An intermediate level of abstraction for computational systems chemistry

Kinetics and coexistence of autocatalytic reaction cycles

Biological reproduction rests ultimately on chemical autocatalysis. Autocatalytic chemical cycles are thought to have played an important role in the chemical complexification en route to life. There are two, related issues: what chemical transformations allow such cycles to form, and at what speed they are operating. Here we investigate the latter question for solitary as well as competitive autocatalytic cycles in resource-unlimited batch and resource-limited chemostat systems. The speed of growth tends to decrease with the length of a cycle. Reversibility of the reproductive step results in parabolic growth that is conducive to competitive coexistence. Reversibility of resource uptake also slows down growth. Unilateral help by a cycle of its competitor tends to favour the competitor (in effect a parasite on the helper), rendering coexistence unlikely. We also show that deep learning is able to predict the outcome of competition just from the topology and the kinetic rate constants, provided the training set is large enough. These investigations pave the way for studying autocatalytic cycles with more complicated coupling, such as mutual catalysis.

Beyond fitness: The information imparted in population states by selection throughout lifecycles

We approach the questions, what part of evolutionary change results from selection, and what is the adaptive information flow into a population undergoing selection, as a problem of quantifying the divergence of typical trajectories realized under selection from the expected dynamics of their counterparts under a null stochastic-process model representing the absence of selection. This approach starts with a formulation of adaptation in terms of information and from that identifies selection from the genetic parameters that generate information flow; it is the reverse of a historical approach that defines selection in terms of fitness, and then identifies adaptive characters as those amplified in relative frequency by fitness. Adaptive information is a relative entropy on distributions of histories computed directly from the generators of stochastic evolutionary population processes, which in large population limits can be approximated by its leading exponential dependence as a large-deviation function. We study a particular class of generators that represent the genetic dependence of explicit transitions around reproductive cycles in terms of stoichiometry, familiar from chemical reaction networks. Following Smith (2023), which showed that partitioning evolutionary events among genetically distinct realizations of lifecycles yields a more consistent causal analysis through the Price equation than the construction from units of selection and fitness, here we show that it likewise yields more complete evolutionary information measures.

The ecology-evolution continuum and the origin of life

Prior research on evolutionary mechanisms during the origin of life has mainly assumed the existence of populations of discrete entities with information encoded in genetic polymers. Recent theoretical advances in autocatalytic chemical ecology establish a broader evolutionary framework that allows for adaptive complexification prior to the emergence of bounded individuals or genetic encoding. This framework establishes the formal equivalence of cells, ecosystems and certain localized chemical reaction systems as autocatalytic chemical ecosystems (ACEs): food-driven (open) systems that can grow due to the action of autocatalytic cycles (ACs). When ACEs are organized in meta-ecosystems, whether they be populations of cells or sets of chemically similar environmental patches, evolution, defined as change in AC frequency over time, can occur. In cases where ACs are enriched because they enhance ACE persistence or dispersal ability, evolution is adaptive and can build complexity. In particular, adaptive evolution can explain the emergence of self-bounded units (e.g. protocells) and genetic inheritance mechanisms. Recognizing the continuity between ecological and evolutionary change through the lens of autocatalytic chemical ecology suggests that the origin of life should be seen as a general and predictable outcome of driven chemical ecosystems rather than a phenomenon requiring specific, rare conditions.

Beyond fitness: the nature of selection acting through the constructive steps of lifecycles

We address the problem of defining selection and extracting the adaptive part of evolutionary change, originally formalized by Fisher and Price. Conventionally, selection and adaptation are defined through fitness attributed to genes or genotypes chosen as units of selection. The construction through fitness is known to suffer ambiguities and omissions as a theory of change due to selection. We construct an alternative framing in which units of selection and fitness are replaced as the main abstractions by formal lifecycle models and reproduction rates through genetically distinct lifecycle realizations. Graphical representations of lifecycles express relations among reproductive stages that cannot be assigned to any one unit of selection. The lifecycle partition refines the statistics of overall reproductive success and resolves modes of selection that fitness either excludes or distorts through additive projections. We derive the Price equation in the basis of lifecycle realizations and compare it to the conventional Price equation for additive fitness of organisms. We show how the lifecycle approach recovers fitnesses acting concurrently at multiple levels, or contrasts forms of competition within and between levels that are invisible to additive fitness. Defining selection through lifecycles recasts population genetics from an object-focused to a construction- and process-focused representation.

Network Analysis Reveals Spatial Clustering and Annotation of Complex Chemical Spaces: Application to Astrochemistry

How are molecules linked to each other in complex systems? In a proof-of-concept study, we have developed the method mol2net (https://zenodo.org/record/7025094) to generate and analyze the molecular network of complex astrochemical data (from high-resolution Orbitrap MS¹ analysis of H₂O:CH₃OH:NH₃ interstellar ice analogs) in a data-driven and unsupervised manner, without any prior knowledge about chemical reactions. The molecular network is clustered according to the initial NH₃ content and unlocked HCN, NH₃, and H₂O as spatially resolved key transformations. In comparison with the PubChem database, four subsets were annotated: (i) saturated C-backbone molecules without N, (ii) saturated N-backbone molecules, (iii) unsaturated C-backbone molecules without N, and (iv) unsaturated N-backbone molecules. These findings were validated with previous results (e.g., identifying the two major graph components as previously described N-poor and N-rich molecular groups) but with additional information about subclustering, key transformations, and molecular structures, and thus, the structural characterization of large complex organic molecules in interstellar ice analogs has been significantly refined.

Implementing parallel arithmetic via acetylation and its application to chemical image processing

Chemical mixtures can be leveraged to store large amounts of data in a highly compact form and have the potential for massive scalability owing to the use of large-scale molecular libraries. With the parallelism that comes from having many species available, chemical-based memory can also provide the physical substrate for computation with increased throughput. Here, we represent non-binary matrices in chemical solutions and perform multiple matrix multiplications and additions, in parallel, using chemical reactions. As a case study, we demonstrate image processing, in which small greyscale images are encoded in chemical mixtures and kernel-based convolutions are performed using phenol acetylation reactions. In these experiments, we use the measured concentrations of reaction products (phenyl acetates) to reconstruct the output image. In addition, we establish the chemical criteria required to realize chemical image processing and validate reaction-based multiplication. Most importantly, this work shows that fundamental arithmetic operations can be reliably carried out with chemical reactions. Our approach could serve as a basis for developing more advanced chemical computing architectures.

The Semi-Enzymatic Origin of Metabolic Pathways: Inferring a Very Early Stage of the Evolution of Life

The early evolution of life is a period with many important events with a lot of big and open questions. One of them is the evolution of metabolic pathways, which means the origin and assembly of enzymes that act together. The retrograde hypothesis was the first attempt to explain the origin and evolutionary history of metabolic pathways; Norman Horowitz developed this first significant hypothesis. This idea was followed by relevant proposals developed by Sam Granick, who proposed the "forward direction hypothesis," and then the successful idea of "Patchwork" assembly proposed independently by Martynas Yčas and Roy Jensen. Since then, a few new hypotheses were proposed; one of the most influential was made by Antonio Lazcano and Stanley Miller in the Journal Molecular Evolution, the "semi-enzymatic origin" of metabolic pathways. This article was cited more than 160 times, including in most papers published about the early evolution of metabolism, placing it as influential work in the field. The ideas proposed in this work and their effects on studying the origin and early evolution of life are analyzed.

Rewriting Theory for the Life Sciences: A Unifying Theory of CTMC Semantics

The Kappa biochemistry and the MØD organo-chemistry frameworks are amongst the most intensely developed applications of rewriting theoretical methods in the life sciences to date. A typical feature of these types of rewriting theories is the necessity to implement certain structural constraints on the objects to be rewritten (a protein is empirically found to have a certain signature of sites, a carbon atom can form at most four bonds, ...). In this paper, we contribute to the theoretical foundations of these types of rewriting theory a number of conceptual and technical developments that permit to implement a universal theory of continuous-time Markov chains (CTMCs) for stochastic rewriting systems. Our core mathematical concepts are a novel rule algebra construction for the relevant setting of rewriting rules with conditions, both in Double- and in Sesqui-Pushout semantics, augmented by a suitable stochastic mechanics formalism extension that permits to derive dynamical evolution equations for pattern-counting statistics.

Re-conceptualizing the origins of life

Over the last several hundred years of scientific progress, we have arrived at a deep understanding of the non-living world. We have not yet achieved an analogous, deep understanding of the living world. The origins of life is our best chance at discovering scientific laws governing life, because it marks the point of departure from the predictable physical and chemical world to the novel, history-dependent living world. This theme issue aims to explore ways to build a deeper understanding of the nature of biology, by modelling the origins of life on a sufficiently abstract level, starting from prebiotic conditions on Earth and possibly on other planets and bridging quantitative frameworks approaching universal aspects of life. The aim of the editors is to stimulate new directions for solving the origins of life. The present introduction represents the point of view of the editors on some of the most promising future directions.This article is part of the themed issue 'Reconceptualizing the origins of life'.