1. Avogadro Scale Engineering & Fabricational Complexity
Symposium on Digital Fabrication
Pretoria, South Africa
June 29, 2006
Molecular Fabrication (Jacobson) Group

2. Complexity vs. Size m 10-10 10-5 10-9 10-7 10-6 10-8 10-4 10-3 10-2
red blood cell
~5 m (SEM)
diatom
30 m
Simple molecules
<1nm
DNA
proteins nm
bacteria
1 m m
10-10
10-5
10-9
10-7
10-6
10-8
10-4
10-3
10-2
SOI transistor
width 0.12m
Semiconductor
Nanocrystal
~1 nm
Circuit design
Copper wiring
width 0.1m
Nanotube Transistor
(Dekker)
IBM PowerPC 750TM Microprocessor
7.56mm×8.799mm
6.35×106 transistors

3. Caruthers Synthesis DNA Synthesis Error Rate: 300 Seconds 1: 102
Per step

4. Replicate Linearly with Proofreading and Error Correction
Fold to 3D Functionality
Error Rate:
1: 106
100 Steps per second
template dependant 5'-3'
primer extension
3'-5' proofreading
exonuclease
5'-3' error-correcting
exonuclease
Beese et al. (1993), Science, 260,

5. Resources for Exponential Scaling
Resources which increase the complexity of a system exponentially with a linear addition of resources
1] Quantum Phase Space
2] Error Correcting Fabrication
3] Fault Tolerant Hardware Architectures
4] Fault Tolerant Software or Codes

6. Error Correction in Biological Systems
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…
E. Coli Retrieval system - Lewin
Biology Employs Error Correcting Fabrication + Error Correcting Codes

7. Threshold Theorem – Von Neumann 1956
= Probability of Individual Gate Working
MAJ p n
MAJ p
MAJ
n=3
Recursion Level P
K=1
K=2 K
MAJ p k
For circuit to be fault tolerant

8. Threshold Theorem - Winograd and Cowan 1963
MAJ p
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. n
MAJ p
MAJ
MAJ p
Number of gates consumed: k
Find k such that
Number of Gates Consumed
Per Perfect Gate is

9. Threshold Theorem – Generalizedp n p
MAJ p
For circuit to be fault tolerant P<p k
Total number of gates:

10. Scaling Properties of Redundant Logic (to first order)
Probability of correct functionality = p[A] ~ e A (small A)
Area = A
P1 = p[A] = e A
P2 = 2p[A/2](1-p[A/2])+p[A/2]2
= eA –(eA)2/4
Area = 2*A/2
Conclusion: P1 > P2

11. Scaling Properties of Majority Logic
n segments P
Total Area = n*(A/n) A
Probability of correct functionality = p[A]
To Lowest Order in A
Conclusion: For most functions n = 1 is optimal. Larger n is worse.

12. Fabricational Complexity
Total Complexity
Complexity Per Unit Volume
Complexity Per Unit Time*Energy
Complexity Per unit Cost
Ffab = ln (W) / [ a3 tfab Efab ]
Ffab = ln (M)e-1 / [ a3 tfab Efab ]

13. Fabricational Complexity
Total Complexity Accessible to a Fabrication Process with
Error p per step and m types of parts is: A G T C A A A G A T A C G T … A G T A G C …

14. Fabricational ComplexityG T C
Fabricational Complexity for n-mer =
Fabricational Cost for n-mer =
Complexity per unit cost

15. Fabricational Complexity
Non Error Correcting: A G T C A G T C
Triply Error Correcting: A G T C A G T C
P = 0.9
n = 300
P = 0.85 n n p

16. Deinococcus radiodurans
(3.2 Mb, Copies of Genome )
Uniformed Services University of the Health
[Nature Biotechnology 18, (January 2000)]
D. radiodurans: 1.7 Million Rads (17kGy) – 200 DS breaks
E. coli: 25 Thousand Rads – 2 or 3 DS breaks

17. D. radiodurans 1.75 million rads, 0 h
photos provided by David Schwartz (University of Wisconsin, Madison)]

18. Autonomous self replicating machines from random building blocks

21. Combining Error Correcting Polymerase and
Error Correcting Codes One Can Replicate a
Genome of Arbitrary Complexity M N
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:

22. M (# of Copies of Genome)
N (Genome Length)

23. Replication Cycle + Step 1 Step 2 Step 3 Parts Template Machine
p per base
p’ per base

24. Information Rich Replication
(Non-Protein Biochemical Systems)
J. Szostak, Nature,409, Jan. 2001

25. Combining Error Correcting Machinery and
Error Correcting Codes One Can Replicate a
Machine of Arbitrary Complexity
For Above Threshold M Copy Number
Jacobson ‘02

26. -Building a Fab for Biology- MIT Molecular Machines (Jacobson) Group
BioFAB
-Building a Fab for Biology-
MIT Molecular Machines (Jacobson) Group

27. MutS Repair System
Lamers et al. Nature 407:711 (2000)

28. Error Removal

29. In Vitro Error Correction Yields >10x Reduction in Errors

30. Error-Removal 1000 bp Fluorescent Gene Synthesis
error-corrected
(>95% fluorescent)
error-enriched
(<10% fluorescent)
Native error rate

31. Error Reduction: GFP Gene synthesis

32. 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
Air inlets
Crushers
Ganglion
Multiple Visual sensors
Muscles
Pincers
Sensory receptors
Stridulatory pegs
Wings