On data and dimension in chemistry -- irreversibility, concealment and emergent conservation laws

TL;DR

This paper explores how the structure and hidden features of chemical reaction networks influence measurable data, revealing new laws that connect data dimension, conservation laws, and network structure, especially in the presence of irreversibility and concealed species.

Contribution

It introduces analytical tools linking data dimension to CRN structure, conservation laws, and hidden species, extending to nonlinear models and addressing irreversibility effects.

Findings

Revealed how irreversible reactions reduce degrees of freedom.

Discovered co-production law relating to emergent conservation laws.

Provided methods to infer network structure from data with concealed species.

Abstract

Chemical systems are interpreted through the species they contain and the reactions they may undergo, i.e., their chemical reaction network (CRN). In spite of their central importance to chemistry, the structure of CRNs continues to be challenging to deduce from data. Although there exist structural laws relating species, reactions, conserved quantities and cycles, there has been limited attention to their measurable consequences. One such is the dimension of the chemical data: the number of independent reactions or equivalently independent species, which corresponds to the number of measured variables minus the number of constraints. In this paper we attempt to relate the experimentally observed dimensional features to conservation laws and underlying CRN structure. Our approach extends to any Markov model as well as many nonlinear models in statistical physics and furnishes new analytical tools to find exact solutions. In particular, we investigate the effects of species that are concealed and reactions that are irreversible. For instance, irreversible reactions can have proportional rates. The resulting reduction in degrees of freedom can be captured by the co-production law relating co-production relationships to emergent non-integer conservation laws and broken cycles. This law resolves a recent conundrum posed by a machine-discovered candidate for a non-integer conservation law, and characterizes certain types of CRN behavior. We also obtain laws that allow us to relate data dimension to network structure in cases where some species cannot be discerned or distinguished by a given analytical technique, allowing to narrow down candidate CRNs from experimental data more effectively.