Fuzzy logic with biomolecules R. Deaton & M. Garzon Soft Computing 5 (2001) pp. 2-9 Summarized by Shin, Soo-Yong 2001.8.3

(C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/ Abstract The uncertain and inexact nature of the chemical reactions used to implement DNA computation An advantage of implementing robust soft computing systems. Dependent on the actual geometry of the Gibbs free-energy landscapes in the space of all duplex formations. (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/

(C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/ Soft computing Fuzzy logic, neural networks, evolutionary computation (inspired by biological paradigms) Takes advantage of the uncertainty in the reactions, Hybridization process is inherently fuzzy! There is a degree of uncertainty Do not consider as “errors”. (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/

(C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/ Biomolecules A, G, C, T (U) DNA-to-DNA template matching (hybridization) A = T ; C  G Operations Gel electrophoresis : sorting & visualization Restriction enzymes : cut-and-paste PCR : copying (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/

(C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/ Biomolecules Determine duplex stability. Nearest-neighbor model : focuses on consecutive base pairs, referred to as base stacks, for which thermodynamic data exists. mismatches (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/

(C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/ Fuzzy Sets Everything is a matter of degree (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/

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

(C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/ If-then rules (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/

Fuzzy systems in biomolecules In general, hybridization is fuzzy! As temperature change, the degree of hybridization ca be changed. (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/

(C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/ DNA-based fuzzy sets Two choices The uncertainty of hybridization to represent fuzzy variables at the level of populations The uncertainty inherent in hybridization between individual strands The set of hybridized oligonucleotide pairs is a fuzzy set. A species of perfectly hybridized duplex would have all base pairs stacked, have a membership value of 1. (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/

Fuzzy hybridization logic If-then rules (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/

Fuzzy hybridization logic Use DNA hybridization, free energy f formation of the duplex (G) And the technology of high-density arrays of DNA, or DNA chips (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/

Encoding membership functions DNA implementation of a membership function Free energy of formation of the DNA duplex, G Very important problems  encoding problems Membership function onto the sequences of the DNA molecules so that their values can be measured experimentally from the physical properties of the duplexes formed under appropriate reaction conditions. Simplest way : nearest-neighbor interationcs. (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/

Encoding membership functions AA/TT AT/AT TA/TA AG/CT GA/TC AC/GT CA/TG GC/GC CG/CG GG/CC AE’/ET TE’/EA CE’/EG GE’/EC 14 nearest-neighbor paris NXY/YX : the number of occurrences of the complementary base pair in the molecules (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/

Encoding membership functions In general, a given molecules can be represented as a linear combination of the independent sequences si : the sequence xi : the number of occurrences of that sequence in the molecules (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/

Encoding membership functions (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/

Encoding membership functions Design molecules representing values of 0.2, 0.4, 0.6, 0.8, 1.0 (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/

Encoding membership functions The molecule representing a membership value of 0.2 EGTAAGGGCATCGE’ E’CATTCCCGTAGCE The representation of this duplex (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/

Encoding membership functions For the next molecules, the membership value is doubled, Take the first molecule and concatenate to it a new molecule that has identical composition, but a different sequences (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/

Encoding membership functions Inputs are encoded into a spectrum of DNA molecules, and might not be exact matches to the membership molecules 3’GCTGTAATCACGGTC5’ Encoding task is really important! (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/

DNA-based fuzzy associative memory (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/

(C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/ Conclusion More effective use of the properties inherent in DNA hybridization Makes fuzzy computing with DNA more tolerant to errors than conventional molecular computing Two problems Duplex stability calculation Encoding problems (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/