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

Structural Properties of an S-system Model of Mycobacterium Tuberculosis Gene Regulation

Magombedze and Mulder in 2013 studied the gene regulatory system of Mycobacterium Tuberculosis (Mtb) by partitioning this into three subsystems based on putative gene function and role in dormancy/latency development. Each subsystem, in the form of S-system, is represented by an embedded chemical reaction network (CRN), defined by a species subset and a reaction subset induced by the set of digraph vertices of the subsystem. For the embedded networks of S-system, we showed interesting structural properties and proved that all S-system CRNs (with at least two species) are discordant. Analyzing the subsystems as subnetworks, where arcs between vertices belonging to different subsystems are retained, we formed a digraph homomorphism from the corresponding subnetworks to the embedded networks. Lastly, we explored the modularity concept of CRN in the context of digraph.Comment: arXiv admin note: substantial text overlap with arXiv:1909.0294

Network Investigation Techniques: Government Hacking and the Need for Adjustment in the Third-Party Doctrine

Modern society is largely dependent on technology, and legal discovery is no longer limited to hard-copy, tangible documents. The clash of technology and the law is an exciting, yet dangerous phenomena; dangerous because our justice system desperately needs technological progress. The clash between scientific advancement and the search for truth has recently taken an interesting form—government hacking. The United States Government has increasingly used Network Investigation Techniques (NITs) to target suspects in criminal investigations. NITs operate by identifying suspects who have taken affirmative steps to conceal their identity while browsing the Internet. The hacking technique has become especially useful to officials attempting to capture suspects utilizing the “dark web.” Unclear, however, is whether an NIT falls within the scope of a Fourth Amendment search when deployed against a user intentionally shielding his or her Internet Protocol Address (IP address). There is a need for an adjustment in the Fourth Amendment’s third-party doctrine. The Fourth Amendment’s protection against search and seizure is largely governed by the reasonable expectation of privacy. Therefore, the Fourth Amendment demands adjustment. A reasonable expectation of privacy, without adjustment to modern trends, is not reasonable. On one hand, society wants the government to prevent criminals from utilizing browsers that keep users anonymous. On the other hand, the need for truth and justice may not outweigh society’s need for privacy. Nevertheless, a thorough examination of the circumstances should be required. Constitutional interpretations are not static—and a static approach to the exclusionary rule is directly at odds to longstanding interpretations of the Constitution. It has long been held that as technology advances the law must adjust. This continues to hold true today. The Supreme Court of the United States must re-evaluate third-party doctrine in light of the digital age

Comparative Analysis of Kinetic Realizations of Insulin Signaling

Several studies have developed dynamical models to understand the underlying mechanisms of insulin signaling, a signaling cascade that leads to the production of glucose - the human body's main source of energy. Reaction network analysis allows us to extract formal properties of dynamical systems without depending on their parameter values. This study focuses on the comparison of reaction network analysis of insulin signaling in healthy cell (INSMS or INSulin Metabolic Signaling) and in type 2 diabetes (INRES or INsulin RESistance). INSMS and INRES are similar with respect to some network, structo-kinetic, and kinetic properties. However, they differ in the following network properties: the networks have different species sets and functional modules, INRES is more complex than INSMS, and INRES loses the concordance of INSMS. Based on structo-kinetic properties, INSMS is injective while INRES is not. And one of the most significant differences between INSMS and INRES in terms of kinetic properties is the loss of ACR species in INRES (INSMS has 8 ACR species). These results show the insights we gain from analyzing kinetic realization, beyond what we already know from analyzing the dynamical systems of insulin signaling in healthy and insulin-resistant cells.Comment: 30 pages, 1 figur

Comparison of reaction networks of Wnt signaling

Wnt signaling is a vital biological mechanism that regulates crucial development processes and maintenance of tissue homeostasis. Here, we extended the parameter-free analysis of four mathematical models of the beta-catenin-dependent Wnt signaling pathway performed by MacLean et al. (PNAS USA 2015) using chemical reaction network theory. We showed that the reaction networks of the four models considered (Lee, Schmitz, MacLean, and Feinberg) coincide in basic structural and kinetic properties except in their mono-stationarity/multi-stationarity, and their capacity for admitting a degenerate equilibrium. Moreover, we showed that the embedded networks of the Lee and Feinberg models are very similar, and the discordance of the Lee network limits its mono-stationarity to mass action kinetics, which challenge the absoluteness of model discrimination into mono-stationarity versus multi-stationarity alone. Focusing, henceforth, on the three multi-stationary networks, we showed that their finest independent decompositions are very different and can be used to study further similarities and differences among them. We also determined equilibria parametrizations of the networks and inferred the presence of species with absolute concentration robustness. Finally, direct comparison of the Schmitz and Feinberg networks with the MacLean network yielded new results in three aspects: structural/kinetic relationships between embedded networks relative to their set of common species, connections between the positive equilibria of the subnetwork of common reactions and the positive equilibria of the whole networks, and construction of maximal concordant subnetwork containing the common reactions of the networks under comparison. Thus, this work can provide general insights in comparing mathematical models of the same or closely-related systems

A Computational Approach to Multistationarity of Power-Law Kinetic Systems

This paper presents a computational solution to determine if a chemical reaction network endowed with power-law kinetics (PLK system) has the capacity for multistationarity, i.e., whether there exist positive rate constants such that the corresponding differential equations admit multiple positive steady states within a stoichiometric class. The approach, which is called the "Multistationarity Algorithm for PLK systems" (MSA), combines (i) the extension of the "higher deficiency algorithm" of Ji and Feinberg for mass action to PLK systems with reactant-determined interactions, and (ii) a method that transforms any PLK system to a dynamically equivalent one with reactant-determined interactions. Using this algorithm, we obtain two new results: the monostationarity of a popular model of anaerobic yeast fermentation pathway, and the multistationarity of a global carbon cycle model with climate engineering, both in the generalized mass action format of biochemical systems theory. We also provide examples of the broader scope of our approach for deficiency one PLK systems in comparison to the extension of Feinberg's "deficiency one algorithm" to such systems