Stoichiometric network analysis of a reaction system with conservation constraints

Stoichiometric Network Analysis (SNA) is a powerful method that can be used to examine instabilities in modelling a broad range of reaction systems without knowing the explicit values of reaction rate constants. Due to a lack of understanding, SNA is rarely used and its full potential is not yet fulfilled. Using the oscillatory carbonylation of a polymeric substrate [poly(ethylene glycol) methyl ether acetylene] as a case study, in this work, we consider two mathematical methods for the application of SNA to the reaction models when conservation constraints between species have an important role. The first method takes conservation constraints into account and uses only independent intermediate species, while the second method applies to the full set of intermediate species, without the separation of independent and dependent variables. Both methods are used for examination of steady state stability by means of a characteristic polynomial and related Jacobian matrix. It was shown that both methods give the same results. Therefore, as the second method is simpler, we suggest it as a more straightforward method for the applications. Published by AIP Publishing

Modelling cholesterol effects on the dynamics of the hypothalamic-pituitary-adrenal (HPA) axis

A mathematical model of the hypothalamic-pituitary-adrenal (HPA) axis with cholesterol as a dynamical variable was derived to investigate the effects of cholesterol, the primary precursor of all steroid hormones, on the ultradian and circadian HPA axis activity. To develop the model, the parameter space was systematically examined by stoichiometric network analysis to identify conditions for ultradian oscillations, determine conditions under which dynamic transitions, i.e. bifurcations occur and identify bifurcation types. The bifurcations were further characterized using numerical simulations. Model predictions agree well with empirical findings reported in the literature, indicating that cholesterol levels may critically affect the global dynamics of the HPA axis. The proposed model provides a base for better understanding of experimental observations, it may be used as a tool for designing experiments and offers useful insights into the characteristics of basic dynamic regulatory mechanisms that, when impaired, may lead to the development of some modern-lifestyle-associated diseases

Mathematical modelling of genipin-bovine serum albumin interaction using fluorescence intensity measurements

The interaction between genipin and a model protein bovine serum albumin (BSA), with and without the addition of acetic acid, has been studied experimentally and by modelling. The number of amino groups available to react was determined to be 5.6 % of the total number of amino acid building blocks on BSA. Fluorescence intensity was used to record the progress of the reaction over the 24 h, while the modelling study focused on capturing the kinetic profiles of the reaction. The experiments revealed a slow start to the BSA and genipin interaction, that subsequently accelerated in an S-shaped curve which the modelling study linked with the existence of the feedback cycle for both reactive amino groups and genipin. At BSA concentrations ≥30 mg/mL the reaction was accelerated in the presence of acid, while below 30 mg/mL the acidified conditions delayed the onset of the reaction. Contrary to the reaction mechanisms previously proposed, a degree of breakdown of the fluorescent links in the products formed was denoted both experimentally and in a modelling study. This indicated the reversibility of the processes forming fluorescent product/s and suggested feasibility of the successful release of the protein following prospective encapsulation within the genipin-crosslinked hydrogel structure.</p

Mathematical modelling of genipin-bovine serum albumin interaction using fluorescence intensity measurements

The interaction between genipin and a model protein bovine serum albumin (BSA), with and without the addition of acetic acid, has been studied experimentally and by modelling. The number of amino groups available to react was determined to be 5.6 % of the total number of amino acid building blocks on BSA. Fluorescence intensity was used to record the progress of the reaction over the 24 h, while the modelling study focused on capturing the kinetic profiles of the reaction. The experiments revealed a slow start to the BSA and genipin interaction, that subsequently accelerated in an S-shaped curve which the modelling study linked with the existence of the feedback cycle for both reactive amino groups and genipin. At BSA concentrations ≥30 mg/mL the reaction was accelerated in the presence of acid, while below 30 mg/mL the acidified conditions delayed the onset of the reaction. Contrary to the reaction mechanisms previously proposed, a degree of breakdown of the fluorescent links in the products formed was denoted both experimentally and in a modelling study. This indicated the reversibility of the processes forming fluorescent product/s and suggested feasibility of the successful release of the protein following prospective encapsulation within the genipin-crosslinked hydrogel structure.</p

Dynamic transitions in a model of the hypothalamic-pituitary-adrenal axis

Dynamic properties of a nonlinear five-dimensional stoichiometric model of the hypothalamicpituitary-adrenal (HPA) axis were systematically investigated. Conditions under which qualitative transitions between dynamic states occur are determined by independently varying the rate constants of all reactions that constitute the model. Bifurcation types were further characterized using continuation algorithms and scale factor methods. Regions of bistability and transitions through supercritical Andronov-Hopf and saddle loop bifurcations were identified. Dynamic state analysis predicts that the HPA axis operates under basal (healthy) physiological conditions close to an Andronov-Hopf bifurcation. Dynamic properties of the stress-control axis have not been characterized experimentally, but modelling suggests that the proximity to a supercritical Andronov-Hopf bifurcation can give the HPA axis both, flexibility to respond to external stimuli and adjust to new conditions and stability, i.e., the capacity to return to the original dynamic state afterwards, which is essential for maintaining homeostasis. The analysis presented here reflects the properties of a low-dimensional model that succinctly describes neurochemical transformations underlying the HPA axis. However, the model accounts correctly for a number of experimentally observed properties of the stress-response axis. We therefore regard that the presented analysis is meaningful, showing how in silico investigations can be used to guide the experimentalists in understanding how the HPA axis activity changes under chronic disease and/or specific pharmacological manipulations

Origins of oscillatory dynamics in the model of reactive oxygen species in the rhizosphere

Oscillatory processes are essential for normal functioning and survival of biological systems, and reactive oxygen species have a prominent role in many of them. A mechanism representing the dynamics of these species in the rhizosphere is analyzed using stoichiometric network analysis with the aim to determine its capabilities to simulate various dynamical states, including oscillations. A detailed analysis has shown that unstable steady states result from four destabilizing feedback cycles, among which the cycle involving hydroquinone, an electron acceptor, and its semi-reduced form is the dominant one responsible for the existence of saddle-node and Andronov-Hopf bifurcations. This requires a higher steady-state concentration for the reduced electron acceptor compared to that of the remaining species, where the level of oxygen steady-state concentration determines whether the Andronov-Hopf or saddle-node bifurcation will occur

Model of the nonlinear reaction system with autocatalysis and autoinhibition: Stability of dynamic states

Self-regulation, achieved through positive (autocatalytic) or negative (autoinhibitory) feedback is commonly encountered in natural, technological and economic systems. The dynamic behavior of such systems is often complex and cannot be easily predicted, necessitating mathematical modelling and theoretical analyses. The aim of this work is to analyze the dynamics of a minimal model system with autocatalytic and autoinhibitory steps coupled through the same species, in order to understand under which critical condition the system loses stability and passes through an Andronov-Hopf bifurcation. The analysis used was improved stoichiometric network analysis (SNA) in combination with bifurcation and sensitivity analysis

Bifurcation analysis of the reduced model of the Bray-Liebhafsky reaction

In this paper, an already published model of the Bray-Liebhafsky reaction was improved by removing the direct autoinhibitory step, which resulted in a new variant of the model with more realistic kinetic scheme than the earlier version. The obtained variant of the model retains all intermediate species (I-, HIO, HIO2 and I-2) that were present in the previous model and has one reaction less. Stability analysis of the improved model was performed by stoichiometric network analysis (SNA). By this method, it was shown that improved model can simulate Andronov-Hopf and saddle-node bifurcations. In order to confirm the results of SNA, bifurcation analysis was performed with the initial concentrations of [H2O2](0) as the control parameter. With selected set of rate constants and constant concentrations of external species, two Andronov-Hopf bifurcations were detected at [H2O2](0) = 5.62 x 10(-2) M and [H2O2](0) = 10.73 M, while the rate constants ought to be changed for a saddle-node to occur. Bifurcation analysis also showed that the interaction between intermediate species I-, HIO and HIO2 has a crucial impact on the emergence of Andronov-Hopf bifurcation