Comparative analysis of carbon cycle models via kinetic representations

The pre-industrial state of the global carbon cycle is a significant aspect of studies related to climate change. In this paper, we recall the power law kinetic representations of the pre-industrial models of Schmitz (2002) and Anderies et al. (2013) from our earlier work. The power law kinetic representations, as uniform formalism, allow for a more extensive analysis and comparison of the different models for the same system. Using the mathematical theories of chemical reaction networks (with power-law kinetics), this work extends the analysis of the kinetic representations of the two models and assesses the similarities and differences in their structural and dynamic properties in relation to model construction assumptions. The analysis includes but is not limited to the coincidence of kinetic and stoichiometric spaces of the networks, capacity for equilibria multiplicity and co-multiplicity, and absolute concentration robustness in some species. Moreover, we bring together previously published results about the power law kinetic representations of the two models and consolidate them with new observations here. We also illustrate how the pre-industrial model of Anderies et al. may serve as a building block in the analysis of a kinetic representation of a global carbon cycle with carbon dioxide removal intervention.Comment: arXiv admin note: text overlap with arXiv:1109.2923 by other author

Absolute concentration robustness in power law kinetic systems

Absolute concentration robustness (ACR) is a condition wherein a species in a chemical kinetic system possesses the same value for any positive steady state the network may admit regardless of initial conditions. Thus far, results on ACR center on chemical kinetic systems with deficiency one. In this contribution, we use the idea of dynamic equivalence of chemical reaction networks to derive novel results that guarantee ACR for some classes of power law kinetic systems with deficiency zero. Furthermore, using network decomposition, we identify ACR in higher deficiency networks (i.e. deficiency $\geq$ 2) by considering the presence of a low deficiency subnetwork with ACR. Network decomposition also enabled us to recognize and define a weaker form of concentration robustness than ACR, which we named as `balanced concentration robustness'. Finally, we also discuss and emphasize our view of ACR as a primarily kinetic character rather than a condition that arises from structural sources.Comment: submitted for publication; 26 pages. arXiv admin note: text overlap with arXiv:1908.0449

Analysis of the earth\u27s carbon cycle models using biochemical systems theory and chemical reaction network theory

The global carbon cycle is a system which accounts for the different pools where carbon is stored (land, atmosphere, ocean and geological stock) and the processes that transfer carbon mass from one pool to another. Since this system is believed to be crucial in controlling the Earth\u27s climate via regulation of the concentration of carbon dioxide (CO2) in the atmosphere, various mathematical models have been developed in order to better understand the system. This thesis proposes to examine global carbon cycle models using a combination of two approaches ¡ Biochemical Systems Theory (BST) and Chemical Reaction Network Theory (CRNT). BST is a canonical modelling framework based on power-law formalism on the other hand, CRNT is an approach that draws conclusions about the dynamical behaviour of a chemical reaction network (CRN) using the graphical structure of the network alone. The aim of the BST-CRNT analysis in this context is to learn the dynamical behaviour of a global carbon cycle model through a dynamically equivalent chemical kinetic system for the model. A chemical kinetic system is obtained by generating an appropriate CRN for a given model while its dynamical system is transformed into a BST system where each rate of carbon mass transfer is approximated with a power-law function. Three existing carbon cycle box models from literature were collected and analyzed using the proposed method. This thesis shows that the BST-CRNT analysis enhances our understanding of the capacity of the global carbon cycle system to reach a steady state, which is a natural starting point for assessing the systems potential to reach a stable equilibrium for which humans can safely operate (i.e. the desired state of the Earth). Furthermore, the method has also generated new results in the mathematical theory of power-law kinetic systems, which may be applicable in the analysis of other biological systems. One result involves a theorem (called Deficiency Zero Theorem) that characterizes the steady states of power-law kinetic systems with a special network decomposition. Another result centers around an algorithm (called Deficiency-One Algorithm) that decides for the capacity of a class of power-law kinetic systems to permit multiple steady states

CRNet translator: Building GMA, S-system models and chemical reaction networks of disease and metabolic pathways

Ordinary Differential Equation (ODE) requires the use of differential equations to describe the dynamically changing phenomena, evolution, and variation and Chemical Reaction Net- work (CRN) is a model that gives a more general interpretation of biochemical networks as it ties aspects of reaction network structure in a precise way. In this study, these computational approaches can be used to model biological networks in the form of disease or metabolic pathways. Given the availability of data from Kyoto Encyclopedia of Genes and Genomes (KEGG), the application can convert the selected pathways to S-system or Generalized Mass-Action (GMA) ODE, and this ODE can be extended to its corresponding CRN to show more intimate relationships between network structure and basic phenomena of biological functions

A deficiency-one algorithm for power-law kinetic systems with reactant-determined interactions

This paper addresses the problem of determining the capacity of a deficiency-one network, endowed with rate laws more general than mass action kinetics, to admit multiple positive steady states—that is, whether there exist rate constants such that the corresponding differential equations admit two distinct stoichiometrically compatible steady states where all concentrations are positive. We extend the Deficiency-One Algorithm of M. Feinberg to deal with PL-RDK systems, which are kinetic systems with power-law rate functions whose kinetic orders are identical for reactions with the same reactant complex. The algorithm is applied to a power-law approximation of the Earth’s pre-industrial carbon cycle model, which gave the original motivation for our study. © 2018, Springer International Publishing AG, part of Springer Nature

A deficiency zero theorem for a class of power–law kinetic systems with non–reactant–determined interactions

The Deficiency Zero Theorem (DZT) provides definitive results about the dynamical behavior of chemical reaction networks with deficiency zero. Thus far, the available DZTs only apply to classes of power-law kinetic systems with reactant-determined interactions (i.e., the kinetic order vectors of the branching reactions of a reactant complex are identical). In this paper, we present the first DZT valid for a class of power-law systems with non-reactant-determined interactions (i.e., there are reactant complexes whose branching reactions have different kinetic order vectors). This class of power-law systems is characterized here by a decomposition into subnetworks with specific properties of their stoichiometric and reactant subspaces, as well as their kinetics. We illustrate our results to a power-law system of a pre-industrial carbon cycle model, from which we abstracted the properties of the above-mentioned decomposition. Specifically, our DZT is applied to a subnetwork of the carbon cycle system to describe the subnetwork’s steady states. It is also shown that the qualitative dynamical properties of the subnetwork may be lifted to the entire network of pre-industrial carbon cycle. © 2019 University of Kragujevac, Faculty of Science. All rights reserved

Birthing a mathematical biology community in the Philippines

The International Workshop on Mathematical Biology, or IWOMB, has already been held for two consecutive years in the Philippines. The first workshop was held on January 7-10, 2018 at Costabella Tropical Beach Resort, Cebu City, Philippines [1]. The second workshop was held on January 6-10, 2019 at Bohol Bee Farm, Bohol, Philippines [2]. Like a mother bearing a child, the IWOMB has been thought of as an avenue to organize and build a strong mathematical biology community dedicated to the training and mentoring of young researchers. IWOMB participants include emerging researchers and graduate students from different provinces of the Philippines and neighboring countries, who are interested in diverse topics on mathematical biology. The workshop also aims to explore research breakthroughs and give birth to fresh ideas from scientific discussions between Filipino and foreign mathematical biology enthusiasts