A topological approach to chemical organizations.

Large chemical reaction networks often exhibit distinctive features that can be interpreted as higher-level structures. Prime examples are metabolic pathways in a biochemical context. We review mathematical approaches that exploit the stoichiometric structure, which can be seen as a particular directed hypergraph, to derive an algebraic picture of chemical organizations. We then give an alternative interpretation in terms of set-valued set functions that encapsulate the production rules of the individual reactions. From the mathematical point of view, these functions define generalized topological spaces on the set of chemical species. We show that organization-theoretic concepts also appear in a natural way in the topological language. This abstract representation in turn suggests the exploration of the chemical meaning of well-established topological concepts. As an example, we consider connectedness in some detail.

Metabolic photofragmentation kinetics for a minimal protocell: rate-limiting factors, efficiency, and implications for evolution.

A key requirement of an autonomous self-replicating molecular machine, a protocell, is the ability to digest resources and turn them into building blocks. Thus a protocell needs a set of metabolic processes fueled by external free energy in the form of available chemical redox potential or light. We introduce and investigate a minimal photodriven metabolic system, which is based on photofragmentation of resource molecules catalyzed by genetic molecules. We represent and analyze the full metabolic set of reaction-kinetic equations and, through a set of approximations, simplify the reaction kinetics so that analytical expressions can be obtained for the building block production. The analytical approximations are compared with the full equation set and with corresponding experimental results to the extent they are available. It should be noted, however, that the proposed metabolic system has not been experimentally implemented, so this investigation is conducted to obtain a deeper understanding of its dynamics and perhaps to anticipate its limitations. We demonstrate that this type of minimal photodriven metabolic scheme is typically rate-limited by the front-end photoexcitation process, while its yield is determined by the genetic catalysis. We further predict that gene-catalyzed metabolic reactions can undergo evolutionary selection only for certain combinations of the involved reaction rates due to their intricate interactions. We finally discuss how the expected range of metabolic rates likely affects other key protocellular processes such as container growth and division as well as gene replication.

A graph-based toy model of chemistry.

Large scale chemical reaction networks are a ubiquitous phenomenon, from the metabolism of living cells to processes in planetary atmospheres and chemical technology. At least some of these networks exhibit distinctive global features such as the "small world" behavior. The systematic study of such properties, however, suffers from substantial sampling biases in the few networks that are known in detail. A computational model for generating them is therefore required. Here we present a Toy Model that provides a consistent framework in which generic properties of extensive chemical reaction networks can be explored in detail and that at the same time preserves the "look-and-feel" of chemistry: Molecules are represented as labeled graphs, i.e., by their structural formulas; their basic properties are derived by a caricature version of the Extended Hückel MO theory that operates directly on the graphs; chemical reaction mechanisms are implemented as graph rewriting rules acting on the structural formulas; reactivities and selectivities are modeled by a variant of the Frontier Molecular Orbital Theory based on the Extended Hückel scheme. The approach is illustrated for two types of reaction networks: Diels-Alder reactions and the formose reaction implicated in prebiotic sugar synthesis.