Necessary and sufficient conditions for directed hypergraphs to be chemical

Abstract: Every transformation system or "reaction network" can be presented as a directed hypergraph in which hyperedges describe the tranformation of reactants into reaction products. Chemically plausible reaction networks allow neither a perpetuum mobile, i.e., a "futile cycle" of reactions with non-vanishing energy production, nor the creation or annihilation of mass. Such RNs are said to be thermodynamically sound and conservative. These conditions turn out to be necessary and sufficient for the existence of a realization in terms of sum formulas, obeying conservation of "atoms". In particular, these realizations can be chosen such that any two species have distinct sum formulas, unless implies that they are "obligatory isomers". In terms of structural formulas, every compound is a labeled multigraph, in essence a Lewis formula, and reactions comprise only a rearrangement of bonds such that the total bond order is preserved. In particular, for every conservative RN, there exists a Lewis realization, in which any two compounds are realized by pairwisely distinct multigraphs. Moreover, we show that any in such a network can be represented as a sequence of small electron pair pushing cycles. Hence every thermodynamically sound and conservative can be represented as abstraction of chemistry as long as no theory describing actual properties of molecules is presupposed.

BiologyChemistryMathematicsPhysics

Audience: researchers in the topic

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Autocatalysis in reaction networks

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Autocatalysis is a key factor in biochemical systems, often featured in models illustrating complex dynamic behaviors like bistability, hysteresis, oscillations, or chaos. While it plays a crucial role from origin-of-life and metabolic processes to population biology and economics, a comprehensive understanding is still a work in progress.

Given its interdisciplinary nature, researchers from various fields, including biology, chemistry, computer science, mathematics, and physics, have contributed to unraveling the intricacies of autocatalysis. Despite this shared interest, direct interaction among these researchers is infrequent.

The purpose of this specialized seminar is to provide a common ground for interdisciplinary researchers to gather, encouraging discussions and fostering collaborations. The seminar occurs bi-monthly in spring and autumn on Thursdays at 4 pm CET, featuring two 30-minute independent talks followed by breakout rooms for in-depth discussions with the speakers.

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