mas.961 how to make something that makes (almost) anything [email protected] complexity, self...
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MAS.961How To Make Something That Makes (Almost)
Anything
Complexity, Self Replication and all that…
Itanium Quad TukwilaTransistor Count: 2BCost: ~$100
Si Wafer with Area sufficient for2 Billion TransistorsCost: ~$0.50
Flash MemoryTransistor Count: 2BCost: ~$3
NetBookCost: ~$200
Sand (Chips and Screen)Cost: ~$0
Plastic Resin / Metal OreCost: ~$4
What governs the cost of placing atoms where we want them? What are the limits?
Fabricational Complexity
Fabricational Complexity Per Unit Cost
MpF N ln1
A G T C G C A A T
N
Fabricational Complexity for N-mer or M Types = NMln
Fabricational Cost for N-mer = NNp
Where is the yield per fabricational step p
Complexity Per Unit CostComplexity Per Unit Time*Energy
Fabricational ComplexityApplication: Why Are There 20 Amino Acids in Biology?(What is the right balance between Codon code redundancy and diversity?)
Qi
iQN
N
n
NW
!)(
!
!
!
500 1000 1500 2000
10
20
30
40
N
*Q
Question: Given N monomeric building blocks of Q different types, what is the optimal number of different types of building blocks Q which maximizes the complexity of the ensemble of all possible constructs?
The complexion for the total number of different ways to arrange N blocks of Q different types (where each type has the same number) is given by:
And the complexity is:
N Blocks of Q Types
QNQNQNQNNQNF )ln()(*)ln(),(
For a given polymer length N we can ask which Q* achieves the half max for complexity such that:
),(5.0*),( NNFQNF
.
…Can we use this map as a guide towards future
directions in fabrication?
Semi-conductor Chip
High Speed Offset Web TFT DVD-6
Liquid Embossing
Design Rule Smallest Dimension (microns) 0.1 10 2 0.25 0.2Number of Types of Elements 8 6 8 2 4Area of SOA Artifact (Sq. Microns) 7.E+10 2.E+12 1.E+12 1.E+10 8.E+09Volume of SOA Artifact (Cubic Microns) 7.E+09 2.E+12 1.E+11 7.E+12 8.E+08Number of Elements in SOA Artifact 7.E+12 2.E+10 3.E+11 2.E+11 2.E+11Volume Per Element(Cubic Microns) 1.E-03 1.E+02 4.E-01 4.E+01 4.E-03Fabrication Time(seconds) 9.E+04 1.E-01 7.E+02 3 6.E+01Time Per Element (Seconds) 1.E-08 7.E-12 2.E-09 2.E-11 3.E-10Fabrication Cost for SOA Artifact($) 1.E+02 1.E-01 2.E+03 3.E-02 2.E-01Cost Per Element 2.E-11 6.E-12 6.E-09 2.E-13 1.E-12Complexity 2.E+13 4.E+10 6.E+11 1.E+11 3.E+11Complexity Per Unit Volume of SOA(um 3̂) 2.E+03 2.E-02 5.E+00 2.E-02 3.E+02Complexity Per Unit Time 2.E+08 3.E+11 9.E+08 4.E+10 5.E+09Yielded Res. Elements Per $ 1.E+11 3.E+11 3.E+08 4.E+12 1.E+12Cost Per Area 2.E-09 6.E-14 2.E-09 3.E-12 3.E-11
Fabricational ComplexityApplication: Identifying New Manufacturing Approach for Semiconductors
Printed Electronics
~Minutes
~ 3Weeks of 7x24 Processing
Lithography Printed Electronics
+
Liquid InorganicSemiconductors[1]
[1] Ridley et al., Science, 286, 746 (1999)Science 297,416 (2000)
High Speed Printing
…Can we use this map as a guide towards future
directions in fabrication?
Genome (Natural)
Gene Chip (Chemical Parallel Synthesis)
Semi-conductor Chip
High Speed Offset Web TFT DVD-6
Liquid Embossing
Design Rule Smallest Dimension (microns) 0.0003 0.0003 0.1 10 2 0.25 0.2Number of Types of Elements 4 4 8 6 8 2 4Area of SOA Artifact (Sq. Microns) NA 7.E+08 7.E+10 2.E+12 1.E+12 1.E+10 8.E+09Volume of SOA Artifact (Cubic Microns) 6.E+01 5.E+06 7.E+09 2.E+12 1.E+11 7.E+12 8.E+08Number of Elements in SOA Artifact 3.E+09 7.E+04 7.E+12 2.E+10 3.E+11 2.E+11 2.E+11Volume Per Element(Cubic Microns) 2.E-08 8.E+01 1.E-03 1.E+02 4.E-01 4.E+01 4.E-03Fabrication Time(seconds) 4.E+03 2.E+04 9.E+04 1.E-01 7.E+02 3 6.E+01Time Per Element (Seconds) 1.E-06 3.E+02 1.E-08 7.E-12 2.E-09 2.E-11 3.E-10Fabrication Cost for SOA Artifact($) 1.E-07 1.E+02 1.E+02 1.E-01 2.E+03 3.E-02 2.E-01Cost Per Element 3.E-17 2.E-03 2.E-11 6.E-12 6.E-09 2.E-13 1.E-12Complexity 4.E+09 9.E+04 2.E+13 4.E+10 6.E+11 1.E+11 3.E+11Complexity Per Unit Volume of SOA(um 3̂) 7.E+07 2.E-02 2.E+03 2.E-02 5.E+00 2.E-02 3.E+02Complexity Per Unit Time 1.E+06 6.E+00 2.E+08 3.E+11 9.E+08 4.E+10 5.E+09Complexity Per Unit Cost 4.E+16 9.E+02 1.E+11 3.E+11 3.E+08 4.E+12 1.E+12Cost Per Area NA 2.E-07 2.E-09 6.E-14 2.E-09 3.E-12 3.E-11
Fabricational Complexity
DNA SynthesisChemical Synthesis
(Open Loop Protection Group)
Biological Synthesis
(Error Correcting Polymerase)
Error Rate: 1:102
Throughput: 300 S per Base Additionhttp://www.med.upenn.edu/naf/services/catalog99.pdf
Error Rate: 1:106
Throughput: 10 mS per Base AdditionBeese et al. (1993), Science, 260, 352-355. http://www.biochem.ucl.ac.uk/bsm/xtal/teach/repl/klenow.html
Throughput Error Rate Product Differential: ~108
template dependant 5'-3' primer extension
5'-3' error-correcting exonuclease
3'-5' proofreading exonuclease
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.
MpF N ln1
Fabricational Complexity Per Unit Cost 2 Ply Error Correction
Non Error Correcting:
2Ply Error Correcting:
A G T C
A G T C
A G T C NppN
MNF
2222
ln
20 40 60 80 100
0.6
0.8
1.2
12 FF
p=0.99
MpF N ln1
Fabricational Complexity Per Unit Cost 3 Ply Error Correction
Non Error Correcting:
3Ply Error Correcting:
A G T C
A G T C
A G T C
A G T C N
pppN
MNF
)1(33
ln233
0.3 0.4 0.5 0.6 0.7 0.8 0.9
0.5
1
1.5
p
15N
10 20 30 40 50
0.05
0.1
0.15
0.2
0.25
0.3
N
4.0p
F
F3
10 20 30 40 50
2.5
5
7.5
10
12.5
15
F
F3
N
6.0p
F
F3
(a) (b) (c)
21p
0dN
dR
For values of
,
and R increases exponentially with N.
1] Error Correcting Fabrication 2] Fault Tolerant Hardware Architectures 3] Fault Tolerant Software or Codes4] Quantum Phase Space
Resources which increase the complexity of a system exponentially with a linear addition of
resources
Resources for Exponential Scaling
Self-Replicating Systems
Advanced_Automation_for_Space_Missions_figure_5-29.gif
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Chemistry: Amplification by compartmentalizationJIAN CHEN*, STEFFI KÖRNER*, STEPHEN L. CRAIG†, DMITRY M. RUDKEVICH‡ & JULIUS REBEK JR*Nature 415, 385 - 386 (2002); doi:10.1038/415385b
Information Poor Replication
Autocatalytic Chemistry
Replicated Parts Lack Complexity
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.
J. Szostak, Nature,409, Jan. 2001
Threshold for LifeWhat is the Threshold for Self Replicating Systems?
Measurement Theory
+ + +
+ +
Step 1 Step 2 Step 3
+
Parts
Template
Machine
Replication Cycle
http://en.wikipedia.org/wiki/File:Stem-loop.svg
Error Correcting Exonuclease
(Ruler)
DNA
50 100 150 200 250 300
0.2
0.4
0.6
0.8
1
Number of Nucleotides
Pro
ba
bil
ity
of
Se
lf R
ep
lic
ati
on
NN
N
N
p
Ep
E
N-1 P :Yield Total
11 :Yield StepPer
:open bonds N ally that Probabilit
:open is bond single ay that Probabilit
Watson Crick .18 nm
How Well Can N Molecules Measure Distance?
/sandwalk.blogspot.com/2007/12/dna-denaturation-and-renaturation-and.html
Threshold for LifeGeneralized 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 photons0.1 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
MechrepEmthingyRep5mer
In Presentations/Saul
Lipson et. al.
Exponential Fabrication
Mean-Green von Neumann MachineX 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