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Theis N, Bahuguna J, Rubin JE, Muldoon B, Prasad KM. Energy in functional brain states correlates with cognition in adolescent-onset schizophrenia and healthy persons. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2023.11.06.565753. [PMID: 37987003 PMCID: PMC10659315 DOI: 10.1101/2023.11.06.565753] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/22/2023]
Abstract
Adolescent-onset schizophrenia (AOS) is a relatively rare and under-studied form of schizophrenia with more severe cognitive impairments and poorer outcome compared to adult-onset schizophrenia. Several neuroimaging studies have reported alterations in regional activations that account for activity in individual regions (first-order model) and functional connectivity that reveals pairwise co-activations (second-order model) in AOS compared to controls. The pairwise maximum entropy model, also called the Ising model, can integrate both first-order and second-order terms to elucidate a comprehensive picture of neural dynamics and captures both individual and pairwise activity measures into a single quantity known as energy, which is inversely related to the probability of state occurrence. We applied the MEM framework to task functional MRI data collected on 23 AOS individuals in comparison with 53 healthy control subjects while performing the Penn Conditional Exclusion Test (PCET), which measures executive function that has been repeatedly shown to be more impaired in AOS compared to adult-onset schizophrenia. Accuracy of PCET performance was significantly reduced among AOS compared to controls as expected. Average cumulative energy achieved for a participant over the course of the fMRI negatively correlated with task performance, and the association was stronger than any first-order associations. The AOS subjects spent more time in higher energy states that represent lower probability of occurrence and were associated with impaired executive function and greater severity of psychopathology suggesting that the neural dynamics may be less efficient compared to controls who spent more time in lower energy states occurring with higher probability and hence are more stable and efficient. The energy landscapes in both conditions featured attractors that corresponded to two distinct subnetworks, namely fronto-temporal and parieto-motor. Attractor basins were larger in the controls than in AOS; moreover, fronto-temporal basin size was significantly correlated with cognitive performance in controls but not among the AOS. The single trial trajectories for the AOS group also showed higher variability in concordance with shallow attractor basins among AOS. These findings suggest that the neural dynamics of AOS features more frequent occurrence of less probable states with shallower attractors, which lack the relation to executive function associated with attractors in control subjects suggesting a diminished capacity of AOS to generate task-effective brain states.
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Affiliation(s)
- Nicholas Theis
- Department of Psychiatry, University of Pittsburgh School of Medicine, Pittsburgh, PA, USA
| | - Jyotika Bahuguna
- Department of Psychology, Carnegie Mellon University, Pittsburgh, PA, USA
| | | | - Brendan Muldoon
- Department of Psychiatry, University of Pittsburgh School of Medicine, Pittsburgh, PA, USA
| | - Konasale M. Prasad
- Department of Psychiatry, University of Pittsburgh School of Medicine, Pittsburgh, PA, USA
- Department of Bioengineering, Swanson School of Engineering, University of Pittsburgh, PA, USA
- Veterans Affairs Pittsburgh Healthcare System, Pittsburgh, PA, USA
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2
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Lynn BK, De Leenheer P, Schuster M. Putting theory to the test: An integrated computational/experimental chemostat model of the tragedy of the commons. PLoS One 2024; 19:e0300887. [PMID: 38598418 PMCID: PMC11006152 DOI: 10.1371/journal.pone.0300887] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/13/2023] [Accepted: 03/06/2024] [Indexed: 04/12/2024] Open
Abstract
Cooperation via shared public goods is ubiquitous in nature, however, noncontributing social cheaters can exploit the public goods provided by cooperating individuals to gain a fitness advantage. Theory predicts that this dynamic can cause a Tragedy of the Commons, and in particular, a 'Collapsing' Tragedy defined as the extinction of the entire population if the public good is essential. However, there is little empirical evidence of the Collapsing Tragedy in evolutionary biology. Here, we experimentally demonstrate this outcome in a microbial model system, the public good-producing bacterium Pseudomonas aeruginosa grown in a continuous-culture chemostat. In a growth medium that requires extracellular protein digestion, we find that P. aeruginosa populations maintain a high density when entirely composed of cooperating, protease-producing cells but completely collapse when non-producing cheater cells are introduced. We formulate a mechanistic mathematical model that recapitulates experimental observations and suggests key parameters, such as the dilution rate and the cost of public good production, that define the stability of cooperative behavior. We combine model prediction with experimental validation to explain striking differences in the long-term cheater trajectories of replicate cocultures through mutational events that increase cheater fitness. Taken together, our integrated empirical and theoretical approach validates and parametrizes the Collapsing Tragedy in a microbial population, and provides a quantitative, mechanistic framework for generating testable predictions of social behavior.
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Affiliation(s)
- Bryan K. Lynn
- Department of Integrative Biology, Oregon State University, Corvallis, Oregon, United States of America
| | - Patrick De Leenheer
- Department of Integrative Biology, Oregon State University, Corvallis, Oregon, United States of America
- Department of Mathematics, Oregon State University, Corvallis, Oregon, United States of America
| | - Martin Schuster
- Department of Microbiology, Oregon State University, Corvallis, Oregon, United States of America
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3
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Anderson CNK, Transtrum MK. Sloppy model analysis identifies bifurcation parameters without normal form analysis. Phys Rev E 2023; 108:064215. [PMID: 38243539 DOI: 10.1103/physreve.108.064215] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2023] [Accepted: 11/30/2023] [Indexed: 01/21/2024]
Abstract
Bifurcation phenomena are common in multidimensional multiparameter dynamical systems. Normal form theory suggests that bifurcations are driven by relatively few combinations of parameters. Models of complex systems, however, rarely appear in normal form, and bifurcations are controlled by nonlinear combinations of the bare parameters of differential equations. Discovering reparameterizations to transform complex equations into a normal form is often very difficult, and the reparameterization may not even exist in a closed form. Here we show that information geometry and sloppy model analysis using the Fisher information matrix can be used to identify the combination of parameters that control bifurcations. By considering observations on increasingly long timescales, we find those parameters that rapidly characterize the system's topological inhomogeneities, whether the system is in normal form or not. We anticipate that this novel analytical method, which we call time-widening information geometry (TWIG), will be useful in applied network analysis.
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Affiliation(s)
| | - Mark K Transtrum
- Department of Physics and Astronomy Brigham Young University and Provo, Utah 84604, USA
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4
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Malaguit JC, Mendoza VMP, Tubay JM, Mata MAE. Identifying patterning behavior in a plant infestation of insect pests. Math Biosci 2023:109032. [PMID: 37285930 DOI: 10.1016/j.mbs.2023.109032] [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: 02/13/2023] [Revised: 04/11/2023] [Accepted: 05/23/2023] [Indexed: 06/09/2023]
Abstract
In this study, we developed a mechanistic model formulated as a system of reaction-diffusion equations (RDE) to explore the spatiotemporal dynamics of a theoretical pest with a tillering host plant in a controlled rectangular plant field. Local perturbation analysis, a recently developed method of analysis for wave propagation, was utilized to determine patterning regimes resulting from the local and global behaviors of the slow and fast diffusing components of the RDE system, respectively. Turing analysis was done to show that the RDE system does not exhibit Turing patterns. With bug mortality as the bifurcation parameter, regions with oscillations and stable coexistence of the pest and tillers were identified. Numerical simulations illustrate the patterning regimes in 1D and 2D settings. The oscillations suggest that recurrences in pest infestation is possible. Moreover, simulations showed that patterns produced in the model are strongly influenced by the pests' homogeneous dynamics inside the controlled environment.
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Affiliation(s)
- Jcob C Malaguit
- Institute of Mathematical Sciences and Physics, University of the Philippines Los Baños, Batong Malake, Los Baños, 4031, Laguna, Philippines.
| | - Victoria May P Mendoza
- Institute of Mathematics, University of the Philippines Diliman, Diliman, Quezon City, 1101, Philippines.
| | - Jerrold M Tubay
- Institute of Mathematical Sciences and Physics, University of the Philippines Los Baños, Batong Malake, Los Baños, 4031, Laguna, Philippines.
| | - May Anne E Mata
- Department of Mathematics, Physics and Computer Science, University of the Philippines Mindanao, Mintal, Davao City, 8000, Philippines.
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5
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Safavi S, Panagiotaropoulos TI, Kapoor V, Ramirez-Villegas JF, Logothetis NK, Besserve M. Uncovering the organization of neural circuits with Generalized Phase Locking Analysis. PLoS Comput Biol 2023; 19:e1010983. [PMID: 37011110 PMCID: PMC10109521 DOI: 10.1371/journal.pcbi.1010983] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/22/2022] [Revised: 04/17/2023] [Accepted: 02/27/2023] [Indexed: 04/05/2023] Open
Abstract
Despite the considerable progress of in vivo neural recording techniques, inferring the biophysical mechanisms underlying large scale coordination of brain activity from neural data remains challenging. One obstacle is the difficulty to link high dimensional functional connectivity measures to mechanistic models of network activity. We address this issue by investigating spike-field coupling (SFC) measurements, which quantify the synchronization between, on the one hand, the action potentials produced by neurons, and on the other hand mesoscopic "field" signals, reflecting subthreshold activities at possibly multiple recording sites. As the number of recording sites gets large, the amount of pairwise SFC measurements becomes overwhelmingly challenging to interpret. We develop Generalized Phase Locking Analysis (GPLA) as an interpretable dimensionality reduction of this multivariate SFC. GPLA describes the dominant coupling between field activity and neural ensembles across space and frequencies. We show that GPLA features are biophysically interpretable when used in conjunction with appropriate network models, such that we can identify the influence of underlying circuit properties on these features. We demonstrate the statistical benefits and interpretability of this approach in various computational models and Utah array recordings. The results suggest that GPLA, used jointly with biophysical modeling, can help uncover the contribution of recurrent microcircuits to the spatio-temporal dynamics observed in multi-channel experimental recordings.
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Affiliation(s)
- Shervin Safavi
- Department of Physiology of Cognitive Processes, Max Planck Institute for Biological Cybernetics, Tübingen, Germany
- IMPRS for Cognitive and Systems Neuroscience, University of Tübingen, Tübingen, Germany
| | - Theofanis I. Panagiotaropoulos
- Department of Physiology of Cognitive Processes, Max Planck Institute for Biological Cybernetics, Tübingen, Germany
- Cognitive Neuroimaging Unit, INSERM, CEA, CNRS, Université Paris-Saclay, NeuroSpin center, 91191 Gif/Yvette, France
| | - Vishal Kapoor
- Department of Physiology of Cognitive Processes, Max Planck Institute for Biological Cybernetics, Tübingen, Germany
- International Center for Primate Brain Research (ICPBR), Center for Excellence in Brain Science and Intelligence Technology (CEBSIT), Chinese Academy of Sciences (CAS), Shanghai 201602, China
| | - Juan F. Ramirez-Villegas
- Department of Physiology of Cognitive Processes, Max Planck Institute for Biological Cybernetics, Tübingen, Germany
- Institute of Science and Technology Austria (IST Austria), Klosterneuburg, Austria
| | - Nikos K. Logothetis
- Department of Physiology of Cognitive Processes, Max Planck Institute for Biological Cybernetics, Tübingen, Germany
- International Center for Primate Brain Research (ICPBR), Center for Excellence in Brain Science and Intelligence Technology (CEBSIT), Chinese Academy of Sciences (CAS), Shanghai 201602, China
- Centre for Imaging Sciences, Biomedical Imaging Institute, The University of Manchester, Manchester, United Kingdom
| | - Michel Besserve
- Department of Physiology of Cognitive Processes, Max Planck Institute for Biological Cybernetics, Tübingen, Germany
- Department of Empirical Inference, Max Planck Institute for Intelligent Systems and MPI-ETH Center for Learning Systems, Tübingen, Germany
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6
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Abbott MC, Machta BB. Far from Asymptopia: Unbiased High-Dimensional Inference Cannot Assume Unlimited Data. ENTROPY (BASEL, SWITZERLAND) 2023; 25:434. [PMID: 36981323 PMCID: PMC10048238 DOI: 10.3390/e25030434] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/03/2023] [Revised: 02/20/2023] [Accepted: 02/22/2023] [Indexed: 06/18/2023]
Abstract
Inference from limited data requires a notion of measure on parameter space, which is most explicit in the Bayesian framework as a prior distribution. Jeffreys prior is the best-known uninformative choice, the invariant volume element from information geometry, but we demonstrate here that this leads to enormous bias in typical high-dimensional models. This is because models found in science typically have an effective dimensionality of accessible behaviors much smaller than the number of microscopic parameters. Any measure which treats all of these parameters equally is far from uniform when projected onto the sub-space of relevant parameters, due to variations in the local co-volume of irrelevant directions. We present results on a principled choice of measure which avoids this issue and leads to unbiased posteriors by focusing on relevant parameters. This optimal prior depends on the quantity of data to be gathered, and approaches Jeffreys prior in the asymptotic limit. However, for typical models, this limit cannot be justified without an impossibly large increase in the quantity of data, exponential in the number of microscopic parameters.
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7
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Quinn KN, Abbott MC, Transtrum MK, Machta BB, Sethna JP. Information geometry for multiparameter models: new perspectives on the origin of simplicity. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2022; 86:10.1088/1361-6633/aca6f8. [PMID: 36576176 PMCID: PMC10018491 DOI: 10.1088/1361-6633/aca6f8] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/03/2021] [Accepted: 11/29/2022] [Indexed: 05/20/2023]
Abstract
Complex models in physics, biology, economics, and engineering are oftensloppy, meaning that the model parameters are not well determined by the model predictions for collective behavior. Many parameter combinations can vary over decades without significant changes in the predictions. This review uses information geometry to explore sloppiness and its deep relation to emergent theories. We introduce themodel manifoldof predictions, whose coordinates are the model parameters. Itshyperribbonstructure explains why only a few parameter combinations matter for the behavior. We review recent rigorous results that connect the hierarchy of hyperribbon widths to approximation theory, and to the smoothness of model predictions under changes of the control variables. We discuss recent geodesic methods to find simpler models on nearby boundaries of the model manifold-emergent theories with fewer parameters that explain the behavior equally well. We discuss a Bayesian prior which optimizes the mutual information between model parameters and experimental data, naturally favoring points on the emergent boundary theories and thus simpler models. We introduce a 'projected maximum likelihood' prior that efficiently approximates this optimal prior, and contrast both to the poor behavior of the traditional Jeffreys prior. We discuss the way the renormalization group coarse-graining in statistical mechanics introduces a flow of the model manifold, and connect stiff and sloppy directions along the model manifold with relevant and irrelevant eigendirections of the renormalization group. Finally, we discuss recently developed 'intensive' embedding methods, allowing one to visualize the predictions of arbitrary probabilistic models as low-dimensional projections of an isometric embedding, and illustrate our method by generating the model manifold of the Ising model.
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Affiliation(s)
- Katherine N Quinn
- Center for the Physics of Biological Function, Princeton University, Princeton, NJ, United States of America
| | - Michael C Abbott
- Department of Physics, Yale University, New Haven, CT, United States of America
| | - Mark K Transtrum
- Department of Physics and Astronomy, Brigham Young University, Provo, UT, United States of America
| | - Benjamin B Machta
- Department of Physics and Systems Biology Institute, Yale University, New Haven, CT, United States of America
| | - James P Sethna
- Department of Physics, Cornell University, Ithaca, NY, United States of America
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8
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A group theoretic approach to model comparison with simplicial representations. J Math Biol 2022; 85:48. [PMID: 36209430 PMCID: PMC9548478 DOI: 10.1007/s00285-022-01807-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/12/2021] [Revised: 05/31/2022] [Accepted: 07/25/2022] [Indexed: 10/28/2022]
Abstract
AbstractThe complexity of biological systems, and the increasingly large amount of associated experimental data, necessitates that we develop mathematical models to further our understanding of these systems. Because biological systems are generally not well understood, most mathematical models of these systems are based on experimental data, resulting in a seemingly heterogeneous collection of models that ostensibly represent the same system. To understand the system we therefore need to understand how the different models are related to each other, with a view to obtaining a unified mathematical description. This goal is complicated by the fact that a number of distinct mathematical formalisms may be employed to represent the same system, making direct comparison of the models very difficult. A methodology for comparing mathematical models based on their underlying conceptual structure is therefore required. In previous work we developed an appropriate framework for model comparison where we represent models, specifically the conceptual structure of the models, as labelled simplicial complexes and compare them with the two general methodologies of comparison by distance and comparison by equivalence. In this article we continue the development of our model comparison methodology in two directions. First, we present a rigorous and automatable methodology for the core process of comparison by equivalence, namely determining the vertices in a simplicial representation, corresponding to model components, that are conceptually related and the identification of these vertices via simplicial operations. Our methodology is based on considerations of vertex symmetry in the simplicial representation, for which we develop the required mathematical theory of group actions on simplicial complexes. This methodology greatly simplifies and expedites the process of determining model equivalence. Second, we provide an alternative mathematical framework for our model-comparison methodology by representing models as groups, which allows for the direct application of group-theoretic techniques within our model-comparison methodology.
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9
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McCrea M, Ermentrout B, Rubin JE. A model for the collective synchronization of flashing in Photinus carolinus. J R Soc Interface 2022; 19:20220439. [PMID: 36285439 PMCID: PMC9597172 DOI: 10.1098/rsif.2022.0439] [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: 06/13/2022] [Accepted: 09/30/2022] [Indexed: 11/05/2022] Open
Abstract
Recent empirical investigations have characterized the synchronized flashing behaviours of male Photinus carolinus fireflies in their natural habitat in Great Smoky Mountain National Park as well as in controlled environments. We develop a model for the flash dynamics of an individual firefly based on a canonical elliptic burster, a slow-fast dynamical system that produces a repeating pattern of multiple flashes followed by a quiescent period. We show that a small amount of noise renders that oscillation very irregular, but when multiple model fireflies interact through their flashes, the behaviour becomes much more periodic. We show that the aggregate behaviour is qualitatively similar to the experimental findings. We next distribute the fireflies in a two-dimensional spatial domain and vary the interaction range. In addition to synchronization, various spatio-temporal patterns involving propagation of activity emerge spontaneously. Finally, we allow a certain number of fireflies to move and demonstrate how their speed affects the rate and degree of synchronization.
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Affiliation(s)
- Madeline McCrea
- Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, USA
| | - Bard Ermentrout
- Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, USA
| | - Jonathan E. Rubin
- Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, USA
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10
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Albanito F, McBey D, Harrison M, Smith P, Ehrhardt F, Bhatia A, Bellocchi G, Brilli L, Carozzi M, Christie K, Doltra J, Dorich C, Doro L, Grace P, Grant B, Léonard J, Liebig M, Ludemann C, Martin R, Meier E, Meyer R, De Antoni Migliorati M, Myrgiotis V, Recous S, Sándor R, Snow V, Soussana JF, Smith WN, Fitton N. How Modelers Model: the Overlooked Social and Human Dimensions in Model Intercomparison Studies. ENVIRONMENTAL SCIENCE & TECHNOLOGY 2022; 56:13485-13498. [PMID: 36052879 PMCID: PMC9494747 DOI: 10.1021/acs.est.2c02023] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/28/2022] [Revised: 08/23/2022] [Accepted: 08/25/2022] [Indexed: 06/15/2023]
Abstract
There is a growing realization that the complexity of model ensemble studies depends not only on the models used but also on the experience and approach used by modelers to calibrate and validate results, which remain a source of uncertainty. Here, we applied a multi-criteria decision-making method to investigate the rationale applied by modelers in a model ensemble study where 12 process-based different biogeochemical model types were compared across five successive calibration stages. The modelers shared a common level of agreement about the importance of the variables used to initialize their models for calibration. However, we found inconsistency among modelers when judging the importance of input variables across different calibration stages. The level of subjective weighting attributed by modelers to calibration data decreased sequentially as the extent and number of variables provided increased. In this context, the perceived importance attributed to variables such as the fertilization rate, irrigation regime, soil texture, pH, and initial levels of soil organic carbon and nitrogen stocks was statistically different when classified according to model types. The importance attributed to input variables such as experimental duration, gross primary production, and net ecosystem exchange varied significantly according to the length of the modeler's experience. We argue that the gradual access to input data across the five calibration stages negatively influenced the consistency of the interpretations made by the modelers, with cognitive bias in "trial-and-error" calibration routines. Our study highlights that overlooking human and social attributes is critical in the outcomes of modeling and model intercomparison studies. While complexity of the processes captured in the model algorithms and parameterization is important, we contend that (1) the modeler's assumptions on the extent to which parameters should be altered and (2) modeler perceptions of the importance of model parameters are just as critical in obtaining a quality model calibration as numerical or analytical details.
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Affiliation(s)
- Fabrizio Albanito
- Institute
of Biological and Environmental Sciences, School of Biological Science, University of Aberdeen, 23 Street Machar Drive, Aberdeen AB24 3UU, U.K.
| | - David McBey
- Institute
of Biological and Environmental Sciences, School of Biological Science, University of Aberdeen, 23 Street Machar Drive, Aberdeen AB24 3UU, U.K.
| | - Matthew Harrison
- Tasmanian
Institute of Agriculture, University of
Tasmania, Newnham Drive, Launceston, Tasmania 7248, Australia
| | - Pete Smith
- Institute
of Biological and Environmental Sciences, School of Biological Science, University of Aberdeen, 23 Street Machar Drive, Aberdeen AB24 3UU, U.K.
| | - Fiona Ehrhardt
- INRAE,
CODIR, Paris 75007, France
- RITTMO
AgroEnvironnement, Colmar 68000, France
| | - Arti Bhatia
- ICAR-Indian
Agricultural Research Institute, New Delhi 110012, India
| | - Gianni Bellocchi
- Université
Clermont Auvergne, INRAE, VetAgro Sup, UREP, Clermont-Ferrand 63000, France
| | - Lorenzo Brilli
- CNR-IBE,
National Research Council Institute for the BioEconomy, Via Caproni 8, Florence 50145, Italy
| | - Marco Carozzi
- UMR
ECOSYS, INRAE, AgroParisTech, Université Paris-Saclay, Thiverval-Grignon 78850, France
| | - Karen Christie
- Tasmanian
Institute of Agriculture, University of
Tasmania, 16-20 Mooreville Road, Burnie, Tasmania 7320, Australia
| | - Jordi Doltra
- Sustainable
Field Crops Programme, Institute of Agrifood
Research and Technology (IRTA) Mas Badia, La Tallada d’Empordà, Girona 17134, Spain
| | - Christopher Dorich
- Natural
Resource Ecology Lab, Colorado
State University, Fort Collins, Colorado 80521, United States
| | - Luca Doro
- Texas A&M AgriLife Research, Blackland
Research and Extension Center, Temple, Texas 76502, United States
- Desertification Research Centre, University
of Sassari, Sassari 07100, Italy
| | - Peter Grace
- Queensland University of Technology, Brisbane, Queensland 4000, Australia
| | - Brian Grant
- Ottawa Research and Development Centre, Agriculture and Agri-Food Canada, Ottawa, Ontario K1A 0C6, Canada
| | - Joël Léonard
- BioEcoAgro
Joint Research Unit, INRAE, Barenton-Bugny 02000, France
| | - Mark Liebig
- USDA-ARS Northern Great Plains Research
Laboratory, P.O. Box 459, Mandan, North Dakota 58554, United States
| | | | - Raphael Martin
- Université
Clermont Auvergne, INRAE, VetAgro Sup, UREP, Clermont-Ferrand 63000, France
| | - Elizabeth Meier
- CSIRO Agriculture
and Food, St
Lucia, Queensland 4067, Australia
| | - Rachelle Meyer
- Faculty of Veterinary & Agricultural
Sciences, University of Melbourne, Parkville, Victoria 3010, Australia
| | - Massimiliano De Antoni Migliorati
- Queensland University of Technology, Brisbane, Queensland 4000, Australia
- Department of Environment and Science, Dutton Park, Queensland 4102, Australia
| | | | - Sylvie Recous
- Université
de Reims Champagne-Ardenne, INRAE, FARE Laboratory, Reims 51100, France
| | - Renáta Sándor
- Agricultural Institute, Centre for Agricultural Research,
ELKH, Martonvásár 2462, Hungary
| | - Val Snow
- AgResearch, P.O. Box 4749, Christchurch 8140, New
Zealand
| | | | - Ward N. Smith
- Ottawa Research and Development Centre, Agriculture and Agri-Food Canada, Ottawa, Ontario K1A 0C6, Canada
| | - Nuala Fitton
- Institute
of Biological and Environmental Sciences, School of Biological Science, University of Aberdeen, 23 Street Machar Drive, Aberdeen AB24 3UU, U.K.
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11
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Whittaker DG, Wang J, Shuttleworth JG, Venkateshappa R, Kemp JM, Claydon TW, Mirams GR. Ion channel model reduction using manifold boundaries. JOURNAL OF THE ROYAL SOCIETY, INTERFACE 2022; 19:20220193. [PMID: 35946166 PMCID: PMC9363999 DOI: 10.1098/rsif.2022.0193] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
Mathematical models of voltage-gated ion channels are used in basic research, industrial and clinical settings. These models range in complexity, but typically contain numerous variables representing the proportion of channels in a given state, and parameters describing the voltage-dependent rates of transition between states. An open problem is selecting the appropriate degree of complexity and structure for an ion channel model given data availability. Here, we simplify a model of the cardiac human Ether-à-go-go related gene (hERG) potassium ion channel, which carries cardiac IKr, using the manifold boundary approximation method (MBAM). The MBAM approximates high-dimensional model-output manifolds by reduced models describing their boundaries, resulting in models with fewer parameters (and often variables). We produced a series of models of reducing complexity starting from an established five-state hERG model with 15 parameters. Models with up to three fewer states and eight fewer parameters were shown to retain much of the predictive capability of the full model and were validated using experimental hERG1a data collected in HEK293 cells at 37°C. The method provides a way to simplify complex models of ion channels that improves parameter identifiability and will aid in future model development.
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Affiliation(s)
- Dominic G Whittaker
- Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, UK
| | - Jiahui Wang
- Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, UK
| | - Joseph G Shuttleworth
- Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, UK
| | | | - Jacob M Kemp
- Department of Biomedical Physiology and Kinesiology, Simon Fraser University, Burnaby, Canada
| | - Thomas W Claydon
- Department of Biomedical Physiology and Kinesiology, Simon Fraser University, Burnaby, Canada
| | - Gary R Mirams
- Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, UK
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12
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Kurniawan Y, Petrie CL, Williams KJ, Transtrum MK, Tadmor EB, Elliott RS, Karls DS, Wen M. Bayesian, frequentist, and information geometric approaches to parametric uncertainty quantification of classical empirical interatomic potentials. J Chem Phys 2022; 156:214103. [DOI: 10.1063/5.0084988] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023] Open
Abstract
In this paper, we consider the problem of quantifying parametric uncertainty in classical empirical interatomic potentials (IPs) using both Bayesian (Markov Chain Monte Carlo) and frequentist (profile likelihood) methods. We interface these tools with the Open Knowledgebase of Interatomic Models and study three models based on the Lennard-Jones, Morse, and Stillinger–Weber potentials. We confirm that IPs are typically sloppy, i.e., insensitive to coordinated changes in some parameter combinations. Because the inverse problem in such models is ill-conditioned, parameters are unidentifiable. This presents challenges for traditional statistical methods, as we demonstrate and interpret within both Bayesian and frequentist frameworks. We use information geometry to illuminate the underlying cause of this phenomenon and show that IPs have global properties similar to those of sloppy models from fields, such as systems biology, power systems, and critical phenomena. IPs correspond to bounded manifolds with a hierarchy of widths, leading to low effective dimensionality in the model. We show how information geometry can motivate new, natural parameterizations that improve the stability and interpretation of uncertainty quantification analysis and further suggest simplified, less-sloppy models.
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Affiliation(s)
- Yonatan Kurniawan
- Department of Physics and Astronomy, Brigham Young University, Provo, Utah 84604, USA
| | - Cody L. Petrie
- Department of Physics and Astronomy, Brigham Young University, Provo, Utah 84604, USA
| | - Kinamo J. Williams
- Department of Physics and Astronomy, Brigham Young University, Provo, Utah 84604, USA
| | - Mark K. Transtrum
- Department of Physics and Astronomy, Brigham Young University, Provo, Utah 84604, USA
| | - Ellad B. Tadmor
- Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - Ryan S. Elliott
- Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - Daniel S. Karls
- Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - Mingjian Wen
- Energy Technologies Area, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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13
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Shoemaker WR, Polezhaeva E, Givens KB, Lennon JT. Seed banks alter the molecular evolutionary dynamics of Bacillus subtilis. Genetics 2022; 221:6576633. [PMID: 35511143 PMCID: PMC9157070 DOI: 10.1093/genetics/iyac071] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2022] [Accepted: 04/23/2022] [Indexed: 11/14/2022] Open
Abstract
Fluctuations in the availability of resources constrain the growth and reproduction of individuals, which subsequently affects the evolution of their respective populations. Many organisms contend with such fluctuations by entering a reversible state of reduced metabolic activity, a phenomenon known as dormancy. This pool of dormant individuals (i.e. a seed bank) does not reproduce and is expected to act as an evolutionary buffer, though it is difficult to observe this effect directly over an extended evolutionary timescale. Through genetic manipulation, we analyze the molecular evolutionary dynamics of Bacillus subtilis populations in the presence and absence of a seed bank over 700 days. The ability of these bacteria to enter a dormant state increased the accumulation of genetic diversity over time and altered the trajectory of mutations, findings that were recapitulated using simulations based on a mathematical model of evolutionary dynamics. While the ability to form a seed bank did not alter the degree of negative selection, we found that it consistently altered the direction of molecular evolution across genes. Together, these results show that the ability to form a seed bank can affect the direction and rate of molecular evolution over an extended evolutionary timescale.
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Affiliation(s)
| | | | | | - Jay T Lennon
- Department of Biology, Indiana University, Bloomington, IN, 47405, USA
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14
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Research Progress in Simultaneous Heat and Mass Transfer of Fruits and Vegetables During Precooling. FOOD ENGINEERING REVIEWS 2022. [DOI: 10.1007/s12393-022-09309-z] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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15
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Poole W, Pandey A, Shur A, Tuza ZA, Murray RM. BioCRNpyler: Compiling chemical reaction networks from biomolecular parts in diverse contexts. PLoS Comput Biol 2022; 18:e1009987. [PMID: 35442944 PMCID: PMC9060376 DOI: 10.1371/journal.pcbi.1009987] [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: 07/23/2021] [Revised: 05/02/2022] [Accepted: 03/03/2022] [Indexed: 11/23/2022] Open
Abstract
Biochemical interactions in systems and synthetic biology are often modeled with chemical reaction networks (CRNs). CRNs provide a principled modeling environment capable of expressing a huge range of biochemical processes. In this paper, we present a software toolbox, written in Python, that compiles high-level design specifications represented using a modular library of biochemical parts, mechanisms, and contexts to CRN implementations. This compilation process offers four advantages. First, the building of the actual CRN representation is automatic and outputs Systems Biology Markup Language (SBML) models compatible with numerous simulators. Second, a library of modular biochemical components allows for different architectures and implementations of biochemical circuits to be represented succinctly with design choices propagated throughout the underlying CRN automatically. This prevents the often occurring mismatch between high-level designs and model dynamics. Third, high-level design specification can be embedded into diverse biomolecular environments, such as cell-free extracts and in vivo milieus. Finally, our software toolbox has a parameter database, which allows users to rapidly prototype large models using very few parameters which can be customized later. By using BioCRNpyler, users ranging from expert modelers to novice script-writers can easily build, manage, and explore sophisticated biochemical models using diverse biochemical implementations, environments, and modeling assumptions. This paper describes a new software package BioCRNpyler (pronounced “Biocompiler”) designed to support rapid development and exploration of mathematical models of biochemical networks and circuits by computational biologists, systems biologists, and synthetic biologists. BioCRNpyler allows its users to generate large complex models using very few lines of code in a way that is modular. To do this, BioCRNpyler uses a powerful new representation of biochemical circuits which defines their parts, underlying biochemical mechanisms, and chemical context independently. BioCRNpyler was developed as a Python scripting language designed to be accessible to beginning users as well as easily extendable and customizable for advanced users. Ultimately, we see Biocrnpyler being used to accelerate computer automated design of biochemical circuits and model driven hypothesis generation in biology.
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Affiliation(s)
- William Poole
- Computation and Neural Systems, California Institute of Technology, Pasadena, California, United States of America
- * E-mail:
| | - Ayush Pandey
- Control and Dynamical Systems, California Institute of Technology, Pasadena, California, United States of America
| | - Andrey Shur
- Bioengineering, California Institute of Technology, Pasadena, California, United States of America
| | - Zoltan A. Tuza
- Bioengineering, Imperial College London, London, England
| | - Richard M. Murray
- Control and Dynamical Systems, California Institute of Technology, Pasadena, California, United States of America
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16
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Vittadello ST, Stumpf MPH. Model comparison via simplicial complexes and persistent homology. ROYAL SOCIETY OPEN SCIENCE 2021; 8:211361. [PMID: 34659787 PMCID: PMC8511761 DOI: 10.1098/rsos.211361] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/31/2021] [Accepted: 09/16/2021] [Indexed: 05/21/2023]
Abstract
In many scientific and technological contexts, we have only a poor understanding of the structure and details of appropriate mathematical models. We often, therefore, need to compare different models. With available data we can use formal statistical model selection to compare and contrast the ability of different mathematical models to describe such data. There is, however, a lack of rigorous methods to compare different models a priori. Here, we develop and illustrate two such approaches that allow us to compare model structures in a systematic way by representing models as simplicial complexes. Using well-developed concepts from simplicial algebraic topology, we define a distance between models based on their simplicial representations. Employing persistent homology with a flat filtration provides for alternative representations of the models as persistence intervals, which represent model structure, from which the model distances are also obtained. We then expand on this measure of model distance to study the concept of model equivalence to determine the conceptual similarity of models. We apply our methodology for model comparison to demonstrate an equivalence between a positional-information model and a Turing-pattern model from developmental biology, constituting a novel observation for two classes of models that were previously regarded as unrelated.
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Affiliation(s)
- Sean T. Vittadello
- School of BioSciences and School of Mathematics and Statistics, The University of Melbourne, Parkville, Victoria 3010, Australia
| | - Michael P. H. Stumpf
- School of BioSciences and School of Mathematics and Statistics, The University of Melbourne, Parkville, Victoria 3010, Australia
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17
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Przedborski M, Sharon D, Chan S, Kohandel M. A mean-field approach for modeling the propagation of perturbations in biochemical reaction networks. Eur J Pharm Sci 2021; 165:105919. [PMID: 34175448 DOI: 10.1016/j.ejps.2021.105919] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2021] [Revised: 05/17/2021] [Accepted: 06/20/2021] [Indexed: 12/12/2022]
Abstract
Often, the time evolution of a biochemical reaction network is crucial for determining the effects of combining multiple pharmaceuticals. Here we illustrate a mathematical framework for modeling the dominant temporal behaviour of a complicated molecular pathway or biochemical reaction network in response to an arbitrary perturbation, such as resulting from the administration of a therapeutic agent. The method enables the determination of the temporal evolution of a target protein as the perturbation propagates through its regulatory network. The mathematical approach is particularly useful when the experimental data that is available for characterizing or parameterizing the regulatory network is limited or incomplete. To illustrate the method, we consider the examples of the regulatory networks for the target proteins c-Myc and Chop, which play an important role in venetoclax resistance in acute myeloid leukemia. First we show how the networks that regulate each target protein can be reduced to a mean-field model by identifying the distinct effects that groups of proteins in the regulatory network have on the target protein. Then we show how limited protein-level data can be used to further simplify the mean-field model to pinpoint the dominant effects of the network perturbation on the target protein. This enables a further reduction in the number of parameters in the model. The result is an ordinary differential equation model that captures the temporal evolution of the expression of a target protein when one or more proteins in its regulatory network have been perturbed. Finally, we show how the dominant effects predicted by the mathematical model agree with RNA sequencing data for the regulatory proteins comprising the molecular network, despite the model not having a priori knowledge of this data. Thus, while the approach gives a simplified model for the expression of the target protein, it allows for the interpretation of the effects of the perturbation on the regulatory network itself. This method can be easily extended to sets of target proteins to model components of a larger systems biology model, and provides an approach for partially integrating RNA sequencing data and protein expression data. Moreover, it is a general approach that can be used to study drug effects on specific protein(s) in any disease or condition.
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Affiliation(s)
- Michelle Przedborski
- Department of Applied Mathematics, University of Waterloo, Waterloo, ON, Canada.
| | - David Sharon
- Princess Margaret Cancer Centre, Toronto, ON, Canada
| | - Steven Chan
- Princess Margaret Cancer Centre, Toronto, ON, Canada
| | - Mohammad Kohandel
- Department of Applied Mathematics, University of Waterloo, Waterloo, ON, Canada
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18
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Harline K, Martínez-Gómez J, Specht CD, Roeder AHK. A Life Cycle for Modeling Biology at Different Scales. FRONTIERS IN PLANT SCIENCE 2021; 12:710590. [PMID: 34539702 PMCID: PMC8446664 DOI: 10.3389/fpls.2021.710590] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2021] [Accepted: 07/22/2021] [Indexed: 05/12/2023]
Abstract
Modeling has become a popular tool for inquiry and discovery across biological disciplines. Models allow biologists to probe complex questions and to guide experimentation. Modeling literacy among biologists, however, has not always kept pace with the rise in popularity of these techniques and the relevant advances in modeling theory. The result is a lack of understanding that inhibits communication and ultimately, progress in data gathering and analysis. In an effort to help bridge this gap, we present a blueprint that will empower biologists to interrogate and apply models in their field. We demonstrate the applicability of this blueprint in two case studies from distinct subdisciplines of biology; developmental-biomechanics and evolutionary biology. The models used in these fields vary from summarizing dynamical mechanisms to making statistical inferences, demonstrating the breadth of the utility of models to explore biological phenomena.
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Affiliation(s)
- Kate Harline
- Section of Plant Biology, School of Integrative Plant Science, Cornell University, Ithaca, NY, United States
- Weill Institute for Cell and Molecular Biology, Cornell University, Ithaca, NY, United States
- *Correspondence: Kate Harline,
| | - Jesús Martínez-Gómez
- Section of Plant Biology, School of Integrative Plant Science, Cornell University, Ithaca, NY, United States
- L.H. Bailey Hortorium, Cornell University, Ithaca, NY, United States
| | - Chelsea D. Specht
- Section of Plant Biology, School of Integrative Plant Science, Cornell University, Ithaca, NY, United States
- L.H. Bailey Hortorium, Cornell University, Ithaca, NY, United States
| | - Adrienne H. K. Roeder
- Section of Plant Biology, School of Integrative Plant Science, Cornell University, Ithaca, NY, United States
- Weill Institute for Cell and Molecular Biology, Cornell University, Ithaca, NY, United States
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19
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Mac S, Mishra S, Ximenes R, Barrett K, Khan YA, Naimark DMJ, Sander B. Modeling the coronavirus disease 2019 pandemic: A comprehensive guide of infectious disease and decision-analytic models. J Clin Epidemiol 2020; 132:133-141. [PMID: 33301904 PMCID: PMC7837043 DOI: 10.1016/j.jclinepi.2020.12.002] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/06/2020] [Revised: 11/22/2020] [Accepted: 12/01/2020] [Indexed: 12/29/2022]
Affiliation(s)
- Stephen Mac
- Institute of Health Policy, Management and Evaluation, University of Toronto, Toronto, Canada; Toronto Health Economics and Technology Assessment (THETA) Collaborative, University Health Network, Toronto, Canada
| | - Sharmistha Mishra
- Institute of Health Policy, Management and Evaluation, University of Toronto, Toronto, Canada; Li Ka Shing Knowledge Institute, St. Michael's Hospital, Toronto, Canada
| | - Raphael Ximenes
- Toronto Health Economics and Technology Assessment (THETA) Collaborative, University Health Network, Toronto, Canada; Escola de Matemática Aplicada, Fundação Getúlio Vargas, Rio de Janeiro, Brazil
| | - Kali Barrett
- Institute of Health Policy, Management and Evaluation, University of Toronto, Toronto, Canada; University Health Network, Toronto, Canada
| | - Yasin A Khan
- Institute of Health Policy, Management and Evaluation, University of Toronto, Toronto, Canada; University Health Network, Toronto, Canada
| | - David M J Naimark
- Institute of Health Policy, Management and Evaluation, University of Toronto, Toronto, Canada; Sunnybrook Health Sciences Centre, Toronto, Canada
| | - Beate Sander
- Institute of Health Policy, Management and Evaluation, University of Toronto, Toronto, Canada; Toronto Health Economics and Technology Assessment (THETA) Collaborative, University Health Network, Toronto, Canada; Public Health Ontario, Toronto, Canada; ICES, Toronto, Canada.
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20
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Putra M, Kesavan M, Brackney K, Hackney DN, Roosa KM. Forecasting the impact of coronavirus disease during delivery hospitalization: an aid for resource utilization. Am J Obstet Gynecol MFM 2020; 2:100127. [PMID: 32342041 PMCID: PMC7182514 DOI: 10.1016/j.ajogmf.2020.100127] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/07/2020] [Revised: 04/18/2020] [Accepted: 04/22/2020] [Indexed: 01/15/2023]
Abstract
Background The ongoing coronavirus disease 2019 pandemic has severely affected the United States. During infectious disease outbreaks, forecasting models are often developed to inform resource utilization. Pregnancy and delivery pose unique challenges, given the altered maternal immune system and the fact that most American women choose to deliver in the hospital setting. Objective This study aimed to forecast the first pandemic wave of coronavirus disease 2019 in the general population and the incidence of severe, critical, and fatal coronavirus disease 2019 cases during delivery hospitalization in the United States. Study Design We used a phenomenological model to forecast the incidence of the first wave of coronavirus disease 2019 in the United States. Incidence data from March 1, 2020, to April 14, 2020, were used to calibrate the generalized logistic growth model. Subsequently, Monte Carlo simulation was performed for each week from March 1, 2020, to estimate the incidence of coronavirus disease 2019 for delivery hospitalizations during the first pandemic wave using the available data estimate. Results From March 1, 2020, our model forecasted a total of 860,475 cases of coronavirus disease 2019 in the general population across the United States for the first pandemic wave. The cumulative incidence of coronavirus disease 2019 during delivery hospitalization is anticipated to be 16,601 (95% confidence interval, 9711–23,491) cases, 3308 (95% confidence interval, 1755–4861) cases of which are expected to be severe, 681 (95% confidence interval, 1324–1038) critical, and 52 (95% confidence interval, 23–81) fatal. Assuming similar baseline maternal mortality rate as the year 2018, we projected an increase in maternal mortality rate in the United States to at least 18.7 (95% confidence interval, 18.0–19.5) deaths per 100,000 live births as a direct result of coronavirus disease 2019. Conclusion Coronavirus disease 2019 in pregnant women is expected to severely affect obstetrical care. From March 1, 2020, we forecast 3308 severe and 681 critical cases with about 52 coronavirus disease 2019–related maternal mortalities during delivery hospitalization for the first pandemic wave in the United States. These results are significant for informing counseling and resource allocation.
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Affiliation(s)
- Manesha Putra
- Division of Maternal-Fetal Medicine, Department of Reproductive Biology, MetroHealth Medical Center, Cleveland, OH.,Division of Maternal-Fetal Medicine, Department of Obstetrics and Gynecology, University Hospitals Cleveland Medical Center, Cleveland, OH.,Department of Reproductive Biology, Case Western Reserve University School of Medicine, Cleveland, OH
| | - Malavika Kesavan
- Department of Reproductive Biology, Case Western Reserve University School of Medicine, Cleveland, OH
| | - Kerri Brackney
- Division of Maternal-Fetal Medicine, Department of Reproductive Biology, MetroHealth Medical Center, Cleveland, OH.,Division of Maternal-Fetal Medicine, Department of Obstetrics and Gynecology, University Hospitals Cleveland Medical Center, Cleveland, OH.,Department of Reproductive Biology, Case Western Reserve University School of Medicine, Cleveland, OH
| | - David N Hackney
- Division of Maternal-Fetal Medicine, Department of Obstetrics and Gynecology, University Hospitals Cleveland Medical Center, Cleveland, OH.,Department of Reproductive Biology, Case Western Reserve University School of Medicine, Cleveland, OH
| | - Kimberlyn M Roosa
- Department of Population Health Sciences, School of Public Health, Georgia State University, Atlanta, GA
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21
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Francis BL, Transtrum MK. Unwinding the model manifold: Choosing similarity measures to remove local minima in sloppy dynamical systems. Phys Rev E 2019; 100:012206. [PMID: 31499860 DOI: 10.1103/physreve.100.012206] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2018] [Indexed: 11/06/2022]
Abstract
In this paper, we consider the problem of parameter sensitivity in models of complex dynamical systems through the lens of information geometry. We calculate the sensitivity of model behavior to variations in parameters. In most cases, models are sloppy, that is, exhibit an exponential hierarchy of parameter sensitivities. We propose a parameter classification scheme based on how the sensitivities scale at long observation times. We show that for oscillatory models, either with a limit cycle or a strange attractor, sensitivities can become arbitrarily large, which implies a high effective dimensionality on the model manifold. Sloppy models with a single fixed point have model manifolds with low effective dimensionality, previously described as a "hyper-ribbon." In contrast, models with high effective dimensionality translate into multimodal fitting problems. We define a measure of curvature on the model manifold which we call the winding frequency that estimates the density of local minima in the model's parameter space. We then show how alternative choices of fitting metrics can "unwind" the model manifold and give low winding frequencies. This prescription translates the model manifold from one of high effective dimensionality into the hyper-ribbon structures observed elsewhere. This translation opens the door for applications of sloppy model analysis and model reduction methods developed for models with low effective dimensionality.
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Affiliation(s)
- Benjamin L Francis
- Department of Physics and Astronomy, Brigham Young University, Provo, Utah 84602, USA
| | - Mark K Transtrum
- Department of Physics and Astronomy, Brigham Young University, Provo, Utah 84602, USA
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22
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Hartoyo A, Cadusch PJ, Liley DTJ, Hicks DG. Parameter estimation and identifiability in a neural population model for electro-cortical activity. PLoS Comput Biol 2019; 15:e1006694. [PMID: 31145724 PMCID: PMC6542506 DOI: 10.1371/journal.pcbi.1006694] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2018] [Accepted: 04/12/2019] [Indexed: 11/18/2022] Open
Abstract
Electroencephalography (EEG) provides a non-invasive measure of brain electrical activity. Neural population models, where large numbers of interacting neurons are considered collectively as a macroscopic system, have long been used to understand features in EEG signals. By tuning dozens of input parameters describing the excitatory and inhibitory neuron populations, these models can reproduce prominent features of the EEG such as the alpha-rhythm. However, the inverse problem, of directly estimating the parameters from fits to EEG data, remains unsolved. Solving this multi-parameter non-linear fitting problem will potentially provide a real-time method for characterizing average neuronal properties in human subjects. Here we perform unbiased fits of a 22-parameter neural population model to EEG data from 82 individuals, using both particle swarm optimization and Markov chain Monte Carlo sampling. We estimate how much is learned about individual parameters by computing Kullback-Leibler divergences between posterior and prior distributions for each parameter. Results indicate that only a single parameter, that determining the dynamics of inhibitory synaptic activity, is directly identifiable, while other parameters have large, though correlated, uncertainties. We show that the eigenvalues of the Fisher information matrix are roughly uniformly spaced over a log scale, indicating that the model is sloppy, like many of the regulatory network models in systems biology. These eigenvalues indicate that the system can be modeled with a low effective dimensionality, with inhibitory synaptic activity being prominent in driving system behavior.
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Affiliation(s)
- Agus Hartoyo
- Centre for Micro-Photonics, Swinburne University of Technology, Hawthorn, Victoria 3122, Australia
| | - Peter J. Cadusch
- Department of Physics and Astronomy, Swinburne University of Technology, Hawthorn, Victoria 3122, Australia
| | - David T. J. Liley
- Centre for Human Psychopharmacology, School of Health Sciences, Swinburne University of Technology, Hawthorn, Victoria 3122, Australia
- Department of Medicine, University of Melbourne, Parkville, Victoria 3010, Australia
| | - Damien G. Hicks
- Centre for Micro-Photonics, Swinburne University of Technology, Hawthorn, Victoria 3122, Australia
- Department of Physics and Astronomy, Swinburne University of Technology, Hawthorn, Victoria 3122, Australia
- Bioinformatics Division, Walter & Eliza Hall Institute of Medical Research, Parkville, Victoria 3052, Australia
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23
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Victori P, Buffa FM. The many faces of mathematical modelling in oncology. Br J Radiol 2019; 92:20180856. [PMID: 30485129 PMCID: PMC6435080 DOI: 10.1259/bjr.20180856] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2018] [Revised: 11/21/2018] [Accepted: 11/22/2018] [Indexed: 11/05/2022] Open
Abstract
The application of modelling to solve problems in biology and medicine, and specifically in oncology and radiation therapy, is increasingly established and holds big promise. We provide an overview of the basic concepts of the field and its current state, along with new tools available and future directions for research. We will outline radiobiology models, examples of other anticancer therapy models, multiscale modelling, and we will discuss mechanistic and phenomenological approaches to modelling.
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Affiliation(s)
- Pedro Victori
- CRUK/MRC Oxford Institute, Department of Oncology, Medical Science Division, University of Oxford, Oxford, United Kingdom
| | - Francesca M Buffa
- CRUK/MRC Oxford Institute, Department of Oncology, Medical Science Division, University of Oxford, Oxford, United Kingdom
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24
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Fröhlich F, Loos C, Hasenauer J. Scalable Inference of Ordinary Differential Equation Models of Biochemical Processes. Methods Mol Biol 2019; 1883:385-422. [PMID: 30547409 DOI: 10.1007/978-1-4939-8882-2_16] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
Ordinary differential equation models have become a standard tool for the mechanistic description of biochemical processes. If parameters are inferred from experimental data, such mechanistic models can provide accurate predictions about the behavior of latent variables or the process under new experimental conditions. Complementarily, inference of model structure can be used to identify the most plausible model structure from a set of candidates, and, thus, gain novel biological insight. Several toolboxes can infer model parameters and structure for small- to medium-scale mechanistic models out of the box. However, models for highly multiplexed datasets can require hundreds to thousands of state variables and parameters. For the analysis of such large-scale models, most algorithms require intractably high computation times. This chapter provides an overview of the state-of-the-art methods for parameter and model inference, with an emphasis on scalability.
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Affiliation(s)
- Fabian Fröhlich
- Institute of Computational Biology, Helmholtz Zentrum München, Neuherberg, Germany
- Center for Mathematics, Technische Universität München, Garching, Germany
| | - Carolin Loos
- Institute of Computational Biology, Helmholtz Zentrum München, Neuherberg, Germany
- Center for Mathematics, Technische Universität München, Garching, Germany
| | - Jan Hasenauer
- Institute of Computational Biology, Helmholtz Zentrum München, Neuherberg, Germany.
- Center for Mathematics, Technische Universität München, Garching, Germany.
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Abstract
Being concerned by the understanding of the mechanism underlying chronic degenerative diseases , we presented in the previous chapter the medical systems biology conceptual framework that we present for that purpose in this volume. More specifically, we argued there the clear advantages offered by a state-space perspective when applied to the systems-level description of the biomolecular machinery that regulates complex degenerative diseases. We also discussed the importance of the dynamical interplay between the risk factors and the network of interdependencies that characterizes the biochemical, cellular, and tissue-level biomolecular reactions that underlie the physiological processes in health and disease. As we pointed out in the previous chapter, the understanding of this interplay (articulated around cellular phenotypic plasticity properties, regulated by specific kinds of gene regulatory networks) is necessary if prevention is chosen as the human-health improvement strategy (potentially involving the modulation of the patient's lifestyle). In this chapter we provide the medical systems biology mathematical and computational modeling tools required for this task.
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Proulx-Giraldeau F, Rademaker TJ, François P. Untangling the Hairball: Fitness-Based Asymptotic Reduction of Biological Networks. Biophys J 2017; 113:1893-1906. [PMID: 29045882 DOI: 10.1016/j.bpj.2017.08.036] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2017] [Revised: 08/16/2017] [Accepted: 08/17/2017] [Indexed: 11/19/2022] Open
Abstract
Complex mathematical models of interaction networks are routinely used for prediction in systems biology. However, it is difficult to reconcile network complexities with a formal understanding of their behavior. Here, we propose a simple procedure (called ϕ¯) to reduce biological models to functional submodules, using statistical mechanics of complex systems combined with a fitness-based approach inspired by in silico evolution. The ϕ¯ algorithm works by putting parameters or combination of parameters to some asymptotic limit, while keeping (or slightly improving) the model performance, and requires parameter symmetry breaking for more complex models. We illustrate ϕ¯ on biochemical adaptation and on different models of immune recognition by T cells. An intractable model of immune recognition with close to a hundred individual transition rates is reduced to a simple two-parameter model. The ϕ¯ algorithm extracts three different mechanisms for early immune recognition, and automatically discovers similar functional modules in different models of the same process, allowing for model classification and comparison. Our procedure can be applied to biological networks based on rate equations using a fitness function that quantifies phenotypic performance.
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Affiliation(s)
| | - Thomas J Rademaker
- Ernest Rutherford Physics Building, McGill University, Montreal, Québec, Canada; Département de Physique Théorique, Université de Genève, Genève, Switzerland
| | - Paul François
- Ernest Rutherford Physics Building, McGill University, Montreal, Québec, Canada.
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Multi-Objective Optimization of Experiments Using Curvature and Fisher Information Matrix. Processes (Basel) 2017. [DOI: 10.3390/pr5040063] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
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29
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Snowden TJ, van der Graaf PH, Tindall MJ. Methods of Model Reduction for Large-Scale Biological Systems: A Survey of Current Methods and Trends. Bull Math Biol 2017; 79:1449-1486. [PMID: 28656491 PMCID: PMC5498684 DOI: 10.1007/s11538-017-0277-2] [Citation(s) in RCA: 49] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/10/2016] [Accepted: 03/30/2017] [Indexed: 01/31/2023]
Abstract
Complex models of biochemical reaction systems have become increasingly common in the systems biology literature. The complexity of such models can present a number of obstacles for their practical use, often making problems difficult to intuit or computationally intractable. Methods of model reduction can be employed to alleviate the issue of complexity by seeking to eliminate those portions of a reaction network that have little or no effect upon the outcomes of interest, hence yielding simplified systems that retain an accurate predictive capacity. This review paper seeks to provide a brief overview of a range of such methods and their application in the context of biochemical reaction network models. To achieve this, we provide a brief mathematical account of the main methods including timescale exploitation approaches, reduction via sensitivity analysis, optimisation methods, lumping, and singular value decomposition-based approaches. Methods are reviewed in the context of large-scale systems biology type models, and future areas of research are briefly discussed.
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Affiliation(s)
- Thomas J Snowden
- Department of Mathematics and Statistics, University of Reading, Reading, RG6 6AX, UK.,Certara QSP, University of Kent Innovation Centre, Canterbury, CT2 7FG, UK
| | - Piet H van der Graaf
- Certara QSP, University of Kent Innovation Centre, Canterbury, CT2 7FG, UK.,Leiden Academic Centre for Drug Research, Universiteit Leiden, Leiden, 2333 CC, Netherlands
| | - Marcus J Tindall
- Department of Mathematics and Statistics, University of Reading, Reading, RG6 6AX, UK. .,The Institute for Cardiovascular and Metabolic Research (ICMR), University of Reading, Reading, RG6 6AX, UK.
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Bohner G, Venkataraman G. Identifiability, reducibility, and adaptability in allosteric macromolecules. J Gen Physiol 2017; 149:547-560. [PMID: 28416647 PMCID: PMC5412534 DOI: 10.1085/jgp.201611751] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/28/2016] [Revised: 02/15/2017] [Accepted: 03/08/2017] [Indexed: 11/24/2022] Open
Abstract
Bohner and Venkataraman propose a link between the sensitivity of allosteric macromolecules to their underlying biophysical parameters, the interrelationships between these parameters, and macromolecular adaptability. They argue that “emergent” combinations of parameters yield mechanistic insight that individual parameters cannot. The ability of macromolecules to transduce stimulus information at one site into conformational changes at a distant site, termed “allostery,” is vital for cellular signaling. Here, we propose a link between the sensitivity of allosteric macromolecules to their underlying biophysical parameters, the interrelationships between these parameters, and macromolecular adaptability. We demonstrate that the parameters of a canonical model of the mSlo large-conductance Ca2+-activated K+ (BK) ion channel are non-identifiable with respect to the equilibrium open probability-voltage relationship, a common functional assay. We construct a reduced model with emergent parameters that are identifiable and expressed as combinations of the original mechanistic parameters. These emergent parameters indicate which coordinated changes in mechanistic parameters can leave assay output unchanged. We predict that these coordinated changes are used by allosteric macromolecules to adapt, and we demonstrate how this prediction can be tested experimentally. We show that these predicted parameter compensations are used in the first reported allosteric phenomena: the Bohr effect, by which hemoglobin adapts to varying pH.
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Affiliation(s)
- Gergő Bohner
- Gatsby Computational Neuroscience Unit, University College London, London WC1E 6BT, England, UK
| | - Gaurav Venkataraman
- Gatsby Computational Neuroscience Unit, University College London, London WC1E 6BT, England, UK.,Wolfson Institute for Biomedical Research, University College London, London WC1E 6BT, England, UK
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White A, Tolman M, Thames HD, Withers HR, Mason KA, Transtrum MK. The Limitations of Model-Based Experimental Design and Parameter Estimation in Sloppy Systems. PLoS Comput Biol 2016; 12:e1005227. [PMID: 27923060 PMCID: PMC5140062 DOI: 10.1371/journal.pcbi.1005227] [Citation(s) in RCA: 37] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2016] [Accepted: 10/27/2016] [Indexed: 12/15/2022] Open
Abstract
We explore the relationship among experimental design, parameter estimation, and systematic error in sloppy models. We show that the approximate nature of mathematical models poses challenges for experimental design in sloppy models. In many models of complex biological processes it is unknown what are the relevant physical mechanisms that must be included to explain system behaviors. As a consequence, models are often overly complex, with many practically unidentifiable parameters. Furthermore, which mechanisms are relevant/irrelevant vary among experiments. By selecting complementary experiments, experimental design may inadvertently make details that were ommitted from the model become relevant. When this occurs, the model will have a large systematic error and fail to give a good fit to the data. We use a simple hyper-model of model error to quantify a model’s discrepancy and apply it to two models of complex biological processes (EGFR signaling and DNA repair) with optimally selected experiments. We find that although parameters may be accurately estimated, the discrepancy in the model renders it less predictive than it was in the sloppy regime where systematic error is small. We introduce the concept of a sloppy system–a sequence of models of increasing complexity that become sloppy in the limit of microscopic accuracy. We explore the limits of accurate parameter estimation in sloppy systems and argue that identifying underlying mechanisms controlling system behavior is better approached by considering a hierarchy of models of varying detail rather than focusing on parameter estimation in a single model. Sloppy models are often unidentifiable, i.e., characterized by many parameters that are poorly constrained by experimental data. Many models of complex biological systems are sloppy, which has prompted considerable debate about the identifiability of parameters and methods of selecting optimal experiments to infer parameter values. We explore how the approximate nature of models affects the prospect for accurate parameter estimates and model predictivity in sloppy models when using optimal experimental design. We find that sloppy models may no longer give a good fit to data generated from “optimal” experiments. In this case, the model has much less predictive power than it did before optimal experimental selection. We use a simple hyper-model of model error to quantify the model’s discrepancy from the physical system and discuss the potential limits of accurate parameter estimation in sloppy systems.
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Affiliation(s)
- Andrew White
- Department of Physics & Astronomy, Brigham Young University, Provo, Utah, United States of America
| | - Malachi Tolman
- Department of Physics & Astronomy, Brigham Young University, Provo, Utah, United States of America
| | - Howard D. Thames
- Department of Biostatistics, UT MD Anderson Cancer Center, Houston, Texas, United States of America
- Department of Experimental Radiation Oncology, UT MD Anderson Cancer Center, Houston, Texas, United States of America
| | - Hubert Rodney Withers
- Department of Experimental Radiation Oncology, UT MD Anderson Cancer Center, Houston, Texas, United States of America
| | - Kathy A. Mason
- Department of Experimental Radiation Oncology, UT MD Anderson Cancer Center, Houston, Texas, United States of America
| | - Mark K. Transtrum
- Department of Physics & Astronomy, Brigham Young University, Provo, Utah, United States of America
- * E-mail:
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