scholarly journals Autocatalytic networks in biology: structural theory and algorithms

2019 ◽  
Vol 16 (151) ◽  
pp. 20180808 ◽  
Author(s):  
Mike Steel ◽  
Wim Hordijk ◽  
Joana C. Xavier
Keyword(s):  
Mathematical Analysis ◽  
General Setting ◽  
Structural Theory ◽  
Living Systems ◽  
General Notion ◽  
Graph Theoretic ◽  
Polynomial Time Algorithms ◽  
The Origin Of Life ◽  
Carry Over ◽  
Autocatalytic Networks

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 sustained from an ambient food set is also referred to more formally as a ‘reflexively autocatalytic food-generated’ (RAF) set. In this paper, we first investigate a simplified setting for studying RAFs, which is nevertheless relevant to real biochemistry and which allows an exact mathematical analysis based on graph-theoretic concepts. This, in turn, allows for the development of efficient (polynomial-time) algorithms for questions that are computationally intractable (NP-hard) in the general RAF setting. We then show how this simplified setting for RAF systems leads naturally to a more general notion of RAFs that are ‘generative’ (they can be built up from simpler RAFs) and for which efficient algorithms carry over to this more general setting. Finally, we show how classical RAF theory can be extended to deal with ensembles of catalysts as well as the assignment of rates to reactions according to which catalysts (or combinations of catalysts) are available.

scholarly journals The structure of autocatalytic networks, with application to early biochemistry

2020 ◽  
Vol 17 (171) ◽  
pp. 20200488
Author(s):  
Mike Steel ◽  
Joana C. Xavier ◽  
Daniel H. Huson
Keyword(s):  
Mathematical Model ◽  
Living Systems ◽  
Bacterial Metabolism ◽  
The Core ◽  
System Building ◽  
Formal Framework ◽  
The Origin Of Life ◽  
Key Features ◽  
Autocatalytic Networks ◽  
New Algorithms

Metabolism across all known living systems combines two key features. First, all of the molecules that are required are either available in the environment or can be built up from available resources via other reactions within the system. Second, the reactions proceed in a fast and synchronized fashion via catalysts that are also produced within the system. Building on early work by Stuart Kauffman, a precise mathematical model for describing such self-sustaining autocatalytic systems (RAF theory) has been developed to explore the origins and organization of living systems within a general formal framework. In this paper, we develop this theory further by establishing new relationships between classes of RAFs and related classes of networks, and developing new algorithms to investigate and visualize RAF structures in detail. We illustrate our results by showing how it reveals further details into the structure of archaeal and bacterial metabolism near the origin of life, and provide techniques to study and visualize the core aspects of primitive biochemistry.

scholarly journals The structure of autocatalytic networks, with application to early biochemistry

2020 ◽  
Author(s):  
Mike Steel ◽  
Joana C. Xavier ◽  
Daniel H. Huson
Keyword(s):  
Mathematical Model ◽  
Living Systems ◽  
Bacterial Metabolism ◽  
The Core ◽  
System Building ◽  
Formal Framework ◽  
The Origin Of Life ◽  
Key Features ◽  
Autocatalytic Networks ◽  
New Algorithms

AbstractMetabolism across all known living systems combines two key features. First, all of the molecules that are required are either available in the environment or can be built up from available resources via other reactions within the system. Second, the reactions proceed in a fast and synchronised fashion via catalysts that are also produced within the system. Building on early work by Stuart Kauffman, a precise mathematical model for describing such self-sustaining autocatalytic systems (RAF theory) has been developed to explore the origins and organisation of living systems within a general formal framework. In this paper, we develop this theory further by establishing new relationships between classes of RAFs and related classes of networks, and developing new algorithms to investigate and visualise RAF structures in detail. We illustrate our results by showing how it reveals further details into the structure of archaeal and bacterial metabolism near the origin of life, and provide techniques to study and visualise the core aspects of primitive biochemistry.

General discussion after session V

1988 ◽  
Vol 325 (1587) ◽  
pp. 611-618 ◽  
Keyword(s):  
Origin Of Life ◽  
Time Perspective ◽  
Applied Mathematics ◽  
Building Blocks ◽  
Living Systems ◽  
Organic Chemical ◽  
General Terms ◽  
The Earth ◽  
The Origin Of Life ◽  
Emergence Of Life

N. C. Wickramasinghe ( Department of Applied Mathematics and Astronomy, University College, Cardiff, U. K. ). The question of the origin of life is, of course, one of the most important scientific questions and it is also one of the most difficult. One is inevitably faced here with a situation where there are very few empirical facts of direct relevance and perhaps no facts relating to the actual transition from organic material to material that can even remotely be described as living. The time perspective of events that relate to this problem has already been presented by Dr Chang. Uncertainty still persists as to the actual first moment of the origin or the emergence of life on the Earth. At some time between 3800 and 3300 Ma BP the first microscopic living systems seem to have emerged. There is a definite moment in time corresponding to a sudden appearance of cellular-type living systems. Now, traditionally the evolution of carbonaceous compounds which led to the emergence of life on Earth could be divided into three principal steps and I shall just remind you what those steps are. The first step is the production of chemical building blocks that lead to the origin of the organic molecules necessary as a prerequisite for the evolution of life. Step two can be described in general terms as prebiotic evolution, the arrangement of these chemical units into some kind of sequence of precursor systems that come almost up to life but not quite; and then stage three is the early biological evolution which actually effects the transition from proto-cellular organic-type forms into truly cellular living systems. The transition is from organic chemistry, prebiotic chemistry to biochemistry. Those are the three principal stages that have been defined by traditional workers in the field, the people who, as Dr Chang said, have had the courage to make these queries and attempt to answer them. Ever since the classic experiments where organic materials were synthesized in the laboratory a few decades back, it was thought that the first step, the production of organic chemical units, is important for the origin of life on the Earth, and that this had to take place in some location on the Earth itself.

Artificial Life as a Tool for Biological Inquiry

1993 ◽  
Vol 1 (1_2) ◽  
pp. 1-13 ◽  
Author(s):  
Charles Taylor ◽  
David Jefferson
Keyword(s):  
Cultural Evolution ◽  
Artificial Life ◽  
Living Systems ◽  
Grand Challenge ◽  
Open Problems ◽  
Maintenance Of Sex ◽  
Open Questions ◽  
Shifting Balance ◽  
The Origin Of Life ◽  
Natural Life

Artificial life embraces those human-made systems that possess some of the key properties of natural life. We are specifically interested in artificial systems that serve as models of living systems for the investigation of open questions in biology. First we review some of the artificial life models that have been constructed with biological problems in mind, and classify them by medium (hardware, software, or “wetware”) and by level of organization (molecular, cellular, organismal, or population). We then describe several “grand challenge” open problems in biology that seem especially good candidates to benefit from artificial life studies, including the origin of life and self-organi- zation, cultural evolution, origin and maintenance of sex, shifting balance in evolution, the relation between fitness and adaptedness, the structure of ecosystems, and the nature of mind.

scholarly journals LIFE AS WE DO NOT KNOW IT

2021 ◽  
Author(s):  
soumya banerjee
Keyword(s):  
Information Processing ◽  
Computational Model ◽  
Origin Of Life ◽  
Critical Role ◽  
Life Forms ◽  
Living Systems ◽  
Computational Simulations ◽  
The Origin Of Life ◽  
Carbon Based

Information plays a critical role in complex biologicalsystems. This article proposes a role for information processing in questions around the origin of life and suggests how computational simulations may yield insights into questions related to the origin of life. Such a computational model of the origin of life would unify thermodynamics with information processing and we would gain an appreciation of why proteins and nucleotides evolved as the substrate of computation andinformation processing in living systems that we see on Earth. Answers to questions like these may give us insights into noncarbon based forms of life that we could search for outside Earth. I hypothesize that carbon-based life forms are only one amongst a continuum of life-like systems in the universe.Investigations into the role of computational substrates that allow information processing is important and could yield insights into:1) novel non-carbon based computational substrates thatmay have “life-like” properties, and2) how life may have actually originated from non-life onEarth. Life may exist as a continuum between non-life and life and we may have to revise our notion of life and how common it is in the universe.Looking at life or life-like phenomena through the lens ofinformation theory may yield a broader view of life.

scholarly journals Mathematical analysis of laboratory microbial experiments demonstrating deterministic chaotic dynamics

2021 ◽  
Author(s):  
Fred Molz ◽  
Boris Faybishenko
Keyword(s):  
Dilution Rate ◽  
Mathematical Analysis ◽  
Chaotic Dynamics ◽  
Minimum Energy ◽  
Living Systems ◽  
Microbial Populations ◽  
Classical Dynamics ◽  
Monod Kinetics ◽  
Model Simulations ◽  
Minimum Energy Dissipation

AbstractPresented is a system of four ordinary differential equations and a mathematical analysis of microbiological experiments in a four-component chemostat—nutrient n, rods r, cocci c, and predators p. The analysis is consistent with the conclusion that previous experiments produced features of deterministic chaotic and classical dynamics depending on dilution rate. The surrogate model incorporates as much experimental detail as possible, but necessarily contains unmeasured parameters. The objective is to understand better the differences between model simulations and experimental results in complex microbial populations. The key methodology for simulation of chaotic dynamics, consistent with the measured dilution rate and microbial volume averages, was to cause the preference of p for r vs. c to vary with the r and c concentrations, to make r more competitive for nutrient than c, and to recycle some dying p biomass, leading to a modified version of the Monod kinetics model. Our mathematical model demonstrated that the occurrence of chaotic dynamics requires a predator, p, preference for r versus c to increase significantly with increases in r and c populations. Also included is a discussion of several generalizations of the existing model and a possible involvement of the minimum energy dissipation principle. This principle appears fundamental to thermodynamic systems including living systems. Several new experiments are suggested.

scholarly journals Molecules, Information and the Origin of Life: What Is Next?

Molecules ◽  
2021 ◽  
Vol 26 (4) ◽  
pp. 1003
Author(s):  
Salvatore Chirumbolo ◽  
Antonio Vella
Keyword(s):  
Origin Of Life ◽  
Water Structure ◽  
Dissipative Structures ◽  
Living Systems ◽  
Complex Nature ◽  
Experimental Science ◽  
New Paradigm ◽  
Information Dynamics ◽  
Long Time ◽  
The Origin Of Life

How life did originate and what is life, in its deepest foundation? The texture of life is known to be held by molecules and their chemical-physical laws, yet a thorough elucidation of the aforementioned questions still stands as a puzzling challenge for science. Focusing solely on molecules and their laws has indirectly consolidated, in the scientific knowledge, a mechanistic (reductionist) perspective of biology and medicine. This occurred throughout the long historical path of experimental science, affecting subsequently the onset of the many theses and speculations about the origin of life and its maintenance. Actually, defining what is life, asks for a novel epistemology, a ground on which living systems’ organization, whose origin is still questioned via chemistry, physics and even philosophy, may provide a new key to focus onto the complex nature of the human being. In this scenario, many issues, such as the role of information and water structure, have been long time neglected from the theoretical basis on the origin of life and marginalized as a kind of scenic backstage. On the contrary, applied science and technology went ahead on considering molecules as the sole leading components in the scenery. Water physics and information dynamics may have a role in living systems much more fundamental than ever expected. Can an organism be simply explained by a mechanistic view of its nature or we need “something else”? Probably, we can earn sound foundations about life by simply changing our prejudicial view about living systems simply as complex, highly ordered machines. In this manuscript we would like to reappraise many fundamental aspects of molecular and chemical biology and reading them through a new paradigm, which includes Prigogine’s dissipative structures and informational dissipation (Shannon dissipation). This would provide readers with insightful clues about how biology and chemistry may be thoroughly revised, referring to new models, such as informational dissipation. We trust they are enabled to address a straightforward contribution in elucidating what life is for science. This overview is not simply a philosophical speculation, but it would like to affect deeply our way to conceive and describe the foundations of organisms’ life, providing intriguing suggestions for readers in the field.

W-Groups under Quadratic Extensions of Fields

2000 ◽  
Vol 52 (4) ◽  
pp. 833-848 ◽  
Author(s):  
Ján Mináč ◽  
Tara L. Smith
Keyword(s):  
General Setting ◽  
Quadratic Extension ◽  
Field Extension ◽  
Galois Groups ◽  
Real Field ◽  
Quadratic Extensions ◽  
Finite Subgroups ◽  
Carry Over ◽  
Rigid Element ◽  
Pythagorean Field

AbstractTo each field F of characteristic not 2, one can associate a certain Galois group , the so-called W-group of F, which carries essentially the same information as the Witt ring W(F) of F. In this paperwe investigate the connection between and (√a), where F(√a) is a proper quadratic extension of F. We obtain a precise description in the case when F is a pythagorean formally real field and a = −1, and show that the W-group of a proper field extension K/F is a subgroup of the W-group of F if and only if F is a formally real pythagorean field and K = F(√−1). This theorem can be viewed as an analogue of the classical Artin-Schreier’s theorem describing fields fixed by finite subgroups of absolute Galois groups. We also obtain precise results in the case when a is a double-rigid element in F. Some of these results carry over to the general setting.

Sign in / Sign up

Export Citation Format

Share Document