ACEs in spaces: Autocatalytic Chemical Ecosystems in Spatial Settings Alex M. Plum 1 and David A. Baum 2,3 1 Department of Physics, University of California San Diego 2 Department of Botany, University of Wisconsin-Madison 3 Wisconsin Institute for Discovery, University of Wisconsin-Madison Autocatalysis is thought to have played an important role in the earliest stages of the origin of life. An autocatalytic cycle’s (AC) constituent chemicals can collectively catalyze their own recre- ation. When the reactions of multiple, interacting ACs are active in a region of space, they form an autocatalytic chemical ecosys- tem (ACE). Previous work demonstrated that, in chemostats, in- teractions between ACs in ACEs can be framed as analogous to those between species in biological ecosystems. Here, we extend this framework to investigate the effects of surface adsorption, desorption, and diffusion on ACE ecology. Simulating ACEs as particle-based stochastic reaction-diffusion systems in spa- tial settings, including open, two-dimensional reaction-diffusion systems and adsorptive mineral surfaces, we demonstrate that spatial structure can support more coexisting ACs and expose new AC traits to selection. Correspondence: David A. Baum (dbaum@wisc.edu) Introduction In models of prebiotic chemical evolution, spatial structure is frequently invoked to facilitate the accumulation of com- plexity. Late in life’s origins, spatial structure would have been endogenous, with autocatalytic metabolisms construct- ing their own encapsulating membranes. However, life’s earliest progenitors likely lacked endogenous membranes to separate their incipient biochemistry from external environ- ments. Spatial structure for the first life-like systems may have been supplied by external settings such as porous rocks or adsorbing mineral surfaces. Here, we focus on the continu- ous two-dimensional settings of mineral surfaces, which have been the focus of several origin of life theories, most notably Wächtershäuser’s surface metabolism model (1). Mineral- water interfaces would have been ubiquitous in the prebiotic environment and could have played a concentrating role for life-like chemistry, constraining diffusion, catalyzing reac- tions, and protecting chemicals from hydrolysis and thermal degradation (1–4). Life’s oldest ancestral chemistry also may have lacked replicating genetic polymers. Nevertheless, to take part in life’s pre-cellular phylogeny, there must at least have been a capacity for self-propagation. In chemical terms, self-propagation requires the existence of at least one auto- catalytic cycle (AC): a cyclic reaction pathway that results in a stoichiometric increase of a set of chemicals with each turn of the cycle (5). We call a chemical reaction network (CRN) containing multiple interacting ACs an autocatalytic chemical ecosystem (ACE). The parallel to ecosystem ecol- ogy follows because, like biological species, ACs can exhibit logistic growth when suitable food fluxes through the ecosys- tem (6). Moreover, as in the ecological case, pairs of ACs can interact like pairs of biological species, showing similar competitive, predator-prey, and mutualistic interactions (7). Moreover, ACEs can undergo ecological succession when the transient introduction of new chemical “seeds” activates new trophic levels composed of ACs that use existing ACs to self- propagate (8). In biological ecosystems, incorporating spa- tial structure is often necessary for accurate predictions of their dynamics. Well-mixed and spatially structured models of ecosystems concur in their predictions when only a single attractor state exists, but not necessarily when the system is multi-stable (9). For example, when there are two stable equi- libria in an ecological model of mutually inhibiting popula- tions, the ecological outcome is fully determined by average initial conditions in mean field models, but in spatial models the outcome can vary among simulations with the same aver- age initial conditions (9). Extrapolating from ecosystem ecol- ogy, well-mixed models like chemostats are appropriate for ACEs with just one attractor state. For these simple ACEs, adding spatial structure to a well-mixed model should not affect the space of ecological possibilities realizable by the underlying CRN. But for more complex, multi-stable ACEs, which are of greater relevance to life’s origins, well-mixed models no longer suffice. As a context to explore the role of spatial structure, we use simple models of ACEs consisting of pairs of mutually inhibiting ACs, designed to exhibit bistabil- ity. We then show that spatial structure can support the coex- istence of otherwise incompatible ACs, potentially increas- ing an ACE’s diversity and productive capacities. Moreover, we show that spatially heterogenous environments can select among competing ACs on the basis of spatially relevant traits like diffusivity to which selection is blind in the well-mixed case. These spatial, stochastic models illustrate the potential for adaptive change in simple CRNs that lack genetic infor- mation encoding. This may have been important to nascent life’s emergence and early accumulation of complexity. Methodology ACs & ACEs. Here, we adopt a stoichiometric definition of autocatalysis (5) that is compatible with reversible chemical kinetics (7). We categorize an AC’s chemicals as members, food, and waste. Member chemicals appear as both reactants and products across the set of AC reactions. Food and waste are categorized relative to the reaction direction that results in arXiv:2212.14445v1 [q-bio.PE] 29 Dec 2022