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Fraunhofer Institute for Integrated Circuits Dresden University of Technology A Probabilistic Approach to Description of Molecular Biological Processes on DNA and Their Object Oriented Simulation U. Hatnik, T. Hinze, M. Sturm Dresden DNA Computation Group email: dnacomp@tcs.inf.tu-dresden.de www: http://wwwtcs.inf.tu-dresden.de/dnacomp U. Hatnik, T. Hinze, M. Sturm 1/13 Simulation of Molecular Biological Processes

Fraunhofer Institute for Integrated Circuits Dresden University of Technology Contents 1. State of the Art in DNA Computing 2. Side Effects of DNA Operations 3. A Probabilistic Approach to DNA Computing 4. An Object Oriented Simulation Tool 5. Selected DNA Operations 6. A PCR Example 7. Conclusions U. Hatnik, T. Hinze, M. Sturm 2/13 Simulation of Molecular Biological Processes

✁ � � � ✂ � Fraunhofer Institute for Integrated Circuits Dresden University of Technology State of the Art in DNA Computing vision establish a universal biocomputer in theory and laboratory biocomputer based on a formal model should feature by – computational completeness (universality), reliability – high operational speed using massive data parallelism – high storage capacity and density, persistence of stored data – DNA reusability, energy efficient processing without mech. wear challenges making DNA operations error resistent reducing side effects bridging the gap between formal models of DNA computing and lab-reality our approach U. Hatnik, T. Hinze, M. Sturm 3/13 Simulation of Molecular Biological Processes

� � ✂ � � � � � � � � Fraunhofer Institute for Integrated Circuits Dresden University of Technology Gap between Models and Lab-Reality side effects of DNA operations not controllable, unreproducible, stochastically occurring effects of molecular biological processes used as DNA operations can sum up in sequences of DNA operations lead to unexpected, unprecise, unreproducible or even unusable final results of experimental DNA computations frequently used abstractions of formal models of DNA computing only linear DNA used as data carrier (words of formal languages) unrestricted approach; arbitrary ( ) number of strand copies unique result strands detectable absolutely reliable all DNA operations performed completely and reproducible idea to bridge the gap specification of DNA operations on molecular level include side effects specified by statistical parameters into the description of DNA operations probabilistic approach U. Hatnik, T. Hinze, M. Sturm 4/13 Simulation of Molecular Biological Processes

Fraunhofer Institute for Integrated Circuits Dresden University of Technology Side Effects of DNA Operations operations performed with affinity purification gel electrophoresis synthesis annealing melting union ligation digestion labeling polymerisation PCR state of the art laboratory techniques point mutation (% mutation rate) classification of side effects mutations (differences in DNA sequence) deletion (% deletion rate, max. length of deletion) insertion loss of linear DNA strands by forming hairpins, artifacts (diff. from lin. DNA structure) bulges, loops, junctions, and compositions of them (% loss rate of tube contents) incomplete reaction (% unprocessed strands) failures in reaction procedure (differences from perfect specification of reaction) unspecificity (% error rate, maximum difference) supercoils strand instabilities caused by temperature or pH impurities by rests of reagences undetectable low DNA concentration (min. # copies) loss of DNA strands (% loss rate of tube contents) : supported in simulation tool in brackets: statistical parameters : significant side effect caused by the operation U. Hatnik, T. Hinze, M. Sturm 5/13 Simulation of Molecular Biological Processes

� � � ✂ � � � Fraunhofer Institute for Integrated Circuits Dresden University of Technology A Probabilistic Approach to DNA Computing properties multiset based, nondeterministic, restricted model description of DNA operations on level of single nucleotides and strand end labels operation param., side effect param. recently supported: synthesis, annealing, melting, union, ligation, digestion, labeling, polymerisation, PCR, affinity purification, gel electrophoresis; formal description by prog. language operation control iteration of molecular events, probability-controlled probabilities of molecular events depend on: DNA pool, number of strand copies, operation parameters, side effect parameters iteration terminates iff empty list (matrix) of possible mol. events U. Hatnik, T. Hinze, M. Sturm 6/13 Simulation of Molecular Biological Processes

Fraunhofer Institute for Integrated Circuits Dresden University of Technology A Probabilistic Approach to DNA Computing iteration exemplified by annealing (simplified) 1. 10 x A A G C T C C G A T G G A G C T 6 x T G A A G C T C C A T C G G A 10 strands 6 strands DNA pool A A G C T C C G A T G G A G C T T G A A G C T C C A T C G G A 2. probability for collision: probability for collision: 10 * 10 10 * 6 0.39 0.23 = = 10 strands 2 2 p p possible complete molecular reactions: possible complete molecular reactions: A A G C T C C G A T G G A G C T G A T A A G C T C C G G A G C T A A G C T C C G A T G G A G C T T C G A G G C C T C G A A A G G C T A C C T C G A A G T T A G 3. loop probability for collision: probability for collision: 6 * 10 6 * 6 0.23 = 0.15 = 4. 6 strands 2 2 p p possible complete molecular reactions: possible complete molecular reactions: T G A A G C T C C A T C G G A A A G C T C C G A T G G A G C T 1 x A A G C T C C G A T G G A G C T no new product A G G C T A C C T C G A A G T A G G C T A C C T C G A A G T 9 x A A G C T C C G A T G G A G C T number of DNA strands: p = 10 + 6 = 16 5 x T G A A G C T C C A T C G G A minimum nucleotide bonding rate for stable hybridized DNA double strands: 50% molecular event: strand hybridization modified DNA pool 1. Create list (matrix) of molecular events and their probabilities including side effects 2. Select one molecular event randomly with respect to the probability distribution 3. Determine all possible reaction products from this molecular event and select one of them 4. Modify DNA pool U. Hatnik, T. Hinze, M. Sturm 7/13 Simulation of Molecular Biological Processes

✂ � � � � � � Fraunhofer Institute for Integrated Circuits Dresden University of Technology An Object Oriented Simulation Tool main features specification of DNA operations on the level of single nucleotides and strand end labels using probabilistic approach number of strand copies considered concentrations of different DNA strands and their influence to the behaviour in op. process each DNA operation processed inside a virtual test tube collecting a multiset of DNA strands, several test tubes supported each DNA operation characterized by a set of specific parameters and side effect parameters arbitrary sequences of DNA operations including propagation of side effects can be visualized and logged Java, simulation tool requires at least Java Development Kit 2.0 other objects algorithms for frame process control object interface algorithms for tubes tubes sets of DNA strands simulation algorithms for sequences sequences sequences sequences model algorithm molecular interactions a) b) (DNA strand, reactants) U. Hatnik, T. Hinze, M. Sturm 8/13 Simulation of Molecular Biological Processes

Fraunhofer Institute for Integrated Circuits Dresden University of Technology Selected DNA Operations – Synthesis operation parameters: tube name: tube1 nucleotide sequence (5’-3’): AGGCACTGAGGTGATTGGC number of strand copies: 8 000 side effect parameters: point mutation rate: 0.06% deletion rate 0.06% maximum deletion length: 11% of strand length output of test tube contents U. Hatnik, T. Hinze, M. Sturm 9/13 Simulation of Molecular Biological Processes

Fraunhofer Institute for Integrated Circuits Dresden University of Technology Selected DNA Operations – Digestion operation parameters: tube name: tube2 5’ 3’ T C G C G A recognition sequence 3’ A G C G C T 5’ and restriction site: side effect parameters: rate of not executed molecular cuts: 5% rate of star activity (unspecificity): 5% 5’ N C G C G N 3’ wildcarded recognition sequence: 3’ N G C G C N 5’ output of test tube contents U. Hatnik, T. Hinze, M. Sturm 10/13 Simulation of Molecular Biological Processes

Fraunhofer Institute for Integrated Circuits Dresden University of Technology A PCR Example (I) 1000 copies template1 1000 copies template2 8000 copies primer1 8000 copies primer2 Synthesis Synthesis Synthesis Synthesis Union 7910 Union correct synthesized strands 7909 (7910 copies of primer2, Union 7909 copies of primer1, 942 copies of template1, 942 941 copies of template2) 941 7 incorrect synthesized strands carrying 6 point mutations and deletions (totally 90 strands of primer2, 91 strands of primer1, 5 58 strands of template1, 59 strands of template2) 5 U. Hatnik, T. Hinze, M. Sturm 11/13 Simulation of Molecular Biological Processes