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 translocation of glucose, the human body's main source of energy. Fortunately, reaction network analysis allows us to extract properties of dynamical systems without depending on their model parameter values. This study focuses on the comparison of insulin signaling in healthy state (INSMS or INSulin Metabolic Signaling) and in type 2 diabetes (INRES or INsulin RESistance) using reaction network analysis. The analysis uses network decomposition to identify the different subsystems involved in insulin signaling (e.g., insulin receptor binding and recycling, GLUT4 translocation, and ERK signaling pathway, among others). Furthermore, results show that INSMS and INRES are similar with respect to some network, structo-kinetic, and kinetic properties. Their differences, however, provide insights into what happens when insulin resistance occurs. First, the variation in the number of species involved in INSMS and INRES suggests that when irregularities occur in the insulin signaling pathway, other complexes (and, hence, other processes) get involved, characterizing insulin resistance. Second, the loss of concordance exhibited by INRES suggests less restrictive interplay between the species involved in insulin signaling, leading to unusual activities in the signaling cascade. Lastly, GLUT4 losing its absolute concentration robustness in INRES may signify that the transporter has lost its reliability in shuttling glucose to the cell, inhibiting efficient cellular energy production. This study also suggests possible applications of the equilibria parametrization and network decomposition, resulting from the analysis, to potentially establish absolute concentration robustness in a species.

Network Modeling for Post-Entry Management of Invasive Pest Species in the Philippines: The Case of the Colorado Potato Beetle, Leptinotarsa decemlineata (Say, 1824) (Coleoptera: Chrysomelidae).

Crop shifting is considered as an important strategy to secure future food supply in the face of climate change. However, use of this adaptation strategy needs to consider the risk posed by changes in the geographic range of pests that feed on selected crops. Failure to account for this threat can lead to disastrous results. Models can be used to give insights on how best to manage these risks. In this paper, the socioecological process graph technique is used to develop a network model of interactions among crops, invasive pests, and biological control agents. The model is applied to a prospective analysis of the potential entry of the Colorado potato beetle into the Philippines just as efforts are being made to scale up potato cultivation as a food security measure. The modeling scenarios indicate the existence of alternative viable pest control strategies based on the use of biological control agents. Insights drawn from the model can be used as the basis to ecologically engineer agricultural systems that are resistant to pests.

Mathematical Modeling of Fluconazole Resistance in the Ergosterol Pathway of Candida albicans.

Candidiasis is reported to be the most common fungal infection in the critical care setting. The causative agent of this infection is a commensal pathogen belonging to the genus Candida, the most common species of which is Candida albicans. The ergosterol pathway in yeast is a common target by many antifungal agents, as ergosterol is an essential component of the cell membrane. The current antifungal agent of choice for the treatment of candidiasis is fluconazole, which is classified under the azole antifungals. In recent years, the significant increase of fluconazole-resistant C. albicans in clinical samples has revealed the need for a search for other possible drug targets. In this study, we constructed a mathematical model of the ergosterol pathway of C. albicans using ordinary differential equations with mass action kinetics. From the model simulations, we found the following results: (i) a partial inhibition of the sterol-methyltransferase enzyme yields a fair amount of fluconazole resistance; (ii) the overexpression of the ERG6 gene, which leads to an increased sterol-methyltransferase enzyme, is a good target of antifungals as an adjunct to fluconazole; (iii) a partial inhibition of lanosterol yields a fair amount of fluconazole resistance; (iv) the C5-desaturase enzyme is not a good target of antifungals as an adjunct to fluconazole; (v) the C14α-demethylase enzyme is confirmed to be a good target of fluconazole; and (vi) the dose-dependent effect of fluconazole is confirmed. This study hopes to aid experimenters in narrowing down possible drug targets prior to costly and time-consuming experiments and serve as a cross-validation tool for experimental data. IMPORTANCE Candidiasis is reported to be the most common fungal infection in the critical care setting, and it is caused by a commensal pathogen belonging to the genus Candida, the most common species of which is Candida albicans. The current antifungal agent of choice for the treatment of candidiasis is fluconazole, which is classified under the azole antifungals. There has been a significant increase in fluconazole-resistant C. albicans in recent years, which has revealed the need for a search for other possible drug targets. We constructed a mathematical model of the ergosterol pathway in C. albicans using ordinary differential equations with mass action kinetics. In our simulations, we found that by increasing the amount of the sterol-methyltransferase enzyme, C. albicans becomes more susceptible to fluconazole. This study hopes to aid experimenters in narrowing down the possible drug targets prior to costly and time-consuming experiments and to serve as a cross-validation tool for experimental data.

Reaction Network Analysis of Metabolic Insulin Signaling.

Absolute concentration robustness (ACR) and concordance are novel concepts in the theory of robustness and stability within Chemical Reaction Network Theory. In this paper, we have extended Shinar and Feinberg's reaction network analysis approach to the insulin signaling system based on recent advances in decomposing reaction networks. We have shown that the network with 20 species, 35 complexes, and 35 reactions is concordant, implying at most one positive equilibrium in each of its stoichiometric compatibility class. We have obtained the system's finest independent decomposition consisting of 10 subnetworks, a coarsening of which reveals three subnetworks which are not only functionally but also structurally important. Utilizing the network's deficiency-oriented coarsening, we have developed a method to determine positive equilibria for the entire network. Our analysis has also shown that the system has ACR in 8 species all coming from a deficiency zero subnetwork. Interestingly, we have shown that, for a set of rate constants, the insulin-regulated glucose transporter GLUT4 (important in glucose energy metabolism), has stable ACR.

Modelling vicious networks with P-graph causality maps.

P-graph causality maps were recently proposed as a methodology for systematic analysis of intertwined causal chains forming network-like structures. This approach uses the bipartite representation of P-graph to distinguish system components ("objects" represented by O-type nodes) from the functions they perform ("mechanisms" represented by M-type nodes). The P-graph causality map methodology was originally applied for determining structurally feasible causal networks to enable a desirable outcome to be achieved. In this work, the P-graph causality map methodology is extended to the analysis of vicious networks (i.e., causal networks with adverse outcomes). The maximal structure generation algorithm is first used to assemble the problem elements into a complete causal network; the solution structure generation algorithm is then used to enumerate all structurally feasible causal networks. Such comprehensive analysis gives insights on how to deactivate vicious networks through the removal of keystone objects and mechanisms. The extended methodology is illustrated with an ex post analysis of the 1984 Bhopal industrial disaster. Prospects for other applications to sustainability issues are also discussed.

A Deterministic Compartmental Modeling Framework for Disease Transmission.

Mathematical models for the spread of diseases help us understand the mechanisms on how diseases spread, evaluate the possible effects of interventions, predict outcomes of epidemics, and forecast the course of outbreaks. Compartmental models are widely used in synthetic biology since they can represent a biological system as an assembly of various parts or compartments with different functions. Here we present a framework for the analysis of a compartmental model for the transmission of diseases using ordinary differential equations. We apply this method on a study about the spread of tuberculosis.

Linear conjugacy of chemical kinetic systems.

Two networks are said to be linearly conjugate if the solution of their dynamic equations can be transformed into each other by a positive linear transformation. The study on dynamical equivalence in chemical kinetic systems was initiated by Craciun and Pantea in 2008 and eventually led to the Johnston-Siegel Criterion for linear conjugacy (JSC). Several studies have applied Mixed Integer Linear Programming (MILP) approach to generate linear conjugates of MAK (mass action kinetic) systems, Bio-CRNs (which is a subset of Hill-type kinetic systems when the network is restricted to digraphs), and PL-RDK (complex factorizable power law kinetic) systems. In this study, we present a general computational solution to construct linear conjugates of any "rate constant-interaction function decomposable" (RID) chemical kinetic systems, wherein each of its rate function is the product of a rate constant and an interaction function. We generate an extension of the JSC to the complex factorizable (CF) subset of RID kinetic systems and show that any non-complex factorizable (NF) RID kinetic system can be dynamically equivalent to a CF system via transformation. We show that linear conjugacy can be generated for any RID kinetic systems by applying the JSC to any NF kinetic system that are transformed to CF kinetic system.

Reaction networks and kinetics of biochemical systems.

This paper further develops the connection between Chemical Reaction Network Theory (CRNT) and Biochemical Systems Theory (BST) that we recently introduced [1]. We first use algebraic properties of kinetic sets to study the set of complex factorizable kinetics CFK(N) on a CRN, which shares many characteristics with its subset of mass action kinetics. In particular, we extend the Theorem of Feinberg-Horn [9] on the coincidence of the kinetic and stoichiometric subsets of a mass action system to CF kinetics, using the concept of span surjectivity. We also introduce the branching type of a network, which determines the availability of kinetics on it and allows us to characterize the networks for which all kinetics are complex factorizable: A "Kinetics Landscape" provides an overview of kinetics sets, their algebraic properties and containment relationships. We then apply our results and those (of other CRNT researchers) reviewed in [1] to fifteen BST models of complex biological systems and discover novel network and kinetic properties that so far have not been widely studied in CRNT. In our view, these findings show an important benefit of connecting CRNT and BST modeling efforts.

Stability analysis of the ODE model representation of amyloidogenic processing in Alzheimer's disease in the presence of SORLA.

The proteolytic breakdown of the amyloid precursor protein (APP) by secretases is a complex cellular process that results in the formation of neurotoxic Aß peptides, causative of neurodegeneration in Alzheimer's disease (AD). Processing involves monomeric and dimeric forms of APP that are transported through distinct cellular compartments where the various secretases reside. Amyloidogenic processing is also influenced by modifiers such as sorting receptor-related protein (SORLA), an inhibitor of APP breakdown and a major AD risk factor. This paper analyzed the temporal behavior of a mathematical model describing APP processing under the influence of SORLA, by performing a stability analysis of the mathematical model. We found one biochemically meaningful equilibrium point ξ. By means of linearization, Hartman-Grobman theorem, and Routh-Hurwitz test, it was shown that ξ is a locally asymptotically stable equilibrium point. The region of attraction of ξ was approximated by using the fluctuation lemma. An immediate consequence of the stability analysis of the reduced system to the temporal behavior of the solutions of the original system was also obtained. The biological implications of these results for the dynamic behavior of the activity of APP and secretases under SORLA's influence were established.