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Niederer SA, Aboelkassem Y, Cantwell CD, Corrado C, Coveney S, Cherry EM, Delhaas T, Fenton FH, Panfilov AV, Pathmanathan P, Plank G, Riabiz M, Roney CH, dos Santos RW, Wang L. Creation and application of virtual patient cohorts of heart models. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2020; 378:20190558. [PMID: 32448064 PMCID: PMC7287335 DOI: 10.1098/rsta.2019.0558] [Citation(s) in RCA: 42] [Impact Index Per Article: 10.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 03/06/2020] [Indexed: 05/21/2023]
Abstract
Patient-specific cardiac models are now being used to guide therapies. The increased use of patient-specific cardiac simulations in clinical care will give rise to the development of virtual cohorts of cardiac models. These cohorts will allow cardiac simulations to capture and quantify inter-patient variability. However, the development of virtual cohorts of cardiac models will require the transformation of cardiac modelling from small numbers of bespoke models to robust and rapid workflows that can create large numbers of models. In this review, we describe the state of the art in virtual cohorts of cardiac models, the process of creating virtual cohorts of cardiac models, and how to generate the individual cohort member models, followed by a discussion of the potential and future applications of virtual cohorts of cardiac models. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.
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Affiliation(s)
| | | | | | | | | | - E. M. Cherry
- Georgia Institute of Technology, Atlanta, GA, USA
| | - T. Delhaas
- Maastricht University, Maastricht, the Netherlands
| | - F. H. Fenton
- Georgia Institute of Technology, Atlanta, GA, USA
| | - A. V. Panfilov
- Ghent University, Gent, Belgium
- Laboratory of Computational Biology and Medicine, Ural Federal University, Ekaterinburg, Russia
| | - P. Pathmanathan
- Center for Devices and Radiological Health, U.S. Food and Administration, Rockville, MD, USA
| | - G. Plank
- Medical University of Graz, Graz, Austria
| | | | | | | | - L. Wang
- Rochester Institute of Technology, La JollaRochester, NY, USA
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Freua MC, Santana MHDA, Ventura RV, Tedeschi LO, Ferraz JBS. Using a system of differential equations that models cattle growth to uncover the genetic basis of complex traits. J Appl Genet 2017; 58:393-400. [PMID: 28382466 DOI: 10.1007/s13353-017-0395-4] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2016] [Revised: 02/12/2017] [Accepted: 03/22/2017] [Indexed: 10/19/2022]
Abstract
The interplay between dynamic models of biological systems and genomics is based on the assumption that genetic variation of the complex trait (i.e., outcome of model behavior) arises from component traits (i.e., model parameters) in lower hierarchical levels. In order to provide a proof of concept of this statement for a cattle growth model, we ask whether model parameters map genomic regions that harbor quantitative trait loci (QTLs) already described for the complex trait. We conducted a genome-wide association study (GWAS) with a Bayesian hierarchical LASSO method in two parameters of the Davis Growth Model, a system of three ordinary differential equations describing DNA accretion, protein synthesis and degradation, and fat synthesis. Phenotypic and genotypic data were available for 893 Nellore (Bos indicus) cattle. Computed values for parameter k1 (DNA accretion rate) ranged from 0.005 ± 0.003 and for α (constant for energy for maintenance requirement) 0.134 ± 0.024. The expected biological interpretation of the parameters is confirmed by QTLs mapped for k1 and α. QTLs within genomic regions mapped for k1 are expected to be correlated with the DNA pool: body size and weight. Single nucleotide polymorphisms (SNPs) which were significant for α mapped QTLs that had already been associated with residual feed intake, feed conversion ratio, average daily gain (ADG), body weight, and also dry matter intake. SNPs identified for k1 were able to additionally explain 2.2% of the phenotypic variability of the complex ADG, even when SNPs for k1 did not match the genomic regions associated with ADG. Although improvements are needed, our findings suggest that genomic analysis on component traits may help to uncover the genetic basis of more complex traits, particularly when lower biological hierarchies are mechanistically described by mathematical simulation models.
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Affiliation(s)
- Mateus Castelani Freua
- Department of Veterinary Medicine, GMAB, Faculdade de Zootecnia e Engenharia de Alimentos, University of São Paulo, Av. Duque de Caxias Norte, 225, Pirassununga, SP, 13635-900, Brazil
| | - Miguel Henrique de Almeida Santana
- Department of Veterinary Medicine, GMAB, Faculdade de Zootecnia e Engenharia de Alimentos, University of São Paulo, Av. Duque de Caxias Norte, 225, Pirassununga, SP, 13635-900, Brazil.
| | - Ricardo Vieira Ventura
- Department of Veterinary Medicine, GMAB, Faculdade de Zootecnia e Engenharia de Alimentos, University of São Paulo, Av. Duque de Caxias Norte, 225, Pirassununga, SP, 13635-900, Brazil.,Centre for Genetic Improvement for Livestock, University of Guelph, 50 Stone Road East, Guelph, ON, N1G 2W1, Canada
| | - Luis Orlindo Tedeschi
- Department of Animal Science, Texas A&M University, 230 Kleberg Center, 2471 TAMU, College Station, TX, 77843, USA
| | - José Bento Sterman Ferraz
- Department of Veterinary Medicine, GMAB, Faculdade de Zootecnia e Engenharia de Alimentos, University of São Paulo, Av. Duque de Caxias Norte, 225, Pirassununga, SP, 13635-900, Brazil
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Corrado C, Whitaker J, Chubb H, Williams S, Wright M, Gill J, ONeill MD, Niederer SA. Personalized Models of Human Atrial Electrophysiology Derived From Endocardial Electrograms. IEEE Trans Biomed Eng 2016; 64:735-742. [PMID: 28207381 DOI: 10.1109/tbme.2016.2574619] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
Abstract
OBJECTIVE Computational models represent a novel framework for understanding the mechanisms behind atrial fibrillation (AF) and offer a pathway for personalizing and optimizing treatment. The characterization of local electrophysiological properties across the atria during procedures remains a challenge. The aim of this work is to characterize the regional properties of the human atrium from multielectrode catheter measurements. METHODS We propose a novel method that characterizes regional electrophysiology properties by fitting parameters of an ionic model to conduction velocity and effective refractory period restitution curves obtained by a s1-s2 pacing protocol applied through a multielectrode catheter. Using an in-silico dataset we demonstrate that the fitting method can constrain parameters with a mean error of 21.9 ± 16.1% and can replicate conduction velocity and effective refractory curves not used in the original fitting with a relative error of 4.4 ± 6.9%. RESULTS We demonstrate this parameter estimation approach on five clinical datasets recorded from AF patients. Recordings and parametrization took approx. 5 and 6 min, respectively. Models fitted restitution curves with an error of ~ 5% and identify a unique parameter set. Tissue properties were predicted using a two-dimensional atrial tissue sheet model. Spiral wave stability in each case was predicted using tissue simulations, identifying distinct stable (2/5), meandering and breaking up (2/5), and unstable self-terminating (1/5) spiral tip patterns for different cases. CONCLUSION AND SIGNIFICANCE We have developed and demonstrated a robust and rapid approach for personalizing local ionic models from a clinically tractable.
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Affiliation(s)
- Cesare Corrado
- Department of Biomedical Engineering, King's College London, London, U.K
| | - John Whitaker
- Department of Biomedical EngineeringKing's College London
| | - Henry Chubb
- Department of Biomedical EngineeringKing's College London
| | | | - Matthew Wright
- Department of Biomedical EngineeringKing's College London
| | - Jaswinder Gill
- Department of Biomedical EngineeringKing's College London
| | - Mark D ONeill
- Department of Biomedical EngineeringKing's College London
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Nordbø Ø, Gjuvsland AB, Nermoen A, Land S, Niederer S, Lamata P, Lee J, Smith NP, Omholt SW, Vik JO. Towards causally cohesive genotype-phenotype modelling for characterization of the soft-tissue mechanics of the heart in normal and pathological geometries. J R Soc Interface 2015; 12:rsif.2014.1166. [PMID: 25833237 DOI: 10.1098/rsif.2014.1166] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
Abstract
A scientific understanding of individual variation is key to personalized medicine, integrating genotypic and phenotypic information via computational physiology. Genetic effects are often context-dependent, differing between genetic backgrounds or physiological states such as disease. Here, we analyse in silico genotype-phenotype maps (GP map) for a soft-tissue mechanics model of the passive inflation phase of the heartbeat, contrasting the effects of microstructural and other low-level parameters assumed to be genetically influenced, under normal, concentrically hypertrophic and eccentrically hypertrophic geometries. For a large number of parameter scenarios, representing mock genetic variation in low-level parameters, we computed phenotypes describing the deformation of the heart during inflation. The GP map was characterized by variance decompositions for each phenotype with respect to each parameter. As hypothesized, the concentric geometry allowed more low-level parameters to contribute to variation in shape phenotypes. In addition, the relative importance of overall stiffness and fibre stiffness differed between geometries. Otherwise, the GP map was largely similar for the different heart geometries, with little genetic interaction between the parameters included in this study. We argue that personalized medicine can benefit from a combination of causally cohesive genotype-phenotype modelling, and strategic phenotyping that captures effect modifiers not explicitly included in the mechanistic model.
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Affiliation(s)
- Øyvind Nordbø
- Department of Mathematical Sciences and Technology, Norwegian University of Life Sciences, PO Box 5003, 1432 Ås, Norway
| | - Arne B Gjuvsland
- Department of Animal and Aquacultural Sciences, Norwegian University of Life Sciences, PO Box 5003, 1432 Ås, Norway
| | - Anders Nermoen
- International Research Institute of Stavanger, PO Box 8046, 4068 Stavanger, Norway
| | - Sander Land
- Biomedical Engineering Department, King's College London, London SE1 7EH, UK
| | - Steven Niederer
- Biomedical Engineering Department, King's College London, London SE1 7EH, UK
| | - Pablo Lamata
- Biomedical Engineering Department, King's College London, London SE1 7EH, UK
| | - Jack Lee
- Biomedical Engineering Department, King's College London, London SE1 7EH, UK
| | - Nicolas P Smith
- Biomedical Engineering Department, King's College London, London SE1 7EH, UK
| | - Stig W Omholt
- Department of Circulation and Medical Imaging, Cardiac Exercise Research Group, NTNU Norwegian University of Science and Technology, PO Box 8905, 7491 Trondheim, Norway
| | - Jon Olav Vik
- Department of Animal and Aquacultural Sciences, Norwegian University of Life Sciences, PO Box 5003, 1432 Ås, Norway
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Groenendaal W, Ortega FA, Kherlopian AR, Zygmunt AC, Krogh-Madsen T, Christini DJ. Cell-specific cardiac electrophysiology models. PLoS Comput Biol 2015; 11:e1004242. [PMID: 25928268 PMCID: PMC4415772 DOI: 10.1371/journal.pcbi.1004242] [Citation(s) in RCA: 74] [Impact Index Per Article: 8.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/01/2014] [Accepted: 03/16/2015] [Indexed: 01/25/2023] Open
Abstract
The traditional cardiac model-building paradigm involves constructing a composite model using data collected from many cells. Equations are derived for each relevant cellular component (e.g., ion channel, exchanger) independently. After the equations for all components are combined to form the composite model, a subset of parameters is tuned, often arbitrarily and by hand, until the model output matches a target objective, such as an action potential. Unfortunately, such models often fail to accurately simulate behavior that is dynamically dissimilar (e.g., arrhythmia) to the simple target objective to which the model was fit. In this study, we develop a new approach in which data are collected via a series of complex electrophysiology protocols from single cardiac myocytes and then used to tune model parameters via a parallel fitting method known as a genetic algorithm (GA). The dynamical complexity of the electrophysiological data, which can only be fit by an automated method such as a GA, leads to more accurately parameterized models that can simulate rich cardiac dynamics. The feasibility of the method is first validated computationally, after which it is used to develop models of isolated guinea pig ventricular myocytes that simulate the electrophysiological dynamics significantly better than does a standard guinea pig model. In addition to improving model fidelity generally, this approach can be used to generate a cell-specific model. By so doing, the approach may be useful in applications ranging from studying the implications of cell-to-cell variability to the prediction of intersubject differences in response to pharmacological treatment. Mathematical models of cardiac cell electrophysiology are widely used as predictive and illuminatory tools, but have been developed for decades using a suboptimal process. The models are typically constructed by manual adjustment of parameters to fit simple data and therefore often underperform when used to predict complex behavior such as arrhythmias. We present a novel method of model parameterization using automated optimization and dynamically rich fitting data and then demonstrate that this approach is better at finding the “real” model of a cell. Application of the method to cardiac myocytes leads to cell-specific models, which may enable well-controlled studies of both cellular- and subject-level population heterogeneity in disease propensity and response to therapies.
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Affiliation(s)
- Willemijn Groenendaal
- Greenberg Division of Cardiology, Weill Cornell Medical College, New York, New York, United States of America
| | - Francis A. Ortega
- Department of Physiology and Biophysics, Weill Cornell Medical College, New York, New York, United States of America
| | - Armen R. Kherlopian
- Department of Physiology and Biophysics, Weill Cornell Medical College, New York, New York, United States of America
| | | | - Trine Krogh-Madsen
- Greenberg Division of Cardiology, Weill Cornell Medical College, New York, New York, United States of America
- Institute for Computational Biomedicine, Weill Cornell Medical College, New York, New York, United States of America
| | - David J. Christini
- Greenberg Division of Cardiology, Weill Cornell Medical College, New York, New York, United States of America
- Department of Physiology and Biophysics, Weill Cornell Medical College, New York, New York, United States of America
- Institute for Computational Biomedicine, Weill Cornell Medical College, New York, New York, United States of America
- * E-mail:
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Tøndel K, Land S, Niederer SA, Smith NP. Quantifying inter-species differences in contractile function through biophysical modelling. J Physiol 2015; 593:1083-111. [PMID: 25480801 DOI: 10.1113/jphysiol.2014.279232] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2014] [Accepted: 11/28/2014] [Indexed: 11/08/2022] Open
Abstract
Animal models and measurements are frequently used to guide and evaluate clinical interventions. In this context, knowledge of inter-species differences in physiology is crucial for understanding the limitations and relevance of animal experimental assays for informing clinical applications. Extensive effort has been put into studying the structure and function of cardiac contractile proteins and how differences in these translate into the functional properties of muscles. However, integrating this knowledge into a quantitative description, formalising and highlighting inter-species differences both in the kinetics and in the regulation of physiological mechanisms, remains challenging. In this study we propose and apply a novel approach for the quantification of inter-species differences between mouse, rat and human. Assuming conservation of the fundamental physiological mechanisms underpinning contraction, biophysically based computational models are fitted to simulate experimentally recorded phenotypes from multiple species. The phenotypic differences between species are then succinctly quantified as differences in the biophysical model parameter values. This provides the potential of quantitatively establishing the human relevance of both animal-based experimental and computational models for application in a clinical context. Our results indicate that the parameters related to the sensitivity and cooperativity of calcium binding to troponin C and the activation and relaxation rates of tropomyosin/crossbridge binding kinetics differ most significantly between mouse, rat and human, while for example the reference tension, as expected, shows only minor differences between the species. Hence, while confirming expected inter-species differences in calcium sensitivity due to large differences in the observed calcium transients, our results also indicate more unexpected differences in the cooperativity mechanism. Specifically, the decrease in the unbinding rate of calcium to troponin C with increasing active tension was much lower for mouse than for rat and human. Our results also predicted crossbridge binding to be slowest in human and fastest in mouse.
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Affiliation(s)
- Kristin Tøndel
- Department of Biomedical Engineering, King's College London, St. Thomas' Hospital, Westminster Bridge Road, London, SE1 7EH, UK; Simula Research Laboratory, Martin Linges v. 17/25, Rolfsbukta 4B, Fornebu, 1364, Norway
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7
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Tøndel K, Martens H. Analyzing complex mathematical model behavior by partial least squares regression‐based multivariate metamodeling. ACTA ACUST UNITED AC 2014. [DOI: 10.1002/wics.1325] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
Affiliation(s)
- Kristin Tøndel
- Simula Research Laboratory AS Fornebu Norway
- Department of Biomedical Engineering King's College London, St. Thomas' Hospital London UK
| | - Harald Martens
- Department of Engineering Cybernetics Norwegian University of Science and Technology Trondheim Norway
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Tøndel K, Niederer SA, Land S, Smith NP. Insight into model mechanisms through automatic parameter fitting: a new methodological framework for model development. BMC SYSTEMS BIOLOGY 2014; 8:59. [PMID: 24886522 PMCID: PMC4078362 DOI: 10.1186/1752-0509-8-59] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/18/2013] [Accepted: 04/29/2014] [Indexed: 11/10/2022]
Abstract
Background Striking a balance between the degree of model complexity and parameter identifiability, while still producing biologically feasible simulations using modelling is a major challenge in computational biology. While these two elements of model development are closely coupled, parameter fitting from measured data and analysis of model mechanisms have traditionally been performed separately and sequentially. This process produces potential mismatches between model and data complexities that can compromise the ability of computational frameworks to reveal mechanistic insights or predict new behaviour. In this study we address this issue by presenting a generic framework for combined model parameterisation, comparison of model alternatives and analysis of model mechanisms. Results The presented methodology is based on a combination of multivariate metamodelling (statistical approximation of the input–output relationships of deterministic models) and a systematic zooming into biologically feasible regions of the parameter space by iterative generation of new experimental designs and look-up of simulations in the proximity of the measured data. The parameter fitting pipeline includes an implicit sensitivity analysis and analysis of parameter identifiability, making it suitable for testing hypotheses for model reduction. Using this approach, under-constrained model parameters, as well as the coupling between parameters within the model are identified. The methodology is demonstrated by refitting the parameters of a published model of cardiac cellular mechanics using a combination of measured data and synthetic data from an alternative model of the same system. Using this approach, reduced models with simplified expressions for the tropomyosin/crossbridge kinetics were found by identification of model components that can be omitted without affecting the fit to the parameterising data. Our analysis revealed that model parameters could be constrained to a standard deviation of on average 15% of the mean values over the succeeding parameter sets. Conclusions Our results indicate that the presented approach is effective for comparing model alternatives and reducing models to the minimum complexity replicating measured data. We therefore believe that this approach has significant potential for reparameterising existing frameworks, for identification of redundant model components of large biophysical models and to increase their predictive capacity.
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Affiliation(s)
- Kristin Tøndel
- Department of Biomedical Engineering, King's College London, St, Thomas' Hospital, Westminster Bridge Road, London SE1 7EH, UK.
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Wang Y, Vik JO, Omholt SW, Gjuvsland AB. Effect of regulatory architecture on broad versus narrow sense heritability. PLoS Comput Biol 2013; 9:e1003053. [PMID: 23671414 PMCID: PMC3649986 DOI: 10.1371/journal.pcbi.1003053] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2012] [Accepted: 03/23/2013] [Indexed: 11/18/2022] Open
Abstract
Additive genetic variance (VA ) and total genetic variance (VG ) are core concepts in biomedical, evolutionary and production-biology genetics. What determines the large variation in reported VA /VG ratios from line-cross experiments is not well understood. Here we report how the VA /VG ratio, and thus the ratio between narrow and broad sense heritability (h(2) /H(2) ), varies as a function of the regulatory architecture underlying genotype-to-phenotype (GP) maps. We studied five dynamic models (of the cAMP pathway, the glycolysis, the circadian rhythms, the cell cycle, and heart cell dynamics). We assumed genetic variation to be reflected in model parameters and extracted phenotypes summarizing the system dynamics. Even when imposing purely linear genotype to parameter maps and no environmental variation, we observed quite low VA /VG ratios. In particular, systems with positive feedback and cyclic dynamics gave more non-monotone genotype-phenotype maps and much lower VA /VG ratios than those without. The results show that some regulatory architectures consistently maintain a transparent genotype-to-phenotype relationship, whereas other architectures generate more subtle patterns. Our approach can be used to elucidate these relationships across a whole range of biological systems in a systematic fashion.
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Affiliation(s)
- Yunpeng Wang
- Centre for Integrative Genetics (CIGENE), Department of Animal and Aquacultural Sciences, Norwegian University of Life Sciences, Ås, Norway
| | - Jon Olav Vik
- Centre for Integrative Genetics (CIGENE), Department of Mathematical Sciences and Technology, Norwegian University of Life Sciences, Ås, Norway
| | - Stig W. Omholt
- Centre for Integrative Genetics (CIGENE), Department of Animal and Aquacultural Sciences, Norwegian University of Life Sciences, Ås, Norway
- NTNU Norwegian University of Science and Technology, Department of Biology, Centre for Biodiversity Dynamics, Realfagsbygget, NO-7491 Trondheim, Norway
| | - Arne B. Gjuvsland
- Centre for Integrative Genetics (CIGENE), Department of Mathematical Sciences and Technology, Norwegian University of Life Sciences, Ås, Norway
- * E-mail:
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Gjuvsland AB, Vik JO, Beard DA, Hunter PJ, Omholt SW. Bridging the genotype-phenotype gap: what does it take? J Physiol 2013; 591:2055-66. [PMID: 23401613 PMCID: PMC3634519 DOI: 10.1113/jphysiol.2012.248864] [Citation(s) in RCA: 52] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022] Open
Abstract
The genotype-phenotype map (GP map) concept applies to any time point in the ontogeny of a living system. It is the outcome of very complex dynamics that include environmental effects, and bridging the genotype-phenotype gap is synonymous with understanding these dynamics. The context for this understanding is physiology, and the disciplinary goals of physiology do indeed demand the physiological community to seek this understanding. We claim that this task is beyond reach without use of mathematical models that bind together genetic and phenotypic data in a causally cohesive way. We provide illustrations of such causally cohesive genotype-phenotype models where the phenotypes span from gene expression profiles to development of whole organs. Bridging the genotype-phenotype gap also demands that large-scale biological ('omics') data and associated bioinformatics resources be more effectively integrated with computational physiology than is currently the case. A third major element is the need for developing a phenomics technology way beyond current state of the art, and we advocate the establishment of a Human Phenome Programme solidly grounded on biophysically based mathematical descriptions of human physiology.
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Affiliation(s)
- Arne B Gjuvsland
- Centre for Integrative Genetics, Department of Mathematical and Technological Sciences, Norwegian University of Life Sciences, Norway
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Niederer SA, Land S, Omholt SW, Smith NP. Interpreting genetic effects through models of cardiac electromechanics. Am J Physiol Heart Circ Physiol 2012; 303:H1294-303. [PMID: 23042948 DOI: 10.1152/ajpheart.00121.2012] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 01/12/2023]
Abstract
Multiscale models of cardiac electromechanics are being increasingly focused on understanding how genetic variation and environment underpin multiple disease states. In this paper we review the current state of the art in both the development of specific models and the physiological insights they have produced. This growing research body includes the development of models for capturing the effects of changes in function in both single and multiple proteins in both specific expression systems and in vivo contexts. Finally, the potential for using this approach for ultimately predicting phenotypes from genetic sequence information is discussed.
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Affiliation(s)
- S A Niederer
- Department of Biomedical Engineering, King's College London, King's Health Partners, Saint Thomas' Hospital, London, UK
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12
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Tøndel K, Indahl UG, Gjuvsland AB, Omholt SW, Martens H. Multi-way metamodelling facilitates insight into the complex input-output maps of nonlinear dynamic models. BMC SYSTEMS BIOLOGY 2012; 6:88. [PMID: 22818032 PMCID: PMC3483253 DOI: 10.1186/1752-0509-6-88] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/20/2011] [Accepted: 06/20/2012] [Indexed: 11/10/2022]
Abstract
BACKGROUND Statistical approaches to describing the behaviour, including the complex relationships between input parameters and model outputs, of nonlinear dynamic models (referred to as metamodelling) are gaining more and more acceptance as a means for sensitivity analysis and to reduce computational demand. Understanding such input-output maps is necessary for efficient model construction and validation. Multi-way metamodelling provides the opportunity to retain the block-wise structure of the temporal data typically generated by dynamic models throughout the analysis. Furthermore, a cluster-based approach to regional metamodelling allows description of highly nonlinear input-output relationships, revealing additional patterns of covariation. RESULTS By presenting the N-way Hierarchical Cluster-based Partial Least Squares Regression (N-way HC-PLSR) method, we here combine multi-way analysis with regional cluster-based metamodelling, together making a powerful methodology for extensive exploration of the input-output maps of complex dynamic models. We illustrate the potential of the N-way HC-PLSR by applying it both to predict model outputs as functions of the input parameters, and in the inverse direction (predicting input parameters from the model outputs), to analyse the behaviour of a dynamic model of the mammalian circadian clock. Our results display a more complete cartography of how variation in input parameters is reflected in the temporal behaviour of multiple model outputs than has been previously reported. CONCLUSIONS Our results indicated that the N-way HC-PLSR metamodelling provides a gain in insight into which parameters that are related to a specific model output behaviour, as well as variations in the model sensitivity to certain input parameters across the model output space. Moreover, the N-way approach allows a more transparent and detailed exploration of the temporal dimension of complex dynamic models, compared to alternative 2-way methods.
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Affiliation(s)
- Kristin Tøndel
- Centre for Integrative Genetics (CIGENE), Dept, of Mathematical Sciences and Technology, Norwegian University of Life Sciences, Ås, Norway.
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Moss R, Grosse T, Marchant I, Lassau N, Gueyffier F, Thomas SR. Virtual patients and sensitivity analysis of the Guyton model of blood pressure regulation: towards individualized models of whole-body physiology. PLoS Comput Biol 2012; 8:e1002571. [PMID: 22761561 PMCID: PMC3386164 DOI: 10.1371/journal.pcbi.1002571] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2012] [Accepted: 05/08/2012] [Indexed: 12/31/2022] Open
Abstract
Mathematical models that integrate multi-scale physiological data can offer insight into physiological and pathophysiological function, and may eventually assist in individualized predictive medicine. We present a methodology for performing systematic analyses of multi-parameter interactions in such complex, multi-scale models. Human physiology models are often based on or inspired by Arthur Guyton's whole-body circulatory regulation model. Despite the significance of this model, it has not been the subject of a systematic and comprehensive sensitivity study. Therefore, we use this model as a case study for our methodology. Our analysis of the Guyton model reveals how the multitude of model parameters combine to affect the model dynamics, and how interesting combinations of parameters may be identified. It also includes a "virtual population" from which "virtual individuals" can be chosen, on the basis of exhibiting conditions similar to those of a real-world patient. This lays the groundwork for using the Guyton model for in silico exploration of pathophysiological states and treatment strategies. The results presented here illustrate several potential uses for the entire dataset of sensitivity results and the "virtual individuals" that we have generated, which are included in the supplementary material. More generally, the presented methodology is applicable to modern, more complex multi-scale physiological models.
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Affiliation(s)
- Robert Moss
- IR4M UMR8081 CNRS, Université Paris-Sud, Orsay, France
- Institut Gustave Roussy, Villejuif, France
- Melbourne School of Population Health, The University of Melbourne, Melbourne, Australia
| | - Thibault Grosse
- IR4M UMR8081 CNRS, Université Paris-Sud, Orsay, France
- Institut Gustave Roussy, Villejuif, France
| | - Ivanny Marchant
- Escuela de Medicina, Departamento de Pre-clínicas, Universidad de Valparaíso, Valparaíso, Chile
| | - Nathalie Lassau
- IR4M UMR8081 CNRS, Université Paris-Sud, Orsay, France
- Institut Gustave Roussy, Villejuif, France
| | - François Gueyffier
- IMTh – Institute for Theoretical Medicine, Lyon, France
- Université Lyon 1, CNRS, UMR 5558, Laboratoire de Biométrie et Biologie Evolutive, Lyon, France
- INSERM, CIC 201, EPICIME, Lyon, France
- Service de Pharmacologie Clinique, Hop L Pradel, Centre Hospitalier Universitaire Lyon, Lyon, France
| | - S. Randall Thomas
- IR4M UMR8081 CNRS, Université Paris-Sud, Orsay, France
- Institut Gustave Roussy, Villejuif, France
- * E-mail:
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Wang Y, Gjuvsland AB, Vik JO, Smith NP, Hunter PJ, Omholt SW. Parameters in dynamic models of complex traits are containers of missing heritability. PLoS Comput Biol 2012; 8:e1002459. [PMID: 22496634 PMCID: PMC3320574 DOI: 10.1371/journal.pcbi.1002459] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2011] [Accepted: 02/19/2012] [Indexed: 12/31/2022] Open
Abstract
Polymorphisms identified in genome-wide association studies of human traits rarely explain more than a small proportion of the heritable variation, and improving this situation within the current paradigm appears daunting. Given a well-validated dynamic model of a complex physiological trait, a substantial part of the underlying genetic variation must manifest as variation in model parameters. These parameters are themselves phenotypic traits. By linking whole-cell phenotypic variation to genetic variation in a computational model of a single heart cell, incorporating genotype-to-parameter maps, we show that genome-wide association studies on parameters reveal much more genetic variation than when using higher-level cellular phenotypes. The results suggest that letting such studies be guided by computational physiology may facilitate a causal understanding of the genotype-to-phenotype map of complex traits, with strong implications for the development of phenomics technology. Despite an ever-increasing number of genome locations reported to be associated with complex human diseases or quantitative traits, only a small proportion of phenotypic variations in a typical quantitative trait can be explained by the discovered variants. We argue that this problem can partly be resolved by combining the statistical methods of quantitative genetics with computational biology. We demonstrate this for the in silico genotype-to-phenotype map of a model heart cell in conjunction with publically accessible genomic data. We show that genome wide association studies (GWAS) on model parameters identify more causal variants and can build better prediction models for the higher-level phenotypes than by performing GWAS on the higher-level phenotypes themselves. Since model parameters are in principle measurable physiological phenotypes, our findings suggest that development of future phenotyping technologies could be guided by mathematical models of the biological systems being targeted.
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Affiliation(s)
- Yunpeng Wang
- Centre for Integrative Genetics, Department of Animal and Aquacultural Sciences, Norwegian University of Life Sciences, Ås, Norway
| | - Arne B. Gjuvsland
- Centre for Integrative Genetics, Department of Mathematical Sciences and Technology, Norwegian University of Life Sciences, Ås, Norway
| | - Jon Olav Vik
- Centre for Integrative Genetics, Department of Mathematical Sciences and Technology, Norwegian University of Life Sciences, Ås, Norway
| | - Nicolas P. Smith
- Department of Biomedical Engineering, St Thomas' Hospital, King's College London, London, United Kingdom
| | - Peter J. Hunter
- Auckland Bioengineering Institute, The University of Auckland, Auckland, New Zealand
| | - Stig W. Omholt
- Centre for Integrative Genetics, Department of Animal and Aquacultural Sciences, Norwegian University of Life Sciences, Ås, Norway
- * E-mail:
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