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

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 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.

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. 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

14. 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

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. 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

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 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.

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. Does not give the desired Structure
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.