Strand Design for Biomolecular Strand Design for Biomolecular ComputationComputation

Arwen Brenneman, Anne Condon

Presented By

Felix Mathew

CS 5813 Formal Languages

AbstractAbstract

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 PresentationContents of the Presentation

1. Introduction to DNA/RNA and Underlying concepts .

2. Differences Between DNA and RNA

3. Bonding in DNA molecules

4. Types of computation using DNA

5. Design of Strands for Classical Computations

6. Self Assembly Computation

7. Secondary Structure of DNA

8. Areas of research in future

9. References

Introduction & BackgroundIntroduction & Background DNA (Deoxyribonucleic acid)

Single Strand

DNADNA

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)

DNAA (Adenine), T (Thymine), C (Cytosine), G (Guanine)

RNAA, 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 End5`

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 DNAStructure of the DNA

Differences between DNA & Differences between DNA & RNARNA

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.

BondingBonding 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 DNABases within a single strand may also

bond and are said to form a secondary

structure.

Types of ComputationTypes of Computation

1. Classical Computations

2. Self-assembly 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.

Design Of Strands for Classical Computations

StabilityStability 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

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 TemperatureLow Range

Non- InteractionNon- 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

MeasuresExceed

A Certain

Threshold

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 ComputationSelf 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.]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 StructureSecondary 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 BondingPrecedent Bonding.

Pseudo-free secondary structurePaired 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 Inverse Secondary Structure Prediction ProblemProblem

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-Runs of the Inverse-MFE & Inverse-partition-functionpartition-function

Input to the algorithmOur desired structure is given as the input

S` =((((..(((….))).(((….))).(((….)))..)))).

Matching parentheses Base pairs

Dots (.) Unpaired Bases

Output of the Inverse-MFE algorithm

Does not give the desired Structure

Output of the Inverse-partition-Output of the Inverse-partition-Function AlgorithmFunction Algorithm

The Desired Structure is given as Output

Areas of Research in the FutureAreas 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.

ReferencesReferencesI. L.Marky, H.Blocker. Predicting DNA duplex stability from

the base sequence.

II. E.B. Baum. DNA sequences useful for computation.

III. C.Pederson. Pseudoknots in RNA secondary structures.

IV. A.Marathe. Combinatorial DNA word design.

V. M. Zuker Algorithms, thermodynamics and Databases for DNA secondary structure.