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Strand Design for Biomolecular Computation

Strand Design for Biomolecular Computation. Arwen Brenneman, Anne Condon. Presented By Felix Mathew CS 5813 Formal Languages. Abstract.

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Strand Design for Biomolecular Computation

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  1. Strand Design for Biomolecular Computation Arwen Brenneman, Anne Condon Presented By Felix Mathew CS 5813 Formal Languages

  2. Abstract Biomolecular computation integrates the fields of biochemistry, molecular biology & Computer Science. In Computer Science one area of research has been on the design of DNA/RNA Strands for DNA computations. Design of these Strands pose many questions and this paper surveys different formulations of DNA Strand design.

  3. Contents of the Presentation • Introduction to DNA/RNA and Underlying concepts . • Differences Between DNA and RNA • Bonding in DNA molecules • Types of computation using DNA • Design of Strands for Classical Computations • Self Assembly Computation • Secondary Structure of DNA • Areas of research in future • References

  4. Introduction & Background DNA (Deoxyribonucleic acid) Single Strand

  5. DNA DNA/RNA Strand • A sequence of four possible Nucleotides. Nucleotide • A phosphate group • A ribose group • A heterocyclic base Four Kinds of Heterocyclic Bases (Alphabets of DNA) DNAA (Adenine), T (Thymine), C (Cytosine), G (Guanine) RNAA, U (Uracil), C, G Nucleotide

  6. Backbone of a DNA/RNA Strand • Formed by alternating Phosphate and Ribose part of each nucleotide. • The Alternating backbone gives the Strand a direction from the ribose end to the Phosphate End. Ribose End 3` Phosphate End5` Heterocyclic bases bond with other bases via Hydrogen Bonding This process is called HYBRIDIZATION. A bonds with T in DNA & A bonds with U in RNA { Two hydrogen bonds} C bonds with G { Three hydrogen bonds}

  7. Structure of the DNA

  8. Differences between DNA & RNA • RNA strands are generally single in nature unlike the double Helix nature of DNA. • Uracil is present in place of Thymine. • Used in the movement of Genetic information from DNA to the site of protein synthesis.

  9. Bonding • DNA is best known for double helix bonding. • A Strand forms the most stable double helix with its Watson-crick Complement. Example 5`-AACATG-3` 3`-TTGTAC-5` Secondary Structure Of DNA Bases within a single strand may also bond and are said to form a secondary structure.

  10. Types of Computation • Classical Computations • Self-assembly Computations.

  11. Design Of Strands for Classical Computations • Short DNA Strands are called Oligonucleotides (Has around 15-50 nucleotides). • A Set of equi-length Strands is referred as a DNA word set. Retrieval of Information from DNA depends on • Stable Duplexes. • Ensure two Distinct words are non-interacting.

  12. Stability Measure of Relative Stability  FREE ENERGY ( kcal/mol ) FREE ENERGY denoted by  δG° FREE ENERGY of a DNA Strand D = 5`-d1d2………………dn-3` & 3`-d1d2………………dn-5` is given by δG°(D/C) = correction factor +  w(gi) where g  nearest neighbour group w -ve weight associated with each group Correction factor depends on  Self complementary/GC pairs LOWER THE FREE ENERGY  MORE STABLE THE DUPLEX

  13. 2-4 RULE Estimates Melting Point as = Twice(No. of AT pairs) + 4(No. of GC pairs) Melting Point Function of Free Energy + Other Parameters. Formulation of Constraints on Stability Free energy Melting Temperature Low Range

  14. Non- Interaction Duplexes between a word & the Watson-crick Complement of another are relatively UNSTABLE, when we compare a perfectly matched duplex formed from a DNA word and its complement. If we see instability when Duplexes are Non-Interacting. Why consider this case ?? Reason: Non-interacting property is needed at times for certain DNA computations and constraints are placed on the design of words to ensure Non-Interaction. • Constraints are placed on • Single Words • Pairs of words • Large groups of words

  15. Constraints on Pairs of Words Defined on pair of equi-length DNA words 5`-d1d2………………dn-3` & 3`-d1d2………………dn-5` Measures • Mismatch Distance Number of positions at which they are not complementary. • Length of repeated runs In a strand is a sequence of identical bases. • Sub-word Distance Length of longest Strand, which is a sub-word of both the Strands. Constraints are Placed if These Measures Exceed A Certain Threshold

  16. Statistical Formulation Based on Principles of Statistical Mechanics Hybridization  j Assigns weight ‘Z’ to each possible Hybridization. Free Energy of this Hybridization δG Statistical Weight exp(δG / RT) Where R is the Molar Gas Constant T is the temperature Ze  Sum of all Statistical Weights Zc Sum of all Z’s Find Set of words where Ze/Zc is small

  17. Self Assembly Computation • Properties of Secondary Structure of DNA as been exploited for doing certain Self Assembly Computations In this case both the input and state transition information are encoded in the same Strand.

  18. Wang tiles [ Winfree et al.] Types of DNA in Vivo • B-form  10 base pairs/spiral twist • Z-form  12 base pairs/spiral twist { due to high incidence of CG pairs }

  19. Secondary Structure Secondary Structure Formation depends on: • Thermodynamic Interactions. • Hydrostatic Forces. • Geometric Forces. • Base solution properties (molar strength, acidity & temperature of the solution) Bonding in secondary structure • Inclusive Bonding • Precedent Bonding.

  20. Pseudo-free secondary structure Paired bases partition the molecule into loops. Examples of Loops • Hair Pin Loop  Strand makes a U-turn To fold back onto itself • Multi-Loop Algorithms That Predict Secondary Structure ZUKER’S Algorithm ( The energy Minimization Algorithm) Predicts optimal Secondary structure of a strand of length n in O(n3) time. Partition Function Algorithm

  21. Inverse Secondary Structure Prediction Problem Open Question: Whether a polynomial time algorithm exists for Inverse secondary structure prediction. Heuristic Algorithms • Inverse-MFE • Inverse-Partition-function Running time of both these algorithms is O(n6) Experiments have shown that the Inverse-partition-function algorithm has a greater likelihood of finding a sequence that folds into our desired structure.

  22. Runs of the Inverse-MFE & Inverse-partition-function Input to the algorithm Our desired structure is given as the input S` =((((..(((….))).(((….))).(((….)))..)))). Matching parentheses  Base pairs Dots (.)  Unpaired Bases

  23. Output of the Inverse-MFE algorithm Does not give the desired Structure

  24. Output of the Inverse-partition-Function Algorithm The Desired Structure is given as Output

  25. Areas of Research in the Future • Efficient Algorithms for Secondary Structure Prediction. • Approaches to Inverse Secondary Structure Prediction at the moment are heuristic in nature. Solving the open question of finding a polynomial time algorithm is an area to work on.

  26. References • L.Marky, H.Blocker. Predicting DNA duplex stability from the base sequence. • E.B. Baum. DNA sequences useful for computation. • C.Pederson. Pseudoknots in RNA secondary structures. • A.Marathe. Combinatorial DNA word design. • M. Zuker Algorithms, thermodynamics and Databases for DNA secondary structure.

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