Symposium on Digital Fabrication Pretoria, South Africa June 29, 2006

1. PLEX M I T CO Y Avogadro Scale Engineering & Fabricational Complexity Symposium on Digital Fabrication Pretoria, South Africa June 29, 2006 Molecular Fabrication (Jacobson) Group jacobson@media.mit.edu

2. 10-10 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 red blood cell ~5 m (SEM) diatom 30 m Complexity vs. Size DNA proteins nm Simple molecules <1nm bacteria 1 m m 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. DNA Synthesis Caruthers Synthesis Error Rate: 1: 102 300 Seconds Per step http://www.med.upenn.edu/naf/services/catalog99.pdf

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, 352-355. http://www.biochem.ucl.ac.uk/bsm/xtal/teach/repl/klenow.html

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. p p p p p p MAJ MAJ p p p MAJ MAJ Threshold Theorem – Von Neumann 1956 = Probability of Individual Gate Working n n=3 k For circuit to be fault tolerant

8. p p p p p p MAJ MAJ p p p MAJ MAJ 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. n Number of gates consumed: k Find k such that Number of Gates Consumed Per Perfect Gate is

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

10. Scaling Properties of Redundant Logic (to first order) P A Probability of correct functionality = p[A] ~ e A (small A) P1 = p[A] = e A Area = 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) / [ a3tfab Efab ] Ffab = ln (M)e-1 / [ a3tfab 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 Complexity A G T C G C A A T n 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 n = 300 P = 0.9 P = 0.85 n n p

16. Deinococcus radiodurans (3.2 Mb, 4-10 Copies of Genome ) Uniformed Services University of the Health [Nature Biotechnology 18, 85-90 (January 2000)] D. radiodurans: 1.7 Million Rads (17kGy) – 200 DS breaks E. coli: 25 Thousand Rads – 2 or 3 DS breaks http://www.ornl.gov/hgmis/publicat/microbial/image3.html

17. D. radiodurans 1.75 million rads, 0 h D. radiodurans 1.75 million rads, 24 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 N M 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. Parts + + + Template + + + Machine Step 1 Step 2 Step 3 Replication Cycle 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. BioFAB -Building a Fab for Biology- MIT Molecular Machines (Jacobson) Group jacobson@media.mit.edu

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-Removal1000 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 http://www.thetech.org/exhibits_events/traveling/robotzoo/about/images/grasshopper.gif