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Diagnostics Group, PMC Advanced Technology DNA Amplification Research & Technology Development

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Wild Type DNA Mutated DNA Cancer mutation diagnosis Unknown mutation in one geneKnown mutations in multiple genes Purpose: Early stage detection of metastasis Example: p53 exon 8 in plasma Desired sensitivity: <= 1% mutant/wt Problem: Detect in heavy wt background Standard solution: COLD PCR Purpose: Either assess prognosis or determine choice of drug treatment Example: kras, BRAF V600E Problem: amplify in parallel while avoiding nonspecific products Standard approach: primer design Mutation 1Mutation 2

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Metastatic Cancer Mutations p53 tumor suppressor k-ras tumor suppressor Trinucleotide Repeat Mutations HTT (Huntington’s Disease) DMPK (Muscular Dystrophy) FMR-1 (Fragile X; Autism’s leading cause) DNA disease diagnostics applications Mutated tumor suppressor DNA must be detected at low copy #’s (0.1%-1% mutant / wt) in blood for early diagnosis Patents: R. Chakrabarti and C.E. Schutt, US Patent 7,772,383, issued 8-10-10; US Patent 7,276,357, issued 10-2-07; US Patent 6,949,368, issued 9-27-05. Licensees: 1) Celera, Abbott Diagnostics: 1 st FDA approved Fragile X PCR diagnostic (2008); 2) New England Biolabs (2012) 3) Roche Molecular Diagnostics* 4) Undisclosed (possibly Asuragen)* *under negotiation

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Kinetic modeling of controlled DNA amplification Aim of this work : to establish a) kinetic models for future use with b) engineering control theory in developing these general diagnostic solutions. Engineering Optimization & Control of PCR Manipulate time-independent PCR parameters (media engineering) Control time-dependent temperature inputs (thermal cycling) MALDI-TOF Sanger SequencingPyrosequencing Cancer Mutation DiagnosisTriplet Repeat Diagnosis Downstream sequence analysis methods Current Equilibrium Models | New Kinetic Models

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Wild Type DNA Mutated DNA The DNA Amplification Control Problem and Cancer Diagnostics: detailed example of need for modified temperature cycling protocols Can’t maximize concentration of target DNA sequence by maximizing any individual kinetic parameter Analogy between a) exiting a tight parking spot b) maximizing the concentration of one DNA sequence in the presence of single nucleotide polymorphisms

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Simplex PCR – State Equations Annealing – State Equations Rate constants to be determined k 1i & k 2i - Theoretical Determination using Relaxation time and Equilibrium Relationships Enzyme Binding – State Equations Rate constants to be determined k e, k -e, k cat /K N – Determine using the available rate of nucleotide addition data and equilibrium enzyme binding data

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Extension Reaction– State Equations Rate constant to be determined k’ cat - Determine using the available rate of nucleotide addition data

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Inputs Primer Sequence Melting, Annealing and Extension Temperature Melting, Annealing and Extension reaction time Salt Concentration values Initial Concentration of template, primer, nucleotide and enzyme. NN Parameters. Length of the target Number of PCR cycles. Determine the Kinetic Parameters Determine the rate constants of Annealing reaction Determine the rate constants for the Enzyme binding reaction. Determine the rate constants for the Extension reaction Theoretically determine the equilibrium constants using the nearest neighbor Method. Theoretically determine the relaxation time Solve the equilibrium and relaxation time equations for forward and backward rate constants of annealing reaction Simulate the Dynamics Solve the rate expression for the annealing and extension reaction together. Fit the number of nucleotide addition per second data (available) for the extension rate expression and determine kcat/Kn Summary of PCR Kinetic Model Assume the forward rate constant of enzyme binding reaction using the available literature data and use the published equilibrium constant to determine the backward rate constant

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Kinetic Model (Annealing/Melting) ΔG – From Nearest Neighbor Model τ – Relaxation time (Theoretical/Experimental) Solve above equations to obtain rate constants individually.

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Relaxation time Perturbation theory used to derive the theoretical expression for RT. S – Stability constant of a single base pair – Geometric mean of over all stability constant. σ – Factor that accounts resistance of first base pair annealing or melting - 10 -4 to 10 -5 (Jost and Everaers, 2009). k i,i-1 - 10 6 sec -1.

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Experimental Validation Comparison of theoretical prediction and experimental values of A9U9 hybridization reaction. Theoretically predicted values perfectly fits with R 2 = 1 There are no constraints that follows Arrhenius law,forced in our theoretical method.

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Datta and LiCata, Nucleic Acids Research, 2003, Vol. 31, No. 19 K d = f(T), Equilibrium constant for Enzyme duplex dissociation reaction. Enzyme Binding Kinetics Optimal temperature – Maximum Association Rate Enzyme binding rate varies greatly between Annealing and extension temperatures Enzyme binding is rate limiting step near primer melting temperatures –implications for choice of annealing/extension temperatures Temperature dependent rate constant is needed to model whole PCR

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Extension Rate constants k cat /K N Innis et al (1988) published data on the number of nucleotides added per enzyme molecule at different temperatures. Using this information it is possible to fit the extension rate equation to find the k cat /K N

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5/1/2015145/1/201514School of Chemical Engineering, Purdue University Extension Kinetics Nucleotide Addition per time at different temperature is given by Innis et al. Proc.Natl.Acad.Sci - Vol 85, pp - 9436-9449, Dec-1988 Temperature (Deg C) Number of Nucleotide Incorporation per molecule of Enzyme Rate of Nucleotide incorporatio n kcat/Kn 751501.50E-075.00E+04 70606.00E-082.00E+04 55242.40E-088.00E+03 371.51.50E-095.00E+02 220.252.50E-108.33E+01

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“Noncompetitive” amplification problems: wherein running each step of the reaction to completion (equilibrium) produces desired efficiency. Goal: Shorter cycle time - important for all high throughput diagnostics applications Given a sequence and cycle time, to find the optimal annealing, extension temperatures and switching time between them Examples: simplex PCR diagnostics with disparate primer Tm's but no nonspecific hybrids “Competitive” amplification problems: wherein two species are produced simultaneously, irrespective of the choice of temperature, and one of those species is not desired. Common in disease diagnostics “Noncompetitive” amplification problems“Competitive” amplification problems Example: Cancer: one known mutation (p53 exon 8), standard sensitivity sufficient Given sequence + cycle time, find optimal annealing, extension temperatures and switching time between them. Examples: 1) Cancer: one unknown mutation in wild-type background: 0.1-1% Sensitivity (p53 exon 8 in plasma) 2) Cancer: multiple known mutations w stable nonspecific primer hybrids (kras, BRAF V600E) 3) Triplet repeat expansions w stable nonspecific primer hybrids (FMR-1) Classification of mutation diagnostics problems from chemical kinetics perspective PCR mutation diagnostics

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Transient kinetics of single cycles: finding optimal annealing/extension temperature schedule (fixed time, variable temperature) Annealing time – 30 sec

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Melting Curve of the primers

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Case 1 Length of the target = 480, Initial Concentration of the DNA during the start of the cycle = 2×10 -14 M

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Annealing Temperature = 55 deg C equilibrium conversion of Primer annealing ~ 100% overall efficiency ~ 70% SP molecules melt to give S and P Enzyme binding is slow at 55 deg C

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Annealing Temperature = 60 deg C equilibrium conversion of Primer annealing ~ 80% overall efficiency ~ 100% No SP molecule is available at 30 th Sec (or @ 72 deg C) As soon as annealing is complete, enzyme binding and subsequent extension reaction starts (disturbs the annealing equilibrium) Enzyme Binding decreases SP

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Case 2 Length of the target = 480, Initial Concentration of the DNA during the start of the cycle = 2×10 -8 M

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Annealing Temperature = 60 deg C There are some SP molecules at 30 th Sec (or @ 72 deg C) Annealing time should be increased

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Summary During the PCR, P/S ratio decreases and hence, the kinetics of Annealing reaction also changes. When concentration of the template increases, Annealing and extension time need to be changes. There is an optimal temperature at which reaction is quick and reaches 100% efficiency. These observation can be formulated as an Optimal Control problem to find optimal time and temperature trajectory for a given template amplification.

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Evolution of the DNA Concentration At 60 deg C, within 22 Cycles, maximum concentration is achieved. At 55 deg C, in 22 cycles, the DNA concentration 22 times lesser than that of at 60 deg C. Concentration after 29 cycles at 55 deg C, can be achieved in 21 cycles if 60 deg C is maintained

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Transient kinetics of single cycles: finding optimal annealing/extension temperature schedule (fixed temperatures, variable time) Modify this for 2 cycles including denaturation step at 95. Follow up in section on multistep dynamics with study of geometric growth of 2-3 cycle problems. Variable time per cycle but overall time fixed (allows formulation as fixed time OCT problem) In total 686 PCR simulations were performed. For a fixed extension time, Annealing time varied to be 30,45,60,75,90,105,120 seconds Extension time also varied to be 30,45,60,75,90,105,120 seconds XXAnnealing temperature varied from 55 to 68 deg C.

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Evolution of the DNA Concentration For first 20 cycles, there is no effect of time – High P/S ratio – No effect of dynamics. After 20 th cycle, increase in time favored the formation of the product Negative slope is due to insufficient Annealing time

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For N nucleotide template – 2N + 4 state equations Typically N ~ 10 3 Need for Optimal Control of DNA Amplification: noncompetitive problems R. Chakrabarti et al. Optimal Control of Evolutionary Dynamics, Phys. Rev. Lett., 2008 K. Marimuthu and R. Chakrabarti, Optimally Controlled DNA amplification, in preparation

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5/1/2015 School of Chemical Engineering, Purdue University 28 DNA Melting Primer Annealing Single Strand – Primer Duplex Extension DNA Melting Again

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Optimal Controlled PCR Software - GUI Feed the PCR State Equations Objective Function (noncompetitive, competitive)

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“Noncompetitive” amplification problems: wherein running each step of the reaction to completion (equilibrium) produces desired efficiency. Goal: Shorter cycle time - important for all high throughput diagnostics applications Given a sequence and cycle time, to find the optimal annealing, extension temperatures and switching time between them Examples: simplex PCR diagnostics with disparate primer Tm's but no nonspecific hybrids “Competitive” amplification problems: wherein two species are produced simultaneously, irrespective of the choice of temperature, and one of those species is not desired. Common in disease diagnostics “Noncompetitive” amplification problems“Competitive” amplification problems Example: Cancer: one known mutation (p53 exon 8), standard sensitivity sufficient Given sequence + cycle time, find optimal annealing, extension temperatures and switching time between them. Examples: 1) Cancer: one unknown mutation in wild-type background: 0.1-1% sensitivity (p53 exon 8 in plasma) 2) Cancer: multiple known mutations w stable nonspecific primer hybrids (kras, BRAF V600E) 3) Triplet repeat expansions w stable nonspecific primer hybrids (FMR-1) Classification of mutation diagnostics problems from chemical kinetics perspective PCR mutation diagnostics

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Melting Curve of Primers

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'CTCGAGGTCCAGAGTACCCGCTGTG‘ ‘GAGGT CCAGGTCT CAT GGGCGACAC’ 'AAACACTGCTGTGGTGGA' Competitive hybridization of mismatched primers May omit

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Kinetics of Multiplex Annealing

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Transient Multiplex Kinetics – GC Content of the primer – 60% At lower temperature with P/S ratio approximately 1, we could slowdown the annealing reaction. Can we achieve kinetic control favoring specific annealing products through elevated temperature and precisely chosen annealing time? Expect to see significant cycle-to-cycle change (decrease) in annealing temperature in optimally controlled competitive problems

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Multiplex Simulation Results Except the 480 bp target, the qualitative variation of relative concentration that predicted theoretically matches experimental results. At higher temperatures (above 60 deg C), both experimental and theoretical matches quantitatively within the experimental error.

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Optimal control: critical to determine annealing/extension profile. Maximize target species and minimize nonspecific hybrids. Requires controllability over higher dimensional subspace than noncompetitive problems Need for Optimal Control of DNA Amplification: competitive problems

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Competitive amplification example 2: COLD PCR mutation enrichment Mutation Enrichment: competition between mutant DNA causing cancer and wild-type DNA amplification. A competitive amplification problem in diagnostics State-of-the-art approach: COLD PCR (licensed by Transgenomic from HMS) Enrichment factor is limited by differences in Tc and homoduplex Tm (example B)

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Sharpening duplex melting curves for COLD PCR ctrl Tm: 73.5 o C With patented small molecule, Tm: 62 o C Tm Depression from no additive RangeDiff HiLo Control73.5078.5070.508.00 1.0M62.0011.5063.5060.003.50 Enrichment factor is improved by reducing overlap between hetero- and homoduplex melt curves PMC-AT patented technology for cancer metastasis detection

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Discussion Points NEB isothermal amplification enzymes Next generation sequencing Scope for interaction: –PMC-AT Software Platform to be integrated with real-time PCR software; which real-time platform? –Partnerships with thermal cycler manufacturers; NEB contacts –Use of NEB engineered polymerases

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Optimally controlled DNA amplification Noncompetitive ProblemsCompetitive problems Cancer Diagnostics: One unknown mutation, standard sensitivity Cancer diagnostics: One unknown mutation, enhanced sensitivity Trinucleotide repeat diagnostics COLD PCR Cancer diagnostics: known mutations in multiple genes New Patents Optimally Controlled DNA amplification: a unified platform for molecular disease diagnostics

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This shifts the equilibrium of the annealing reaction and allows the extension reaction to happen immediately. Since Enzyme binding and extension can happen at annealing temperature, higher annealing temperature can make the extension faster even during the annealing time. In addition to this, the given extension time completes the reaction. Whereas at lower annealing temperature, enzyme binding slow, by the time annealing time is complete, the un reacted duplexes melts at extension temperature to give back single strands. Combined Annealing and Extension(Cont.) May omit

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Transient kinetics of single cycles: finding optimal annealing/extension temperature schedule (fixed temperatures, variable time) Modify this for 2 cycles including denaturation step at 95. Follow up in section on multistep dynamics with study of geometric growth of 2-3 cycle problems. Variable time per cycle but overall time fixed (allows formulation as fixed time OCT problem) omit?

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Case 1 Length of the target = 800, Initial Concentration of the DNA during the start of the cycle = 2×10 -14 M

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Annealing Temperature = 60 deg C Extension Reaction is not complete Extension time should be increased

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Case 4 Length of the target = 800, Initial Concentration of the DNA during the start of the cycle = 2×10 -8 M

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Annealing Temperature = 60 deg C Extension Reaction is not complete SP Molecules gives S and P back Both Annealing and Extension time should be increased.

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