Supplementary information for

Substantial Expansion of Detectable Size Range inIonic Current Sensing through Pores by Using aMicrofluidic Bridge Circuit
Hirotoshi Yasaki1,2*, Takao Yasui1,2,3*, Takeshi Yanagida4,5*, Noritada Kaji1,2, Masaki Kanai4, Kazuki
Nagashima4, Tomoji Kawai5*, and Yoshinobu Baba1,2,6*

1

Department of Biomolecular Engineering, Graduate School of Engineering, Nagoya University, Furo-cho,

Chikusa-ku, Nagoya 464-8603, Japan2

ImPACT Research Center for Advanced Nanobiodevices, Nagoya University, Furo-cho, Chikusa-ku,Nagoya 464-8603, Japan3Japan Science and Technology Agency (JST), PRESTO, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012,

Japan
4Laboratory of Integrated Nanostructure Materials Institute of Materials Chemistry and Engineering, Kyushu

University, 6-1 Kasuga-koen, Kasuga, Fukuoka 816-8580, Japan
5

Institute of Scientific and Industrial Research, Osaka University, Mihogaoka, Ibaraki 567-0047, Osaka,

Japan
6

Health Research Institute, National Institute of Advanced Industrial Science and Technology (AIST),

Takamatsu 761-0395, Japan

S1

This file includes:
1. Supplementary Figures (Figs. S1-S3)
2. Derivation and validation of theoretical equation (Fig. S4)
3. Validation of accuracy of 200 nm particle detection result

S2

1. Supplementary Figures

Figure S1. Detectable particle volumes reported in the literature and our results. Green dots show
reported data points obtained by conventional methods2, 4, 5, 14, 22-25 and the green band shows their reported
detection range.

Orange dots and band showing our data points and our detection range.

line represents the 100% pore volume.

The red dotted

The reported methods have the inherent limitation of detectablesamples of a 1 % pore volume; on the other hand, our developed method achieved detection of samples of a0.01 % pore volume.

S3

Figure S2. Overlay of 100 signals of 3.1 µm polystyrene particles. All signals had the same shape, andthat proved the high reproducibility of our method. Micropore dimensions were 7.5 µm height × 4.0 µm
width × 80 µm length; applied voltage, 12 V.

S4

Translocation time in micropores.
Similar to the tendency of the conventional methods, there is a trade-off between signal amplitude
and translocation time; a longer micropore shows a smaller signal amplitude and longer translocation time(Figs. S3a-3c).

It should be noted, however, that our methodology would have a long enough translocation

time (>200 ms) to distinguish various interactions between the sample and pores (Fig. S3d).

Sincetranslocation time of samples had a relationship to the applied electric fields or sample surface charge (Fig.
S3e), our methodology would be capable of identifying biological samples based on surface charges,
depending on the sample types.

Figure S3. Translocation time in micropores. (a) A schematic illustration of the micropore and a signal
for 2.08 µm diameter particles; micropore dimensions of 7.5 µm height × 4.0 µm width × 80 µm length;
applied voltage, 12 V.

We defined the micropore as being from positions B to C and positions A and D asshowing ends of a channel including the micropore.

(b, c) Signal amplitude and translocation time of 3.10

µm diameter particles; micropore dimensions of 7.5 height × 4.0 µm width.
deviation for a series of measurements (N = 200).

Error bars show the standard(d) A relationship between electric field andtranslocation time in the micropore (B to C in Fig. S2a) and in the channel (with ends at A and D in Fig.
S3a).

The micropore was 80 µm long and the channel was 150 µm long.

deviation for a series of measurements (N = 100).

Error bars show the standard(e) A relationship between zeta potential of 3.10 µm
S5diameter particles and translocation time in the channel (with ends at A and D in Fig. S3a); micropore
dimensions of 6.6 µm height × 4.5 µm width × 16 µm length.

S6Channel length was 40 µm.

2. Derivation of theoretical equation

Figure S4.

Schematic illustrations of the current sensing method for derivation of theoreticalequation.
(a) Schematic illustrations of sample particle translocation, electric circuit diagrams, and schematic current
value in the microfluidic bridge circuit.
sample particles in the micropore.
particles in the micropore.

The left side shows the situation before and after passage of

The right side shows the situation for the time of passage of the sample

Red lines are for the sample circuit, blue lines are for the bridge lines, and blacklines are for the balance circuit.

The sample circuit has a voltage source (Vs) and resistors for theS7

micropore (Rx) and sample flow channels (Rs1 and Rs2).
Rb2) and an Ampere meter (A).

The bridge lines have resistors for them (Rb1 andThe balance circuit has a voltage source (Vb), a variable resistor (Rv), and a1-kΩ resistor (R1-kΩ). Red filled squares show increased resistance by sample introduction.

Red andblack arrows show flow direction of current in the sample circuit and the balance circuit, respectively.
Blue arrows show flow direction of current by deviation of potential differences between the two circuits,sample and balance.

The numbers “1” and “2” are the electrical potential of the micropore entrance andthe electrical potential of the cathode of the voltage source in the balance circuit, respectively. P1kΩ andPpore are the potential differences of both ends for the 1-kΩ resistor and the micropore, respectively.

(b) Arelationship between particle volume and calculated resistance change of a micropore by using the equation
for calculating electric resistance value of conductor; micropore dimensions of 7.5 µm height × 4.0 µmwidth × 80 µm length.

The micropore without particles has a resistance of 6.72 MΩ.

shows an expanded image for the resistance change less than 3 kΩ.
curve result.

S8

The inset figure

The black dotted line is the fittingOur method uses two electrical circuits: a sample circuit and a balance circuit. We derived atheoretical equation to calculate signal amplitudes, which are detected in this method, based on Ohm’s lawand Kirchhoff's law.

In the balanced state, no current flows in the bridge channels (situation of the left-side

drawing in Fig. S3a), and the following equations are formulated for each “isolated” circuit: = =


 ++

1


 +2

where Rs1, Rs2, Rx, R1-kΩ, and Rv are the electrical resistances of sample flow channels, the micropore, the1-kΩ resistor, and the variable resistor, respectively. Vf and Vp are the applied voltages for the sample andbalance circuits, respectively.

Isample and Ibalance are currents in the sample and balance circuits, respectively.

Since potential differences between both ends of the micropore (Rx) and the 1-kΩ resistor (R1-kΩ) are thesame in the balanced state, Eqs. (S1) and (S2) are transformed as:×  =  ×  .
3
When a sample is passing through the micropore, the current in the sample circuit changes from Is toIsample+∆Isample: + ∆ =


+

+∆+

4

where ∆Rx and ∆Isample are resistance change of the micropore and current change in sample circuit bysample introduction, respectively.

At the same time, the potential difference between both ends of themicropore (Ppore) is increased by the increasing resistance, and the signal (Isignal) flows to an Ampere meterto make up the potential difference between points 1and 2 (situation of the right-side drawing in Fig. S3a).
At this time, the balanced state is lost.

The following equation is the sum of the voltages of the circuitsurrounded by the orange dotted line:! + ∆ − #$ % + ∆#$   +  +=  +  + ∆ 

where Rb1 and Rb2 are the electrical resistances of the bridge channels.

5

∆Ibalance is current change in sample

circuit by sample introduction. The following equation is the expansion equation of eq (S5).
 +  ∆ + ∆ + ∆ ∆ −   − ∆  =#$   +  +  +  + #$ ∆6
Since ∆Isample and Isignal are small enough compared with Isample and Ibalance, the fourth term on the left side(∆Isample∆Rx) and the second term on the right side (Isignal∆Rx) can be ignored, and Eq. (S6) can betransformed by Eq. (S3) as follows.
 ∆ ≈ #$   +   + !#$ + ∆ % + !#$ + ∆ %The following equation is the sum of the voltages of the black circuit.
 =   + ∆  + ! + ∆ + #$ %Equation (S8) can be transformed by Eq. (S2) as follows.

∆ =− ∙ #$
+


S9

S9

S8

7

Based on Eq. (S9), the following approximate expression is obtained when Rv is large enough comparedwith R1-kΩ.
|∆ | ≪ 0#$ 0(S10)The following equation is the sum of the voltages of the red circuit.
 − #$ = ! + ∆ % 1 + 1 +

S11When ∆Rx is small enough compared with Rx, Eq. (S11) can be transformed by Eq. (S1) as follows.
∆ ≈1+1 +∙ #$S12

Based on Eq. (S12), the following approximate expression is obtained when Rx is small enough comparedwith Rs1+RS2.

0∆ 0 ≪ 0#$ 0
Based on Eq. (S10) and Eq. (S13), Eq. (S7) can be transformed as follows.
 ∆ ≈ #$   +  +  + 
14

(S13)

Therefore, the detected current signals can be theoretically predicted by Eq. (S8) (this is Eq. (1) of the maintext).

#$ =∆ +  + +×
+ +

15

Channel resistances (Rb1, Rb2, Rs1, and Rs2) can be calculated by Eq. (S16):

3
16
4
where ρ, L, and A are the electrolyte solution resistivity, channel length, and cross-sectional area of the=2×

channels, respectively.

Based on Eqs. (S15) and (S16), the signal amplitude is in proportion to the appliedvoltage (Vs), and in inverse proportion to the resistance of the sample circuit (RS1+Rx+RS2), the sum of theresistances of the bridge channels, the micropore, and the 1-kΩ resistor (Rb1+Rb2+R1-kΩ+Rx), and theelectrolyte solution resistivity (ρ).

S10

3. Validation of accuracy of 200 nm particle detection result

In the detection of 200 nm particles in the 14 µm long micropore, resistivity (ρ) of themicrochannels filled with 5×TBE buffer was 0.319 kΩ•cm, resistance of the sample circuit (RS1+Rx+RS2)
was 18.8 MΩ, the sum of resistances of the bridge channels, the micropore, and the 1-kΩ resistor(Rb1+Rb2+R1-kΩ +Rx) was 13 MΩ, applied voltage (Vs) was 53 V, and resistance change of the micropore by
the 200 nm diameter particle introduction (∆Rx) was 0.84 kΩ. Using eq (S8), we could calculate Isignal as 180pA.

Therefore, the detected value was accurate.

S11