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 2Department of Pathology and Laboratory Medicine, Perelman School of Medicine 3Department of Microbiology, Perelman School of Medicine 4Center for Clinical Epidemiology and Biostatistics, Perelman School of Medicine 5Department 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: [email protected]

1 Supplementary Information Supplementary File Titles Supplementary Figure 1 A micrograph of the reaction-diffusion microconduit’s cross-section Supplementary Figure 2 An exploded view of the nuclemeter chip Supplementary Figure 3 The experimental setup for nuclemeter chip testing Supplementary Figure 4 Evaluation of the sensitivity of benchtop “tubed-based” LAMP Supplementary Figure 5 Real-time monitoring of RT-LAMP amplification of various HIV viral RNA targets on a benchtop PCR machine Supplementary Figure 6 The position of the reaction front as a function of the number of target molecules at different times Supplementary Figure 7 The effect of HPMC concentration on the reaction front and the front velocity Supplementary Figure 8 Images of the emission intensity during the LAMP amplification reaction in the nuclemeter’s sample chamber Supplementary Figure 9 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 Supplementary Figure 10 The spatial distribution of the concentration at various times as used to estimate the diffusion coefficient D. Supplementary Video 1 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. Supplementary Note 1 Optimization of HPMC concentration Supplementary Note 2 Estimation of the reaction rate constant Supplementary Note 3 Estimating the diffusion coefficient Supplementary Note 4 Image Processing

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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.

3 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.

4 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.

5 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.

6 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.

7 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.

8 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

9 reaction front (XF) as a function of time. The HPMC sieving matrix concentrations are 0.01%, 0.04%, 0.09%, and 0.13%.

10 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 - ) (S1) dt cmax

3 -1 3 where c is the concentration (mol/m ), k (s ) is the reproductive parameter, and cmax (mol/m ) 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. It is

c convenient to introduce the normalized concentration cˆ = as we have done in the cmax manuscript. Accordingly, equation (S1) reduces to dcˆ =kg cˆ g(1 - c ˆ ) (S2) dt with the initial condition:

cˆ(0) = c ˆ0 (S3)

Equation (S2) with initial condition (S3) admits the solution:

cˆ0 cˆ( t ) = . (S4) (1-cˆ0 )exp( - kt ) + c ˆ 0

By minimizing the discrepancy between the predictions of equation (S4) and the experimental data, we estimated the reaction rate constant k and and cˆ 0. Fig. 9 depicts the

-1 predictions of equation (S4) with the optimal estimate k = 0.008 s and cˆ0 = 0.006 (solid lines) along with the experimental data (symbols). The number of target molecules is 103 copies.

11 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.

12 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:

抖cˆ2 c ˆ = D0＃ tt , x 0 (S5) 抖t x2 with the initial and boundary conditions cˆ(0, t) - 1 = c ˆ(� , t) = c ˆ( x ,0) 0 (S6)

13 c In the above, cˆ = where c(0, t) is assumed to be time-independent. Since the volume of c(0, t) 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

x cˆ = erfc( ) . (S7) 2 Dt 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.

14 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:

Ir- I b Ic = , If- I b

Ir where Ic is the corrected emission intensity, is the filtered intensity, Ib 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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