Stuart M. Marshall

Assembly theory (AT) aims to distinguish living from non-living systems by explaining and quantifying selection and evolution. The theory proposes that the degree of assembly depends on the number of complex objects, with complexity measured using a combination of the object’s assembly index (AI) and its abundance. We previously provided experimental evidence supporting AT’s predictive power, finding that abiotic systems do not randomly produce organic molecules with an AI greater than approximately 15 in detectable amounts. Hazen et al . (Hazen et al . 2024 J. R. Soc. Interface 21 , 20230632. (doi:10.1098/rsif.2023.0632)) proposed inorganic molecules that theoretically have AIs greater than 15, suggesting similar complexity to biological molecules. However, our AIs are experimentally measured for organic, covalently bonded molecules, whereas Hazen’s are theoretical, derived from crystal structures of charged units that are not isolable in solution. This distinction underscores the challenge in experimentally validating theoretical AIs.

Assembly theory (referred to in prior works as pathway assembly) has been developed to explore the extrinsic information required to distinguish a given object from a random ensemble. In prior work, we explored the key concepts relating to deconstructing an object into its irreducible parts and then evaluating the minimum number of steps required to rebuild it, allowing for the reuse of constructed sub-objects. We have also explored the application of this approach to molecules, as molecular assembly, and how molecular assembly can be inferred experimentally and used for life detection. In this article, we formalise the core assembly concepts mathematically in terms of assembly spaces and related concepts and determine bounds on the assembly index. We explore examples of constructing assembly spaces for mathematical and physical objects and propose that objects with a high assembly index can be uniquely identified as those that must have been produced using directed biological or technological processes rather than purely random processes, thereby defining a new scale of aliveness. We think this approach is needed to help identify the new physical and chemical laws needed to understand what life is, by quantifying what life does.

Assembly theory is used to map molecular and gene assembly pathways exploring evolutionary trajectories looking for novelty.

One thing that discriminates living things from inanimate matter is their ability to generate similarly complex or non-random structures in a large abundance. From DNA sequences to folded protein structures, living cells, microbial communities and multicellular structures, the material configurations in biology can easily be distinguished from non-living material assemblies. Many complex artefacts, from ordinary bioproducts to human tools, though they are not living things, are ultimately produced by biological processes—whether those processes occur at the scale of cells or societies, they are the consequences of living systems. While these objects are not living, they cannot randomly form, as they are the product of a biological organism and hence are either technological or cultural biosignatures. A generalized approach that aims to evaluate complex objects as possible biosignatures could be useful to explore the cosmos for new life forms. However, it is not obvious how it might be possible to create such a self-contained approach. This would require us to prove rigorously that a given artefact is too complex to have formed by chance. In this paper, we present a new type of complexity measure, which we call ‘Pathway Complexity’, that allows us not only to threshold the abiotic–biotic divide, but also to demonstrate a probabilistic approach based on object abundance and complexity which can be used to unambiguously assign complex objects as biosignatures. We hope that this approach will not only open up the search for biosignatures beyond the Earth, but also allow us to explore the Earth for new types of biology, and to determine when a complex chemical system discovered in the laboratory could be considered alive. This article is part of the themed issue ‘Reconceptualizing the origins of life’.