Chakrabarti Group (Bionetwork Control), Purdue UniversityDiagnostics Group, PMC Advanced Technology

PCR Diagnostics Research & Technology Development

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

Cancer mutation diagnosis

Wild Type DNA

Mutated DNA

Cancer mutation diagnosis

Cancer mutation diagnosis

Unknown mutation in one gene Unknown mutation in one gene Known mutations in multiplegenes

Known mutations in multiplegenes

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: 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

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 1 Mutation 2Mutation 2

Trinucleotide repeat diagnosis

Trinucleotide repeatdiagnosis

Trinucleotide repeatdiagnosis

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)

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)

Preexpansion Preexpansion Full expansionFull expansion

50-200 base pairs

High chance of expanding to full mutation in future generations

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

>= 200 base pairs

causes hypermethylation of a regulatory CpG region upstream of gene, which silences transcription

 

Technology and Strategic Goals of PMC-AT Diagnostics

Aim of this talk: to establish the need for a) kinetic models b) engineering control theory

in developing these general diagnostic solutions.

Engineering Optimization

& Control of PCR

Engineering Optimization

& Control of PCR

Manipulate time-independentPCR parameters (mediaengineering)

Manipulate time-independentPCR parameters (mediaengineering)

Control time-dependent temperature inputs (thermal cycling)

Control time-dependent temperature inputs (thermal cycling)

MALDI-TOFMALDI-TOF Sanger SequencingSanger Sequencing PyrosequencingPyrosequencing

Cancer Mutation DiagnosisCancer Mutation Diagnosis Triplet Repeat DiagnosisTriplet Repeat Diagnosis

Downstream sequence analysis methods

Downstream sequence analysis methods

New patentsNew patentsExisting patentsExisting patents

Current Equilibrium Models | New Kinetic Models

04/18/23 School of Chemical Engineering, Purdue University

6

DNA Melting

PrimerAnnealing

Single Strand – Primer Duplex

Extension

DNA MeltingAgain21

, 21 SSDmm kk

DNASS tt kk 12

11 ,

21

22,

22

22

21 PSPS kk

DNAEDE

DENDENDE

DENSPENSPE

SPEESP

kcatN

kcatkk

kcatkk

kk

nn

nn

ee

'

.

.

.]..[.

.]..[.

.

21,

1

1,

,

11,

11

12

11 PSPS kk

Parallel Parking and Bionetwork Control

Tight spots: Move perpendicular to curb through sequences composed of Left, Forward + Left, Reverse + Right, Forward + Right, Reverse

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

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

Wild Type DNA

Mutated DNA

Maximization of the amplification of mutated DNA.

Derivation of optimal temperature profile is important.

Multi objective optimal control problem

The DNA Amplification Control Problem and Cancer DiagnosticsThe DNA Amplification Control Problem and Cancer Diagnostics

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

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

04/18/23 9School of Chemical Engineering, Purdue University

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.

04/18/23 10School of Chemical Engineering, Purdue

University

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.

04/18/23 1104/18/23 11School of Chemical Engineering, Purdue University

Summary of PCR Kinetic Model

Get the Primer/Template Sequence

Find the Equilibrium constant at different temperatures using Nearest

Neighbor Model

Find the Relaxation time

Find the Annealing Rate

Constants

Theoretical Prediction of Annealing Kinetics

Available experimental data for the extension rate constants – Estimate

Arrhenius rate parameters

Find the Extension Rate

Constants

04/18/23 1204/18/23 12School of Chemical Engineering, Purdue University

Kinetic Model (Annealing/Melting)

RT

GKkk exp/ 21

ΔG – From Nearest Neighbor Model

eqeq SS CCkk 2121

1

DSS kk 21 ,21

τ – Relaxation time(Theoretical/Experimental)

Solve above equations to obtain rate constants individually.

04/18/23 1304/18/23 13School of Chemical Engineering, Purdue University

Relaxation time

DSS kk 21 ,21

eqeq SS CCkk 2121

1

N

k

k

k

k

k

k

k

kDDDDSS

NN

NN

,1

1,

2,1

1,2

1,0

0,1

0,1

1,0

.......32121

Nii ss

ssk

11)1(1,

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.

04/18/23 14School of Chemical Engineering, Purdue University

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.

Number of Molecules hybridized completely1

Total number of molecules x

04/18/23 1504/18/23 15School of Chemical Engineering, Purdue University

Extension Kinetics.

SPEESPee kk

.,

Kd = k-e /ke = 103.7 nM1 @700C = 16.8 nM @ 550C

1

,

.... DENSPENSPE kcatkk nn

n

ncatN

k

kkK

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 – 45733 – Tosaka et al (2001), The Journal of Biological Chemistry, 276(29), 27562-

27567

 

PCR mutation diagnosticsPCR mutation diagnostics

Classification of mutation diagnostics problems from chemical kinetics perspective Classification of mutation diagnostics problems from chemical kinetics perspective

 

“Noncompetitive” amplification problems“Noncompetitive” amplification problems “Competitive” amplification problems“Competitive” amplification problems

Running each step to completion (equilibrium) produces desired efficiency

Goal: Shorter cycle time using kinetic models.

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

>= 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

 

“Noncompetitive” amplification problems“Noncompetitive” amplification problems “Competitive” 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.

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 stablenonspecific primer hybrids (FMR-1)

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 stablenonspecific primer hybrids (FMR-1)

Classification of mutation diagnostics problems from chemical kinetics perspective Classification of mutation diagnostics problems from chemical kinetics perspective

PCR mutation diagnosticsPCR mutation diagnostics

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

0 50 100 1500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Reaction Time in Seconds

Rel

ativ

e C

once

ntra

tion

(with

res

pect

to in

itial

sin

gle

stra

nd c

once

ntra

tion)

Annealing Time = 120 sExtension Time = 30 s

Evolution of DNA duringcycle 1(from single strand 1)

Evolution of Single Strand Primer Duplex duringcycle 1(from single strand 1)

Evolution of Single Strand Primer Duplex duringcycle 23(from single strand 1)

Evolution of DNA duringcycle 23(from single strand 1)

“Noncompetitive” amplification: transient behavior of reaction species

Bovine glycolipid transfer protein (GLTP) mRNA

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

TrDNADESS

DNAfDNAtT

CCCCx

Txfdt

dxst

CtCMin

.....,.....,

,

121 .

2max

)(

For N nucleotide template – 2N + 4 state equations

Typically N ~ 103

Optimal Control of DNA Amplification:noncompetitive problems

R. Chakrabarti et al. Optimal Control of Evolutionary Dynamics, Phys. Rev. Lett., 2008K. Marimuthu and R. Chakrabarti, Optimally Controlled DNA amplification, in preparation

Preliminary Results of the OCT

45 50 55 60 65 70 750

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Temperature in Deg C

Eq

uili

bri

um

Co

nv

ers

ion

Mismatched sequence

GC % = 64

GC % = 50

'CTCGAGGTCCAGAGTACCCGCTGTG‘‘GAGGT CCAGGTCT CAT GGGCGACAC’

'AAACACTGCTGTGGTGGA'

Competitive hybridization of mismatched primersCompetitive hybridization of mismatched primers

  Optimal control: critical to determine annealing/extension profile. Maximize target species, minimize nonspecific hybrids.

Requires controllability over higher dimensional subspace than noncompetitive problems

Optimal Control of DNA Amplification: competitive problems

1 2 1 1 2 1

2max 2

1 2( )

. , .

( ( ))

( , )

, ,..... .... , ,.... .....

non specificDNA f DNA DNA f

T t

ns ns ns nss s E D DNA s s E D DNA

Min w C t C w C t

dxst f x T

dt

x C C C C C C C C

Competitive amplification example 2: mutation enrichment

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)

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.

Competitive amplification example 2: COLD PCR mutation enrichmentCompetitive amplification example 2: COLD PCR mutation enrichment

Optimally controlled DNA amplification

Optimally controlled DNA amplification

Noncompetitive ProblemsNoncompetitive Problems Competitive problemsCompetitive problems

Cancer Diagnostics: One unknown mutation, standard sensitivity

Cancer Diagnostics: One unknown mutation, standard sensitivity

Cancer diagnostics: One unknown mutation, enhanced sensitivity

Cancer diagnostics: One unknown mutation, enhanced sensitivity

Trinucleotide repeat diagnosticsTrinucleotide repeat diagnostics

COLD PCRCOLD PCR

Cancer diagnostics: known mutations in multiple genesCancer diagnostics: known mutations in multiple genes

New PatentsNew Patents

Optimally Controlled DNA amplification: a unified platformfor molecular disease diagnosticsOptimally Controlled DNA amplification: a unified platformfor molecular disease diagnostics

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

Thank you