Changes in the hypothalamic-pituitary-adrenal (HPA) axis activity constitute a key component of bipolar mania, but the extent and nature of these alterations are not fully understood. We use here the ...lateral hypothalamic-kindled (LHK) rat model to deliberately induce an acute manic-like episode and measure serum corticosterone concentrations to assess changes in HPA axis activity. A mathematical model is developed to succinctly describe the entwined biochemical transformations that underlay the HPA axis and emulate by numerical simulations the considerable increase in serum corticosterone concentration induced by LHK. Synergistic combination of the LHK rat model and dynamical systems theory allows us to quantitatively characterize changes in HPA axis activity under controlled induction of acute manic-like states and provides a framework to study in silico how the dynamic integration of neurochemical transformations underlying the HPA axis is disrupted in these states.
The stoichiometric network analysis (SNA) introduced by B. L. Clarke is applied to a simplified model of the complex oscillating Bray−Liebhafsky reaction under batch conditions, which was not ...examined by this method earlier. This powerful method for the analysis of steady-states stability is also used to transform the classical differential equations into dimensionless equations. This transformation is easy and leads to a form of the equations combining the advantages of classical dimensionless equations with the advantages of the SNA. The used dimensionless parameters have orders of magnitude given by the experimental information about concentrations and currents. This simplifies greatly the study of the slow manifold and shows which parameters are essential for controlling its shape and consequently have an important influence on the trajectories. The effectiveness of these equations is illustrated on two examples: the study of the bifurcations points and a simple sensitivity analysis, different from the classical one, more based on the chemistry of the studied system.
Dynamic properties of a nonlinear five-dimensional stoichiometric model of the hypothalamic-pituitary-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.
•A general model for sensitivity and intrinsic noise in plasmonic sensors is derived.•Noise increases and sensitivity decreases with decreasing plasmonic sensor active area.•Complete stochastic ...behaviour determined by the deterministic response.•Transients can be used to determine multiple analytes by single sensor element.•Simulations reveal the optimal read-out moment with minimal relative fluctuations.
The basic parameters of a sensor element defining its ultimate performance are sensitivity and intrinsic noise. In plasmonic gas sensors both are determined by refractive index changes due to adsorption and desorption (a–d) of target analyte particles to the sensor active area. In this paper we present a general model that can be simultaneously used to determine sensitivity and intrinsic noise of a plasmonic sensor both during transients and in steady-state and is valid for multi-analyte environments. The model utilizes the conventional probabilistic approach. It is derived without any assumptions about the stochastic nature of the fundamental (a–d) process. It reveals how all stochastic properties of the processes with (pseudo) first order kinetics with the initial number of particles equal to zero can be fully determined from the deterministic solution, without any previous stochastic analysis. Based on the proposed model it is possible to establish the optimum moment for readout when fluctuations are minimal. Transients last longer and fluctuations are lower at lower temperatures. The insight into the transient dynamics opens the possibility to use a single element sensor for multiple analyte sensing. Another result is that a–d noise is higher for smaller adsorption areas, which may be important for micro and nanosystems generally, since each of them has to be kept immersed in some kind of environment and thus be subject to contamination by adsorption that can significantly influence their behavior. Besides being applicable for plasmonic sensors of trace amounts of gases and other nanoplasmonic devices used in sensing, the model is applicable for other adsorption-based sensors, as well as for the investigations of stochastic phenomena in micro and nanostructures.
The influence of the initial malonic acid concentration MA0 (8.00 x 10(-3) < or = MA0 < or = 4.30 x 10(-2) mol dm(-3)) in the presence of bromate (6.20 x 10(-2) mol dm(-3)), bromide (1.50 x 10(-5) ...mol dm(-3)), sulfuric acid (1.00 mol dm(-3)) and cerium sulfate (2.50 x 10(-3) mol dm(-3)) on the dynamics and the kinetics of the Belousov-Zhabotinsky (BZ) reactions was examined under batch conditions at 30.0 degrees C. The kinetics of the BZ reaction was analyzed by the earlier proposed method convenient for the examinations of the oscillatory reactions. In the defined region of parameters where oscillograms with only large-amplitude relaxation oscillations appeared, the pseudo-first order of the overall malonic acid decomposition with a corresponding rate constant of 2.14 x 10(-2) min(-1) was established. The numerical results on the dynamics and kinetics of the BZ reaction, carried out by the known skeleton model including the Br2O species, were in good agreement with the experimental ones. The already found saddle node infinite period (SNIPER) bifurcation point in transition from a stable quasi-steady state to periodic orbits and vice versa is confirmed by both experimental and numerical investigations of the system under consideration. Namely, the large-amplitude relaxation oscillations with increasing periods between oscillations in approaching the bifurcation points at the beginning and the end of the oscillatory domain, together with excitability of the stable quasi-steady states in their vicinity are obtained.
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.
nema
The intermittency or intermittent bursting as the type of dynamic state when two qualitatively different behaviors replace one another randomly during the course of the reaction, although all the ...control parameters remain constant, is found in the BriggsRauscher oscillating system moderated by a very small amount of phenol. Within a range of phenol concentrations, the oscillation amplitude is diminished considerably, and after oscillations cease, they repeat intermittently, giving several bursts of oscillations. For the concentrations used here, the range of phenol concentrations where intermittent bursting oscillations occur in a closed reactor is ca. 1.8×10−5 to 3.6×10−5 M. Bursting also occurs in an open reactor and can be sustained indefinitely at 5.53×10−5 M concentration. The intermittent bursting behavior is robust, and can be achieved at a variety of conditions.
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