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Manser CL, Perez-Carrasco R. A mathematical framework for measuring and tuning tempo in developmental gene regulatory networks. Development 2024; 151:dev202950. [PMID: 38780527 DOI: 10.1242/dev.202950] [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: 04/12/2024] [Accepted: 05/13/2024] [Indexed: 05/25/2024]
Abstract
Embryo development is a dynamic process governed by the regulation of timing and sequences of gene expression, which control the proper growth of the organism. Although many genetic programmes coordinating these sequences are common across species, the timescales of gene expression can vary significantly among different organisms. Currently, substantial experimental efforts are focused on identifying molecular mechanisms that control these temporal aspects. In contrast, the capacity of established mathematical models to incorporate tempo control while maintaining the same dynamical landscape remains less understood. Here, we address this gap by developing a mathematical framework that links the functionality of developmental programmes to the corresponding gene expression orbits (or landscapes). This unlocks the ability to find tempo differences as perturbations in the dynamical system that preserve its orbits. We demonstrate that this framework allows for the prediction of molecular mechanisms governing tempo, through both numerical and analytical methods. Our exploration includes two case studies: a generic network featuring coupled production and degradation, with a particular application to neural progenitor differentiation; and the repressilator. In the latter, we illustrate how altering the dimerisation rates of transcription factors can decouple the tempo from the shape of the resulting orbits. We conclude by highlighting how the identification of orthogonal molecular mechanisms for tempo control can inform the design of circuits with specific orbits and tempos.
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Affiliation(s)
- Charlotte L Manser
- Department of Life Sciences, Imperial College London, South Kensington Campus, Imperial College London, London SW7 2AZ, UK
| | - Ruben Perez-Carrasco
- Department of Life Sciences, Imperial College London, South Kensington Campus, Imperial College London, London SW7 2AZ, UK
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2
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González-Forero M. A mathematical framework for evo-devo dynamics. Theor Popul Biol 2024; 155:24-50. [PMID: 38043588 DOI: 10.1016/j.tpb.2023.11.003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2021] [Revised: 11/10/2023] [Accepted: 11/28/2023] [Indexed: 12/05/2023]
Abstract
Natural selection acts on phenotypes constructed over development, which raises the question of how development affects evolution. Classic evolutionary theory indicates that development affects evolution by modulating the genetic covariation upon which selection acts, thus affecting genetic constraints. However, whether genetic constraints are relative, thus diverting adaptation from the direction of steepest fitness ascent, or absolute, thus blocking adaptation in certain directions, remains uncertain. This limits understanding of long-term evolution of developmentally constructed phenotypes. Here we formulate a general, tractable mathematical framework that integrates age progression, explicit development (i.e., the construction of the phenotype across life subject to developmental constraints), and evolutionary dynamics, thus describing the evolutionary and developmental (evo-devo) dynamics. The framework yields simple equations that can be arranged in a layered structure that we call the evo-devo process, whereby five core elementary components generate all equations including those mechanistically describing genetic covariation and the evo-devo dynamics. The framework recovers evolutionary dynamic equations in gradient form and describes the evolution of genetic covariation from the evolution of genotype, phenotype, environment, and mutational covariation. This shows that genotypic and phenotypic evolution must be followed simultaneously to yield a dynamically sufficient description of long-term phenotypic evolution in gradient form, such that evolution described as the climbing of a fitness landscape occurs in "geno-phenotype" space. Genetic constraints in geno-phenotype space are necessarily absolute because the phenotype is related to the genotype by development. Thus, the long-term evolutionary dynamics of developed phenotypes is strongly non-standard: (1) evolutionary equilibria are either absent or infinite in number and depend on genetic covariation and hence on development; (2) developmental constraints determine the admissible evolutionary path and hence which evolutionary equilibria are admissible; and (3) evolutionary outcomes occur at admissible evolutionary equilibria, which do not generally occur at fitness landscape peaks in geno-phenotype space, but at peaks in the admissible evolutionary path where "total genotypic selection" vanishes if exogenous plastic response vanishes and mutational variation exists in all directions of genotype space. Hence, selection and development jointly define the evolutionary outcomes if absolute mutational constraints and exogenous plastic response are absent, rather than the outcomes being defined only by selection. Moreover, our framework provides formulas for the sensitivities of a recurrence and an alternative method to dynamic optimization (i.e., dynamic programming or optimal control) to identify evolutionary outcomes in models with developmentally dynamic traits. These results show that development has major evolutionary effects.
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Melnyk K, Friedman L, Komogortsev OV. What can entropy metrics tell us about the characteristics of ocular fixation trajectories? PLoS One 2024; 19:e0291823. [PMID: 38166054 PMCID: PMC10760742 DOI: 10.1371/journal.pone.0291823] [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: 12/10/2022] [Accepted: 09/06/2023] [Indexed: 01/04/2024] Open
Abstract
In this study, we provide a detailed analysis of entropy measures calculated for fixation eye movement trajectories from the three different datasets. We employed six key metrics (Fuzzy, Increment, Sample, Gridded Distribution, Phase, and Spectral Entropies). We calculate these six metrics on three sets of fixations: (1) fixations from the GazeCom dataset, (2) fixations from what we refer to as the "Lund" dataset, and (3) fixations from our own research laboratory ("OK Lab" dataset). For each entropy measure, for each dataset, we closely examined the 36 fixations with the highest entropy and the 36 fixations with the lowest entropy. From this, it was clear that the nature of the information from our entropy metrics depended on which dataset was evaluated. These entropy metrics found various types of misclassified fixations in the GazeCom dataset. Two entropy metrics also detected fixation with substantial linear drift. For the Lund dataset, the only finding was that low spectral entropy was associated with what we call "bumpy" fixations. These are fixations with low-frequency oscillations. For the OK Lab dataset, three entropies found fixations with high-frequency noise which probably represent ocular microtremor. In this dataset, one entropy found fixations with linear drift. The between-dataset results are discussed in terms of the number of fixations in each dataset, the different eye movement stimuli employed, and the method of eye movement classification.
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Affiliation(s)
- Kateryna Melnyk
- Department of Computer Science, Texas State University, San Marcos, TX, United States of America
| | - Lee Friedman
- Department of Computer Science, Texas State University, San Marcos, TX, United States of America
| | - Oleg V. Komogortsev
- Department of Computer Science, Texas State University, San Marcos, TX, United States of America
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4
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Greulich P. Quantitative Modelling in Stem Cell Biology and Beyond: How to Make Best Use of It. CURRENT STEM CELL REPORTS 2023; 9:67-76. [PMID: 38145009 PMCID: PMC10739548 DOI: 10.1007/s40778-023-00230-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 10/17/2023] [Indexed: 12/26/2023]
Abstract
Purpose of Review This article gives a broad overview of quantitative modelling approaches in biology and provides guidance on how to employ them to boost stem cell research, by helping to answer biological questions and to predict the outcome of biological processes. Recent Findings The twenty-first century has seen a steady increase in the proportion of cell biology publications employing mathematical modelling to aid experimental research. However, quantitative modelling is often used as a rather decorative element to confirm experimental findings, an approach which often yields only marginal added value, and is in many cases scientifically questionable. Summary Quantitative modelling can boost biological research in manifold ways, but one has to take some careful considerations before embarking on a modelling campaign, in order to maximise its added value, to avoid pitfalls that may lead to wrong results, and to be aware of its fundamental limitations, imposed by the risks of over-fitting and "universality".
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Affiliation(s)
- Philip Greulich
- School of Mathematical Sciences, University of Southampton, Southampton, UK
- Institute for Life Sciences, University of Southampton, Southampton, UK
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5
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Jacob E, Perrillat-Mercerot A, Palgen JL, L'Hostis A, Ceres N, Boissel JP, Bosley J, Monteiro C, Kahoul R. Empirical methods for the validation of time-to-event mathematical models taking into account uncertainty and variability: application to EGFR + lung adenocarcinoma. BMC Bioinformatics 2023; 24:331. [PMID: 37667175 PMCID: PMC10478282 DOI: 10.1186/s12859-023-05430-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2022] [Accepted: 07/26/2023] [Indexed: 09/06/2023] Open
Abstract
BACKGROUND Over the past several decades, metrics have been defined to assess the quality of various types of models and to compare their performance depending on their capacity to explain the variance found in real-life data. However, available validation methods are mostly designed for statistical regressions rather than for mechanistic models. To our knowledge, in the latter case, there are no consensus standards, for instance for the validation of predictions against real-world data given the variability and uncertainty of the data. In this work, we focus on the prediction of time-to-event curves using as an application example a mechanistic model of non-small cell lung cancer. We designed four empirical methods to assess both model performance and reliability of predictions: two methods based on bootstrapped versions of parametric statistical tests: log-rank and combined weighted log-ranks (MaxCombo); and two methods based on bootstrapped prediction intervals, referred to here as raw coverage and the juncture metric. We also introduced the notion of observation time uncertainty to take into consideration the real life delay between the moment when an event happens, and the moment when it is observed and reported. RESULTS We highlight the advantages and disadvantages of these methods according to their application context. We have shown that the context of use of the model has an impact on the model validation process. Thanks to the use of several validation metrics we have highlighted the limit of the model to predict the evolution of the disease in the whole population of mutations at the same time, and that it was more efficient with specific predictions in the target mutation populations. The choice and use of a single metric could have led to an erroneous validation of the model and its context of use. CONCLUSIONS With this work, we stress the importance of making judicious choices for a metric, and how using a combination of metrics could be more relevant, with the objective of validating a given model and its predictions within a specific context of use. We also show how the reliability of the results depends both on the metric and on the statistical comparisons, and that the conditions of application and the type of available information need to be taken into account to choose the best validation strategy.
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Affiliation(s)
- Evgueni Jacob
- Novadiscovery, 1 Place Giovanni Da Verrazzano, 69009, Lyon, France.
| | | | | | - Adèle L'Hostis
- Novadiscovery, 1 Place Giovanni Da Verrazzano, 69009, Lyon, France
| | - Nicoletta Ceres
- Novadiscovery, 1 Place Giovanni Da Verrazzano, 69009, Lyon, France
| | | | - Jim Bosley
- Novadiscovery, 1 Place Giovanni Da Verrazzano, 69009, Lyon, France
| | - Claudio Monteiro
- Novadiscovery, 1 Place Giovanni Da Verrazzano, 69009, Lyon, France
| | - Riad Kahoul
- Novadiscovery, 1 Place Giovanni Da Verrazzano, 69009, Lyon, France
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Roesch E, Greener JG, MacLean AL, Nassar H, Rackauckas C, Holy TE, Stumpf MPH. Julia for biologists. Nat Methods 2023; 20:655-664. [PMID: 37024649 PMCID: PMC10216852 DOI: 10.1038/s41592-023-01832-z] [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: 09/21/2021] [Accepted: 02/27/2023] [Indexed: 04/08/2023]
Abstract
Major computational challenges exist in relation to the collection, curation, processing and analysis of large genomic and imaging datasets, as well as the simulation of larger and more realistic models in systems biology. Here we discuss how a relative newcomer among programming languages-Julia-is poised to meet the current and emerging demands in the computational biosciences and beyond. Speed, flexibility, a thriving package ecosystem and readability are major factors that make high-performance computing and data analysis available to an unprecedented degree. We highlight how Julia's design is already enabling new ways of analyzing biological data and systems, and we provide a list of resources that can facilitate the transition into Julian computing.
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Affiliation(s)
- Elisabeth Roesch
- School of Mathematics and Statistics, University of Melbourne, Melbourne, Victoria, Australia
- Melbourne Integrative Genomics, University of Melbourne, Melbourne, Victoria, Australia
- JuliaHub, Somerville, MA, USA
| | - Joe G Greener
- Medical Research Council Laboratory of Molecular Biology, Cambridge, UK
| | - Adam L MacLean
- Department of Quantitative and Computational Biology, University of Southern California, Los Angeles, CA, USA
| | | | - Christopher Rackauckas
- JuliaHub, Somerville, MA, USA
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, USA
- Pumas-AI, Centreville, VA, USA
| | - Timothy E Holy
- Departments of Neuroscience and Biomedical Engineering, Washington University in St. Louis, St. Louis, MO, USA
| | - Michael P H Stumpf
- School of Mathematics and Statistics, University of Melbourne, Melbourne, Victoria, Australia.
- Melbourne Integrative Genomics, University of Melbourne, Melbourne, Victoria, Australia.
- School of BioSciences, The University of Melbourne, Melbourne, Victoria, Australia.
- ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems, Melbourne, Victoria, Australia.
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Menezes J, Rangel E. Locally adaptive aggregation of organisms under death risk in rock-paper-scissors models. Biosystems 2023; 227-228:104901. [PMID: 37121500 DOI: 10.1016/j.biosystems.2023.104901] [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: 01/04/2023] [Revised: 04/07/2023] [Accepted: 04/07/2023] [Indexed: 05/02/2023]
Abstract
We run stochastic simulations of the spatial version of the rock-paper-scissors game, considering that individuals use sensory abilities to scan the environment to detect the presence of enemies. If the local dangerousness level is above a tolerable threshold, individuals aggregate instead of moving randomly on the lattice. We study the impact of the locally adaptive aggregation on the organisms' spatial organisation by measuring the characteristic length scale of the spatial domains occupied by organisms of a single species. Our results reveal that aggregation is beneficial if triggered when the local density of opponents does not exceed 30%; otherwise, the behavioural strategy may harm individuals by increasing the average death risk. We show that if organisms can perceive further distances, they can accurately scan and interpret the signals from the neighbourhood, maximising the effects of the locally adaptive aggregation on the death risk. Finally, we show that the locally adaptive aggregation behaviour promotes biodiversity independently of the organism's mobility. The coexistence probability rises if organisms join conspecifics, even in the presence of a small number of enemies. We verify that our conclusions hold for more complex systems by simulating the generalised rock-paper-scissors models with five and seven species. Our discoveries may be helpful to ecologists in understanding systems where organisms' self-defence behaviour adapts to local environmental cues.
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Affiliation(s)
- J Menezes
- Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands; School of Science and Technology, Federal University of Rio Grande do Norte, Caixa Postal 1524, 59072-970, Natal, RN, Brazil.
| | - E Rangel
- School of Science and Technology, Federal University of Rio Grande do Norte, Caixa Postal 1524, 59072-970, Natal, RN, Brazil; Department of Computer Engineering and Automation, Federal University of Rio Grande do Norte, Av. Senador Salgado Filho 300, Natal, 59078-970, Brazil
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8
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On the Analytical Solution of Fractional SIR Epidemic Model. APPLIED COMPUTATIONAL INTELLIGENCE AND SOFT COMPUTING 2023. [DOI: 10.1155/2023/6973734] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023] Open
Abstract
This article presents the solution of the fractional SIR epidemic model using the Laplace residual power series method. We introduce the fractional SIR model in the sense of Caputo’s derivative; it is presented by three fractional differential equations, in which the third one depends on the first coupled equations. The Laplace residual power series method (LRPSM) is implemented in this research to solve the proposed model, in which we present the solution in a form of convergent series expansion that converges rapidly to the exact one. We analyze the results and compare the obtained approximate solutions to those obtained from other methods. Figures and tables are illustrated to show the efficiency of the LRPSM in handling the proposed SIR model.
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9
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Cotner M, Meng S, Jost T, Gardner A, De Santiago C, Brock A. Integration of quantitative methods and mathematical approaches for the modeling of cancer cell proliferation dynamics. Am J Physiol Cell Physiol 2023; 324:C247-C262. [PMID: 36503241 PMCID: PMC9886359 DOI: 10.1152/ajpcell.00185.2022] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2022] [Revised: 11/21/2022] [Accepted: 11/21/2022] [Indexed: 12/15/2022]
Abstract
Physiological processes rely on the control of cell proliferation, and the dysregulation of these processes underlies various pathological conditions, including cancer. Mathematical modeling can provide new insights into the complex regulation of cell proliferation dynamics. In this review, we first examine quantitative experimental approaches for measuring cell proliferation dynamics in vitro and compare the various types of data that can be obtained in these settings. We then explore the toolbox of common mathematical modeling frameworks that can describe cell behavior, dynamics, and interactions of proliferation. We discuss how these wet-laboratory studies may be integrated with different mathematical modeling approaches to aid the interpretation of the results and to enable the prediction of cell behaviors, specifically in the context of cancer.
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Affiliation(s)
- Michael Cotner
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas
| | - Sarah Meng
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas
| | - Tyler Jost
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas
| | - Andrea Gardner
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas
| | - Carolina De Santiago
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas
| | - Amy Brock
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas
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10
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Lessons Learned from Two Decades of Modeling the Heat-Shock Response. Biomolecules 2022; 12:biom12111645. [DOI: 10.3390/biom12111645] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/14/2022] [Revised: 10/18/2022] [Accepted: 10/25/2022] [Indexed: 11/09/2022] Open
Abstract
The Heat Shock Response (HSR) is a highly conserved genetic system charged with protecting the proteome in a wide range of organisms and species. Experiments since the early 1980s have elucidated key elements in these pathways and revealed a canonical mode of regulation, which relies on a titration feedback. This system has been subject to substantial modeling work, addressing questions about resilience, design and control. The compact core regulatory circuit, as well as its apparent conservation, make this system an ideal ‘hydrogen atom’ model for the regulation of stress response. Here we take a broad view of the models of the HSR, focusing on the different questions asked and the approaches taken. After 20 years of modeling work, we ask what lessons had been learned that would have been hard to discover without mathematical models. We find that while existing models lay strong foundations, many important questions that can benefit from quantitative modeling are still awaiting investigation.
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11
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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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12
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Maddu S, Cheeseman BL, Sbalzarini IF, Müller CL. Stability selection enables robust learning of differential equations from limited noisy data. Proc Math Phys Eng Sci 2022; 478:20210916. [PMID: 35756878 PMCID: PMC9199075 DOI: 10.1098/rspa.2021.0916] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2021] [Accepted: 05/12/2022] [Indexed: 11/29/2022] Open
Abstract
We present a statistical learning framework for robust identification of differential equations from noisy spatio-temporal data. We address two issues that have so far limited the application of such methods, namely their robustness against noise and the need for manual parameter tuning, by proposing stability-based model selection to determine the level of regularization required for reproducible inference. This avoids manual parameter tuning and improves robustness against noise in the data. Our stability selection approach, termed PDE-STRIDE, can be combined with any sparsity-promoting regression method and provides an interpretable criterion for model component importance. We show that the particular combination of stability selection with the iterative hard-thresholding algorithm from compressed sensing provides a fast and robust framework for equation inference that outperforms previous approaches with respect to accuracy, amount of data required, and robustness. We illustrate the performance of PDE-STRIDE on a range of simulated benchmark problems, and we demonstrate the applicability of PDE-STRIDE on real-world data by considering purely data-driven inference of the protein interaction network for embryonic polarization in Caenorhabditis elegans. Using fluorescence microscopy images of C. elegans zygotes as input data, PDE-STRIDE is able to learn the molecular interactions of the proteins.
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Affiliation(s)
- Suryanarayana Maddu
- Faculty of Computer Science, Technische Universität Dresden, Dresden, Germany.,Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany.,Center for Systems Biology Dresden, Dresden, Germany.,Cluster of Excellence Physics of Life, TU Dresden, Germany
| | - Bevan L Cheeseman
- Faculty of Computer Science, Technische Universität Dresden, Dresden, Germany.,Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany.,Center for Systems Biology Dresden, Dresden, Germany.,Cluster of Excellence Physics of Life, TU Dresden, Germany
| | - Ivo F Sbalzarini
- Faculty of Computer Science, Technische Universität Dresden, Dresden, Germany.,Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany.,Center for Systems Biology Dresden, Dresden, Germany.,Cluster of Excellence Physics of Life, TU Dresden, Germany
| | - Christian L Müller
- Center for Computational Mathematics, Flatiron Institute, New York, NY, USA
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Li S, Jian J, Poopal RK, Chen X, He Y, Xu H, Yu H, Ren Z. Mathematical modeling in behavior responses: The tendency-prediction based on a persistence model on real-time data. Ecol Modell 2022. [DOI: 10.1016/j.ecolmodel.2021.109836] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023]
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14
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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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15
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In Silico Reconstruction of Sperm Chemotaxis. Int J Mol Sci 2021; 22:ijms22179104. [PMID: 34502014 PMCID: PMC8431315 DOI: 10.3390/ijms22179104] [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: 07/26/2021] [Revised: 08/18/2021] [Accepted: 08/19/2021] [Indexed: 11/16/2022] Open
Abstract
In echinoderms, sperm swims in random circles and turns in response to a chemoattractant. The chemoattractant evokes transient Ca2+ influx in the sperm flagellum and induces turning behavior. Recently, the molecular mechanisms and biophysical properties of this sperm response have been clarified. Based on these experimental findings, in this study, we reconstructed a sperm model in silico to demonstrate an algorithm for sperm chemotaxis. We also focused on the importance of desensitizing the chemoattractant receptor in long-range chemotaxis because sperm approach distantly located eggs, and they must sense the chemoattractant concentration over a broad range. Using parameters of the sea urchin, simulations showed that a number of sperm could reach the egg from millimeter-order distances with desensitization, indicating that we could organize a functional sperm model, and that desensitization of the receptor is essential for sperm chemotaxis. Then, we compared the model with starfish sperm, which has a different desensitization scheme and analyzed the properties of the model against various disturbances. Our approach can be applied as a novel tool in chemotaxis research.
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17
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Nukala U, Rodriguez Messan M, Yogurtcu ON, Wang X, Yang H. A Systematic Review of the Efforts and Hindrances of Modeling and Simulation of CAR T-cell Therapy. AAPS JOURNAL 2021; 23:52. [PMID: 33835308 DOI: 10.1208/s12248-021-00579-9] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/02/2020] [Accepted: 03/06/2021] [Indexed: 01/08/2023]
Abstract
Chimeric antigen receptor (CAR) T-cell therapy is an immunotherapy that has recently become highly instrumental in the fight against life-threatening diseases. A variety of modeling and computational simulation efforts have addressed different aspects of CAR T-cell therapy, including T-cell activation, T- and malignant cell population dynamics, therapeutic cost-effectiveness strategies, and patient survival. In this article, we present a systematic review of those efforts, including mathematical, statistical, and stochastic models employing a wide range of algorithms, from differential equations to machine learning. To the best of our knowledge, this is the first review of all such models studying CAR T-cell therapy. In this review, we provide a detailed summary of the strengths, limitations, methodology, data used, and data gap in currently published models. This information may help in designing and building better models for enhanced prediction and assessment of the benefit-risk balance associated with novel CAR T-cell therapies, as well as with the data need for building such models.
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Affiliation(s)
- Ujwani Nukala
- Office of Biostatistics and Epidemiology, Center for Biologics Evaluation and Research, US FDA, Silver Spring, Maryland, USA
| | - Marisabel Rodriguez Messan
- Office of Biostatistics and Epidemiology, Center for Biologics Evaluation and Research, US FDA, Silver Spring, Maryland, USA
| | - Osman N Yogurtcu
- Office of Biostatistics and Epidemiology, Center for Biologics Evaluation and Research, US FDA, Silver Spring, Maryland, USA
| | - Xiaofei Wang
- Office of Tissues and Advanced Therapies, Center for Biologics Evaluation and Research, US FDA, Silver Spring, Maryland, USA
| | - Hong Yang
- Office of Biostatistics and Epidemiology, Center for Biologics Evaluation and Research, US FDA, Silver Spring, Maryland, USA.
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18
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Predicting the Disposition of the Antimalarial Drug Artesunate and Its Active Metabolite Dihydroartemisinin Using Physiologically Based Pharmacokinetic Modeling. Antimicrob Agents Chemother 2021; 65:AAC.02280-20. [PMID: 33361307 DOI: 10.1128/aac.02280-20] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2020] [Accepted: 12/14/2020] [Indexed: 01/03/2023] Open
Abstract
Artemisinin-based combination therapies (ACTs) have proven to be effective in helping to combat the global malaria epidemic. To optimally apply these drugs, information about their tissue-specific disposition is required, and one approach to predict these pharmacokinetic characteristics is physiologically based pharmacokinetic (PBPK) modeling. In this study, a whole-body PBPK model was developed to simulate the time-dependent tissue concentrations of artesunate (AS) and its active metabolite, dihydroartemisinin (DHA). The model was developed for both rats and humans and incorporated drug metabolism of the parent compound and major metabolite. Model calibration was conducted using data from the literature in a Bayesian framework, and model verification was assessed using separate sets of data. Results showed good agreement between model predictions and the validation data, demonstrating the capability of the model in predicting the blood, plasma, and tissue pharmacokinetics of AS and DHA. It is expected that such a tool will be useful in characterizing the disposition of these chemicals and ultimately improve dosing regimens by enabling a quantitative assessment of the tissue-specific drug levels critical in the evaluation of efficacy and toxicity.
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19
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Hernandez-Vargas EA. Modeling Viral Infections. SYSTEMS MEDICINE 2021. [DOI: 10.1016/b978-0-12-801238-3.11620-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022] Open
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20
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Gonay L, Spourquet C, Baudoin M, Lepers L, Lemoine P, Fletcher AG, Hanert E, Pierreux CE. Modelling of Epithelial Growth, Fission and Lumen Formation During Embryonic Thyroid Development: A Combination of Computational and Experimental Approaches. Front Endocrinol (Lausanne) 2021; 12:655862. [PMID: 34163435 PMCID: PMC8216395 DOI: 10.3389/fendo.2021.655862] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 01/19/2021] [Accepted: 04/22/2021] [Indexed: 12/18/2022] Open
Abstract
Organogenesis is the phase of embryonic development leading to the formation of fully functional organs. In the case of the thyroid, organogenesis starts from the endoderm and generates a multitude of closely packed independent spherical follicular units surrounded by a dense network of capillaries. Follicular organisation is unique and essential for thyroid function, i.e. thyroid hormone production. Previous in vivo studies showed that, besides their nutritive function, endothelial cells play a central role during thyroid gland morphogenesis. However, the precise mechanisms and biological parameters controlling the transformation of the multi-layered thyroid epithelial primordium into a multitude of single-layered follicles are mostly unknown. Animal studies used to improve understanding of organogenesis are costly and time-consuming, with recognised limitations. Here, we developed and used a 2-D vertex model of thyroid growth, angiogenesis and folliculogenesis, within the open-source Chaste framework. Our in silico model, based on in vivo images, correctly simulates the differential growth and proliferation of central and peripheral epithelial cells, as well as the morphogen-driven migration of endothelial cells, consistently with our experimental data. Our simulations further showed that reduced epithelial cell adhesion was critical to allow endothelial invasion and fission of the multi-layered epithelial mass. Finally, our model also allowed epithelial cell polarisation and follicular lumen formation by endothelial cell abundance and proximity. Our study illustrates how constant discussion between theoretical and experimental approaches can help us to better understand the roles of cellular movement, adhesion and polarisation during thyroid embryonic development. We anticipate that the use of in silico models like the one we describe can push forward the fields of developmental biology and regenerative medicine.
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Affiliation(s)
- Leolo Gonay
- Earth and Life Institute, UCLouvain, Louvain-La-Neuve, Belgium
- de Duve Institute, UCLouvain, Woluwé-Saint-Lambert, Belgium
| | | | - Matthieu Baudoin
- Earth and Life Institute, UCLouvain, Louvain-La-Neuve, Belgium
- de Duve Institute, UCLouvain, Woluwé-Saint-Lambert, Belgium
| | - Ludovic Lepers
- Earth and Life Institute, UCLouvain, Louvain-La-Neuve, Belgium
- de Duve Institute, UCLouvain, Woluwé-Saint-Lambert, Belgium
| | | | - Alexander G. Fletcher
- School of Mathematics and Statistics, University of Sheffield, Sheffield, United Kingdom
| | - Emmanuel Hanert
- Earth and Life Institute, UCLouvain, Louvain-La-Neuve, Belgium
| | - Christophe E. Pierreux
- de Duve Institute, UCLouvain, Woluwé-Saint-Lambert, Belgium
- *Correspondence: Christophe E. Pierreux,
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21
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An Experimental Analysis of Deep Learning Architectures for Supervised Speech Enhancement. ELECTRONICS 2020. [DOI: 10.3390/electronics10010017] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Recent speech enhancement research has shown that deep learning techniques are very effective in removing background noise. Many deep neural networks are being proposed, showing promising results for improving overall speech perception. The Deep Multilayer Perceptron, Convolutional Neural Networks, and the Denoising Autoencoder are well-established architectures for speech enhancement; however, choosing between different deep learning models has been mainly empirical. Consequently, a comparative analysis is needed between these three architecture types in order to show the factors affecting their performance. In this paper, this analysis is presented by comparing seven deep learning models that belong to these three categories. The comparison includes evaluating the performance in terms of the overall quality of the output speech using five objective evaluation metrics and a subjective evaluation with 23 listeners; the ability to deal with challenging noise conditions; generalization ability; complexity; and, processing time. Further analysis is then provided while using two different approaches. The first approach investigates how the performance is affected by changing network hyperparameters and the structure of the data, including the Lombard effect. While the second approach interprets the results by visualizing the spectrogram of the output layer of all the investigated models, and the spectrograms of the hidden layers of the convolutional neural network architecture. Finally, a general evaluation is performed for supervised deep learning-based speech enhancement while using SWOC analysis, to discuss the technique’s Strengths, Weaknesses, Opportunities, and Challenges. The results of this paper contribute to the understanding of how different deep neural networks perform the speech enhancement task, highlight the strengths and weaknesses of each architecture, and provide recommendations for achieving better performance. This work facilitates the development of better deep neural networks for speech enhancement in the future.
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22
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Groves I, Placzek M, Fletcher AG. Of mitogens and morphogens: modelling Sonic Hedgehog mechanisms in vertebrate development. Philos Trans R Soc Lond B Biol Sci 2020; 375:20190660. [PMID: 32829689 PMCID: PMC7482217 DOI: 10.1098/rstb.2019.0660] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 02/10/2020] [Indexed: 12/22/2022] Open
Abstract
Sonic Hedgehog (Shh) Is a critical protein in vertebrate development, orchestrating patterning and growth in many developing systems. First described as a classic morphogen that patterns tissues through a spatial concentration gradient, subsequent studies have revealed a more complex mechanism, in which Shh can also regulate proliferation and differentiation. While the mechanism of action of Shh as a morphogen is well understood, it remains less clear how Shh might integrate patterning, proliferation and differentiation in a given tissue, to ultimately direct its morphogenesis. In tandem with experimental studies, mathematical modelling can help gain mechanistic insights into these processes and bridge the gap between Shh-regulated patterning and growth, by integrating these processes into a common theoretical framework. Here, we briefly review the roles of Shh in vertebrate development, focusing on its functions as a morphogen, mitogen and regulator of differentiation. We then discuss the contributions that modelling has made to our understanding of the action of Shh and highlight current challenges in using mathematical models in a quantitative and predictive way. This article is part of a discussion meeting issue 'Contemporary morphogenesis'.
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Affiliation(s)
- Ian Groves
- School of Mathematics and Statistics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH, UK
- Department of Biomedical Science, University of Sheffield, Firth Court, Western Bank, Sheffield, S10 2TN, UK
- Bateson Centre, University of Sheffield, Firth Court, Western Bank, Sheffield, S10 2TN, UK
| | - Marysia Placzek
- Department of Biomedical Science, University of Sheffield, Firth Court, Western Bank, Sheffield, S10 2TN, UK
- Bateson Centre, University of Sheffield, Firth Court, Western Bank, Sheffield, S10 2TN, UK
| | - Alexander G. Fletcher
- School of Mathematics and Statistics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH, UK
- Bateson Centre, University of Sheffield, Firth Court, Western Bank, Sheffield, S10 2TN, UK
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23
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Guzmán-Herrera A, Arias Del Angel JA, Rivera-Yoshida N, Benítez M, Franci A. Dynamical patterning modules and network motifs as joint determinants of development: Lessons from an aggregative bacterium. JOURNAL OF EXPERIMENTAL ZOOLOGY PART B-MOLECULAR AND DEVELOPMENTAL EVOLUTION 2020; 336:300-314. [PMID: 32419346 DOI: 10.1002/jez.b.22946] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/12/2019] [Revised: 03/26/2020] [Accepted: 04/04/2020] [Indexed: 12/15/2022]
Abstract
Development and evolution are dynamical processes under the continuous control of organismic and environmental factors. Generic physical processes, associated with biological materials and certain genes or molecules, provide a morphological template for the evolution and development of organism forms. Generic dynamical behaviors, associated with recurring network motifs, provide a temporal template for the regulation and coordination of biological processes. The role of generic physical processes and their associated molecules in development is the topic of the dynamical patterning module (DPM) framework. The role of generic dynamical behaviors in biological regulation is studied via the identification of the associated network motifs (NMs). We propose a joint DPM-NM perspective on the emergence and regulation of multicellularity focusing on a multicellular aggregative bacterium, Myxococcus xanthus. Understanding M. xanthus development as a dynamical process embedded in a physical substrate provides novel insights into the interaction between developmental regulatory networks and generic physical processes in the evolutionary transition to multicellularity.
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Affiliation(s)
- Alejandra Guzmán-Herrera
- Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, Mexico City, Mexico.,MRC Laboratory for Molecular Cell Biology, University College London, London, UK
| | - Juan A Arias Del Angel
- Laboratorio Nacional de Ciencias de la Sostenibilidad, Instituto de Ecología, Universidad Nacional Autónoma de México, Mexico City, Mexico.,Centro de Ciencias de la Complejidad, Universidad Nacional Autónoma de México, Mexico City, Mexico.,Programa de Doctorado en Ciencias Biomédicas, Universidad Nacional Autónoma de México, Mexico City, Mexico
| | - Natsuko Rivera-Yoshida
- Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, Mexico City, Mexico
| | - Mariana Benítez
- Laboratorio Nacional de Ciencias de la Sostenibilidad, Instituto de Ecología, Universidad Nacional Autónoma de México, Mexico City, Mexico.,Centro de Ciencias de la Complejidad, Universidad Nacional Autónoma de México, Mexico City, Mexico
| | - Alessio Franci
- Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, Mexico City, Mexico
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24
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Dalle Pezze P, Karanasios E, Kandia V, Manifava M, Walker SA, Gambardella Le Novère N, Ktistakis NT. ATG13 dynamics in nonselective autophagy and mitophagy: insights from live imaging studies and mathematical modeling. Autophagy 2020; 17:1131-1141. [PMID: 32320309 PMCID: PMC8143212 DOI: 10.1080/15548627.2020.1749401] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023] Open
Abstract
During macroautophagy/autophagy, the ULK complex nucleates autophagic precursors, which give rise to autophagosomes. We analyzed, by live imaging and mathematical modeling, the translocation of ATG13 (part of the ULK complex) to the autophagic puncta in starvation-induced autophagy and ivermectin-induced mitophagy. In nonselective autophagy, the intensity and duration of ATG13 translocation approximated a normal distribution, whereas wortmannin reduced this effect and shifted to a log-normal distribution. During mitophagy, multiple translocations of ATG13 with increasing time between peaks were observed. We hypothesized that these multiple translocations arise because the engulfment of mitochondrial fragments required successive nucleation of phagophores on the same target, and a mathematical model based on this idea reproduced the oscillatory behavior. Significantly, model and experimental data were also in agreement that the number of ATG13 translocations is directly proportional to the diameter of the targeted mitochondrial fragments. Thus, our data provide novel insights into the early dynamics of selective and nonselective autophagy.Abbreviations: ATG: autophagy related 13; CFP: cyan fluorescent protein; dsRED: Discosoma red fluorescent protein; GABARAP: GABA type A receptor-associated protein; GFP: green fluorescent protein; IVM: ivermectin; MAP1LC3/LC3: microtubule-associated protein 1 light chain 3; MTORC1: mechanistic target of rapamycin kinase complex 1; PIK3C3/VPS34: phosphatidylinositol 3-kinase catalytic subunit type 3; PtdIns3P: PtdIns-3-phosphate; ULK: unc-51 like autophagy activating kinase.
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Affiliation(s)
| | | | - Varvara Kandia
- The Babraham Institute, Babraham Research Campus, Cambridge, UK
| | - Maria Manifava
- The Babraham Institute, Babraham Research Campus, Cambridge, UK
| | - Simon A Walker
- The Babraham Institute, Babraham Research Campus, Cambridge, UK
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25
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Banwarth-Kuhn M, Sindi S. How and why to build a mathematical model: A case study using prion aggregation. J Biol Chem 2020; 295:5022-5035. [PMID: 32005659 PMCID: PMC7152750 DOI: 10.1074/jbc.rev119.009851] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Abstract
Biological systems are inherently complex, and the increasing level of detail with which we are able to experimentally probe such systems continually reveals new complexity. Fortunately, mathematical models are uniquely positioned to provide a tool suitable for rigorous analysis, hypothesis generation, and connecting results from isolated in vitro experiments with results from in vivo and whole-organism studies. However, developing useful mathematical models is challenging because of the often different domains of knowledge required in both math and biology. In this work, we endeavor to provide a useful guide for researchers interested in incorporating mathematical modeling into their scientific process. We advocate for the use of conceptual diagrams as a starting place to anchor researchers from both domains. These diagrams are useful for simplifying the biological process in question and distinguishing the essential components. Not only do they serve as the basis for developing a variety of mathematical models, but they ensure that any mathematical formulation of the biological system is led primarily by scientific questions. We provide a specific example of this process from our own work in studying prion aggregation to show the power of mathematical models to synergistically interact with experiments and push forward biological understanding. Choosing the most suitable model also depends on many different factors, and we consider how to make these choices based on different scales of biological organization and available data. We close by discussing the many opportunities that abound for both experimentalists and modelers to take advantage of collaborative work in this field.
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Affiliation(s)
- Mikahl Banwarth-Kuhn
- Department of Applied Mathematics, School of Natural Sciences, University of California, Merced, California 95343
| | - Suzanne Sindi
- Department of Applied Mathematics, School of Natural Sciences, University of California, Merced, California 95343
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26
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Coy R, Al-Badri G, Kayal C, O'Rourke C, Kingham PJ, Phillips JB, Shipley RJ. Combining in silico and in vitro models to inform cell seeding strategies in tissue engineering. J R Soc Interface 2020; 17:20190801. [PMID: 32208821 DOI: 10.1098/rsif.2019.0801] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Abstract
The seeding density of therapeutic cells in engineered tissue impacts both cell survival and vascularization. Excessively high seeded cell densities can result in increased death and thus waste of valuable cells, whereas lower seeded cell densities may not provide sufficient support for the tissue in vivo, reducing efficacy. Additionally, the production of growth factors by therapeutic cells in low oxygen environments offers a way of generating growth factor gradients, which are important for vascularization, but hypoxia can also induce unwanted levels of cell death. This is a complex problem that lends itself to a combination of computational modelling and experimentation. Here, we present a spatio-temporal mathematical model parametrized using in vitro data capable of simulating the interactions between a therapeutic cell population, oxygen concentrations and vascular endothelial growth factor (VEGF) concentrations in engineered tissues. Simulations of collagen nerve repair constructs suggest that specific seeded cell densities and non-uniform spatial distributions of seeded cells could enhance cell survival and the generation of VEGF gradients. These predictions can now be tested using targeted experiments.
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Affiliation(s)
- R Coy
- CoMPLEX, University College London, London, UK.,UCL Centre for Nerve Engineering, University College London, London, UK
| | - G Al-Badri
- UCL Centre for Nerve Engineering, University College London, London, UK.,Department of Mathematics, University College London, London, UK
| | - C Kayal
- UCL Centre for Nerve Engineering, University College London, London, UK.,Department of Mechanical Engineering, University College London, London, UK
| | - C O'Rourke
- UCL Centre for Nerve Engineering, University College London, London, UK.,Department of Biomaterials and Tissue Engineering, UCL Eastman Dental Institute, University College London, London, UK
| | - P J Kingham
- Department of Integrative Medical Biology, Umeå University, Umeå, Sweden
| | - J B Phillips
- UCL Centre for Nerve Engineering, University College London, London, UK.,Department of Pharmacology, UCL School of Pharmacy, University College London, London, UK
| | - R J Shipley
- UCL Centre for Nerve Engineering, University College London, London, UK.,Department of Mechanical Engineering, University College London, London, UK
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27
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Madeo D, Mocenni C. Self-regulation versus social influence for promoting cooperation on networks. Sci Rep 2020; 10:4830. [PMID: 32179794 PMCID: PMC7075901 DOI: 10.1038/s41598-020-61634-7] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/11/2019] [Accepted: 02/27/2020] [Indexed: 11/09/2022] Open
Abstract
Cooperation is a relevant and controversial phenomenon in human societies. Indeed, although it is widely recognized essential for tackling social dilemmas, finding suitable policies for promoting cooperation can be arduous and expensive. More often, it is driven by pre-established schemas based on norms and punishments. To overcome this paradigm, we highlight the interplay between the influence of social interactions on networks and spontaneous self-regulating mechanisms on individuals behavior. We show that the presence of these mechanisms in a prisoner's dilemma game, may oppose the willingness of individuals to defect, thus allowing them to behave cooperatively, while interacting with others and taking conflicting decisions over time. These results are obtained by extending the Evolutionary Game Equations over Networks to account for self-regulating mechanisms. Specifically, we prove that players may partially or fully cooperate whether self-regulating mechanisms are sufficiently stronger than social pressure. The proposed model can explain unconditional cooperation (strong self-regulation) and unconditional defection (weak self-regulation). For intermediate self-regulation values, more complex behaviors are observed, such as mutual defection, recruiting (cooperate if others cooperate), exploitation of cooperators (defect if others cooperate) and altruism (cooperate if others defect). These phenomena result from dynamical transitions among different game structures, according to changes of system parameters and cooperation of neighboring players. Interestingly, we show that the topology of the network of connections among players is crucial when self-regulation, and the associated costs, are reasonably low. In particular, a population organized on a random network with a Scale-Free distribution of connections is more cooperative than on a network with an Erdös-Rényi distribution, and, in turn, with a regular one. These results highlight that social diversity, encoded within heterogeneous networks, is more effective for promoting cooperation.
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Affiliation(s)
- Dario Madeo
- Department of Information Engineering and Mathematics, University of Siena, Via Roma 56, 53100, Siena, Italy.
| | - Chiara Mocenni
- Department of Information Engineering and Mathematics, University of Siena, Via Roma 56, 53100, Siena, Italy
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28
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Mathematical Model of ATM Activation and Chromatin Relaxation by Ionizing Radiation. Int J Mol Sci 2020; 21:ijms21041214. [PMID: 32059363 PMCID: PMC7072770 DOI: 10.3390/ijms21041214] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2019] [Revised: 01/29/2020] [Accepted: 02/09/2020] [Indexed: 12/24/2022] Open
Abstract
We propose a comprehensive mathematical model to study the dynamics of ionizing radiation induced Ataxia-telangiectasia mutated (ATM) activation that consists of ATM activation through dual mechanisms: the initiative activation pathway triggered by the DNA damage-induced local chromatin relaxation and the primary activation pathway consisting of a self-activation loop by interplay with chromatin relaxation. The model is expressed as a series of biochemical reactions, governed by a system of differential equations and analyzed by dynamical systems techniques. Radiation induced double strand breaks (DSBs) cause rapid local chromatin relaxation, which is independent of ATM but initiates ATM activation at damage sites. Key to the model description is how chromatin relaxation follows when active ATM phosphorylates KAP-1, which subsequently spreads throughout the chromatin and induces global chromatin relaxation. Additionally, the model describes how oxidative stress activation of ATM triggers a self-activation loop in which PP2A and ATF2 are released so that ATM can undergo autophosphorylation and acetylation for full activation in relaxed chromatin. In contrast, oxidative stress alone can partially activate ATM because phosphorylated ATM remains as a dimer. The model leads to predictions on ATM mediated responses to DSBs, oxidative stress, or both that can be tested by experiments.
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29
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Mohseni-Salehi FS, Zare-Mirakabad F, Sadeghi M, Ghafouri-Fard S. A Stochastic Model of DNA Double-Strand Breaks Repair Throughout the Cell Cycle. Bull Math Biol 2020; 82:11. [PMID: 31933029 DOI: 10.1007/s11538-019-00692-z] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2018] [Accepted: 12/20/2019] [Indexed: 01/15/2023]
Abstract
Cell cycle phase is a decisive factor in determining the repair pathway of DNA double-strand breaks (DSBs) by non-homologous end joining (NHEJ) or homologous recombination (HR). Recent experimental studies revealed that 53BP1 and BRCA1 are the key mediators of the DNA damage response (DDR) with antagonizing roles in choosing the appropriate DSB repair pathway in G1, S, and G2 phases. Here, we present a stochastic model of biochemical kinetics involved in detecting and repairing DNA DSBs induced by ionizing radiation during the cell cycle progression. A three-dimensional stochastic process is defined to monitor the cell cycle phase and DSBs repair at times after irradiation. To estimate the model parameters, a Metropolis Monte Carlo method is applied to perform maximum likelihood estimation utilizing the kinetics of γ-H2AX and RAD51 foci formation in G1, S, and G2 phases. The recruitment of DSB repair proteins is verified by comparing our model predictions with the corresponding experimental data on human cells after exposure to X and γ-radiation. Furthermore, the interaction between 53BP1 and BRCA1 is simulated for G1 and S/G2 phases determining the competition between NHEJ and HR pathways in repairing induced DSBs throughout the cell cycle. In accordance with recent biological data, the numerical results demonstrate that the maximum proportion of HR occurs in S phase cells and the high level of NHEJ takes place in G1 and G2 phases. Moreover, the stochastic realizations of the total yield of simple and complex DSBs ligation are compared for G1 and S/G2 damaged cells. Finally, the proposed stochastic model is validated when DSBs induced by different particle radiation such as iron, silicon, oxygen, proton, and carbon.
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Affiliation(s)
- Fazeleh S Mohseni-Salehi
- Mathematics and Computer Science Department, Amirkabir University of Technology (Tehran Polytechinc), Tehran, Iran
| | - Fatemeh Zare-Mirakabad
- Mathematics and Computer Science Department, Amirkabir University of Technology (Tehran Polytechinc), Tehran, Iran.
| | - Mehdi Sadeghi
- School of Biological Science, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran
- National Institute of Genetic Engineering and Biotechnology, Tehran, Iran
| | - Soudeh Ghafouri-Fard
- Department of Medical Genetics, Shahid Beheshti University of Medical Sciences, Tehran, Iran
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30
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Nichol D, Robertson-Tessi M, Anderson ARA, Jeavons P. Model genotype-phenotype mappings and the algorithmic structure of evolution. J R Soc Interface 2019; 16:20190332. [PMID: 31690233 PMCID: PMC6893500 DOI: 10.1098/rsif.2019.0332] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2019] [Accepted: 10/04/2019] [Indexed: 12/13/2022] Open
Abstract
Cancers are complex dynamic systems that undergo evolution and selection. Personalized medicine approaches in the clinic increasingly rely on predictions of tumour response to one or more therapies; these predictions are complicated by the inevitable evolution of the tumour. Despite enormous amounts of data on the mutational status of cancers and numerous therapies developed in recent decades to target these mutations, many of these treatments fail after a time due to the development of resistance in the tumour. The emergence of these resistant phenotypes is not easily predicted from genomic data, since the relationship between genotypes and phenotypes, termed the genotype-phenotype (GP) mapping, is neither injective nor functional. We present a review of models of this mapping within a generalized evolutionary framework that takes into account the relation between genotype, phenotype, environment and fitness. Different modelling approaches are described and compared, and many evolutionary results are shown to be conserved across studies despite using different underlying model systems. In addition, several areas for future work that remain understudied are identified, including plasticity and bet-hedging. The GP-mapping provides a pathway for understanding the potential routes of evolution taken by cancers, which will be necessary knowledge for improving personalized therapies.
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Affiliation(s)
- Daniel Nichol
- Department of Computer Science, University of Oxford, Oxford, UK
- Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center and Research Institute, Tampa, FL, USA
| | - Mark Robertson-Tessi
- Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center and Research Institute, Tampa, FL, USA
| | - Alexander R. A. Anderson
- Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center and Research Institute, Tampa, FL, USA
| | - Peter Jeavons
- Department of Computer Science, University of Oxford, Oxford, UK
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31
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Massive computational acceleration by using neural networks to emulate mechanism-based biological models. Nat Commun 2019; 10:4354. [PMID: 31554788 PMCID: PMC6761138 DOI: 10.1038/s41467-019-12342-y] [Citation(s) in RCA: 25] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/04/2019] [Accepted: 08/30/2019] [Indexed: 12/11/2022] Open
Abstract
For many biological applications, exploration of the massive parametric space of a mechanism-based model can impose a prohibitive computational demand. To overcome this limitation, we present a framework to improve computational efficiency by orders of magnitude. The key concept is to train a neural network using a limited number of simulations generated by a mechanistic model. This number is small enough such that the simulations can be completed in a short time frame but large enough to enable reliable training. The trained neural network can then be used to explore a much larger parametric space. We demonstrate this notion by training neural networks to predict pattern formation and stochastic gene expression. We further demonstrate that using an ensemble of neural networks enables the self-contained evaluation of the quality of each prediction. Our work can be a platform for fast parametric space screening of biological models with user defined objectives. Mechanistic models provide valuable insights, but large-scale simulations are computationally expensive. Here, the authors show that it is possible to explore the dynamics of a mechanistic model over a large set of parameters by training an artificial neural network on a smaller set of simulations.
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Kumar M, Ji B, Zengler K, Nielsen J. Modelling approaches for studying the microbiome. Nat Microbiol 2019; 4:1253-1267. [PMID: 31337891 DOI: 10.1038/s41564-019-0491-9] [Citation(s) in RCA: 81] [Impact Index Per Article: 16.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2017] [Accepted: 05/21/2019] [Indexed: 02/08/2023]
Abstract
Advances in metagenome sequencing of the human microbiome have provided a plethora of new insights and revealed a close association of this complex ecosystem with a range of human diseases. However, there is little knowledge about how the different members of the microbial community interact with each other and with the host, and we lack basic mechanistic understanding of these interactions related to health and disease. Mathematical modelling has been demonstrated to be highly advantageous for gaining insights into the dynamics and interactions of complex systems and in recent years, several modelling approaches have been proposed to enhance our understanding of the microbiome. Here, we review the latest developments and current approaches, and highlight how different modelling strategies have been applied to unravel the highly dynamic nature of the human microbiome. Furthermore, we discuss present limitations of different modelling strategies and provide a perspective of how modelling can advance understanding and offer new treatment routes to impact human health.
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Affiliation(s)
- Manish Kumar
- Department of Biology and Biological Engineering, Chalmers University of Technology, Gothenburg, Sweden.,Department of Pediatrics, University of California, San Diego, CA, USA
| | - Boyang Ji
- Department of Biology and Biological Engineering, Chalmers University of Technology, Gothenburg, Sweden
| | - Karsten Zengler
- Department of Pediatrics, University of California, San Diego, CA, USA.,Department of Bioengineering, University of California, San Diego, CA, USA.,Center for Microbiome Innovation, University of California, San Diego, CA, USA
| | - Jens Nielsen
- Department of Biology and Biological Engineering, Chalmers University of Technology, Gothenburg, Sweden. .,Novo Nordisk Foundation Center for Biosustainability, Technical University of Denmark, Lyngby, Denmark.
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Connor Y, Tekleab Y, Tekleab S, Nandakumar S, Bharat D, Sengupta S. A mathematical model of tumor-endothelial interactions in a 3D co-culture. Sci Rep 2019; 9:8429. [PMID: 31182723 PMCID: PMC6557844 DOI: 10.1038/s41598-019-44713-2] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2017] [Accepted: 05/23/2019] [Indexed: 11/09/2022] Open
Abstract
Intravasation and extravasation of cancer cells through blood/lymph vessel endothelium are essential steps during metastasis. Successful invasion requires coordinated tumor-endothelial crosstalk, utilizing mechanochemical signaling to direct cytoskeletal rearrangement for transmigration of cancer cells. However, mechanisms underlying physical interactions are difficult to observe due to the lack of experimental models easily combined with theoretical models that better elucidate these pathways. We have previously demonstrated that an engineered 3D in vitro endothelial-epithelial co-culture system can be used to isolate both molecular and physical tumor-endothelial interactions in a platform that is easily modeled, quantified, and probed for experimental investigation. Using this platform with mathematical modeling, we show that breast metastatic cells display unique behavior with the endothelium, exhibiting a 3.2-fold increase in interaction with the endothelium and a 61-fold increase in elongation compared to normal breast epithelial cells. Our mathematical model suggests energetic favorability for cellular deformation prior to breeching endothelial junctions, expending less energy as compared to undeformed cells, which is consistent with the observed phenotype. Finally, we show experimentally that pharmacological inhibition of the cytoskeleton can disrupt the elongatation and alignment of metastatic cells with endothelial tubes, reverting to a less invasive phenotype.
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Affiliation(s)
- Yamicia Connor
- Harvard-MIT Division of Health Sciences and Technology, Cambridge, MA, 02139, USA.,Brigham and Women's Hospital, Department of Medicine, Boston, MA, 02115, USA.,Harvard Medical School, Health Sciences & Technology, Boston, MA, 02115, USA.,Beth Israel Deaconess Medical Center, Department of Medicine, Boston, MA, 02215, USA
| | - Yonatan Tekleab
- Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, Cambridge, MA, 02139, USA
| | - Sarah Tekleab
- Brigham and Women's Hospital, Department of Medicine, Boston, MA, 02115, USA
| | - Shyama Nandakumar
- Brigham and Women's Hospital, Department of Medicine, Boston, MA, 02115, USA
| | - Divya Bharat
- Brigham and Women's Hospital, Department of Medicine, Boston, MA, 02115, USA
| | - Shiladitya Sengupta
- Harvard-MIT Division of Health Sciences and Technology, Cambridge, MA, 02139, USA. .,Brigham and Women's Hospital, Department of Medicine, Boston, MA, 02115, USA. .,Harvard Medical School, Health Sciences & Technology, Boston, MA, 02115, USA.
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34
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Goodhill GJ. Theoretical Models of Neural Development. iScience 2018; 8:183-199. [PMID: 30321813 PMCID: PMC6197653 DOI: 10.1016/j.isci.2018.09.017] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2018] [Revised: 08/06/2018] [Accepted: 09/19/2018] [Indexed: 12/22/2022] Open
Abstract
Constructing a functioning nervous system requires the precise orchestration of a vast array of mechanical, molecular, and neural-activity-dependent cues. Theoretical models can play a vital role in helping to frame quantitative issues, reveal mathematical commonalities between apparently diverse systems, identify what is and what is not possible in principle, and test the abilities of specific mechanisms to explain the data. This review focuses on the progress that has been made over the last decade in our theoretical understanding of neural development.
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Affiliation(s)
- Geoffrey J Goodhill
- Queensland Brain Institute and School of Mathematics and Physics, The University of Queensland, St Lucia, QLD 4072, Australia.
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35
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Álvarez-Buylla Roces ME, Martínez-García JC, Dávila-Velderrain J, Domínguez-Hüttinger E, Martínez-Sánchez ME. Medical Systems Biology. ADVANCES IN EXPERIMENTAL MEDICINE AND BIOLOGY 2018; 1069:1-33. [PMID: 30076565 DOI: 10.1007/978-3-319-89354-9_1] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
Abstract
The aim of this volume is to encourage the use of systems-level methodologies to contribute to the improvement of human-health . We intend to motivate biomedical researchers to complement their current theoretical and empirical practice with up-to-date systems biology conceptual approaches. Our perspective is based on the deep understanding of the key biomolecular regulatory mechanisms that underlie health, as well as the emergence and progression of human-disease . We strongly believe that the contemporary systems biology perspective opens the door to the effective development of novel methodologies to the improvement of prevention . This requires a deeper and integrative understanding of the involved underlying systems-level mechanisms. In order to explain our proposal in a simple way, in this chapter we privilege the conceptual exposition of our chosen framework over formal considerations. The formal exposition of our proposal will be expanded and discussed later in the next chapters.
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36
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Gavagnin E, Yates CA. Stochastic and Deterministic Modeling of Cell Migration. HANDBOOK OF STATISTICS 2018. [DOI: 10.1016/bs.host.2018.06.002] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
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37
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Sahlgren C, Meinander A, Zhang H, Cheng F, Preis M, Xu C, Salminen TA, Toivola D, Abankwa D, Rosling A, Karaman DŞ, Salo-Ahen OMH, Österbacka R, Eriksson JE, Willför S, Petre I, Peltonen J, Leino R, Johnson M, Rosenholm J, Sandler N. Tailored Approaches in Drug Development and Diagnostics: From Molecular Design to Biological Model Systems. Adv Healthc Mater 2017; 6. [PMID: 28892296 DOI: 10.1002/adhm.201700258] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/26/2017] [Revised: 05/04/2017] [Indexed: 12/13/2022]
Abstract
Approaches to increase the efficiency in developing drugs and diagnostics tools, including new drug delivery and diagnostic technologies, are needed for improved diagnosis and treatment of major diseases and health problems such as cancer, inflammatory diseases, chronic wounds, and antibiotic resistance. Development within several areas of research ranging from computational sciences, material sciences, bioengineering to biomedical sciences and bioimaging is needed to realize innovative drug development and diagnostic (DDD) approaches. Here, an overview of recent progresses within key areas that can provide customizable solutions to improve processes and the approaches taken within DDD is provided. Due to the broadness of the area, unfortunately all relevant aspects such as pharmacokinetics of bioactive molecules and delivery systems cannot be covered. Tailored approaches within (i) bioinformatics and computer-aided drug design, (ii) nanotechnology, (iii) novel materials and technologies for drug delivery and diagnostic systems, and (iv) disease models to predict safety and efficacy of medicines under development are focused on. Current developments and challenges ahead are discussed. The broad scope reflects the multidisciplinary nature of the field of DDD and aims to highlight the convergence of biological, pharmaceutical, and medical disciplines needed to meet the societal challenges of the 21st century.
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Affiliation(s)
- Cecilia Sahlgren
- Faculty of Science and Engineering; Cell Biology; Åbo Akademi University; FI-20520 Turku Finland
- Turku Centre for Biotechnology; Åbo Akademi University and University of Turku; FI-20520 Turku Finland
- Department of Biomedical Engineering; Technical University of Eindhoven; 5613 DR Eindhoven Netherlands
| | - Annika Meinander
- Faculty of Science and Engineering; Cell Biology; Åbo Akademi University; FI-20520 Turku Finland
| | - Hongbo Zhang
- Faculty of Science and Engineering; Pharmaceutical Sciences Laboratory; Åbo Akademi University; FI-20520 Turku Finland
| | - Fang Cheng
- Faculty of Science and Engineering; Cell Biology; Åbo Akademi University; FI-20520 Turku Finland
| | - Maren Preis
- Faculty of Science and Engineering; Pharmaceutical Sciences Laboratory; Åbo Akademi University; FI-20520 Turku Finland
| | - Chunlin Xu
- Faculty of Science and Engineering; Natural Materials Technology; Åbo Akademi University; FI-20500 Turku Finland
| | - Tiina A. Salminen
- Faculty of Science and Engineering; Structural Bioinformatics Laboratory; Åbo Akademi University; FI-20520 Turku Finland
| | - Diana Toivola
- Faculty of Science and Engineering; Cell Biology; Åbo Akademi University; FI-20520 Turku Finland
- Turku Center for Disease Modeling; University of Turku; FI-20520 Turku Finland
| | - Daniel Abankwa
- Department of Biomedical Engineering; Technical University of Eindhoven; 5613 DR Eindhoven Netherlands
| | - Ari Rosling
- Faculty of Science and Engineering; Polymer Technologies; Åbo Akademi University; FI-20500 Turku Finland
| | - Didem Şen Karaman
- Faculty of Science and Engineering; Pharmaceutical Sciences Laboratory; Åbo Akademi University; FI-20520 Turku Finland
| | - Outi M. H. Salo-Ahen
- Faculty of Science and Engineering; Pharmaceutical Sciences Laboratory; Åbo Akademi University; FI-20520 Turku Finland
- Faculty of Science and Engineering; Structural Bioinformatics Laboratory; Åbo Akademi University; FI-20520 Turku Finland
| | - Ronald Österbacka
- Faculty of Science and Engineering; Physics; Åbo Akademi University; FI-20500 Turku Finland
| | - John E. Eriksson
- Faculty of Science and Engineering; Cell Biology; Åbo Akademi University; FI-20520 Turku Finland
- Turku Centre for Biotechnology; Åbo Akademi University and University of Turku; FI-20520 Turku Finland
| | - Stefan Willför
- Faculty of Science and Engineering; Natural Materials Technology; Åbo Akademi University; FI-20500 Turku Finland
| | - Ion Petre
- Faculty of Science and Engineering; Computer Science; Åbo Akademi University; FI-20500 Turku Finland
| | - Jouko Peltonen
- Faculty of Science and Engineering; Physical Chemistry; Åbo Akademi University; FI-20500 Turku Finland
| | - Reko Leino
- Faculty of Science and Engineering; Organic Chemistry; Johan Gadolin Process Chemistry Centre; Åbo Akademi University; FI-20500 Turku Finland
| | - Mark Johnson
- Faculty of Science and Engineering; Structural Bioinformatics Laboratory; Åbo Akademi University; FI-20520 Turku Finland
| | - Jessica Rosenholm
- Faculty of Science and Engineering; Pharmaceutical Sciences Laboratory; Åbo Akademi University; FI-20520 Turku Finland
| | - Niklas Sandler
- Faculty of Science and Engineering; Pharmaceutical Sciences Laboratory; Åbo Akademi University; FI-20520 Turku Finland
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38
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Sahlgren C, Meinander A, Zhang H, Cheng F, Preis M, Xu C, Salminen TA, Toivola D, Abankwa D, Rosling A, Karaman DŞ, Salo-Ahen OMH, Österbacka R, Eriksson JE, Willför S, Petre I, Peltonen J, Leino R, Johnson M, Rosenholm J, Sandler N. Tailored Approaches in Drug Development and Diagnostics: From Molecular Design to Biological Model Systems. Adv Healthc Mater 2017. [DOI: 10.1002/adhm.201700258 10.1002/adhm.201700258] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/26/2023]
Affiliation(s)
- Cecilia Sahlgren
- Faculty of Science and Engineering; Cell Biology; Åbo Akademi University; FI-20520 Turku Finland
- Turku Centre for Biotechnology; Åbo Akademi University and University of Turku; FI-20520 Turku Finland
- Department of Biomedical Engineering; Technical University of Eindhoven; 5613 DR Eindhoven Netherlands
| | - Annika Meinander
- Faculty of Science and Engineering; Cell Biology; Åbo Akademi University; FI-20520 Turku Finland
| | - Hongbo Zhang
- Faculty of Science and Engineering; Pharmaceutical Sciences Laboratory; Åbo Akademi University; FI-20520 Turku Finland
| | - Fang Cheng
- Faculty of Science and Engineering; Cell Biology; Åbo Akademi University; FI-20520 Turku Finland
| | - Maren Preis
- Faculty of Science and Engineering; Pharmaceutical Sciences Laboratory; Åbo Akademi University; FI-20520 Turku Finland
| | - Chunlin Xu
- Faculty of Science and Engineering; Natural Materials Technology; Åbo Akademi University; FI-20500 Turku Finland
| | - Tiina A. Salminen
- Faculty of Science and Engineering; Structural Bioinformatics Laboratory; Åbo Akademi University; FI-20520 Turku Finland
| | - Diana Toivola
- Faculty of Science and Engineering; Cell Biology; Åbo Akademi University; FI-20520 Turku Finland
- Turku Center for Disease Modeling; University of Turku; FI-20520 Turku Finland
| | - Daniel Abankwa
- Department of Biomedical Engineering; Technical University of Eindhoven; 5613 DR Eindhoven Netherlands
| | - Ari Rosling
- Faculty of Science and Engineering; Polymer Technologies; Åbo Akademi University; FI-20500 Turku Finland
| | - Didem Şen Karaman
- Faculty of Science and Engineering; Pharmaceutical Sciences Laboratory; Åbo Akademi University; FI-20520 Turku Finland
| | - Outi M. H. Salo-Ahen
- Faculty of Science and Engineering; Pharmaceutical Sciences Laboratory; Åbo Akademi University; FI-20520 Turku Finland
- Faculty of Science and Engineering; Structural Bioinformatics Laboratory; Åbo Akademi University; FI-20520 Turku Finland
| | - Ronald Österbacka
- Faculty of Science and Engineering; Physics; Åbo Akademi University; FI-20500 Turku Finland
| | - John E. Eriksson
- Faculty of Science and Engineering; Cell Biology; Åbo Akademi University; FI-20520 Turku Finland
- Turku Centre for Biotechnology; Åbo Akademi University and University of Turku; FI-20520 Turku Finland
| | - Stefan Willför
- Faculty of Science and Engineering; Natural Materials Technology; Åbo Akademi University; FI-20500 Turku Finland
| | - Ion Petre
- Faculty of Science and Engineering; Computer Science; Åbo Akademi University; FI-20500 Turku Finland
| | - Jouko Peltonen
- Faculty of Science and Engineering; Physical Chemistry; Åbo Akademi University; FI-20500 Turku Finland
| | - Reko Leino
- Faculty of Science and Engineering; Organic Chemistry; Johan Gadolin Process Chemistry Centre; Åbo Akademi University; FI-20500 Turku Finland
| | - Mark Johnson
- Faculty of Science and Engineering; Structural Bioinformatics Laboratory; Åbo Akademi University; FI-20520 Turku Finland
| | - Jessica Rosenholm
- Faculty of Science and Engineering; Pharmaceutical Sciences Laboratory; Åbo Akademi University; FI-20520 Turku Finland
| | - Niklas Sandler
- Faculty of Science and Engineering; Pharmaceutical Sciences Laboratory; Åbo Akademi University; FI-20520 Turku Finland
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Spatial organization of organelles in fungi: Insights from mathematical modelling. Fungal Genet Biol 2017; 103:55-59. [PMID: 28351675 PMCID: PMC5476193 DOI: 10.1016/j.fgb.2017.03.006] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/12/2016] [Revised: 03/15/2017] [Accepted: 03/22/2017] [Indexed: 01/03/2023]
Abstract
Modelling of dynein motility reveals a stochastic role in dynein comet formation. Modelling helps to elucidate mechanisms in spatial organization of early endosomes. A combination of diffusion and directed motion distributes ribosomes and peroxisomes.
Mathematical modelling in cellular systems aims to describe biological processes in a quantitative manner. Most accurate modelling is based on robust experimental data. Here we review recent progress in the theoretical description of motor behaviour, early endosome motility, ribosome distribution and peroxisome transport in the fungal model system Ustilago maydis and illustrate the power of modelling in our quest to understand molecular details and cellular roles of membrane trafficking in filamentous fungi.
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40
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Nguyen VK, Klawonn F, Mikolajczyk R, Hernandez-Vargas EA. Analysis of Practical Identifiability of a Viral Infection Model. PLoS One 2016; 11:e0167568. [PMID: 28036339 PMCID: PMC5201286 DOI: 10.1371/journal.pone.0167568] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/22/2016] [Accepted: 11/16/2016] [Indexed: 11/27/2022] Open
Abstract
Mathematical modelling approaches have granted a significant contribution to life sciences and beyond to understand experimental results. However, incomplete and inadequate assessments in parameter estimation practices hamper the parameter reliability, and consequently the insights that ultimately could arise from a mathematical model. To keep the diligent works in modelling biological systems from being mistrusted, potential sources of error must be acknowledged. Employing a popular mathematical model in viral infection research, existing means and practices in parameter estimation are exemplified. Numerical results show that poor experimental data is a main source that can lead to erroneous parameter estimates despite the use of innovative parameter estimation algorithms. Arbitrary choices of initial conditions as well as data asynchrony distort the parameter estimates but are often overlooked in modelling studies. This work stresses the existence of several sources of error buried in reports of modelling biological systems, voicing the need for assessing the sources of error, consolidating efforts in solving the immediate difficulties, and possibly reconsidering the use of mathematical modelling to quantify experimental data.
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Affiliation(s)
- Van Kinh Nguyen
- Systems Medicine of Infectious Diseases, Department of Systems Immunology and Braunschweig Integrated Centre of Systems Biology, Helmholtz Centre for Infection Research, Braunschweig, Germany
- Epidemiology Department, Ho Chi Minh University of Medicine and Pharmacy, Ho Chi Minh, Vietnam
- PhD Programme “Epidemiology”, Braunschweig-Hannover, Germany
| | - Frank Klawonn
- Biostatistics, Helmholtz Centre for Infection Research, Braunschweig, Germany
- Department of Computer Science, Ostfalia University, Wolfenbüttel, Germany
| | - Rafael Mikolajczyk
- Epidemiological and Statistical Methods, Helmholtz Centre for Infection Research, Braunschweig, Germany
- German Centre for Infection Research, site Hannover-Braunschweig, Germany
- Hannover Medical School, Hannover, Germany
- [Institute of] Medical Epidemiology, Biometry and Informatics, Martin-Luther University Halle-Wittenberg, Germany
| | - Esteban A. Hernandez-Vargas
- Systems Medicine of Infectious Diseases, Department of Systems Immunology and Braunschweig Integrated Centre of Systems Biology, Helmholtz Centre for Infection Research, Braunschweig, Germany
- * E-mail:
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41
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Cao Y, Ryser MD, Payne S, Li B, Rao CV, You L. Collective Space-Sensing Coordinates Pattern Scaling in Engineered Bacteria. Cell 2016; 165:620-30. [PMID: 27104979 DOI: 10.1016/j.cell.2016.03.006] [Citation(s) in RCA: 73] [Impact Index Per Article: 9.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2015] [Revised: 12/11/2015] [Accepted: 03/01/2016] [Indexed: 01/12/2023]
Abstract
Scale invariance refers to the maintenance of a constant ratio of developing organ size to body size. Although common, its underlying mechanisms remain poorly understood. Here, we examined scaling in engineered Escherichia coli that can form self-organized core-ring patterns in colonies. We found that the ring width exhibits perfect scale invariance to the colony size. Our analysis revealed a collective space-sensing mechanism, which entails sequential actions of an integral feedback loop and an incoherent feedforward loop. The integral feedback is implemented by the accumulation of a diffusive chemical produced by a colony. This accumulation, combined with nutrient consumption, sets the timing for ring initiation. The incoherent feedforward is implemented by the opposing effects of the domain size on the rate and duration of ring maturation. This mechanism emphasizes a role of timing control in achieving robust pattern scaling and provides a new perspective in examining the phenomenon in natural systems.
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Affiliation(s)
- Yangxiaolu Cao
- Department of Biomedical Engineering, Duke University, Durham, NC 27708, USA
| | - Marc D Ryser
- Department of Mathematics, Duke University, Durham, NC 27708, USA
| | - Stephen Payne
- Department of Biomedical Engineering, Duke University, Durham, NC 27708, USA
| | - Bochong Li
- Department of Biomedical Engineering, Duke University, Durham, NC 27708, USA
| | - Christopher V Rao
- Department of Chemical and Biomolecular Engineering, University of Illinois, Urbana Champaign, IL 61801, USA
| | - Lingchong You
- Department of Biomedical Engineering, Duke University, Durham, NC 27708, USA; Duke Center for Genomic and Computational Biology, Duke University, Durham, NC 27708, USA.
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42
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Atwell K, Dunn SJ, Osborne JM, Kugler H, Hubbard EJA. How computational models contribute to our understanding of the germ line. Mol Reprod Dev 2016; 83:944-957. [PMID: 27627621 DOI: 10.1002/mrd.22735] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2016] [Accepted: 09/04/2016] [Indexed: 11/05/2022]
Abstract
Computational models are an invaluable tool in modern biology. They provide a framework within which to summarize existing knowledge, enable competing hypotheses to be compared qualitatively and quantitatively, and to facilitate the interpretation of complex data. Moreover, models allow questions to be investigated that are difficult to approach experimentally. Theories can be tested in context, identifying the gaps in our understanding and potentially leading to new hypotheses. Models can be developed on a variety of scales and with different levels of mechanistic detail, depending on the available data, the biological questions of interest, and the available mathematical and computational tools. The goal of this review is to provide a broad picture of how modeling has been applied to reproductive biology. Specifically, we look at four uses of modeling: (i) comparing hypotheses; (ii) interpreting data; (iii) exploring experimentally challenging questions; and (iv) hypothesis evaluation and generation. We present examples of each of these applications in reproductive biology, drawing from a range of organisms-including Drosophila, Caenorhabditis elegans, mouse, and humans. We aim to describe the data and techniques used to construct each model, and to highlight the benefits of modeling to the field, as complementary to experimental work. Mol. Reprod. Dev. 83: 944-957, 2016 © 2016 Wiley Periodicals, Inc.
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Affiliation(s)
- Kathryn Atwell
- Computational Biology Group, Department of Computer Science, University of Oxford, Oxford, United Kingdom.,Biological Computation, Microsoft Research, Cambridge, United Kingdom
| | - Sara-Jane Dunn
- Biological Computation, Microsoft Research, Cambridge, United Kingdom
| | - James M Osborne
- School of Mathematics and Statistics, University of Melbourne, Melbourne, Australia
| | - Hillel Kugler
- Biological Computation, Microsoft Research, Cambridge, United Kingdom.,Faculty of Engineering, Bar-Ilan University, Ramat Gan, Israel
| | - E Jane Albert Hubbard
- Skirball Institute of Biomolecular Medicine, Department of Cell Biology, and Kimmel Center for Stem Cell Biology, New York University School of Medicine, New York, New York
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43
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Yu JS, Bagheri N. Multi-class and multi-scale models of complex biological phenomena. Curr Opin Biotechnol 2016; 39:167-173. [PMID: 27115496 DOI: 10.1016/j.copbio.2016.04.002] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2015] [Revised: 03/28/2016] [Accepted: 04/01/2016] [Indexed: 02/06/2023]
Abstract
Computational modeling has significantly impacted our ability to analyze vast (and exponentially increasing) quantities of experimental data for a variety of applications, such as drug discovery and disease forecasting. Single-scale, single-class models persist as the most common group of models, but biological complexity often demands more sophisticated approaches. This review surveys modeling approaches that are multi-class (incorporating multiple model types) and/or multi-scale (accounting for multiple spatial or temporal scales) and describes how these models, and combinations thereof, should be used within the context of the problem statement. We end by highlighting agent-based models as an intuitive, modular, and flexible framework within which multi-scale and multi-class models can be implemented.
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Affiliation(s)
- Jessica S Yu
- Chemical & Biological Engineering, Northwestern University, Evanston, IL, United States
| | - Neda Bagheri
- Chemical & Biological Engineering, Northwestern University, Evanston, IL, United States.
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44
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Álvarez-Buylla ER, Dávila-Velderrain J, Martínez-García JC. Systems Biology Approaches to Development beyond Bioinformatics: Nonlinear Mechanistic Models Using Plant Systems. Bioscience 2016. [DOI: 10.1093/biosci/biw027] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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45
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Ohta N, Waki K, Mochizuki A, Satou Y. A Boolean Function for Neural Induction Reveals a Critical Role of Direct Intercellular Interactions in Patterning the Ectoderm of the Ascidian Embryo. PLoS Comput Biol 2015; 11:e1004687. [PMID: 26714026 PMCID: PMC4695095 DOI: 10.1371/journal.pcbi.1004687] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2015] [Accepted: 12/01/2015] [Indexed: 01/12/2023] Open
Abstract
A complex system of multiple signaling molecules often produce differential gene expression patterns in animal embryos. In the ascidian embryo, four signaling ligands, Ephrin-A.d (Efna.d), Fgf9/16/20, Admp, and Gdf1/3-r, coordinately induce Otx expression in the neural lineage at the 32-cell stage. However, it has not been determined whether differential inputs of all of these signaling pathways are really necessary. It is possible that differential activation of one of these signaling pathways is sufficient and the remaining signaling pathways are activated in all cells at similar levels. To address this question, we developed a parameter-free method for determining a Boolean function for Otx expression in the present study. We treated activities of signaling pathways as Boolean values, and we also took all possible patterns of signaling gradients into consideration. We successfully determined a Boolean function that explains Otx expression in the animal hemisphere of wild-type and morphant embryos at the 32-cell stage. This Boolean function was not inconsistent with three sensing patterns, which represented whether or not individual cells received sufficient amounts of the signaling molecules. These sensing patterns all indicated that differential expression of Otx in the neural lineage is primarily determined by Efna.d, but not by differential inputs of Fgf9/16/20, Admp, and Gdf1/3-r signaling. To confirm this hypothesis experimentally, we simultaneously knocked-down Admp, Gdf1/3-r, and Fgf9/16/20, and treated this triple morphant with recombinant bFGF and BMP4 proteins, which mimic Fgf9/16/20 and Admp/Gdf1/3-r activity, respectively. Although no differential inputs of Admp, Gdf1/3-r and Fgf9/16/20 signaling were expected under this experimental condition, Otx was expressed specifically in the neural lineage. Thus, direct cell–cell interactions through Efna.d play a critical role in patterning the ectoderm of the early ascidian embryo. It is often difficult to understand a complex system of multiple signaling molecules in animal embryos only with experimental procedures. Although theoretical analysis might solve this problem, it is often difficult to precisely determine parameters for signaling gradients and kinetics of signaling molecules. In the present study, we developed a parameter-free method for determining a Boolean function for understanding a complex signaling system using gene expression patterns of signaling molecules and geometrical configurations of individual cells within the embryo. In the ascidian embryo, four signaling ligands, Ephrin-A.d (Efna.d), Fgf9/16/20, Admp, and Gdf1/3-r, coordinately induce Otx expression in the neural lineage at the 32-cell stage. In addition to determining a Boolean function, our method determined sensing patterns, which represented whether or not individual cells received sufficient amounts of the signaling molecules. The sensing patterns predicted that differential expression of Otx in the neural lineage is primarily determined by Efna.d, but not by differential inputs of Fgf9/16/20, Admp, and Gdf1/3-r. We confirmed this prediction by an experiment. As a result, we found that only Efna.d signaling pathway is differentially activated between ectodermal cells and the remaining signaling pathways are activated in all ectodermal cells at similar levels.
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Affiliation(s)
- Naoyuki Ohta
- Department of Zoology, Graduate School of Science, Kyoto University, Sakyo, Kyoto, Japan
| | - Kana Waki
- Department of Zoology, Graduate School of Science, Kyoto University, Sakyo, Kyoto, Japan
| | - Atsushi Mochizuki
- RIKEN Advanced Science Institute, Wako, Saitama, Japan
- CREST, Japan Science and Technology Agency, Kawaguchi, Saitama, Japan
| | - Yutaka Satou
- Department of Zoology, Graduate School of Science, Kyoto University, Sakyo, Kyoto, Japan
- CREST, Japan Science and Technology Agency, Kawaguchi, Saitama, Japan
- * E-mail:
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Bertens LMF, Kleijn J, Hille SC, Heiner M, Koutny M, Verbeek FJ. Modeling biological gradient formation: combining partial differential equations and Petri nets. NATURAL COMPUTING 2015; 15:665-675. [PMID: 27881934 PMCID: PMC5101295 DOI: 10.1007/s11047-015-9531-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Both Petri nets and differential equations are important modeling tools for biological processes. In this paper we demonstrate how these two modeling techniques can be combined to describe biological gradient formation. Parameters derived from partial differential equation describing the process of gradient formation are incorporated in an abstract Petri net model. The quantitative aspects of the resulting model are validated through a case study of gradient formation in the fruit fly.
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Affiliation(s)
| | - Jetty Kleijn
- LIACS, Leiden University, Leiden, The Netherlands
| | - Sander C Hille
- Mathematical Institute, Leiden University, Leiden, The Netherlands
| | - Monika Heiner
- Department of Computer Science, Brandenburg Technical University Cottbus-Senftenberg, Cottbus, Germany
| | - Maciej Koutny
- School of Computing Science, Newcastle University, Newcastle Upon Tyne, UK
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47
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Iterative experiment design guides the characterization of a light-inducible gene expression circuit. Proc Natl Acad Sci U S A 2015; 112:8148-53. [PMID: 26085136 DOI: 10.1073/pnas.1423947112] [Citation(s) in RCA: 37] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
Abstract
Systems biology rests on the idea that biological complexity can be better unraveled through the interplay of modeling and experimentation. However, the success of this approach depends critically on the informativeness of the chosen experiments, which is usually unknown a priori. Here, we propose a systematic scheme based on iterations of optimal experiment design, flow cytometry experiments, and Bayesian parameter inference to guide the discovery process in the case of stochastic biochemical reaction networks. To illustrate the benefit of our methodology, we apply it to the characterization of an engineered light-inducible gene expression circuit in yeast and compare the performance of the resulting model with models identified from nonoptimal experiments. In particular, we compare the parameter posterior distributions and the precision to which the outcome of future experiments can be predicted. Moreover, we illustrate how the identified stochastic model can be used to determine light induction patterns that make either the average amount of protein or the variability in a population of cells follow a desired profile. Our results show that optimal experiment design allows one to derive models that are accurate enough to precisely predict and regulate the protein expression in heterogeneous cell populations over extended periods of time.
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48
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Boissel JP, Auffray C, Noble D, Hood L, Boissel FH. Bridging Systems Medicine and Patient Needs. CPT-PHARMACOMETRICS & SYSTEMS PHARMACOLOGY 2015. [PMID: 26225243 PMCID: PMC4394618 DOI: 10.1002/psp4.26] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
While there is widespread consensus on the need both to change the prevailing research and development (R&D) paradigm and provide the community with an efficient way to personalize medicine, ecosystem stakeholders grapple with divergent conceptions about which quantitative approach should be preferred. The primary purpose of this position paper is to contrast these approaches. The second objective is to introduce a framework to bridge simulation outputs and patient outcomes, thus empowering the implementation of systems medicine.
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Affiliation(s)
| | - C Auffray
- European Institute for Systems Biology & Medicine, CNRS-UCBL-ENS, Université de Lyon France
| | - D Noble
- Department of Physiology, Anatomy & Genetics, University of Oxford Oxford, UK
| | - L Hood
- Institute for Systems Biology Seattle, Washington, USA
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Weber JK, Pande VS. Entropy-production-driven oscillators in simple nonequilibrium networks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:032136. [PMID: 25871083 DOI: 10.1103/physreve.91.032136] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/09/2014] [Indexed: 06/04/2023]
Abstract
The development of tractable nonequilibrium simulation methods represents a bottleneck for efforts to describe the functional dynamics that occur within living cells. We here employ a nonequilibrium approach called the λ ensemble to characterize the dissipative dynamics of a simple Markovian network driven by an external potential. In the highly dissipative regime brought about by the λ bias, we observe a dynamical structure characteristic of cellular architectures: The entropy production drives a damped oscillator over state populations in the network. We illustrate the properties of such oscillations in weakly and strongly driven regimes, and we discuss how control structures associated with the "dynamical phase transition" in the system can be related to switches and oscillators in cellular dynamics.
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Affiliation(s)
- Jeffrey K Weber
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
| | - Vijay S Pande
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
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50
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Wilkenfeld DA, Hellmann JK. Understanding beyond grasping propositions: a discussion of chess and fish. STUDIES IN HISTORY AND PHILOSOPHY OF SCIENCE 2014; 48:46-51. [PMID: 25571746 DOI: 10.1016/j.shpsa.2014.09.003] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
In this paper, we argue that, contra Strevens (2013), understanding in the sciences is sometimes partially constituted by the possession of abilities; hence, it is not (in such cases) exhausted by the understander's bearing a particular psychological or epistemic relationship to some set of structured propositions. Specifically, the case will be made that one does not really understand why a modeled phenomenon occurred unless one has the ability to actually work through (meaning run and grasp at each step) a model simulation of the underlying dynamic.
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