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Self-Assembled Nanostructures, Molecular Automata, and Chemical Reaction Networks

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Self-Assembled Nanostructures, Molecular Automata, and Chemical Reaction Networks Molecules Computing: Self-Assembled Nanostructures, Molecular Automata, and Chemical Reaction Networks Thesis by David Soloveichik In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 2008 (Defended May 5, 2008) ii c 2008 David Soloveichik All Rights Reserved iii Contents Acknowledgements vi Abstract vii 1 Introduction 1 1.1 ThePromiseofBionanotechnology . ........... 1 1.2 TheMathematicsofComputerScience. ............ 2 1.3 TheCriteriaforSuccess. .......... 3 1.4 TheContributions................................ ........ 3 1.4.1 TileSelf-Assembly. ...... 3 1.4.2 RestrictionEnzymeAutomata . ........ 4 1.4.3 ChemicalReactionNetworks . ....... 4 Bibliography ....................................... ...... 6 2 Complexity of Self-Assembled Shapes 8 2.1 Abstract........................................ ..... 8 2.2 Introduction.................................... ....... 8 2.3 TheTileAssemblyModel .. .... .... ... .... .... .... ... ....... 9 2.3.1 GuaranteeingUniqueProduction. .......... 10 2.4 ArbitrarilyScaledShapesandTheirComplexity . ................. 11 2.5 Relating Tile-Complexity and Kolmogorov Complexity . .................. 12 2.6 TheProgrammableBlockConstruction . ............ 13 2.6.1 Overview...................................... .. 13 2.6.2 ArchitectureoftheBlocks . ........ 14 2.6.2.1 GrowthBlocks................................ 14 2.6.2.2 SeedBlock.................................. 17 2.6.3 TheUnpackingProcess. ...... 17 2.6.4 Programming Blocks and the Value of the Scaling Factor c .............. 21 2.6.5 UniquenessoftheTerminalAssembly . .......... 21 2.7 GeneralizationsofShapeComplexity . ............. 22 2.7.1 OptimizingtheMainResult(Section2.5) . ............ 22 2.7.2 StrengthFunctions .. .... .... ... .... .... .... .... ...... 23 2.7.3 WangTilingvsSelf-AssemblyofShapes . .......... 23 2.7.4 SetsofShapes .................................. ... 25 2.7.5 ScaleComplexityofShapeFunctions . .......... 26 2.7.6 OtherUsesofProgrammableGrowth . ........ 27 2.8 Appendix ........................................ .... 28 2.8.1 Local Determinism Guarantees Unique Production: ProofofTheorem2.3.1 . 28 2.8.2 Scale-Equivalence and “∼=”areEquivalenceRelations . 28 Bibliography ....................................... ...... 29 iv 3 Complexity of Compact Proofreading for Self-Assembled Patterns 31 3.1 Abstract........................................ ..... 31 3.2 Introduction.................................... ....... 31 3.2.1 TheAbstractTileAssemblyModel . ........ 33 3.2.2 TheKineticTileAssemblyModelandErrors . ........... 33 3.2.3 Quarter-PlanePatterns . ........ 34 3.3 MakingSelf-AssemblyRobust . .......... 35 3.4 Compact ProofreadingSchemes for Simple Patterns . ................. 37 3.5 ALowerBound..................................... .... 39 3.6 Appendix ........................................ .... 41 3.6.1 Extension of Chen and Goel’s Theorem to Infinite Seed BoundaryAssemblies . 41 3.6.2 AnOverlayProofreadingScheme . ........ 41 Bibliography ....................................... ...... 43 4 Combining Self-Healing and Proofreading in Self-Assembly 45 4.1 Abstract........................................ ..... 45 4.2 Introduction.................................... ....... 45 4.3 ModelingErrors.................................. ....... 48 4.3.1 ErroneousTileAdditionsDuringGrowth . ........... 48 4.3.2 WholesaleRemovalofTiles . ....... 49 4.4 Self-HealingProofreadingConstruction . ................ 49 4.5 Extensions...................................... ...... 54 4.5.1 Random Walks in the r2 = f Regime ......................... 54 4.5.2 PreventingSpuriousNucleation6 . .......... 55 Bibliography ....................................... ...... 56 5 The Computational Power of Benenson Automata 58 5.1 Abstract........................................ ..... 58 5.2 Introduction.................................... ....... 58 5.3 FormalizationofBenensonAutomata . ............ 61 5.4 Characterizing the Computational Power of Benenson Automata ............... 62 5.5 SimulatingBranchingProgramsandCircuits . ............... 63 5.5.1 GeneralBranchingPrograms. ........ 63 5.5.2 Fixed-WidthBranchingPrograms . ......... 64 5.5.3 PermutationBranchingPrograms . ......... 66 5.5.4 SimulatingCircuits. ....... 68 5.5.5 Achieving 1-EncodedAutomata ............................ 68 5.6 Shallow Circuits to Simulate Benenson automata . ................ 69 5.7 Discussion...................................... ...... 70 Bibliography ....................................... ...... 71 6 Computation with Finite Stochastic Chemical Reaction Networks 72 6.1 Abstract........................................ ..... 72 6.2 Introduction.................................... ....... 72 6.3 StochasticModelofChemicalKinetics . ............. 73 6.4 Time/Space-BoundedAlgorithms . ........... 74 6.5 UnboundedAlgorithms. ........ 79 6.6 Discussion...................................... ...... 81 6.7 Appendix ........................................ .... 81 6.7.1 ClockAnalysis ................................. .... 81 6.7.2 Time/Space-BoundedRMSimulation . ......... 82 6.7.3 Time/Space-BoundedCTMSimulation . ......... 83 6.7.4 UnboundedRMSimulation . ..... 84 6.7.5 UnboundedCTMSimulation. ...... 84 v 6.7.6 DecidabilityofReachability . .......... 85 Bibliography ....................................... ...... 85 7 Robust Stochastic Chemical Reaction Networks 88 7.1 Abstract........................................ ..... 88 7.2 Introduction.................................... ....... 88 7.3 ModelandDefinitions .............................. ....... 90 7.4 RobustnessExamples. .... .... .... ... .... .... .... .. ........ 91 7.5 BoundedTau-Leaping. .... .... .... ... .... .... .... .. ........ 93 7.5.1 TheAlgorithm .................................. ... 93 7.5.2 UpperBoundontheNumberofLeaps. ....... 95 7.6 On the Computational Complexity of the Prediction ProblemforRobustSSAProcesses . 96 7.7 Discussion...................................... ...... 98 7.8 Appendix ........................................ .... 98 7.8.1 Proof of Theorem 7.5.1: Upper Bound on the Number of Leaps ........... 98 7.8.2 ProvingRobustnessbyMonotonicity . .......... 102 7.8.3 RobustEmbeddingofaTMinanSCRN . ..... 103 7.8.4 Proof of Theorem 7.6.1: Lower Bound on the Computational Complexity of the Pre- dictionProblem..................................... 105 7.8.5 OnImplementingBTLonaRandomizedTM . ....... 106 Bibliography ....................................... ...... 106 8 Enzyme-Free Nucleic Acid Logic Circuits 109 8.1 Abstract........................................ ..... 109 8.2 Introduction.................................... ....... 109 8.3 GateConstructionandVerification . ............. 110 8.4 CircuitConstruction. .......... 110 8.5 Conclusion ...................................... ..... 114 Bibliography ....................................... ...... 114 9 DNA as a Universal Substrate for Chemical Kinetics 116 9.1 Abstract........................................ ..... 116 9.2 Introduction.................................... ....... 116 9.3 CascadesofStrandDisplacementReactions . ............... 117 9.4 ArbitraryUnimolecularReactions . ............. 119 9.5 ArbitraryBimolecularReactions . ............. 120 9.6 SystematicConstruction . .......... 122 9.7 Example......................................... .... 123 9.8 Conclusion ...................................... ..... 125 Bibliography ....................................... ...... 125 vi Acknowledgements I thank Erik Winfree for being an ideal advisor, who inspired me, challenged me, and let me have the freedom to go on my own. He is an exceptional scientist and a good human being. Amazingly, everything I found interesting, he found interesting too. The network of relations that is my brain is in profounddebt to Matthew Cook for demonstrationsof thinking clearly. Erik and Matt have been my role modelsand I hope will continue to be my friends. I thank my collaborator and friend Georg Seelig, who taught me physics. Paul W.K. Rothemund was my famed office-mate who taught me to fly RC airplanes and how to throw a boomerang like a man. I thank Ho-Lin Chen, Rebecca Schulman, Nadine Dabby, Joseph Schaeffer, Dave Zhang, Rizal Hariadi, Jongmin Kim, Peng Yin, Lulu Qian, and all the members of the Winfree group, past and present, for making the place as friendly and engaging as it was, and for wonderful, irreplaceable discussions. I thank Yaser Abu-Mostafa for a wonderful rotation experience, Shuki Bruck for inviting me to his stimu- lating group meetings, Chris Umans for teaching a fascinating complexity theory course, and John Doyle for providing positive feedback on my thesis work. I thank the ARCS Foundation, NSF, NIH, and the Caltech CNS program for funding. My mom and dad, and my grandma, have been my foundation. Their sacrifices for my sake are immea- surable. I cannot be grateful enough to have been born into my family, to have had my childhood, and to have them live only a drive away now. I thank my wife’s family for their support from the very first time we met. To thank my wife Esther for everything she has meant to me demands more than acknowledgment, and loving her dearly is only the first step. This thesis is dedicated to our son Elie. vii Abstract Many endeavors of molecular-level engineering either rely on biological material such as nucleic acids and restriction enzymes, or are inspired by biological processes such as self-assembly or cellular regulatory net- works. This
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