Small-molecule autocatalytic networks are universal metabolic fossils.

Life and the genetic code are self-referential and so are autocatalytic networks made of simpler, small molecules. Several origins of life theories postulate autocatalytic chemical networks preceding the primordial genetic code, yet demonstration with biochemical systems is lacking. Here, small-molecule reflexively autocatalytic food-generated networks (RAFs) ranging in size from 3 to 619 reactions were found in all of 6683 prokaryotic metabolic networks searched. The average maximum RAF size is 275 reactions for a rich organic medium and 93 for a medium with a single organic cofactor, NAD. In the rich medium, all universally essential metabolites are produced with the exception of glycerol-1-p (archaeal lipid precursor), phenylalanine, histidine and arginine. The 300 most common reactions, present in at least 2732 RAFs, are mostly involved in amino acid biosynthesis and the metabolism of carbon, 2-oxocarboxylic acid and purines. ATP and NAD are central in generating network complexity, and because ATP is also one of the monomers of RNA, autocatalytic networks producing redox and energy currencies are a strong candidate niche of the origin of a primordial information-processing system. The wide distribution of small-molecule autocatalytic networks indicates that molecular reproduction may be much more prevalent in the Universe than hitherto predicted. This article is part of the theme issue 'Emergent phenomena in complex physical and socio-technical systems: from cells to societies'.

Is There a Fourth Law for Non-Ergodic Systems That Do Work to Construct Their Expanding Phase Space?

Substantial grounds exist to doubt the universal validity of the Newtonian Paradigm that requires a pre-stated, fixed phase space. Therefore, the Second Law of Thermodynamics, stated only for fixed phase spaces, is also in doubt. The validity of the Newtonian Paradigm may stop at the onset of evolving life. Living cells and organisms are Kantian Wholes that achieve constraint closure, so do thermodynamic work to construct themselves. Evolution constructs an ever-expanding phase space. Thus, we can ask the free energy cost per added degree of freedom. That cost is roughly linear or sublinear in the mass constructed. However, the resulting expansion of the phase space is exponential or even hyperbolic. Thus, the evolving biosphere does thermodynamic work to construct itself into an ever-smaller sub-domain of its ever-expanding phase space at ever less free energy cost per added degree of freedom. The universe is not correspondingly disordered. Entropy, remarkably, really does decrease. A testable implication of this, termed here the Fourth Law of Thermodynamics, is that at constant energy input, the biosphere will construct itself into an ever more localized subregion of its ever-expanding phase space. This is confirmed. The energy input from the sun has been roughly constant for the 4 billion years since life started to evolve. The localization of our current biosphere in its protein phase space is at least 10-2540. The localization of our biosphere with respect to all possible molecules of CHNOPS comprised of up to 350,000 atoms is also extremely high. The universe has not been correspondingly disordered. Entropy has decreased. The universality of the Second Law fails.

Quantum Gravity If Non-Locality Is Fundamental.

I take non-locality to be the Michelson-Morley experiment of the early 21st century, assume its universal validity, and try to derive its consequences. Spacetime, with its locality, cannot be fundamental, but must somehow be emergent from entangled coherent quantum variables and their behaviors. There are, then, two immediate consequences: (i). if we start with non-locality, we need not explain non-locality. We must instead explain an emergence of locality and spacetime. (ii). There can be no emergence of spacetime without matter. These propositions flatly contradict General Relativity, which is foundationally local, can be formulated without matter, and in which there is no "emergence" of spacetime. If these be true, then quantum gravity cannot be a minor alteration of General Relativity but must demand its deep reformulation. This will almost inevitably lead to: matter not only curves spacetime, but "creates" spacetime. We will see independent grounds for the assertion that matter both curves and creates spacetime that may invite a new union of quantum gravity and General Relativity. This quantum creation of spacetime consists of: (i) fully non-local entangled coherent quantum variables. (ii) The onset of locality via decoherence. (iii) A metric in Hilbert space among entangled quantum variables by the sub-additive von Neumann entropy between pairs of variables. (iv) Mapping from metric distances in Hilbert space to metric distances in classical spacetime by episodic actualization events. (v) Discrete spacetime is the relations among these discrete actualization events. (vi) "Now" is the shared moment of actualization of one among the entangled variables when the amplitudes of the remaining entangled variables change instantaneously. (vii) The discrete, successive, episodic, irreversible actualization events constitute a quantum arrow of time. (viii) The arrow of time history of these events is recorded in the very structure of the spacetime constructed. (ix) Actual Time is a succession of two or more actual events. The theory inevitably yields a UV cutoff of a new type. The cutoff is a phase transition between continuous spacetime before the transition and discontinuous spacetime beyond the phase transition. This quantum creation of spacetime modifies General Relativity and may account for Dark Energy, Dark Matter, and the possible elimination of the singularities of General Relativity. Relations to Causal Set Theory, faithful Lorentzian manifolds, and past and future light cones joined at "Actual Now" are discussed. Possible observational and experimental tests based on: (i). the existence of Sub- Planckian photons, (ii). knee and ankle discontinuities in the high-energy gamma ray spectrum, and (iii). possible experiments to detect a creation of spacetime in the Casimir system are discussed. A quantum actualization enhancement of repulsive Casimir effect would be anti-gravitational and of possible practical use. The ideas and concepts discussed here are not yet a theory, but at most the start of a framework that may be useful.

A Testable Theory for the Emergence of the Classical World.

The transition from the quantum to the classical world is not yet understood. Here, we take a new approach. Central to this is the understanding that measurement and actualization cannot occur except on some specific basis. However, we have no established theory for the emergence of a specific basis. Our framework entails the following: (i) Sets of N entangled quantum variables can mutually actualize one another. (ii) Such actualization must occur in only one of the 2N possible bases. (iii) Mutual actualization progressively breaks symmetry among the 2N bases. (iv) An emerging "amplitude" for any basis can be amplified by further measurements in that basis, and it can decay between measurements. (v) The emergence of any basis is driven by mutual measurements among the N variables and decoherence with the environment. Quantum Zeno interactions among the N variables mediates the mutual measurements. (vi) As the number of variables, N, increases, the number of Quantum Zeno mediated measurements among the N variables increases. We note that decoherence alone does not yield a specific basis. (vii) Quantum ordered, quantum critical, and quantum chaotic peptides that decohere at nanosecond versus femtosecond time scales can be used as test objects. (viii) By varying the number of amino acids, N, and the use of quantum ordered, critical, or chaotic peptides, the ratio of decoherence to Quantum Zeno effects can be tuned. This enables new means to probe the emergence of one among a set of initially entangled bases via weak measurements after preparing the system in a mixed basis condition. (ix) Use of the three stable isotopes of carbon, oxygen, and nitrogen and the five stable isotopes of sulfur allows any ten atoms in the test protein to be discriminably labeled and the basis of emergence for those labeled atoms can be detected by weak measurements. We present an initial mathematical framework for this theory, and we propose experiments.

Attractor-Specific and Common Expression Values in Random Boolean Network Models (with a Preliminary Look at Single-Cell Data).

Random Boolean Networks (RBNs for short) are strongly simplified models of gene regulatory networks (GRNs), which have also been widely studied as abstract models of complex systems and have been used to simulate different phenomena. We define the "common sea" (CS) as the set of nodes that take the same value in all the attractors of a given network realization, and the "specific part" (SP) as the set of all the other nodes, and we study their properties in different ensembles, generated with different parameter values. Both the CS and of the SP can be composed of one or more weakly connected components, which are emergent intermediate-level structures. We show that the study of these sets provides very important information about the behavior of the model. The distribution of distances between attractors is also examined. Moreover, we show how the notion of a "common sea" of genes can be used to analyze data from single-cell experiments.

On the Criticality of Adaptive Boolean Network Robots.

Systems poised at a dynamical critical regime, between order and disorder, have been shown capable of exhibiting complex dynamics that balance robustness to external perturbations and rich repertoires of responses to inputs. This property has been exploited in artificial network classifiers, and preliminary results have also been attained in the context of robots controlled by Boolean networks. In this work, we investigate the role of dynamical criticality in robots undergoing online adaptation, i.e., robots that adapt some of their internal parameters to improve a performance metric over time during their activity. We study the behavior of robots controlled by random Boolean networks, which are either adapted in their coupling with robot sensors and actuators or in their structure or both. We observe that robots controlled by critical random Boolean networks have higher average and maximum performance than that of robots controlled by ordered and disordered nets. Notably, in general, adaptation by change of couplings produces robots with slightly higher performance than those adapted by changing their structure. Moreover, we observe that when adapted in their structure, ordered networks tend to move to the critical dynamical regime. These results provide further support to the conjecture that critical regimes favor adaptation and indicate the advantage of calibrating robot control systems at dynamical critical states.

Inferring evolutionary pathways and directed genotype networks of foodborne pathogens.

Modelling the emergence of foodborne pathogens is a crucial step in the prediction and prevention of disease outbreaks. Unfortunately, the mechanisms that drive the evolution of such continuously adapting pathogens remain poorly understood. Here, we combine molecular genotyping with network science and Bayesian inference to infer directed genotype networks-and trace the emergence and evolutionary paths-of Salmonella Typhimurium (STM) from nine years of Australian disease surveillance data. We construct networks where nodes represent STM strains and directed edges represent evolutionary steps, presenting evidence that the structural (i.e., network-based) features are relevant to understanding the functional (i.e., fitness-based) progression of co-evolving STM strains. This is argued by showing that outbreak severity, i.e., prevalence, correlates to: (i) the network path length to the most prevalent node (r = -0.613, N = 690); and (ii) the network connected-component size (r = 0.739). Moreover, we uncover distinct exploration-exploitation pathways in the genetic space of STM, including a strong evolutionary drive through a transition region. This is examined via the 6,897 distinct evolutionary paths in the directed network, where we observe a dominant 66% of these paths decrease in network centrality, whilst increasing in prevalence. Furthermore, 72.4% of all paths originate in the transition region, with 64% of those following the dominant direction. Further, we find that the length of an evolutionary path strongly correlates to its increase in prevalence (r = 0.497). Combined, these findings indicate that longer evolutionary paths result in genetically rare and virulent strains, which mostly evolve from a single transition point. Our results not only validate our widely-applicable approach for inferring directed genotype networks from data, but also provide a unique insight into the elusive functional and structural drivers of STM bacteria.

Transition Therapy: Tackling the Ecology of Tumor Phenotypic Plasticity.

Phenotypic switching in cancer cells has been found to be present across tumor types. Recent studies on Glioblastoma report a remarkably common architecture of four well-defined phenotypes coexisting within high levels of intra-tumor genetic heterogeneity. Similar dynamics have been shown to occur in breast cancer and melanoma and are likely to be found across cancer types. Given the adaptive potential of phenotypic switching (PHS) strategies, understanding how it drives tumor evolution and therapy resistance is a major priority. Here we present a mathematical framework uncovering the ecological dynamics behind PHS. The model is able to reproduce experimental results, and mathematical conditions for cancer progression reveal PHS-specific features of tumors with direct consequences on therapy resistance. In particular, our model reveals a threshold for the resistant-to-sensitive phenotype transition rate, below which any cytotoxic or switch-inhibition therapy is likely to fail. The model is able to capture therapeutic success thresholds for cancers where nonlinear growth dynamics or larger PHS architectures are in place, such as glioblastoma or melanoma. By doing so, the model presents a novel set of conditions for the success of combination therapies able to target replication and phenotypic transitions at once. Following our results, we discuss transition therapy as a novel scheme to target not only combined cytotoxicity but also the rates of phenotypic switching.

The Expected Number of Viable Autocatalytic Sets in Chemical Reaction Systems.

The emergence of self-sustaining autocatalytic networks in chemical reaction systems has been studied as a possible mechanism for modeling how living systems first arose. It has been known for several decades that such networks will form within systems of polymers (under cleavage and ligation reactions) under a simple process of random catalysis, and this process has since been mathematically analyzed. In this paper, we provide an exact expression for the expected number of self-sustaining autocatalytic networks that will form in a general chemical reaction system, and the expected number of these networks that will also be uninhibited (by some molecule produced by the system). Using these equations, we are able to describe the patterns of catalysis and inhibition that maximize or minimize the expected number of such networks. We apply our results to derive a general theorem concerning the trade-off between catalysis and inhibition, and to provide some insight into the extent to which the expected number of self-sustaining autocatalytic networks coincides with the probability that at least one such system is present.

The World Is Not a Theorem.

The evolution of the biosphere unfolds as a luxuriant generative process of new living forms and functions. Organisms adapt to their environment, exploit novel opportunities that are created in this continuous blooming dynamics. Affordances play a fundamental role in the evolution of the biosphere, for organisms can exploit them for new morphological and behavioral adaptations achieved by heritable variations and selection. This way, the opportunities offered by affordances are then actualized as ever novel adaptations. In this paper, we maintain that affordances elude a formalization that relies on set theory: we argue that it is not possible to apply set theory to affordances; therefore, we cannot devise a set-based mathematical theory to deduce the diachronic evolution of the biosphere.

Constraint Closure Drove Major Transitions in the Origins of Life.

Life is an epiphenomenon for which origins are of tremendous interest to explain. We provide a framework for doing so based on the thermodynamic concept of work cycles. These cycles can create their own closure events, and thereby provide a mechanism for engendering novelty. We note that three significant such events led to life as we know it on Earth: (1) the advent of collective autocatalytic sets (CASs) of small molecules; (2) the advent of CASs of reproducing informational polymers; and (3) the advent of CASs of polymerase replicases. Each step could occur only when the boundary conditions of the system fostered constraints that fundamentally changed the phase space. With the realization that these successive events are required for innovative forms of life, we may now be able to focus more clearly on the question of life's abundance in the universe.

Autocatalytic chemical networks at the origin of metabolism.

Modern cells embody metabolic networks containing thousands of elements and form autocatalytic sets of molecules that produce copies of themselves. How the first self-sustaining metabolic networks arose at life's origin is a major open question. Autocatalytic sets smaller than metabolic networks were proposed as transitory intermediates at the origin of life, but evidence for their role in prebiotic evolution is lacking. Here, we identify reflexively autocatalytic food-generated networks (RAFs)-self-sustaining networks that collectively catalyse all their reactions-embedded within microbial metabolism. RAFs in the metabolism of ancient anaerobic autotrophs that live from H2 and CO2 provided with small-molecule catalysts generate acetyl-CoA as well as amino acids and bases, the monomeric components of protein and RNA, but amino acids and bases without organic catalysts do not generate metabolic RAFs. This suggests that RAFs identify attributes of biochemical origins conserved in metabolic networks. RAFs are consistent with an autotrophic origin of metabolism and furthermore indicate that autocatalytic chemical networks preceded proteins and RNA in evolution. RAFs uncover intermediate stages in the emergence of metabolic networks, narrowing the gaps between early Earth chemistry and life.

Dynamics of a birth-death process based on combinatorial innovation.

A feature of human creativity is the ability to take a subset of existing items (e.g. objects, ideas, or techniques) and combine them in various ways to give rise to new items, which, in turn, fuel further growth. Occasionally, some of these items may also disappear (extinction). We model this process by a simple stochastic birth-death model, with non-linear combinatorial terms in the growth coefficients to capture the propensity of subsets of items to give rise to new items. In its simplest form, this model involves just two parameters (P, α). This process exhibits a characteristic 'hockey-stick' behaviour: a long period of relatively little growth followed by a relatively sudden 'explosive' increase. We provide exact expressions for the mean and variance of this time to explosion and compare the results with simulations. We then generalise our results to allow for more general parameter assignments, and consider possible applications to data involving human productivity and creativity.

Theory of chemical evolution of molecule compositions in the universe, in the Miller-Urey experiment and the mass distribution of interstellar and intergalactic molecules.

Chemical evolution is essential in understanding the origins of life. We present a theory for the evolution of molecule masses and show that small molecules grow by random diffusion and large molecules by a preferential attachment process leading eventually to life's molecules. It reproduces correctly the distribution of molecules found via mass spectroscopy for the Murchison meteorite and estimates the start of chemical evolution back to 12.8 billion years following the birth of stars and supernovae. From the Frontier mass between the random and preferential attachment dynamics the birth time of molecule families can be estimated. Amino acids emerge about 165 million years after chemical elements emerge in stars. Using the scaling of reaction rates with the distance of the molecules in space we recover correctly the few days emergence time of amino acids in the Miller-Urey experiment. The distribution of interstellar and extragalactic molecules are both consistent with the evolutionary mass distribution, and their age is estimated to 108 and 65 million years after the start of evolution. From the model, we can determine the number of different molecule compositions at the time of the emergence of Earth to be 1.6 million and the number of molecule compositions in interstellar space to a mere 719 species.

Answering Schrödinger's "What Is Life?"

In his "What Is Life?" Schrödinger poses three questions: (1) What is the source of order in organisms? (2) How do organisms remain ordered in the face of the Second Law of Thermodynamics? (3) Are new laws of physics required? He answers his first question with his famous "aperiodic solid". He leaves his second and third questions unanswered. I try to show that his first answer is also the answer to his second question. Aperiodic solids such as protein enzymes are "boundary conditions" that constrain the release of energy into a few degrees of freedom in non-equilibrium processes such that thermodynamic work is done. This work propagates and builds structures and controls processes. These constitute his causally efficacious "code script" controlling development. The constrained release of energy also delays the production of entropy that can be exported from cells as it forms. Therefore, cells remain ordered. This answers his second question. However, "What is life?" must also ask about the diachronic evolution of life. Here, the surprising answer to this extended version of Schrödinger's third question is that there are no new entailing laws of physics. No laws at all entail the evolution of ours or any biosphere.

Emergence of Organisms.

Since early cybernetics studies by Wiener, Pask, and Ashby, the properties of living systems are subject to deep investigations. The goals of this endeavour are both understanding and building: abstract models and general principles are sought for describing organisms, their dynamics and their ability to produce adaptive behavior. This research has achieved prominent results in fields such as artificial intelligence and artificial life. For example, today we have robots capable of exploring hostile environments with high level of self-sufficiency, planning capabilities and able to learn. Nevertheless, the discrepancy between the emergence and evolution of life and artificial systems is still huge. In this paper, we identify the fundamental elements that characterize the evolution of the biosphere and open-ended evolution, and we illustrate their implications for the evolution of artificial systems. Subsequently, we discuss the most relevant issues and questions that this viewpoint poses both for biological and artificial systems.

Ensembles, dynamics, and cell types: Revisiting the statistical mechanics perspective on cellular regulation.

Genetic regulatory networks control ontogeny. For fifty years Boolean networks have served as models of such systems, ranging from ensembles of random Boolean networks as models for generic properties of gene regulation to working dynamical models of a growing number of sub-networks of real cells. At the same time, their statistical mechanics has been thoroughly studied. Here we recapitulate their original motivation in the context of current theoretical and empirical research. We discuss ensembles of random Boolean networks whose dynamical attractors model cell types. A sub-ensemble is the critical ensemble. There is now strong evidence that genetic regulatory networks are dynamically critical, and that evolution is exploring the critical sub-ensemble. The generic properties of this sub-ensemble predict essential features of cell differentiation. In particular, the number of attractors in such networks scales as the DNA content raised to the 0.63 power. Data on the number of cell types as a function of the DNA content per cell shows a scaling relationship of 0.88. Thus, the theory correctly predicts a power law relationship between the number of cell types and the DNA contents per cell, and a comparable slope. We discuss these new scaling values and show prospects for new research lines for Boolean networks as a base model for systems biology.

Criticality Distinguishes the Ensemble of Biological Regulatory Networks.

The hypothesis that many living systems should exhibit near-critical behavior is well motivated theoretically, and an increasing number of cases have been demonstrated empirically. However, a systematic analysis across biological networks, which would enable identification of the network properties that drive criticality, has not yet been realized. Here, we provide a first comprehensive survey of criticality across a diverse sample of biological networks, leveraging a publicly available database of 67 Boolean models of regulatory circuits. We find all 67 networks to be near critical. By comparing to ensembles of random networks with similar topological and logical properties, we show that criticality in biological networks is not predictable solely from macroscale properties such as mean degree ⟨K⟩ and mean bias in the logic functions ⟨p⟩, as previously emphasized in theories of random Boolean networks. Instead, the ensemble of real biological circuits is jointly constrained by the local causal structure and logic of each node. In this way, biological regulatory networks are more distinguished from random networks by their criticality than by other macroscale network properties such as degree distribution, edge density, or fraction of activating conditions.

A note on random catalytic branching processes.

A variety of evolutionary processes in biology can be viewed as settings where organisms 'catalyse' the formation of new types of organisms. One example, relevant to the origin of life, is where transient biological colonies (e.g. prokaryotes or protocells) give rise to new colonies via lateral gene transfer. In this short note, we describe and analyse a simple random process which models such settings. By applying theory from general birth-death processes, we describe how the survival of a population under catalytic diversification depends on interplay of the catalysis rate and the initial population size. We also note how such process can also be viewed within the framework of 'self-sustaining autocatalytic networks'.

Niche emergence as an autocatalytic process in the evolution of ecosystems.

The utilisation of the ecospace and the change in diversity through time has been suggested to be due to the effect of niche partitioning, as a global long-term pattern in the fossil record. However, niche partitioning, as a way to coexist, could be a limited means to share the environmental resources and condition during evolutionary time. In fact, a physical limit impedes a high partitioning without a high restriction of the niche's variables. Here, we propose that niche emergence, rather than niche partitioning, is what mostly drives ecological diversity. In particular, we view ecosystems in terms of autocatalytic sets: catalytically closed and self-sustaining reaction (or interaction) networks. We provide some examples of such ecological autocatalytic networks, how this can give rise to an expanding process of niche emergence (both in time and space), and how these networks have evolved over time (so-called evoRAFs). Furthermore, we use the autocatalytic set formalism to show that it can be expected to observe a power-law in the size distribution of extinction events in ecosystems. In short, we elaborate on our earlier argument that new species create new niches, and that biodiversity is therefore an autocatalytic process.