Solving Kinetic Inversion Problems via a Physically Bounded Gauss−Newton (PGN) Method

Tang, Weiyong; Zhang, Libin; Linninger, Andreas A.; Tranter, Robert S.; Brezinsky, Kenneth

doi:10.1021/ie048872n

Cited by 36 publications

(34 citation statements)

References 42 publications

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“…(1) which we implemented with non-linear constrained optimization algorithms developed by our group. 69,79,80 The resulting network is an acyclic binary graph composed of cylindrical elements, where N is the number of segments belonging to the tree.…”

Section: Methodsmentioning

confidence: 99%

Cerebral Microcirculation and Oxygen Tension in the Human Secondary Cortex

et al. 2013

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The three-dimensional spatial arrangement of the cortical microcirculatory system is critical for understanding oxygen exchange between blood vessels and brain cells. A three-dimensional computer model of a 3 × 3 × 3 mm3 subsection of the human secondary cortex was constructed to quantify oxygen advection in the microcirculation, tissue oxygen perfusion, and consumption in the human cortex. This computer model accounts for all arterial, capillary and venous blood vessels of the cerebral microvascular bed as well as brain tissue occupying the extravascular space. Microvessels were assembled with optimization algorithms emulating angiogenic growth; a realistic capillary bed was built with space filling procedures. The extravascular tissue was modeled as a porous medium supplied with oxygen by advection–diffusion to match normal metabolic oxygen demand. The resulting synthetic computer generated network matches prior measured morphometrics and fractal patterns of the cortical microvasculature. This morphologically accurate, physiologically consistent, multi-scale computer network of the cerebral microcirculation predicts the oxygen exchange of cortical blood vessels with the surrounding gray matter. Oxygen tension subject to blood pressure and flow conditions were computed and validated for the blood as well as brain tissue. Oxygen gradients along arterioles, capillaries and veins agreed with in vivo trends observed recently in imaging studies within experimental tolerances and uncertainty.

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Section: Methodsmentioning

confidence: 99%

Cerebral Microcirculation and Oxygen Tension in the Human Secondary Cortex

et al. 2013

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“…It is well-known that multiple solutions may exist with equal error margins (Tang et al, 2005; Vajda and Rabitz, 1988; Zsely et al, 2004). Various combinations of parameters can fit the experimental data equally well within the experimental uncertainty, or some of the parameters may be interdependent.…”

Section: Discussionmentioning

confidence: 99%

“…In fact, the parameters of the model can be determined only if the sensitivity coefficients are non-zero and linearly independent (Beck and Arnold, 1977). More rigorously, Tang et al (2005) used the “physically bounded Gauss-Newton” (PGN) method by utilizing the sensitivity matrix as a global map to determine the unknown kinetic parameters of complex reaction networks that contain dozens of species and hundreds of reactions.…”

Section: Introductionmentioning

confidence: 99%

Resolution and uniqueness of estimated parameters of a model of thin filament regulation in solution

Mijailovich

Álamo

et al. 2010

Computational Biology and Chemistry

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The estimation of chemical kinetic rate constants for any non-trivial model is complex due to the nonlinear effects of second order chemical reactions. We developed an algorithm to accomplish this goal based on the Damped Least Squares (DLS) inversion method and then tested the effectiveness of this method on the McKillop-Geeves (MG) model of thin filament regulation. The kinetics of MG model is defined by a set of nonlinear ordinary differential equations (ODEs) that predict the evolution of troponin-tropomyosin-actin and actin-myosin states. The values of the rate constants are estimated by integrating these ODEs numerically and fitting them to a series of stopped-flow pyrene fluorescence transients of myosin-S1 fragment binding to regulated actin in solution. The accuracy and robustness of the estimated rate constants are evaluated for DLS and two other methods, namely quasi-Newton (QN) and simulated annealing (SA). The comparison of these methods revealed that SA provides the best estimates of the model parameters because of its global optimization scheme. However it converges slowly and does quantify the uniqueness of the estimated parameters. On the other hand the QN method converges rapidly but only if the initial guess of the parameters is close to the optimum values, otherwise it diverges. Overall, the DLS method proves to be the most convenient method. It converges fast and was able to provide excellent estimates of kinetic parameters. Furthermore, DLS provides the model resolution matrix, which quantifies the interdependence of model parameters thereby evaluating the uniqueness of their estimated values. This property is essential for estimating of the dependence of the model parameters on experimental conditions (e.g. Ca2+ concentration) when it is assessed from noisy experimental data such as pyrene fluorescence from stopped-flow transients. The advantages of the DLS method observed in this study should be further examined in other physicochemical systems to firmly establish the observed effectiveness of DSL vs. the other parameter estimation methods.

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“…Encouragingly, the subject of model optimization has become more ''acceptable'' in recent years, as evidenced by the rising number of publications of new optimization [72,73] and error-analysis [48,49,74] methods for extracting kinetic information from experimental observations. Recent efforts of Ruscic and co-workers on ''Active Thermochemical Tables'' [75] and of Frenkel and co-workers on ''ThermoData Engine'' [76] corroborate further the benefits of global multidataset optimization.…”

Section: Gri-mechmentioning

confidence: 99%