DNA Computing by Self Assembly

Erik Winfree, Caltech

Self Assembly of a Box

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

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

Purposes

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..

Precursors

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

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

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

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

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

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

Upper Right A = CATAC

Lower Left B = GTATG

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

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

Power: only 7 tiles required

Experimental Demonstrations

1d array – Adleman DNA Computing1994

2d array – Winfree 1998

3d array – Open

Next: Example of Winfree construction

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=001 = 1 10=1

XORing

000000000010000000000

000000000101000000000

000000001000100000000

000000010101010000000

000000100000001000000

000001010000010100000

000010001000100010000

000101010101010101000

001000000000000000100

……..

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

Slight variant of Sierpinski Triangle

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

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

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?

Nanocircuits

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

RAM Demultiplexer

2 bands = earlier bit counter example

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

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

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

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

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

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

Interested?

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