Self-Organization in Natural Systems

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Self-Organization in Natural Systems

MANO Jean Pierre

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• What are the mechanisms for integrating subunits into a coherently structured entity?


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• What are the mechanisms for integrating subunits activity into a coherently structured entity?– From simple neurons to

the thinking brain– From individuals to the

society– From molecule to

pattern


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pattern


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pattern

C3H4O4

NaBrNaBrO3

HSO3

C12H8N2SO2Fe

Malonic acidSodium bromideSodium bromateSulfuric acid1,10 Phenanthroline ferrous sulfate


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• Definitions• Pattern formation

In living and non-living systems• Social systems

Sociality and gregarism• Cellular systems

Cells build animals• Properties of self-organized

systems

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systems

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Definitions

• What is Chaos ? [Poincarré] [Lorenz] [Prigogine]

disorder, confusion, is opposed to order and method

“Chaos” define a particular state of a system that is characterized by the following behaviors:

• Do not repeat• Sensible to initial conditions: sharp differences can produce wide

divergent results• Moreover, ordered and characterized by an unpredictable

determinism– When moving away from equillibrium state => high organization– Non equillibrium phasis: bifurcations– Amplification => Symetry break

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Definitions

• What is Self-organization in natural systems?Self-organization is a process in which pattern at the global level of a system emerges solely from numerous interactions among the lower level components of the system. [Deneubourg 1977]Moreover, the rules specifying interactions among the system’s components are executed using only local information, without reference to the global patternIn other words, the pattern is an emergent property of the system, rather than a property imposed on the system by an external influence

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• What is an emergent property ?• Many Agents• Simple rules• Many interactions• DecentralizationEmergent properties• Unreductibility• Macro-level (odre magnitude difference)• Feed-back effect on the micro-level

Definitions

Conditions

Observations

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systems

13/80Non-living pattern formation

• Based on physical and chemical properties– Belousov-

Zhabotinsky reaction– Bénard convection

cells– Sand dune ripples– Glass cracks – Mud cracks

















18/80Pattern formation in biological systems

• Patterns characterizing individuals– Giraffe coat– Zebra– Leopard– Vermiculated rabbitfish– Cone shells– Finger prints– Morel– Metamerization– Occular dominance

stripes



stripes



stripes



stripes



stripes



stripes


• Patterns characterizing individuals– Giraffe coat– Zebra– Leopard– Vermiculated rabbitfish– Cone shells– Finger prints– Morel– Metamerisation– Occular dominance

stripes



stripes



stripes



stripes

• Most of those patterns are in fact fixed states of reactions that have occurred long time ago…



stripes

• Most of those patterns are in fact fixed states of reactions that have occurred long time ago…

Mechanisms ?

… or process is still running.

29/80Activation-inhibition mechanism

The activator autocatalyzes its own production, and also activates the inhibitor. The inhibitor disrupts the autocatalytic process. Meanwhile, the two substances diffuse through the system at different rates, with the inhibitor migrating faster. The result: local activation and long-range inhibition

Inspired by equations of reaction-diffusion [Turing 1949]

Slow diffusion

Quick diffusion

ACTIVATEUR

INHIBITEUR

+

+ACTIVAT

OR

INHIBITOR

-

Degradation

Degradation

autocatalyzis

inhibition

30/80Activation-inhibition mechanism

• Activation-inhibition and self-organization share a common mechanism– Starting point: a homogeneous substrate

(lacking pattern)– Positive feedback

(short-range activation, autocatalyzes)– Negative feedback

(long-range inhibition)

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systems

Low dynamicHigh

dynamic

32/80Pattern formation in colonies activity

• Patterns resulting from the activity of a society of…

social insects– Ants– Bees– Wasps– Termites

Mammalians– African Mole-rats– Humans



social insects– Ant– Bees– Wasps– Termites









Mammalians– African Mole-rats – Humans













• Several orders of size magnitude difference

• Those patterns result of the permanent activity of society’s elements…Causality and

mechanisms ?


• Environmental constraints – Openess– Heterogeneity…

• Template– Gradients– Grids…

• Stigmergy [Grassé 1959] Indirect interactions between animals– Local environmental changes (pheromones, mud

pellets…)


• Patterns occurring during collective movement

MicroorganismsInsects and CrustaceansSocial insectsFishesBirdsMammalians





























































Those patterns result from a permanent

reorganization……mechanisms ?Alignment -

attraction• No leader• No preexisting tracks• High sensitivity to

heterogeneities• Based on the nearest

neighbor perception




Those patterns results from a permanent

reorganization……mechanisms ?

• No leader• No preexisting tracks• High sensitivity to


neighbor perception








neighbor perception








neighbor perception

64/80Attraction-repulsion mechanisms

• Relations between Activation-inhibition mechanisms and attraction-repulsion mechanisms

• They share a common mechanism– Starting point: a

homogeneous substrate (lacking or different pattern)

– Positive feedback (local activation or attraction rate to aggregates size)

– Negative feedback (long-range inhibition, depletion in individuals)

Short range effect

Long range effect

+

+-ATTRACTIONSTRENGTH

CONSUMPTION of FREEPARTICLE

Slow diffusion

Quick diffusion

ACTIVATEUR

INHIBITEUR

+

+ACTIVAT

OR

INHIBITOR

-

Degradation

Degradation

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systems

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How cells build the animal ?• From one cell to the next generation…

• From one cell to the thinking brain…

• Planed mechanisms:– Expression of the genetic program

• Scale changes– And long range communication

• Self-organizing mechanisms– Reaction-diffusion (activation-inhibition)– Cells migrations (Aggregation-repulsion)

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How cells build the animal ?• Why has evolution “chosen” these types of

solutions?• Biological Constraints

– Physical – Energetical – Turn over – Replication -

• Limited amount of genetic information• Enormous amount of

– Morphogenic– Physiological– Behavioral

Self-organization is one solution to this problem

complexity

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How cells build the animal ?

•Cell proliferation•Cell differentiation•Cell communication•Cell memory

•Regenerative potential

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Strict genetic program

Complex triggering

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Amplification of a behaviour

(metabolism)

trigger: cell environment




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ContactMechanical

Direct

Secretion diffusion

At different range and time

Indirect

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Nucleus (DNA)Cytoplasm– RNA– Prote

ins– …– toxin

s

Controled exchanges

Internal state, memoryof previous events (environments)

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• Accidental changes in cell environment– Backward

differentiation• Not all animals

– Global communication (blood circulationand nervous system)

• Not all cells• Wounds should

respect – Gradients– Periods of

sensibility

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• Low dynamic : STRUCTURES

• High dynamic : FUNCTIONING– Neural activity– Immune system

answer

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systems

76/80Self-Organization in Natural Systems

• The modeling is relatively easy.– Environment– Time– Topology

• Unraveling the real biological mechanisms remain extremely difficult

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Many agents Many interactionsSimples rulesDecentralization

Emergent properties

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• Adaptive advantages of self-organized systems– Robustness– Error tolerance– Self-repair– Ease of implementation– Simple agents.

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Conclusion

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• Why is all of this important?– Many biological systems have evolved

decentralized solutions to their vital challenges.

– Through self-organization, evolution has stumbled upon a wide range of extremely efficient, relatively simple solutions for solving very complex problems.

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Reference and further readings

• Complexity: The Emerging Science at the Edge of Order and Chaos. aldrop 1992.

• Turtles, Termites and Traffic Jams: Explorations in Massively Parallel Microworlds. Resnick 1994.

• The Quark and the Jaguar: Adventures in the Simple and the Complex. Gell-Mann 1994.

• The Self-Made Tapestry: Pattern Formation in Nature. Ball 1999.

• Emergence: From Chaos to Order. Holland 1998.• A brief history of stigmergy. Theraulaz, Bonabeau 1999 Artif. Life 5• The formation of spatial patterns in social insects:

from simple behaviours to complex structures Theraulaz, Gautrais, Camazine, Deneubourg

• Self-organization in Nature Deneubourg Camazine 2002• Comment les cellules construisent l’animal Chandebois

2003

Documents

Self-Organization in Natural Systems