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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