Theoretical and Experimental DNA Computation (Natural ...

More documents

Recommendations

Info

Vertex 1 Vertex 2 Vertex 3 ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ £ £ £ £ £ £ £ £ £ £ £ £ ¢ Vertex 4 Vertex 5 Vertex 6 Vertex 7 5.4 Adleman’s Implementation 113 ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ § § § § § § § § § § § § § § § ¤ ¨ ¨ ¨ ¨ ¨ © © © © © © � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ¨ � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � (a) V1 to V2 V1 to V4 V1 to V7 V2 to V3 V2 to V4 V3 to V2 V3 to V4 V4 to V3 V4 to V5 V5 to V2 V5 to V6 V6 to V2 V6 to V7 Fig. 5.3. Adleman’s scheme for encoding paths - schematic representation of oligos � � � � � � (b) � � � � � � � � � � � � � � � � � � � � � � � �� V1 V2 V3 V2 Fig. 5.4. Example path created in Adleman’s scheme strand representing the HP is present with high probability. This approach solves the problem of generating an exponential number of different paths using a polynomial number of initial oligonucleotides. � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� V1 V2 V3 V4 V5 V6 V7 Fig. 5.5. Unique Hamiltonian path
114 5 Physical Implementations Stage 2: PCR was first used to massively amplify the population of oligonucleotides encoding paths starting at v1 and ending at v7. Next, strands that do not encode paths containing exactly n visits were removed. The product of the PCR amplification was run on an agarose gel to isolate strands of length 140 b.p. A series of affinity purification steps was then used to isolate strands encoding paths that visited each vertex exactly once. Stage 3: Graduated PCR was used to identify the unique HP that this problem instance provides. For an n-vertex graph, we run n−1 PCR reactions, with the strand representing v1 as the left primer and the complement of the strand representing vi as the right primer in the i th lane. The presence of molecules encoding the unique HP depicted in Fig. 5.2 should produce bands of length 40, 60, 80, 100, 120, and 140 b.p. in lanes 1 through 6, respectively. This is exactly what Adleman observed. The graduated PCR approach is depicted in Fig. 5.6. α β λ δ α β λ δ α β λ δ α β λ δ α β λ δ Long Short Run strands through gel to sort them on length Fig. 5.6. Graduated PCR Add primers PCR produces many copies of strands Adleman’s experiment was remarkable in that it was the first to demonstrate in the laboratory the feasibility of DNA computing. However, we note that it was performed on a single problem instance with just one HP. No control experiments were performed for cases without Hamiltonian Paths. The final detection step is problematic, due to reliance on the error prone PCR procedure. In addition, the use of affinity purification is also error prone, which may
Page 2 and 3:
Natural Computing Series Series Edi
Page 4:
Martyn Amos Department of Computer
Page 8 and 9:
Preface DNA computation has emerged
Page 10:
Preface IX acknowledged. Finally, I
Page 13 and 14:
XII Contents 4 Complexity Issues ..
Page 16 and 17:
Introduction “Where a calculator
Page 18 and 19:
Introduction 3 Even though their un
Page 20 and 21:
1 DNA: The Molecule of Life “All
Page 22 and 23:
1.3 DNA as the Carrier of Genetic I
Page 24 and 25:
1.3 DNA as the Carrier of Genetic I
Page 26 and 27:
Synthesis 1.4 Operations on DNA 11
Page 28 and 29:
Gel electrophoresis 1.4 Operations
Page 30 and 31:
5’ 3’ A T A G A G T T 3’ TCA
Page 32 and 33:
1.4 Operations on DNA 17 Others may
Page 34 and 35:
Vector Strand to be inserted (targe
Page 36:
1.5 Summary 1.6 Bibliographical Not
Page 39 and 40:
24 2 Theoretical Computer Science:
Page 41 and 42:
Page 43 and 44:
Page 45 and 46:
Page 47 and 48:
Page 49 and 50:
Page 51 and 52:
Page 53 and 54:
Page 55 and 56:
Page 57 and 58:
Page 59 and 60:
Page 61 and 62:
46 3 Models of Molecular Computatio
Page 63 and 64:
Page 65 and 66:
Page 67 and 68:
Page 69 and 70:
Page 71 and 72:
Page 73 and 74:
Page 75 and 76:
Page 77 and 78: 62 3 Models of Molecular Computatio
Page 87 and 88: 72 4 Complexity Issues is that, alt
Page 89 and 90: 74 4 Complexity Issues The weak par
Page 91 and 92: 76 4 Complexity Issues 4.3 A Strong
Page 93 and 94: 78 4 Complexity Issues Ω = {∧,
Page 95 and 96: 80 4 Complexity Issues 0 1 0 1 x1 x
Page 97 and 98: 82 4 Complexity Issues connecting a
Page 99 and 100: 84 4 Complexity Issues Level simula
Page 101 and 102: 86 4 Complexity Issues At level D(S
Page 103 and 104: 88 4 Complexity Issues xANDy)) and
Page 105 and 106: 90 4 Complexity Issues Input matrix
Page 107 and 108: 92 4 Complexity Issues memory acces
Page 109 and 110: 94 4 Complexity Issues denoted by P
Page 111 and 112: 96 4 Complexity Issues The final st
Page 113 and 114: 98 4 Complexity Issues 1)), ADDR[])
Page 115 and 116: 100 4 Complexity Issues Size(STI)=O
Page 117 and 118: 102 4 Complexity Issues best attain
Page 119 and 120: 104 4 Complexity Issues 10. LDC 0 1
Page 121 and 122: 106 4 Complexity Issues ACC[] := bi
Page 124 and 125: 5 Physical Implementations “No am
Page 126 and 127: 5.3 Initial Set Construction Within
Page 130 and 131: 5.5 Evaluation of Adleman’s Imple
Page 132 and 133: 5.6 Implementation of the Parallel
Page 134 and 135: 5.8 Experimental Investigations 119
Page 138 and 139: Create initial strand library Confi
Page 144 and 145: Experiment 25. New full-length chai
Page 150 and 151: 5.9 Other Laboratory Implementation
Page 160: 5.11 Bibliographical Notes 145 whic
Page 163 and 164: 148 6 Cellular Computing of truly i
Page 165 and 166: 150 6 Cellular Computing 6.2 Succes
Page 167 and 168: 152 6 Cellular Computing are “glu
Page 169 and 170: 154 6 Cellular Computing x y z x (a
Page 171 and 172: 156 6 Cellular Computing 6.7 Biblio
Page 173 and 174: 158 References 14. Martyn Amos, Ste
Page 175 and 176: 160 References 53. Dónall A. Mac D
Page 177 and 178: 162 References 92. D. Knuth. The Ar
Page 179 and 180:
164 References 135. Kensaku Sakamot
Page 182 and 183:
Index ALGOL, 102 AND, 23-24, 42, 87
Page 184 and 185:
iological, 74, 114, 150 Feynman, R.
Page 186 and 187:
Petrinet,63 phage, 18-20 phosphate,
Page 188:
Natural Computing Series W.M. Spear
show all

Theoretical and Experimental DNA Computation (Natural ...

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?