Set-base dynamical parameter estimation and model invalidation for biochemical reaction networks

<p>Abstract</p> <p>Background</p> <p>Mathematical modeling and analysis have become, for the study of biological and cellular processes, an important complement to experimental research. However, the structural and quantitative knowledge available for such processes is frequently limited, and measurements are often subject to inherent and possibly large uncertainties. This results in competing model hypotheses, whose kinetic parameters may not be experimentally determinable. Discriminating among these alternatives and estimating their kinetic parameters is crucial to improve the understanding of the considered process, and to benefit from the analytical tools at hand.</p> <p>Results</p> <p>In this work we present a set-based framework that allows to discriminate between competing model hypotheses and to provide guaranteed outer estimates on the model parameters that are consistent with the (possibly sparse and uncertain) experimental measurements. This is obtained by means of exact proofs of model invalidity that exploit the polynomial/rational structure of biochemical reaction networks, and by making use of an efficient strategy to balance solution accuracy and computational effort.</p> <p>Conclusions</p> <p>The practicability of our approach is illustrated with two case studies. The first study shows that our approach allows to conclusively rule out wrong model hypotheses. The second study focuses on parameter estimation, and shows that the proposed method allows to evaluate the global influence of measurement sparsity, uncertainty, and prior knowledge on the parameter estimates. This can help in designing further experiments leading to improved parameter estimates.</p

Heterogeneity reduces sensitivity of cell death for TNF-Stimuli

Background Apoptosis is a form of programmed cell death essential for the maintenance of homeostasis and the removal of potentially damaged cells in multicellular organisms. By binding its cognate membrane receptor, TNF receptor type 1 (TNF-R1), the proinflammatory cytokine Tumor Necrosis Factor (TNF) activates pro-apoptotic signaling via caspase activation, but at the same time also stimulates nuclear factor kappaB (NF-kappaB)-mediated survival pathways. Differential dose-response relationships of these two major TNF signaling pathways have been described experimentally and using mathematical modeling. However, the quantitative analysis of the complex interplay between pro- and anti-apoptotic signaling pathways is an open question as it is challenging for several reasons: the overall signaling network is complex, various time scales are present, and cells respond quantitatively and qualitatively in a heterogeneous manner. Results This study analyzes the complex interplay of the crosstalk of TNF-R1 induced pro- and anti-apoptotic signaling pathways based on an experimentally validated mathematical model. The mathematical model describes the temporal responses on both the single cell level as well as the level of a heterogeneous cell population, as observed in the respective quantitative experiments using TNF-R1 stimuli of different strengths and durations. Global sensitivity of the heterogeneous population was quantified by measuring the average gradient of time of death versus each population parameter. This global sensitivity analysis uncovers the concentrations of Caspase-8 and Caspase-3, and their respective inhibitors BAR and XIAP, as key elements for deciding the cell's fate. A simulated knockout of the NF-kappaB-mediated anti-apoptotic signaling reveals the importance of this pathway for delaying the time of death, reducing the death rate in the case of pulse stimulation and significantly increasing cell-to-cell variability. Conclusions Cell ensemble modeling of a heterogeneous cell population including a global sensitivity analysis presented here allowed us to illuminate the role of the different elements and parameters on apoptotic signaling. The receptors serve to transmit the external stimulus; procaspases and their inhibitors control the switching from life to death, while NF-kappaB enhances the heterogeneity of the cell population. The global sensitivity analysis of the cell population model further revealed an unexpected impact of heterogeneity, i.e. the reduction of parametric sensitivity

Graph problems arising from parameter identification of discrete dynamical systems

This paper focuses on combinatorial feasibility and optimization problems that arise in the context of parameter identification of discrete dynamical systems. Given a candidate parametric model for a physical system and a set of experimental observations, the objective of parameter identification is to provide estimates of the parameter values for which the model can reproduce the experiments. To this end, we define a finite graph corresponding to the model, to each arc of which a set of parameters is associated. Paths in this graph are regarded as feasible only if the sets of parameters corresponding to the arcs of the path have nonempty intersection. We study feasibility and optimization problems on such feasible paths, focusing on computational complexity. We show that, under certain restrictions on the sets of parameters, some of the problems become tractable, whereas others are NP-hard. In a similar vein, we define and study some graph problems for experimental design, whose goal is to support the scientist in optimally designing new experiment

Dynamics of the Landau-Pomeranchuk-Migdal Effect in Au+Au Collisions at 200 AGeV

We study the role played by the Landau-Pomeranchuk-Midgal (LPM) effect in relativistic collisions of hadrons and heavy nuclei, within a parton cascade model. We find that the LPM effect strongly affects the gluon multiplication due to radiation and considerably alters the space-time evolution of the dynamics of the collision. It ensures a multiplicity distribution of hadrons in aggreement with the experimental proton-proton data. We study the production of single photons in relativistic heavy ion collisions and find that the inclusion of LPM suppression leads to a reduction in the single photon yield at small and intermediate transverse momenta. The parton cascade calculation of the single photon yield including the LPM effect is shown to be in good agreement with the recent PHENIX data taken at the Relativistic Heavy-Ion Collider.Comment: 12 pages, 4 figure

Influence of discretization errors on set-based parameter estimation

In this paper we investigate the relationship between parameter estimates obtained for a nonlinear discrete-time (DT) approximation of a continuous-time (CT) nonlinear model and the parameters corresponding to the CT model itself. Preliminary results based on a set-based parameter estimation approach are proposed. The focus is thereby directed on formalizing the problem of ensuring that the set of consistent parameters of the CT model are also related to the consistent parameters of the DT model. Therefore, we propose two approaches to handle this problem. The first is based on a direct treatment of the discretization error, while the other is based on a differential geometric relationship of Euler discretization and the CT model. Two examples, one academic example and another one applying the proposed results to a well-known biological process, namely the Michaelis-Menten (MM) reaction, are presented to illustrate the usefulness of the result

Rasgos petrográficos y geoquímicos de los granitoides y rocas metamórficas del área Morille-Martinamor (Salamanca. centro oeste de España)

7 páginas, 4 figuras.[ES] Las rocas metamórficas del área (cuarcitas con distintos grados de pureza, porfiroides, pelíticas, calcosilicatadas, migmatíticas y sus equivalentes cataclásticos) permiten establecer un origen sedimentario con posible y variable aporte calcoalcalino ácido en algunos tipos, sin que los niveles ca1cosilicatados presenten características ortoderivadas. Los granitos están ligados, en su mayoría, a las peculiaridades típicas de términos leucocráticos generados por anatexia cortical y se agrupan sin diferencias manifiestas entre sus diferentes facies. Los ortoneises, claramente anteriores, exhiben un comportamiento específico, situado entre los típicos de ambos grupos.[EN] The metamorphic rocks from Morille-Martinamor area (quartz-feldspathic, aluminous, clac-silicate, migmatic and cataclastic rocks) are varied; the geochemical and mineralogical features allow to found a sedimentary arigin with possible and variable acid calcoalkaline contribution for some groups, without orthoderived characteristic for the studied calc-silicate levels. The granites mainly are linked to the typical traits of leucocratic range, which are generated by crustal anatexis, and they are grouped without strong differences. The orthogneiss are older and show a typical behaviour, fairly placed between the two groups.Peer reviewe

Guaranteed steady state bounds for uncertain (bio-)chemical processes using infeasibility certificates

Analysis and safety considerations of chemical and biological processes require complete knowledge of the set of all feasible steady states. Nonlinearities, uncertain parameters, and discrete variables complicate the task of obtaining this set. In this paper, the problem of outer-approximating the region of feasible steady states, for processes described by uncertain nonlinear differential algebraic equations including discrete variables and discrete changes in the dynamics, is addressed. The calculation of the outer bounds is based on a relaxed version of the corresponding feasibility problem. It uses the Lagrange dual problem to obtain certificates for regions in state space not containing steady states. These infeasibility certificates can be computed efficiently by solving a semidefinite program, rendering the calculation of an outer bounding set computationally feasible. The derived method guarantees globally valid outer bounds for the feasible steady states. The method is exemplified by the analysis of a simple chemical reactor showing parametric uncertainties and large variability due to the appearance of bifurcations characterising the ignition and extinction of a reaction. © 2010 Elsevier Ltd All rights reserved.status: publishe