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

Diffusive coupling can discriminate between similar reaction mechanisms in an allosteric enzyme system

<p>Abstract</p> <p>Background</p> <p>A central question for the understanding of biological reaction networks is how a particular dynamic behavior, such as bistability or oscillations, is realized at the molecular level. So far this question has been mainly addressed in well-mixed reaction systems which are conveniently described by ordinary differential equations. However, much less is known about how molecular details of a reaction mechanism can affect the dynamics in diffusively coupled systems because the resulting partial differential equations are much more difficult to analyze.</p> <p>Results</p> <p>Motivated by recent experiments we compare two closely related mechanisms for the product activation of allosteric enzymes with respect to their ability to induce different types of reaction-diffusion waves and stationary Turing patterns. The analysis is facilitated by mapping each model to an associated complex Ginzburg-Landau equation. We show that a sequential activation mechanism, as implemented in the model of Monod, Wyman and Changeux (MWC), can generate inward rotating spiral waves which were recently observed as glycolytic activity waves in yeast extracts. In contrast, in the limiting case of a simple Hill activation, the formation of inward propagating waves is suppressed by a Turing instability. The occurrence of this unusual wave dynamics is not related to the magnitude of the enzyme cooperativity (as it is true for the occurrence of oscillations), but to the sensitivity with respect to changes of the activator concentration. Also, the MWC mechanism generates wave patterns that are more stable against long wave length perturbations.</p> <p>Conclusions</p> <p>This analysis demonstrates that amplitude equations, which describe the spatio-temporal dynamics near an instability, represent a valuable tool to investigate the molecular effects of reaction mechanisms on pattern formation in spatially extended systems. Using this approach we have shown that the occurrence of inward rotating spiral waves in glycolysis can be explained in terms of an MWC, but not with a Hill mechanism for the activation of the allosteric enzyme phosphofructokinase. Our results also highlight the importance of enzyme oligomerization for a possible experimental generation of Turing patterns in biological systems.</p

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

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

The relation between socioeconomic and demographic factors and tumour stage in women diagnosed with breast cancer in Denmark, 1983–1999

The authors investigated the association between socioeconomic position and stage of breast cancer at the time of diagnosis in a nationwide Danish study. All 28 765 women with a primary invasive breast cancer diagnosed between 1983 and 1999 were identified in a nationwide clinical database and information on socioeconomic variables was obtained from Statistics Denmark. The risk of being diagnosed with a high-risk breast cancer, that is size >20 mm, lymph-node positive, ductal histology/high histologic grade and hormone receptor negative, was analysed by multivariate logistic regression. The adjusted odds ratio (OR) for high-risk breast cancer was reduced with longer education with a 12% reduced risk (95% confidence interval (CI), 0.80,0.96) in women with higher education and increased with reduced disposable income (low income group: OR, 1.22; 95% CI, 1.10,1.34). There was an urban–rural gradient, with higher risk among rural women (OR 1.10; 95 % CI, 1.02, 1.18) and lower risk among women in the capital suburbs (OR, 0.85; 95% CI, 0.78, 0.93) and capital area (OR, 0.93; 95% CI, 0.84–1.02). These factors were significant only for postmenopausal women, although similar patterns were observed among the premenopausal women, suggesting a subgroup of aggressive premenopausal breast cancers less influenced by socioeconomic factors

Relationship of Circulating Soluble Urokinase Plasminogen Activator Receptor (suPAR) Levels to Disease Control in Asthma and Asthmatic Pregnancy

Asthma has a high burden of morbidity if not controlled and may frequently complicate pregnancy, posing a risk for pregnancy outcomes. Elevated plasma level of the inflammatory biomarker soluble urokinase plasminogen activator receptor (suPAR) is related to a worse prognosis in many conditions such as infectious, autoimmune, or pregnancy-related diseases; however the value of suPAR in asthma and asthmatic pregnancy is unknown. The present study aimed to investigate the suPAR, CRP and IL-6 levels in asthma (asthmatic non-pregnant, ANP; N = 38; female N = 27) and asthmatic pregnancy (AP; N = 15), compared to healthy non-pregnant controls (HNP; N = 29; female N = 19) and to healthy pregnant women (HP; N = 58). The relationship between suPAR levels and asthma control was also evaluated. The diagnostic efficacy of suPAR in asthma control was analyzed using ROC analysis. IL-6 and CRP levels were comparable in all study groups. Circulating suPAR levels were lower in HP and AP than in HNP and ANP subjects, respectively (2.01 [1.81-2.38] and 2.39 [2.07-2.69] vs. 2.60 [1.82-3.49] and 2.84 [2.33-3.72] ng/mL, respectively, p = 0.0001). suPAR and airway resistance correlated in ANP (r = 0.47, p = 0.004). ROC analysis of suPAR values in ANP patients with PEF above and below 80% yielded an AUC of 0.75 (95% CI: 0.57-0.92, p = 0.023) and with ACT total score above and below 20 an AUC of 0.80 (95% CI: 0.64-0.95, p = 0.006). The cut-off value of suPAR to discriminate between controlled and not controlled AP and ANP was 4.04 ng/mL. In conclusion, suPAR may help the objective assessment of asthma control, since it correlates with airway resistance and has good sensitivity in the detection of impaired asthma control. Decrease in circulating suPAR levels detected both in healthy and asthmatic pregnant women presumably represents pregnancy induced immune tolerance