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

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.

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

Introduction & Background DNA (Deoxyribonucleic acid) Single Strand

DNA DNA/RNA Strand Nucleotide A sequence of four possible Nucleotides. 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

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}

Structure of the DNA

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.

Bonding Secondary Structure Of DNA 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.

Types of Computation Classical Computations Self-assembly Computations.

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.

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

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

Constraints are placed on 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

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

Find Set of words where Ze/Zc is small 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

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.

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 }

Secondary Structure Inclusive Bonding Precedent Bonding. 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.

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

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.

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

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

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

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.

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.