1 DNA Computing: Concept and Design Ruoya Wang April 21, 2008 MATH 8803 Final presentation

2 The DNA molecule Serves as a long-term storage of genetic information. The information is stored as unique sequences composed of two base pairs: A↔T and G↔C. The complexities of all living organisms are the result of simple manipulations of their encoded DNA sequences.

3 DNA computing A relatively new form of computing that, instead of using silicon-based technology, utilizes the abilities of the DNA molecule and biochemistry. Pioneered and experimentally verified by computer scientist Leonard Adleman of USC. “Molecular Computation of Solutions To Combinatorial Problems” Science 266(11) Although the field is still in its infancy, many significant advancements have been made since its inception.

4 Adleman’s DNA computer Proof-of-concept experiment. Solved a 7-nodal instance of a directed Hamiltonian path problem (i.e. the traveling salesman). The typically brute-force algorithm consists of: 1.Randomly produce all possible paths through the graph. 2.Keep only the paths that begins and ends at the predefined vertices. 3.Keep only the paths that entered the same number of vertices as the number of vertices of the graph. 4.Keep only the paths entered each vertex exactly once. 5.The remaining path is the answer. Adleman translated the algorithm to a form that could be implemented using DNA and biochemistry.

5 Adleman’s DNA computer Computer algorithm to molecular biochemistry 1.Designated each vertex of the graph with a unique and random 20-mer DNA sequence and run all the sequences through a ligation reaction. 2.Sequences starting and ending at the specified vertices were extracted using PCR with primers designed for those sequences mer sequences were extracted by running the remaining sequences from step 2 through gel electrophoresis. Result amplified by PCR. 4.Using biotin-avidin magnetic bead system, only sequence with one of each vertex was extracted: ssDNA ↔ O i ↔ biotin-avidin ↔ magnetic beads Where i = 1,2,3,4,5,6,7 5.Product of step 4 is PCR amplified and run on a gel.

6 Further developments Adleman successfully demonstrated the viability of DNA computing through his experiments. Further research by Adleman and other groups solved more complex combinatorial problems. A novel direction was taken when the concept of an autonomous DNA computer was introduced by Benenson et al. –Exploited cleaving enzyme and the native potential free energy in DNA during spontaneous hydrolysis. Autonomous logic control was based on concept of finite state automata. –Previous DNA computers relied on ATP and heat for ligation reactions and denaturing respectively.

7 Finite state automata FSA or finite state machine describes the behavior of a system using a finite number of states or conditions. The states represent all possible behaviors of the system. Transitions between the states are dependent on an input alphabet and transition conditions. Formally a state machine M is defined by the following quintuple: M = {S, Σ, φ, s i, F } S = finite, non-empty set of states Σ = alphabet of finite, non-empty set of symbols φ = transition function defining the transition rules s i = initial state F = final states

8 A state machine Propose a state machine that determines if there is an even number of a particular symbol in a binary alphabet (i.e. abba…). Assign conditions: S = {S0, S1} Σ = {a, b} φ = {S0→S1:a, S1→S0:a, S0→S0:b, S1→S1:b} s i = {S0} F = {S0}

9 A state machine ababbaa φ = {S0→S1:a, S1→S0:a, S0→S0:b, S1→S1:b}

10 Autonomous DNA computer Benenson et al. had to translate and incorporate FSA to DNA computing. Assigned a unique 5-base sequence to each symbol plus a terminator sequence.

11 Fok I Autonomous computer must not only have its own logic system, but also its own fuel. Fok I is a type IIs restriction endonuclease. Recognition site: 5’-GGATG(N) 9 ↓-3’ 3’-CCTAC(N) 13 ↑-5’ Cleaves if a noncovalent hybridization complex exists between the recognition and cleavage sites.

12 Transition functions The transition function defined by: φ = {S0→S1:a, S1→S0:a, S0→S0:b, S1→S1:b} was assigned to sequences of DNA. Blue nucleotides is the recognition site for Fok I, gray are nucleotide spacers, and the yellow are the detectors (unique for each transition rule)

13 Computation cycle 13 9 Legend Final state

14 Clinical applications The terminator sequence is replaced by a ssDNA in a hairpin loop. This ssDNA can be programmed to target specific mRNA sequences that regulate biological processes. Designed a DNA computer that could analyze, in-vitro, the levels of mRNA genes associated with small-cell lung cancer (SCLC) and prostate cancer (PC).

15 Diagnostic rules

16 The future DNA computing research remains active and holds many promises in the future in fields such as biochemical sensing, genetic engineering, and medical diagnosis. There are however, many problems that still need to be addressed, mainly: –The imprecision of biochemistry. Mis-hybridization. Enzymatic digestions are not always complete. –Amount of DNA required to scale up the process. –Adverse effects in living organisms if it is to be used in-vivo.