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

2. (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, 

3. (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, 

4. (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, 

5. (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
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6. (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
Fuzzy Sets
Everything is
a matter of degree
(C) 2001, SNU Biointelligence Lab, 

7. (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
Membership functions
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8. (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
If-then rules
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9. Fuzzy systems in biomolecules
In general, hybridization is fuzzy!
As temperature change, the degree of hybridization ca be changed.
(C) 2001, SNU Biointelligence Lab, 

10. (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.
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11. Fuzzy hybridization logic
If-then rules
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12. 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
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13. 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, 

14. 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
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15. 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
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16. Encoding membership functions
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17. Encoding membership functions
Design molecules representing values of 0.2, 0.4, 0.6, 0.8, 1.0
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18. Encoding membership functions
The molecule representing a membership value of 0.2
EGTAAGGGCATCGE’
E’CATTCCCGTAGCE
The representation of this duplex
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19. 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
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20. 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!
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21. DNA-based fuzzy associative memory
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22. (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,