How Does Nature Compute? Lila Kari Dept. of Computer Science - - PowerPoint PPT Presentation

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How Does Nature Compute? Lila Kari Dept. of Computer Science - - PowerPoint PPT Presentation

Aug 12, 2023 316 likes •717 views

How Does Nature Compute? Lila Kari Dept. of Computer Science University of Western Ontario London, ON, Canada http://www.csd.uwo.ca/~lila/ lila@csd.uwo.ca Computers: What can they accomplish? Fly spaceships to Mars Control aircraft

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SLIDE 1

How Does Nature Compute?

Lila Kari

  • Dept. of Computer Science

University of Western Ontario London, ON, Canada

http://www.csd.uwo.ca/~lila/ lila@csd.uwo.ca

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SLIDE 2

Lila Kari, University of Western Ontario

Computers: What can they accomplish?

  • Fly spaceships to Mars
  • Control aircraft
  • Robot aided manufacturing
  • Computer games
  • Expedite journal submissions
  • Email
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SLIDE 3

Lila Kari, University of Western Ontario

Computers: What do they actually do?

  • Computers = a collection of switches (bits)

that are on (1) or off (0).

  • Can execute only simple operations

§ Flipping a bit’s value § Zeroing a bit § Testing a bit

How do they do it?

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SLIDE 4

Lila Kari, University of Western Ontario

INGREDIENTS (Input: Bit string) (SOFTWARE) (HARDWARE) RECIPE OVEN, UTENSILS (Algorithm) (Electronic Computer) CAKE (Output:Bit string)

Harel, D. Computers Ltd. 2000

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SLIDE 5

Lila Kari, University of Western Ontario

Formal Models of Computing:

Turing Machines

  • Data

§ String of symbols written on a tape

  • Operations

§ Read a square § Overwrite the symbol with another § Move left or right

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SLIDE 6

Lila Kari, University of Western Ontario

Turing Machine

Computation = Finite list of instructions

“If you are in state S and read input symbol X then write Y and move Left/Right”

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SLIDE 7

Lila Kari, University of Western Ontario

Turing Machine

  • Turing machines are capable of universal

computation (everything that can be computed can be computed by a TM)

  • The abstract notion of computation (Turing

machine, algorithm, program) is hardware independent

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SLIDE 8

Lila Kari, University of Western Ontario

History of Hardware

  • Abacus
  • Pascal
  • Jacquard
  • Babbage
  • Hollerith
  • ENIAC
  • Chip

Abacus

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SLIDE 9

Lila Kari, University of Western Ontario

History of Hardware

  • Abacus
  • Pascal
  • Jacquard
  • Babbage
  • Hollerith
  • ENIAC
  • Chip

Mechanical adding machine (1642)

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SLIDE 10

Lila Kari, University of Western Ontario

History of Hardware

  • Abacus
  • Pascal
  • Jacquard
  • Babbage
  • Hollerith
  • ENIAC
  • Chip

Jacquard’s punch card loom (1801)

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SLIDE 11

Lila Kari, University of Western Ontario

History of Hardware

  • Abacus
  • Pascal
  • Jacquard
  • Babbage
  • Hollerith
  • ENIAC
  • Chip

Babbage’s difference engine (1833)

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SLIDE 12

Lila Kari, University of Western Ontario

History of Hardware

  • Abacus
  • Pascal
  • Jacquard
  • Babbage
  • Hollerith
  • ENIAC
  • Chip

Hollerith punch card system (1890)

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SLIDE 13

Lila Kari, University of Western Ontario

History of Hardware

  • Abacus
  • Pascal
  • Jacquard
  • Babbage
  • Hollerith
  • ENIAC
  • Chip

ENIAC (1939-45) -167 sq.m.

  • 18,000 vacuum tubes
  • not programmable
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SLIDE 14

Lila Kari, University of Western Ontario

History of Hardware

  • Abacus
  • Pascal
  • Jacquard
  • Babbage
  • Hollerith
  • ENIAC
  • Chip

Modern computer chip

  • Transistors
  • Integrated circuit
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SLIDE 15

Lila Kari, University of Western Ontario

INGREDIENTS (Input:DNA strands) (SOFTWARE) (HARDWARE) RECIPE OVEN, UTENSILS (Algorithm) (DNA Strands, Enzymes) CAKE (Output: DNA)

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SLIDE 16

Lila Kari, University of Western Ontario

DNA Computer

  • Input / Output (DNA)

§ Data encoded using the DNA alphabet {A, C, G, T} and synthesized as DNA strands

  • Bio-operations

§ Cut § Paste § Copy § Anneal § Recombination

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SLIDE 17

Lila Kari, University of Western Ontario

Biomolecular (DNA) Computing

  • Hamiltonian Path Problem [Adleman, Science, 1994]
  • DNA-based addition [Guarnieri et al, Science, 1996]
  • Maximal Clique Problem [Ouyang et al, Science, 1997]
  • DNA computing by self-assembly [Winfree et al, Nature 1998]
  • Computations by circular insertions, deletions [Daley et al,1999]
  • DNA computing on surfaces [Liu et al, Nature, 2000]
  • Molecular computation by DNA hairpin formation

[Sakamoto et al, Science, 2000]

  • Programmable and autonomous computing machines made of

biomolecules [Benenson et al, Nature, 2001]

  • 20-variable Satisfiability [Braich et al., Science 2002]
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SLIDE 18

Lila Kari, University of Western Ontario

How Does Nature Compute?

  • Technical difficulties encountered in

experimental DNA computations (error- detection, error-correction) are routinely solved by biological systems in nature

  • Idea: study and utilize the computational

abilities of unicellular organisms

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SLIDE 19

Lila Kari, University of Western Ontario

Ciliates: Unicellular Protozoa

Photo courtesy of L.F. Landweber

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SLIDE 20

Lila Kari, University of Western Ontario

Ciliates: Genetic Info Exchange

Photo courtesy of L.F. Landweber

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SLIDE 21

Lila Kari, University of Western Ontario

Ciliates: Gene Rearrangement

Photo courtesy of L.F. Landweber

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SLIDE 22

Lila Kari, University of Western Ontario

Ciliates: Bio-operations

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SLIDE 23

Lila Kari, University of Western Ontario

Ciliates: Results

  • Guided Recombination System = A formal

computational model based on contextual circular insertions and deletions

  • Such systems have the computational power
  • f Turing Machines (Landweber, Kari, ’99)
  • The model is consistent with the limited

knowledge of this biological process

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SLIDE 24

Lila Kari, University of Western Ontario

Essential Feature of Biocomputing: Self-Assembly

  • Use knowledge of how simple components

(DNA molecules, enzymes) interact

  • Design a setup such that the computation

happens essentially by itself

  • Useful in nano-technology where

components are too small for existing tools

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SLIDE 25

Lila Kari, University of Western Ontario

Model of Self-Assembly

  • Tile

§ A 1 x 1 square § Each side is “painted” with a certain kind of glue § Tiles cannot be rotated § Two “adjacent” tiles will “stick” only if they have matching glues at the touching edges

  • Tile system

§ T = A finite number of tile types (as above) § Unlimited supply of each tile type available

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SLIDE 26

Lila Kari, University of Western Ontario

Yes

(Classic) Tiling Problem

  • Can any square, of any size, be tiled using
  • nly the available tile types, without

violating the glue-matching rule?

No

Harel, D. Computers Ltd. 2000

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SLIDE 27

Lila Kari, University of Western Ontario

Self-Assembly Problems

  • What is the minimal number of tile types

that can self-assemble into a given shape and nothing else?

  • What is the optimal initial concentration of

tile types that ensures fastest self-assembly?

  • What happens if “bonds” have different

strengths?

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SLIDE 28

Lila Kari, University of Western Ontario

The Ribbon Problem

  • Given a tile system, can we determine

whether or not it can produce shapes that grow indefinitely?

  • Can we decide whether or not a set of given

tiles can produce unlimited-size ribbons?

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SLIDE 29

Lila Kari, University of Western Ontario

Generating Ribbons

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Lila Kari, University of Western Ontario

Answer

  • There is no algorithm, and there never will

be, for solving the Ribbon Problem!

[Adleman, Kari, Kari, Reishus, 2002]

  • You can devise a program that might work

quite well, on some of the inputs. But there always will be inputs upon which your algorithm will misbehave; it will either run forever, or produce the wrong output.

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Lila Kari, University of Western Ontario

Computable vs. Uncomputable!

  • An algorithmic problem that admits no

solution is termed uncomputable

  • If it is a Yes/No problem, it is termed

undecidable

  • The Ribbon Problem is undecidable
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SLIDE 32

Lila Kari, University of Western Ontario

Sometimes we cannot do it!

The uncomputable (undecidable) The computable (decidable)

Harel, D. Computers Ltd. 2000

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SLIDE 33

Lila Kari, University of Western Ontario

Experimental Self-Assembly

  • Self-assembly using capillary forces (Rothemund)
  • DNA computing by self-assembly (Winfree, Seeman)
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SLIDE 34

Lila Kari, University of Western Ontario

Experimental Self-Assembly

  • Self-assembly using capillary forces (Rothemund)
  • DNA computing by self-assembly (Winfree, Seeman)
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SLIDE 35

Lila Kari, University of Western Ontario

Experimental Self-Assembly

  • Self-assembly using capillary forces (Rothemund)
  • DNA computing by self-assembly (Winfree, Seeman)
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SLIDE 36

Lila Kari, University of Western Ontario

DNA computing by self-assembly (Winfree, Seeman, Mao, LaBean, Reif)

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SLIDE 37

Lila Kari, University of Western Ontario

Potential Advantages of Biomolecular (DNA) Computing

  • Information density

1 gram of DNA (1 cm3 when dry) = 1 trillion CDs 1 lb DNA – more memory then all computers together.

  • Speed

Thousand to million times faster than an electronic computer due to massive parallelism

  • Energy consumption

thousand times more energy efficient

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SLIDE 38

Lila Kari, University of Western Ontario

IMPACT OF DNA COMPUTING

  • Sheds new light into the nature of computation
  • Opens prospects of radically different computers
  • Could lend new insights into the information

processing abilities of cells

  • “Biology and Computer Science – life and

computation – are related” (Adleman)

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SLIDE 39

Lila Kari, University of Western Ontario

“If we knew what it was that we were doing, it wouldn’t be called research, would it?” (Einstein)