SUPPLEMENTARY INFORMATION Simultaneous DNA amplification ... · Simultaneous DNA amplification and...

SUPPLEMENTARY INFORMATION

Simultaneous DNA amplification and detection using a pH-sensing

semiconductor system

Christofer Toumazou1,2, Leila M. Shepherd1, Samuel C. Reed1, Ginny I. Chen1, Alpesh Patel1,3, David

M. Garner1,3, Chan-Ju A. Wang1,3, Chung-Pei Ou1, Krishna Amin-Desai1, Panteleimon Athanasiou1,

Hua Bai1, Ines M. Q. Brizido1, Benjamin Caldwell1, Daniel Coomber-Alford1, Pantelis Georgiou2,

Karen S. Jordan1, John C. Joyce1, Maurizio La Mura1, Daniel Morley1, Sreekala Sathyavruthan1, Sara

Temelso1, Risha E. Thomas1 & Linglan Zhang1.

1 DNA Electronics Ltd. Ugli Campus Block C, 56 Wood Lane, W12 7SB, London, United Kingdom.

2 Imperial College London, Department of Electrical and Electronic Engineering, South Kensington

Campus, Exhibition Road, London, SW7 2AZ, United Kingdom.

3 These authors contributed equally to this work.

Correspondence should be addressed to: Christofer Toumazou ([email protected]) or Leila

Shepherd ([email protected]).

Nature Methods: doi:10.1038/nmeth.2520

Supplementary Figure 1: Correlation of ΔpH and amplification. a. Tube-based pH-LAMP of NAT2 amplified from purified human genomic DNA. 40min

amplification reactions were performed, and the pH and amplification yields (three replicates) were measured at the indicated times. The averaged pH of non-template control (NTC) baseline signals at each time point was subtracted from the pH of NAT2 amplification reaction. The mean, copy number and standard deviation of ΔpH (solid) and amplification yield (open) are plotted against time (min).

b. A representative agarose gel of A) showing the pH-LAMP of NAT2 and non-template control (NTC) where the reactions were terminated at 20, 30 and 40 minutes after initiation.

20 30 40

NAT2

20 30 40

NTC

700 400 300 150 100

75

50

25

a.

b.

Supplementary Figure 1


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*1-ΔpH *2-ΔpH *1-ΔpH *2-ΔpH *1-ΔpH *2-ΔpH

*1/*1 *1/*2 *2/*2

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CYP2C9

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CYP2C9 *1/*1 *1/*2 *2/*2

a.



Supplementary Figure 2: single nucleotide polymorphism (SNP) genotyping of the CYP2C9 gene

from purified genomic DNA and minimally-prepared saliva samples using the tube-based pH-PCR method. The CYP2C9 gene encodes one of the cytochrome P450 superfamily, which function as major drug metabolizing enzymes1. We designed the experiment to discriminate between the wild type (CYP2C9*1, C430) and mutant (CYP2C9*2, C430T) alleles using allele-specific primers.

a. Tube-based pH-PCR of three different genotypes of CYP2C9*2. Purified genomic DNA (Coriell Institute) of known genotypes were each analysed by pH-PCR reactions where one contained a set of allele-specific primers targeting the wild type allele (*1) and the other contained a set of allele-specific primers targeting the mutant allele (*2). The pH was measured at the start and finish of each reaction. The averaged absolute change in pH (ΔpH) and standard deviation from two separate experiments (two replicates per experiment) over 40 cycles of the PCR reactions were plotted. Homozygous wild type

(*1/*1; blue), heterozygous (*1/*2; red) and homozygous mutant (*2/*2; turquoise) genomic DNA samples are illustrated. Note, due to the lack of homozygous mutant genotype, an artificial plasmid construct containing a partial sequence of the mutant CYP2C9*2 allele was used for the *2/*2 datapoints. We successfully verified the genotypes of these samples using tube-based pH-PCR where homozygous wild type, heterozygous, and homozygous mutant samples can be distinguished by the amplification dependent pH change. The homozygous wild type displayed a greater pH change in reactions containing wild type allele specific primers (CYP2C9*1), whereas homozygous mutant displayed a greater pH change in reactions containing mutant allele specific primers (CYP2C9*2). For the heterozygous sample, both the wild type and mutant allele-specific reactions displayed amplification as indicated by a similar magnitude of pH change.

b. Population genotyping of CYP2C9 (*1 and *2) from crude saliva samples to illustrate the amplification specificity and discrimination capability of pH-PCR. For each sample, the ΔpH

of a reaction with wild type (*1) primers were plotted against ΔpH of a reaction with mutant (*2) primers. Homozygous wild type (blue diamonds), heterozygous (red squares) and homozygous mutant (turquoise triangles) samples are illustrated. Note, due to the lack of homozygous mutant genotype, an artificial plasmid construct containing CYP2C9*2 was used

for the *2/*2 datapoints. The variation in the pH within each genotype is due to different levels of genomic DNA content from the collected saliva samples. The results showed that the three different genotypes could be clustered into different regions on the ΔpH plot. We verified the genotypes of these saliva samples by the TaqMan genotyping assay (Applied Biosystems), and found that pH-PCR was able to correctly identify the genotypes of all saliva samples.


Supplementary Figure 3: Architecture of the CMOS. CMOS fabricated IC with 40 ISFETs, 10 temperature sensors, heaters, signal processing circuitry, and analogue to digital conversion all integrated onto a chip2 (Garner D. et al. 2010, ISSCC).




Supplementary Figure 4: The IC with its battery-powered handheld microelectronic analyser. a. The IC is mounted onto an SD card with corresponding electronic analyser. b. The systems architecture of a. comprising the system components and digital logic. The

signal readout can be displayed via a touchscreen device or a PC. c. Illustration of an IC packaged to connect to a USB electronic analyser. d. Two different types of electronic analysers.

a

b

c d


GH1 1 2 3 4 5

NTC

500

300

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100

(bp) 1000

700 600

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Supplementary Figure 5: Comparison between fluorescence-based PCR and pH-sensing semiconductor-based PCR. a. The conventional fluorescent SYBR green PCR method

was performed using the Eppendorf Mastercycler apparatus and Applied Biosystem SYBR green PCR master mix in a 35ul reaction volume. The on-chip pH-PCR was performed in a 2ul reaction chamber as described in the online methods. For each reaction, 10,000 copies of human genomic DNA was added to the reaction mixture containing the GH1 gene primer set . The red lines represent three analytical replicates of the conventional fluorescent qPCR; the blue lines represent the on-chip pH-PCR amplification curves from three separate chips; the green lines are two no template control reactions from the conventional fluorescent qPCR platform; the orange lines are two no-template control reactions from the on-chip pH-PCR platform.

b. The amplification product recovered from the on-chip pH-PCR for GH1 and no-template control (NTC) at the end of the reaction from a. Samples were separated on a 2% agarose gel and visualized by SYBR green.

a

b



Supplementary Figure 6: Evaluation of pUC19 using on-chip pH-PCR. On-chip pH-PCR amplification plots of 1ng of pUC19 plasmid . Three chips were used to analyse pUC19 and two chips were used as no template control. The three pUC19 amplification curves represents ISFET signals from three separate chips; the two NTC curves represents ISFET signals from two separate chips.


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Expt 1 Expt 2 Expt 3


Supplementary Figure 7: Evaluation of inter- and intra-chip reproducibility. Three independent experiments were conducted against GH1 (Expt 1 and 3) and CYP2C9*1 (Expt 2) using the on-chip pH-PCR with purified genomic DNA as input. For Expt 1, 2, and 3, the number of chips used per experiment are 5, 8 and 10 respectively. a. Mean and standard deviation of Ct values from four ISFETs within a chip (two ISFETs per

chamber; two chambers per chip) are shown as bar graph. Note, coefficient of variations (CV) for inter- and intra-chip are shown in Supplementary Table 1.

b. Amplification plots for the 20 ISFETs (five chips) in Expt 1.

a

b


Supplementary Figure 8: Amplification plots for a 10-fold serial diluted human genomic DNA sample. Representative pH-LAMP amplification curves (Log) of NAT2 conducted from 10, 100, 1000 and 10000 copies of K562 human genomic DNA (see Figure 4b). An electrical signal threshold is defined (horizontal red dash line), and the time at which this threshold is crossed is determined for each sample.



Wt/Wt

Mut/Mut


Supplementary Figure 9: Evaluation of BRAF V600E using the pH-sensing IC platform. Purified genomic DNA harbouring homozygous wild type (V600) or homozygous mutant (V600E) BRAF gene were each analysed on a three-chamber flow cell IC platform using pH-LAMP amplification method. Representative amplification curves for BRAF wild type (top panel) and mutant (bottom panel) samples are shown. Blue line = reactions containing wild type allele specific primers; Red line = reactions containing mutant allele specific primers.


a

b


Supplementary Figure 10: Multiplex analysis of two loci on one chip. Purified genomic DNA from two individual saliva samples (a and b) were analysed by on-chip pH-LAMP targeting two allelic variant (Wt and Mut) from each of the two known biomarkers of aging, NAD(P)H dehydrogenase (NQO1, rs1800566) and Matrix Metalloproteinase-1 (MMP1, rs1799750). The experiment was performed using a 12-chamber flow cell mounted on the quad chip where each quadrant was used to evaluate individual allelic variants (NQO WT, NQO1 Mut, MMP1 WT and MMP1 Mut). The genotype of saliva sample 1 (a) is NQO1 mutant and MMP1 heterozygous; the genotype of saliva sample 2 (b) is NQO1 mutant and MMP1 wildtype. The genotypes of these two saliva samples were confirmed by TaqMan genotyping assay (ABI).. The solid lines are shown in the figure legend and the dash lines are the corresponding no template controls.

NQO 1 WT NQO 1 Mut MMP 1 WT MMP 1 Mut

NQO 1 WT NQO 1 Mut MMP 1 WT MMP 1 Mut


b

Supplementary Figure 11. Primer extension assay of ssDNA using IC platform to genotype CYP2C9*2 and CYP2C9*3 alleles. a. Schematic of IC and fluidics showing reaction chambers set up with probes targeting a panel of

markers. b. ssDNA fragments of CYP2C9*2 were incubated with allele specific DNA probe prior to reaction

initiation by polymerase addition immediately before injected onto the chip. Chamber 1 containing 5mM CYPC2C9*2 ssDNA fragment and 7.5mM mutant interrogation probe (Pink) and chamber 2 containing same 5mM ssDNA with 7.5mM wild type probe (yellow) shows a pH drop, indicating the sample being CYP2C9*2 heterozygous. When comparing Chamber 5, which contained 5mM CYP2C9*3 ssDNA fragment and 7.5mM wild type interrogation probe (orange) and Chamber 4, which contained 5mM the same ssDNA fragment and 7.5mM mutant interrogation probe (purple), significantly different patterns were observed, indicating the sample lacks the CYP2C9*3 allele. This chip run concluded that the sample queried CYP2C9*2 heterozygous and CYP2C9*3 wild type. The summary of the data showing correct call rates from multiple runs using the IC for multiplexed genotyping of CYP2C9*2 and CYP2C9*3 is shown below (supplementary Table 3).

c. Acrylamide gel electrophoresis of samples from chip run. Gel image confirms the extension from both DNA probe-types of CYP2C9*2 (lower band on Lane *2 Mut and *2 Wt), while only the wild type allele of CYP2C9*3 showed correct extension (lower band on Lane*3 Wt).


a c


Experiments$No. chips

ISFET to ISFET variation

within a chamber

(CV)*

Chamber to chamber

variation within a

chip (CV)**

Chip to Chip variation

(CV)***

ISFET

variations

(CV)****

Expt 1 5 0.0197 0.0339 0.0299 0.0482

Expt 2 8 0.0236 0.0273 0.0211 0.0501

Expt 3 10 0.0473 0.0409 0.0973 0.1121

Inter-assay CV 0.0302 0.0340 0.0494 0.0701

*** CV of means between chips in an experiment

* Average CV between two ISFETs within a chamber across all chips in an experiment

** Average CV between two chambers within a chip across all chips in an experiment

**** CV between all ISFETs across all chips in an experiment$Three independent experiments were conducted against GH1 (Expt 1 and 3) and CYP2C9*1 (Expt 2) using the on-

chip pH-PCR with purified genomic DNA as input.

Supplementary Table 1: Coefficient of Variation for intra- and inter-chip from three independent

experiments


*1/*1 *1/*2 *2/*2$$ *1/*1 *1/*17 *17/*17

Wild type Heterozygous Mutant Wild type Heterozygous Mutant

Total sample no.

Sample no. 16 6 8 21 2 9

Correct calls 15 6 8 21 2 7

Percentage 94% 100% 100% 100% 100% 78%

Overall percentage

$ Genotypes were called in a blinded trial using samples that had been previously genotyped by TaqMan SNP genotyping assay.

To increase sampling number and provide a level of confidence to the accuracy of the call rates, selective saliva and genomic

samples were replicated.

$$ Due to the lack of CYP2C19*2 homozygous mutant in the collected saliva sample, commercially available purified human

genomic DNA (Coriell Institute) was used.

Supplementary Table 2: Call rates of CYP2C19*2 and CYP2C19*17 genotyping assay using pH-LAMP from saliva

samples.

CYP2C19*2 $ CYP2C19*17 $

30 32

98% 93%


** Genotypes were called in a blinded trial using samples which had been previously

genotyped in a reference laboratory.

Supplementary Table 3: Call rates of multiplexed genotyping of CYP2C9*2 and CYP2C9*3 using primer extension assay.

**


Supplementary Table 4: Primer sets used in this study

Allele Primer name Primer Sequence (5' to 3')

pUC19 Forward 1 CACAATTCCACACAACATACGAGCCG

Reverse 1 GAGCCTATGGAAAAACGCCAGCAAC

Forward 2 TGTTGCCGGGAAGCTAGAGTAAGT

Reverse 2 ATGCAGTGCTGCCATAACCATGAG

CYP2C9*2 Forward_Wt_G GCGGGCTTCCTCTTGAACGCG

Forward_Mut_A GCGGGCTTCCTCTTGAACGCA

Reverse GGAGGATGGAAAACAGAGACTTACAGAGCTC

GH1 Forward 1 CAGTGCCTTCCCAACCATTCCCTTA

Reverse 1 ATCCACTCACGGATTTCTGTTGTGTTTC

NAT2 F3 ACAGAAGAGAGAGGAATCTGGT

B3 GATGAAGCCCACCAAACAGTA

FIP TGTTTCTTCTTTGGCAGGAGATGAGAAGGACCAAATCAGGAGAGAGCA

BIP ATGAATACATACAGACGTCTCCCTGGGGTCTGCAAGGAAC

LoopF GAAATTCTTTGTTTGTAATATAC

LoopB CATCTTCATTTATAACCACATC

CYP2C19*17 F3 GTG AAG CCT GTT TTA TG

B3 CCTGTTGGTGCC

FIP Wt GCT TTG AGA ACA GGA TGA ATG TGG TAT ATA TTC AGA AT

FIP Mut ACT TTG AGA ACA GGA TGA ATG TGG TAT ATA TTC AGA AT

BIP Wt CATCTCTGATGTAAAGCTGGCAGAACTGG

BIP Mut TATCTCTGATGTAAAGCTGGCAGAACTGG

LoopF TAG CAA AAC AAA ACA AC

LoopB GAGATAATGCGCCAC

CYP2C19*2 F3 CCAGACCTTGGCATATTGTATC

B3 AGGGTTGTTGATGTCCAT

FIP Wt CCGGGAAATAATCTTTTAATTTAAATTATTGTTTTCTCTAG

BIP Wt CGGGAACCCGTGTTCTTTTACTTTCTCC

FIP Mut CTGGGAAATAATCTTTTAATTTAAATTATTGTTTTCTCTAG

BIP Mut CAGGAACCCGTGTTCTTTTACTTTCTCC

LoopF GATAGTGGGAAAATTATTGC

LoopB CAAATTACTTAAAAACCTTGCTT

BRAF V600E F3 GGAAAATGAGATCTACTG

B3 TCTCAGGGCCAA

FIP Wt ACTGTAGCTAGCAGATATATTTCTTCATGAAGACCT

BIP Wt TGAAATCTCGATTCCACAAAATGGATCCAGA

FIP Mut TCTGTAGCTAGCAGATATATTTCTTCATGAAGACCT

BIP Mut AGAAATCTCGATTCCACAAAATGGATCCAGA

LoopF ACCAAAATCACCTATTT

LoopB GGAGTGGGTCCC


Supplementary Table 5: Purified human genomic DNA used in this study

Allele Name Genotype Genotype Coriell/genomic ID SNP/Gene ID

CYP2C9*2 Wild type C/C NA07348 rs1799853

CYP2C19*17 Wild type C/C NA10854 rs12248560

CYP2C19*17 Mutant T/T NA10848 rs12248560

CYP2C19*17 Heterozygous C/T NA10831 rs12248560

CYP2C19*2 Wild type G/G NA10835 rs17885098

CYP2C19*2 Mutant A/A NA12717 rs17885098

CYP2C19*2 Heterozygous A/G NA11832 rs17885098

BRAF V600 Wild type T/T K562 rs113488022

BRAF V600E Mutant A/A WC00048 rs113488022

NAT2 N/A N/A K562 NT_167187.1

NAT2 N/A N/A NA10835 NT_167187.1

GH1 N/A N/A NA12751


SUPPLEMENTARY NOTE 1: Integration of semiconductor physics with molecular chemistry The ISFET was first introduced in 1970 by Bergveld3, where the metal gate from a FET was omitted and the gate oxide layer was exposed to an ionic solution. The threshold voltage of this first device was responsive to the ionic strength of the solution, thus making ISFET an ideal glass-free pH sensor. In the present day, ISFETs have been utilised for various biological sensing applications and the fabrication of ISFETs has since been integrated into the CMOS processing4. This manuscript describes the use of ISFETs to detect nucleic acid amplification chemistries. The relationship between the reaction chemistry and the fundamental physics behind the ISFETs can be qualitatively accounted by a straightforward equation. Below, the derivation of the equation, and how the equation can be applied to shape the signal curves for a nucleic acid amplification reaction is presented. Semiconductor physics The ISFETs in our IC are created using a standard MOSFET from a given CMOS technology, with the gate oxide of the device coupled to the top metal passivation via a floating gate metal stack. The gate bias of the device is applied using a reference electrode, typically Ag/AgCl, which also provides a stable phase-boundary potential to the solution5. The sensing layer can be any insulator with a high dielectric constant, typically a metal or silicon oxide or nitride e.g. Al2O3, Ta2O5, HfO2, SiO2 and Si3N4. For fabrication avoiding any modifications to standard CMOS semiconductor manufacturing, the protective passivation layer of standard CMOS which is typically Si3N4 on SiO2can be used, and this is the method of choice for this study as it significantly reduces the cost of fabrication. The sensing layer, being an insulator, accumulates protons through site binding at its surface due to the presence of charged sites and the Gouy-Chapman-Helmholtz capacitive double layer formed when a voltage is applied on the reference electrode in solution6. The protons then modulate the charge distribution in the channel (between source and drain) of the ISFET, changing the threshold voltage of the device. A change in ionic concentration can thus be measured by observing the threshold voltage of the transistor. When the ISFET is biased with a stable reference electrode, ions in solution bind to the passivation layer causing an accumulation of charge which in turn modulates the threshold voltage of the transistor7. This results in a dependence of the ISFET threshold voltage to pH which can be observed as a shift in the threshold voltage of the device (Supplementary note Fig. 1).


Supplementary note figure 1: Illustration of an array of reaction chambers coupled to the ISFETs. The expression for the threshold voltage of an ISFET is typically defined as: ( ) ( ) [1] wherein

( ) (√ √ ) [2]

and [3] Whereby Vth (MOSFET) is the threshold voltage of the intrinsic MOSFET from which the ISFET is made and Vchem is a grouping of the chemically related terms, including pH8. Ut (= kT/q) is the thermal voltage of the device, is a grouping of non-chemically related potentials and α is a number ranging from 0-1, describing the reduction in sensitivity from the ideal Nernstian response, typically 59mV/pH at room temperature. This allows for a more intuitive description of the ISFET characteristics as is contains a term relating to the pH of the electrolyte. Next, unifying equation [1], [2] and [3] and taking the first derivative we calculate the change in threshold voltage of the ISFET as a function of ΔpH: ( ) [4] Thus, equation 4 illustrates that a change in the threshold voltage is directly proportional to a change in pH8.


Nucleic acid incorporation chemistries and Vth(ISFET)

As shown in this manuscript, incorporation of a nucleotide into a strand of DNA results in the release of a proton. A single nucleotide incorporation reaction can be defined by the following equation:

HxdNTP + DNA DNA+1 + HyPPi + Hz [5]

Where DNA represents the target strand DNA, HxdNTP represents the triphosphate nucleotide which can be any of the four bases (dATP, dCTP, dTTP, dGTP). The hydrolysis and incorporation of a nucleotide results in the extension of DNA by a single base, represented as DNA+1. In addition, pyrophosphate, HyPPi, and hydrogen ions, Hz, are released. It must be noted that this reaction is in a unique dynamic equilibrium:

whereby the number of hydrogen ions released, Hz, is a function of those bound to the original dNTP, Hx, and those consumed by the pyrophosphate, Hy. However, in order to trigger a change in the pH value, there exists a proton disequilibrium between both sides of the reaction wherein z > x - y or z < x - y.

We can now rearrange Equation [4] to give the hydrogen ion production as:

Hz = DNA - DNA+1 + HxdNTP - HyPPi [6]

Given that a change in pH is a function of the protons generated and the buffer capacity (β), we may generalise that a change in the reaction pH as a result of nucleotide incorporation may be given by:

[7]

Where A1 is defined as the number of insertions at a single nucleic acid strand and A2 is defined as the number of copies of nucleic acid strands, hence A1A2 is defined as the total number of nucleotides incorporated in a reaction at a given time or cycle.

In equation 7, pH is directly proportional to A1A2, thus an increase in total number of nucleotide

insertion will result in an increase in pH. We have demonstrated the relationship between

pH and nucleotide incorporation in Figure 2 of the manuscript, where we observed a strong

correlation between increased pH and increased number of nucleotide incorporated.

Conversely, pH is inversely proportional to buffer capacity, where an increase in buffering

capacity will result in a decrease in pH. The balance between the buffering capacity and the number of nucleotide insertions dictates the magnitude of pH change.

We can now unify the equation of threshold voltage of the ISFET with change in pH as a function of nucleic acid synthesis reaction by combining equation 4 and 7:

( )

[8]


Equation 8 combines both the ISFET characteristics and the reaction chemistry of DNA. This generic equation can be applied to qualitatively describe an amplification curve. For example, in a PCR reaction, the amount of amplicon should double in each cycle, resulting in an exponential increase in protons. However during the early (lag) phase of the amplification reaction, the quantity of protons generated are not sufficient to overcome the buffering capacity of the solution as well as the detection limit on the sensing layer, thus little change in Vth is observed. Eventually, as the amplicon continues to increase exponentially, enough protons accumulate to overcome the buffering capacity, yielding a detectable signal (exponential phase) (Supplementary note Fig. 2).

During the non-exponential phase of the reaction, two scenarios likely influence the rate of amplification and entrance into the plateau phase. The first is the exhaustion of one or more of the reaction components which may become limiting as the reaction proceeds. The second scenario is the reduction in polymerase activity under suboptimal pH condition, which transpires when protons continue to accumulate, thus decreasing the overall pH of the reaction. Both scenarios are likely contributed to the characteristics of the non-exponential phase and the eventual plateau phase, during which the amplification slows and eventually stops.

Supplementary note Figure 2: pH dependent amplification plot showing the lag phase, exponential phase and non-exponential phase.


REFERENCE

1. Hiratsuka, M. In vitro assessment of the allelic variants of cytochrome P450. Drug Metab Pharmacokinet 27, 68-84 (2012).

2. D.M. Garner et al. A multichannel DNA SoC for rapid point-of-care gene detection. 2010 IEEE International Solid-State Circuits Conference - (ISSCC) 57, 492-493 (2010).

3. Bergveld, P. Development of an Ion-Sensitive Solid-State Device for Neurophysiological Measurements. IEEE Trans. Biomed. Eng. 70-71 (1970).

4. Bausells, J., Carrabina, J., Errachid, A. & Merlos, A. Ion-sensitive field-effect transistors fabricated in a commercial CMOS technology. Sens. Actuators B Chem. 57, 56-62 (1999).

5. Janata, J and Huber, R. Solid State Chemical Sensors. Academic Press (1985). 6. Bard, A. J. and Faulkner, L. Electrochemical Methods, 2nd ed., John Wiley and Sons (2001). 7. Bergveld, P, DeRooij, N. and Zemel, J. Physical mechanisms for chemically sensitive semiconductor

devices. Nature 273, 438-443 (1978). 8. Shepherd, L.M. and Toumazou, C. A biochemical translinear principle with weak inversion ISFETs.

IEEE Trans. circuits and systems I-regular papers 52, 2614-2619 (2005).


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