Transcript Predicated assembly and biomimetics in micro/nano

MAS.961
How To Make Something That Makes (Almost)
Anything
Complexity, Self Replication and all that…
[email protected]
What governs the cost of placing atoms where we
want them? What are the limits?
Itanium Quad Tukwila
Transistor Count: 2B
Cost: ~$100
NetBook
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: ~$4
Fabricational Complexity
N
A G T C G C A AT
Fabricational Complexity for N-mer or M Types = ln M
Fabricational Cost for N-mer =
 Np
N
Where p is the yield per fabricational step
Fabricational Complexity Per Unit Cost
F1  p ln M
N
Complexity Per Unit Cost
Complexity Per Unit Time*Energy
N
Fabricational Complexity
Application: Why Are There 20 Amino Acids in Biology?
(What is the right balance between Codon code redundancy and diversity?)
N Blocks of Q Types
Question: Given N monomeric building blocks
of Q different types, what is the optimal number
of different types of building blocks Q which
maximizes the complexity of the ensemble of all
possible constructs?
The complexion for the total number of different ways
to arrange N blocks of Q different types (where each type
.
has the same number)
is given by:
And the complexity is:
W
N!
N!

 ni ! ( N Q) !Q
i
F ( N , Q)  N ln(N )  Q * ( N Q) ln(N Q)  N Q
40
For a given polymer length N
we can ask which Q*
achieves the half max for
complexity such that:
F ( N , Q*)  0.5F ( N , N )
30
Q*
20
10
500
1000
N
1500
2000
Fabricational Complexity
Application: Identifying New Manufacturing Approach for Semiconductors
Semi-conductor
Chip
Design Rule Smallest Dimension
(microns)
Number of Types of Elements
Area of SOA Artifact (Sq. Microns)
Volume of SOA Artifact (Cubic Microns)
Number of Elements in SOA Artifact
Volume Per Element(Cubic Microns)
Fabrication Time(seconds)
Time Per Element (Seconds)
Fabrication Cost for SOA Artifact($)
Cost Per Element
Complexity
Complexity Per Unit Volume of SOA(um^3)
Complexity Per Unit Time
Yielded Res. Elements Per $
Cost Per Area
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
High Speed Offset
Web
TFT
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
DVD-6
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
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
Liquid
Embossing
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
…Can we use this map as a guide towards future
directions in fabrication?
Printed Electronics
Lithography
Printed Electronics
+
High Speed Printing
~ 3Weeks of
7x24 Processing
Liquid Inorganic
Semiconductors[1]
~Minutes
[1] Ridley et al., Science
286, 746 (1999)
Science 297,416 (2000)
Fabricational Complexity
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
Gene Chip
(Chemical SemiParallel
conductor
Synthesis) Chip
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
High
Speed
Offset
Web
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
…Can we use this map as a guide towards future
directions in fabrication?
DNA Synthesis
Chemical Synthesis
(Open Loop Protection Group)
Biological Synthesis
(Error Correcting Polymerase)
Error Rate: 1:102
Throughput: 300 S per Base Addition
Error Rate: 1:106
Throughput: 10 mS per Base Addition
http://www.med.upenn.edu/naf/services/catalog99.pdf
Beese et al. (1993), Science, 260, 352-355. http://www.biochem.ucl.ac.uk/bsm/xtal/teach/repl/klenow.html
template dependant 5'-3'
primer extension
3'-5' proofreading
exonuclease
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.
5'-3' error-correcting
exonuclease
Fabricational Complexity Per Unit Cost
2 Ply Error Correction
Non Error Correcting:
F1  p ln M
N
2Ply Error Correcting:
F2 
N ln M

2N 2 p  p
A G T C
A G T C

2 N
A G T C
p=0.99
1.2
F2 F1
20
0.8
0.6
40
60
80
100
Fabricational Complexity Per Unit Cost
3 Ply Error Correction
Non Error Correcting:
F1  p ln M
N
3Ply Error Correcting:
F3 
N ln M

3N p  3 p (1  p)
,
For values of
A G T C
3
2
A G T C

N
A G T C
A G T C
p 1 2
dR
0
dN
and R increases exponentially with N.
F3 F3
F F
F3
F
0.3
(a)
N  15
12.5
1.5
p  0.4
0.2
1
(c)
15
(b)
0.25
p  0.6
10
0.15
7.5
0.1
5
0.05
2.5
0.5
0.3
0.4
0.5
0.6
p
0.7
0.8
0.9
10
20
30
N
40
50
10
20
30
N
40
50
Resources for Exponential Scaling
Resources which increase the complexity of a
system exponentially with a linear addition of
resources
1] Error Correcting Fabrication
2] Fault Tolerant Hardware Architectures
3] Fault Tolerant Software or Codes
4] Quantum Phase Space
Self-Replicating Systems
Advanced_Automation_for_Space_Missions_figure_5-29.gif
Information Poor Replication
Autocatalytic Chemistry
Replicated Parts Lack Complexity
Information Rich Replication
(Non-Protein Biochemical Systems)
RNA-Catalyzed RNA Polymerization
14 base extension.
RNA-Catalyzed RNA Polymerization: Accurate and General RNA-Templated Primer Extension
Science 2001 May 18; 292: 1319-1325
Wendy K. Johnston, Peter J. Unrau, Michael S. Lawrence, Margaret E. Glasner, and David P. Bartel
J. Szostak, Nature,409,
Jan. 2001
Threshold for Life
What is the Threshold for Self Replicating Systems?
Measurement Theory
Replication Cycle
DNA
Parts
+
+
+
+
+
+
Step 1
Step 2
Template
Error Correcting
Exonuclease
(Ruler)
Machine
Probability thata single bond is open: 
Probability thatall N bonds open: E  
Per Step Yield : p  1  E  1  


N
N
N
/sandwalk.blogspot.com/2007/12/dnadenaturation-and-renaturation-and.html
http://en.wikipedia.org/wiki/File:Stem-loop.svg
Probability of Self Replication
How Well Can N Molecules Measure Distance?
T otalYield : P  p N  1 -  N
Watson Crick
.18 nm
Step 3
1
0.8
0.6
0.4
0.2
50
100
150
200
250
Number of Nucleotides
300
Threshold for Life
Generalized Theory
Measurement Theory
Machine of N Blocks at Temperature T
Measures the Correctness of the new added block.
Energy: Energy consumption per replication (dominated by measurement just like in Szilard Maxwell’s Demon):
Must Determine size (position) to within 1 atom: Heisenberg limit: lambda / number of photons
0.1 nm = 5000 * 500nm photons ~ 5 Kev per addition
Number of Building Blocks: N Block machine must serve as a stable reference point to make measurement on
the new added block.
Autonomous self replicating machines from
random building blocks
Mechrep
Emthingy
Rep5mer
In Presentations/Saul
Lipson et. al.
Exponential Fabrication
Mean-Green von Neumann Machine
X Prize Rules
Prize Awarded to First Team to construct multiple copies of a machine
that:
1. Consumes readly available raw materials (garbage,rocks, soil, air,
water)
2. Produces renewable energy at reasonable area/power (concentrated
solar,photovoltaic cells, wind)
3. Manufactures every part required to replicate itself