The Fidelity of the Tag-Antitag System J. A. Rose, R. J. Deaton, M. Hagiya, And A. Suyama DNA7...
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Transcript of The Fidelity of the Tag-Antitag System J. A. Rose, R. J. Deaton, M. Hagiya, And A. Suyama DNA7...
The Fidelity of the Tag-Antitag SyThe Fidelity of the Tag-Antitag Systemstem
J. A. Rose, R. J. Deaton, M. Hagiya, And A. Suyama
DNA7 poster
2001.8.22
Summarized by Shin, Soo-Yong
(C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
AbstractAbstract
Tag/antitag(TAT) pairs should be designed to have a minimum potential for error-producing cross-hybridization.
Using principles from equilibrium chemistry, and expression is derived which estimates the probability of error hybridization per tag ().
Java based s/w Mjonir is developed.
(C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
DNA chip fidelityDNA chip fidelity
Quantity Cio and Ci : initial & equilibrium concentrations o
f the tag member of tag-antitag pair {i, i*} Kij* : total equilibrium constant of biomolecular duplex for
mation between tag i and antitag j*. Mean error probability per antitag-hybridized tag
Kij*e : total error equilibrium constant formation between ta
g i and antitag j*. SNR: conventional, experimentally observed measure of h
ybridization error, signal to noise ratio
SNRKCC
KCC
i j ijji
i j
eijji 1
* **
* **
(C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
DNA chip fidelityDNA chip fidelity
Antitags are assumed to be present in equal, excess concentration Ca relative to each tag, so that
TAT encodings are assumed to be sufficiently well encoded so that the total equilibrium constants of error interaction is small relative to that of the full-length, planned TAT interactions.
Equilibrium constants of hairpin formation for an antitag and it matching tag are roughly equal.
1** )1( hp
jaj KCC
hpi
hpi KK *
iiia
hpi
iii
i j hpj
eij
iiahpi
hpi
i
KCK
KC
K
K
KCK
KC
*2
*
**
*
*2
)1(
1)1(
1
(C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
Temperature DependenceTemperature Dependence
Ki,e Hii*o : sum of the statistical weights and entha
lpies of formation of all error configurations involving tag i.
Temperature beneath the melting transition of planned TAT pairs (hairpin is neglected)
2
*
,
0*
0,
*
,
1
)(1
RTKC
KC
HHKC
KC
dT
d
iiia
eii
i iieiiia
eii
(C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
Temperature DependenceTemperature Dependence
Case I : sum of the enthalpies of formation of planned interaction dominates the sum of the enthalpies of the set of unplanned interactions
The maximum fidelity is predicted to be obtained by application of the minimum practical reaction temperature
Case II : relatively small number of short, unplanned interactions is to exceed the total enthalpy of the set of planned interactions.
The dependence of the enthalpy of duplex formation on the length of the duplex is approximately linear.
Maximum fidelity is predicted at the highest practical temperature
0*
0, iiei HHH
0*
0, iiei HH
0*
0, iiei HH
Error-free
Error-prone
(C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
Temperature DependenceTemperature Dependence
Case III : error-free + error-prone Multiphastic temperature dependence.
(C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
Input dependenceInput dependence
The variation of over the set of all dilute inputs Error response
Error rate in response to an input distributed uniformly over all tag species (white input)
Error rate in response to an impulse-like input composed of a single tag species , i
iiia
hpi
ii
i j hpj
eij
iiahpi
hpi
w
KCK
K
K
K
KCK
K
*2
*
**
*
*2
)1(
1)1(
1
* *
*
* 1
1
jhpj
eij
ii
hpi
i K
K
K
K
(C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
Input dependenceInput dependence
The complete set of error-impulse responses, Si{i}: error spectrum of the chip Extrema of the error response for a DNA chip correspo
nd to the extreme members of the error spectrum. - = sup Si
+ = inf Si
Error spectral width : Vanishes for encodings which are uniform with respect to both
planned and unplanned TAT intereractions
1010 loglogw
(C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
Simulations of encoding fidelitySimulations of encoding fidelity
BIND package The error performance of primer sequences relative to a
single, longer template molecule is evaluated by computing an estimate of the melting temperature of each primer at each position along the template.
Total entropy and enthalpy of duplex formation are evaluated on an alignment by alignment basis, using NN model.
Neglects the competition between antitags for primer interaction.
No hairpin formation
(C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
Simulations of encoding fidelitySimulations of encoding fidelity
NucleicPark Estimate of the probability/strand of mishybridization,
at equilibrium. Equilibrium constants of duplex formation are estimate
d using a staggered zipper model + Watson-Crick NN model of duplex energetics.
No bulged configurations, dangling ends, mismatched base pairs, antitag anchorage, hairpin
(C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
Simulations of encoding fidelitySimulations of encoding fidelity
Mjolnir Java-based package Physically accurate, polynomial-time estimation of the
equilibrium constant of formation for each of the duplex and hairpin configurations.
Statistical Zipper Model (SZM) Set of duplex structures with significant occupancy reduces to
those which contain a single duplex region, a configurational subspace whose size scales polynomially with lengh
(C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
Estimation of Equilibrium Estimation of Equilibrium ConstantsConstants Overall statistical weight of duplex formation
between TAT pair {i, j*}
k rx
kijij RT
GK
0*;
* exp
k : the set of double-stranded configurations which are accessible to species i and j*G0
ij*;k : Gibbs free energy of formation for configuration kR : the molar gas constantTrx : Kelvin temperature
(C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
Estimation of Equilibrium Estimation of Equilibrium ConstantsConstants Validity of a NN model of duplex energetics
000000*; chip
endsstrand
danglesym
endsduplex
initnn
nnkij GGGGGG
Free energy of stacking, NN method
Initiation parameter which accounts for the combined free energy of strand association & end unraveling
Entropic penalty, appplied only to palindromic duplexes
Small energetic correction for each dangling end
Impact of antitag anchorage
(C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
Estimation of Equilibrium Estimation of Equilibrium ConstantsConstants Standard SZM
Only duplexes containing standard Watson-Crick pairs Less than approximately 100 base pairs Based on good agreement with experimentally derived
DNA melting curves Containing internal loop
(C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
Estimation of Equilibrium Estimation of Equilibrium ConstantsConstants Standard SZM (drawbacks)
Neglect all staggered Watson-Crick mismatches. For example, tandem GA
Demonstrate surprising stability when situated within a WC duplex
General negligibility of bulged configurations
(C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
Estimation of Equilibrium Estimation of Equilibrium ConstantsConstants Modified SZM
Neglects internal loops, multiple-base bulges, multiple bulges
Includes single internal mismatches, single tandem GAs or GTs, single one base bulge
Treat the bulge as a small energetically destabilizing perturbation of the unbulged duplex
(C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
Estimation of Equilibrium Estimation of Equilibrium Constants (with Modified SZM)Constants (with Modified SZM)
k : the set of all simple hairpin structures accessible to tag i
Fend(n) : generalized statistical weight of the terminal loop
1/2 : loss of half a staking interaction at the non-loop terminus of the duplex
Zi;k : statistical weight of stacking
k
kihpi KK ;
)(;2/1
; nFZK endkihpki
5.12/1
)1(
)()(
n
nMnFend
(C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
The Fidelity of Perfectly Aligned The Fidelity of Perfectly Aligned Hamming EncodingsHamming Encodings WC based Hamming encoding scheme does not
consistently enhance fidelity, relative to a simple random encoding strategy. (for L = N = 16)
(C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
The Scaling Behavior of the FidelThe Scaling Behavior of the Fidelity of Random Encodingsity of Random Encodings
8.1227.43.543.24
06.611.13.353.45log
88.510.17.467.45log
10
10
rx
rx
rxw
TLNw
TLN
TLN
Weight error response
worst spectral error response
Error spectral width
(C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
The Scaling Behavior of the FidelThe Scaling Behavior of the Fidelity of Random Encodingsity of Random Encodings
(C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
ConclusionsConclusions
A great advantage of the current model Provides predictions which, due to their quantitative
nature, lend themselves to direct experimental testing.
If high fidelity required, more sophisticated encoding is required than simple random encoding.