1. Horn Clause Computation by Self-Assembly of DNA Molecules
H. Uejima, M. Hagiya, S. Kobayashi
DNA7
Summarized by In-hee, Lee

2. © 2001, SNU BioIntelligence Lab, http://bi.snu.ac.kr/
1. Introduction
Horn Clause computation
Closely related to the high-level programming language PROLOG
Tiling
Autonomous molecular computation
Sides of a tile correspond to the sticky ends of a DNA molecule, and labeled by the sequences of the sticky ends
Tiles assemble with each other at the sides whose labels are complementary
© 2001, SNU BioIntelligence Lab,

3. 2. Inference by Self-assembly of DNA
Simple Horn Clause Model
V = {A, B, C, …}
Fact: formula of the form A
Rule: AB1 B2 …  Bn
Horn clause is either a fact or a rule
Set of Horn clause is called Horn program
Resolution principle
© 2001, SNU BioIntelligence Lab,

4. 2. Inference by Self-assembly of DNA
Molecular computation model
Detect(P, A)
P1  P2
T(P)
The procedure
© 2001, SNU BioIntelligence Lab,

5. © 2001, SNU BioIntelligence Lab, http://bi.snu.ac.kr/
2.1 DNA Implementation
Implementation of clauses
Fig. 1
© 2001, SNU BioIntelligence Lab,

6. © 2001, SNU BioIntelligence Lab, http://bi.snu.ac.kr/
2.1 DNA Implementation
Implementation of operations
Detect(P, A)
With magnetic beads, keep only the molecules with query molecules
Ligate the molecules
Check whether there exists a circular molecules. (exonuclase)
© 2001, SNU BioIntelligence Lab,

7. 3. Substitution by String Tiling
Extension for first-order logic
Atomic formula:
If ti does not contain variables for any i, it is a ground atom
The Procedure
© 2001, SNU BioIntelligence Lab,

8. 3. Substitution by String Tiling
Restrictions on MakeClause(P)
Term in a rule should be of the form
Arity of a predicate should be at most two
Arity of a function should be one
Variable used in the first argument of an atom should always be X, and the variable in the second argument should always be Y
A fact should contain no variables
© 2001, SNU BioIntelligence Lab,

9. © 2001, SNU BioIntelligence Lab, http://bi.snu.ac.kr/
3.1 DNA Implementation
Seed tile for
Implementation of substitution
Fig. 2
© 2001, SNU BioIntelligence Lab,

10. © 2001, SNU BioIntelligence Lab, http://bi.snu.ac.kr/
3.1 DNA Implementation
Structure of a seed tile
© 2001, SNU BioIntelligence Lab,

11. 3. Substitution by String Tiling
Computational power
We can construct a restricted simple Horn program to simulate a nondeterministic Turing machine which computes a problem in NP.
A polynomial number of operations using self-assembly of DNA molecules can compute any problem in NP.
© 2001, SNU BioIntelligence Lab,

12. © 2001, SNU BioIntelligence Lab, http://bi.snu.ac.kr/
4. Discussion
3D conformation of branching molecules
Bias and errors in hybridization
Analysis of chemical reactions
Reaction rate, space complexity
Analysis from the aspects of thermodynamics and kinetics is necessary
Random substitutions
Combinatorial explosion of string tiles
© 2001, SNU BioIntelligence Lab,