Parameter balancing in kinetic models of cell metabolism.
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ABSTRACT:
SUBMITTER: Lubitz T
PROVIDER: S-EPMC2999964 | biostudies-literature |
REPOSITORIES: biostudies-literature
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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.
| S-EPMC3568022 | biostudies-literature
Project description:MOTIVATION:Kinetic models contain unknown parameters that are estimated by optimizing the fit to experimental data. This task can be computationally challenging due to the presence of local optima and ill-conditioning. While a variety of optimization methods have been suggested to surmount these issues, it is difficult to choose the best one for a given problem a priori. A systematic comparison of parameter estimation methods for problems with tens to hundreds of optimization variables is currently missing, and smaller studies provided contradictory findings. RESULTS:We use a collection of benchmarks to evaluate the performance of two families of optimization methods: (i) multi-starts of deterministic local searches and (ii) stochastic global optimization metaheuristics; the latter may be combined with deterministic local searches, leading to hybrid methods. A fair comparison is ensured through a collaborative evaluation and a consideration of multiple performance metrics. We discuss possible evaluation criteria to assess the trade-off between computational efficiency and robustness. Our results show that, thanks to recent advances in the calculation of parametric sensitivities, a multi-start of gradient-based local methods is often a successful strategy, but a better performance can be obtained with a hybrid metaheuristic. The best performer combines a global scatter search metaheuristic with an interior point local method, provided with gradients estimated with adjoint-based sensitivities. We provide an implementation of this method to render it available to the scientific community. AVAILABILITY AND IMPLEMENTATION:The code to reproduce the results is provided as Supplementary Material and is available at Zenodo https://doi.org/10.5281/zenodo.1304034. SUPPLEMENTARY INFORMATION:Supplementary data are available at Bioinformatics online.
| S-EPMC6394396 | biostudies-literature
Project description:BackgroundStochastic effects can be important for the behavior of processes involving small population numbers, so the study of stochastic models has become an important topic in the burgeoning field of computational systems biology. However analysis techniques for stochastic models have tended to lag behind their deterministic cousins due to the heavier computational demands of the statistical approaches for fitting the models to experimental data. There is a continuing need for more effective and efficient algorithms. In this article we focus on the parameter inference problem for stochastic kinetic models of biochemical reactions given discrete time-course observations of either some or all of the molecular species.ResultsWe propose an algorithm for inference of kinetic rate parameters based upon maximum likelihood using stochastic gradient descent (SGD). We derive a general formula for the gradient of the likelihood function given discrete time-course observations. The formula applies to any explicit functional form of the kinetic rate laws such as mass-action, Michaelis-Menten, etc. Our algorithm estimates the gradient of the likelihood function by reversible jump Markov chain Monte Carlo sampling (RJMCMC), and then gradient descent method is employed to obtain the maximum likelihood estimation of parameter values. Furthermore, we utilize flux balance analysis and show how to automatically construct reversible jump samplers for arbitrary biochemical reaction models. We provide RJMCMC sampling algorithms for both fully observed and partially observed time-course observation data. Our methods are illustrated with two examples: a birth-death model and an auto-regulatory gene network. We find good agreement of the inferred parameters with the actual parameters in both models.ConclusionsThe SGD method proposed in the paper presents a general framework of inferring parameters for stochastic kinetic models. The method is computationally efficient and is effective for both partially and fully observed systems. Automatic construction of reversible jump samplers and general formulation of the likelihood gradient function makes our method applicable to a wide range of stochastic models. Furthermore our derivations can be useful for other purposes such as using the gradient information for parametric sensitivity analysis or using the reversible jump samplers for full Bayesian inference. The software implementing the algorithms is publicly available at http://cbcl.ics.uci.edu/sgd.
| S-EPMC2914651 | biostudies-literature
Project description:BackgroundKinetic models of biochemical systems usually consist of ordinary differential equations that have many unknown parameters. Some of these parameters are often practically unidentifiable, that is, their values cannot be uniquely determined from the available data. Possible causes are lack of influence on the measured outputs, interdependence among parameters, and poor data quality. Uncorrelated parameters can be seen as the key tuning knobs of a predictive model. Therefore, before attempting to perform parameter estimation (model calibration) it is important to characterize the subset(s) of identifiable parameters and their interplay. Once this is achieved, it is still necessary to perform parameter estimation, which poses additional challenges.MethodsWe present a methodology that (i) detects high-order relationships among parameters, and (ii) visualizes the results to facilitate further analysis. We use a collinearity index to quantify the correlation between parameters in a group in a computationally efficient way. Then we apply integer optimization to find the largest groups of uncorrelated parameters. We also use the collinearity index to identify small groups of highly correlated parameters. The results files can be visualized using Cytoscape, showing the identifiable and non-identifiable groups of parameters together with the model structure in the same graph.ResultsOur contributions alleviate the difficulties that appear at different stages of the identifiability analysis and parameter estimation process. We show how to combine global optimization and regularization techniques for calibrating medium and large scale biological models with moderate computation times. Then we evaluate the practical identifiability of the estimated parameters using the proposed methodology. The identifiability analysis techniques are implemented as a MATLAB toolbox called VisId, which is freely available as open source from GitHub ( https://github.com/gabora/visid ).ConclusionsOur approach is geared towards scalability. It enables the practical identifiability analysis of dynamic models of large size, and accelerates their calibration. The visualization tool allows modellers to detect parts that are problematic and need refinement or reformulation, and provides experimentalists with information that can be helpful in the design of new experiments.
| S-EPMC5420165 | biostudies-literature
Project description:MotivationTime-series measurements of metabolite concentration have become increasingly more common, providing data for building kinetic models of metabolic networks using ordinary differential equations (ODEs). In practice, however, such time-course data are usually incomplete and noisy, and the estimation of kinetic parameters from these data is challenging. Practical limitations due to data and computational aspects, such as solving stiff ODEs and finding global optimal solution to the estimation problem, give motivations to develop a new estimation procedure that can circumvent some of these constraints.ResultsIn this work, an incremental and iterative parameter estimation method is proposed that combines and iterates between two estimation phases. One phase involves a decoupling method, in which a subset of model parameters that are associated with measured metabolites, are estimated using the minimization of slope errors. Another phase follows, in which the ODE model is solved one equation at a time and the remaining model parameters are obtained by minimizing concentration errors. The performance of this two-phase method was tested on a generic branched metabolic pathway and the glycolytic pathway of Lactococcus lactis. The results showed that the method is efficient in getting accurate parameter estimates, even when some information is missing.
| S-EPMC6281308 | biostudies-literature
Project description:Stochastic chemical kinetics has become a staple for mechanistically modeling various phenomena in systems biology. These models, even more so than their deterministic counterparts, pose a challenging problem in the estimation of kinetic parameters from experimental data. As a result of the inherent randomness involved in stochastic chemical kinetic models, the estimation methods tend to be statistical in nature. Three classes of estimation methods are implemented and compared in this paper. The first is the exact method, which uses the continuous-time Markov chain representation of stochastic chemical kinetics and is tractable only for a very restricted class of problems. The next class of methods is based on Markov chain Monte Carlo (MCMC) techniques. The third method, termed conditional density importance sampling (CDIS), is a new method introduced in this paper. The use of these methods is demonstrated on two examples taken from systems biology, one of which is a new model of single-cell viral infection. The applicability, strengths and weaknesses of the three classes of estimation methods are discussed. Using simulated data for the two examples, some guidelines are provided on experimental design to obtain more information from a limited number of measurements.
| S-EPMC4946376 | biostudies-literature
Project description:In systems biology, experimentally measured parameters are not always available, necessitating the use of computationally based parameter estimation. In order to rely on estimated parameters, it is critical to first determine which parameters can be estimated for a given model and measurement set. This is done with parameter identifiability analysis. A kinetic model of the sucrose accumulation in the sugar cane culm tissue developed by Rohwer et al. was taken as a test case model. What differentiates this approach is the integration of an orthogonal-based local identifiability method into the unscented Kalman filter (UKF), rather than using the more common observability-based method which has inherent limitations. It also introduces a variable step size based on the system uncertainty of the UKF during the sensitivity calculation. This method identified 10 out of 12 parameters as identifiable. These ten parameters were estimated using the UKF, which was run 97 times. Throughout the repetitions the UKF proved to be more consistent than the estimation algorithms used for comparison.
| S-EPMC3224596 | biostudies-literature
Project description:The current manuscript addresses the problem of parameter estimation for kinetic models of chemical reaction networks from observed time series partial experimental data of species concentrations. It is demonstrated how the Kron reduction method of kinetic models, in conjunction with the (weighted) least squares optimization technique, can be used as a tool to solve the above-mentioned ill-posed parameter estimation problem. First, a new trajectory-independent measure is introduced to quantify the dynamical difference between the original mathematical model and the corresponding Kron-reduced model. This measure is then crucially used to estimate the parameters contained in the kinetic model so that the corresponding values of the species' concentrations predicted by the model fit the available experimental data. The new parameter estimation method is tested on two real-life examples of chemical reaction networks: nicotinic acetylcholine receptors and Trypanosoma brucei trypanothione synthetase. Both weighted and unweighted least squares techniques, combined with Kron reduction, are used to find the best-fitting parameter values. The method of leave-one-out cross-validation is utilized to determine the preferred technique. For nicotinic receptors, the training errors due to the application of unweighted and weighted least squares are 3.22 and 3.61 respectively, while for Trypanosoma synthetase, the application of unweighted and weighted least squares result in training errors of 0.82 and 0.70 respectively. Furthermore, the problem of identifiability of dynamical systems, i.e., the possibility of uniquely determining the parameters from certain types of output, has also been addressed.
| S-EPMC10526083 | biostudies-literature
Project description:Whole-cell models that explicitly represent all cellular components at the molecular level have the potential to predict phenotype from genotype. However, even for simple bacteria, whole-cell models will contain thousands of parameters, many of which are poorly characterized or unknown. New algorithms are needed to estimate these parameters and enable researchers to build increasingly comprehensive models. We organized the Dialogue for Reverse Engineering Assessments and Methods (DREAM) 8 Whole-Cell Parameter Estimation Challenge to develop new parameter estimation algorithms for whole-cell models. We asked participants to identify a subset of parameters of a whole-cell model given the model's structure and in silico "experimental" data. Here we describe the challenge, the best performing methods, and new insights into the identifiability of whole-cell models. We also describe several valuable lessons we learned toward improving future challenges. Going forward, we believe that collaborative efforts supported by inexpensive cloud computing have the potential to solve whole-cell model parameter estimation.
| S-EPMC4447414 | biostudies-literature
Project description:SummaryKinetic models of metabolism are crucial to understand the inner workings of cell metabolism. By taking into account enzyme regulation, detailed kinetic models can provide accurate predictions of metabolic fluxes. Comprehensive consideration of kinetic regulation requires highly parameterized non-linear models, which are challenging to build and fit using available modelling tools. Here, we present a computational package implementing the GRASP framework for building detailed kinetic models of cellular metabolism. By defining the mechanisms of enzyme regulation and a reference state described by reaction fluxes and their corresponding Gibbs free energy ranges, GRASP can efficiently sample an arbitrarily large population of thermodynamically feasible kinetic models. If additional experimental data are available (fluxes, enzyme and metabolite concentrations), these can be integrated to generate models that closely reproduce these observations using an approximate Bayesian computation fitting framework. Within the same framework, model selection tasks can be readily performed.Availability and implementationGRASP is implemented as an open-source package in the MATLAB environment. The software runs in Windows, macOS and Linux, is documented (graspk.readthedocs.io) and unit-tested. GRASP is freely available at github.com/biosustain/GRASP.Supplementary informationSupplementary data are available at Bioinformatics Advances online.
| S-EPMC9710608 | biostudies-literature