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External flows of energy, entropy, and matter can cause sudden transitions in the stability of biological and industrial systems, fundamentally altering their dynamical function. How might we control and design these transitions in chemical reaction networks? Here, we analyze transitions giving rise to complex behavior in random reaction networks subject to external driving forces. In the absence of driving, we characterize the uniqueness of the steady state and identify the percolation of a giant connected component in these networks as the number of reactions increases. When subject to chemical driving (influx and outflux of chemical species), the steady state can undergo bifurcations, leading to multistability or oscillatory dynamics. By quantifying the prevalence of these bifurcations, we show how chemical driving and network sparsity tend to promote the emergence of these complex dynamics and increased rates of entropy production. We show that catalysis also plays an important role in the emergence of complexity, strongly correlating with the prevalence of bifurcations. Our results suggest that coupling a minimal number of chemical signatures with external driving can lead to features present in biochemical processes and abiogenesis.
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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.
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- PAR ID:
- 10634736
- Publisher / Repository:
- AIP Publishing
- Date Published:
- Journal Name:
- Chaos: An Interdisciplinary Journal of Nonlinear Science
- Volume:
- 34
- Issue:
- 9
- ISSN:
- 1054-1500
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript
- Journal Article:
- https://doi.org/10.1063/5.0207358
