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Gawthrop PJ, Pan M. Sensitivity analysis of biochemical systems using bond graphs. J R Soc Interface 2023; 20:20230192. [PMID: 37464805 DOI: 10.1098/rsif.2023.0192] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2023] [Accepted: 06/22/2023] [Indexed: 07/20/2023] Open
Abstract
The sensitivity of systems biology models to parameter variation can give insights into which parameters are most important for physiological function, and also direct efforts to estimate parameters. However, in general, kinetic models of biochemical systems do not remain thermodynamically consistent after perturbing parameters. To address this issue, we analyse the sensitivity of biological reaction networks in the context of a bond graph representation. We find that the parameter sensitivities can themselves be represented as bond graph components, mirroring potential mechanisms for controlling biochemistry. In particular, a sensitivity system is derived which re-expresses parameter variation as additional system inputs. The sensitivity system is then linearized with respect to these new inputs to derive a linear system which can be used to give local sensitivity to parameters in terms of linear system properties such as gain and time constant. This linear system can also be used to find so-called sloppy parameters in biological models. We verify our approach using a model of the Pentose Phosphate Pathway, confirming the reactions and metabolites most essential to maintaining the function of the pathway.
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Affiliation(s)
- Peter J Gawthrop
- Department of Biomedical Engineering, Faculty of Engineering & Information Technology, University of Melbourne, Melbourne, Victoria 3010, Australia
| | - Michael Pan
- School of Mathematics and Statistics, Faculty of Science, University of Melbourne, Melbourne, Victoria 3010, Australia
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Shahidi N, Pan M, Tran K, Crampin EJ, Nickerson DP. SBML to bond graphs: From conversion to composition. Math Biosci 2022; 352:108901. [PMID: 36096376 DOI: 10.1016/j.mbs.2022.108901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/29/2022] [Revised: 08/15/2022] [Accepted: 09/05/2022] [Indexed: 11/29/2022]
Abstract
The Systems Biology Markup Language (SBML) is a popular software-independent XML-based format for describing models of biological phenomena. The BioModels Database is the largest online repository of SBML models. Several tools and platforms are available to support the reuse and composition of SBML models. However, these tools do not explicitly assess whether models are physically plausible or thermodynamically consistent. This often leads to ill-posed models that are physically impossible, impeding the development of realistic complex models in biology. Here, we present a framework that can automatically convert SBML models into bond graphs, which imposes energy conservation laws on these models. The new bond graph models are easily mergeable, resulting in physically plausible coupled models. We illustrate this by automatically converting and coupling a model of pyruvate distribution to a model of the pentose phosphate pathway.
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Affiliation(s)
- Niloofar Shahidi
- Auckland Bioengineering Institute, University of Auckland, Auckland, 1010, New Zealand.
| | - Michael Pan
- Systems Biology Laboratory, School of Mathematics and Statistics, and Department of Biomedical Engineering, University of Melbourne, Melbourne, 3010, Victoria, Australia; School of Mathematics and Statistics, Faculty of Science, University of Melbourne, Melbourne, 3010, Victoria, Australia
| | - Kenneth Tran
- Auckland Bioengineering Institute, University of Auckland, Auckland, 1010, New Zealand
| | - Edmund J Crampin
- Systems Biology Laboratory, School of Mathematics and Statistics, and Department of Biomedical Engineering, University of Melbourne, Melbourne, 3010, Victoria, Australia; School of Mathematics and Statistics, Faculty of Science, University of Melbourne, Melbourne, 3010, Victoria, Australia; ARC Centre of Excellence in Convergent Bio-Nano Science and Technology, Faculty of Engineering and Information Technology, University of Melbourne, Melbourne, 3010, Victoria, Australia; School of Medicine, University of Melbourne, Melbourne, 3010, Victoria, Australia
| | - David P Nickerson
- Auckland Bioengineering Institute, University of Auckland, Auckland, 1010, New Zealand
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Gawthrop PJ, Pan M. Network thermodynamics of biological systems: A bond graph approach. Math Biosci 2022; 352:108899. [PMID: 36057321 DOI: 10.1016/j.mbs.2022.108899] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/04/2022] [Revised: 08/26/2022] [Accepted: 08/26/2022] [Indexed: 10/14/2022]
Abstract
Edmund Crampin (1973-2021) was at the forefront of Systems Biology research and his work will influence the field for years to come. This paper brings together and summarises the seminal work of his group in applying energy-based bond graph methods to biological systems. In particular, this paper: (a) motivates the need to consider energy in modelling biology; (b) introduces bond graphs as a methodology for achieving this; (c) describes extensions to modelling electrochemical transduction; (d) outlines how bond graph models can be constructed in a modular manner and (e) describes stoichiometric approaches to deriving fundamental properties of reaction networks. These concepts are illustrated using a new bond graph model of photosynthesis in chloroplasts.
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Affiliation(s)
- Peter J Gawthrop
- Systems Biology Laboratory, School of Mathematics and Statistics, and Department of Biomedical Engineering, University of Melbourne, Victoria 3010, Australia.
| | - Michael Pan
- Systems Biology Laboratory, School of Mathematics and Statistics, and Department of Biomedical Engineering, University of Melbourne, Victoria 3010, Australia; School of Mathematics and Statistics, University of Melbourne, Victoria 3010, Australia
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Shahidi N, Pan M, Tran K, Crampin EJ, Nickerson DP. A semantics, energy-based approach to automate biomodel composition. PLoS One 2022; 17:e0269497. [PMID: 35657966 PMCID: PMC9165793 DOI: 10.1371/journal.pone.0269497] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2022] [Accepted: 05/20/2022] [Indexed: 11/19/2022] Open
Abstract
Hierarchical modelling is essential to achieving complex, large-scale models. However, not all modelling schemes support hierarchical composition, and correctly mapping points of connection between models requires comprehensive knowledge of each model's components and assumptions. To address these challenges in integrating biosimulation models, we propose an approach to automatically and confidently compose biosimulation models. The approach uses bond graphs to combine aspects of physical and thermodynamics-based modelling with biological semantics. We improved on existing approaches by using semantic annotations to automate the recognition of common components. The approach is illustrated by coupling a model of the Ras-MAPK cascade to a model of the upstream activation of EGFR. Through this methodology, we aim to assist researchers and modellers in readily having access to more comprehensive biological systems models.
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Affiliation(s)
- Niloofar Shahidi
- Auckland Bioengineering Institute, The University of Auckland, Auckland, New Zealand
| | - Michael Pan
- Systems Biology Laboratory, School of Mathematics and Statistics, and Department of Biomedical Engineering, University of Melbourne, Melbourne, Victoria, Australia
- ARC Centre of Excellence in Convergent Bio-Nano Science and Technology, Faculty of Engineering and Information Technology, University of Melbourne, Melbourne, Victoria, Australia
- School of Mathematics and Statistics, Faculty of Science, University of Melbourne, Victoria, Australia
| | - Kenneth Tran
- Auckland Bioengineering Institute, The University of Auckland, Auckland, New Zealand
| | - Edmund J. Crampin
- Systems Biology Laboratory, School of Mathematics and Statistics, and Department of Biomedical Engineering, University of Melbourne, Melbourne, Victoria, Australia
- ARC Centre of Excellence in Convergent Bio-Nano Science and Technology, Faculty of Engineering and Information Technology, University of Melbourne, Melbourne, Victoria, Australia
- School of Mathematics and Statistics, Faculty of Science, University of Melbourne, Victoria, Australia
- School of Medicine, University of Melbourne, Melbourne, Victoria, Australia
| | - David P. Nickerson
- Auckland Bioengineering Institute, The University of Auckland, Auckland, New Zealand
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Gawthrop PJ. Energy-Based Modeling of the Feedback Control of Biomolecular Systems With Cyclic Flow Modulation. IEEE Trans Nanobioscience 2021; 20:183-192. [PMID: 33566764 DOI: 10.1109/tnb.2021.3058440] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
Energy-based modelling brings engineering insight to the understanding of biomolecular systems. It is shown how well-established control engineering concepts, such as loop-gain, arise from energy feedback loops and are therefore amenable to control engineering insight. In particular, a novel method is introduced to allow the transfer function based approach of classical linear control to be utilised in the analysis of feedback systems modelled by network thermodynamics and thus amalgamate energy-based modelling with control systems analysis. The approach is illustrated using a class of metabolic cycles with activation and inhibition leading to the concept of Cyclic Flow Modulation.
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Gawthrop PJ, Pan M. Network Thermodynamical Modeling of Bioelectrical Systems: A Bond Graph Approach. Bioelectricity 2021; 3:3-13. [PMID: 34476374 DOI: 10.1089/bioe.2020.0042] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Interactions among biomolecules, electrons, and protons are essential to many fundamental processes sustaining life. It is therefore of interest to build mathematical models of these bioelectrical processes not only to enhance understanding but also to enable computer models to complement in vitro and in vivo experiments. Such models can never be entirely accurate; it is nevertheless important that the models are compatible with physical principles. Network Thermodynamics, as implemented with bond graphs, provide one approach to creating physically compatible mathematical models of bioelectrical systems. This is illustrated using simple models of ion channels, redox reactions, proton pumps, and electrogenic membrane transporters thus demonstrating that the approach can be used to build mathematical and computer models of a wide range of bioelectrical systems.
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Affiliation(s)
- Peter J Gawthrop
- Systems Biology Laboratory, Department of Biomedical Engineering, Melbourne School of Engineering, University of Melbourne, Melbourne, Australia.,Systems Biology Laboratory, School of Mathematics and Statistics, University of Melbourne, Melbourne, Australia
| | - Michael Pan
- Systems Biology Laboratory, Department of Biomedical Engineering, Melbourne School of Engineering, University of Melbourne, Melbourne, Australia.,Systems Biology Laboratory, School of Mathematics and Statistics, University of Melbourne, Melbourne, Australia
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Physically-plausible modelling of biomolecular systems: A simplified, energy-based model of the mitochondrial electron transport chain. J Theor Biol 2020; 493:110223. [PMID: 32119969 DOI: 10.1016/j.jtbi.2020.110223] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2019] [Revised: 01/21/2020] [Accepted: 02/27/2020] [Indexed: 11/20/2022]
Abstract
Advances in systems biology and whole-cell modelling demand increasingly comprehensive mathematical models of cellular biochemistry. Such models require the development of simplified representations of specific processes which capture essential biophysical features but without unnecessarily complexity. Recently there has been renewed interest in thermodynamically-based modelling of cellular processes. Here we present an approach to developing of simplified yet thermodynamically consistent (hence physically plausible) models which can readily be incorporated into large scale biochemical descriptions but which do not require full mechanistic detail of the underlying processes. We illustrate the approach through development of a simplified, physically plausible model of the mitochondrial electron transport chain and show that the simplified model behaves like the full system.
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