Empirical Quantification of Predictive Uncertainty Due to Model Discrepancy by Training with an Ensemble of Experimental Designs: An Application to Ion Channel Kinetics

When using mathematical models to make quantitative predictions for clinical or industrial use, it is important that predictions come with a reliable estimate of their accuracy (uncertainty quantification). Because models of complex biological systems are always large simplifications, model discrepa...

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Published in:	Bulletin of mathematical biology Vol. 86; no. 1; p. 2
Main Authors:	Shuttleworth, Joseph G., Lei, Chon Lok, Whittaker, Dominic G., Windley, Monique J., Hill, Adam P., Preston, Simon P., Mirams, Gary R.
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.01.2024 Springer Nature B.V
Subjects:	Cell Biology Electrophysiology Estimates Industrial applications Ion Channels Kinetics Life Sciences Mathematical and Computational Biology Mathematical Concepts Mathematical models Mathematics Mathematics and Statistics Models, Biological Models, Theoretical Original Article Parameter estimation Pharmacovigilance Potassium channels Predictions Product safety Random noise Random variables Uncertainty Uncertainty quantification Discrepancy Mathematical model Ion channel Experimental design Misspecification
ISSN:	0092-8240, 1522-9602, 1522-9602
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Abstract	When using mathematical models to make quantitative predictions for clinical or industrial use, it is important that predictions come with a reliable estimate of their accuracy (uncertainty quantification). Because models of complex biological systems are always large simplifications, model discrepancy arises—models fail to perfectly recapitulate the true data generating process. This presents a particular challenge for making accurate predictions, and especially for accurately quantifying uncertainty in these predictions. Experimentalists and modellers must choose which experimental procedures ( protocols ) are used to produce data used to train models. We propose to characterise uncertainty owing to model discrepancy with an ensemble of parameter sets, each of which results from training to data from a different protocol. The variability in predictions from this ensemble provides an empirical estimate of predictive uncertainty owing to model discrepancy, even for unseen protocols. We use the example of electrophysiology experiments that investigate the properties of hERG potassium channels. Here, ‘information-rich’ protocols allow mathematical models to be trained using numerous short experiments performed on the same cell. In this case, we simulate data with one model and fit it with a different (discrepant) one. For any individual experimental protocol, parameter estimates vary little under repeated samples from the assumed additive independent Gaussian noise model. Yet parameter sets arising from the same model applied to different experiments conflict—highlighting model discrepancy. Our methods will help select more suitable ion channel models for future studies, and will be widely applicable to a range of biological modelling problems.
AbstractList	When using mathematical models to make quantitative predictions for clinical or industrial use, it is important that predictions come with a reliable estimate of their accuracy (uncertainty quantification). Because models of complex biological systems are always large simplifications, model discrepancy arises—models fail to perfectly recapitulate the true data generating process. This presents a particular challenge for making accurate predictions, and especially for accurately quantifying uncertainty in these predictions. Experimentalists and modellers must choose which experimental procedures ( protocols ) are used to produce data used to train models. We propose to characterise uncertainty owing to model discrepancy with an ensemble of parameter sets, each of which results from training to data from a different protocol. The variability in predictions from this ensemble provides an empirical estimate of predictive uncertainty owing to model discrepancy, even for unseen protocols. We use the example of electrophysiology experiments that investigate the properties of hERG potassium channels. Here, ‘information-rich’ protocols allow mathematical models to be trained using numerous short experiments performed on the same cell. In this case, we simulate data with one model and fit it with a different (discrepant) one. For any individual experimental protocol, parameter estimates vary little under repeated samples from the assumed additive independent Gaussian noise model. Yet parameter sets arising from the same model applied to different experiments conflict—highlighting model discrepancy. Our methods will help select more suitable ion channel models for future studies, and will be widely applicable to a range of biological modelling problems. When using mathematical models to make quantitative predictions for clinical or industrial use, it is important that predictions come with a reliable estimate of their accuracy (uncertainty quantification). Because models of complex biological systems are always large simplifications, model discrepancy arises-models fail to perfectly recapitulate the true data generating process. This presents a particular challenge for making accurate predictions, and especially for accurately quantifying uncertainty in these predictions. Experimentalists and modellers must choose which experimental procedures (protocols) are used to produce data used to train models. We propose to characterise uncertainty owing to model discrepancy with an ensemble of parameter sets, each of which results from training to data from a different protocol. The variability in predictions from this ensemble provides an empirical estimate of predictive uncertainty owing to model discrepancy, even for unseen protocols. We use the example of electrophysiology experiments that investigate the properties of hERG potassium channels. Here, 'information-rich' protocols allow mathematical models to be trained using numerous short experiments performed on the same cell. In this case, we simulate data with one model and fit it with a different (discrepant) one. For any individual experimental protocol, parameter estimates vary little under repeated samples from the assumed additive independent Gaussian noise model. Yet parameter sets arising from the same model applied to different experiments conflict-highlighting model discrepancy. Our methods will help select more suitable ion channel models for future studies, and will be widely applicable to a range of biological modelling problems. When using mathematical models to make quantitative predictions for clinical or industrial use, it is important that predictions come with a reliable estimate of their accuracy (uncertainty quantification). Because models of complex biological systems are always large simplifications, model discrepancy arises-models fail to perfectly recapitulate the true data generating process. This presents a particular challenge for making accurate predictions, and especially for accurately quantifying uncertainty in these predictions. Experimentalists and modellers must choose which experimental procedures (protocols) are used to produce data used to train models. We propose to characterise uncertainty owing to model discrepancy with an ensemble of parameter sets, each of which results from training to data from a different protocol. The variability in predictions from this ensemble provides an empirical estimate of predictive uncertainty owing to model discrepancy, even for unseen protocols. We use the example of electrophysiology experiments that investigate the properties of hERG potassium channels. Here, 'information-rich' protocols allow mathematical models to be trained using numerous short experiments performed on the same cell. In this case, we simulate data with one model and fit it with a different (discrepant) one. For any individual experimental protocol, parameter estimates vary little under repeated samples from the assumed additive independent Gaussian noise model. Yet parameter sets arising from the same model applied to different experiments conflict-highlighting model discrepancy. Our methods will help select more suitable ion channel models for future studies, and will be widely applicable to a range of biological modelling problems.When using mathematical models to make quantitative predictions for clinical or industrial use, it is important that predictions come with a reliable estimate of their accuracy (uncertainty quantification). Because models of complex biological systems are always large simplifications, model discrepancy arises-models fail to perfectly recapitulate the true data generating process. This presents a particular challenge for making accurate predictions, and especially for accurately quantifying uncertainty in these predictions. Experimentalists and modellers must choose which experimental procedures (protocols) are used to produce data used to train models. We propose to characterise uncertainty owing to model discrepancy with an ensemble of parameter sets, each of which results from training to data from a different protocol. The variability in predictions from this ensemble provides an empirical estimate of predictive uncertainty owing to model discrepancy, even for unseen protocols. We use the example of electrophysiology experiments that investigate the properties of hERG potassium channels. Here, 'information-rich' protocols allow mathematical models to be trained using numerous short experiments performed on the same cell. In this case, we simulate data with one model and fit it with a different (discrepant) one. For any individual experimental protocol, parameter estimates vary little under repeated samples from the assumed additive independent Gaussian noise model. Yet parameter sets arising from the same model applied to different experiments conflict-highlighting model discrepancy. Our methods will help select more suitable ion channel models for future studies, and will be widely applicable to a range of biological modelling problems.
ArticleNumber	2
Author	Whittaker, Dominic G. Mirams, Gary R. Hill, Adam P. Windley, Monique J. Lei, Chon Lok Preston, Simon P. Shuttleworth, Joseph G.
Author_xml	– sequence: 1 givenname: Joseph G. orcidid: 0000-0003-4884-6526 surname: Shuttleworth fullname: Shuttleworth, Joseph G. organization: Centre for Mathematical Medicine & Biology, School of Mathematical Sciences, University of Nottingham – sequence: 2 givenname: Chon Lok orcidid: 0000-0003-0904-554X surname: Lei fullname: Lei, Chon Lok organization: Institute of Translational Medicine, Faculty of Health Sciences, University of Macau, Department of Biomedical Sciences, Faculty of Health Sciences, University of Macau – sequence: 3 givenname: Dominic G. orcidid: 0000-0002-2757-5491 surname: Whittaker fullname: Whittaker, Dominic G. organization: Centre for Mathematical Medicine & Biology, School of Mathematical Sciences, University of Nottingham, 4 Systems Modeling & Translational Biology – sequence: 4 givenname: Monique J. orcidid: 0000-0001-6829-3856 surname: Windley fullname: Windley, Monique J. organization: Computational Cardiology Laboratory, Victor Chang Cardiac Research Institute, School of Clinical Medicine, Faculty of Medicine and Health, University of New South Wales – sequence: 5 givenname: Adam P. orcidid: 0000-0002-6403-1282 surname: Hill fullname: Hill, Adam P. organization: Computational Cardiology Laboratory, Victor Chang Cardiac Research Institute, School of Clinical Medicine, Faculty of Medicine and Health, University of New South Wales – sequence: 6 givenname: Simon P. orcidid: 0000-0002-1910-4227 surname: Preston fullname: Preston, Simon P. organization: Centre for Mathematical Medicine & Biology, School of Mathematical Sciences, University of Nottingham – sequence: 7 givenname: Gary R. orcidid: 0000-0002-4569-4312 surname: Mirams fullname: Mirams, Gary R. email: gary.mirams@nottingham.ac.uk organization: Centre for Mathematical Medicine & Biology, School of Mathematical Sciences, University of Nottingham
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Keywords	Uncertainty quantification Discrepancy Mathematical model Ion channel Experimental design Misspecification
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SubjectTerms	Cell Biology Electrophysiology Estimates Industrial applications Ion Channels Kinetics Life Sciences Mathematical and Computational Biology Mathematical Concepts Mathematical models Mathematics Mathematics and Statistics Models, Biological Models, Theoretical Original Article Parameter estimation Pharmacovigilance Potassium channels Predictions Product safety Random noise Random variables Uncertainty
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Title	Empirical Quantification of Predictive Uncertainty Due to Model Discrepancy by Training with an Ensemble of Experimental Designs: An Application to Ion Channel Kinetics
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