Diagnostics Group, PMC Advanced Technology

Diagnostics Group, PMC Advanced Technology

DNA Amplification Research & Technology Development

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

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 (2012)

3) Roche Molecular Diagnostics*4) Undisclosed (possibly Asuragen)* *under negotiation

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

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

Current Equilibrium Models | New Kinetic Models

Wild Type DNA

Mutated DNA

The DNA Amplification Control Problem and Cancer Diagnostics:detailed example of need for modified temperature cycling protocolsThe 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

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

Simplex PCR – State Equations

1 2 1 1 2 2 1,2ii i i i i i i i

d Sk S P k S P k S S k DNA i

dt

1 2 1,2i ii i i i i i

d S Pk S P k S P i

dt

1,2i i id P d S P

idt dt

N

cateeK

NPSEkPSEkPSEkPSE

dt

d 11111111

...

N

cateeK

NPSEkPSEkPSEkPSE

dt

d 22222222

...

Annealing – State Equations

Rate constants to be determined k1i & k2i - Theoretical Determination using Relaxation time and Equilibrium Relationships Enzyme Binding – State Equations

Rate constants to be determined ke , k-e , kcat /KN – Determine using the available rate of nucleotide addition data and equilibrium enzyme binding data

iiN

cati TETEN

K

kTE

dt

d... 1 2

11

122

12

21

11 ,...,.........,,, nni DDDDDDT

ncat DEkDNAdt

d.'

21

22

11

11

..nD

PST

nD

PSTN

cat TETENK

kN

dt

d

DNAdt

dPSE

dt

dPSE

dt

dE

dt

d 2211 ..

ncatnnN

catn DEkDEDEN

K

kDE

dt

d.... '2

11

1

Extension Reaction– State Equations

Rate constant to be determined k’cat - Determine using the available rate of nucleotide addition data

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

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.

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.

Experimental ValidationComparison of theoretical prediction and experimental values of

A9U9 hybridization reaction.

Theoretically predicted values perfectly fits with R2 = 1

There are no constraints that follows Arrhenius law ,forced in our theoretical method.

0

20

40

60

80

100

120

0 10 20 30 40 50 60 70 80

Equl

ibri

um c

onst

ant

Kd in

nM

Temperature in Deg C

Variation of Equlibrium Rate constant of Enzyme binding extension reaction

Datta and LiCata, Nucleic Acids Research, 2003, Vol. 31, No. 19

Kd = 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

Extension Rate constants kcat /KN

• Innis et al (1988) published data on the number of nucleotides added per enzyme molecule at different temperatures.

Sum of all the DNA

molecule Concentrationscat

N

d kN N

dt K

• Using this information it is possible to fit the extension rate equation to find the kcat /KN

04/19/23 1404/19/23 14School 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

incorporation

kcat/Kn

75 150 1.50E-07 5.00E+04

70 60 6.00E-08 2.00E+04

55 24 2.40E-08 8.00E+03

37 1.5 1.50E-09 5.00E+02

22 0.25 2.50E-10 8.33E+01

“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.



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)



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

PCR mutation diagnosticsPCR mutation diagnostics

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

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

Annealing time – 30 sec

Melting Curve of the primers

Case 1 Length of the target = 480,

Initial Concentration of the DNA during the start of the cycle = 2×10-14 M

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

Annealing Temperature = 60 deg Cequilibrium conversion of Primer annealing ~ 80%

overall efficiency ~ 100% No SP

molecule is available at 30th 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


There are some SP molecules at 30th Sec (or @ 72 deg C)

Annealing time should be increased

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.

Evolution of the DNA ConcentrationEvolution 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

Transient kinetics of single cycles: finding optimal annealing/extension temperature schedule (fixed temperatures, variable time)

Transient kinetics of single cycles: finding optimal annealing/extension temperature schedule (fixed temperatures, variable time)

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

Evolution of the DNA ConcentrationEvolution of the DNA Concentration

For first 20 cycles, there is no effect of time – High P/S ratio – No effect of dynamics.

After 20th cycle, increase in time favored the formation of the product

Negative slope is due to insufficient Annealing time

TrDNADESS

DNAfDNAtT

CCCCx

Txfdt

dxst

CtCMin

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

,

121 .

2max

)(

For N nucleotide template – 2N + 4 state equations

Typically N ~ 103

Need for 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

04/19/23 School of Chemical Engineering, Purdue University

28

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

Optimal Controlled PCR Software - GUI

Feed the PCR State Equations

Objective Function(noncompetitive, competitive)

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





Examples: 1) Cancer: one unknown mutation in wild-type background: 0.1-1% sensitivity (p53 exon 8 in plasma)



Examples: 1) Cancer: one unknown mutation in wild-type background: 0.1-1% sensitivity (p53 exon 8 in plasma)



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

PCR mutation diagnosticsPCR mutation diagnostics

Melting Curve of Primers

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

May omit

Kinetics of Multiplex Annealing

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

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.

•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

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: 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

Sharpening duplex melting curves for COLD PCR

ctrl Tm: 73.5oC

With patented small molecule, Tm: 62oC

Tm

Depression from no additive

Range Diff

Hi Lo

Control 73.50 78.50 70.50 8.001.0M 62.00 11.50 63.50 60.00 3.50

Enrichment factor is improved by reducing overlap between hetero- and homoduplex melt curves

PMC-AT patented technology for cancer metastasis detection

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

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

• 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

Transient kinetics of single cycles: finding optimal annealing/extension temperature schedule (fixed temperatures, variable time)Transient kinetics of single cycles: finding optimal annealing/extension temperature schedule (fixed temperatures, variable time)

omit?


Extension Reaction is not complete

Extension time should be increased


Extension Reaction is not complete

SP Molecules gives S and P back

Both Annealing and Extension time should be increased.

Diagnostics Group, PMC Advanced Technology

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