Parametric, nonparametric and parametric modelling of a chaotic circuit time series

The determination of a differential equation underlying a measured time series is a frequently arising task in nonlinear time series analysis. In the validation of a proposed model one often faces the dilemma that it is hard to decide whether possible discrepancies between the time series and model output are caused by an inappropriate model or by bad estimates of parameters in a correct type of model, or both. We propose a combination of parametric modelling based on Bock's multiple shooting algorithm and nonparametric modelling based on optimal transformations as a strategy to test proposed models and if rejected suggest and test new ones. We exemplify this strategy on an experimental time series from a chaotic circuit where we obtain an extremely accurate reconstruction of the observed attractor.Comment: 19 pages, 8 Fig

A mathematical model for breath gas analysis of volatile organic compounds with special emphasis on acetone

Recommended standardized procedures for determining exhaled lower respiratory nitric oxide and nasal nitric oxide have been developed by task forces of the European Respiratory Society and the American Thoracic Society. These recommendations have paved the way for the measurement of nitric oxide to become a diagnostic tool for specific clinical applications. It would be desirable to develop similar guidelines for the sampling of other trace gases in exhaled breath, especially volatile organic compounds (VOCs) which reflect ongoing metabolism. The concentrations of water-soluble, blood-borne substances in exhaled breath are influenced by: (i) breathing patterns affecting gas exchange in the conducting airways; (ii) the concentrations in the tracheo-bronchial lining fluid; (iii) the alveolar and systemic concentrations of the compound. The classical Farhi equation takes only the alveolar concentrations into account. Real-time measurements of acetone in end-tidal breath under an ergometer challenge show characteristics which cannot be explained within the Farhi setting. Here we develop a compartment model that reliably captures these profiles and is capable of relating breath to the systemic concentrations of acetone. By comparison with experimental data it is inferred that the major part of variability in breath acetone concentrations (e.g., in response to moderate exercise or altered breathing patterns) can be attributed to airway gas exchange, with minimal changes of the underlying blood and tissue concentrations. Moreover, it is deduced that measured end-tidal breath concentrations of acetone determined during resting conditions and free breathing will be rather poor indicators for endogenous levels. Particularly, the current formulation includes the classical Farhi and the Scheid series inhomogeneity model as special limiting cases.Comment: 38 page

Hybrid optimization method with general switching strategy for parameter estimation

This article is available from: http://www.biomedcentral.com/1752-0509/2/26[Background] Modeling and simulation of cellular signaling and metabolic pathways as networks of biochemical reactions yields sets of non-linear ordinary differential equations. These models usually depend on several parameters and initial conditions. If these parameters are unknown, results from simulation studies can be misleading. Such a scenario can be avoided by fitting the model to experimental data before analyzing the system. This involves parameter estimation which is usually performed by minimizing a cost function which quantifies the difference between model predictions and measurements. Mathematically, this is formulated as a non-linear optimization problem which often results to be multi-modal (non-convex), rendering local optimization methods detrimental.[Results] In this work we propose a new hybrid global method, based on the combination of an evolutionary search strategy with a local multiple-shooting approach, which offers a reliable and efficient alternative for the solution of large scale parameter estimation problems.[Conclusion] The presented new hybrid strategy offers two main advantages over previous approaches: First, it is equipped with a switching strategy which allows the systematic determination of the transition from the local to global search. This avoids computationally expensive tests in advance. Second, using multiple-shooting as the local search procedure reduces the multi-modality of the non-linear optimization problem significantly. Because multiple-shooting avoids possible spurious solutions in the vicinity of the global optimum it often outperforms the frequently used initial value approach (single-shooting). Thereby, the use of multiple-shooting yields an enhanced robustness of the hybrid approach.This work was supported by the European Community as part of the FP6 COSBICS Project (STREP FP6-512060), the German Federal Ministry of Education and Research, BMBF-project FRISYS (grant 0313921) and Xunta de Galicia (PGIDIT05PXIC40201PM).Peer reviewe

Rho-kinase-dependent F-actin rearrangement is involved in the inhibition of PI3-kinase/Akt during ischemia–reperfusion-induced endothelial cell apoptosis

Activation of cytoskeleton regulator Rho-kinase during ischemia–reperfusion (I/R) plays a major role in I/R injury and apoptosis. Since Rho-kinase is a negative regulator of the pro-survival phosphatidylinositol 3-kinase (PI3-kinase)/Akt pathway, we hypothesized that inhibition of Rho-kinase can prevent I/R-induced endothelial cell apoptosis by maintaining PI3-kinase/Akt activity and that protective effects of Rho-kinase inhibition are facilitated by prevention of F-actin rearrangement. Human umbilical vein endothelial cells were subjected to 1 h of simulated ischemia and 1 or 24 h of simulated reperfusion after treatment with Rho-kinase inhibitor Y-27632, PI3-kinase inhibitor wortmannin, F-actin depolymerizers cytochalasinD and latrunculinA and F-actin stabilizer jasplakinolide. Intracellular ATP levels decreased following I/R. Y-27632 treatment reduced I/R-induced apoptosis by 31% (P < 0.01) and maintained Akt activity. Both effects were blocked by co-treatment with wortmannin. Y-27632 treatment prevented the formation of F-actin bundles during I/R. Similar results were observed with cytochalasinD treatment. In contrast, latrunculinA and jasplakinolide treatment did not prevent the formation of F-actin bundles during I/R and had no effect on I/R-induced apoptosis. Apoptosis and Akt activity were inversely correlated (R2 = 0.68, P < 0.05). In conclusion, prevention of F-actin rearrangement by Rho-kinase inhibition or by cytochalasinD treatment attenuated I/R-induced endothelial cell apoptosis by maintaining PI3-kinase and Akt activity

A Combined Approach for the Identification of Continuous Nonlinear Systems

The identification of a nonlinear continuous output-only system from a time series is considered for the case that the functional form of the model is not known beforehand. To estimate both functions and parameters, a combination of nonparametric modeling based on nonlinear regression and parametric modeling based on a multiple shooting algorithm is proposed. This strategy to determine nonlinear differential equations is exemplified on experimental data from a chaotic circuit where an accurate reconstruction of the observed attractor is obtained

Identification of rate constants and non-observable absorption spectra in nonlinear biochemical reaction dynamics

On analyzing data of biochemical reaction dynamics monitored by time-resolved spectroscopy, one faces the problem that the concentration time courses of the involved components are not directly observed, but the superposition of their absorption spectra. Furthermore the single spectra are often unknown, because the corresponding reagents cannot be isolated. We propose a method based on Bock's multiple shooting algorithm to estimate the rate constants and individual spectra simultaneously. Applying this procedure to a biochemical reaction we identify the specific rate constants characterizing the reaction dynamics as well as the nonobservable absorption spectra. The results lead to a better understanding of the kinetics of a novel modification reaction which was used as trapping reaction in disulfide bond mediated protein folding reactions