Diagnostics Group, PMC Advanced Technology

1
DNA Amplification Research Technology
Development
Diagnostics Group, PMC Advanced Technology
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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 lt 1 mutant/wt
• Problem Detect in heavy wt background
• Standard solution COLD PCR

Wild Type DNA
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DNA disease diagnostics applications

• Metastatic Cancer Mutations
• p53 tumor suppressor
• k-ras tumor suppressor
• Trinucleotide Repeat Mutations
• HTT (Huntingtons Disease)
• DMPK (Muscular Dystrophy)
• FMR-1 (Fragile X Autisms leading cause)

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
4
Kinetic modeling of controlled DNA amplification
Engineering Optimization Control of PCR
Control time-dependent temperature inputs
(thermal cycling)
Manipulate time-independent PCR parameters
(media engineering)
Current Equilibrium Models New
Kinetic Models
 
Cancer Mutation Diagnosis
Triplet Repeat Diagnosis
Downstream sequence analysis methods
MALDI-TOF
Sanger Sequencing
Pyrosequencing
Aim of this work to establish a) kinetic models
for future use with b) engineering control theory
in developing these general diagnostic solutions.
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The DNA Amplification Control Problem and Cancer
Diagnostics detailed example of need for
modified temperature cycling protocols
Mutated DNA
Wild Type DNA

• Cant 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 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
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Extension Reaction State Equations
Rate constant to be determined kcat -
Determine using the available rate of nucleotide
addition data
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Summary of PCR Kinetic Model
Theoretically determine the equilibrium constants
using the nearest neighbor Method.

• 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.

Theoretically determine the relaxation time
Solve the equilibrium and relaxation time
equations for forward and backward rate constants
of annealing reaction

• 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

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

• 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
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Kinetic Model (Annealing/Melting)
?G From Nearest Neighbor Model
t 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.
• s 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.

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Experimental Validation
Comparison 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.
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Enzyme Binding Kinetics
Kd f(T), Equilibrium constant for Enzyme
duplex dissociation reaction.
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
Datta and LiCata, Nucleic Acids Research, 2003,
Vol. 31, No. 19
Temperature dependent rate constant is needed to
model whole PCR
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Extension Rate constants kcat /KN

• 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 kcat /KN

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Extension Kinetics
Temperature (Deg C) Number of Nucleotide Incorporation per molecule of Enzyme Rate of Nucleotide incorporation kcat/Kn
75 150 1.50E-07 5.00E04
70 60 6.00E-08 2.00E04
55 24 2.40E-08 8.00E03
37 1.5 1.50E-09 5.00E02
22 0.25 2.50E-10 8.33E01
Nucleotide Addition per time at different
temperature is given by Innis et al.
Proc.Natl.Acad.Sci - Vol 85, pp - 9436-9449,
Dec-1988
5/2/2017
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5/2/2017
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School of Chemical Engineering, Purdue University
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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

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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 210-14 M
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Annealing Temperature 55 deg C
overall efficiency 70
equilibrium conversion of Primer annealing 100
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 30th Sec (or _at_ 72
deg C)
Enzyme Binding decreases SP

• As soon as annealing is complete, enzyme binding
  and subsequent extension reaction starts
  (disturbs the annealing equilibrium)

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Case 2 Length of the target 480, Initial
Concentration of the DNA during the start of the
cycle 210-8 M
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Annealing Temperature 60 deg C
There are some SP molecules at 30th Sec (or _at_ 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
Concentration after 29 cycles at 55 deg C, can
be achieved in 21 cycles if 60 deg C is maintained

• 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.

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

• 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

In total 686 PCR simulations were performed.
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)
XXAnnealing temperature varied from 55 to 68 deg
C.
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Negative slope is due to insufficient Annealing
time
Evolution 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
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Need for 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
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DNA Melting Again
Single Strand Primer Duplex Extension
DNA Melting
Primer Annealing
5/2/2017
School of Chemical Engineering, Purdue University
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Optimal Controlled PCR Software - GUI
Feed the PCR State Equations
Objective Function (noncompetitive, competitive)
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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

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Melting Curve of Primers
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Competitive hybridization of mismatched primers
'CTCGAGGTCCAGAGTACCCGCTGTG GAGGT CCAGGTCT CAT
GGGCGACAC
'AAACACTGCTGTGGTGGA'
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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Need for Optimal Control of DNA Amplification
competitive problems

•  
• Optimal control critical to determine
  annealing/extension profile. Maximize target
  species and minimize nonspecific hybrids.
• Requires controllability over higher dimensional
  subspace than noncompetitive problems

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Competitive amplification example 2 COLD PCR
mutation enrichment
(example B)

• 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

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Sharpening duplex melting curves for COLD PCR

• Enrichment factor is improved by reducing
  overlap between hetero- and homoduplex melt
  curves
• PMC-AT patented technology for cancer metastasis
  detection

  Tm Depression from no additive Range Range Diff
  Tm Depression from no additive Hi Lo  
Control 73.50 78.50 70.50 8.00
1.0M 62.00 11.50 63.50 60.00 3.50
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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 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
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Combined Annealing and Extension(Cont.)

• 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.

May omit
43
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 210-14 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 210-8 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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