throbber
Novel Molecular Engineering Approaches for Genotyping and
`DNA Sequencing
`
`Chunmei Qiu
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`Submitted in partial fulfillment of the
`requirements for the degree
`of Doctor of Philosophy
`in the Graduate School of Arts and Sciences
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`COLUMBIA UNIVERISTY
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`2011
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`Page a
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`Illumina Ex. 1094
`IPR Petition - USP 10,435,742
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`© 2011
`Chunmei Qiu
`All Rights Reserved
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`ABSTRACT
`
`Novel Molecular Engineering Approaches for Genotyping and DNA
`
`Sequencing
`
`Chunmei Qiu
`
`The completion of the Human Genome Project has increased the need for investigation
`
`of genetic sequences and their biological functions, which will significantly contribute to
`
`the advances in biomedical sciences, human genetics and personalized medicine.
`
`Matrix-assisted
`
`laser
`
`desorption/ionization
`
`time-of-flight mass
`
`spectrometry
`
`(MALDI-TOF MS) offers an attractive option for DNA analysis due to its high accuracy,
`
`sensitivity and speed. In the first part of the thesis, we report the design, synthesis and
`
`evaluation of a novel set of mass tagged, cleavable biotinylated dideoxynucleotides
`
`(ddNTP-N3-biotins) for DNA polymerase extension reaction and its application in DNA
`
`sequencing and single nucleotide polymorphism (SNP) genotyping by mass spectrometry.
`
`These nucleotide analogs have a biotin moiety attached to the 5 position of the
`
`pyrimidines (C and U) or the 7 position of the purines (A and G) via a chemically
`
`cleavable azido-based linker, with different length linker arms serving as mass tags that
`
`contribute large mass differences among the nucleotides to increase resolution in MS
`
`analysis. It has been demonstrated that these modified nucleotides can be efficiently
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`incorporated by DNA polymerase, and the DNA strand bearing biotinylated nucleotides
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`can be captured by streptavidin coated beads and efficiently released using
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`tris(2-carboxyethyl) phosphine in aqueous solution which is compatible with DNA and
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`downstream procedures. Reversible solid phase capture (SPC) mass spectrometry
`
`sequencing using ddNTP-N3-biotins was performed, and various DNA templates,
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`including biological samples, were accurately sequenced achieving a read-length of 37
`
`bases. In mass spectrometric SNP genotyping, we have successfully exploited our
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`reversible solid phase capture (SPC)-single base extension (SBE) assay and been able to
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`detect as low as 2.5% heteroplasmy in mitochondrial DNA samples, with interrogation of
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`human mitochondrial genome position 8344 which is associated with an important
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`mitochondrial disease (myoclonic epilepsy with ragged red fibers, MERRF); we have
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`also quantified the heteroplasmy level of a real MERRF patient and determined several
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`mitochondrial MERRF mutations in a multiplex approach. These results demonstrated
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`that our improved mass spectrometry genotyping technologies have great potential in
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`DNA analysis, with particular applications in sequencing short-length targets or detecting
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`SNPs with high accuracy and sensitivity requirements, such as DNA fragments with
`
`small
`
`indels, or SNPs
`
`in pooled samples. To
`
`truly
`
`implement
`
`this mass
`
`spectrometry-based genotyping method, we further explored the use of a lab-on-a-chip
`
`microfluidic device with the potential for high throughput, miniaturization, and
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`automation. The microdevice primarily consists of a micro-reaction chamber for single
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`base extension and cleavage reactions with an integrated micro heater and temperature
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`sensor for on-chip temperature control, a microchannel loaded with streptavidin magnetic
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`beads for solid phase capture, and a microchannel packed with C18-modified
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`reversed-phase silica particles as a stationary phase for desalting before MALDI-TOF
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`analysis. By performing each functional step, we have demonstrated 100% on-chip single
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`base incorporation, sufficient capture and release of the biotin-ddNTP terminated single
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`base extension products, and high sample recovery from the C18 reverse-phase
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`microchannel with as little as 0.5 pmol DNA molecules. The feasibility of the
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`microdevice has shown its promise to improve mass spectrometric DNA sequencing and
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`SNP genotyping to a new paradigm.
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`DNA sequencing by synthesis (SBS) appears to be a very promising molecular tool for
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`genome analysis with the potential to achieve the $1000 Genome goal. However, the
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`current short read-length is still a challenge. Therefore, the second part of the thesis
`
`focuses on strategies to overcome the short read-length of SBS. We developed a novel
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`primer walking strategy to increase the read-length of SBS with cleavable fluorescent
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`nucleotide reversible terminators (CF-NRTs) and nucleotide reversible terminators (NRTs)
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`or hybrid-SBS with cleavable fluorescent nucleotide permanent terminators and NRTs.
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`The idea of the walking strategy is to recover the initial template after one round of
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`sequencing and re-initiate a second round of sequencing at a downstream base to cover
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`more bases overall. The combination of three natural nucleotides and one NRT
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`effectively regulated the primer walking: the primer extension temporarily paused when
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`the NRT was incorporated, and resumed after removing the 3’ capping group to restore
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`the 3’-OH group. We have successfully demonstrated the integration of this primer
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`walking strategy into the sequencing by synthesis approach, and were able to obtain a
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`total read-length of 53 bases, nearly doubling the read-length of the previous sequencing.
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`On the other hand, we explored the sequencing bead-on-chip approach to increase the
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`throughput of SBS and hence the total genome coverage per run. The various prerequisite
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`conditions have been optimized, allowing the accurate sequencing of several bases on the
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`bead surface, which demonstrated the feasibility of this approach. Both of these
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`approaches could be integrated into current SBS platforms, allowing increased overall
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`coverage and lowering overall costs.
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`As a step beyond genotyping, the in vivo visualization of biomolecules, like DNA and its
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`encoded RNA and proteins, provides further information about their biological functions
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`and mechanisms. The third part of the thesis focuses on the development of a novel
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`quantum dot (QD)-based binary molecular probe, which takes advantage of fluorescent
`
`resonance energy transfer (FRET), for detection of nucleic acids, aiming at their eventual
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`use for detection of mRNAs involved in long term memory studies in the model
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`organism Aplysia californica. We reported the design, synthesis, and characterization of a
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`binary probe (BP) that consists of carboxylic quantum dot (CdSe/ZnS core shell)-DNA
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`(QD-DNA) conjugated donor and a cyanine-5 (Cy5)-DNA acceptor for the detection of a
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`sensorin mRNA-based synthetic DNA molecule. We have demonstrated that in the
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`absence of target DNA, the QD fluorescence is the main signal observed (605 nm); in the
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`presence of the complementary target DNA sequence, a decrease of QD emission and an
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`increase of Cy5 emission at 667 nm was observed. We have demonstrated the distance
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`dependence of FRET, with the finding that the target with 16 base separation between the
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`QD and Cy5 after probe hybridization gave the most efficient FRET. Further studies are
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`in progress to evaluate the effectiveness of this QD-based probe inside a cell extract and
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`in living cells.
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`Table of Contents
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`List of Figures and Tables..............................................................................................x
`
`Acknowledgements......................................................................................................xx
`
`Abbreviations and Symbols ..................................................................................... xxiii
`
`
`
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`Chapter 1 Introduction to Genomic Analysis Technologies -- DNA sequencing,
`
`Genotyping, Nucleic Acid Detection .............................................................................1
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`1.1 Introduction to DNA sequencing technology ...................................................2
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`1.1.1 Background and significance..................................................................2
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`1.1.2 DNA sequencing technologies overview................................................4
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`1.1.2.1 Conventional Sanger Sequencing .................................................5
`
`1.1.2.2 Mass Spectrometry based sequencing ..........................................6
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`1.1.2.3 Sequencing by hybridization.........................................................9
`
`1.1.2.4 Sequencing by synthesis .............................................................10
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`1.1.2.4.1 Pyrosequencing.................................................................11
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`1.1.2.4.2 Sequencing by ligation......................................................13
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`1.1.2.4.3 Sequencing by synthesis with cleavable fluorescent nucleotide
`
`reversible terminators.......................................................................15
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`1.1.2.4.4 Single molecule sequencing-by-synthesis ........................17
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`1.1.2.5 Sequencing by direct physical recognition of the DNA molecule22
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`1.1.2.5.1 Nanopore sequencing........................................................22
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`1.1.2.5.2 Tunneling and transmission electron microscopy based single
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`molecule DNA sequencing ..............................................................26
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`1.1.3 Conclusion ............................................................................................28
`
`1.2 Introduction to SNP genotyping technology...................................................29
`
`1.2.1 Background and Significance ...............................................................29
`
`1.2.2 Overview of SNP genotyping technologies..........................................30
`
`1.2.2.1 SNP genotyping by enzymatic cleavage.....................................31
`
`1.2.2.2 SNP genotyping by allele specific hybridization........................33
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`1.2.2.3 SNP genotyping by allele specific ligation.................................36
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`1.2.2.4 SNP genotyping by allele specific primer extension ..................39
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`1.2.3 Conclusion ............................................................................................43
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`1.3 Introduction to the detection of nucleic acids by oligonucleotide probes ......44
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`1.3.1 Background and significance................................................................44
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`1.3.2 Overview of oligonucleotide probes for detection of nucleic acids .....45
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`1.3.2.1 Molecular beacons ......................................................................45
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`1.3.2.2 Binary oligonucleotide probes ....................................................48
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`1.3.3 Conclusion ............................................................................................49
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`References.............................................................................................................50
`
`Part I Mass Spectrometric DNA Sequencing and SNP Genotyping with Cleavable
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`Biotinylated Dideoxynucleotides
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`Chapter 2 Design and Synthesis of Cleavable Biotinylated Dideoxynucleotides for DNA
`
`Sequencing and Genotyping by MALDI-TOF Mass Spectrometry ............................61
`
`2.1 Introduction.....................................................................................................61
`
`2.2 Experimental Rationale and Overview ...........................................................65
`
`2.3 Results and Discussion ...................................................................................67
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`2.3.1 Design and synthesis of cleavable biotinylated dideoxynucleotides ....67
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`2.3.2 Polymerase extension using ddNTP-N3-biotins, solid phase capture and
`
`cleavage..........................................................................................................70
`
`2.3.3 Comparison with non-cleavable biotinylated dideoxynucleotides .......75
`
`2.4 Materials and Methods....................................................................................77
`
`2.4.1 Synthesis of ddNTP-N3-biotins.............................................................77
`
`2.4.2 Polymerase extension using ddNTP-N3-biotins, solid phase capture and
`
`cleavage..........................................................................................................82
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`2.4.3 Comparison of ddATP-N3-biotin and biotin-11-ddATP.......................83
`
`2.5 Conclusion ......................................................................................................84
`
`References.............................................................................................................85
`
`Chapter 3 DNA Sequencing by MALDI-TOF Mass Spectrometry using Cleavable
`
`Biotinylated Dideoxynucleotides.................................................................................88
`
`3. 1 Introduction....................................................................................................88
`
`3.2 Experimental Rationale and Overview ...........................................................94
`
`3.3 Results and Discussion ...................................................................................96
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`3.3.1 DNA sequencing on synthetic template................................................96
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`3.3.2 DNA sequencing on biological template ..............................................97
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`3.4 Materials and Methods....................................................................................99
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`3.4.1 Sanger DNA sequencing reaction .........................................................99
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`3.4.2 PCR reactions for generating biological template ..............................100
`
`3.4.3 DNA sequencing on biological template ............................................101
`
`3.4.4 Solid-phase purification of DNA-sequencing products
`
`for mass
`
`spectrometry measurements.........................................................................101
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`3.5 Conclusion ....................................................................................................102
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`References...........................................................................................................103
`
`Chapter 4 SNP Genotyping of Mitochondrial DNA by MALDI-TOF MS using Cleavable
`
`Biotinylated Dideoxynucleotides...............................................................................104
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`4.1 Introduction...................................................................................................104
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`4.2 Experimental Rationale and Overview .........................................................108
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`4.3 Results and Discussion ................................................................................. 111
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`4.3.1 PCR amplification of targeted region in mitochondrial DNA ............ 111
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`4.3.2 A8344G uniplex genotyping...............................................................113
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`4.3.3 5-plex genotyping ...............................................................................116
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`4.3.4 Quantitative mutation analysis for mitochondrial sample ..................118
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`4.3.5 Sensitivity of SPC-SBE MALDI-TOF MS for detecting low heteroplasmy
`
`of mitochondrial DNA .................................................................................121
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`4.4 Materials and Methods..................................................................................125
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`4.4.1 PCR amplification...............................................................................125
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`4.4.2 Quantification of mtDNA in the samples............................................126
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`4.4.3 Single base extension using cleavable biotinylated dideoxynucleotides for
`
`MALDI-TOF MS detection .........................................................................128
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`4.4.4 Direct Sanger DNA Sequencing and PCR-RFLP Assay.....................129
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`4.5 Conclusion ....................................................................................................130
`
`References...........................................................................................................131
`
`Chapter 5 Exploration of the Integrated Microdevice for SNP Genotyping by
`
`MALDI-TOF Mass Spectrometry..............................................................................135
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`5.1 Introduction...................................................................................................135
`
`5.2 Experiment Rationale and Overview............................................................137
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`5.3 Results and Discussion .................................................................................141
`
`5.3.1 Temperature Sensor Calibration..........................................................141
`
`5.3.2 On-chip testing....................................................................................142
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`5.3.2.1 On-chip single base extension ..................................................143
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`5.3.2.2 On-chip solid phase capture......................................................144
`
`5.3.2.3 On-chip desalting......................................................................145
`
`5.4 Materials and Methods..................................................................................146
`
`5.4.1 Microfluidic Device fabrication..........................................................147
`
`5.4.2 Experimental setup..............................................................................149
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`5.4.3 Microdevice performance testing .......................................................151
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`5.4.3.1 Temperature Sensor Calibration................................................151
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`5.4.3.2 Single base extension................................................................151
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`5.4.3.3 Solid phase capture and cleavage test.......................................152
`
`5.4.3.4 C18 reversed phase desalting....................................................153
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`5.5 Conclusion ....................................................................................................153
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`References...........................................................................................................154
`
`Part II Strategies to Improve Sequencing by Synthesis with Cleavable Fluorescent
`
`Nucleotide Reversible Terminators
`
`Chapter 6 Development of Primer “Walking” Strategy to Increase the Read-Length of
`
`Sequencing by Synthesis............................................................................................157
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`6.1 Introduction...................................................................................................157
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`6.2 Experimental Rationale and Overview .........................................................168
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`6.3 Results and Discussion .................................................................................171
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`6.3.1 Optimization of primer annealing to DNA template on solid surface 171
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`6.3.2 Sequencing by synthesis on linear DNA template..............................173
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`6.3.2 Primer resetting and walking for extending read-length.....................175
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`6.3.2.1 Primer walking using three natural nucleotides........................176
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`6.3.2.2 Primer walking using three natural nucleotides and one reversible
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`nucleotide terminator ............................................................................182
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`6.4 Materials and Methods..................................................................................187
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`6.4.1 Primer hybridization ...........................................................................189
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`6.3.2 Primer resetting and walking ..............................................................191
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`6.3.2.1 Primer walking using three natural nucleotides........................192
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`6.3.2.2 Primer walking using three natural nucleotides and one reversible
`
`nucleotide terminator ............................................................................193
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`6.4 Conclusion ....................................................................................................195
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`References...........................................................................................................196
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`Chapter 7 Exploration of an “Emulsion PCR-Bead-on-Chip” Approach to Improve the
`
`Throughput of Sequencing by Synthesis ...................................................................198
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`7.1 Introduction...................................................................................................198
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`7.2 Experiment Rationale and Overview............................................................201
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`7.3 Results and Discussion .................................................................................203
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`7.3.1 Covalent attachment of DNA onto the beads......................................203
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`7.3.2 Biological affinity attachment of DNA onto the beads.......................204
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`7.3.3 Nucleotide incorporation studies on bead surfaces.............................206
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`7.3.3.1 Pyrosequencing.........................................................................206
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`7.3.3.2 Incorporation of fluorescence labeled ddNTPs and natural dNTPs
`
`...............................................................................................................207
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`7.3.3.3 Sequencing by synthesis on beads using CF-NRTs/NRTs........208
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`7.3.4 PCR on beads in solution and beads in emulsion ...............................210
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`7.4 Materials and Methods..................................................................................212
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`7.4.1 DNA attachment to beads ...................................................................212
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`7.4.2 Nucleotide incorporation test on beads...............................................215
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`7.4.3 Sequencing by synthesis with cleavable fluorescent nucleotide reversible
`
`terminators on beads ....................................................................................216
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`7.4.4 PCR on beads and emulsion-beads in droplet.....................................218
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`7.5 Conclusion ....................................................................................................219
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`References...........................................................................................................220
`
`Part III Detection of Nucleic Acids with Molecular Probes
`
`Chapter 8 Quantum Dot based FRET Binary Probes for Detection of Nucleic Acids223
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`8.1 Introduction...................................................................................................223
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`8.2 Experimental Rationale and Overview .........................................................226
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`8.3 Results and Discussion .................................................................................228
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`8.3.1 The synthesis of QD-DNA conjugates................................................228
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`8.3.2 Hybridization kinetics studies.............................................................230
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`8.3.3 Comparison of FRET efficiency between carboxyl-QD-DNA conjugate
`
`and streptavidin-QD-DNA conjugate based binary probes .........................232
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`8.3.4 Distance dependent FRET studies with carboxyl-QD binary probes .233
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`8.4 Materials and Methods..................................................................................236
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`8.4.1 Synthesis of QD-DNA conjugates ......................................................237
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`8.4.2 Hybridization of QD-DNA and Cy5-DNA with different targets.......238
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`8.4.3 Steady-state fluorescence and time-resolved fluorescence measurement239
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`8.5 Conclusion ....................................................................................................239
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`References...........................................................................................................240
`
`Chapter 9 Summary and Future Outlook...................................................................242
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`9.1 Mass spectrometric DNA sequencing and SNP genotyping with cleavable
`
`biotinylated dideoxynucleotides1, 2 .....................................................................242
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`9.2 Strategies to improve sequencing by synthesis with cleavable fluorescent
`
`nucleotide reversible terminators3.......................................................................243
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`9.3 Detection of nucleic acids with molecular probes4.......................................244
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`9.4 Future outlook...............................................................................................245
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`9.4.1 Mass spectrometric DNA sequencing and SNP genotyping...............245
`
`9.4.2 DNA sequencing by synthesis ............................................................246
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`9.4.3 In vivo visualization of nucleic acids..................................................247
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`
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`References……...….…………………………………………………………………248
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`List of Figures and Tables
`
`Fig. 1.1 Chemical structures of 2’-deoxyribonucleotides (dNTPs). Each nucleotide is
`composed of a base (adenine, guanine, cytosine or thymine), a sugar and a
`phosphate group..............................................................................................3
`
`Fig. 1.2. Principle of Sanger sequencing. ...............................................................6
`
`Fig. 1.3. Schematic process of mass spectrometry assisted sequencing. (A) Sanger
`sequencing reaction based MS sequencing; (B) Enzymatic digestion based MS
`sequencing.......................................................................................................8
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`Fig.1.4. Schematic view of pyrosequencing.25 .....................................................11
`
`Fig. 1.5. Principle of sequencing by ligation. (A) DNA template molecule with two
`mate-pair tags of unique sequence which are flanked and separated by universal
`sequences complementary to amplification or sequencing primers. (B) Steps of
`sequencing by ligation. .................................................................................13
`
`Fig. 1.6. Principle of sequencing by synthesis with cleavable fluorescent nucleotide
`reversible terminators....................................................................................17
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`Fig. 1.7 Schematic of the single molecule sequencing-by-synthesis approach with
`virtual terminators.49 .....................................................................................19
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`Fig. 1.8 Principle of single-molecule, real-time DNA (SMRT) sequencing. 31....21
`
`Fig. 1.9. Schematic of various Nanopore sequencing method. (A) Fundamental
`principle of nanopore sequencing; (B) Nanopore sequencing approach by
`Oxford Technology;65 (C) duplexes halting translocation sequencing by MspA
`nanopore;66 (D) Nanopore single-molecule optical detection approach;69 (E)
`Schematic of the DNA transistor. The light blue regions with voltage labeled are
`the conductors, while the light green regions are insulators.67 .....................23
`
`Fig. 1.10 (A) Reveo STM-based sequencing.49 (B) DNA sequencing by direct
`inspection of DNA using electron microscopy 9...........................................27
`
`Fig. 1.11. Schematic diagram of SNP enzymatic cleavage assay. (A)PCR-RFLP
`assay; (B) Invasive cleavage assay. ..............................................................32
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`Fig. 1.12 Approaches of SNP genotyping by allele specific hybridization. (A) DNA
`microarray hybridization; (B) TaqMan assay................................................35
`
`Fig. 1.13 Methods for SNP genotyping by ligation. (A) Fluorescence based ligation
`assay; (B) Ligation-rolling circle amplification assay. .................................39
`
`Fig. 1.14 Allele specific primer extension. (A) Fluorescence based detection; (B)
`Mass spectrometry based detection. .............................................................41
`
`Fig. 1.15. Principle of oligonucleotide probes for detection of nucleic acid. (A)
`molecular beacons; (B) binary probes...................................................................47
`
`Fig. 2.1. Principle of matrix-assisted laser desorption/ionization time-of-flight mass
`spectrometry (MALDI-TOF MS).7...............................................................62
`
`Fig. 2.2. Scheme of single base extension, solid phase capture and cleavage using
`chemically cleavable dideoxynucleotides.....................................................66
`
`Fig. 2.3. Structures of cleavable dideoxynucleotides (ddNTP-N3-biotins). Note that
`the length of the portion of the linker between the base and the N3 group, the
`segment which remains attached to the extended DNA after TCEP cleavage,
`varies between the two purine (A and G) and the two pyrimidine bases (C and
`U) bases, enabling clear discrimination of their sizes by MALDI-TOF mass
`spectrometry..................................................................................................69
`
`Fig. 2.4. MALDI-TOF mass spectra of the DNA extension products, their subsequent
`cleavage products in solution, and released DNA products from streptavidin
`coated magnetic beads. (A) primers extended with ddATP-N3-biotin (1) (8889
`m/z); (B) their cleavage products (2) (8416 m/z); (C) released products from
`solid phase (3) (8416 m/z); (D) primers extended with ddGTP-N3-biotin (4)
`(9018 m/z); (E) their cleavage products (5) (8545 m/z); (F) released products
`from solid phase (6) (8545 m/z) (G) primers extended with ddCTP-N3-biotin (7)
`(8866 m/z); (H) their cleavage products (8) (8393 m/z); (I) released products
`from solid phase (9) (8866 m/z); (J) primers extended with ddUTP-N3-biotin
`(10) (8980 m/z); (K) their cleavage products (11) (8507 m/z); (L) released
`products from solid phase (12) (8507 m/z)...................................................72
`
`Fig. 2.5. Polymerase extension reaction using ddATP-N3-biotin as a substrate and
`TCEP cleavage of DNA fragments containing ddA-N3-biotin on streptavidin
`coated beads. The DNA polymerase Thermo Sequenase
`incorporates
`ddATP-N3-biotin to generate the extension product (1). Cleavage by TCEP of
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`the DNA extension products captured on streptavidin-coated beads produces
`released products (3), while the biotin moiety remains on the solid surface of
`the beads........................................................................................................73
`
`Fig. 2.6. Staudinger reaction with TCEP to cleave the azido-based linker and release
`the DNA extension products from the streptavidin coated surface...............74
`
`Fig. 2.7. Comparison of cleavable biotinylated dideoxynucleotide (ddATP-N3-biotin)
`and uncleavable biotinylated dideoxynucleotide
`(biotin-11-ddATP).
`(A)
`Chemical structures of ddATP-N3-biotin and biotin-11-ddATP); (B) the
`purification process
`for each nucleotide. Note: after cleavage,
`the
`biotin-11-ddATP
`incorporated DNA
`template requires an extra ethanol
`precipitation step; (C) mass spectrum of final product for starting template: a,
`0.5 pmol, b, 1.0 pmol, c, 2.5 pmol. ...............................................................76
`
`Fig. 2.8. Structures of 5- or 7-propargylamino-ddNTPs.......................................78
`
`Fig. 2.9. Synthesis and structures of Biotin-N3-linker attached ddNTPs ................81
`
`Fig. 3.1. The mass spectra of mock A, C, G, and T sequencing reactions containing
`mixtures of synthetic oligonucleotides. (A) Individual spectra; (B) The spectra
`are overlaid and displayed on the same mass scale. 5...................................90
`
`Fig. 3.2. Solid-phase-capture (SPC) sequencing. (A) A SPC-sequencing scheme to
`isolate pure DNA fragments for MS analysis; (B) A DNA sequencing mass
`spectrum generated after extension with biotinylated terminators.11............92
`
`Fig. 3.3. Scheme for purification of DNA-sequencing fragments for MALDI-TOF
`MS analysis. DNA-sequencing fragments are isolated from the sequencing
`solution containing excess primers, falsely stopped fragments and salts by
`streptavidin-coated magnetic beads. Then the sequencing fragments are cleaved
`from the beads with TCEP for MALDI-TOF MS analysis, leaving the biotin
`moiety still bound to the surface...................................................................95
`
`Fig. 3.4. Mass-sequencing spectrum generated using ddNTP-N3-biotins on a
`synthetic template. The nested insets show increasing magnifications of the
`lower inte

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