Artificial Life (and Systems Biology)
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Artificial Life (and Systems Biology)
Jens Christian Claussen (U Lübeck)
1. Introduction 2. Cellular Automata, AL in silico, and AL in vitro
3. Information Theory 4. Statistical Mechanics 5. Complexity and Information
6. Self-Organized Criticality, Fitness Landscapes, Evolutionary Game Theory
7. Complex Networks, Network motifs 8. Random Boolean Networks
9. Genes, Switches, Modules and Robustness 10. Repressilator
11. Genetic algorithms, Evolutionary algorithms / optimization
12. (Swarm Intelligence, Artificial Societies, Socio-Economic Systems models)
Jens Christian Claussen – p. 1/11What is Systems Biology?
... The overlap of systems biology and artificial life can be expected to grow in this process,...
Jan T. Kim & Roland Eils: “Systems Biology and Artificial Life: Towards Predictive
Modeling of Biological Systems”, Artif. Life 14, 1 (2008)
Jens Christian Claussen – p. 2/11What is Systems Biology?
“Systems biology is a biology-based inter-disciplinary study field that
focuses on the systematic study of complex interactions in biological
systems, thus using a new perspective (holism instead of reduction) to
study them.” (wikipedia)
“Systems biology... is about putting together rather than taking apart,
integration rather than reduction. It requires that we develop ways of
thinking about integration that are as rigorous as our reductionist
programmes, but different....It means changing our philosophy, in the full
sense of the term”(Denis Noble, The Music of Life)
Artificial life (commonly Alife or alife) is a field of study and an associated
art form which examine systems related to life, its processes, and its
evolution through simulations using computer models, robotics, and
biochemistry. (wikipedia)
“Cybernetics is the interdisciplinary study of the structure of regulatory
systems. Cybernetics is closely related to control theory and systems
theory.” (wikipedia)
Jens Christian Claussen – p. 3/11Read books!
Christoph Adami: Introduction to Artificial Life
(Springer, 1998)
Edda Klipp et al.: Systems Biology (2009) replaces 2005
Uri Alon: An Introduction to Systems Biology (2007)
Martin Nowak: Evolutionary Dynamics (2006)
Erwin Schrödinger: Was ist Leben (1943)
Denis Noble: The Music of Life
Jens Christian Claussen – p. 4/11Summary
Systems Biology, Artificial Life and Cybernetics
... are (approaches of) Quantitative Biological Modeling
Life: To understand the definition of, conditions for, mechanisms of
Approaches: From hard (silico) to wet (in vitro) to ... wildlife
Cellular automata and Self-Replicating codes Artificial Chemistry and Artificial Cells
From Top-down vs. bottom-up to more integrated models, multiscale
Systems Biology is about putting together (including all details we have?)
Jens Christian Claussen – p. 5/11Summary
Systems Biology, Artificial Life and Cybernetics
... are (approaches of) Quantitative Biological Modeling
Life: To understand the definition of, conditions for, mechanisms of
Approaches: From hard (silico) to wet (in vitro) to ... wildlife
Cellular automata and Self-Replicating codes Artificial Chemistry and Artificial Cells
From Top-down vs. bottom-up to more integrated models, multiscale
Systems Biology is about putting together (including all details we have?)
Limitations! Many-Parameter-Uncertainty? highdim Visualization?
Language: (continuous and discrete and stochastic) dynamical systems
To be complemented with statistical (physics) analysis of simplified
models ... to understand complexity classes and address systematic questions
Needs mathematics, nonlinear dynamics & statistical physics, information
theory, informatics, control theory, ... ... and serves solely to understand biology.
Jens Christian Claussen – p. 5/11Summary
Systems Biology, Artificial Life and Cybernetics
... are (approaches of) Quantitative Biological Modeling
Life: To understand the definition of, conditions for, mechanisms of
Approaches: From hard (silico) to wet (in vitro) to ... wildlife
Cellular automata and Self-Replicating codes Artificial Chemistry and Artificial Cells
From Top-down vs. bottom-up to more integrated models, multiscale
Systems Biology is about putting together (including all details we have?)
Limitations! Many-Parameter-Uncertainty? highdim Visualization?
Language: (continuous and discrete and stochastic) dynamical systems
To be complemented with statistical (physics) analysis of simplified
models ... to understand complexity classes and address systematic questions
Needs mathematics, nonlinear dynamics & statistical physics, information
theory, informatics, control theory, ... ... and serves solely to understand biology.
... hopefully, also useful to improve medicine.
“Im Focus das Leben”
Jens Christian Claussen – p. 5/11Definitions of Life?
How can “life” be defined?
Jens Christian Claussen – p. 6/11Definitions of Life?
How can “life” be defined?
Although the definition of life is notoriously controversial [. . .] a
molecular assemblage should be considered alive if it continually
regenerates itself, replicates itself, and is capable of evolving.
Rasmussen et al., Science 303, 963 (2004)
Simulating the same molecular reactions ab initio, is this still “alive”?
But, it is simply a computer code (Turing machine)!
Then, what is the simplest “alife” system?
In silico and In carbon approaches
Simulations of Units (any level. Extremes: Blue Brain, artificial organs)
Simulations of Populations (agents, robots, ...)
Carbon-based artificial life (artificial chemistry, self-replicating CA)
Turing & von Neumann automata; Cellular Automata (CA)
Jens Christian Claussen – p. 7/11Turing (1936) and von Neumann (1951) automata
Turing machine: abstract automaton, can be in one of a finite number
of states (1, . . . n)
– capable of reading and writing on a tape of instructions
mbox(symbols 0 and 1)
– characterized by rules: state change depending on own state and
currently read bit on an (arbitrarily long) tape
– actions: reading, moving the head, and writing information
Universality: Turing machine can emulate any other Turing machine
First application:
Mc Culloch & Pitts Neurons as universal computational units
von Neuman automata: automata that construct automata
Somehow simpler: Cellular automata (von Neumann / Stanislaw
Ulam; Codd 1968; Pesavento 1995)
Langton 1984/86: Use only ingredients necessary for reproduction
Jens Christian Claussen – p. 8/11Cellular automata
Definition (CA): A CA is a lattice of sites, each of which can assume k
values. Each site of the CA is updated at discrete time values (in
parallel) by a finite state automaton residing at each state, which
assigns a new value depending on the value of the sites around it.
For a 1-dim CA with a r = 1 neighborhood, the update rule reads
ai (t + 1) = Φ(ai−1 (t), ai (t), ai+1 (t))
Generalizations to higher dimensions are straightforward!
Jens Christian Claussen – p. 9/11Cellular automata
Definition (CA): A CA is a lattice of sites, each of which can assume k
values. Each site of the CA is updated at discrete time values (in
parallel) by a finite state automaton residing at each state, which
assigns a new value depending on the value of the sites around it.
For a 1-dim CA with a r = 1 neighborhood, the update rule reads
ai (t + 1) = Φ(ai−1 (t), ai (t), ai+1 (t))
Generalizations to higher dimensions are straightforward!
Example: Rule 90 and Rule 150 cellular automata
(xn−1 (t), xn (t), xn+1 (t)) 111 110 101 100 011 010 001 000
x90
n (t) 0 1 0 1 1 0 1 0
x150
n (t) 1 0 0 1 0 1 1 0
In 1D, there are 256 such “elementary cellular automata” (ECA).
Classification of CA: I (limit point), II (limit cycle), III (aperiodic,
“chaotic”), IV (“very complex”)
Jens Christian Claussen – p. 9/11Conway’s “ Game of Life”
Conway’s “Game of Life” is a two-state CA defined on a Moore
neighborhood (8 neighbors around own site) on a 2-dim lattice as
a(x, y) = 1 → a(x, y) = 1 if 2 or 3 neighbors are in state 1
(a living cell with 2 or 3 neighbors remains alive)
a(x, y) = 0 → a(x, y) = 1 if exactly 3 neighbors are in state 1
(at the position of a dead cell with exactly 3 neighbors, a new cell is born)
a(x, y) = ∗ → a(x, y) = 0 in all other cases
all other cells die (from loneliness or overcrowding), or else remain dead
Jens Christian Claussen – p. 10/11Conway’s “ Game of Life”
Conway’s “Game of Life” is a two-state CA defined on a Moore
neighborhood (8 neighbors around own site) on a 2-dim lattice as
a(x, y) = 1 → a(x, y) = 1 if 2 or 3 neighbors are in state 1
(a living cell with 2 or 3 neighbors remains alive)
a(x, y) = 0 → a(x, y) = 1 if exactly 3 neighbors are in state 1
(at the position of a dead cell with exactly 3 neighbors, a new cell is born)
a(x, y) = ∗ → a(x, y) = 0 in all other cases
all other cells die (from loneliness or overcrowding), or else remain dead
Allows for universal computation!
Langton (8-state version):
Self-replicating solutions!
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