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Erik Winfree, Caltech. DNA Computing by Self Assembly. Self Assembly of a Box. Information and Algorithms. Electronic microprocessors control electro-mechanical devices Biochemical circuits control molecular/chemical events

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information and algorithms
Information and Algorithms
  • Electronic microprocessors control electro-mechanical devices
  • Biochemical circuits control molecular/chemical events
  • General Goal: design biochemical algorithms/circuits that are programmable and can perform functions
self assembly model
Self Assembly Model
  • Model we will investigate: molecular self assembly of heterogeneous crystals
  • Idea: use periodic order of crystals to perform arbitrarily complex computation
  • What are purposes of self assembly?
  • 2 main schools of thought
  • 1. Use massive parallelism of chemistry and lots of DNA at a time to solve difficult combinatorial optimization problems, such as SAT/TSP
  • 2. Use self assembly algorithms to fabricate exact shapes / circuits/ patterns etc..
  • Idea of self assembly arose from 3 ideas
  • 1. DNA computing (Adleman 1994)
  • 2. Tiling theory (Grun. & Shep. 1986)
  • 3. DNA nanotechnology (Seeman 1982)
dna computing
DNA Computing

Adleman 1994 – Solved 6 node Hamiltonian Path Problem

Nodes labeled with random 20mer

Edge(u, v) = last 10 BP of u + first 10 BP of v

hamiltonian path
Hamiltonian Path

Used DNA hybridization to generate random paths through graph

Added programmable binding to impose conditions (start city, end city, num cities, no repeats..)

1st meaningful computation by DNA

Heralded as a landmark achievement

steps of process
Steps of process
  • Generate random paths (DNA molecules) through graph
  • Use PCR to amplify all paths that start at first city and end at last city (use primers)
  • Test if path contains city 1. Amplify paths that pass test. Repeat tests for cities 2 through n.
  • If anything left, return YES. Else return NO.
tiling theory
Tiling – arrangement of basic shapes to cover infinite plane

Wang 1963 – Showed infinite num of square tiles with 4 colored sides can create Turing machine history

Wang Tiles are very powerful. Use DNA molecules to simulate Wang tiles in self assembly

Tiling Theory
dna nanotechnology
DNA Nanotechnology

Seeman 1982 – use DNA as a building block for nanostructures

Block: Four armed DNA double-crossover molecules (DX)

Label 4 arms of DX molecules with labels like Wang tiles

dx molecule wang tile
DX Molecule = Wang tile

Adjacent tiles = sequences at sticky ends of 2 molecules go together

Upper Right A = CATAC

Lower Left B = GTATG

simplified tile assembly model
Simplified Tile Assembly Model
  • Given a set of possible tiles and possible bonds
  • 4 sides of tile have bonds, bond has strength (0, 1,2)
  • 2 tiles can bond together if their bonds fit, and if total strength (sums of bond strengths on common sides) is > threshold
  • Growth starts with a seed tile
binary counter
Binary Counter

Using 3 border tiles, 2 ‘0-bit’ tiles, 2 ‘1-bit’ tiles, can simulate a binary counter

Power: only 7 tiles required

experimental demonstrations
Experimental Demonstrations

1d array – Adleman DNA Computing1994

2d array – Winfree 1998

3d array – Open

Next: Example of Winfree construction

xor practice
XOR Practice

Everyone try this out.

Start with a 1 in a sea of 0’s.

To generate next row, each tile checks its two neighbors, performs XOR and places the result below it in the next row

XOR 00 = 0 11=0

01 = 1 10=1












sierpinski triangle
Sierpinski Triangle

1st 2d process to be experimentally demonstrated = Sierpinski Gasket

Best result so far: 8 by 16 error-free triangle

Poor results due to 1-10% tile binding error

sample tile solution
Sample Tile Solution

Slight variant of Sierpinski Triangle

application 1 solve np hard problems
Application 1: Solve NP hard problems
  • NP-complete problems: exponential number of solutions, hard to find correct solution, but easy to verify
  • Idea: Chemistry can generate all possible solutions and filter solutions quickly
  • Hack: Push exponential dimension of problem into volume of DNA needed
  • 1 mL DNA = 260 bits of information
apply self assembly
Let massive parallelism solve problem

In self assembly, generate input as initial set of tiles

See if Yes or No tile is produced at end

Apply self assembly
current results
Current results
  • Problems solved –Hamiltonian Path, Satisfiability, etc..
  • Assuming no errors, 40-variable SAT needs 30 mL DNA and several hours
  • 1012 operations/second, inferior to computers
  • Winfree: No “low hanging fruit” for self assembly here
application 2 programmable nanofabrication
Application 2: Programmable Nanofabrication
  • Fabricate molecular electronic circuits
  • Current technology hitting the limit soon
  • Solution: create molecular structures like carbon nanotubes.
  • How to arrange tiny chemical components into fixed patterns?
  • Solution: Use self assembly to create molecular components
  • Small pieces such as NAND/OR gates can be created
  • Hard to create large microprocessors
  • Self assembly good to make circuits that have “concise” descriptions, eg recursive formulations
dna circuit picture
DNA Circuit Picture

RAM Demultiplexer

2 bands = earlier bit counter example

summary achievements
Summary – Achievements
  • Robust, readily programmable
  • Dozens of crystals have been successfully used as DNA tiles
  • Self assembly has concrete experimental results, unlike other molecular computing technologies
summary current problems
Summary – Current Problems
  • Current DNA tiles distorted, 1% positioning error in experiments.
  • Size of tile is limited – all crystals < 10 microns.
  • 1 – 10 % step error. eg tiles bond incorrectly quite often. Very big problem.
    • => New model: error correcting tiles in self assembly
yet more problems
Yet more problems
  • Undesired nucleation – self assembly starts by itself
  • Problem occurs because biological system starts when it wants to minimize energy
  • Solution: Have programmable control of nucleation. Add energy barriers to force assembly to start with seed tile.
future questions
Future Questions
  • Natural question: What shapes can be made by self assembly?
  • Has parallels to Computability / Chomsky Language Theory
  • Minimum number of steps to make a shape?
  • Minimum number of tiles to make shape?
final thoughts
Final Thoughts
  • Although bio systems are like “circuits,” remember they:
    • Contain large amounts of randomness
    • Have very high error rates
    • Contain hidden biological processes that cannot be described
  • So CS people don’t be surprised if experimental results are different from theoretical predictions
more thoughts
More thoughts
  • Winfree: We have already harnessed the electron to create electronic computers
  • No real progress has been made on chemical or nano computers
  • So: Algorithmic self assembly systems may be best best at next generation computers
  • Winfree, E. 2003. DNA Computing by Self-Assembly. NAE's The Bridge, 33(4):31-38
  • dna.caltech.edu
  • Contains a plethora of papers about numerous aspects of self assembly