Fabricational Complexity
MIT Molecular Machines (Jacobson) Group
jacobson@media.mit.edu
3.9.13
What Drives The Cost of Placing Atoms Where We Want
Them? What are The Fundamental Limits?
Itanium Quad Tukwila
Transistor Count: 2B
Cost: ~$50
SmartPhone
Cost: ~$200
Flash Memory
Transistor Count: 2B
Cost: ~$3
Sand (Chips and Screen)
Cost: ~$0
Si Wafer with Area
sufficient for
2 Billion Transistors
Cost: ~$0.50
Plastic Resin / Metal Ore
Cost: ~$4
Fabricational Complexity
A
T
C
G
A
G
C
T
T
C
T
G
C
A
C
G
N BLOCKS
Fabricational Complexity for N Blocks or M Types =
Fabricational Cost for N Blocks = Np
N
ln M
Where p is the Yield Per Fabricational Step
Fabricational Complexity Per Unit Cost
F  p N ln M
Complexity Per Unit Cost
Complexity Per Unit Time*Energy
N
Complexity Per Unit Cost
Genome
(Natural)
Design Rule Smallest Dimension
(microns)
0.0003
Number of Types of Elements
4
Area of SOA Artifact (Sq. Microns)
NA
Volume of SOA Artifact (Cubic Microns)
6.E+01
Number of Elements in SOA Artifact
3.E+09
Volume Per Element(Cubic Microns)
2.E-08
Fabrication Time(seconds)
4.E+03
Time Per Element (Seconds)
1.E-06
Fabrication Cost for SOA Artifact($)
1.E-07
Cost Per Element
3.E-17
Complexity
4.E+09
Complexity Per Unit Volume of SOA(um^3) 7.E+07
Complexity Per Unit Time
1.E+06
Complexity Per Unit Cost
4.E+16
Cost Per Area
NA
High
SemiSpeed
Chemical conductor Offset
Synthesis Chip
Web
0.0003
4
7.E+08
5.E+06
7.E+04
8.E+01
2.E+04
3.E+02
1.E+02
2.E-03
9.E+04
2.E-02
6.E+00
9.E+02
2.E-07
0.1
8
7.E+10
7.E+09
7.E+12
1.E-03
9.E+04
1.E-08
1.E+02
2.E-11
2.E+13
2.E+03
2.E+08
1.E+11
2.E-09
10
6
2.E+12
2.E+12
2.E+10
1.E+02
1.E-01
7.E-12
1.E-01
6.E-12
4.E+10
2.E-02
3.E+11
3.E+11
6.E-14
TFT
2
8
1.E+12
1.E+11
3.E+11
4.E-01
7.E+02
2.E-09
2.E+03
6.E-09
6.E+11
5.E+00
9.E+08
3.E+08
2.E-09
Liquid
DVD-6 Embossing
0.25
2
1.E+10
7.E+12
2.E+11
4.E+01
3
2.E-11
3.E-02
2.E-13
1.E+11
2.E-02
4.E+10
4.E+12
3.E-12
0.2
4
8.E+09
8.E+08
2.E+11
4.E-03
6.E+01
3.E-10
2.E-01
1.E-12
3.E+11
3.E+02
5.E+09
1.E+12
3.E-11
Printed Electronics
Towards $10 Tablets & E Books
Lithography
Printed Electronics
[1] Ridley et al., Science, 286, 746 (1999)
Science 297,416 (2000)
+
Printing
~ 3Weeks of
7x24 Processing
Liquid Inorganic
Semiconductors[1]
~Minutes
Fabricational Complexity
A
T
C
G
A
G
C
T
T
C
T
G
C
A
C
G
N BLOCKS
ln M
1
Np
Fabricational Complexity for N Blocks or M Types =
Fabricational Cost for N Blocks w/ Error Correction =
Where p is the Yield Per Fabricational Step
Fabricational Complexity Per Unit Cost
F  p ln M
Complexity Per Unit Cost
Complexity Per Unit Time*Energy
N
Yielding N Devices with Error Correction
(Why A Small Amount of Error Correction Has A Very Large Effect)
N Devices
N
N!
Y [M ]  
p k (1  p) N  k
k  M M !( N  M )!
Fraction of Chips with M or More Perfect Devices (i.e. N-M or Fewer Errors).
Y [ N  1]
Y [N ]
Y [ N  2]
Y [ N  3]
0.75
0.97
0.997
0.9998
0.5
0.85
0.97
0.99
0.25
0.60
0.84
0.95
0.1
0.33
0.60
0.80
0.01
0.06
0.16
0.32
Table 1. Yields as a function of the number of repaired errors.
J. Jacobson 02/12/09
Error Correcting
Fabrication - TFT
http://www.sdtech.co.kr/device3.html
http://laser.gist.ac.kr/board/bbs/board.php?bo_table=rese_02
http://www.sdtech.co.kr/data/file/pro03/1890065063_Z6N9yvt4_EC9DB4EBAFB8ECA780_1.jpg
Moore’s Law Without Moore’s 2nd Law
Error Correcting Manufacturing
• Error Corrected TFT
• Error Corrected CMOS
• Error Corrected DNA Synthesis
Moore’s Law
Exponential Resource -> Exponential Gain
http://www.webenweb.co.uk/museum/comps.htm
http://www.chipsetc.com/the-transistor.html
Super Geometric Scaling
Linear Resource-> Exponential Gain
DNA Synthesis
Chemical Synthesis
(Open Loop Protection Group)
Biological Synthesis
(Error Correcting Polymerase)
Error Rate: 1:102
Throughput: 300 S per Base Addition
http://www.med.upenn.edu/naf/services/catalog99.pdf
Error Rate:
1:106
Throughput:
10 mS per
Base Addition
template dependant 5'-3'
primer extension
3'-5' proofreading
exonuclease
Beese et al. (1993), Science,
260, 352-355.
http://www.biochem.ucl.ac.uk/b
sm/xtal/teach/repl/klenow.html
5'-3' error-correcting
Throughput Error Rate Product Differential: ~108
Example: [A] Synthesize 1500 Nucleotide Base Gene. Error Rate = 0.99
(0.99)1500 ~ 10-7. [B] 3000 Nucleotide Base Gene. (0.99)3000 ~ 10-13.
exonuclease
Error Correcting Gene Synthesis
X
X
X
Error Rate 1:104
Lamers et al. Nature 407:711 (2000)
Nucleic Acids Research 2004
32(20):e162
Nucleic Acids Research 2004
32(20):e162
Deinococcus radiodurans
(3.2 Mb, 4-10 Copies of Genome )
Nature Biotechnology 18, 85-90 (January 2000)
D. radiodurans
1.75 million rads, 0 h
D. radiodurans
1.75 million rads, 24 h
D. radiodurans:
E. coli:
1.7 Million Rads (17kGy) – 200 DS breaks
25 Thousand Rads – 2 or 3 DS breaks
http://openi.nlm.nih.gov/imgs/rescaled512/1079854_1471-2180-5-17-11.png
photos provided by David Schwartz (University of Wisconsin, Madison)]
http://www.ornl.gov/hgmis/publicat/microbial/image3.html
Synthetic Complexities of Various Systems
Complexity (uProcessor/program):
x ~ 1K byte = 8000
Atoms: ~ 20 [C,N,O]
Complexion: W~ 320
x = 32
Nucleotides: ~ 1000
Complexion: W~41000
x = 2000 = 2Kb
DNA Polymerase
Product: C = 4 states
x=2
x[Product / Parts] =~ .00025
Product: C = 4 states
x=2
x[Product / Parts] =~ .0625
Product: 107 Nucleotides
x = 2x107
x[Product / Parts] =104
x >1 Product has sufficient complexity to encode for parts / assembler
Threshold for Life
What is the Threshold for Self Replicating Systems?
Measurement Theory
DNA
Error Correcting
Exonuclease
(Ruler)
How Well Can N Molecules Measure Distance?
Probability that a single bond is open : q
Where : q  e- E Bond / kT E Bond  3k
N Nucleotides : Probability that all N/2 bonds open : Q  q N / 2
Per Step Yield : p  1  Q  1  q N / 2
Total Yield : P  p
N

 1- q

N/2 N
Probability of Self Replication
/sandwalk.blogspot.com/2007/12/dnadenaturation-and-renaturation-and.html
http://en.wikipedia.org/wiki/File:Stem-loop.svg
Watson Crick
.18 nm
1.0
0.8
0.6
0.4
0.2
Threshold length: 1541 bp for 50% yield. 379 bp for 10-6 yield.
500
1000
1500
2000
2500
Number of Nucleotides
3000
Threshold for Life
What is the Threshold for Self Replicating Systems?
Measurement Theory
Threshold for assembling blocks of m –mers (monomer, dimer , trimer etc.)
The longer the block the greater the binding energy.
Probability that a single bond is open : q
Where : q  e- E Bond / kT E Bond  3k
N nucleotides  N/2 bonds
Probability that all N/2 bonds open : Q  q N / 2
Per Step Yield : p  1  Q  1  q

N /2

N /m
Total Yield : P  p N / m  1 - q N/2
m
N for 50% Yield
Number of Build Steps
1
(A,G,T,C)
1541
1541
2
(AA,AG,AT …)
1381
691
3
(AAA,AAG…)
1286
429
10
994
100
50
564
12
100
336
4
123
245
2
Minimum Machine Size N
To be Self-Replicating
Threshold Machine Complexity N
for Self-Replication
1500
Yield
___ 50%
___ 10%
___ 1%
___ 1E-6
1000
500
20
40
60
80
100
Number of Nucleotides m
Per Building Block
120
NOTES