Noise-induced macroscopic bifurcations in globally-coupled chaotic units

Large populations of globally-coupled identical maps subjected to independent additive noise are shown to undergo qualitative changes as the features of the stochastic process are varied. We show that for strong coupling, the collective dynamics can be described in terms of a few effective macroscopic degrees of freedom, whose deterministic equations of motion are systematically derived through an order parameter expansion.Comment: Phys. Rev. Lett., accepte

Model evaluation for glycolytic oscillations in yeast biotransformations of xenobiotics

Anaerobic glycolysis in yeast perturbed by the reduction of xenobiotic ketones is studied numerically in two models which possess the same topology but different levels of complexity. By comparing both models' predictions for concentrations and fluxes as well as steady or oscillatory temporal behavior we answer the question what phenomena require what kind of minimum model abstraction. While mean concentrations and fluxes are predicted in agreement by both models we observe different domains of oscillatory behavior in parameter space. Generic properties of the glycolytic response to ketones are discussed

Prognostic impact of urokinase-type plasminogen activator (uPA) and its inhibitor (PAI-1) in cytosols and pellet extracts derived from 892 breast cancer patients

To evaluate the clinical relevance of urokinase-type plasminogen activator (uPA) and its type-1 inhibitor (PAI-1) measured by a recently developed enzyme-linked immunosorbent assay (ELISA), we analysed both components in samples derived from 892 patients with primary breast cancer (median follow-up 99 months). The assays were performed in cytosolic extracts as well as in corresponding detergent extracts of pellets obtained after ultracentrifugation, which was carried out when preparing the cytosolic fractions for routine steroid hormone receptor determination. Statistically significant correlations were found between the cytosolic levels and those determined in the pellet extracts (Spearman correlation coefficient rs = 0.60, P < 0.0001 for uPA and rs = 0.65, P < 0.0001 for PAI-1). Furthermore, strong correlations were found between the levels of both uPA (rs = 0.85, P < 0.0001) and PAI-1 (rs = 0.90, P < 0.0001) in the cytosols and their levels previously measured with ELISAs based on commercial reagents. In both Cox univariate and multivariate analysis, high cytosolic levels of uPA or PAI-1 were significantly associated with increased rates of relapse and death. The levels of uPA and PAI-1 in the pellet extracts also provided prognostic information, although to a lesser extent compared with the cytosolic extracts. The prediction of prognosis on the basis of uPA and PAI-1 assessed by an alternative ELISA once again emphasizes the established prognostic role and usefulness of these parameters in selection of breast cancer patients at high or low risk of recurrence. © 1999 Cancer Research Campaig

uPARAP/Endo180 is essential for cellular uptake of collagen and promotes fibroblast collagen adhesion

The uptake and lysosomal degradation of collagen by fibroblasts constitute a major pathway in the turnover of connective tissue. However, the molecular mechanisms governing this pathway are poorly understood. Here, we show that the urokinase plasminogen activator receptor–associated protein (uPARAP)/Endo180, a novel mesenchymally expressed member of the macrophage mannose receptor family of endocytic receptors, is a key player in this process. Fibroblasts from mice with a targeted deletion in the uPARAP/Endo180 gene displayed a near to complete abrogation of collagen endocytosis. Furthermore, these cells had diminished initial adhesion to a range of different collagens, as well as impaired migration on fibrillar collagen. These studies identify a central function of uPARAP/Endo180 in cellular collagen interactions

Soluble urokinase receptor released from human carcinoma cells: a plasma parameter for xenograft tumour studies

The urokinase plasminogen activator receptor (uPAR) plays a critical role in urokinase-mediated plasminogen activation and thereby in the process leading to invasion and metastasis. Soluble urokinase receptor (suPAR) is released from tumours, and in cancer patients the blood level of soluble receptor is increased. Using an enzyme-linked, immunosorbent assay (ELISA)-specific for the human urokinase receptor, release of soluble receptor was measured in cultures of human breast carcinoma cells, in tumour extracts and in plasma from mice with xenografted human tumours. Soluble human urokinase receptor (shuPAR) was released into culture supernatant during the growth of the human breast cancer cell line MDA-MB-231 BAG, and the level of shuPAR in conditioned medium determined by ELISA was a linear function of both viable cell number and time of incubation. Western blotting showed that the form of shuPAR measured by ELISA in conditioned medium consisted virtually exclusively of the three-domain full-length protein, while uPAR in cell lysates consisted of full-length uPAR as well as the domains (2+3) cleavage product. shuPAR was also released into the plasma of nude mice during growth of MDA-MB-231 BAG, MDA-MB-435 BAG and HCT 116 cells as subcutaneously xenografted tumours. Western blotting demonstrated that the shuPAR released from the xenografted human tumours into plasma consisted of the three-domain full-length protein, despite the finding of some cleaved uPAR in detergent extracts of tumour tissue. The levels of shuPAR determined by ELISA in the plasma of host mice during the growth of xenografted cell lines were highly correlated with tumour volume. © 1999 Cancer Research Campaig

Computational Approaches and Analysis for a Spatio-Structural-Temporal Invasive Carcinoma Model

Spatio-temporal models have long been used to describe biological systems of cancer, but it has not been until very recently that increased attention has been paid to structural dynamics of the interaction between cancer populations and the molecular mechanisms associated with local invasion. One system that is of particular interest is that of the urokinase plasminogen activator (uPA) wherein uPA binds uPA receptors on the cancer cell surface, allowing plasminogen to be cleaved into plasmin, which degrades the extracellular matrix and this way leads to enhanced cancer cell migration. In this paper, we develop a novel numerical approach and associated analysis for spatio-structuro-temporal modelling of the uPA system for up to two-spatial and two-structural dimensions. This is accompanied by analytical exploration of the numerical techniques used in simulating this system, with special consideration being given to the proof of stability within numerical regimes encapsulating a central differences approach to approximating numerical gradients. The stability analysis performed here reveals instabilities induced by the coupling of the structural binding and proliferative processes. The numerical results expound how the uPA system aids the tumour in invading the local stroma, whilst the inhibitor to this system may impede this behaviour and encourage a more sporadic pattern of invasion.PostprintPeer reviewe

Prognostic value of tissue-type plasminogen activator (tPA) and its complex with the type-1 inhibitor (PAI-1) in breast cancer

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A combined model reduction algorithm for controlled biochemical systems

Background: Systems Biology continues to produce increasingly large models of complex biochemical reaction networks. In applications requiring, for example, parameter estimation, the use of agent-based modelling approaches, or real-time simulation, this growing model complexity can present a significant hurdle. Often, however, not all portions of a model are of equal interest in a given setting. In such situations methods of model reduction offer one possible approach for addressing the issue of complexity by seeking to eliminate those portions of a pathway that can be shown to have the least effect upon the properties of interest. Methods: In this paper a model reduction algorithm bringing together the complementary aspects of proper lumping and empirical balanced truncation is presented. Additional contributions include the development of a criterion for the selection of state-variable elimination via conservation analysis and use of an ‘averaged’ lumping inverse. This combined algorithm is highly automatable and of particular applicability in the context of ‘controlled’ biochemical networks. Results: The algorithm is demonstrated here via application to two examples; an 11 dimensional model of bacterial chemotaxis in Escherichia coli and a 99 dimensional model of extracellular regulatory kinase activation (ERK) mediated via the epidermal growth factor (EGF) and nerve growth factor (NGF) receptor pathways. In the case of the chemotaxis model the algorithm was able to reduce the model to 2 state-variables producing a maximal relative error between the dynamics of the original and reduced models of only 2.8% whilst yielding a 26 fold speed up in simulation time. For the ERK activation model the algorithm was able to reduce the system to 7 state-variables, incurring a maximal relative error of 4.8%, and producing an approximately 10 fold speed up in the rate of simulation. Indices of controllability and observability are additionally developed and demonstrated throughout the paper. These provide insight into the relative importance of individual reactants in mediating a biochemical system’s input-output response even for highly complex networks. Conclusions: Through application, this paper demonstrates that combined model reduction methods can produce a significant simplification of complex Systems Biology models whilst retaining a high degree of predictive accuracy. In particular, it is shown that by combining the methods of proper lumping and empirical balanced truncation it is often possible to produce more accurate reductions than can be obtained by the use of either method in isolation