The Fidelity of the Tag-Antitag System J. A. Rose, R. J. Deaton, M. Hagiya, And A. Suyama DNA7 poster 2001.8.22 Summarized by Shin, Soo-Yong

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.


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

* **

* **


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


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



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



Case III : error-free + error-prone Multiphastic temperature dependence.


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


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


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



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



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


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


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


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


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


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


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


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)


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


The Scaling Behavior of the FidelThe Scaling Behavior of the Fidelity of Random Encodingsity of Random Encodings


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.

Documents

The Fidelity of the Tag-Antitag System J. A. Rose, R. J. Deaton, M. Hagiya, And A. Suyama DNA7 poster 2001.8.22 Summarized by Shin, Soo-Yong