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All living systems -- from the origin of life to modern cells -- rely on a set of biochemical reactions that are simultaneously self-sustaining and autocatalytic. This notion of an autocatalytic set has been formalized graph-theoretically…

Molecular Networks · Quantitative Biology 2016-05-13 Wim Hordijk , Mike Steel

A key step in the origin of life is the emergence of a primitive metabolism. This requires the formation of a subset of chemical reactions that is both self-sustaining and collectively autocatalytic. A generic theory to study such processes…

Molecular Networks · Quantitative Biology 2019-10-22 Oliver Weller-Davies , Mike Steel , Jotun Hein

Self-sustaining autocatalytic networks play a central role in living systems, from metabolism at the origin of life, simple RNA networks, and the modern cell, to ecology and cognition. A collectively autocatalytic network that can be…

Molecular Networks · Quantitative Biology 2018-03-29 Mike Steel , Wim Hordijk

In previous work, RAF theory has been developed as a tool for making theoretical progress on the origin of life question, providing insight into the structure and occurrence of self-sustaining and collectively autocatalytic sets within…

Molecular Networks · Quantitative Biology 2013-10-18 Joshua I Smith , Mike Steel , Wim Hordijk

The emergence of an autocatalytic network from an available set of elements is a fundamental step in early evolutionary processes, such as the origin of metabolism. Given a set of elements, the reactions between them (chemical or…

Molecular Networks · Quantitative Biology 2023-08-30 Mike Steel

Autocatalysis lies at the heart of many (bio)chemical processes and is key to processes leading up to the origin of life. Two seemingly very different formalisms have emerged that define autocatalysis. Kauffman introduced collective…

Molecular Networks · Quantitative Biology 2026-05-26 Richard Golnik , Thomas Gatter , Wim Hordijk , Peter F. Stadler , Nicola Vassena

The emergence of autocatalytic sets of molecules seems to have played an important role in the origin of life context. Although the possibility to reproduce this emergence in laboratory has received considerable attention, this is still far…

Adaptation and Self-Organizing Systems · Physics 2015-02-04 Alessandro Filisetti , Marco Villani , Chiara Damiani , Alex Graudenzi , Andrea Roli , Wim Hordijk , Roberto Serra

Two alternative views of an economy are combined and studied. The first view is that of technological evolution as a process of combinatorial innovation. Recently a simple mathematical model (TAP) was introduced to study such a…

Molecular Networks · Quantitative Biology 2022-04-13 Wim Hordijk , Stuart Kauffman

Autocatalytic sets are self-catalyzing and self-sustaining chemical reaction networks that are believed to have played an important role in the origin of life. They have been studied extensively both theoretically as well as experimentally.…

Molecular Networks · Quantitative Biology 2023-03-06 Wim Hordijk

Background: Autocatalytic sets are often considered a necessary (but not sufficient) condition for the origin and early evolution of life. Although the idea of autocatalytic sets was already conceived of many years ago, only recently have…

Molecular Networks · Quantitative Biology 2012-06-06 Wim Hordijk , Mike Steel

Autocatalytic Sets are reaction networks theorised as networks at the basis of life. Their main feature is the ability of spontaneously emerging and self-reproducing. The Reflexively and Food-generated theory provides a formal definition of…

Molecular Networks · Quantitative Biology 2020-10-19 Alessandro Ravoni

We show that in a particular model of catalytic reaction systems, known as the binary polymer model, there is a mathematical invariance between two versions of the model: (1) random catalysis and (2) template-based catalysis. In particular,…

Populations and Evolution · Quantitative Biology 2011-10-06 Wim Hordijk , Mike Steel

An autocatalytic pattern matching polymer system is studied as an abstract model for chemical ecosystem evolution. Highly ordered populations with particular sequence patterns appear spontaneously out of a vast number of possible states.…

Molecular Networks · Quantitative Biology 2015-06-17 Shinpei Tanaka , Harold Fellermann , Steen Rasmussen

The ability of a chemical reaction network to generate itself by catalyzed reactions from constantly present environmental food sources is considered a fundamental property in origin-of-life research. Based on Kaufmann's autocatalytic sets,…

Molecular Networks · Quantitative Biology 2023-08-16 Dimitri Loutchko

Background: The idea that autocatalytic sets played an important role in the origin of life is not new. However, the likelihood of autocatalytic sets emerging spontaneously has long been debated. Recently, progress has been made along two…

Molecular Networks · Quantitative Biology 2012-11-16 Wim Hordijk , Mike Steel

We determine conditions under which a random biochemical system is likely to contain a subsystem that is both autocatalytic and able to survive on some ambient `food' source. Such systems have previously been investigated for their…

Molecular Networks · Quantitative Biology 2007-05-23 Elchanan Mossel , Mike Steel

Autocatalytic sets are sets of entities that mutually catalyse each other's production through chemical reactions from a basic food source. Recently, the reflexively autocatalytic and food generated theory has introduced a formal definition…

Adaptation and Self-Organizing Systems · Physics 2020-09-15 Alessandro Ravoni

Self-sustaining autocatalytic chemical networks represent a necessary, though not sufficient condition for the emergence of early living systems. These networks have been formalised and investigated within the framework of RAF theory, which…

Molecular Networks · Quantitative Biology 2012-12-19 Mike Steel , Wim Hordijk , Joshua Smith

The emergence of self-sustaining autocatalytic networks in chemical reaction systems has been studied as a possible mechanism for modelling how living systems first arose. It has been known for several decades that such networks will form…

Molecular Networks · Quantitative Biology 2020-11-24 Stuart Kauffman , Mike Steel

Biological responses often obey Weber's law, according to which the magnitude of the response depends only on the fold change in the external input. In this study, we demonstrate that a system involving a simple autocatalytic reaction shows…

Biological Physics · Physics 2015-03-19 Masayo Inoue , Kunihiko Kaneko
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