Dynamische Bioinformatik Systembiologie Teil 12

1
Dynamische Bioinformatik / SystembiologieTeil 12

• Peter Dittrich
• Jenaer Centrum für Bioinfomatik und
• Friedrich-Schiller-Universität Jena
• Institut für Informatik

2
Motivation

• Informationsverarbeitung mittels chemischer
  Systeme findet man überall in der Natur
• im Zellkern und Organellen
• in der Zelle
• zwischen Zellen
• zwischen Organen
• zwischen Organismen
• zur Steuerung/Regelung von Wachstum und
  Immunabwehr
• usw.

- Speichern - Übermitteln - Verarbeiten
3
(No Transcript)
4
Molecular Computing

• (Liberman 1972, 1979), (Conrad 1972)Disussion,
  Maschinerie der Zelle für Informationsverarbeitung
  zu nutzen
• (Seelig Rössler 1972) chemische System als
  logische Schaltung

5
Chemical Computing - Chemisches Rechnen

• Informationsverarbeitung mit ChemieWir können
  unterscheiden
• Real Chemical Computing - Molecular
  Computing(Rechnen mit realen Molekülen)
• Artificial Chemical Computing(künstliches
  informationsverarbeitendes System verwendet
  Metaphern der Chemie)

6
Welche Moleküle ?

• Enzymez.B. Bacteriorhodopsin
• Bio-Polymere (meistens DNA)
• andere, z.B BZ-Reaktion

7
Prinzipien

• Mustererkennung (Docking, Anlagerung)
• räumliche Strukturbildung
• Konformationsänderung
• optische Aktivität
• chemische Kinetik

8
Klassifikation nach Ebene

• macroscopicRechenprozess kann mit Hilfe von
  makroskopischen Größen (z.B. Konzentration)
  beschrieben werden.Bsp. Das chemische Neuron,
  BZ-Reaktion
• microscopicEinzelne Moleküle führen
  Rechenprozess aus.Bsp. DNA Computing
• mesoscopic (Wenn wir uns nicht entscheiden
  können)

9
Input

• Materie
• Licht
• Selektionsdruck
• Reaktionsbeziehungen

10
Makroskopisches chemisches RechnenBeispiel
chemisches Neuron
nach Hjelmfelt, Weinberger, Ross 1991
11
Makroskopisches chemisches RechnenBeispiel
Parität
12
Makroskopisches chemisches RechnenBeispiel
Parität
13
Makroskopisches chemisches RechnenBeispiel
hyperzyklischer Speicher
14
Makroskopisches chemisches RechnenBeispiel
hyperzyklischer Speicher
15
Makroskopisches chemisches RechnenBeispiel
hyperzyklischer Speicher
16
Microscopic Mikroskopisches chemisches
RechnenBsp. DNA Computing, Variante des
Hamiltonschen Problems, Adleman 1994
17
Microscopic Mikroskopisches chemisches
RechnenBsp. DNA Computing, Variante des
Hamiltonschen Problems, Adleman 1994
18
Algorithmus

• Erzeuge zufällige Pfade
• Behalte Pfade, die mit v_start beginnen und mit
  v_ende enden.
• Behalte davon die Pfade, die genau 7 Knoten
  enthalten.
• Behalte die Pfade, die jeden der 7 Knoten
  enthalten.
• Bleibt eine Pfad übrig? Falls ja gt Antwort
  JaSonst gt Antwort Nein

19
Chemische Informationsverarbeitung mittels
Reaktions-Diffusions Systemen(Andrew Adamatzky,
Bristol)
20
Three constituents of reaction-diffusion and
excitation

• Diffusion Molecules of reagents move randomly
  due to persistent collisions with molecules of a
  solvent
• Reaction Molecules are created and annihilated
  in the result of interaction between the reagents
• Excitation Auto-catalytic reaction coupled with
  molecular diffusion gives constant velocity fronts

by Andrew Adamtzky
21
To implement a computation in a
reaction-diffusion medium we need to ...

• encode an algorithm into a set of reactions and
  coefficients of diffusive coupling
• encode data into spatial distribution of
  reagents
• let waves of reagents run, collide one with
  another and produce a precipitate in the result
  of the collisions
• decode spatial distribution of the precipitate
  into results of the computation

by Andrew Adamtzky
22
Reaction-diffusion processors

• Computational geometry and optimisation
• Computation of Voronoi diagram
• Computation of skeleton of planar shape
• Approximation of shortest paths and spanning tree

• Navigation of robots
• Phototaxis

• Universal processors
• Collision-based computing

by Andrew Adamtzky
23
Reaction-diffusion processors

• Computational geometry and optimisation
• Computation of Voronoi diagram
• Computation of skeleton of planar shape
• Approximation of shortest paths and spanning tree

• Navigation of robots
• Phototaxis

• Universal processors
• Collision-based computing

by Andrew Adamtzky
24
Skeleton

• A skeleton of a planar contour is a set of
  centres of bitangent circles which lie entirely
  inside the contour

by Andrew Adamtzky
25
Skeletonization

• project a shape onto excitable medium to excite
  edges of the shape
• waves of excitation spread inward the contour
• the waves interact one with another and generate
  strips of a precipitate
• concentration profile of the precipitate
  represents segments of the skeleton

by Andrew Adamtzky
26
Laboratory Prototype

• A planar contour is cut out of filter paper for
  electrophoresis and saturated with FeCl3 6H2O
• Agar gel mixed with the K4Fe(CN)6 3H2O forms
  a planar substrate
• Light blue colour is due to formation of
  Fe4Fe(CN)63 precipitate

K4Fe(CN)6FeCl3 KFeFe(CN)63KCl 3KFeFe(CN)6
FeCl FeCl3 3KCl Fe4Fe(CN)63
by Andrew Adamtzky
27
Voronoi diagram
Voronoi cell Given set P of planar points a
Voronoi cell of point p from P contains all
points that are close to p than to any other
point of the set P.
Voronoi diagram A union of boundaries of the
Voronoi cells of the points from P is a Voronoi
diagram of P.
by Andrew Adamtzky
28
Reaction-diffusiontessellation

• We place drops of reagents at sites of the given
  set
• Diffusive wave spread and interact with each
  other
• The different reagents react and form a
  precipitate
• Sites that contain the precipitate represent
  edges of Voronoi cells

by Andrew Adamtzky
29
Laboratory Prototype

• The thin layer of agar gel mixed with palladium
  chloride is a planar substrate.
• Sites corresponding to planar points which must
  be separated by Voronoi bisectors are supplied
  with drops of potassium iodide.
• The bisectors of Voronoi cells are represented
  by the sites of the substrate where palladium
  chloride exhausted.

PdCl22KI PdI22KCl
by Andrew Adamtzky
30
Navigating Robots by Excitable Media

• How to employ an excitable medium, in the form
  of a molecular array with actuators, to provide a
  controller for a (nano) robot

by Andrew Adamtzky
31
Ciliate Robots Distributed Phototaxis

• Every molecule of a 2D array has a propulsive
  actuator
• Edge molecules are light-sensitive
• The excitation is passed from one molecule to
  another one

by Andrew Adamtzky
32
Actuators Are Positioned by Excitation Waves

• An actuator positions itself away from the
  direction of from which excitation arrives
• The actuator produces a local propulsive force

by Andrew Adamtzky
33
How does it work...?

• The edges molecules are excited by light
  patterns of excitation travel inward the array
• The waves of the excitation modifies the local
  orientations of actuators
• Local propulsive forces are generated by the
  actuators
• The interaction between the local forces and the
  environment implicitly causes the rotation and
  translation motion of the robot

by Andrew Adamtzky
34
Dynamics of Excitations and Typology of Robot
Trajectories
Graceful motion
Cycloidal motion
Pirouette motion
Excitations Actuators
Trajectories
by Andrew Adamtzky
35

• The chemical medium, constituting the controller,
  is light sensitive
• Micro-volumes at those edges of a reactor which
  are closer to the light target are excited
• They generate robust waves of excitation that
  travel inward the reactor space
• Velocity vectors of the wave fronts, being
  inverted, indicate a direction toward the source
  of light

by Andrew Adamtzky
36
Typical activity patterns for 2D excitable
lattice controllers with interval-based
excitation of lattice nodes
by Andrew Adamtzky
37
Examples of excitable lattices moving toward a
light source
by Andrew Adamtzky
38
Laboratory Experiments
U-bot
Sensors-to-lattice coupling
The trajectory
by Andrew Adamtzky
39
Literatur

• Adamatzky, A. (2002) ....
• Adleman,L. (1997)
• Hale, J. and H. Koçak (1991), Dynamics and
  Bifurcations, Springer Verlag, New York
• Bossel, H. (1992), Modellbildung und Simulation,
  Vieweg, Braunschweig
• Jetschke, G. (1989), Mathematik der
  Selbstorganisation. Deutscher Verlag der
  Wissenschaften, Berlin
• William H. Press, Brian P. Flannery, Saul A.
  Teukolsky, William T. Vetterling (1992),
  Numerical Recipes in C - The Art of Scientific
  Computing, Cambridge University Press, Cambridge,
  UKhttp//www.nr.com/