How catalytic mechanisms reveal themselves in multiple steady-state data: II. An ethylene hydrogenation example

Ellison, Phillipp; Feinberg, Martin; Yue, Ming-Huei; Saltsburg, Howard

doi:10.1016/s1381-1169(99)00372-6

Cited by 23 publications

(6 citation statements)

References 9 publications

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“…Thus, we provide a richer and more powerful framework for the application of this basic technique. Chemical reaction network theory (CRNT) [8,9] and stoichiometric network analysis [10] likewise embrace a parameter-free philosophy and can also be exploited for model selection [11][12][13].…”

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confidence: 99%

Parameter-free model discrimination criterion based on steady-state coplanarity

Harrington

Thorne

et al. 2012

Proc. Natl. Acad. Sci. U.S.A.

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We introduce a procedure for deciding when a mass-action model is incompatible with observed steady-state data that does not require any parameter estimation. Thus, we avoid the difficulties of nonlinear optimization typically associated with methods based on parameter fitting. Instead, we borrow ideas from algebraic geometry to construct a transformation of the model variables such that any set of steady states of the model under that transformation lies on a common plane, irrespective of the values of the model parameters. Model rejection can then be performed by assessing the degree to which the transformed data deviate from coplanarity. We demonstrate our method by applying it to models of multisite phosphorylation and cell death signaling. Our framework offers a parameter-free perspective on the statistical model selection problem, which can complement conventional statistical methods in certain classes of problems where inference has to be based on steady-state data and the model structures allow for suitable algebraic relationships among the steady-state solutions.I n many branches of science and engineering, one is often interested in the problem of model selection: Given observed data and a set of candidate models for the process generating that data, which is the most appropriate model for that process? Such a situation commonly arises when the inner workings of a process are not completely understood, so that multiple models are consistent with the current state of knowledge. For mechanistic models, e.g., ordinary differential equation (ODE) or stochastic dynamical models, most selection techniques involve parameter estimation, which typically requires some form of optimization, exploration of the parameter space, or formal inference procedure (1, 2). For sufficiently complicated models, however, this task can become infeasible, owing to the nonlinearity and multimodality of the objective function (which penalizes any differences between the data and the model predictions), as well as the high dimensionality of the parameter space (3).Here, we present a framework for the discrimination of massaction ODE models (and suitable generalizations thereof) that does not require or rely upon such estimated parameters. Our method (Fig. 1) operates on steady-state data and combines techniques from algebraic geometry, linear algebra, and statistics to determine when a given model is incompatible with the data under all choices of the model parameters. The core idea is to use the model equations to construct a transformation of the original variables such that any set of steady states of the model under that transformation possesses a simple geometric structure, irrespective of parameter values. In this case, we insist that the transformed steady states lie on a plane, which we detect numerically; if the observed data are not coplanar under the transformation induced by a given model, then we can confidently reject that model.The idea of transformation to coplanarity has been employed before, but previous efforts ...

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confidence: 99%

Parameter-free model discrimination criterion based on steady-state coplanarity

Harrington

Thorne

et al. 2012

Proc. Natl. Acad. Sci. U.S.A.

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“…The Eq. (7a) indicates the relationships of the two steady states, which can be used to identify mechanism as the steady states of some species are measured (Ellison and Feinberg, 2000). The more numbers of the inequalities and the equations of Eq.…”

Section: Multiple Steady States In a Deficiency One Subnetworkmentioning

confidence: 99%

Computational multiple steady states for enzymatic esterification of ethanol and oleic acid in an isothermal CSTR

Ho¹,

Chuang²,

Chao³

et al. 2005

Biosystems

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“…Some particularly sound results are stated in the deficiency-zero and deficiency-one theorems [12,13]. Explicit conditions for multiple equilibria were given in [14][15][16][17] whereas graph-oriented methods have been proposed in [18]. In connection with the stability of equilibria, a thermodynamic based stability criterion for biochemical networks under uncertainty has been proposed in [19].…”

Section: Introductionmentioning

confidence: 99%

Routes to Multiple Equilibria for Mass‐Action Kinetic Systems

2018

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In this work we explore two potential mechanisms inducing multiple equilibria for weakly reversible networks with mass-action kinetics. The study is performed on a class of polynomial dynamic systems that, under some mild assumptions, are able to accommodate in their state-space form weakly reversible mass-action kinetic networks. The contribution is twofold. We provide an explicit representation of the set of all positive equilibria attained by the system class in terms of a set of (positive parameter dependent) algebraic relations. With this in hand, we prove that deficiency-one networks can only admit multiple equilibria via folding of the equilibrium manifold, whereas a bifurcation leading to multiple branches is only possible in networks with deficiencies larger than one. Interestingly, some kinetic networks within this latter class are capable of sustaining multiple equilibria for any reaction simplex, as we illustrate with one example.

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How catalytic mechanisms reveal themselves in multiple steady-state data: II. An ethylene hydrogenation example

Cited by 23 publications

References 9 publications

Parameter-free model discrimination criterion based on steady-state coplanarity

Parameter-free model discrimination criterion based on steady-state coplanarity

Computational multiple steady states for enzymatic esterification of ethanol and oleic acid in an isothermal CSTR

Routes to Multiple Equilibria for Mass‐Action Kinetic Systems

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