The emergence of a self-catalysing structure in abstract origin-of-life models

We formalize a class of abstract and simple biochemical models that have been proposed for understanding the origin of life. We then analyse conditions under which 'life-like' substructures will tend to arise in such models

Interior operators and their relationship to autocatalytic networks

Given a set of elements, the reactions between them (chemical or otherwise), and certain elements catalysing certain reactions, a Reflexively Autocatalytic F-generated (RAF) set is a subset $R'$ of reactions that is self-generating from a given food set, and with each reaction in $R'$ being catalysed from within $R'$. RAF theory has been applied to various phenomena in theoretical biology, and a key feature of the approach is that it is possible to efficiently identify and classify RAFs within large systems. This is possible because RAFs can be described as the (nonempty) subsets of the reactions that are the fixed points of an (efficiently computable) interior map that operates on subsets of reactions. Although the main generic results concerning RAFs can be derived using just this property, we show that for systems with at least 12 reactions there are generic results concerning RAFs that cannot be proven using the interior operator property alone.Comment: 11 pages, 1 figur

Autocatalytic sets in a partitioned biochemical network

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 catalytic polymer networks. We present here an extension in which there are two "independent" polymer sets, where catalysis occurs within and between the sets, but there are no reactions combining polymers from both sets. Such an extension reflects the interaction between nucleic acids and peptides observed in modern cells and proposed forms of early life.Comment: 28 pages, 8 figure

Required Levels of Catalysis for Emergence of Autocatalytic Sets in Models of Chemical Reaction Systems

The formation of a self-sustaining autocatalytic chemical network is a necessary but not sufficient condition for the origin of life. The question of whether such a network could form “by chance” within a sufficiently complex suite of molecules and reactions is one that we have investigated for a simple chemical reaction model based on polymer ligation and cleavage. In this paper, we extend this work in several further directions. In particular, we investigate in more detail the levels of catalysis required for a self-sustaining autocatalytic network to form. We study the size of chemical networks within which we might expect to find such an autocatalytic subset, and we extend the theoretical and computational analyses to models in which catalysis requires template matching

Field-control, phase-transitions, and life's emergence

Instances of critical-like characteristics in living systems at each organizational level as well as the spontaneous emergence of computation (Langton), indicate the relevance of self-organized criticality (SOC). But extrapolating complex bio-systems to life's origins, brings up a paradox: how could simple organics--lacking the 'soft matter' response properties of today's bio-molecules--have dissipated energy from primordial reactions in a controlled manner for their 'ordering'? Nevertheless, a causal link of life's macroscopic irreversible dynamics to the microscopic reversible laws of statistical mechanics is indicated via the 'functional-takeover' of a soft magnetic scaffold by organics (c.f. Cairns-Smith's 'crystal-scaffold'). A field-controlled structure offers a mechanism for bootstrapping--bottom-up assembly with top-down control: its super-paramagnetic components obey reversible dynamics, but its dissipation of H-field energy for aggregation breaks time-reversal symmetry. The responsive adjustments of the controlled (host) mineral system to environmental changes would bring about mutual coupling between random organic sets supported by it; here the generation of long-range correlations within organic (guest) networks could include SOC-like mechanisms. And, such cooperative adjustments enable the selection of the functional configuration by altering the inorganic network's capacity to assist a spontaneous process. A non-equilibrium dynamics could now drive the kinetically-oriented system towards a series of phase-transitions with appropriate organic replacements 'taking-over' its functions.Comment: 54 pages, pdf fil

Multiscale Dynamics of an Adaptive Catalytic Network

We study the multiscale structure of the Jain-Krishna adaptive network model. This model describes the co-evolution of a set of continuous-time autocatalytic ordinary differential equations and its underlying discrete-time graph structure. The graph dynamics is governed by deletion of vertices with asymptotically weak concentrations of prevalence and then re-insertion of vertices with new random connections. In this work we prove several results about convergence of the continuous-time dynamics to equilibrium points. Furthermore, we motivate via formal asymptotic calculations several conjectures regarding the discrete-time graph updates. In summary, our results clearly show that there are several time scales in the problem depending upon system parameters, and that analysis can be carried out in certain singular limits. This shows that for the Jain-Krishna model, and potentially many other adaptive network models, a mixture of deterministic and/or stochastic multiscale methods is a good approach to work towards a rigorous mathematical analysis.Comment: 21 page