Validation of a model of regulation in the tryptophan operon against multiple experiment data using global optimisation

This paper is concerned with validating a mathematical model of regulation in the tryptophan operon using global optimization. Although a number of models for this biochemical network are proposed, in many cases only qualitative agreement between the model output and experimental data was demonstrated, since very little information is currently available to guide the selection of parameter values for the models. This paper presents a model validating method using both multiple experimental data and global optimization

Stabilizing unstable periodic orbits in the Lorenz equations using time-delayed feedback control

For many years it was believed that an unstable periodic orbit with an odd number of real Floquet multipliers greater than unity cannot be stabilized by the time-delayed feedback control mechanism of Pyragus. A recent paper by Fiedler et al uses the normal form of a subcritical Hopf bifurcation to give a counterexample to this theorem. Using the Lorenz equations as an example, we demonstrate that the stabilization mechanism identified by Fiedler et al for the Hopf normal form can also apply to unstable periodic orbits created by subcritical Hopf bifurcations in higher-dimensional dynamical systems. Our analysis focuses on a particular codimension-two bifurcation that captures the stabilization mechanism in the Hopf normal form example, and we show that the same codimension-two bifurcation is present in the Lorenz equations with appropriately chosen Pyragus-type time-delayed feedback. This example suggests a possible strategy for choosing the feedback gain matrix in Pyragus control of unstable periodic orbits that arise from a subcritical Hopf bifurcation of a stable equilibrium. In particular, our choice of feedback gain matrix is informed by the Fiedler et al example, and it works over a broad range of parameters, despite the fact that a center-manifold reduction of the higher-dimensional problem does not lead to their model problem.Comment: 21 pages, 8 figures, to appear in PR

Time-delayed feedback control in astrodynamics

In this paper we present time-delayed feedback control (TDFC) for the purpose of autonomously driving trajectories of nonlinear systems into periodic orbits. As the generation of periodic orbits is a major component of many problems in astodynamics we propose this method as a useful tool in such applications. To motivate the use of this method we apply it to a number of well known problems in the astrodynamics literature. Firstly, TDFC is applied to control in the chaotic attitude motion of an asymmetric satellite in an elliptical orbit. Secondly, we apply TDFC to the problem of maintaining a spacecraft in a periodic orbit about a body with large ellipticity (such as an asteroid) and finally, we apply TDFC to eliminate the drift between two satellites in low Earth orbits to ensure their relative motion is bounded

Classification and stability of simple homoclinic cycles in R^5

The paper presents a complete study of simple homoclinic cycles in R^5. We find all symmetry groups Gamma such that a Gamma-equivariant dynamical system in R^5 can possess a simple homoclinic cycle. We introduce a classification of simple homoclinic cycles in R^n based on the action of the system symmetry group. For systems in R^5, we list all classes of simple homoclinic cycles. For each class, we derive necessary and sufficient conditions for asymptotic stability and fragmentary asymptotic stability in terms of eigenvalues of linearisation near the steady state involved in the cycle. For any action of the groups Gamma which can give rise to a simple homoclinic cycle, we list classes to which the respective homoclinic cycles belong, thus determining conditions for asymptotic stability of these cycles.Comment: 34 pp., 4 tables, 30 references. Submitted to Nonlinearit

Immunohistochemical localization of fibronectin as a tool for the age determination of human skin wounds

We analyzed the distribution of fibronectin in routinely embedded tissue specimens from 53 skin wounds and 6 postmortem wounds. In postmortem wounds a faint but focal positive staining was exclusively found at the margin of the specimens which dit not extend into the adjacent stroma. Vital wounds were classified into 3 groups. The first comprising lesions with wound ages ranging from a few seconds to 30 min, the second comprising those with wound ages upt to 3 weeks, and the third group with lesions more than 3 weeks old. Ten out of 17 lesions with a wound age up to 30 min showed a clear positive reaction within the wound area. Three specimens in this group were completely negative, while in 4 additional cases the result was not significantly different from postmortem lesions. These 7 cases were characterized by acute death with extremely short survival times (only seconds). In wounds up to 3 weeks old fibronectin formed a distinct network containing an increasing number of inflammatory cells corresponding to the wound age. In 2 cases with a survival time of 17 days and in all wounds older than 3 weeks fibronectin was restricted to the surface of fibroblasts and to parallel arranged fibers in the granulation tissue without any network structures. We present evidence that fibronectin is a useful marker for vital wounds with a survival time of more than a few minutes. Fibronectin appears before neutrophilic granulocytes migrate into the wound area. Since a faint positive fibronectin staining is seen in postmortem lesions and bleedings, we propose that only those wounds which show strong positive fibronectin staining also extending into the adjacent stroma should be regarded as vital

Prolonged ozone exposure in an allergic airway disease model: Adaptation of airway responsiveness and airway remodeling

BACKGROUND: Short-term exposure to high concentrations of ozone has been shown to increase airway hyper-responsiveness (AHR). Because the changes in AHR and airway inflammation and structure after chronic ozone exposure need to be determined, the goal of this study was to investigate these effects in a murine model of allergic airway disease. METHODS: We exposed BALB/c mice to 2 ppm ozone for 4, 8, and 12 weeks. We measured the enhanced pause (Penh) to methacholine and performed cell differentials in bronchoalveolar lavage fluid. We quantified the levels of IL-4 and IFN-γ in the supernatants of the bronchoalveolar lavage fluids using enzyme immunoassays, and examined the airway architecture under light and electron microscopy. RESULTS: The groups exposed to ozone for 4, 8, and 12 weeks demonstrated decreased Penh at methacholine concentrations of 12.5, 25, and 50 mg/ml, with a dose-response curve to the right of that for the filtered-air group. Neutrophils and eosinophils increased in the group exposed to ozone for 4 weeks compared to those in the filtered-air group. The ratio of IL-4 to INF-γ increased significantly after exposure to ozone for 8 and 12 weeks compared to the ratio for the filtered-air group. The numbers of goblet cells, myofibroblasts, and smooth muscle cells showed time-dependent increases in lung tissue sections from the groups exposed to ozone for 4, 8, and 12 weeks. CONCLUSION: These findings demonstrate that the increase in AHR associated with the allergic airway does not persist during chronic ozone exposure, indicating that airway remodeling and adaptation following repeated exposure to air pollutants can provide protection against AHR