A single-parameter family of adjustments for fitting enzyme kinetic models to progress-curve data.
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ABSTRACT:
SUBMITTER: Duggleby RG
PROVIDER: S-EPMC1135537 | biostudies-other | 1989 Jan
REPOSITORIES: biostudies-other
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Project description:A method is described whereby net rate constants can be directly inferred from the progress curves of enzyme intermediates without the need for model specification, numerical analysis, curve fitting, or the steady-state approximation. Specifically, if an enzyme intermediate in an ultimately irreversible serial subsequence is perturbed from and returns back to its equilibrium state as the substrate is consumed, then its net rate constant is given by the ratio of the total substrate consumed and the area under the progress curve for the enzyme intermediate. A rigorous analysis demonstrates this result to hold independent of the complete enzymatic reaction in which the subsequence is embedded, making it broadly applicable to a very wide range of kinetic mechanisms, including those complicated by inhibition. As a theoretical consequence, it is shown that traditionally steady-state parameters such as kcat, kcat/KM, and net rate constants can be expressed as limiting ratios of averages without requiring the steady-state hypothesis. Finally, a mock data set is generated for a system of contemporary interest that can serve as both an example of how the methodology would be used in practice and a proof of concept.
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Project description:Kinetic modeling of metabolic pathways has become a major field of systems biology. It combines structural information about metabolic pathways with quantitative enzymatic rate laws. Some of the kinetic constants needed for a model could be collected from ever-growing literature and public web resources, but they are often incomplete, incompatible, or simply not available. We address this lack of information by parameter balancing, a method to complete given sets of kinetic constants. Based on Bayesian parameter estimation, it exploits the thermodynamic dependencies among different biochemical quantities to guess realistic model parameters from available kinetic data. Our algorithm accounts for varying measurement conditions in the input data (pH value and temperature). It can process kinetic constants and state-dependent quantities such as metabolite concentrations or chemical potentials, and uses prior distributions and data augmentation to keep the estimated quantities within plausible ranges. An online service and free software for parameter balancing with models provided in SBML format (Systems Biology Markup Language) is accessible at www.semanticsbml.org. We demonstrate its practical use with a small model of the phosphofructokinase reaction and discuss its possible applications and limitations. In the future, parameter balancing could become an important routine step in the kinetic modeling of large metabolic networks.
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Project description:BackgroundAn efficient and reliable parameter estimation method is essential for the creation of biological models using ordinary differential equation (ODE). Most of the existing estimation methods involve finding the global minimum of data fitting residuals over the entire parameter space simultaneously. Unfortunately, the associated computational requirement often becomes prohibitively high due to the large number of parameters and the lack of complete parameter identifiability (i.e. not all parameters can be uniquely identified).ResultsIn this work, an incremental approach was applied to the parameter estimation of ODE models from concentration time profiles. Particularly, the method was developed to address a commonly encountered circumstance in the modeling of metabolic networks, where the number of metabolic fluxes (reaction rates) exceeds that of metabolites (chemical species). Here, the minimization of model residuals was performed over a subset of the parameter space that is associated with the degrees of freedom in the dynamic flux estimation from the concentration time-slopes. The efficacy of this method was demonstrated using two generalized mass action (GMA) models, where the method significantly outperformed single-step estimations. In addition, an extension of the estimation method to handle missing data is also presented.ConclusionsThe proposed incremental estimation method is able to tackle the issue on the lack of complete parameter identifiability and to significantly reduce the computational efforts in estimating model parameters, which will facilitate kinetic modeling of genome-scale cellular metabolism in the future.
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Project description:Highly efficient and rapid lead compound evaluation for estimation of inhibition parameters and type of inhibition is proposed. This is based on a single progress-curve measurement in the presence of each candidate compound, followed by the simultaneous analysis of all of these curves using the ENZO enzyme kinetics suite, which can be implemented as a web application. In the first step, all of the candidate ligands are tested as competitive inhibitors. Where the theoretical curves do not correspond to the experimental data, minimal additional measurements are added, with subsequent processing according to modified reaction mechanisms.
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Project description:A method is described for fitting the velocities obtained from progress curves to a steady-state rate equation. It is based on the method of Markus & Plesser [(1981) in Kinetic Data Analysis: Design and Analysis of Enzyme and Kinetic Data (Edrenyi, ed.), pp. 317-339, Plenum Press, New York]. The obstacle of needing good initial estimates of kinetic parameters is removed by using the parameters provided graphically by a minor modification of the method of Yun & Suelter [(1977) Biochim, Biophys. Acta 480, 1-13]. This progress-curved-based method allows the same discrimination among rival models as do the initial-velocity-based methods, with a great saving of experimental time. The BASIC and FORTRAN 77 programs are deposited as Supplementary Publication SUP 50132 (17 pages) at the British Library (Lending Division), Boston Spa, Wetherby, West Yorkshire LS23 7BQ, U.K., from whom copies can be obtained on the terms indicated in Biochem. J. (1986) 233, 5-6.
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Project description:Kinetic modeling is widely used to analyze dynamic imaging data, estimating kinetic parameters that quantify functional or physiologic processes in vivo. Typical kinetic models give rise to nonlinear solution equations in multiple dimensions, presenting a complex fitting environment. This work generalizes previously described separable nonlinear least-squares techniques for fitting serial compartment models with up to three tissue compartments and five rate parameters.The approach maximally separates the linear and nonlinear aspects of the modeling equations, using a formulation modified from previous basis function methods to avoid a potential mathematical degeneracy. A fast and robust algorithm for solving the linear subproblem with full user-defined constraints is also presented. The generalized separable parameter space technique effectively reduces the dimensionality of the nonlinear fitting problem to one dimension for 2K-3K compartment models, and to two dimensions for 4K-5K models.Exhaustive search fits, which guarantee identification of the true global minimum fit, required approximately 10 ms for 2K-3K and 1.1 s for 4K-5K models, respectively. The technique is also amenable to fast gradient-descent iterative fitting algorithms, where the reduced dimensionality offers improved convergence properties. The objective function for the separable parameter space nonlinear subproblem was characterized and found to be generally well-behaved with a well-defined global minimum. Separable parameter space fits with the Levenberg-Marquardt algorithm required fewer iterations than comparable fits for conventional model formulations, averaging 1 and 7 ms for 2K-3K and 4K-5K models, respectively. Sensitivity to initial conditions was likewise reduced.The separable parameter space techniques described herein generalize previously described techniques to encompass 1K-5K compartment models, enable robust solution of the linear subproblem with full user-defined constraints, and are amenable to rapid and robust fitting using iterative gradient-descent type algorithms.
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Project description:The inference of reaction rate parameters in biochemical network models from time series concentration data is a central task in computational systems biology. Under the assumption of well mixed conditions the network dynamics are typically described by the chemical master equation, the Fokker Planck equation, the linear noise approximation or the macroscopic rate equation. The inverse problem of estimating the parameters of the underlying network model can be approached in deterministic and stochastic ways, and available methods often compare individual or mean concentration traces obtained from experiments with theoretical model predictions when maximizing likelihoods, minimizing regularized least squares functionals, approximating posterior distributions or sequentially processing the data. In this article we assume that the biological reaction network can be observed at least partially and repeatedly over time such that sample moments of species molecule numbers for various time points can be calculated from the data. Based on the chemical master equation we furthermore derive closed systems of parameter dependent nonlinear ordinary differential equations that predict the time evolution of the statistical moments. For inferring the reaction rate parameters we suggest to not only compare the sample mean with the theoretical mean prediction but also to take the residual of higher order moments explicitly into account. Cost functions that involve residuals of higher order moments may form landscapes in the parameter space that have more pronounced curvatures at the minimizer and hence may weaken or even overcome parameter sloppiness and uncertainty. As a consequence both deterministic and stochastic parameter inference algorithms may be improved with respect to accuracy and efficiency. We demonstrate the potential of moment fitting for parameter inference by means of illustrative stochastic biological models from the literature and address topics for future research.
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