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

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

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)

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)

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

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 !

Results 10 Input molecules 30 Transition molecules of each type. 100 FokI molecules lengthaverage time lengthtime of first