Autocatalytic set
Encyclopedia
An autocatalytic set is a collection of entities, each of which can be created catalytically
by other entities within the set, such that as a whole, the set is able to catalyze its own production. In this way the set as a whole is said to be autocatalytic
. Autocatalytic sets were originally and most concretely defined in terms of molecular entities
, but have more recently been metaphorically extended to the study of systems in sociology
and economics
.
Autocatalytic sets also have the ability to replicate themselves if they are split apart into two physically separated spaces. Computer models illustrate that split autocatalytic sets will reproduce all of the reactions of the original set in each half, much like cellular mitosis
. In effect, using the principles of autocatalysis, a small metabolism can replicate itself with very little high level organization. This property is why autocatalysis is a contender as the foundational mechanism for complex evolution.
Prior to Watson and Crick
, biologists considered autocatalytic sets the way metabolism
functions in principle, i.e. one protein
helps to synthesize another protein and so on. After the discovery of the double helix, the central dogma of molecular biology
was formulated, which is that DNA
is transcribed to RNA
which is translated to protein. The molecular structure of DNA and RNA, as well as the metabolism that maintains their reproduction, are believed to be too complex to have arisen spontaneously in one step from a soup of chemistry.
Several models of the origin of life are based on the notion that life may have arisen through the development of an initial molecular autocatalytic set which evolved over time. Most of these models which have emerged from the studies of complex system
s predict that life arose not from a molecule with any particular trait (such as self-replicating RNA) but from an autocatalytic set. The first empirical support came from Lincoln and Joyce, who obtained autocatalytic sets in which "two [RNA] enzymes catalyze each other’s synthesis from a total of four component substrates." Furthermore, an evolutionary process that began with a population of these self-replicators yielded a population dominated by recombinant
replicators.
Modern life has the traits of an autocatalytic set, since no particular molecule, nor any class of molecules, is able to replicate itself. There are several models based on autocatalytic sets, including those of Stuart Kauffman
and others.
s, chemical reaction
s can be roughly defined as pairs r=(A, B) of subsets from M.
a1 + a2 + ... + an → b1 + b2 + ... + bm
Let R be the set of allowable reactions. A pair (M, R) is a reaction system (RS).
A molecule m ∈ A ∩ B of a reaction r is a catalyst of this reaction.
A RS is autocatalytic, if all the catalysts for all its reactions are in M.
The above definition is not sufficient to describe dependency on external resources or nutrients.
This can be formulated by a closure
over a generating subset of M.
Formally, cl(S) denotes the smallest subset Y of M that contains S such that for each reaction (A, B)
A ⊆ S ∪ Y ⇒ B ⊆ Y
A RS is generated (over some resources S), if all reactants A in its reactions are in cl(S) and none
of the resources is a catalyst.
A generated autocatalytic set is an RS that is both autocatalytic and generated.
for the same reason. These theoretical results make autocatalytic sets attractive for scientific explanation of the very early origin of life.
entities, since the set of possible reactions (and molecules) would become infinite. Therefore, a derivation of arbitrarily long polymer
s as needed to model DNA, RNA or proteins is not possible, yet. Studies of the RNA World suffer from the same problem.
,
no agreed-upon notion of autocatalytic sets exists today.
While above, the notion of catalyst is secondary insofar that only the set as
a whole has to catalyse its own production, it is primary in other definitions,
giving the term "Autocatalytic Set" a different emphasis. There, every reaction
(or function, transformation) has to be mediated by a catalyst. As a consequence,
while mediating its respective reaction, every catalyst denotes
its reaction, too, resulting in a self denoting system, which is interesting
for two reasons. First, real metabolism is structured in this manner.
Second, self denoting systems can be considered as an intermediate step
towards self describing systems.
From both a structural and a natural historical point of view, one can
identify the ACS as seized in the formal definition the more original
concept, while in the second, the reflection of the system in itself is
already brought to an explicit presentation, since catalysts represent
the reaction induced by them. In ACS literature, both concept are present,
but differently emphasised.
To complete the classification from the other side, generalised self
reproducing systems move beyond self-denotation. There, no
unstructured entities carry the transformations anymore, but structured,
described ones. Formally, a generalised self reproducing system consists
of two function, u and c, together with their descriptions Desc(u) and
Desc(c) along following definition:
u : Desc(X) -> X
c : Desc(X) -> Desc(X)
where the function 'u' is the "universal" constructor
, that constructs
everything in its domain from appropriate descriptions, while 'c' is a copy
function for any description. Practically, 'u' and 'c' can fall apart into many subfunctions or catalysts.
Note that the (trivial) copy function 'c' is necessary because though the universal constructor 'u'
would be able to construct any description, too, the description it would base on, would in
general be longer than the result, rendering full self replication impossible.
This last concept can be attributed to von Neumann
's
work on self reproducing
automata, where he holds a self description necessary for any
non trivial (generalised) self reproducing system to avoid interferences. Von Neumann planned to design
such a system for a model chemistry, too.
to be considered autonomous or not. Often, autonomy of the sets is silently
assumed.
Likely, the above context has a strong emphasis on autonomous self replication
and early origin of life. But the concept of autocatalytic sets is really more general and
in practical use in various technical areas, e.g. where self-sustaining tool chains are
handled. Clearly, such sets are not autonomous and are objects of human agency.
Examples of practical importance of non-autonomous autocatalytic sets can be found e.g. in the field
of compiler construction
and in operating systems
,
where the self referential nature of the respective constructions is explicitly discussed,
very often in terms of the chicken and egg problem.
Catalysis
Catalysis is the change in rate of a chemical reaction due to the participation of a substance called a catalyst. Unlike other reagents that participate in the chemical reaction, a catalyst is not consumed by the reaction itself. A catalyst may participate in multiple chemical transformations....
by other entities within the set, such that as a whole, the set is able to catalyze its own production. In this way the set as a whole is said to be autocatalytic
Autocatalysis
A single chemical reaction is said to have undergone autocatalysis, or be autocatalytic, if the reaction product itself is the catalyst for that reaction....
. Autocatalytic sets were originally and most concretely defined in terms of molecular entities
Molecular entity
According to the IUPAC Gold Book a molecular entity is "any constitutionally or isotopically distinct atom, molecule, ion, ion pair, radical, radical ion, complex, conformer, etc., identifiable as a separately distinguishable entity"....
, but have more recently been metaphorically extended to the study of systems in sociology
Sociology
Sociology is the study of society. It is a social science—a term with which it is sometimes synonymous—which uses various methods of empirical investigation and critical analysis to develop a body of knowledge about human social activity...
and economics
Economics
Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...
.
Autocatalytic sets also have the ability to replicate themselves if they are split apart into two physically separated spaces. Computer models illustrate that split autocatalytic sets will reproduce all of the reactions of the original set in each half, much like cellular mitosis
Mitosis
Mitosis is the process by which a eukaryotic cell separates the chromosomes in its cell nucleus into two identical sets, in two separate nuclei. It is generally followed immediately by cytokinesis, which divides the nuclei, cytoplasm, organelles and cell membrane into two cells containing roughly...
. In effect, using the principles of autocatalysis, a small metabolism can replicate itself with very little high level organization. This property is why autocatalysis is a contender as the foundational mechanism for complex evolution.
Prior to Watson and Crick
Watson and Crick
James D. Watson and Francis Crick were the two co-discoverers of the structure of DNA in 1953. They used x-ray diffraction data collected by Rosalind Franklin and proposed the double helix or spiral staircase structure of the DNA molecule...
, biologists considered autocatalytic sets the way metabolism
Metabolism
Metabolism is the set of chemical reactions that happen in the cells of living organisms to sustain life. These processes allow organisms to grow and reproduce, maintain their structures, and respond to their environments. Metabolism is usually divided into two categories...
functions in principle, i.e. one protein
Protein
Proteins are biochemical compounds consisting of one or more polypeptides typically folded into a globular or fibrous form, facilitating a biological function. A polypeptide is a single linear polymer chain of amino acids bonded together by peptide bonds between the carboxyl and amino groups of...
helps to synthesize another protein and so on. After the discovery of the double helix, the central dogma of molecular biology
Central dogma of molecular biology
The central dogma of molecular biology was first articulated by Francis Crick in 1958 and re-stated in a Nature paper published in 1970:In other words, the process of producing proteins is irreversible: a protein cannot be used to create DNA....
was formulated, which is that DNA
DNA
Deoxyribonucleic acid is a nucleic acid that contains the genetic instructions used in the development and functioning of all known living organisms . The DNA segments that carry this genetic information are called genes, but other DNA sequences have structural purposes, or are involved in...
is transcribed to RNA
RNA
Ribonucleic acid , or RNA, is one of the three major macromolecules that are essential for all known forms of life....
which is translated to protein. The molecular structure of DNA and RNA, as well as the metabolism that maintains their reproduction, are believed to be too complex to have arisen spontaneously in one step from a soup of chemistry.
Several models of the origin of life are based on the notion that life may have arisen through the development of an initial molecular autocatalytic set which evolved over time. Most of these models which have emerged from the studies of complex system
Complex system
A complex system is a system composed of interconnected parts that as a whole exhibit one or more properties not obvious from the properties of the individual parts....
s predict that life arose not from a molecule with any particular trait (such as self-replicating RNA) but from an autocatalytic set. The first empirical support came from Lincoln and Joyce, who obtained autocatalytic sets in which "two [RNA] enzymes catalyze each other’s synthesis from a total of four component substrates." Furthermore, an evolutionary process that began with a population of these self-replicators yielded a population dominated by recombinant
Recombination
Recombination may refer to:* Recombination , the process by which genetic material is broken and joined to other genetic material* Recombination , in semiconductors, the elimination of mobile charge carriers...
replicators.
Modern life has the traits of an autocatalytic set, since no particular molecule, nor any class of molecules, is able to replicate itself. There are several models based on autocatalytic sets, including those of Stuart Kauffman
Stuart Kauffman
Stuart Alan Kauffman is an American theoretical biologist and complex systems researcher concerning the origin of life on Earth...
and others.
Formal definition
Given a set M of moleculeMolecule
A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...
s, chemical reaction
Chemical reaction
A chemical reaction is a process that leads to the transformation of one set of chemical substances to another. Chemical reactions can be either spontaneous, requiring no input of energy, or non-spontaneous, typically following the input of some type of energy, such as heat, light or electricity...
s can be roughly defined as pairs r=(A, B) of subsets from M.
a1 + a2 + ... + an → b1 + b2 + ... + bm
Let R be the set of allowable reactions. A pair (M, R) is a reaction system (RS).
A molecule m ∈ A ∩ B of a reaction r is a catalyst of this reaction.
A RS is autocatalytic, if all the catalysts for all its reactions are in M.
The above definition is not sufficient to describe dependency on external resources or nutrients.
This can be formulated by a closure
Closure (mathematics)
In mathematics, a set is said to be closed under some operation if performance of that operation on members of the set always produces a unique member of the same set. For example, the real numbers are closed under subtraction, but the natural numbers are not: 3 and 8 are both natural numbers, but...
over a generating subset of M.
Formally, cl(S) denotes the smallest subset Y of M that contains S such that for each reaction (A, B)
A ⊆ S ∪ Y ⇒ B ⊆ Y
A RS is generated (over some resources S), if all reactants A in its reactions are in cl(S) and none
of the resources is a catalyst.
A generated autocatalytic set is an RS that is both autocatalytic and generated.
Probability that a random set is autocatalytic
Studies of the above model show that random RS can be autocatalytic with high probability under some assumptions. This comes from the fact that with a growing number of molecules, the number of possible reactions and catalysations grows even larger if the molecules grow in complexity, producing stochastically enough reactions and catalysations to make a part of the RS self-supported. An autocatalytic set then extends very quickly with growing number of moleculesfor the same reason. These theoretical results make autocatalytic sets attractive for scientific explanation of the very early origin of life.
Formal limitations
Formally, it is difficult to treat molecules as anything but unstructuredentities, since the set of possible reactions (and molecules) would become infinite. Therefore, a derivation of arbitrarily long polymer
Polymer
A polymer is a large molecule composed of repeating structural units. These subunits are typically connected by covalent chemical bonds...
s as needed to model DNA, RNA or proteins is not possible, yet. Studies of the RNA World suffer from the same problem.
Linguistic aspects
Contrary to the above definition, which applies to the field of Artificial chemistryArtificial chemistry
An artificial chemistry is a computer model used to simulate various types of systems. Artificial chemistry is in some ways similar to a chemical reaction, hence the name...
,
no agreed-upon notion of autocatalytic sets exists today.
While above, the notion of catalyst is secondary insofar that only the set as
a whole has to catalyse its own production, it is primary in other definitions,
giving the term "Autocatalytic Set" a different emphasis. There, every reaction
(or function, transformation) has to be mediated by a catalyst. As a consequence,
while mediating its respective reaction, every catalyst denotes
its reaction, too, resulting in a self denoting system, which is interesting
for two reasons. First, real metabolism is structured in this manner.
Second, self denoting systems can be considered as an intermediate step
towards self describing systems.
From both a structural and a natural historical point of view, one can
identify the ACS as seized in the formal definition the more original
concept, while in the second, the reflection of the system in itself is
already brought to an explicit presentation, since catalysts represent
the reaction induced by them. In ACS literature, both concept are present,
but differently emphasised.
To complete the classification from the other side, generalised self
reproducing systems move beyond self-denotation. There, no
unstructured entities carry the transformations anymore, but structured,
described ones. Formally, a generalised self reproducing system consists
of two function, u and c, together with their descriptions Desc(u) and
Desc(c) along following definition:
u : Desc(X) -> X
c : Desc(X) -> Desc(X)
where the function 'u' is the "universal" constructor
Universal constructor
A universal constructor may refer to*Universal assembler, a hypothesized nanotechnology device for building a large class of nanomachines including itself, or...
, that constructs
everything in its domain from appropriate descriptions, while 'c' is a copy
function for any description. Practically, 'u' and 'c' can fall apart into many subfunctions or catalysts.
Note that the (trivial) copy function 'c' is necessary because though the universal constructor 'u'
would be able to construct any description, too, the description it would base on, would in
general be longer than the result, rendering full self replication impossible.
This last concept can be attributed to von Neumann
John von Neumann
John von Neumann was a Hungarian-American mathematician and polymath who made major contributions to a vast number of fields, including set theory, functional analysis, quantum mechanics, ergodic theory, geometry, fluid dynamics, economics and game theory, computer science, numerical analysis,...
's
work on self reproducing
Self-replication
Self-replication is any behavior of a dynamical system that yields construction of an identical copy of that dynamical system. Biological cells, given suitable environments, reproduce by cell division. During cell division, DNA is replicated and can be transmitted to offspring during reproduction...
automata, where he holds a self description necessary for any
non trivial (generalised) self reproducing system to avoid interferences. Von Neumann planned to design
such a system for a model chemistry, too.
Non-autonomous autocatalytic sets
Virtually all articles on autocatalytic sets leave open whether the sets areto be considered autonomous or not. Often, autonomy of the sets is silently
assumed.
Likely, the above context has a strong emphasis on autonomous self replication
and early origin of life. But the concept of autocatalytic sets is really more general and
in practical use in various technical areas, e.g. where self-sustaining tool chains are
handled. Clearly, such sets are not autonomous and are objects of human agency.
Examples of practical importance of non-autonomous autocatalytic sets can be found e.g. in the field
of compiler construction
Bootstrapping (compilers)
In computer science, bootstrapping is the process of writing a compiler in the target programming language which it is intended to compile...
and in operating systems
Self-hosting
The term self-hosting was coined to refer to the use of a computer program as part of the toolchain or operating system that produces new versions of that same program—for example, a compiler that can compile its own source code. Self-hosting software is commonplace on personal computers and larger...
,
where the self referential nature of the respective constructions is explicitly discussed,
very often in terms of the chicken and egg problem.