Chakrabarti Group (Bionetwork Control), Purdue University

1. PCR Diagnostics Research & Technology Development Chakrabarti Group (Bionetwork Control), Purdue University Diagnostics Group, PMC Advanced Technology

2. 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: 1st FDA approved Fragile X PCR diagnostic (2008); 2) New England Biolabs: other undisclosed disease diagnostics (Dec 2011) 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)

3. Cancer mutation diagnosis Cancer mutation diagnosis Unknown mutation in one gene Known mutations in multiple genes Mutated DNA Mutation 1 Mutation 2 • 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 • 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 Wild Type DNA

4. Trinucleotide repeat diagnosis Trinucleotide repeat diagnosis Preexpansion Full expansion • 50-200 base pairs • High chance of expanding to • full mutation in future generations • >= 200 base pairs • causes hypermethylation of a regulatory CpG region upstream of gene, which silences transcription • Problem 1:Avoid multiple nonspecific annealing products due to high-GC primers nearly 100% GC (annealing) • Problem 2: Increase product yield despite high melting temperature (denaturation)

5. Technology and Strategic Goals of PMC-AT Diagnostics Engineering Optimization & Control of PCR Control time-dependent temperature inputs (thermal cycling) Manipulate time-independent PCR parameters (media engineering) Existing patents New patents Current Equilibrium Models | New Kinetic Models Cancer Mutation Diagnosis Triplet Repeat Diagnosis Downstream sequence analysis methods Sanger Sequencing Pyrosequencing MALDI-TOF Aim of this talk: to establish the need for a) kinetic models b) engineering control theory in developing these general diagnostic solutions.

6. DNA Melting Again Single Strand – Primer Duplex Extension DNA Melting Primer Annealing 9/9/2014 School of Chemical Engineering, Purdue University 6

7. Parallel Parking and Bionetwork Control • Stepping on gas not enough: can’t move directly in direction of interest • Must change directions repeatedly • Left, Forward + Right, Reverse enough in most situations • Tight spots: Move perpendicular to curb through sequences composed of Left, Forward + Left, Reverse + Right, Forward + Right, Reverse

8. The DNA Amplification Control Problem and Cancer Diagnostics Mutated DNA Wild Type DNA • 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 • Maximization of the amplification of mutated DNA. • Derivation of optimal temperature profile is important. • Multi objective optimal control problem

9. Motivation (I) • PCR is a time dependent cyclic reaction. • Equilibrium thermodynamics does not have information about time. • Most complex reactions have been successfully optimized and controlled favorably using classical optimal control principles. • Optimal control needs kinetic model for the PCR to optimize its efficiency. • Kinetic model of the PCR is the ‘key’ to maximize efficiency. 9/9/2014 School of Chemical Engineering, Purdue University 9

10. Previous Work • Very few kinetics models available for PCR. No experimental sequence dependent correlation for kinetic parameters. • Stolovitzky and Cecchi (1996): Sequence independent kinetic parameters with single stage annealing and extension ( Melting step was not modeled) • Mehra and Hu (2005): Assumed sequence independent kinetic parameters for melting, annealing and extension reactions. • Gevertz et al (2005): Combined equilibrium and kinetic models; sequence independent kinetic parameters. School of Chemical Engineering, Purdue University

11. Summary of PCR Kinetic Model Get the Primer/Template Sequence Theoretical Prediction of Annealing Kinetics Find the Equilibrium constant at different temperatures using Nearest Neighbor Model Find the Annealing Rate Constants Find the Relaxation time Find the Extension Rate Constants Available experimental data for the extension rate constants – Estimate Arrhenius rate parameters 9/9/2014 9/9/2014 School of Chemical Engineering, Purdue University 11 11

12. Kinetic Model (Annealing/Melting) ΔG – From Nearest Neighbor Model τ – Relaxation time (Theoretical/Experimental) Solve above equations to obtain rate constants individually. 9/9/2014 9/9/2014 School of Chemical Engineering, Purdue University 12 12

13. 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). • ki,i-1 - 106 sec-1. 9/9/2014 9/9/2014 School of Chemical Engineering, Purdue University 13 13

14. Assumptions • DNA hybridization – Two state model • Two state model – Proved to be applicable for DNA with 10 – 50 base pairs. • Two state model – Conventional chemical reaction – Conversion of hybridization reaction • Gibbs free energy – Nearest Neighbor method– Including mismatching and Hairpin loops. Denaturation and annealing 9/9/2014 School of Chemical Engineering, Purdue University 14

15. Extension Kinetics. Kd = k-e /ke = 103.7 nM1 @700C = 16.8 nM @ 550C Michaelis Menten Constant kcat / KN = 3.8 sec-1 μM-1 @720C2,3 = 1.4 sec-1 μM-1 @550C = 0.5 sec-1 μM-1 @450C • 1- Datta & Licata (2003), Nucleic Acids Research, 31(19), 5590 – 5597 • 2 – Huang et al (1992), Nucleic Acids Research, 20(17), 4567 – 4573 • 3 – Tosaka et al (2001), The Journal of Biological Chemistry, 276(29), 27562-27567 9/9/2014 9/9/2014 School of Chemical Engineering, Purdue University 15 15

16. Classification of mutation diagnostics problems from chemical kinetics perspective PCR mutation diagnostics “Noncompetitive” amplification problems “Competitive” amplification problems • >= 2 species are produced simultaneously, irrespective of the choice of temperature, and one of those species is not desired • Equilibrium strategies generally not sufficient • Goal: Maximize concentration of target while minimizing undesired products • Running each step to completion (equilibrium) produces desired efficiency • Goal: Shorter cycle time using kinetic models. “Noncompetitive” amplification problems “Competitive” amplification problems • Running each step to completion (equilibrium) produces desired efficiency • Goal: Shorter cycle time using kinetic models. • >= 2 species are produced simultaneously, irrespective of the choice of temperature, and one of those species is not desired • Equilibrium strategies generally not sufficient • Goal: Maximize concentration of target while minimizing undesired products [Given sequence + cycle time, find optimal annealing, extension temperatures and switching time between them.] • “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

17. Classification of mutation diagnostics problems from chemical kinetics perspective PCR mutation diagnostics “Noncompetitive” amplification problems “Competitive” amplification problems 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) 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. • “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

18. “Noncompetitive” amplification: finding optimal annealing/extension temperature schedule

19. “Noncompetitive” amplification: transient behavior of reaction species

20. “Noncompetitive” amplification: finding optimal annealing/extension temperature schedule Bovine glycolipid transfer protein (GLTP) mRNA

21. Optimal Control of DNA Amplification: noncompetitive problems For N nucleotide template – 2N + 4 state equations Typically N ~ 103 R. Chakrabarti et al. Optimal Control of Evolutionary Dynamics, Phys. Rev. Lett., 2008 K. Marimuthu and R. Chakrabarti, Optimally Controlled DNA amplification, in preparation

22. Preliminary Results of the OCT

23. Competitive hybridization of mismatched primers 'CTCGAGGTCCAGAGTACCCGCTGTG‘ ‘GAGGT CCAGGTCT CAT GGGCGACAC’ 'AAACACTGCTGTGGTGGA'

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

25. Competitive amplification example 2: mutation enrichment (example B) • Mutation Enrichment: competition between mutant DNA causing cancer and wild-type DNA amplification. • A competitive amplification problem in diagnostics that has been addressed w/ only equilibrium cycling strategies • State-of-the-art approach: COLD PCR (licensed by Transgenomic from HMS)

26. Competitive amplification example 2: COLD PCR mutation enrichment • For: metastasis (blood, primarily detection); diagnosis (tumor cells) • K-ras, p53 are tumor suppressors: mutations strongly correlated w prognosis • COLD PCR reduces detection limit from 10% to 0.1-1% • COLD PCR deals with the competition by introducing an additional step (heteroduplex hybridization). Slows down the PCR procedure. • Optimally controlled PCR: for fixed time per cycle, solve the problem of maximizing single stranded mutant DNA concentration while maximizing double stranded wild-type concentration, through kinetic modeling and OCT.

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

28. Summary • DNA disease diagnostic tests can be classified as noncompetitive or competitive amplification problems • Optimal control theory (OCT) provides general framework for both • Standard and COLD PCRs are special cases of optimally controlled DNA amplification May show flow chart w OC DNA amplification on top, w subdivision into competitive, noncompetitive problems

29. Thank you