Self-organization in computation and chemistry: Return to AlChemy.

How do complex adaptive systems, such as life, emerge from simple constituent parts? In the 1990s, Walter Fontana and Leo Buss proposed a novel modeling approach to this question, based on a formal model of computation known as the λ calculus. The model demonstrated how simple rules, embedded in a combinatorially large space of possibilities, could yield complex, dynamically stable organizations, reminiscent of biochemical reaction networks. Here, we revisit this classic model, called AlChemy, which has been understudied over the past 30 years. We reproduce the original results and study the robustness of those results using the greater computing resources available today. Our analysis reveals several unanticipated features of the system, demonstrating a surprising mix of dynamical robustness and fragility. Specifically, we find that complex, stable organizations emerge more frequently than previously expected, that these organizations are robust against collapse into trivial fixed points, but that these stable organizations cannot be easily combined into higher order entities. We also study the role played by the random generators used in the model, characterizing the initial distribution of objects produced by two random expression generators, and their consequences on the results. Finally, we provide a constructive proof that shows how an extension of the model, based on the typed λ calculus, could simulate transitions between arbitrary states in any possible chemical reaction network, thus indicating a concrete connection between AlChemy and chemical reaction networks. We conclude with a discussion of possible applications of AlChemy to self-organization in modern programming languages and quantitative approaches to the origin of life.

Investigating and Quantifying Molecular Complexity Using Assembly Theory and Spectroscopy.

Current approaches to evaluate molecular complexity use algorithmic complexity, rooted in computer science, and thus are not experimentally measurable. Directly evaluating molecular complexity could be used to study directed vs undirected processes in the creation of molecules, with potential applications in drug discovery, the origin of life, and artificial life. Assembly theory has been developed to quantify the complexity of a molecule by finding the shortest path to construct the molecule from building blocks, revealing its molecular assembly index (MA). In this study, we present an approach to rapidly infer the MA of molecules from spectroscopic measurements. We demonstrate that the MA can be experimentally measured by using three independent techniques: nuclear magnetic resonance (NMR), tandem mass spectrometry (MS/MS), and infrared spectroscopy (IR). By identifying and analyzing the number of absorbances in IR spectra, carbon resonances in NMR, or molecular fragments in tandem MS, the MA of an unknown molecule can be reliably estimated. This represents the first experimentally quantifiable approach to determining molecular assembly. This paves the way to use experimental techniques to explore the evolution of complex molecules as well as a unique marker of where an evolutionary process has been operating.

False Positives and the Challenge of Testing the Alien Hypothesis.

The origin of life and the detection of alien life have historically been treated as separate scientific research problems. However, they are not strictly independent. Here, we discuss the need for a better integration of the sciences of life detection and origins of life. Framing these dual problems within the formalism of Bayesian hypothesis testing, we demonstrate via simple examples how high confidence in life detection claims require either (1) a strong prior hypothesis about the existence of life in a particular alien environment, or conversely, (2) signatures of life that are not susceptible to false positives. As a case study, we discuss the role of priors and hypothesis testing in recent results reporting potential detection of life in the venusian atmosphere and in the icy plumes of Enceladus. While many current leading biosignature candidates are subject to false positives because they are not definitive of life, our analyses demonstrate why it is necessary to shift focus to candidate signatures that are definitive. This indicates a necessity to develop methods that lack substantial false positives, by using observables for life that rely on prior hypotheses with strong theoretical and empirical support in identifying defining features of life. Abstract theories developed in pursuit of understanding universal features of life are more likely to be definitive and to apply to life-as-we-don't-know-it. We discuss Molecular Assembly theory as an example of such an observable which is applicable to life detection within the solar system. In the absence of alien examples these are best validated in origin of life experiments, substantiating the need for better integration between origins of life and biosignature science research communities. This leads to a conclusion that extraordinary claims in astrobiology (e.g., definitive detection of alien life) require extraordinary explanations, whereas the evidence itself could be quite ordinary.

Life detection in a universe of false positives: Can the Fatal Flaws of Exoplanet Biosignatures be Overcome Absent a Theory of Life?

Astrobiology aims to determine the distribution and diversity of life in the universe. But as the word "biosignature" suggests, what will be detected is not life itself, but an observation implicating living systems. Our limited access to other worlds suggests this observation is more likely to reflect out-of-equilibrium gasses than a writhing octopus. Yet, anything short of a writhing octopus will raise skepticism about what has been detected. Resolving that skepticism requires a theory to delineate processes due to life and those due to abiotic mechanisms. This poses an existential question for life detection: How do astrobiologists plan to detect life on exoplanets via features shared between non-living and living systems? We argue that you cannot without an underlying theory of life. We illustrate this by analyzing the hypothetical detection of an "Earth 2.0" exoplanet. Without a theory of life, we argue the community should focus on identifying unambiguous features of life via four areas: examining life on Earth, building life in the lab, probing the solar system, and searching for technosignatures. Ultimately, we ask, what exactly do astrobiologists hope to learn by searching for life?

Exploring and mapping chemical space with molecular assembly trees.

The rule-based search of chemical space can generate an almost infinite number of molecules, but exploration of known molecules as a function of the minimum number of steps needed to build up the target graphs promises to uncover new motifs and transformations. Assembly theory is an approach to compare the intrinsic complexity and properties of molecules by the minimum number of steps needed to build up the target graphs. Here, we apply this approach to prebiotic chemistry, gene sequences, plasticizers, and opiates. This allows us to explore molecules connected to the assembly tree, rather than the entire space of molecules possible. Last, by developing a reassembly method, based on assembly trees, we found that in the case of the opiates, a new set of drug candidates could be generated that would not be accessible via conventional fragment-based drug design, thereby demonstrating how this approach might find application in drug discovery.

A robotic prebiotic chemist probes long term reactions of complexifying mixtures.

To experimentally test hypotheses about the emergence of living systems from abiotic chemistry, researchers need to be able to run intelligent, automated, and long-term experiments to explore chemical space. Here we report a robotic prebiotic chemist equipped with an automatic sensor system designed for long-term chemical experiments exploring unconstrained multicomponent reactions, which can run autonomously over long periods. The system collects mass spectrometry data from over 10 experiments, with 60 to 150 algorithmically controlled cycles per experiment, running continuously for over 4 weeks. We show that the robot can discover the production of high complexity molecules from simple precursors, as well as deal with the vast amount of data produced by a recursive and unconstrained experiment. This approach represents what we believe to be a necessary step towards the design of new types of Origin of Life experiments that allow testable hypotheses for the emergence of life from prebiotic chemistry.

Identifying molecules as biosignatures with assembly theory and mass spectrometry.

The search for alien life is hard because we do not know what signatures are unique to life. We show why complex molecules found in high abundance are universal biosignatures and demonstrate the first intrinsic experimentally tractable measure of molecular complexity, called the molecular assembly index (MA). To do this we calculate the complexity of several million molecules and validate that their complexity can be experimentally determined by mass spectrometry. This approach allows us to identify molecular biosignatures from a set of diverse samples from around the world, outer space, and the laboratory, demonstrating it is possible to build a life detection experiment based on MA that could be deployed to extraterrestrial locations, and used as a complexity scale to quantify constraints needed to direct prebiotically plausible processes in the laboratory. Such an approach is vital for finding life elsewhere in the universe or creating de-novo life in the lab.

Spontaneous formation of autocatalytic sets with self-replicating inorganic metal oxide clusters.

Here we show how a simple inorganic salt can spontaneously form autocatalytic sets of replicating inorganic molecules that work via molecular recognition based on the {PMo12} ≡ [PMo12O40]3- Keggin ion, and {Mo36} ≡ [H3Mo57M6(NO)6O183(H2O)18]22- cluster. These small clusters are able to catalyze their own formation via an autocatalytic network, which subsequently template the assembly of gigantic molybdenum-blue wheel {Mo154} ≡ [Mo154O462H14(H2O)70]14-, {Mo132} ≡ [MoVI72MoV60O372(CH3COO)30(H2O)72]42- ball-shaped species containing 154 and 132 molybdenum atoms, and a {PMo12}⊂{Mo124Ce4} ≡ [H16MoVI100MoV24Ce4O376(H2O)56 (PMoVI10MoV2O40)(C6H12N2O4S2)4]5- nanostructure. Kinetic investigations revealed key traits of autocatalytic systems including molecular recognition and kinetic saturation. A stochastic model confirms the presence of an autocatalytic network involving molecular recognition and assembly processes, where the larger clusters are the only products stabilized by the cycle, isolated due to a critical transition in the network.

Individual perception dynamics in drunk games.

We study the effects of individual perceptions of payoffs in two-player games. In particular we consider the setting in which individuals' perceptions of the game are influenced by their previous experiences and outcomes. Accordingly, we introduce a framework based on evolutionary games where individuals have the capacity to perceive their interactions in different ways. Starting from the narrative of social behaviors in a pub as an illustration, we first study the combination of the Prisoner's Dilemma and Harmony Game as two alternative perceptions of the same situation. Considering a selection of game pairs, our results show that the interplay between perception dynamics and game payoffs gives rise to nonlinear phenomena unexpected in each of the games separately, such as catastrophic phase transitions in the cooperation basin of attraction, Hopf bifurcations and cycles of cooperation and defection. Combining analytical techniques with multiagent simulations, we also show how introducing individual perceptions can cause nontrivial dynamical behaviors to emerge, which cannot be obtained by analyzing the system at a macroscopic level. Specifically, initial perception heterogeneities at the microscopic level can yield a polarization effect that is unpredictable at the macroscopic level. This framework opens the door to the exploration of new ways of understanding the link between the emergence of cooperation and individual preferences and perceptions, with potential applications beyond social interactions.

Environmental control programs the emergence of distinct functional ensembles from unconstrained chemical reactions.

Many approaches to the origin of life focus on how the molecules found in biology might be made in the absence of biological processes, from the simplest plausible starting materials. Another approach could be to view the emergence of the chemistry of biology as process whereby the environment effectively directs "primordial soups" toward structure, function, and genetic systems over time. This does not require the molecules found in biology today to be made initially, and leads to the hypothesis that environment can direct chemical soups toward order, and eventually living systems. Herein, we show how unconstrained condensation reactions can be steered by changes in the reaction environment, such as order of reactant addition, and addition of salts or minerals. Using omics techniques to survey the resulting chemical ensembles we demonstrate there are distinct, significant, and reproducible differences between the product mixtures. Furthermore, we observe that these differences in composition have consequences, manifested in clearly different structural and functional properties. We demonstrate that simple variations in environmental parameters lead to differentiation of distinct chemical ensembles from both amino acid mixtures and a primordial soup model. We show that the synthetic complexity emerging from such unconstrained reactions is not as intractable as often suggested, when viewed through a chemically agnostic lens. An open approach to complexity can generate compositional, structural, and functional diversity from fixed sets of simple starting materials, suggesting that differentiation of chemical ensembles can occur in the wider environment without the need for biological machinery.

Universal scaling across biochemical networks on Earth.

The application of network science to biology has advanced our understanding of the metabolism of individual organisms and the organization of ecosystems but has scarcely been applied to life at a planetary scale. To characterize planetary-scale biochemistry, we constructed biochemical networks using a global database of 28,146 annotated genomes and metagenomes and 8658 cataloged biochemical reactions. We uncover scaling laws governing biochemical diversity and network structure shared across levels of organization from individuals to ecosystems, to the biosphere as a whole. Comparing real biochemical reaction networks to random reaction networks reveals that the observed biological scaling is not a product of chemistry alone but instead emerges due to the particular structure of selected reactions commonly participating in living processes. We show that the topology of biochemical networks for the three domains of life is quantitatively distinguishable, with >80% accuracy in predicting evolutionary domain based on biochemical network size and average topology. Together, our results point to a deeper level of organization in biochemical networks than what has been understood so far.

Prebiotic RNA Network Formation: A Taxonomy of Molecular Cooperation.

Cooperation is essential for evolution of biological complexity. Recent work has shown game theoretic arguments, commonly used to model biological cooperation, can also illuminate the dynamics of chemical systems. Here we investigate the types of cooperation possible in a real RNA system based on the Azoarcus ribozyme, by constructing a taxonomy of possible cooperative groups. We construct a computational model of this system to investigate the features of the real system promoting cooperation. We find triplet interactions among genotypes are intrinsically biased towards cooperation due to the particular distribution of catalytic rate constants measured empirically in the real system. For other distributions cooperation is less favored. We discuss implications for understanding cooperation as a driver of complexification in the origin of life.

The Emergence of Life as a First-Order Phase Transition.

It is well known that life on Earth alters its environment over evolutionary and geological timescales. An important open question is whether this is a result of evolutionary optimization or a universal feature of life. In the latter case, the origin of life would be coincident with a shift in environmental conditions. Here we present a model for the emergence of life in which replicators are explicitly coupled to their environment through the recycling of a finite supply of resources. The model exhibits a dynamic, first-order phase transition from nonlife to life, where the life phase is distinguished by selection on replicators. We show that environmental coupling plays an important role in the dynamics of the transition. The transition corresponds to a redistribution of matter in replicators and their environment, driven by selection on replicators, exhibiting an explosive growth in diversity as replicators are selected. The transition is accurately tracked by the mutual information shared between replicators and their environment. In the absence of successfully repartitioning system resources, the transition fails to complete, leading to the possibility of many frustrated trials before life first emerges. Often, the replicators that initiate the transition are not those that are ultimately selected. The results are consistent with the view that life's propensity to shape its environment is indeed a universal feature of replicators, characteristic of the transition from nonlife to life. We discuss the implications of these results for understanding life's emergence and evolutionary transitions more broadly. Key Words: Origin of life-Prebiotic evolution-Astrobiology-Biopolymers-Life. Astrobiology 17, 266-276.