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

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

Caruthers Synthesis DNA Synthesis Error Rate: 300 Seconds 1: 102 Per step http://www.med.upenn.edu/naf/services/catalog99.pdf

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

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

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

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

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

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

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

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.

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 ]

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 …

Fabricational Complexity G T C Fabricational Complexity for n-mer = Fabricational Cost for n-mer = Complexity per unit cost

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

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

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

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:

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

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

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

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

-Building a Fab for Biology- MIT Molecular Machines (Jacobson) Group BioFAB -Building a Fab for Biology- MIT Molecular Machines (Jacobson) Group jacobson@media.mit.edu

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

Error Removal

In Vitro Error Correction Yields >10x Reduction in Errors

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

Error Reduction: GFP Gene synthesis

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