1. Modeling a Molecular Computing Device Using  -Calculus Semester Project Ya ’ ara Goldschmidt Department of Applied Math – Bioinformatics June 2001

2. First Stage: Basic Reactions Second Stage: The Markov model.

3. Basic Reactions There are 3 sets of basic reactions, each with different rates (According to Kobi ’ s request – so he can test which is the best one, They are at the folders called: rateSet1, rateSet2, rateSet3). eTI T + I  TI breakTI eTFok T + Fok  TFok breakTFok eTIFok TI + Fok  TIFok breakTIFok eITFok TFok + I  TIFok breakITFok eNS TIFok  T + Fok + Inew I – input (DNA) T – Transition State (DNA) Fok – Nuclease (Enzyme)

4. Implementation of the Markov Model Input : –DNA sequence of C and G (of length N>3). –# copies of the DNA sequence –# Transition molecules. –# FokI molecules Output : –The time each DNA molecule finished reacting (was left with no letters)

5. Implementation of the Model Transition molecules: –There are 16 possible transitions: 8 possible triplets of C and G, and for each one the next letter can be either C or G. G C GCC CCCCCG CGC CGG GGC GGG GCG C G

6. Implementation of the Model The process : –First 3 letters are inspected, according to the fourth letter, the right transition molecule will react with the input DNA molecule, and create (with the fokI enzyme) a new Input molecule. –The new molecule is the same as its previous one, but lacks its first letter. –The process repeats until the last letter is reached and consumed. –NOTE: all steps until the creation of a new DNA molecule are reversible !

7. Results 10 Input molecules 30 Transition molecules of each type. 100 FokI molecules lengthaverage time 1047.86705 945.9702 848.7026 518.81022 48.428226 23370.9579 17278.1055 12113.1984 lengthtime of first 1022.27881 915.71252 84.625907 59.07831 40.350219 23256.3178 1773.78339 1227.01769