An
autocatalytic set is a collection of entities, each of which can be created
catalyticallyCatalysis is the process in which the rate of a chemical reaction is either increased or decreased by means of a chemical substance known as a catalyst. Unlike other reagents that participate in the chemical reaction, a catalyst is not consumed by the reaction itself. The catalyst may participate...
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
autocatalyticA single chemical reaction is said to have undergone autocatalysis, or be autocatalytic, if the reaction product is itself the catalyst for that reaction....
. Autocatalytic sets were originally and most concretely defined in terms of
molecular entitiesAccording to 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
sociologySociology is the scientific or systematic study of human societies. It is a branch of social science that uses various methods of empirical investigation and critical analysis to develop and refine a body of knowledge about human social structure and activity, often with the goal of applying such...
and
economicsEconomics is the social science that studies 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
mitosisMitosis is the process by which a eukaryotic cell separates the chromosomes in its cell nucleus into two identical sets in two daughter nuclei. It is generally followed immediately by cytokinesis, which divides the nuclei, cytoplasm, organelles and cell membrane into two daughter cells containing...
. 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 CrickWatson and Crick refers to the duo of James D. Watson and Francis Crick who, using x-ray data collected by Rosalind Franklin, proposed the double helix structure of the DNA molecule in 1953...
, biologists considered autocatalytic sets the way
metabolismMetabolism is the set of chemical reactions that occur in living organisms to maintain life. These processes allow organisms to grow and reproduce, maintain their structures, and respond to their environments. Metabolism is usually divided into two categories. Catabolism breaks down organic matter,...
functions in principle, i.e. one
proteinProteins are organic compounds made of amino acids arranged in a linear chain and folded into a globular form. The amino acids in a polymer chain are joined together by the peptide bonds between the carboxyl and amino groups of adjacent amino acid residues...
helps to synthesize another protein and so on. After the discovery of the
double helixIn geometry a double helix typically consists of two congruent helices with the same axis, differing by a translation along the axis, which may or may not be half-way....
, the
central dogma of molecular biologyThe central dogma of molecular biology was first enunciated by Francis Crick in 1958 and re-stated in a Nature paper published in 1970:In other words, 'once information gets into protein, it can't flow back to nucleic acid.'...
was formulated, which is that
DNADeoxyribonucleic acid is a nucleic acid that contains the genetic instructions used in the development and functioning of all known living organisms and some viruses. The main role of DNA molecules is the long-term storage of information...
is transcribed to
RNARibonucleic acid is a biologically important type of molecule that consists of a long chain of nucleotide units. Each nucleotide consists of a nitrogenous base, a ribose sugar, and a phosphate...
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 systemA 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.
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 KauffmanStuart 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
moleculeA molecule is defined as an electrically neutral group of at least two atoms in a definite arrangement held together by very strong chemical bonds. Molecules are distinguished from polyatomic ions in this strict sense...
s,
chemical reactionA chemical reaction is a process that leads to the transformation of one set of chemical substances to another. They are studied by chemists under a field of science called chemistry. Chemical reactions can be either spontaneous, requiring no input of energy, or non-spontaneous, often coming about...
s can be roughly defined as pairs r=(A, B) of subsets from M.
a
1 + a
2 + ... + a
n → b
1 + b
2 + ... + b
m
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
closureIn mathematics, a set is said to be closed under some operation if performance of that operation on members of the set always produces a member of the set...
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 growing number of molecules, the number of possible reactions and catalysations grows even stronger 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 molecules
for the same reason.
Such studies make autocatalytic sets candidates for a theoretical explanation of the very early origin of life, but are empirically unsupported in real chemistry.
Formal limitations
Formally, it is difficult to treat molecules as anything but unstructured
entities, since the set of possible reactions (and molecules) would become infinite. Therefore, a derivation of arbitrarily long
polymerA polymer is a large molecule composed of repeating structural units typically connected by covalent chemical bonds. While polymer in popular usage suggests plastic, the term actually refers to a large class of natural and synthetic materials with a variety of properties.Due to the extraordinary...
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 chemistryAn 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" constructorA 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 NeumannJohn von Neumann was a Hungarian American mathematician who made major contributions to a vast range of fields, including set theory, functional analysis, quantum mechanics, ergodic theory, continuous geometry, economics and game theory, computer science, numerical analysis, hydrodynamics John...
's
work on
self reproducingSelf-replication is any process by which a thing might make a copy of itself. Biological cells, given suitable environments, reproduce by cell division. During cell division, DNA is replicated and can be transmitted to offspring during reproduction. Biological viruses can reproduce, but only by...
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 are
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 constructionBootstrapping is a term used in computer science to describe the techniques involved in writing a compiler in the target programming language which it is intended to compile...
and in
operating systemsThe 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.