SUPPLEMENTARY MATERIAL
Nuclemeter: A Reaction-Diffusion based method for
Quantifying Nucleic Acids Undergoing Enzymatic
Amplification
Changchun Liu1*, Mohamed M. Sadik1, Michael G. Mauk1, Paul H. Edelstein2, Frederic D. Bushman3,
Robert Gross4,5, and Haim H. Bau1,
1
Department of Mechanical Engineering and Applied Mechanics, School of Engineering and Applied Science
2
Department of Pathology and Laboratory Medicine, Perelman School of Medicine
3
Department of Microbiology, Perelman School of Medicine
4
Center for Clinical Epidemiology and Biostatistics, Perelman School of Medicine
5
Department of Medicine, Perelman School of Medicine
University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
*
Corresponding author
Dr. Changchun Liu
Department of Mechanical Engineering and Applied Mechanics
University of Pennsylvania
216 Towne Building
220 South 33rd St.
Philadelphia, Pennsylvania 19104-6315, USA
Phone: (215)898-1380
E-mail: lchangc@seas.upenn.edu
1
Supplementary Information
Supplementary File
Titles
Supplementary Figure 1
Supplementary Figure 2
Supplementary Figure 3
Supplementary Figure 4
Supplementary Figure 5
A micrograph of the reaction-diffusion microconduit’s cross-section
An exploded view of the nuclemeter chip
The experimental setup for nuclemeter chip testing
Evaluation of the sensitivity of benchtop “tubed-based” LAMP
Real-time monitoring of RT-LAMP amplification of various HIV viral
RNA targets on a benchtop PCR machine
The position of the reaction front as a function of the number of target
molecules at different times
The effect of HPMC concentration on the reaction front and the front
velocity
Images of the emission intensity during the LAMP amplification
reaction in the nuclemeter’s sample chamber
Normalized emission intensity as a function of the time: experimental
data and a best fit curve used to estimate the reaction rate constant k
(1/s) of the RT-LAMP
The spatial distribution of the concentration at various times as used to
estimate the diffusion coefficient D.
The propagation of the reaction-diffusion fronts in the four
reaction-diffusion microconduits of the nuclemeter chip. The various
sample chambers, from left to right, contain 104, 103, 102, and 0 (no
target control) HIV 1 RNA target molecules.
Optimization of HPMC concentration
Estimation of the reaction rate constant
Estimating the diffusion coefficient
Image Processing
Supplementary Figure 6
Supplementary Figure 7
Supplementary Figure 8
Supplementary Figure 9
Supplementary Figure 10
Supplementary Video 1
Supplementary Note 1
Supplementary Note 2
Supplementary Note 3
Supplementary Note 4
2
100 μm
Fig. 1: A micrograph of the reaction-diffusion microconduit’s cross-section. The blue dashed
line indicates the interface between the PMMA film and the PMMA chip body.
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Fig. 2: An exploded view of the nuclemeter chip. The nuclemeter chip consists of three
layers: a top PMMA film, a PMMA chip body, and a bottom PCR Sealers™ tape. The
various features of the chip body were milled with a CNC machine.
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Fig. 3: The experimental setup for HIV viral load test with the nuclemeter chip. The
custom-made, portable processor includes an USB-based, fluorescence microscope
(AM4113T-GFBW Dino-Lite Premier, AnMo Electronics, Taipei, Taiwan). The processor
can be powered either with four AA batteries or by grid power. The fluorescence image of
the nuclemeters was directly displayed on the computer screen. The USB microscope can be
replaced with LED illumination and a smartphone camera.
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Fig. 4: Evaluation of the limits of detection of benchtop, “tubed-based”, RT-LAMP.
Real-time, benchtop monitoring of RT-LAMP amplification of HIV viral RNA with 50, 5,
and 0 (negative control) target RNA copies per tube.
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Fig. 5: Real-time, benchtop monitoring of RT-LAMP amplification of HIV viral RNA with
104, 103, 102, and 0 (negative control) target RNA molecules per tube on the benchtop PCR
machine. The tubes include 0.04% (w/v) HPMC to replicate the conditions in the nuclemeter
chip.
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Fig. 6: The position of the reaction front (XF) as a function of the number of target molecules
(n = 3) at times (from bottom to top) 32, 40, 48 and 56 min after the start of incubation.
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Supplementary Note 1: Optimization of HPMC concentration
To obtain a well-defined reaction front and avoid rapid diffusion of nucleic acids along
the reaction-diffusion conduit, we add hydroxypropyl methyl cellulose (HPMC) to
RT-LAMP master mixture. Previously, HPMC has been widely used as a high-efficiency
sieving matrix to separate nucleic acid fragments in microchip-based capillary electrophoresis
due to its low background fluorescence and its ability to form a sieving network. We
evaluated the effect of HPMC concentration on the reaction front profile and velocity during
amplification process with a target HIV RNA concentration of 103 copies/ chamber. As seen
in Fig. 7a, the higher the HPMC concentration is, the better defined is the reaction front.
When the HPMC concentration is high (above 0.13%), the reaction-diffusion velocity
decreases greatly (Fig. 7b). In the experiments reported here, we used 0.04% HPMC
concentration as a reasonable compromise between front sharpness and speed.
Fig. 7: The effect of HPMC concentration on the reaction front sharpness and velocity. The
initial HIV RNA concentration is 103 copies/ chamber. (a) Fluorescence images of the
reaction front at different HPMC sieving matrix concentrations. (b) The position of the
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reaction front (XF) as a function of time. The HPMC sieving matrix concentrations are 0.01%,
0.04%, 0.09%, and 0.13%.
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Supplementary Note 2: Estimation of the reaction rate constant
To estimate the reaction rate constant, we carried out LAMP amplification in the
nuclemeter’s sample well (Fig. 8). We approximate the amplification process with
dc
c
 kc 1 
)
dt
cmax
(S1)
where c is the concentration (mol/m3), k (s-1) is the reproductive parameter, and cmax (mol/m3)
is the saturation concentration. We assume that the fluorescence emission intensity is
proportional to the concentration. This assumption is not critical and we could have
formulated equation (S1) in terms of the emission intensity instead of the concentration.
is convenient to introduce the normalized concentration cˆ 
c
cmax
It
as we have done in the
manuscript. Accordingly, equation (S1) reduces to
dcˆ
 k cˆ (1  cˆ)
dt
(S2)
cˆ(0)  cˆ0
(S3)
with the initial condition:
Equation (S2) with initial condition (S3) admits the solution:
cˆ(t ) 
cˆ0
.
(1  cˆ0 ) exp(kt )  cˆ0
(S4)
By minimizing the discrepancy between the predictions of equation (S4) and the
experimental data, we estimated the reaction rate constant k and and ĉ 0.
Fig. 9 depicts the
predictions of equation (S4) with the optimal estimate k = 0.008 s-1 and ĉ0 = 0.006 (solid
lines) along with the experimental data (symbols). The number of target molecules is 103
copies.
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Fig. 8: Nuclemeter’s sample well emission (a) before RT-LAMP amplification, (b) shortly
after the onset of amplification, and (c) at saturation of amplification. The number of target
molecules is 103 copies.
Fig. 9: Fluorescent emission from the nuclemeter’s sample chamber (Fig. 8) as a function of
the time. The solid line and the symbols correspond, respectively, to the best fit line based on
equation S4 and the experimental data. The number of target molecules is 103 copies.
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Supplementary Note 3. Estimating the Diffusion Coefficient (D)
Fig. 10: (a) The concentration distribution of the labeled primers in the microconduit at various times
in the absence of an amplification reaction.
(b) The emission intensity (normalized with the initial
concentration) as a function of position at various times. The lines correspond to theoretical
predictions and the symbols to the experimental data (with optimal estimate for the diffusion
coefficient).
To estimate the diffusion coefficient of nucleic acids in the HPMC polymer solution, we
introduced
oligonucleotides
tagged
with
a
fluorescent
dye
(HEX-GGTGTCTCATTGTTTATACTA) into the sample well and monitored the nucleic
acid diffusion in the microconduit as a function of time (Fig. 10a). This experiment was
carried out at the LAMP incubation temperature of 62.5 oC, but in the absence of enzymes so
that no amplification took place. The normalized signal intensity (normalized concentration)
is depicted (dashed lines) in Fig. 10b as a function of position along the conduit at various
times.
We model the concentration distribution with a diffusion equation in a semi-infinite
medium:
cˆ
 2cˆ
D 2
t
x
0  t , x  0
(S5)
with the initial and boundary conditions
cˆ  0, t  1  cˆ  , t   cˆ  x,0  0
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(S6)
In the above, cˆ 
c
where c(0, t) is assumed to be time-independent. Since the volume
c(0, t)
of the sample chamber far exceeds the volume of the conduit, the error introduced by
assuming that c(0,t) remains constant throughout the process is quite small, as we have
verified both by scaling analysis and by obtaining a more accurate solution for equation (S5)
that allows for time-dependence of c(0, t) as mandated by mass conservation.
Equations (S5) and (S6) admit the classical solution
cˆ  erfc(
x
).
2 Dt
(S7)
Using the MatLab Optimization toolbox (The MathWorks, Inc., Natick, MA), we found
that D ~ 10-10 m2s-1 minimized the discrepancy between the predictions of equation (S7) and
the experimental data. The predictions of equation (S7) with the optimal D are depicted
(dashed lines) along with the experimental data (symbols) in Fig. 10b.
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Supplementary Note 4: Image Processing and Analysis
Images were processed post-acquisition to facilitate comparison with numerical
simulations. Initially, the noise was removed from all images using a low pass filter. Then,
the images were corrected by applying the following scaling:
Ic 
I r  Ib
,
I f  Ib
where I c is the corrected emission intensity, I r is the filtered intensity, I b is the
background intensity, and I f is the flat maximum intensity. The background intensity is the
average of the first five video frames when there are too few amplicons to generate a
significant signal. The maximum intensity was obtained from the last frame acquired. The
intensity signal at each position x was averaged along the width of the conduit. All image
processing and mathematical calculations were performed with MatLab.
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