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Grandits T, Augustin CM, Haase G, Jost N, Mirams GR, Niederer SA, Plank G, Varró A, Virág L, Jung A. Neural network emulation of the human ventricular cardiomyocyte action potential for more efficient computations in pharmacological studies. eLife 2024; 12:RP91911. [PMID: 38598284 PMCID: PMC11006416 DOI: 10.7554/elife.91911] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/11/2024] Open
Abstract
Computer models of the human ventricular cardiomyocyte action potential (AP) have reached a level of detail and maturity that has led to an increasing number of applications in the pharmaceutical sector. However, interfacing the models with experimental data can become a significant computational burden. To mitigate the computational burden, the present study introduces a neural network (NN) that emulates the AP for given maximum conductances of selected ion channels, pumps, and exchangers. Its applicability in pharmacological studies was tested on synthetic and experimental data. The NN emulator potentially enables massive speed-ups compared to regular simulations and the forward problem (find drugged AP for pharmacological parameters defined as scaling factors of control maximum conductances) on synthetic data could be solved with average root-mean-square errors (RMSE) of 0.47 mV in normal APs and of 14.5 mV in abnormal APs exhibiting early afterdepolarizations (72.5% of the emulated APs were alining with the abnormality, and the substantial majority of the remaining APs demonstrated pronounced proximity). This demonstrates not only very fast and mostly very accurate AP emulations but also the capability of accounting for discontinuities, a major advantage over existing emulation strategies. Furthermore, the inverse problem (find pharmacological parameters for control and drugged APs through optimization) on synthetic data could be solved with high accuracy shown by a maximum RMSE of 0.22 in the estimated pharmacological parameters. However, notable mismatches were observed between pharmacological parameters estimated from experimental data and distributions obtained from the Comprehensive in vitro Proarrhythmia Assay initiative. This reveals larger inaccuracies which can be attributed particularly to the fact that small tissue preparations were studied while the emulator was trained on single cardiomyocyte data. Overall, our study highlights the potential of NN emulators as powerful tool for an increased efficiency in future quantitative systems pharmacology studies.
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Affiliation(s)
- Thomas Grandits
- Department of Mathematics and Scientific Computing, University of GrazGrazAustria
- NAWI Graz, University of GrazGrazAustria
| | - Christoph M Augustin
- Gottfried Schatz Research Center for Cell Signaling, Metabolism and Aging - Division of Medical Physics and Biophysics, Medical University of GrazGrazAustria
- BioTechMed-GrazGrazAustria
| | - Gundolf Haase
- Department of Mathematics and Scientific Computing, University of GrazGrazAustria
| | - Norbert Jost
- Department of Pharmacology and Pharmacotherapy, University of SzegedSzegedHungary
- HUN-REN-TKI, Research Group of PharmacologyBudapestHungary
| | - Gary R Mirams
- Centre for Mathematical Medicine & Biology, School of Mathematical Sciences, University of NottinghamNottinghamUnited Kingdom
| | - Steven A Niederer
- Division of Imaging Sciences & Biomedical Engineering, King’s College LondonLondonUnited Kingdom
| | - Gernot Plank
- Gottfried Schatz Research Center for Cell Signaling, Metabolism and Aging - Division of Medical Physics and Biophysics, Medical University of GrazGrazAustria
- BioTechMed-GrazGrazAustria
| | - András Varró
- Department of Pharmacology and Pharmacotherapy, University of SzegedSzegedHungary
- HUN-REN-TKI, Research Group of PharmacologyBudapestHungary
| | - László Virág
- Department of Pharmacology and Pharmacotherapy, University of SzegedSzegedHungary
| | - Alexander Jung
- Gottfried Schatz Research Center for Cell Signaling, Metabolism and Aging - Division of Medical Physics and Biophysics, Medical University of GrazGrazAustria
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Grandits T, Augustin CM, Haase G, Jost N, Mirams GR, Niederer SA, Plank G, Varró A, Virág L, Jung A. Neural network emulation of the human ventricular cardiomyocyte action potential: a tool for more efficient computation in pharmacological studies. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.08.16.553497. [PMID: 38234850 PMCID: PMC10793461 DOI: 10.1101/2023.08.16.553497] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/19/2024]
Abstract
Computer models of the human ventricular cardiomyocyte action potential (AP) have reached a level of detail and maturity that has led to an increasing number of applications in the pharmaceutical sector. However, interfacing the models with experimental data can become a significant computational burden. To mitigate the computational burden, the present study introduces a neural network (NN) that emulates the AP for given maximum conductances of selected ion channels, pumps, and exchangers. Its applicability in pharmacological studies was tested on synthetic and experimental data. The NN emulator potentially enables massive speed-ups compared to regular simulations and the forward problem (find drugged AP for pharmacological parameters defined as scaling factors of control maximum conductances) on synthetic data could be solved with average root-mean-square errors (RMSE) of 0.47mV in normal APs and of 14.5mV in abnormal APs exhibiting early afterdepolarizations (72.5% of the emulated APs were alining with the abnormality, and the substantial majority of the remaining APs demonstrated pronounced proximity). This demonstrates not only very fast and mostly very accurate AP emulations but also the capability of accounting for discontinuities, a major advantage over existing emulation strategies. Furthermore, the inverse problem (find pharmacological parameters for control and drugged APs through optimization) on synthetic data could be solved with high accuracy shown by a maximum RMSE of 0.21 in the estimated pharmacological parameters. However, notable mismatches were observed between pharmacological parameters estimated from experimental data and distributions obtained from the Comprehensive in vitro Proarrhythmia Assay initiative. This reveals larger inaccuracies which can be attributed particularly to the fact that small tissue preparations were studied while the emulator was trained on single cardiomyocyte data. Overall, our study highlights the potential of NN emulators as powerful tool for an increased efficiency in future quantitative systems pharmacology studies.
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Affiliation(s)
- Thomas Grandits
- Department of Mathematics and Scientific Computing, University of Graz
- NAWI Graz, University of Graz
| | - Christoph M Augustin
- Gottfried Schatz Research Center for Cell Signaling, Metabolism and Aging - Division of Medical Physics and Biophysics, Medical University of Graz
- BioTechMed-Graz
| | - Gundolf Haase
- Department of Mathematics and Scientific Computing, University of Graz
| | - Norbert Jost
- Department of Pharmacology and Pharmacotherapy, University of Szeged
- HUN-REN-TKI, Research Group of Pharmacology
| | - Gary R Mirams
- Centre for Mathematical Medicine & Biology, School of Mathematical Sciences, University of Nottingham
| | - Steven A Niederer
- Division of Imaging Sciences & Biomedical Engineering, King's College London
| | - Gernot Plank
- Gottfried Schatz Research Center for Cell Signaling, Metabolism and Aging - Division of Medical Physics and Biophysics, Medical University of Graz
- BioTechMed-Graz
| | - András Varró
- Department of Pharmacology and Pharmacotherapy, University of Szeged
- HUN-REN-TKI, Research Group of Pharmacology
| | - László Virág
- Department of Pharmacology and Pharmacotherapy, University of Szeged
| | - Alexander Jung
- Gottfried Schatz Research Center for Cell Signaling, Metabolism and Aging - Division of Medical Physics and Biophysics, Medical University of Graz
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Shuttleworth JG, Lei CL, Whittaker DG, Windley MJ, Hill AP, Preston SP, Mirams GR. Empirical Quantification of Predictive Uncertainty Due to Model Discrepancy by Training with an Ensemble of Experimental Designs: An Application to Ion Channel Kinetics. Bull Math Biol 2023; 86:2. [PMID: 37999811 PMCID: PMC10673765 DOI: 10.1007/s11538-023-01224-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2023] [Accepted: 10/09/2023] [Indexed: 11/25/2023]
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.
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Affiliation(s)
- Joseph G Shuttleworth
- Centre for Mathematical Medicine & Biology, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK
| | - Chon Lok Lei
- Institute of Translational Medicine, Faculty of Health Sciences, University of Macau, Macau, China
- Department of Biomedical Sciences, Faculty of Health Sciences, University of Macau, Macau, China
| | - Dominic G Whittaker
- Centre for Mathematical Medicine & Biology, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK
- 4 Systems Modeling & Translational Biology, Stevenage, GSK, UK
| | - Monique J Windley
- Computational Cardiology Laboratory, Victor Chang Cardiac Research Institute, Darlinghurst, NSW, Australia
- School of Clinical Medicine, Faculty of Medicine and Health, University of New South Wales, Sydney, NSW, Australia
| | - Adam P Hill
- Computational Cardiology Laboratory, Victor Chang Cardiac Research Institute, Darlinghurst, NSW, Australia
- School of Clinical Medicine, Faculty of Medicine and Health, University of New South Wales, Sydney, NSW, Australia
| | - Simon P Preston
- Centre for Mathematical Medicine & Biology, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK
| | - Gary R Mirams
- Centre for Mathematical Medicine & Biology, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK.
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Moreno JD, Silva JR. Emerging methods to model cardiac ion channel and myocyte electrophysiology. BIOPHYSICS REVIEWS 2023; 4:011315. [PMID: 37034130 PMCID: PMC10071990 DOI: 10.1063/5.0127713] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/23/2022] [Accepted: 02/28/2023] [Indexed: 04/03/2023]
Abstract
In the field of cardiac electrophysiology, modeling has played a central role for many decades. However, even though the effort is well-established, it has recently seen a rapid and sustained evolution in the complexity and predictive power of the models being created. In particular, new approaches to modeling have allowed the tracking of parallel and interconnected processes that span from the nanometers and femtoseconds that determine ion channel gating to the centimeters and minutes needed to describe an arrhythmia. The connection between scales has brought unprecedented insight into cardiac arrhythmia mechanisms and drug therapies. This review focuses on the generation of these models from first principles, generation of detailed models to describe ion channel kinetics, algorithms to create and numerically solve kinetic models, and new approaches toward data gathering that parameterize these models. While we focus on application of these models for cardiac arrhythmia, these concepts are widely applicable to model the physiology and pathophysiology of any excitable cell.
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Affiliation(s)
- Jonathan D. Moreno
- Division of Cardiology, Department of Medicine, Washington University in St. Louis, St. Louis, Missouri 63130, USA
| | - Jonathan R. Silva
- Department of Biomedical Engineering, Washington University in St. Louis, St. Louis, Missouri 63130, USA
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