Autocatalysis, Autopoiesis and Relational Biology

AutoCatalysis, Autopoiesis, and Relational Biology



The term autopoiesis is often encountered in the systems literature and is generally interpreted loosely as concerned with self-organizing systems and life. While this is partially true, the concept is actually very detailed and particular, and its implications are very far-reaching. This is not always fully appreciated, not least because of the difficulty of the original papers. Auto­poiesis was coined by Humberto Maturana and Francisco Varela to describe the nature of living as opposed to nonliving systems – it is thus an explanation of the nature of life. This, in itself, is an important enough subject and their theory has far-reaching implications for biology. They went further, however, and also developed fundamental ideas about the nervous system, perception, language, and cognition in general. These, too, have very significant impli­cations, not least for methodologies concerned with taking action within human activity systems, the design of systems in general and computer systems in particular, and for cognitive science and artificial intelligence.


Autopoiesis is a concept developed by Humberto Maturana and Francisco Varela in order to analyze the nature of living systems. It takes into account the circular organization of metabolism and it redefines the concepts of structure and organization.

Any system can be decomposed into processes and components, which interact through processes to generate other components. The definition of an Autopoietic system considers that “it is organized as a bounded network of processes of production, transformation and destruction of components that produces the components which: a)through their interactions and transformations continuously regenerate and realize the network of processes (relations) that produced them and b)constitute it (the machine) as a concrete entity in the space in which they (the components) exist by specifying the topological domain of its realization as such a network”.


From Autopoietic and (M,R) systems



In 1972, in the middle of a cataclysmic political turmoil, two Chilean biologists introduced the concept of Autopoietic systems6 (‘‘auto’’=self and ‘‘poiesis’’= generating or producing) as a theoretical construction on the nature of living systems centering on two main notions: the circular organization of metabolism and a redefinition of the systemic concepts of structure and organization. Maturana and Varela’s starting point was that any system can be decomposed into processes and components. Components interact through processes to generate other components.

The notion of circular organization is given in Autopoiesis, and it is immediately clarified in the theory by the very definition of an Autopoietic system:

‘‘an Autopoietic system is organized as a bounded network of processes of production, transformation and destruction of components which:

  1. (i)  through their interactions and transformations continuously regenerate and realize the network of processes that produced them
  2. (ii)  constitute the system as a concrete entity in the space in which the components exist by specifying the topological realization of the system as such a network’’ (Varela et al., 1974; Maturana and Varela, 1975, 1980).

In an Autopoietic system, the result of any given process is the production of components that eventually would be transformed by other processes in the network into the components of the first process. This property, termed operational closure, is an organizational property that perfectly coexists with the fact that living systems are, from a physical point of view, energetically and materially open systems. The molecules that enter the system determine the system’s organization, which generates pathways whose operation produces molecular structures that determine the physical system and the system’s organization (Fig. 7) (Fleischaker, 1990). Thus an Autopoietic system does not have inputs or outputs, instead it creates a web of molecular processes that result in the maintenance of the autopoietic organization. Because an Autopoietic system’s internal dynamics are self-determined, there is no need to refer any operational (or organizational) aspect to the outside. Thus the environment does not inform, instruct or otherwise define the internal dynamics, it only perturbs the system’s dynamics. This does not mean that an Autopoietic system is completely independent from its medium. Instead it means that the system specifies its own internal states and the domain of its changes. In this context, external events act as perturbations that only trigger internal changes. But the magnitude and direction of these changes are defined by the internal dynamics of the system and not by the external perturbations (Maturana and Mpodozis, 2000).


The second clause demands that an Autopoietic system has ‘‘sufficiently complex’’ dynamics to self- produce the boundaries that separate the systems from the ‘‘non-system’’. This apparently trivial clause has profound implications as it touches upon the problem of autonomy and also serves to weed out from the Autopoietic forest some pure formal systems. Thus Autopoietic systems are not simple relational devices that connect components with components via complex graphs. Autopoietic systems must conform to an important topological property: their boundary (in the space where their components exist) is actively produced by the network of processes that define the system’s identity. This property of Autopoietic systems couples a purely relational property (operational closure) with a topological property and it demands that an Autopoietic system must be an autonomous unity, topographically and functionally segregated from its medium, but yet dependent from this medium (Weber, 2001). In the realm of molecules, the coupling of these two conditions necessarily implies that the minimal metabolism must be rather more complex than the spatial coupling of a direct chemical reaction with its reverse reaction.


From Autopoietic and (M,R) systems


Relational Biology

In the 1930s, Nicolas Rashevsky, a physicist by training, championed the biophysical approach to understanding living systems. Rashevsky and his stu- dents created a systematic theoretical effort that consisted of applying theories from physics to explain biological phenomena like cell division and neural processing (Rashevsky, 1938). Around 1950, Rashevsky became convinced that his intense and novel ‘‘bio- physical’’ approach was fundamentally limited for understanding living systems as a whole. He realized that his previous work had dealt only with bit parts of the phenomena of living systems, without considering their peculiar organization. Thus, Rashevsky coined the term Metric Biology to refer to all aspects where a reductionist approach to biology was valid and the term Relational Biology to aspects that depended on the organization of living systems rather than the matter found inside them (Rashevsky, 1954).

In 1958–1959, as a graduate student of Nicolas Rashevsky, Robert Rosen published three papers (Rosen, 1958a, b, 1959) that were a rigorous attempt to formalize the intuitive notions of relational biology. His formalism (known as (M,R) systems) used mathematical language based on a modern and abstract branch of mathematics (Theory of Categories (Eilenberg and MacLane, 1945)). Since not many biologists are well-enough versed in algebraic theory to evaluate its utility, (M,R) systems has not had the wide impact it may deserve. Despite the limited audience Rosen could capture with his ideas, Rosen continued to develop the theory of (M,R) systems and the use of the theory of categories in Biology for 40 years until his death in 1998.

(M R) Systems 

Metabolism-repair systems ((M,R)) were introduced by Robert Rosen as an abstract representation of cell metabolic activity. The representation was obtained in the context of Relational Biology, which means that organization prevails over the physico- chemical structure of the components involved. This fact was determinant for algebraically formalizing (M,R) systems using the theory of categories.

Two elements are considered in the construction of (M,R) systems: the metabolic activity (M) and the repair functions (R) acting on the unities of the metabolic process.

The metabolic system M is considered as an input-output system. In the categorical representation, inputs and outputs are the objects of the category and the processes connecting these elements are represented by the arrows of the category.


From Autocatalytic Sets: From the Origin of Life to the Economy


Autocatalytic Sets

The framework was originally developed in the context of a chemical reaction system, which can be described formally as a set (collection) of molecules; possible chemical reactions between these molecules; and, additionally, catalysts. A catalyst is a molecule that significantly increases the rate at which a chemical reaction happens, without being consumed in that reaction. In this context, catalysts can be viewed as providing functionality, because they determine which reactions happen at high enough rates to be relevant. In fact, without catalysts, life would most likely not be possible at all, because the chemical reactions vital for life would not happen fast enough, and they would not be synchronized with one another. Finally, we assume that there are small numbers of molecules, called the food set, that are assumed to be freely available from the environment. This reflects the notion that at least certain types of molecules (e.g., water, hydrogen, nitrogen, carbon dioxide, iron) would have been around on the early Earth, before the origin of life, and could be used freely as chemical building blocks.


Given such a chemical reaction system, a subset of its chemical reactions, together with the molecules involved in them, is called an autocatalytic set if (a) every reaction in the subset is catalyzed by at least one molecule from this subset and (b) every molecule in the subset can be produced from the food set by a series of reactions from this subset only. This two-part definition formally captures the idea of a functionally closed (part a) and self-sustaining (part b) system. The molecules mutually help (through catalysis) in each others’ production, and the set as a whole can be built up and maintained (through these mutually catalyzed reactions) from a steady supply of food molecules.


Stuart Kauffman (1971) was one of the first scientists to introduce this notion of autocatalytic sets. He subsequently constructed a simple mathematical model of chemical reaction systems to argue that such autocatalytic sets will arise spontaneously (Kauffman 1986, 1993). In his model (known as the binary polymer model), molecules are represented by simple bit strings (sequences of zeros and ones) of maximum length n. The chemical reactions consist of either gluing two bit strings together into a larger one (e.g., 000 + 11 → 00011), or cutting one bit string into two smaller ones (e.g., 010101 → 01 + 0101). The molecules (bit strings) are then assigned randomly, with a given probability, p, as catalysts for the possible reactions. In other words, there is a probability, p, that an arbitrary molecule will catalyze an arbitrary reaction. By changing the values of the parameters n and p and randomly generating the catalysis assignments, different instances of the model can be created.


Kauffman then developed a mathematical argument to show that, in his binary polymer model, given a fixed value for the probability of catalysis, p, and a large enough value for the maximum molecule length, n, the existence of autocatalytic sets is basically inevitable. However, this argument was later criticized (Lifson 1997) because it implies an exponential increase in the (average) level of catalysis. In other words, every time the maximum length n of the molecules (bit strings) in the model is increased by one, each molecule will end up catalyzing about twice as many reactions as before. This will indeed eventually lead to the existence of autocatalytic sets (for large enough n), but at a chemically unrealistically high level of catalysis. Furthermore, this notion of autocatalytic sets was also criticized for lacking evolvability (Vasas et al. 2010). In Kauffman’s argument, an autocatalytic set will appear as one “giant connected component” in the chemical reaction network. This, however, implies that there is no room for change, growth, or adaptation— in other words, no possibility for the autocatalytic set to evolve.


Key Ideas and Concepts:

  • Relational Biology
  • System Biology
  • Biosemiotics
  • Anticipation
  • Autopoiesis
  • Social Autopoiesis
  • MR systems
  • Self Reference
  • Mathematical Biology
  • Theoretical Biology
  • Socio-Cybernetics
  • Cyber Semiotics
  • Autocatalysis
  • Hyper Recursive/Incursive Automata


Each of these Idea needs a separate post.  Can not do justice to them all here.  Will try to write future posts expanding these ideas.

Autopoiesis, Autocatalysis, and Relational biology have been extended into other areas of inquiry.  Autopoiesis has been extended into Social systems theory through work of Niklas Luhmann.  Other researchers have extended it into organizational theory for firms.  Relational Biology has also extended into Futures research using concept of biology of Anticipation.


Key People:

  • Robert Rosen
  • Niklas Luhmann
  • Humburto Maturana
  • F Varela
  • Roberto Poli
  • Nicholas Rashevsky
  • John Kineman
  • M Nadin
  • A H Louie
  • Dirk Baecker
  • Soren Brier
  • Stuart Kaufman
  • Daniel Dubois
  • Donald C. Mikulecky
  • Milan Zeleny
  • Tibor Ganti


Key Sources of Research:


A relational theory of biological systems

Robert Rosen


Anticipatory Systems

Robert Rosen


A relational theory of biological systems II

Robert Rosen


The representation of biological systems from the standpoint of the theory of categories

Robert Rosen


Robert Rosen’s anticipatory systems

A.H. Louie’s_anticipatory_systems/links/09e4150cdd961e4a87000000.pdf


A Critical Evaluation of Luhmann’s Theory of Social Systems



Systems biology: The reincarnation of systems theory applied in biology?

Olaf Wolkenhauer

Date received (in revised form): 5th June 2001







Dr. John Jay Kineman, Ph.D


The Dawn of Mathematical Biology


Daniel Sander Hoffmann


Modeling Living Systems

Peter Andras


theory of organismic sets and mathematical relations


Tracing organizing principles:

Learning from the history of systems biology



Eliseo Fernández


Autopoietic and (M,R) systems

Juan Carlos Letelier, Gonzalo Mar!ın, Jorge Mpodozis






Some Thoughts on A. H. Louie’s ‘‘More Than Life Itself: A Reflection on Formal Systems and Biology’’

Claudio Gutie ́rrez • Sebastia ́n Jaramillo • Jorge Soto-Andrade


Relational Models of Social Systems



A Unified Approach to Biological and Social Organisms

N. Rashevsky


Rosen’s (M,R) system in process algebra

Derek Gatherer1,3* and Vashti Galpin2



The reflection of life: functional entailment and imminence in relational biology,

by A. H. Louie,

Springer, New York, NY, 2013, xxxii + 243 pp., ISBN 978-1-4614-6927-8


Even more than life itself: beyond complexity

Donald C. Mikulecky


Rosen R (1991)

 Life itself: a comprehensive inquiry into the nature, origin, and fabrication of life.

Columbia University Press, New York


Rosen R (2000)

Essays on life itself.

Columbia University Press, New York


Prolegomena: What Speaks in Favorof an Inquiry into Anticipatory Processes?

Mihai Nadin



Eliseo Fernández


An Introduction to the Ontology of Anticipation

Roberto Poli


Autopoiesis 40 years Later. A Review and a Reformulation

Pablo Razeto-Barry


The mathematical biophysics of Nicolas Rashevsky

Paul Cull


The spread of hierarchical cycles

A.H. Louiea* and Roberto Poli


Louie, A.H.,


More than life itself: a synthetic continuation in relational biology.


Catalysis at the Origin of Life Viewed in the Light of the (M,R)-Systems of Robert Rosen

Athel Cornish-Bowden* and María Luz Cμrdenas



Luhmann, Niklas.

“Insistence on systems theory: Perspectives from Germany-An essay.”

Social Forces (1983): 987-998.


Luhmann N. (1986)

The autopoiesis of social systems.

In: Geyer F. & van der Zouwen J. (eds.) Sociocybernetic paradoxes. Sage, London: 172–192.



Gotthard Bechmann and Nico Stehr


Luhmann, N.

“Essays on Self Reference.




Mingers J. (2002)

Can social systems be autopoietic? Assessing Luhmann’s social theory.

Sociological Review 50(2): 278–299.


Mingers J. (1989)

An Introduction to Autopoiesis – Implications and Applications.

Systems Practice 2(2): 159–180.



Maturana H. R. (1980)

Autopoiesis: Reproduction, heredity and evolution.

In: Zeleny M. (ed.) Autopoiesis, dissipative structures and spontaneous social orders, AAAS Selected Symposium 55 (AAAS National Annual Meeting, Houston TX, 3–8 January 1979). Westview Press, Boulder CO: 45–79







Varela F. J. (1980)

Describing the logic of the living. The adequacy and limitations of the idea of autopoiesis.

In: Zeleny M. (ed.) Autopoiesis: A theory of living organization. North-Holland, New York: 36–48



What Is Autopoiesis?

Milan Zeleny


Autopoiesis, a Theory of Living Organizations

Milan Zeleny


Maturana H. R. (1980)

Man and society.

In: Benseler F., Hejl P. M. & Köck W. K. (eds.) Autopoiesis, communication, and society: The theory of autopoietic systems in the social sciences


Order through fluctuation: Self-organization and social system

Ilya Prigogine

In Erich Jantsch (ed.), Evolution and Consciousness: Human Systems in Transition. Reading Ma: Addison-Wesley 93–130 (1976)


Maturana H. R. (1981)


In: Zeleny M. (ed.) Autopoiesis: A theory of the living organization. Westview Press, Boulder CO: 21–33.


Maturana H. R. (2002)
Autopoiesis, structural coupling and cognition: A history of these and other notions in the biology of cognition.
Cybernetics & Human Knowing 9(3–4): 5–34.



Pier Luigi Luisi

Autopoiesis: a review and a reappraisal


From autopoiesis to neurophenomenology:
Francisco Varela’s exploration of the biophysics of being



Life and mind: From autopoiesis to neurophenomenology. A tribute to Francisco Varela

EVAN THOMPSON,%20Evan%20-%20Life%20and%20Mind%20From%20autopoiesis%20to%20neurophenomenology.pdf


Autopoiesis, Communication, and Society: The Theory of Autopoietic Systems in the Social Sciences

Frank Benseler, Peter M. Hejl & Wolfram K. Köck


Boden M. (2000)

Autopoiesis and life.

Cognitive Science Quarterly 1: 117–145.


Systems Typologies in the Light of Autopoiesis: A Reconceptualization of Boulding’s Hierarchy, and a Typology of Self-Referential Systems

John Mingers’s_Hierarchy_and_a_typology_of_self-referential_systems/links/550181e60cf24cee39f79f7c.pdf


The Problems of Social Autopoiesis

John Mingers


Varela F. J. (1996)

The early days of autopoiesis: Heinz and Chile.

Systems Research 13(3): 407–417


Uribe R. B. (1981)

Modeling autopoiesis.

In: Zeleny M. (ed.) Autopoiesis: A theory of living organization. Elsevier North Holland, New York: 49–62.


Some Remarks on Autocatalysis and Autopoiesis

Barry McMullin



Category Theoretical Distinction between Autopoiesis and (M,R) Systems

Tatsuya Nomura


Smith J. D. (2014)

Self-concept: Autopoiesis as the Basis for a Conceptual Framework.

Systems Research and Behavioral Science 31(1): 32–46.


Fleischaker G. R. (1992)

Questions concerning the ontology of autopoiesis and the limits of its utility.

International Journal of General Systems, 21(2): 131–141.


Villalobos M. & Ward D. (2015)

Living systems: Autopoiesis, autonomy and enaction.

Philosophy & Technology 28(2): 225–239.


A Calculus for Autopoiesis

Dirk Baecker

June 1, 2012


The Sciences of Complexity and “Origins of Order”

Stuart A. Kauffman



Approaches to the Origin of Life on Earth

Stuart A. Kauffman



The phase transition in random catalytic sets


Rudolf Hanel, Stuart A. Kauffman, and Stefan Thurner


 Autocatalytic Sets: From the Origin of Life to the Economy

Wim Hordijk


Autocatalysis, Information and Coding

Peter R. Willis


Autocatalytic sets and boundaries

Wim Hordijk and Mike Steel*~hmac=6760deec426b5c9098efc365d7e9f047b20e06f02e1216aca77226e764abda13


Catalysis at the Origin of Life Viewed in the Light of the (M,R)-Systems of Robert Rosen

Athel Cornish-Bowden and María Luz Cμrdenas


Closure to efficient causation, computability and artificial life

Mar ́ıa Luz Ca ́rdenasa,∗ Juan-Carlos Letelierb, Claudio Gutie ́rrezc, Athel Cornish-Bowdena and Jorge Soto-Andrade


Autopoietic and (M,R) systems

Juan Carlos Letelier*, Gonzalo Mar!ın, Jorge Mpodozis



J. C. Letelier(1) and A. N. Zaretzky



Economics And The Collectively Autocatalytic Structure Of The Real Economy

November 21, 201112:28 PM ET






Author: Mayank Chaturvedi

You can contact me using this email mchatur at the rate of AOL.COM. My professional profile is on

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