Development of a hybrid model for a partially known intracellular signaling pathway through correction term estimation and neural network modeling
Developing an accurate first-principle model is an important step in employing systems biology approaches to analyze an intracellular signaling pathway. However, an accurate first-principle model is difficult to be developed since it requires in-depth mechanistic understandings of the signaling path...
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| Published in | PLoS computational biology Vol. 16; no. 12; p. e1008472 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
United States
Public Library of Science
14.12.2020
Public Library of Science (PLoS) |
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| Online Access | Get full text |
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| Abstract | Developing an accurate first-principle model is an important step in employing systems biology approaches to analyze an intracellular signaling pathway. However, an accurate first-principle model is difficult to be developed since it requires in-depth mechanistic understandings of the signaling pathway. Since underlying mechanisms such as the reaction network structure are not fully understood, significant discrepancy exists between predicted and actual signaling dynamics. Motivated by these considerations, this work proposes a hybrid modeling approach that combines a first-principle model and an artificial neural network (ANN) model so that predictions of the hybrid model surpass those of the original model. First, the proposed approach determines an optimal subset of model states whose dynamics should be corrected by the ANN by examining the correlation between each state and outputs through relative order. Second, an L2-regularized least-squares problem is solved to infer values of the correction terms that are necessary to minimize the discrepancy between the model predictions and available measurements. Third, an ANN is developed to generalize relationships between the values of the correction terms and the system dynamics. Lastly, the original first-principle model is coupled with the developed ANN to finalize the hybrid model development so that the model will possess generalized prediction capabilities while retaining the model interpretability. We have successfully validated the proposed methodology with two case studies, simplified apoptosis and lipopolysaccharide-induced NF
κ
B signaling pathways, to develop hybrid models with
in silico
and
in vitro
measurements, respectively. |
|---|---|
| AbstractList | Developing an accurate first-principle model is an important step in employing systems biology approaches to analyze an intracellular signaling pathway. However, an accurate first-principle model is difficult to be developed since it requires in-depth mechanistic understandings of the signaling pathway. Since underlying mechanisms such as the reaction network structure are not fully understood, significant discrepancy exists between predicted and actual signaling dynamics. Motivated by these considerations, this work proposes a hybrid modeling approach that combines a first-principle model and an artificial neural network (ANN) model so that predictions of the hybrid model surpass those of the original model. First, the proposed approach determines an optimal subset of model states whose dynamics should be corrected by the ANN by examining the correlation between each state and outputs through relative order. Second, an L2-regularized least-squares problem is solved to infer values of the correction terms that are necessary to minimize the discrepancy between the model predictions and available measurements. Third, an ANN is developed to generalize relationships between the values of the correction terms and the system dynamics. Lastly, the original first-principle model is coupled with the developed ANN to finalize the hybrid model development so that the model will possess generalized prediction capabilities while retaining the model interpretability. We have successfully validated the proposed methodology with two case studies, simplified apoptosis and lipopolysaccharide-induced NFκB signaling pathways, to develop hybrid models with in silico and in vitro measurements, respectively.Developing an accurate first-principle model is an important step in employing systems biology approaches to analyze an intracellular signaling pathway. However, an accurate first-principle model is difficult to be developed since it requires in-depth mechanistic understandings of the signaling pathway. Since underlying mechanisms such as the reaction network structure are not fully understood, significant discrepancy exists between predicted and actual signaling dynamics. Motivated by these considerations, this work proposes a hybrid modeling approach that combines a first-principle model and an artificial neural network (ANN) model so that predictions of the hybrid model surpass those of the original model. First, the proposed approach determines an optimal subset of model states whose dynamics should be corrected by the ANN by examining the correlation between each state and outputs through relative order. Second, an L2-regularized least-squares problem is solved to infer values of the correction terms that are necessary to minimize the discrepancy between the model predictions and available measurements. Third, an ANN is developed to generalize relationships between the values of the correction terms and the system dynamics. Lastly, the original first-principle model is coupled with the developed ANN to finalize the hybrid model development so that the model will possess generalized prediction capabilities while retaining the model interpretability. We have successfully validated the proposed methodology with two case studies, simplified apoptosis and lipopolysaccharide-induced NFκB signaling pathways, to develop hybrid models with in silico and in vitro measurements, respectively. Developing an accurate first-principle model is an important step in employing systems biology approaches to analyze an intracellular signaling pathway. However, an accurate first-principle model is difficult to be developed since it requires in-depth mechanistic understandings of the signaling pathway. Since underlying mechanisms such as the reaction network structure are not fully understood, significant discrepancy exists between predicted and actual signaling dynamics. Motivated by these considerations, this work proposes a hybrid modeling approach that combines a first-principle model and an artificial neural network (ANN) model so that predictions of the hybrid model surpass those of the original model. First, the proposed approach determines an optimal subset of model states whose dynamics should be corrected by the ANN by examining the correlation between each state and outputs through relative order. Second, an L2-regularized least-squares problem is solved to infer values of the correction terms that are necessary to minimize the discrepancy between the model predictions and available measurements. Third, an ANN is developed to generalize relationships between the values of the correction terms and the system dynamics. Lastly, the original first-principle model is coupled with the developed ANN to finalize the hybrid model development so that the model will possess generalized prediction capabilities while retaining the model interpretability. We have successfully validated the proposed methodology with two case studies, simplified apoptosis and lipopolysaccharide-induced NF κ B signaling pathways, to develop hybrid models with in silico and in vitro measurements, respectively. Introduction An intracellular signaling pathway is a biochemical reaction network of cells to adjust their metabolism, gene expression, and other necessary actions so that the cells can appropriately respond to perturbations present in their environment [1, 2]. Since an intracellular signaling pathway is complex involving interactions among a large number of biomolecules inside a cell, it is common to implement a systems biology approach, which integrates experimental observations and mathematical modeling, to analyze the signaling pathway comprehensively [3, 4]. [...]it is desirable to minimize the number of components in a hybrid model that should be inferred from experimental measurements to minimize the possibility of overfitting, which may compromise the generalizability of the hybrid model. [31, 32] is adopted, where differential equations of model states are adjusted by correction terms inferred from experiments. Since an intracellular signaling pathway is often high-dimensional and its origin of prediction inaccuracy is unknown beforehand, a graphical approach is implemented to determine a subset of model states that have the highest correlations with the measurements. [...]this study aims to develop a functional map that can compute the value of w at time t for given values of the model states x(t) and t; that is, we aim to develop for prediction generalizability of the hybrid model. Developing an accurate first-principle model is an important step in employing systems biology approaches to analyze an intracellular signaling pathway. However, an accurate first-principle model is difficult to be developed since it requires in-depth mechanistic understandings of the signaling pathway. Since underlying mechanisms such as the reaction network structure are not fully understood, significant discrepancy exists between predicted and actual signaling dynamics. Motivated by these considerations, this work proposes a hybrid modeling approach that combines a first-principle model and an artificial neural network (ANN) model so that predictions of the hybrid model surpass those of the original model. First, the proposed approach determines an optimal subset of model states whose dynamics should be corrected by the ANN by examining the correlation between each state and outputs through relative order. Second, an L2-regularized least-squares problem is solved to infer values of the correction terms that are necessary to minimize the discrepancy between the model predictions and available measurements. Third, an ANN is developed to generalize relationships between the values of the correction terms and the system dynamics. Lastly, the original first-principle model is coupled with the developed ANN to finalize the hybrid model development so that the model will possess generalized prediction capabilities while retaining the model interpretability. We have successfully validated the proposed methodology with two case studies, simplified apoptosis and lipopolysaccharide-induced NFκB signaling pathways, to develop hybrid models with in silico and in vitro measurements, respectively. Developing an accurate first-principle model is an important step in employing systems biology approaches to analyze an intracellular signaling pathway. However, an accurate first-principle model is difficult to be developed since it requires in-depth mechanistic understandings of the signaling pathway. Since underlying mechanisms such as the reaction network structure are not fully understood, significant discrepancy exists between predicted and actual signaling dynamics. Motivated by these considerations, this work proposes a hybrid modeling approach that combines a first-principle model and an artificial neural network (ANN) model so that predictions of the hybrid model surpass those of the original model. First, the proposed approach determines an optimal subset of model states whose dynamics should be corrected by the ANN by examining the correlation between each state and outputs through relative order. Second, an L2-regularized least-squares problem is solved to infer values of the correction terms that are necessary to minimize the discrepancy between the model predictions and available measurements. Third, an ANN is developed to generalize relationships between the values of the correction terms and the system dynamics. Lastly, the original first-principle model is coupled with the developed ANN to finalize the hybrid model development so that the model will possess generalized prediction capabilities while retaining the model interpretability. We have successfully validated the proposed methodology with two case studies, simplified apoptosis and lipopolysaccharide-induced NF κ B signaling pathways, to develop hybrid models with in silico and in vitro measurements, respectively. An intracellular signaling pathway is often represented by a set of nonlinear ordinary differential equations, which translate our current knowledge about the signaling pathway into a testable mathematical model. However, predictions from such models are often subject to high uncertainty since many signaling pathways are only partially known beforehand. In this study, we propose a systematic approach to develop a hybrid model to improve model accuracy by combining machine learning and the first-principle modeling. Specifically, model correction terms are learned from discrepancy between model predictions and measurements, and these terms are added to the first-principle model to enhance the prediction accuracy. Once these correction terms are learned from the data, an artificial neural network (ANN) model is developed to find an empirical relation between the model and the correction terms so that the developed ANN can be used to posses improved predictive capabilities even in new operating conditions (i.e., generalizability). The final hybrid model is then constructed by coupling the first-principle model with the developed ANN. Developing an accurate first-principle model is an important step in employing systems biology approaches to analyze an intracellular signaling pathway. However, an accurate first-principle model is difficult to be developed since it requires in-depth mechanistic understandings of the signaling pathway. Since underlying mechanisms such as the reaction network structure are not fully understood, significant discrepancy exists between predicted and actual signaling dynamics. Motivated by these considerations, this work proposes a hybrid modeling approach that combines a first-principle model and an artificial neural network (ANN) model so that predictions of the hybrid model surpass those of the original model. First, the proposed approach determines an optimal subset of model states whose dynamics should be corrected by the ANN by examining the correlation between each state and outputs through relative order. Second, an L2-regularized least-squares problem is solved to infer values of the correction terms that are necessary to minimize the discrepancy between the model predictions and available measurements. Third, an ANN is developed to generalize relationships between the values of the correction terms and the system dynamics. Lastly, the original first-principle model is coupled with the developed ANN to finalize the hybrid model development so that the model will possess generalized prediction capabilities while retaining the model interpretability. We have successfully validated the proposed methodology with two case studies, simplified apoptosis and lipopolysaccharide-induced NF[kappa]B signaling pathways, to develop hybrid models with in silico and in vitro measurements, respectively. Introduction An intracellular signaling pathway is a biochemical reaction network of cells to adjust their metabolism, gene expression, and other necessary actions so that the cells can appropriately respond to perturbations present in their environment [1, 2]. Since an intracellular signaling pathway is complex involving interactions among a large number of biomolecules inside a cell, it is common to implement a systems biology approach, which integrates experimental observations and mathematical modeling, to analyze the signaling pathway comprehensively [3, 4]. [...]it is desirable to minimize the number of components in a hybrid model that should be inferred from experimental measurements to minimize the possibility of overfitting, which may compromise the generalizability of the hybrid model. [31, 32] is adopted, where differential equations of model states are adjusted by correction terms inferred from experiments. Since an intracellular signaling pathway is often high-dimensional and its origin of prediction inaccuracy is unknown beforehand, a graphical approach is implemented to determine a subset of model states that have the highest correlations with the measurements. [...]this study aims to develop a functional map that can compute the value of w at time t for given values of the model states x(t) and t; that is, we aim to develop for prediction generalizability of the hybrid model. |
| Audience | Academic |
| Author | Kwon, Joseph S. Lee, Dongheon Jayaraman, Arul |
| AuthorAffiliation | 1 Artie McFerrin Department of Chemical Engineering, Texas A&M University, College Station, Texas, USA 3 Department of Biomedical Engineering, Texas A&M University, College Station, Texas, USA University of Pennsylvania, UNITED STATES 2 Texas A&M Energy Institute, Texas A&M University, College Station, Texas, USA |
| AuthorAffiliation_xml | – name: University of Pennsylvania, UNITED STATES – name: 2 Texas A&M Energy Institute, Texas A&M University, College Station, Texas, USA – name: 3 Department of Biomedical Engineering, Texas A&M University, College Station, Texas, USA – name: 1 Artie McFerrin Department of Chemical Engineering, Texas A&M University, College Station, Texas, USA |
| Author_xml | – sequence: 1 givenname: Dongheon orcidid: 0000-0002-4066-9222 surname: Lee fullname: Lee, Dongheon – sequence: 2 givenname: Arul orcidid: 0000-0001-9276-8284 surname: Jayaraman fullname: Jayaraman, Arul – sequence: 3 givenname: Joseph S. orcidid: 0000-0002-7903-5681 surname: Kwon fullname: Kwon, Joseph S. |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/33315899$$D View this record in MEDLINE/PubMed |
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| Copyright | COPYRIGHT 2020 Public Library of Science 2020 Lee et al. This is an open access article distributed under the terms of the Creative Commons Attribution License: http://creativecommons.org/licenses/by/4.0/ (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. 2020 Lee et al 2020 Lee et al |
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| DOI | 10.1371/journal.pcbi.1008472 |
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| IngestDate | Fri Nov 26 17:12:21 EST 2021 Wed Aug 27 01:30:36 EDT 2025 Thu Aug 21 14:11:37 EDT 2025 Thu Jul 10 19:33:24 EDT 2025 Fri Jul 25 12:02:48 EDT 2025 Tue Jun 17 21:00:37 EDT 2025 Tue Jun 10 20:46:40 EDT 2025 Fri Jun 27 04:03:45 EDT 2025 Fri Jun 27 04:11:20 EDT 2025 Thu Apr 03 07:04:46 EDT 2025 Thu Apr 24 23:06:20 EDT 2025 Tue Jul 01 04:04:49 EDT 2025 |
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| Issue | 12 |
| Language | English |
| License | This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Creative Commons Attribution License |
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| Notes | new_version ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 content type line 23 Current address: Department of Biomedical Engineering, Duke University, Durham, North Carolina, USA The authors have declared that no competing interests exist. |
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| Snippet | Developing an accurate first-principle model is an important step in employing systems biology approaches to analyze an intracellular signaling pathway.... Introduction An intracellular signaling pathway is a biochemical reaction network of cells to adjust their metabolism, gene expression, and other necessary... |
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| SubjectTerms | Accuracy Algorithms Apoptosis Biology and Life Sciences Biomolecules Case studies Cellular signal transduction Computer and Information Sciences Correlation analysis Differential equations Error-correcting codes Gene expression Intracellular Intracellular signalling Knowledge Least-Squares Analysis Lipopolysaccharides - pharmacology Mathematical models Medicine and Health Sciences Metabolism Neural networks Neural Networks, Computer NF-kappa B - metabolism Ordinary differential equations Physical Sciences Signal transduction Signal Transduction - drug effects Signaling Terminology |
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| Title | Development of a hybrid model for a partially known intracellular signaling pathway through correction term estimation and neural network modeling |
| URI | https://www.ncbi.nlm.nih.gov/pubmed/33315899 https://www.proquest.com/docview/2479467398 https://www.proquest.com/docview/2470283255 https://pubmed.ncbi.nlm.nih.gov/PMC7769624 https://doaj.org/article/51308e5df62a46df978b0c7d2300eaee http://dx.doi.org/10.1371/journal.pcbi.1008472 |
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