From local Reactions to Global Emergence: Sheaf-theoretic Insights into Prebiotic Chemical Evolution | Chapter 4 | Chemistry and Biochemistry: Research Progress Vol. 9

 

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