Symposium on Digital FabricationPretoria, South Africa
June 29, 2006
Avogadro Scale Engineering &Fabricational Complexity
Molecular Fabrication (Jacobson) Group [email protected]
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 [email protected]
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
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