MS&E 319, Spring 2004. Molecular Self-Assembly: Models and Algorithms

Instructor: Ashish Goel

HW 1. Due 4/29/4.

 

  1. Install xgrow, and explore running xgrow with some example tile sets. This simulator is available from http://www.dna.caltech.edu/Xgrow/xgrow_www.html
  2. Consider the counter that uses different primes to count based on Chinese remaindering. To understand this counter, run the program xgrow on the tile set primes_2_3_5.tiles using the command

xgrow primes_2_3_5.tiles block=12 size=32 T=3

 

Also use this as an example to understand xgrow. Drop by my office (make an appointment) if none of this makes sense. The tile set was automatically generated by the program primes.C, which is well-commented. Use this program to generate some more simple prime counters. Red tiles correspond to tiles labeled 0.

  1. Now read the paper Optimal self-assembly of counters at temperature two. Observe that the prime counters are not partial order systems (and hence their dependence graph may be acyclic). Also, the prime counters do not have the deterministic RC property.
    1. Prove that the prime counter system assembles into a unique terminal assembly.
    2. Analyze the assembly time of this system.