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Dattner I, Ship H, Voit EO. Separable Nonlinear Least-Squares Parameter Estimation for Complex Dynamic Systems. COMPLEXITY 2020; 2020:6403641. [PMID: 34113070 PMCID: PMC8188859 DOI: 10.1155/2020/6403641] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Nonlinear dynamic models are widely used for characterizing processes that govern complex biological pathway systems. Over the past decade, validation and further development of these models became possible due to data collected via high-throughput experiments using methods from molecular biology. While these data are very beneficial, they are typically incomplete and noisy, which renders the inference of parameter values for complex dynamic models challenging. Fortunately, many biological systems have embedded linear mathematical features, which may be exploited, thereby improving fits and leading to better convergence of optimization algorithms. In this paper, we explore options of inference for dynamic models using a novel method of separable nonlinear least-squares optimization and compare its performance to the traditional nonlinear least-squares method. The numerical results from extensive simulations suggest that the proposed approach is at least as accurate as the traditional nonlinear least-squares, but usually superior, while also enjoying a substantial reduction in computational time.
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Affiliation(s)
- Itai Dattner
- Department of Statistics, University of Haifa, 199 Aba Khoushy Ave., Mount Carmel, Haifa 3498838, Israel
| | - Harold Ship
- Department of Statistics, University of Haifa, 199 Aba Khoushy Ave., Mount Carmel, Haifa 3498838, Israel
| | - Eberhard O. Voit
- The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, 950 Atlantic Drive, Atslanta, GA 30332–2000, USA
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Faraji M, Fonseca LL, Escamilla-Treviño L, Barros-Rios J, Engle N, Yang ZK, Tschaplinski TJ, Dixon RA, Voit EO. Mathematical models of lignin biosynthesis. BIOTECHNOLOGY FOR BIOFUELS 2018; 11:34. [PMID: 29449882 PMCID: PMC5806469 DOI: 10.1186/s13068-018-1028-9] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/09/2017] [Accepted: 01/20/2018] [Indexed: 05/26/2023]
Abstract
BACKGROUND Lignin is a natural polymer that is interwoven with cellulose and hemicellulose within plant cell walls. Due to this molecular arrangement, lignin is a major contributor to the recalcitrance of plant materials with respect to the extraction of sugars and their fermentation into ethanol, butanol, and other potential bioenergy crops. The lignin biosynthetic pathway is similar, but not identical in different plant species. It is in each case comprised of a moderate number of enzymatic steps, but its responses to manipulations, such as gene knock-downs, are complicated by the fact that several of the key enzymes are involved in several reaction steps. This feature poses a challenge to bioenergy production, as it renders it difficult to select the most promising combinations of genetic manipulations for the optimization of lignin composition and amount. RESULTS Here, we present several computational models than can aid in the analysis of data characterizing lignin biosynthesis. While minimizing technical details, we focus on the questions of what types of data are particularly useful for modeling and what genuine benefits the biofuel researcher may gain from the resulting models. We demonstrate our analysis with mathematical models for black cottonwood (Populus trichocarpa), alfalfa (Medicago truncatula), switchgrass (Panicum virgatum) and the grass Brachypodium distachyon. CONCLUSIONS Despite commonality in pathway structure, different plant species show different regulatory features and distinct spatial and topological characteristics. The putative lignin biosynthes pathway is not able to explain the plant specific laboratory data, and the necessity of plant specific modeling should be heeded.
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Affiliation(s)
- Mojdeh Faraji
- The Wallace H. Coulter, Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, 313, Ferst Drive, Atlanta, GA 30332 USA
- BioEnergy Sciences Center (BESC), Oak Ridge National Lab, Oak Ridge, TN USA
| | - Luis L. Fonseca
- The Wallace H. Coulter, Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, 313, Ferst Drive, Atlanta, GA 30332 USA
- BioEnergy Sciences Center (BESC), Oak Ridge National Lab, Oak Ridge, TN USA
| | - Luis Escamilla-Treviño
- BioEnergy Sciences Center (BESC), Oak Ridge National Lab, Oak Ridge, TN USA
- Department of Biological Sciences, University of North Texas, 1155 Union Circle #305220, Denton, TX 76203-5017 USA
| | - Jaime Barros-Rios
- BioEnergy Sciences Center (BESC), Oak Ridge National Lab, Oak Ridge, TN USA
- Department of Biological Sciences, University of North Texas, 1155 Union Circle #305220, Denton, TX 76203-5017 USA
| | - Nancy Engle
- BioEnergy Sciences Center (BESC), Oak Ridge National Lab, Oak Ridge, TN USA
- Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, TN 37831 USA
| | - Zamin K. Yang
- BioEnergy Sciences Center (BESC), Oak Ridge National Lab, Oak Ridge, TN USA
- Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, TN 37831 USA
| | - Timothy J. Tschaplinski
- BioEnergy Sciences Center (BESC), Oak Ridge National Lab, Oak Ridge, TN USA
- Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, TN 37831 USA
| | - Richard A. Dixon
- BioEnergy Sciences Center (BESC), Oak Ridge National Lab, Oak Ridge, TN USA
- Department of Biological Sciences, University of North Texas, 1155 Union Circle #305220, Denton, TX 76203-5017 USA
| | - Eberhard O. Voit
- The Wallace H. Coulter, Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, 313, Ferst Drive, Atlanta, GA 30332 USA
- BioEnergy Sciences Center (BESC), Oak Ridge National Lab, Oak Ridge, TN USA
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Voit EO. The best models of metabolism. WILEY INTERDISCIPLINARY REVIEWS. SYSTEMS BIOLOGY AND MEDICINE 2017; 9:10.1002/wsbm.1391. [PMID: 28544810 PMCID: PMC5643013 DOI: 10.1002/wsbm.1391] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2017] [Revised: 03/31/2017] [Accepted: 04/01/2017] [Indexed: 12/25/2022]
Abstract
Biochemical systems are among of the oldest application areas of mathematical modeling. Spanning a time period of over one hundred years, the repertoire of options for structuring a model and for formulating reactions has been constantly growing, and yet, it is still unclear whether or to what degree some models are better than others and how the modeler is to choose among them. In fact, the variety of options has become overwhelming and difficult to maneuver for novices and experts alike. This review outlines the metabolic model design process and discusses the numerous choices for modeling frameworks and mathematical representations. It tries to be inclusive, even though it cannot be complete, and introduces the various modeling options in a manner that is as unbiased as that is feasible. However, the review does end with personal recommendations for the choices of default models. WIREs Syst Biol Med 2017, 9:e1391. doi: 10.1002/wsbm.1391 For further resources related to this article, please visit the WIREs website.
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Affiliation(s)
- Eberhard O Voit
- Department of Biomedical Engineering, Georgia Institute of Technology, Atlanta, GA, USA
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