1. 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

2. (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/Abstract 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.

3. (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/ DNA chip fidelity Quantity C i o and C i : initial & equilibrium concentrations of the tag member of tag-antitag pair {i, i*} K ij* : total equilibrium constant of biomolecular duplex formation between tag i and antitag j*. Mean error probability per antitag-hybridized tag K ij* e : total error equilibrium constant formation between tag i and antitag j*. SNR: conventional, experimentally observed measure of hybridization error, signal to noise ratio

4. (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/ DNA chip fidelity Antitags are assumed to be present in equal, excess concentration C a 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.

5. (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/ Temperature Dependence K i,e  H ii* o : sum of the statistical weights and enthalpies of formation of all error configurations involving tag i. Temperature beneath the melting transition of planned TAT pairs (hairpin is neglected)

6. (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/ Temperature 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 Error-free Error-prone

7. (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/ Temperature Dependence Case III : error-free + error-prone  Multiphastic temperature dependence.

8. (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/ Input 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

9. (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/ Input dependence The complete set of error-impulse responses, S i  {  i }: error spectrum of the chip  Extrema of the error response for a DNA chip correspond to the extreme members of the error spectrum.  - = sup S i  + = inf S i  Error spectral width :  Vanishes for encodings which are uniform with respect to both planned and unplanned TAT intereractions

10. (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/ Simulations 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

11. (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/ Simulations of encoding fidelity NucleicPark  Estimate of the probability/strand of mishybridization, at equilibrium.  Equilibrium constants of duplex formation are estimated using a staggered zipper model + Watson- Crick NN model of duplex energetics.  No bulged configurations, dangling ends, mismatched base pairs, antitag anchorage, hairpin

12. (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/ Simulations 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

13. (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/ Estimation of Equilibrium Constants Overall statistical weight of duplex formation between TAT pair {i, j*} k : the set of double-stranded configurations which are accessible to species i and j*  G 0 ij*;k : Gibbs free energy of formation for configuration k R : the molar gas constant T rx : Kelvin temperature

14. (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/ Estimation of Equilibrium Constants Validity of a NN model of duplex energetics 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

15. (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/ Estimation of Equilibrium Constants 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

16. (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/ Estimation of Equilibrium Constants 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

17. (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/ Estimation of Equilibrium Constants 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

18. (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/ Estimation of Equilibrium Constants (with Modified SZM)  k : the set of all simple hairpin structures accessible to tag i  F end (n) : generalized statistical weight of the terminal loop  1/2 : loss of half a staking interaction at the non-loop terminus of the duplex  Z i;k : statistical weight of stacking

19. (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/ The Fidelity of Perfectly Aligned Hamming Encodings WC based Hamming encoding scheme does not consistently enhance fidelity, relative to a simple random encoding strategy. (for L = N = 16)

20. (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/ The Scaling Behavior of the Fidelity of Random Encodings Weight error response worst spectral error response Error spectral width

21. (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/ The Scaling Behavior of the Fidelity of Random Encodings

22. (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/Conclusions 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.