The emergence of life required isolated prebiotic chemical
reactions to integrate into coordinated systems, yet how this transition
occurred across early Earth's diverse environments remains unclear. We present
a mathematical framework using sheaf theory to model how local chemical
processes in distinct microenvironments could have scaled to create global
biochemical networks.
We systematically characterised ten prebiotic
microenvironments—including hydrothermal vents, mineral surfaces, lipid
membranes, and ice eutectic phases—using formal concept analysis to identify
twelve key physicochemical attributes such as polar solvents, mineral
catalysis, and redox gradients. These attributes define a topological space
where microenvironments share common properties from open sets, allowing us to
apply sheaf-theoretic methods.
Our sheaf construction shows that physicochemical attributes
act as selective "carriers" that are active only in specific
microenvironmental combinations. The locality and glueing conditions of the
sheaf theory model how chemical processes maintain internal consistency while integrating
across overlapping niches. This reveals hierarchical structures showing how
attributes propagate across scales, with hydrothermal vents, mineral surfaces,
and lipid membranes emerging as critical hubs concentrating multiple catalytic
and compartmentalising properties.
These findings suggest prebiotic chemical evolution emerged
not from a single optimal environment, but from the integration of disparate
microenvironments, each contributing specialised conditions that collectively
enabled complex biochemical networks. Our framework provides mathematical
rigour for understanding prebiotic chemistry's spatial and functional
organisation, offering predictive insights into which environmental
combinations most likely facilitated life's origin.
Author(s) Details
Javier Burgos Salcedo
Facultad de Ingeniería, Fundación Universitaria San Mateo y Corporación
Para la Investigación y la Innovación CIINAS, Colombia.
Please see the book here :- https://doi.org/10.9734/bpi/cbrp/v9/6861
