Symposium on Digital FabricationPretoria, South Africa

June 29, 2006

Avogadro Scale Engineering &Fabricational Complexity

Molecular Fabrication (Jacobson) Group jacobson@media.mit.edu

M I TCO

PL

EX

Y

Simple molecules<1nm

IBM PowerPC 750TM Microprocessor

7.56mm×8.799mm6.35×106 transistors

Semiconductor Nanocrystal~1 nm

10-10 10-510-9 10-7 10-610-8 10-4 10-3 10-2

m

Circuit designCopper wiringwidth 0.1m

red blood cell~5 m (SEM)DNA

proteins nm

bacteria1 m

Nanotube Transistor(Dekker)

Complexity vs. Size

SOI transistorwidth 0.12m

diatom30 m

Caruthers Synthesis

DNA Synthesis

http://www.med.upenn.edu/naf/services/catalog99.pdf

Error Rate:1: 102

300 SecondsPer step

http://www.biochem.ucl.ac.uk/bsm/xtal/teach/repl/klenow.html

1. Beese et al. (1993), Science, 260, 352-355.

Replicate Linearly with Proofreading and Error Correction

Fold to 3D Functionality

template dependant 5'-3' primer extension

5'-3' error-correcting exonuclease

3'-5' proofreading exonuclease

Error Rate:1: 106

100 Steps per second

1] Quantum Phase Space 2] Error Correcting Fabrication 3] Fault Tolerant Hardware Architectures 4] Fault Tolerant Software or Codes

Resources which increase the complexity of a system exponentially with a linear addition of

resources

Resources for Exponential Scaling

Fault Tolerant Translation Codes (Hecht):NTN encodes 5 different nonpolar residues (Met, Leu, Ile, Val and Phe)NAN encodes 6 different polar residues (Lys, His, Glu, Gln, Asp and Asn)

Local Error Correction:Ribozyme: 1:103

Error Correcting Polymerase: 1:108 fidelity

DNA Repair Systems:MutS System

Recombination - retrieval - post replication repair Thymine Dimer bypass.Many others…

Error Correction in Biological Systems

E. Coli Retrieval system - Lewin

Biology Employs Error Correcting Fabrication + Error Correcting Codes

n MAJ

p

p

p

MAJMAJ

p

p

p

MAJ

p

p

p

k

Threshold Theorem – Von Neumann 1956

mng

mg

n

nm

ppm

nP

)1(2/)1(

1

kk

gk

gg

gggg

pP

ppPP

ppppP

2)12(

4322212

2321

3

3)3(3)(3

3)1(3

Recursion Level P

K=1

K=2

K

n=3

For circuit to be fault tolerant

3/1

3 212

Th

k

P

ppPkk

= Probability of Individual Gate Working gp

n MAJ

p

p

p

MAJMAJ

p

p

p

MAJ

p

p

p

k

Threshold Theorem - Winograd and Cowan 1963

A circuit containing N error-free gates can be simulated with probability of failure ε using O(N poly(log(⋅ N/ε))) error-prone gates which fail with probability p, provided p < pth, where pth is a constant threshold independent of N.

Number of gates consumed: k3

Find k such that NpPkk

k /3 212

2ln

ln3ln)/ln(2ln

ln

~0

pN

k

)/ln(~3 0 NPolyk Number of Gates ConsumedPer Perfect Gate is

n p

p

p

p

MAJp

p

p

p

p

p

p

p

k

Threshold Theorem – Generalized

mnmn

m

mnmn

nm

ppm

nppp

m

npP

)1()1()1(2/)1(

02/)1(

2/)1( nnk ckpP

For circuit to be fault tolerant P<p

2/)1( /1 nthreshold ckp

Total number of gates: )( knO

Area = A

Area = 2*A/2

Probability of correct functionality = p[A] ~ e A (small A)

Scaling Properties of Redundant Logic (to first order)

P1 = p[A] = e A

P

A

P2 = 2p[A/2](1-p[A/2])+p[A/2]2

= eA –(eA)2/4

Conclusion: P1 > P2

Total Area = n*(A/n)

Probability of correct functionality = p[A]

Scaling Properties of Majority Logic

P

A

n segments

knkn

nknmajority pp

k

nP

)1(

2/)1(

2/1

2/)1(]0['

1 n

nAp

nTo Lowest Order in A

Conclusion: For most functions n = 1 is optimal. Larger n is worse.

Fabricational Complexity

Ffab = ln (W) / [ a3 fab Efab ]

Ffab = ln (M)-1 / [ a3 fab Efab ]

•Total Complexity•Complexity Per Unit Volume•Complexity Per Unit Time*Energy•Complexity Per unit Cost

Fabricational Complexity

21 )1(

lnlnp

pmmpF n

n

nFAB

Total Complexity Accessible to a Fabrication Process withError p per step and m types of parts is:

A

A G

G T C

A T A C G T …

A G T A G C …

p2p3p

A A

200 400 600 800 1000

10

20

30

40

50

60

70

nn mp ln

n0.2 0.4 0.6 0.8

20

40

60

80

FABF

p

Fabricational Complexity

Complexity per unit cost

mpf nFAB ln

A G T C G C A A T

n

Fabricational Complexity for n-mer = nmln

Fabricational Cost for n-mer = nnp

mpf nFAB ln

Fabricational Complexity

Non Error Correcting:

Triply Error Correcting:

mpppfn

FAB ln)1(3332

3

A G T C

A G T C

A G T C

A G T C

50 100 150 200 250 300

20

40

60

80

100

120

140

P = 0.9

n

FAB

FAB

f

f 3

p

0.86 0.88 0.92 0.94 0.96 0.98

500

1000

1500

2000

2500

3000

n = 300

50 100 150 200

0.05

0.1

0.15

0.2

0.25

0.3

FAB

FAB

f

f 3

n

P = 0.85

http://www.ornl.gov/hgmis/publicat/microbial/image3.html

[Nature Biotechnology 18, 85-90 (January 2000)]

Uniformed Services University of the Health

Deinococcus radiodurans (3.2 Mb, 4-10 Copies of Genome )

D. radiodurans: 1.7 Million Rads (17kGy) – 200 DS breaksE. coli: 25 Thousand Rads – 2 or 3 DS breaks

D. radiodurans 1.75 million rads, 24 h

D. radiodurans 1.75 million rads, 0 h

photos provided by David Schwartz (University of Wisconsin, Madison)]

Autonomous self replicating machines from random building blocks

Basic Idea:

M strands of N Bases

Result: By carrying out a consensus vote one requires only

To replicate with error below some epsilon such that the global replication error is:

EP

NM ln

Combining Error Correcting Polymerase and Error Correcting Codes One Can Replicate a

Genome of Arbitrary Complexity

M

N

100 200 300 400 500

10

15

20

25

30

M (

# of

Cop

ies

o f G

enom

e)

N (Genome Length)

EPM

+ + +

+ +

Step 1 Step 2 Step 3

+

Parts

Template

Machine

Replication Cycle

p per base p’ per base

31p N

Information Rich Replication (Non-Protein Biochemical Systems)

RNA-Catalyzed RNA Polymerization: Accurate and General RNA-Templated Primer Extension

Science 2001 May 18; 292: 1319-1325Wendy K. Johnston, Peter J. Unrau, Michael S. Lawrence, Margaret E. Glasner, and David P. Bartel

RNA-Catalyzed RNA Polymerization

14 base extension. Effective Error Rate: ~ 1:103

J. Szostak, Nature,409, Jan. 2001

50 100 150 200

0.2

0.4

0.6

0.8

1

For Above Threshold M Copy Number3

1

NP

EP

N

7M

3M

Combining Error Correcting Machinery and Error Correcting Codes One Can Replicate a

Machine of Arbitrary Complexity

Jacobson ‘02

MIT Molecular Machines (Jacobson) Group jacobson@media.mit.edu

BioFAB-Building a Fab for Biology-

MutS Repair System

Lamers et al. Nature 407:711 (2000)

Error Removal

In Vitro Error Correction Yields >10x Reduction in Errors

error-enriched(<10% fluorescent)

error-corrected(>95% fluorescent)

Error-Removal1000 bp Fluorescent Gene Synthesis

Native error rate

Error Reduction: GFP Gene synthesis

http://www.thetech.org/exhibits_events/traveling/robotzoo/about/images/grasshopper.gif

1.Air inlets 2.Crushers 3.Ganglion 4.Multiple Visual sensors 5.Muscles 6.Pincers 7.Sensory receptors 8.Stridulatory pegs 9.Wings

Molecular Machines Group-MIT

Faculty

Joseph Jacobson

Research Scientists and Post Docs

Peter Carr

Sangjun Moon

Graduate Students

Brian Chow

David Kong

Chris Emig

Jae Bum Joo

Jason Park

Sam Hwang