed is basically same as the widely and currently
accepted mechanism [38–49]. It suggests that the ion transfer between two aqueous solutions acrossthe membrane is not needed at all for the generation of oscillating potential (action potential-like
potential), and potential oscillation is caused merely by the mobile ion adsorption-desorption process
occurring at the surface of surfactant monolayer, and that mechanism is basically within the conceptof Ling’s adsorption theory [1,7]. In the electrochemistry research field, people involved in theinvestigation on the potential oscillation phenomena have employed the fundamentally same theory
as Ling’s adsorption theory without knowing it.
From the standpoint of nonlinear dynamics, Yoshikawa et al. proposed a mathematical modelof the potential oscillation, which was induced between two electrolytic solutions separated by oil
membrane [41]. They emphasized that the repetition of surfactant monolayer formation-destruction
process at the interface between electrolytic solution and oil membrane caused the potential oscillation.
Their theory was mathematics- and physics-based rigid theory. Although they employed someassumptions for building the mathematical model such that van der Waals equation for the surfacepressure vs. surfactant concentration was expressed by – Z + Z3 (Z: surfactant concentration), thoseassumptions are quite plausible from the standpoint of chemistry and physical chemistry. Although
their theory did not offer the molecular level mechanism of how the repetition of surfactant monolayer
formation-destruction process induced the nonzero potential, it is quite reasonable theory, as longas the repetition of surfactant monolayer formation-destruction process can be interpreted as therepetition of capacitor formation-destruction process as illustrated in Figure 12. Hence, the molecularlevel model in Figure 12, which is based on the Ling’s adsorption theory, is quite plausible from thestandpoint of mathematics, physics, chemistry and physical chemistry.
We would like to raise a question again. Why do we have to use the GHK equation instead of
Ling’s adsorption theory in physiology, despite the fact that the successful outcomes have been realized
in the electrochemistry research field by the fundamentally same theory as the Ling’s adsorption theory
as so far described? What is the primary reason to attach more importance to the GHK equation than
to the Ling’s adsorption theory in physiology research field? As described in at the end of Section 4.2,
we do not have a decisive reason to rule out the Ling’s adsorption theory as a membrane potential
generation mechanism at all. It is necessary to put forth a firm explanation to rule out the Ling’s
adsorption theory, if someone would like to fully justify GHK equation: We need scientific reasons why
the Ling’s adsorption theory is not that suitable as a membrane potential generation mechanism or why
we have to use distinct two theories—GHK equation and another theory fundamentally same as Ling’sMembranes 2016, 6, 11

12 of 14

adsorption theory—in accordance with the research field physiology or electrochemistry. We believethat Ling’s adsorption theory is a simpler, more comprehensive and more suitable theory than GHK
equation for explaining membrane potential behavior. Even though still people think that the GHK
equation is a valid theory, we at least need to find a reason to rule out the Ling’s adsorption theory.
5. Conclusions
Membrane potential can even be generated across the impermeable membrane and action
potential-like potential can be induced in nonliving system containing no ion channels or pumps.
The membrane potential generation including the induction of action potential does not appear to
be a phenomenon particular to the living system only. Without living or biological matters, such aphenomenon can be induced. The authors of this paper disagree with the current theory of membranepotential generation mechanism. The most simple and plausible explanation of those observations is
the Ling’s adsorption theory. Electrical properties of cell are explicable without the functionalities of ionchannels and/or pumps. Therefore, it is not fully nonsensical to speculate that the electrical propertiesof living system are governed by the same mechanism as what governs the electrical properties ofnonliving system. Ling’s adsorption theory is a quite comprehensive theory and, it is applicable toboth living and nonliving systems as an explanation of their electrical behavior.
People might argue that because Ling’s adsorption theory can explain the membrane potential
behavior, it does not follow that the GHK equation is doubtful. However, the reverse is also true. i.e.,
because GHK equation can explain the membrane potential behavior, it does not follow that the Ling’s
adsorption theory is doubtful.
Ling’s adsorption theory attributes the membrane potential generation to the mobile ion
adsorption on the adsorption sites, and undoubtedly the mobile ion adsorption on the adsorption siteof membrane takes place whether the membrane is permeable or not. Therefore, it is necessary at least
to find a mechanism of eliminating the potential generated by ion adsorption on the adsorption sitesof “semipermeable” membrane, as long as they believe the full validity of GHK equation.
The readers of this paper might feel more or less uneasy with the discussion described in thispaper, since the authors did not show any explicit mathematical expression of Ling’s adsorption theory.
However, the authors are now in the middle of more comprehensive and quantitative study of Ling’s
adsorption theory by developing the mathematical formulas of Ling’s adsorption. Hopefully, we canpublish it within a few months.
Acknowledgments: The authors would like to express our gratitude to The MIKIYA Science and Technology
Foundation for the financial support for conducting this work. We also would like to express our gratitude to
Takeda Sangyo Co., Ltd. (Tokyo, Japan) for providing us with thin urethane films MG 90.
Author Contributions: Tamagawa designed whole study described in this study. Funatani is a student Tamagawa
supervises. Ikeda contributes to the theoretical analysis part of this paper.
Conflicts of Interest: The authors declare no conflict of interest.

References
1.
2.
3.
4.

5.

Ling, G.N. A Revolution in the Physiology of the Living Cell; Krieger Publishing Co.: Malabar, FL, USA, 1992.
Sachs, F.; Qin, F. Gated, ion-selective channels observed with patch pipettes in the absence of membranes:
Novel properties of a Gigaseal. Biophys. J. 1993, 65, 1101–1107. [CrossRef]
Bogner, P.; Nagy, E.; Miseta, A. On the role of Na, K-ATPase: A challenge for the membrane—Pump andassociation-induction hypotheses. Physiol. Chem. Phys. Med. NMR 1998, 30, 81–87. [PubMed]
Ling, G.N. Explaining on request a correlation between membrane Na, K-ATPase and K+ content inerythrocytes and other findings in the preceding paper. Physiol. Chem. Phys. Med. NMR 1998, 30, 89–97.
[PubMed]Erisir, A.; Lau, D.; Rudy, B.; Leonard, C.S. Function of specific K+ channels in sustained high-frequency firingof fast-spiking neocortical interneurons. J. Neurophysiol. 1999, 85, 2476–2489.

Membranes 2016, 6, 11

6.
7.
8.
9.
10.
11.
12.
13.
14.
15.

16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.

13 of 14

Clay, J.R.; Shrier, A. Action potentials occur spontaneously in squid giant axons with moderately alkaline
intracellular pH. Biol. Bull. 2001, 201, 186–192. [CrossRef] [PubMed]
Ling, G.N. Life at the Cell and Below-Cell Level: The Hidden History of a Fundamental Revolution in Biology;
Pacific Press: New York, NY, USA, 2001.
Sahin, A.; Cengelogu, Y.; Ersoz, M. The membrane potentials of periderm and cuticular membranes.
Turk. J. Chem. 2002, 26, 777–782.
Schumacher, M.; Adelman, J.P. An open and shut case. Nature 2002, 417, 501–502. [CrossRef] [PubMed]
Jiang, Y.; Lee, A.; Chen, J.; Cadene, M.; Chalt, B.T.; MacKinnon, R. The open pore conformation potassiumchannels. Nature 2002, 417, 523–526. [CrossRef] [PubMed]
Jiang, Y.; Lee, A.; Chen, J.; Cadene, M.; Chalt, B.T.; MacKinnon, R. Crystal structure and mechanism of
a calcium-gated potassium channel. Nature 2002, 417, 515–522. [CrossRef] [PubMed]
Clapham, D.E. TRP channels as cellular sensors. Nature 2003, 426, 517–524. [CrossRef] [PubMed]
Bernard, C.; Johnston, D. Distance-dependent modifiable threshold for action potential back-propagation in
hippocampal dendrites. J. Neurophysiol. 2003, 90, 1807–1816. [CrossRef] [PubMed]
Bean, B.P. The action potential in mammalian central neurons. Nature 2007, 8, 451–465. [CrossRef] [PubMed]
Liu, P.W.; Bean, B.P. Kv2 Channel regulation of action potential repolarization and firing patterns in superiorcervical ganglion neurons and hippocampal CA1 pyramidal neurons. J. Neurosci. 2014, 34, 4991–5002.
[CrossRef] [PubMed]
Goaillard, J.-M.; Dufour, M.A. The pros and cons of degeneracy. eLife 2014, 3, e02615. [CrossRef] [PubMed]
Cronin, J. Mathematical Aspects of Hodgkin-Huxley Neural Theory; Cambridge University Press: Cambridge,
UK, 1987.
Ermentrout, G.B.; Terman, D.H. Mathematical Foundations of Neuroscience; Springer: New York, USA, 2010.
Colacicco, G. Electrical potential at an oil/water interface. Nature 1965, 207, 936–938. [CrossRef]
Colacicco, G. Reversal of potential across a liquid non-aqueous membrane with regard to membrane
excitability. Nature 1965, 207, 1045–1047. [CrossRef] [PubMed]
Tamagawa, H.; Morita, S. Membrane potential generated by ion adsorption. Membranes 2014, 4, 257–274.
[CrossRef] [PubMed]
Tamagawa, H. Membrane potential generation without ion transport. Ionics 2014. published online.
Cheng, K.L. Capacitor theory for nonfaradaic potentiometry. Microchem. J. 1990, 42, 5–24. [CrossRef]
Huang, C.-M.; Jean, Y.C.; Cheng, K.L. Isotopic evidence disproving Ion exchange reaction between H+ andNa+ in pH glass electrode. J. Electrochem. Soc. 1995, 142, L175–L176. [CrossRef]
Cheng, K.L. Explanation of misleading Nernst slope by Boltzmann equation. Microchem. J. 1998, 59, 457–461.
[CrossRef]
Temsamani, K.R.; Cheng, K.L. Studies of chloride adsorption on the Ag/AgCl electrode. Sens. Actuators B
2001, 76, 551–555. [CrossRef]
Cheng, K.L. Recent development of non-faradaic potentiometry. Microchem. J. 2002, 72, 269–276. [CrossRef]
Teorell, T. Electrokinetic membrane processes in relation to properties of excitable tissues I. experiments on
oscillatory transport phenomena in artificial membranes. J. Gen. Physiol. 1959, 42, 831–845. [CrossRef]
Kishimoto, U. Hodgkin-Huxley riron no mondaiten (problems around Hodgkin-Huxley theory).
Seibutubutsuri (Biophysics) 1968, 8, 8–15. (In Japanese).
Shinagawa, Y. Makudeni no butsuriteki kiso (physical basis of membrane potential). Maku (Membrane) 1976,
1, 176–183. (In Japanese).
Ishima, Y.; Przybylski, A.T.; Fox, S.W. Electrical membrane phenomena in spherules from proteinoid andlecithin. Biosystems 1981, 13, 243–251. [CrossRef]
Przybylski, A.T.; Stratten, W.P.; Syren, R.M.; Fox, S.W. Membrane, action, and oscillatory potentials in
simulated protocells. Naturwissenschaften 1982, 69, 561–563. [CrossRef] [PubMed]
Yoshikawa, K.; Matsubara, Y. Spontaneous oscillation of electrical potential across organic liquid membranes.
Biophys. Chem. 1983, 17, 183–185. [CrossRef]
Przybylski, A.T.; Fox, S.W. Excitable artificial cells of proteinoid. Appl. Biochem. Biotechnol. 1984, 10, 301–307.
[CrossRef] [PubMed]
Przybylski, A.T. Excitable cell made of thermal proteinoids. Biosystems 1985, 17, 281–288. [CrossRef]

Membranes 2016, 6, 11

36.

37.

38.
39.
40.
41.
42.
43.

44.
45.
46.
47.
48.
49.
50.

14 of 14

Yoshikawa, K.; Sakabe, K.; Matsubara, Y.; Ota, T. Oscillation of electrical potential in a porous membrane
doped with grycerol α-monoolate induced by an Na+ /K+ concentration gradient. Biophys. Chem. 1984, 20,
107–109. [CrossRef]
Yoshikawa, K.; Sakabe, K.; Matsubara, Y.; Ota, T. Self-excitation in a porous membrane doped with sorbitanmonooleate (Span-80) induced by an Na+ /K+ concentration gradient. Biophys. Chem. 1985, 21, 33–39.
[CrossRef]
Yoshikawa, K.; Omochi, T.; Matsubara, Y.; Kourai, H. A possibility to recognize chirality by an excitableartificial liquid membrane. Biophys. Chem. 1986, 24, 111–119. [CrossRef]
Yoshikawa, K.; Omochi, T.; Matsubara, Y. Chemoreception of sugars by an excitable liquid membrane.
Biophys. Chem. 1986, 23, 211–214. [CrossRef]
Vaughan, G.; Przybylski, A.T.; Fox, S.W. Thermal proteinoids as excitability-inducing materials. Biosystems
1987, 20, 219–223. [CrossRef]
Yoshikawa, K.; Shoji, M.; Nakata, S.; Maeda, S. An Excitable liquid membrane possibly mimicking thesensing mechanism of taste. Langmuir 1988, 4, 759–762. [CrossRef]
Nakajo, N.; Yoshikawa, K.; Shoji, M.; Ueda, I. Spontaneous oscillation of artificial membrane: Equivalence in
effects of temperature and volatile anesthetic. Biochem. Biophys. Res. Commun. 1990, 167, 450–455. [CrossRef]
Yagisawa, K.; Naito, M.; Gondaira, K.; Kambara, T. A model for self-sustained potential oscillation of lipid
bilayer membranes induced by the gel-liquid crystal phase transitions. Biophys. J. 1993, 64, 1461–1475.
[CrossRef]
Li, H.; Wang, M. Design of oscillations across the artificial liquid membrane between water and oil phases.
Chem. Phys. Lett. 2000, 330, 503–508. [CrossRef]
Srividhya, J.; Gopinathan, M.S. Modeling experimental oscillations in liquid membranes with delay equations.
J. Phys. Chem. B 2003, 107, 1438–1443. [CrossRef]
Kumar, A.; Pradeep, T. Stabilization of monolayers by metal nanoparticles manifested in oscillations ofinterfacial potentials. Mater. Sci. Eng. C 2004, 24, 535–539. [CrossRef]
Gao, J.; Wang, L.; Yang, W.; Yang, F. Electrical potential oscillation in an anionic surfactant system withbarbitone in octanol as an oil phase. J. Iran. Chem. Soc. 2005, 2, 71–77. [CrossRef]
Ogawa, T.; Shimazaki, H.; Aoyagi, S.; Sakai, K. Electrical oscillation at a water/octanol interface ina hydrophobic container. J. Colloid Interface Sci. 2007, 305, 195–197. [CrossRef] [PubMed]
Gao, J.Z.; Dai, H.X.; Chen, H.; Ren, J.; Yang, W. Study on the oscillating phenomena of electrical potential
across a liquid membrane. Chin. Chem. Lett. 2007, 18, 309–312. [CrossRef]
Kovalchuk, N.M. Spontaneous non-linear oscillations of interfacial tension at oil/water interface. Open Chem.
2015, 13, 1–16. [CrossRef]© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open accessarticle distributed under the terms and conditions of the Creative Commons by Attribution(CC-BY) license (http://creativecommons.org/licenses/by/4.0/).