IDEAS home Printed from https://ideas.repec.org/a/plo/pcbi00/1000696.html
   My bibliography  Save this article

Parameter Estimation and Model Selection in Computational Biology

Author

Listed:
  • Gabriele Lillacci
  • Mustafa Khammash

Abstract

A central challenge in computational modeling of biological systems is the determination of the model parameters. Typically, only a fraction of the parameters (such as kinetic rate constants) are experimentally measured, while the rest are often fitted. The fitting process is usually based on experimental time course measurements of observables, which are used to assign parameter values that minimize some measure of the error between these measurements and the corresponding model prediction. The measurements, which can come from immunoblotting assays, fluorescent markers, etc., tend to be very noisy and taken at a limited number of time points. In this work we present a new approach to the problem of parameter selection of biological models. We show how one can use a dynamic recursive estimator, known as extended Kalman filter, to arrive at estimates of the model parameters. The proposed method follows. First, we use a variation of the Kalman filter that is particularly well suited to biological applications to obtain a first guess for the unknown parameters. Secondly, we employ an a posteriori identifiability test to check the reliability of the estimates. Finally, we solve an optimization problem to refine the first guess in case it should not be accurate enough. The final estimates are guaranteed to be statistically consistent with the measurements. Furthermore, we show how the same tools can be used to discriminate among alternate models of the same biological process. We demonstrate these ideas by applying our methods to two examples, namely a model of the heat shock response in E. coli, and a model of a synthetic gene regulation system. The methods presented are quite general and may be applied to a wide class of biological systems where noisy measurements are used for parameter estimation or model selection.Author Summary: Parameter estimation is a key issue in systems biology, as it represents the crucial step to obtaining predictions from computational models of biological systems. This issue is usually addressed by “fitting” the model simulations to the observed experimental data. Such approach does not take the measurement noise into full consideration. We introduce a new method built on the combination of Kalman filtering, statistical tests, and optimization techniques. The filter is well-known in control and estimation theory and has found application in a wide range of fields, such as inertial guidance systems, weather forecasting, and economics. We show how the statistics of the measurement noise can be optimally exploited and directly incorporated into the design of the estimation algorithm in order to achieve more accurate results, and to validate/invalidate the computed estimates. We also show that a significant advantage of our estimator is that it offers a powerful tool for model selection, allowing rejection or acceptance of competing models based on the available noisy measurements. These results are of immediate practical application in computational biology, and while we demonstrate their use for two specific examples, they can in fact be used to study a wide class of biological systems.

Suggested Citation

  • Gabriele Lillacci & Mustafa Khammash, 2010. "Parameter Estimation and Model Selection in Computational Biology," PLOS Computational Biology, Public Library of Science, vol. 6(3), pages 1-17, March.
  • Handle: RePEc:plo:pcbi00:1000696
    DOI: 10.1371/journal.pcbi.1000696
    as

    Download full text from publisher

    File URL: https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1000696
    Download Restriction: no

    File URL: https://journals.plos.org/ploscompbiol/article/file?id=10.1371/journal.pcbi.1000696&type=printable
    Download Restriction: no

    File URL: https://libkey.io/10.1371/journal.pcbi.1000696?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Ryan N Gutenkunst & Joshua J Waterfall & Fergal P Casey & Kevin S Brown & Christopher R Myers & James P Sethna, 2007. "Universally Sloppy Parameter Sensitivities in Systems Biology Models," PLOS Computational Biology, Public Library of Science, vol. 3(10), pages 1-8, October.
    2. T. G. Müller & D. Faller & J. Timmer & I. Swameye & O. Sandra & U. Klingmüller, 2004. "Tests for cycling in a signalling pathway," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 53(4), pages 557-568, November.
    3. Michael B. Elowitz & Stanislas Leibler, 2000. "A synthetic oscillatory network of transcriptional regulators," Nature, Nature, vol. 403(6767), pages 335-338, January.
    4. Xiaodian Sun & Li Jin & Momiao Xiong, 2008. "Extended Kalman Filter for Estimation of Parameters in Nonlinear State-Space Models of Biochemical Networks," PLOS ONE, Public Library of Science, vol. 3(11), pages 1-13, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Dimitrios V Vavoulis & Volko A Straub & John A D Aston & Jianfeng Feng, 2012. "A Self-Organizing State-Space-Model Approach for Parameter Estimation in Hodgkin-Huxley-Type Models of Single Neurons," PLOS Computational Biology, Public Library of Science, vol. 8(3), pages 1-1, March.
    2. Zarifeh Heidary & Jafar Ghaisari & Shiva Moein & Shaghayegh Haghjooy Javanmard, 2020. "The double-edged sword role of fibroblasts in the interaction with cancer cells; an agent-based modeling approach," PLOS ONE, Public Library of Science, vol. 15(5), pages 1-14, May.
    3. Fuaada Mohd Siam & Muhamad Hanis Nasir, 2019. "Comparison of parameter fitting on the model of irradiation effects on bystander cells between Nelder-Mead simplex and particle swarm optimization," Journal of Advances in Technology and Engineering Research, A/Professor Akbar A. Khatibi, vol. 5(3), pages 142-150.
    4. Sungho Shin & Ophelia S Venturelli & Victor M Zavala, 2019. "Scalable nonlinear programming framework for parameter estimation in dynamic biological system models," PLOS Computational Biology, Public Library of Science, vol. 15(3), pages 1-29, March.
    5. Agus Hartoyo & Peter J Cadusch & David T J Liley & Damien G Hicks, 2019. "Parameter estimation and identifiability in a neural population model for electro-cortical activity," PLOS Computational Biology, Public Library of Science, vol. 15(5), pages 1-27, May.
    6. Marissa Renardy & Tau-Mu Yi & Dongbin Xiu & Ching-Shan Chou, 2018. "Parameter uncertainty quantification using surrogate models applied to a spatial model of yeast mating polarization," PLOS Computational Biology, Public Library of Science, vol. 14(5), pages 1-26, May.
    7. Afnizanfaizal Abdullah & Safaai Deris & Mohd Saberi Mohamad & Sohail Anwar, 2013. "An Improved Swarm Optimization for Parameter Estimation and Biological Model Selection," PLOS ONE, Public Library of Science, vol. 8(4), pages 1-16, April.
    8. Takanori Hasegawa & Rui Yamaguchi & Masao Nagasaki & Satoru Miyano & Seiya Imoto, 2014. "Inference of Gene Regulatory Networks Incorporating Multi-Source Biological Knowledge via a State Space Model with L1 Regularization," PLOS ONE, Public Library of Science, vol. 9(8), pages 1-19, August.
    9. Alireza Yazdani & Lu Lu & Maziar Raissi & George Em Karniadakis, 2020. "Systems biology informed deep learning for inferring parameters and hidden dynamics," PLOS Computational Biology, Public Library of Science, vol. 16(11), pages 1-19, November.
    10. Se Ho Park & Seokmin Ha & Jae Kyoung Kim, 2023. "A general model-based causal inference method overcomes the curse of synchrony and indirect effect," Nature Communications, Nature, vol. 14(1), pages 1-11, December.
    11. Afnizanfaizal Abdullah & Safaai Deris & Sohail Anwar & Satya N V Arjunan, 2013. "An Evolutionary Firefly Algorithm for the Estimation of Nonlinear Biological Model Parameters," PLOS ONE, Public Library of Science, vol. 8(3), pages 1-16, March.
    12. Wenlong He & Peng Xia & Xinan Zhang & Tianhai Tian, 2022. "Bayesian Inference Algorithm for Estimating Heterogeneity of Regulatory Mechanisms Based on Single-Cell Data," Mathematics, MDPI, vol. 10(24), pages 1-15, December.
    13. Yong-Jun Shin & Ali H Sayed & Xiling Shen, 2012. "Adaptive Models for Gene Networks," PLOS ONE, Public Library of Science, vol. 7(2), pages 1-6, February.
    14. González Javier & Vujačić Ivan & Wit Ernst, 2013. "Inferring latent gene regulatory network kinetics," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 12(1), pages 109-127, March.
    15. Joseph D Taylor & Samuel Winnall & Alain Nogaret, 2020. "Estimation of neuron parameters from imperfect observations," PLOS Computational Biology, Public Library of Science, vol. 16(7), pages 1-22, July.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Takanori Hasegawa & Rui Yamaguchi & Masao Nagasaki & Satoru Miyano & Seiya Imoto, 2014. "Inference of Gene Regulatory Networks Incorporating Multi-Source Biological Knowledge via a State Space Model with L1 Regularization," PLOS ONE, Public Library of Science, vol. 9(8), pages 1-19, August.
    2. Christian A Tiemann & Joep Vanlier & Maaike H Oosterveer & Albert K Groen & Peter A J Hilbers & Natal A W van Riel, 2013. "Parameter Trajectory Analysis to Identify Treatment Effects of Pharmacological Interventions," PLOS Computational Biology, Public Library of Science, vol. 9(8), pages 1-15, August.
    3. Juliane Liepe & Sarah Filippi & Michał Komorowski & Michael P H Stumpf, 2013. "Maximizing the Information Content of Experiments in Systems Biology," PLOS Computational Biology, Public Library of Science, vol. 9(1), pages 1-13, January.
    4. Filippi Sarah & Barnes Chris P. & Cornebise Julien & Stumpf Michael P.H., 2013. "On optimality of kernels for approximate Bayesian computation using sequential Monte Carlo," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 12(1), pages 87-107, March.
    5. Jin Wang & Bo Huang & Xuefeng Xia & Zhirong Sun, 2006. "Funneled Landscape Leads to Robustness of Cell Networks: Yeast Cell Cycle," PLOS Computational Biology, Public Library of Science, vol. 2(11), pages 1-10, November.
    6. Samuel Bandara & Johannes P Schlöder & Roland Eils & Hans Georg Bock & Tobias Meyer, 2009. "Optimal Experimental Design for Parameter Estimation of a Cell Signaling Model," PLOS Computational Biology, Public Library of Science, vol. 5(11), pages 1-12, November.
    7. Avraham E Mayo & Yaakov Setty & Seagull Shavit & Alon Zaslaver & Uri Alon, 2006. "Plasticity of the cis-Regulatory Input Function of a Gene," PLOS Biology, Public Library of Science, vol. 4(4), pages 1-1, March.
    8. Ankit Gupta & Mustafa Khammash, 2022. "Frequency spectra and the color of cellular noise," Nature Communications, Nature, vol. 13(1), pages 1-18, December.
    9. Bottani, Samuel & Grammaticos, Basile, 2008. "A simple model of genetic oscillations through regulated degradation," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1468-1482.
    10. Margherita Carletti & Malay Banerjee, 2019. "A Backward Technique for Demographic Noise in Biological Ordinary Differential Equation Models," Mathematics, MDPI, vol. 7(12), pages 1-16, December.
    11. Adel Dayarian & Madalena Chaves & Eduardo D Sontag & Anirvan M Sengupta, 2009. "Shape, Size, and Robustness: Feasible Regions in the Parameter Space of Biochemical Networks," PLOS Computational Biology, Public Library of Science, vol. 5(1), pages 1-12, January.
    12. Weiyue Ji & Handuo Shi & Haoqian Zhang & Rui Sun & Jingyi Xi & Dingqiao Wen & Jingchen Feng & Yiwei Chen & Xiao Qin & Yanrong Ma & Wenhan Luo & Linna Deng & Hanchi Lin & Ruofan Yu & Qi Ouyang, 2013. "A Formalized Design Process for Bacterial Consortia That Perform Logic Computing," PLOS ONE, Public Library of Science, vol. 8(2), pages 1-9, February.
    13. Amrita X Sarkar & Eric A Sobie, 2010. "Regression Analysis for Constraining Free Parameters in Electrophysiological Models of Cardiac Cells," PLOS Computational Biology, Public Library of Science, vol. 6(9), pages 1-11, September.
    14. Hongwei Shao & Tao Peng & Zhiwei Ji & Jing Su & Xiaobo Zhou, 2013. "Systematically Studying Kinase Inhibitor Induced Signaling Network Signatures by Integrating Both Therapeutic and Side Effects," PLOS ONE, Public Library of Science, vol. 8(12), pages 1-16, December.
    15. Konstantinos I Papadimitriou & Guy-Bart V Stan & Emmanuel M Drakakis, 2013. "Systematic Computation of Nonlinear Cellular and Molecular Dynamics with Low-Power CytoMimetic Circuits: A Simulation Study," PLOS ONE, Public Library of Science, vol. 8(2), pages 1-24, February.
    16. Inés P Mariño & Alexey Zaikin & Joaquín Míguez, 2017. "A comparison of Monte Carlo-based Bayesian parameter estimation methods for stochastic models of genetic networks," PLOS ONE, Public Library of Science, vol. 12(8), pages 1-25, August.
    17. Zhdanov, Vladimir P., 2012. "Periodic perturbation of genetic oscillations," Chaos, Solitons & Fractals, Elsevier, vol. 45(5), pages 577-587.
    18. Dhiman, Aman & Poria, Swarup, 2018. "Allee effect induced diversity in evolutionary dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 108(C), pages 32-38.
    19. Javier Santos-Moreno & Eve Tasiudi & Hadiastri Kusumawardhani & Joerg Stelling & Yolanda Schaerli, 2023. "Robustness and innovation in synthetic genotype networks," Nature Communications, Nature, vol. 14(1), pages 1-17, December.
    20. Chen Jia & Ramon Grima, 2024. "Holimap: an accurate and efficient method for solving stochastic gene network dynamics," Nature Communications, Nature, vol. 15(1), pages 1-14, December.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:plo:pcbi00:1000696. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ploscompbiol (email available below). General contact details of provider: https://journals.plos.org/ploscompbiol/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.