References References � “ “Self-Assembling DNA Graphs Self-Assembling DNA Graphs” ”, P. Sa- , P. Sa-Aradyen Aradyen, , � Self-Assembling DNA Self-Assembling DNA N. Jonoska Jonoska, N. C. , N. C. Seeman Seeman, DNA Computing, , DNA Computing, N. th International Workshop on DNA-Based 8 8 th International Workshop on DNA-Based Graphs Graphs Computers, pp. 1-9, 2003 Computers, pp. 1-9, 2003 � “ “Computation by Self-Assembly of DNA Computation by Self-Assembly of DNA � Jibran Rashid Jibran Rashid Graphs” ”, P. Sa- , P. Sa-Aradyen Aradyen, N. , N. Jonoska Jonoska, N. C. , N. C. Graphs CPSC 607 CPSC 607 Seeman Seeman, Genetic Programming and Evolvable , Genetic Programming and Evolvable Machines, Vol. 4, pp. 123-137, 2003 Machines, Vol. 4, pp. 123-137, 2003 Outline Self-Assembly Outline Self-Assembly � Motivation Motivation � Self-assembly is the ubiquitous process by which Self-assembly is the ubiquitous process by which � � � Proposed Methods Proposed Methods objects autonomously assemble into complexes. 1 1 objects autonomously assemble into complexes. � � General framework for problem solving via Self- General framework for problem solving via Self- � Assembly � It may be utilized as a tool to enable the It may be utilized as a tool to enable the Assembly � development of complex information processing development of complex information processing � Experiment Design Experiment Design � units e.g. DNA Computing where the inherent units e.g. DNA Computing where the inherent � Experiment Results Experiment Results � 3D structure of DNA can be used as a 3D structure of DNA can be used as a � Conclusions Conclusions � computational device computational device � Issues Issues… …. . � [1] [1] http://www.usc.edu/dept/molecular-science/index.html http://www.usc.edu/dept/molecular-science/index.html Different Proposals – – Branched Branched Different Proposals Different Proposals – – Tiling Tiling Different Proposals Junction Molecules Junction Molecules � Branched junction molecules and graph-like DNA Branched junction molecules and graph-like DNA � structures � DNA tiles made of double and triple cross-over DNA tiles made of double and triple cross-over structures � molecules molecules – – for self-assembly of 2D arrays for self-assembly of 2D arrays � Splicing of tree like structures Splicing of tree like structures � � Autonomous Molecular Computation Autonomous Molecular Computation � � Simulate Horn Clause computation via self-assembly of three Simulate Horn Clause computation via self-assembly of three � � Based on Tiling Theory Based on Tiling Theory – – Arrangement of basic shaped that Arrangement of basic shaped that � junctions and hairpins junctions and hairpins cover infinite place. Infinite number of square tiles with 4 cover infinite place. Infinite number of square tiles with 4 colored slides can simulate Turing Machines. Use DNA to colored slides can simulate Turing Machines. Use DNA to � Proposals for solutions to various problems e.g. 3SAT, Proposals for solutions to various problems e.g. 3SAT, � simulate these tiles via self-assembly 1 1 simulate these tiles via self-assembly Hamiltonian Path & 3-Coloring a graph Hamiltonian Path & 3-Coloring a graph � Sides of a tile correspond to the sticky ends Sides of a tile correspond to the sticky ends � � These solutions have not been confirmed experimentally These solutions have not been confirmed experimentally � � Labeled by the sequences of the sticky ends Labeled by the sequences of the sticky ends � � Able to construct regular graphs (degrees of all vertices are Able to construct regular graphs (degrees of all vertices are � � Tiles assemble with each other according to WC Tiles assemble with each other according to WC � the same) the same) complementarity complementarity � XOR operation was experimentally confirmed XOR operation was experimentally confirmed � [1] http://ai.stanford.edu/~serafim/CS374_2004/Presentations/CS374_2004_Lecture19a_I_DNAassembly.ppt [1] http://ai.stanford.edu/~serafim/CS374_2004/Presentations/CS374_2004_Lecture19a_I_DNAassembly.ppt
Key Idea Example – – 3SAT 3SAT Key Idea Example � Problem is encoded via a graph such that for a Problem is encoded via a graph such that for a � ( x y z ) ( x y z ) ( x y z ) � = � � � � � � � � given problem instance the graph is self- given problem instance the graph is self- assembled using WC assembled using WC complementarity complementarity if and if and only if a solution exists i.e. a satisfying only if a solution exists i.e. a satisfying assignment to the variables exists (3SAT) OR assignment to the variables exists (3SAT) OR the graph is 3-colorable the graph is 3-colorable � Usually need to remove partially formed 3D Usually need to remove partially formed 3D � DNA structures or graphs that are larger than DNA structures or graphs that are larger than the original problem encoding the original problem encoding The graph on the left corresponds to the above 3SAT instance. A possible self-assembled graph structure for the formula is depicted on the right. Examples – – 3-Coloring 3-Coloring Experiment Examples Experiment For a given graph G, a DNA graph structure corresponding to For a given graph G, a DNA graph structure corresponding to � Goal: To self-assemble the following non- Goal: To self-assemble the following non- � � � G can be formed by vertex and edge building blocks if and G can be formed by vertex and edge building blocks if and regular graph (5 vertices & 8 edges) in the regular graph (5 vertices & 8 edges) in the only if G is 3-colorable. only if G is 3-colorable. The following two laboratory The following two laboratory steps are required: steps are required: laboratory (Not solving any graph coloring laboratory (Not solving any graph coloring � � Combine all building blocks and allow the complementary ends to Combine all building blocks and allow the complementary ends to 1. 1. problem currently) problem currently) hybridize and be hybridize and be ligated ligated (probably need to use PCR to amplify the (probably need to use PCR to amplify the number of solution graph structures) number of solution graph structures) Determine whether the required graph structure has formed by: Determine whether the required graph structure has formed by: 2. 2. Remove partially formed 3D DNA structures Remove partially formed 3D DNA structures a) a) Use gel electrophoresis to remove graphs that are larger than the original Use gel electrophoresis to remove graphs that are larger than the original b) b) graph graph If graph structures remain in the test tube, then If graph structures remain in the test tube, then then then graphs is 3-colorable graphs is 3-colorable c) c) Design of the Self-Assembly Design of the Self-Assembly Design of the Self-Assembly Design of the Self-Assembly � The five vertices are designed to be junction molecules The five vertices are designed to be junction molecules � Strands labeled using Strands labeled using � 32 P � ATP � � 3-armed junctions for vertices v 3-armed junctions for vertices v 1 , v 3 , v 4 & v 5 1 , v 3 , v 4 & v � 5 The labeling of a v The labeling of a v 2 2 strand was not strand was not � 4-armed junction for v 4-armed junction for v 2 � 2 successful and no successful and no ligation ligation was was � Sticky ends (represented by shaded area) designed such that the final Sticky ends (represented by shaded area) designed such that the final � visible visible graph structure is one cyclic molecule graph structure is one cyclic molecule � Six DNA strands required for each edge: Six DNA strands required for each edge: � � Two strands each from the two junction molecules representing the Two strands each from the two junction molecules representing the � vertices vertices � Two strands to form the duplex molecule of the edge Two strands to form the duplex molecule of the edge � � Length of e Length of e 1 1 = e = e 2 2 =e =e 5 5 = e = e 8 8 = 4 helical turns = 42 base pairs = 4 helical turns = 42 base pairs � � Length of e Length of e 3 3 = e = e 4 4 = e = e 7 7 = 6 helical turns = 63 base pairs = 6 helical turns = 63 base pairs � � Length of e Length of e 6 = 8 helical turns = 84 base pairs 6 = 8 helical turns = 84 base pairs � � Sticky edges of length 6 and 8 Sticky edges of length 6 and 8 bp bp �
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