Thermodynamics of random reaction networks

What makes a reaction network "chemical"?

BACKGROUND

Reaction networks (RNs) comprise a set X of species and a set [Formula: see text] of reactions [Formula: see text], each converting a multiset of educts [Formula: see text] into a multiset [Formula: see text] of products. RNs are equivalent to directed hypergraphs. However, not all RNs necessarily admit a chemical interpretation. Instead, they might contradict fundamental principles of physics such as the conservation of energy and mass or the reversibility of chemical reactions. The consequences of these necessary conditions for the stoichiometric matrix [Formula: see text] have been discussed extensively in the chemical literature. Here, we provide sufficient conditions for [Formula: see text] that guarantee the interpretation of RNs in terms of balanced sum formulas and structural formulas, respectively.

RESULTS

Chemically plausible RNs 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. For finite RNs, both conditions can be expressed equivalently as properties of the stoichiometric matrix [Formula: see text]. The first condition is vacuous for reversible networks, but it excludes irreversible futile cycles and-in a stricter sense-futile cycles that even contain an irreversible reaction. The second condition is equivalent to the existence of a strictly positive reaction invariant. It is also 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 [Formula: see text] 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. Finally, we show that, in general, there are infinitely many realizations for a given conservative RN.

CONCLUSIONS

"Chemical" RNs are directed hypergraphs with a stoichiometric matrix [Formula: see text] whose left kernel contains a strictly positive vector and whose right kernel does not contain a futile cycle involving an irreversible reaction. This simple characterization also provides a concise specification of random models for chemical RNs that additionally constrain [Formula: see text] by rank, sparsity, or distribution of the non-zero entries. Furthermore, it suggests several interesting avenues for future research, in particular, concerning alternative representations of reaction networks and infinite chemical universes.

Local connections and the larval competency strongly influence marine metapopulation persistence

The relationship between metapopulation stability and connectivity has long been investigated in ecology, however, most of these studies are focused on theoretical species and habitat networks, having limited ability to capture the complexity of real-world metapopulations. Network analysis became more important in modeling connectivity, but it is still uncertain which network metrics are reliable predictors of persistence. Here we quantify the impact of connectivity and larval life history on marine metapopulation persistence across the complex seascape of southeast Australia. Our work coupled network-based approaches and eigenanalysis to efficiently estimate metapopulation-wide persistence and the subpopulation contributions. Larval dispersal models were used to quantify species-specific metapopulation connectivity for five important fisheries species, each summarized as a migration matrix. Eigenanalysis helped to reveal metapopulation persistence and determine the importance of node-level network properties. Across metapopulations, the number of local outgoing connections was found to have the largest impact on metapopulation persistence, implying these hub subpopulations may be the most influential in real-world metapopulations. Results also suggest the length of the pre-competency period may be the most influential parameter on metapopulation persistence. Finally, we identified two major hot spots of local connectivity in southeast Australia, each contributing strongly to multispecies persistence. Managers and ecologists would benefit by employing similar approaches in making more efficient and more ecologically informed decisions and focusing more on local connectivity patterns and larval competency characteristics to better understand and protect real-world metapopulation persistence. Practically this could mean developing more marine protected areas at shorter distances and supporting collaborative research into the early life histories of the species of interest.

Topology Universality and Dissimilarity in a Class of Scale-Free Networks

We study the effect of subtle changes on the evolution in the scale-free (SF) networks. Three extended models are evolved based on competition and inner anti-preferential deletion in growth and preferential attachment processes. By nonlinear and dynamic controlling on randomness and determinacy, three models can self-organize into scale-free networks, and diverse scaling exponents appear. Moreover, the model with more determinacy has more stringent parameter control than randomness, especially in the edge deletion. Our results suggest that the nature of the topology universality and dissimilarity in SF networks may be the subtle changes of randomness and determinacy.