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Coulier A, Singh P, Sturrock M, Hellander A. Systematic comparison of modeling fidelity levels and parameter inference settings applied to negative feedback gene regulation. PLoS Comput Biol 2022; 18:e1010683. [PMID: 36520957 PMCID: PMC9799300 DOI: 10.1371/journal.pcbi.1010683] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2022] [Revised: 12/29/2022] [Accepted: 10/25/2022] [Indexed: 12/23/2022] Open
Abstract
Quantitative stochastic models of gene regulatory networks are important tools for studying cellular regulation. Such models can be formulated at many different levels of fidelity. A practical challenge is to determine what model fidelity to use in order to get accurate and representative results. The choice is important, because models of successively higher fidelity come at a rapidly increasing computational cost. In some situations, the level of detail is clearly motivated by the question under study. In many situations however, many model options could qualitatively agree with available data, depending on the amount of data and the nature of the observations. Here, an important distinction is whether we are interested in inferring the true (but unknown) physical parameters of the model or if it is sufficient to be able to capture and explain available data. The situation becomes complicated from a computational perspective because inference needs to be approximate. Most often it is based on likelihood-free Approximate Bayesian Computation (ABC) and here determining which summary statistics to use, as well as how much data is needed to reach the desired level of accuracy, are difficult tasks. Ultimately, all of these aspects-the model fidelity, the available data, and the numerical choices for inference-interplay in a complex manner. In this paper we develop a computational pipeline designed to systematically evaluate inference accuracy for a wide range of true known parameters. We then use it to explore inference settings for negative feedback gene regulation. In particular, we compare a detailed spatial stochastic model, a coarse-grained compartment-based multiscale model, and the standard well-mixed model, across several data-scenarios and for multiple numerical options for parameter inference. Practically speaking, this pipeline can be used as a preliminary step to guide modelers prior to gathering experimental data. By training Gaussian processes to approximate the distance function values, we are able to substantially reduce the computational cost of running the pipeline.
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Affiliation(s)
- Adrien Coulier
- Department of Information Technology, Uppsala University, Uppsala, Sweden
| | - Prashant Singh
- Science for Life Laboratory, Department of Information Technology, Uppsala University, Uppsala, Sweden
| | - Marc Sturrock
- Department of Physiology, Royal College of Surgeons in Ireland, Dublin, Ireland
| | - Andreas Hellander
- Department of Information Technology, Uppsala University, Uppsala, Sweden
- * E-mail:
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Subic T, Sbalzarini IF. A Gaussian jump process formulation of the reaction–diffusion master equation enables faster exact stochastic simulations. J Chem Phys 2022; 157:194110. [DOI: 10.1063/5.0123073] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
We propose a Gaussian jump process model on a regular Cartesian lattice for the diffusion part of the Reaction–Diffusion Master Equation (RDME). We derive the resulting Gaussian RDME (GRDME) formulation from analogy with a kernel-based discretization scheme for continuous diffusion processes and quantify the limits of its validity relative to the classic RDME. We then present an exact stochastic simulation algorithm for the GRDME, showing that the accuracies of GRDME and RDME are comparable, but exact simulations of the GRDME require only a fraction of the computational cost of exact RDME simulations. We analyze the origin of this speedup and its scaling with problem dimension. The benchmarks suggest that the GRDME is a particularly beneficial model for diffusion-dominated systems in three dimensional spaces, often occurring in systems biology and cell biology.
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Affiliation(s)
- Tina Subic
- Technische Universität Dresden, Faculty of Computer Science, Dresden, Germany
- Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany
- Center for Systems Biology Dresden, Dresden, Germany
| | - Ivo F. Sbalzarini
- Technische Universität Dresden, Faculty of Computer Science, 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, Dresden, Germany
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3
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Li C, Liu H, Zhang T, Zhang Y. Stability and Bifurcation Analysis of a Diffusive miR-9/Hes1 Network With Time Delay. IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2022; 19:1870-1880. [PMID: 33417562 DOI: 10.1109/tcbb.2021.3050006] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
In this paper, a model of miR-9/Hes1 interaction network involving one time delay and diffusion effect under the Neumann boundary conditions is studied. First of all, the stability of the positive equilibrium and the existence of local Hopf bifurcation and Turing-Hopf bifurcation are investigated by analyzing the associated characteristic equation. Second, a algorithm for determining the direction, stability and period of the corresponding bifurcating periodic solutions is presented. The obtained results suggest that the quiescent progenitors (high steady-state Hes1) can be easily excited into oscillation by time delay whereas the differentiated state (low steady-state Hes1) is basically unaffected, and the integrated effect of delay and diffusion can induce the occurrence of spatially inhomogeneous patterns. More importantly, spatially homogeneous/inhomogeneous periodic solutions can exist simultaneously when the diffusion coefficients of Hes1 mRNA and Hes1 protein are appropriately small, conversely, there is only spatially homogeneous periodic solutions. Intriguingly, both temporal patterns and spatial-temporal patterns show that time delay can prompt Hes1 protein to shift from the high concentration state to the low concentration one ("ON" → "OFF"), where Hes1 protein shows low level whereas miR-9 shows high level. Finally, some numerical examples are presented to verify and visualize theoretical results.
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Mathematical Modelling of p53 Signalling during DNA Damage Response: A Survey. Int J Mol Sci 2021; 22:ijms221910590. [PMID: 34638930 PMCID: PMC8508851 DOI: 10.3390/ijms221910590] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2021] [Revised: 09/14/2021] [Accepted: 09/26/2021] [Indexed: 02/05/2023] Open
Abstract
No gene has garnered more interest than p53 since its discovery over 40 years ago. In the last two decades, thanks to seminal work from Uri Alon and Ghalit Lahav, p53 has defined a truly synergistic topic in the field of mathematical biology, with a rich body of research connecting mathematic endeavour with experimental design and data. In this review we survey and distill the extensive literature of mathematical models of p53. Specifically, we focus on models which seek to reproduce the oscillatory dynamics of p53 in response to DNA damage. We review the standard modelling approaches used in the field categorising them into three types: time delay models, spatial models and coupled negative-positive feedback models, providing sample model equations and simulation results which show clear oscillatory dynamics. We discuss the interplay between mathematics and biology and show how one informs the other; the deep connections between the two disciplines has helped to develop our understanding of this complex gene and paint a picture of its dynamical response. Although yet more is to be elucidated, we offer the current state-of-the-art understanding of p53 response to DNA damage.
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Coulier A, Hellander S, Hellander A. A multiscale compartment-based model of stochastic gene regulatory networks using hitting-time analysis. J Chem Phys 2021; 154:184105. [PMID: 34241042 PMCID: PMC8116061 DOI: 10.1063/5.0010764] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Spatial stochastic models of single cell kinetics are capable of capturing both fluctuations in molecular numbers and the spatial dependencies of the key steps of intracellular regulatory networks. The spatial stochastic model can be simulated both on a detailed microscopic level using particle tracking and on a mesoscopic level using the reaction-diffusion master equation. However, despite substantial progress on simulation efficiency for spatial models in the last years, the computational cost quickly becomes prohibitively expensive for tasks that require repeated simulation of thousands or millions of realizations of the model. This limits the use of spatial models in applications such as multicellular simulations, likelihood-free parameter inference, and robustness analysis. Further approximation of the spatial dynamics is needed to accelerate such computational engineering tasks. We here propose a multiscale model where a compartment-based model approximates a detailed spatial stochastic model. The compartment model is constructed via a first-exit time analysis on the spatial model, thus capturing critical spatial aspects of the fine-grained simulations, at a cost close to the simple well-mixed model. We apply the multiscale model to a canonical model of negative-feedback gene regulation, assess its accuracy over a range of parameters, and demonstrate that the approximation can yield substantial speedups for likelihood-free parameter inference.
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Affiliation(s)
- Adrien Coulier
- Department of Information Technology, Uppsala University, Box 337, SE-755 01 Uppsala, Sweden
| | - Stefan Hellander
- Department of Information Technology, Uppsala University, Box 337, SE-755 01 Uppsala, Sweden
| | - Andreas Hellander
- Department of Information Technology, Uppsala University, Box 337, SE-755 01 Uppsala, Sweden
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6
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Mathematical Modeling of ceRNA-Based Interactions. Methods Mol Biol 2021. [PMID: 34165711 DOI: 10.1007/978-1-0716-1503-4_7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/31/2023]
Abstract
Competing endogenous RNA (ceRNA) molecules have emerged as key players in regulating gene expression, increasing the complexity of the range of possible dynamics within a cell. The actions of competing RNA typically are sponging behaviors, in a manner that fine-tunes gene expression, but there are particular network structures that may show destabilization due to ceRNA interactions. In this chapter, we discuss how these interactions can be modeled and probed from a mathematical, first-principles perspective.
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Wrede F, Hellander A. Smart computational exploration of stochastic gene regulatory network models using human-in-the-loop semi-supervised learning. Bioinformatics 2020; 35:5199-5206. [PMID: 31141124 DOI: 10.1093/bioinformatics/btz420] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2018] [Revised: 04/24/2019] [Accepted: 05/26/2019] [Indexed: 01/09/2023] Open
Abstract
MOTIVATION Discrete stochastic models of gene regulatory network models are indispensable tools for biological inquiry since they allow the modeler to predict how molecular interactions give rise to nonlinear system output. Model exploration with the objective of generating qualitative hypotheses about the workings of a pathway is usually the first step in the modeling process. It involves simulating the gene network model under a very large range of conditions, due to the large uncertainty in interactions and kinetic parameters. This makes model exploration highly computational demanding. Furthermore, with no prior information about the model behavior, labor-intensive manual inspection of very large amounts of simulation results becomes necessary. This limits systematic computational exploration to simplistic models. RESULTS We have developed an interactive, smart workflow for model exploration based on semi-supervised learning and human-in-the-loop labeling of data. The workflow lets a modeler rapidly discover ranges of interesting behaviors predicted by the model. Utilizing that similar simulation output is in proximity of each other in a feature space, the modeler can focus on informing the system about what behaviors are more interesting than others by labeling, rather than analyzing simulation results with custom scripts and workflows. This results in a large reduction in time-consuming manual work by the modeler early in a modeling project, which can substantially reduce the time needed to go from an initial model to testable predictions and downstream analysis. AVAILABILITY AND IMPLEMENTATION A python-package is available at https://github.com/Wrede/mio.git. SUPPLEMENTARY INFORMATION Supplementary data are available at Bioinformatics online.
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Affiliation(s)
- Fredrik Wrede
- Department of Information Technology, Uppsala University, Uppsala SE-75105, Sweden
| | - Andreas Hellander
- Department of Information Technology, Uppsala University, Uppsala SE-75105, Sweden
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Hellander S, Hellander A. Hierarchical algorithm for the reaction-diffusion master equation. J Chem Phys 2020; 152:034104. [PMID: 31968960 PMCID: PMC6964990 DOI: 10.1063/1.5095075] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023] Open
Abstract
We have developed an algorithm coupling mesoscopic simulations on different levels in a hierarchy of Cartesian meshes. Based on the multiscale nature of the chemical reactions, some molecules in the system will live on a fine-grained mesh, while others live on a coarse-grained mesh. By allowing molecules to transfer from the fine levels to the coarse levels when appropriate, we show that we can save up to three orders of magnitude of computational time compared to microscopic simulations or highly resolved mesoscopic simulations, without losing significant accuracy. We demonstrate this in several numerical examples with systems that cannot be accurately simulated with a coarse-grained mesoscopic model.
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Affiliation(s)
- Stefan Hellander
- Department of Information Technology, Uppsala University, Box 337, SE-755 01 Uppsala, Sweden
| | - Andreas Hellander
- Department of Information Technology, Uppsala University, Box 337, SE-755 01 Uppsala, Sweden
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Dhawan A, Harris AL, Buffa FM, Scott JG. Endogenous miRNA sponges mediate the generation of oscillatory dynamics for a non-coding RNA network. J Theor Biol 2019; 481:54-60. [PMID: 30385313 DOI: 10.1016/j.jtbi.2018.10.055] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2018] [Revised: 10/26/2018] [Accepted: 10/29/2018] [Indexed: 10/28/2022]
Abstract
Oscillations are crucial to the normal function of living organisms, across a wide variety of biological processes. In eukaryotes, oscillatory dynamics are thought to arise from interactions at the protein and RNA levels; however, the role of non-coding RNA in regulating these dynamics remains understudied. In this work, we show how non-coding RNA acting as microRNA (miRNA) sponges in a conserved miRNA - transcription factor feedback motif, can give rise to oscillatory behaviour, and how to test for this experimentally. Control of these non-coding RNA can dynamically create oscillations or stability, and we show how this behaviour predisposes to oscillations in the stochastic limit. These results, supported by emerging evidence for the role of miRNA sponges in development, point towards key roles of different species of miRNA sponges, such as circular RNA, potentially in the maintenance of yet unexplained oscillatory behaviour. These results help to provide a paradigm for understanding functional differences between the many redundant, but distinct RNA species thought to act as miRNA sponges in nature, such as long non-coding RNA, pseudogenes, competing mRNA, circular RNA, and3' UTRs.
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Affiliation(s)
- Andrew Dhawan
- Department of Oncology, University of Oxford, Oxford, United Kingdom
| | - Adrian L Harris
- Department of Oncology, University of Oxford, Oxford, United Kingdom
| | - Francesca M Buffa
- Department of Oncology, University of Oxford, Oxford, United Kingdom
| | - Jacob G Scott
- Departments of Translational Hematology and Oncology Research, Cleveland Clinic, Cleveland, United States.
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Lötstedt P. The Linear Noise Approximation for Spatially Dependent Biochemical Networks. Bull Math Biol 2019; 81:2873-2901. [PMID: 29644520 PMCID: PMC6677697 DOI: 10.1007/s11538-018-0428-0] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/09/2018] [Accepted: 03/29/2018] [Indexed: 10/26/2022]
Abstract
An algorithm for computing the linear noise approximation (LNA) of the reaction-diffusion master equation (RDME) is developed and tested. The RDME is often used as a model for biochemical reaction networks. The LNA is derived for a general discretization of the spatial domain of the problem. If M is the number of chemical species in the network and N is the number of nodes in the discretization in space, then the computational work to determine approximations of the mean and the covariances of the probability distributions is proportional to [Formula: see text] in a straightforward implementation. In our LNA algorithm, the work is proportional to [Formula: see text]. Since N usually is larger than M, this is a significant reduction. The accuracy of the approximation in the algorithm is estimated analytically and evaluated in numerical experiments.
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Affiliation(s)
- Per Lötstedt
- Division of Scientific Computing, Department of Information Technology, Uppsala University, SE-75105, Uppsala, Sweden.
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11
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Smith S, Grima R. Spatial Stochastic Intracellular Kinetics: A Review of Modelling Approaches. Bull Math Biol 2019; 81:2960-3009. [PMID: 29785521 PMCID: PMC6677717 DOI: 10.1007/s11538-018-0443-1] [Citation(s) in RCA: 27] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2018] [Accepted: 05/03/2018] [Indexed: 01/22/2023]
Abstract
Models of chemical kinetics that incorporate both stochasticity and diffusion are an increasingly common tool for studying biology. The variety of competing models is vast, but two stand out by virtue of their popularity: the reaction-diffusion master equation and Brownian dynamics. In this review, we critically address a number of open questions surrounding these models: How can they be justified physically? How do they relate to each other? How do they fit into the wider landscape of chemical models, ranging from the rate equations to molecular dynamics? This review assumes no prior knowledge of modelling chemical kinetics and should be accessible to a wide range of readers.
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Affiliation(s)
- Stephen Smith
- School of Biological Sciences, University of Edinburgh, Mayfield Road, Edinburgh, EH9 3JR, Scotland, UK
| | - Ramon Grima
- School of Biological Sciences, University of Edinburgh, Mayfield Road, Edinburgh, EH9 3JR, Scotland, UK.
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12
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Oscillations in well-mixed, deterministic feedback systems: Beyond ring oscillators. J Theor Biol 2019; 481:44-53. [PMID: 31059715 PMCID: PMC6859483 DOI: 10.1016/j.jtbi.2019.05.004] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/09/2018] [Revised: 04/30/2019] [Accepted: 05/03/2019] [Indexed: 01/20/2023]
Abstract
I present a way of breaking down regulatory networks to find Hopf bifurcations. This helps find optimal conditions for oscillations in dynamical systems models of these networks. In a model of negative auto-regulation of a gene by its dimeric protein, it is optimal for the monomer to degrade faster than the mRNA and the mRNA to degrade faster than the dimer. Adding a weak positive feedback loop to a repressilator increases the probability of oscillations. The optimal degradation rate of species in the sub-loop is higher than that of species outside it. The opposite is true for a negative feedback sub-loop or a very strong positive feedback sub-loop.
A ring oscillator is a system in which one species regulates the next, which regulates the next and so on until the last species regulates the first. In addition, the number of the regulations which are negative, and so result in a reduction in the regulated species, is odd, making the overall feedback in the loop negative. In ring oscillators, the probability of oscillations is maximised if the degradation rates of the species are equal. When there is more than one loop in the regulatory network, the dynamics can be more complicated. Here, a systematic way of organising the characteristic equation of ODE models of regulatory networks is provided. This facilitates the identification of Hopf bifurcations. It is shown that the probability of oscillations in non-ring systems is maximised for unequal degradation rates. For example, when there is a ring and a second ring employing a subset of the genes in the first ring, then the probability of oscillations is maximised when the species in the sub-ring degrade more slowly than those outside, for a negative feedback subring. When the sub-ring forms a positive feedback loop, the optimal degradation rates are larger for the species in the sub-ring, provided the positive feedback is not too strong. By contrast, optimal degradation rates are smaller for the species in the sub-ring, when the positive feedback is very strong. Adding a positive feedback loop to a repressilator increases the probability of oscillations, provided the positive feedback is not too strong, whereas adding a negative feedback loop decreases the probability of oscillations. The work is illustrated with numerical simulations of example systems: an autoregulatory gene model in which transcription is downregulated by the protein dimer and three-species and four-species gene regulatory network examples.
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Macnamara CK, Mitchell EI, Chaplain MA. Spatial-Stochastic modelling of synthetic gene regulatory networks. J Theor Biol 2019; 468:27-44. [DOI: 10.1016/j.jtbi.2019.02.003] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2017] [Revised: 01/18/2019] [Accepted: 02/05/2019] [Indexed: 02/06/2023]
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14
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Bouchnita A, Hellander S, Hellander A. A 3D Multiscale Model to Explore the Role of EGFR Overexpression in Tumourigenesis. Bull Math Biol 2019; 81:2323-2344. [PMID: 31016574 PMCID: PMC6612322 DOI: 10.1007/s11538-019-00607-y] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2019] [Accepted: 04/15/2019] [Indexed: 11/30/2022]
Abstract
The epidermal growth factor receptor (EGFR) signalling cascade is one of the main pathways that regulate the survival and division of mammalian cells. It is also one of the most altered transduction pathways in cancer. Acquired mutations in the EGFR/ERK pathway can cause the overexpression of EGFR on the surface of the cell, while others downregulate the inactivation of switched on intracellular proteins such as Ras and Raf. This upregulates the activity of ERK and promotes cell division. We develop a 3D multiscale model to explore the role of EGFR overexpression on tumour initiation. In this model, cells are described as individual objects that move, interact, divide, proliferate, and die by apoptosis. We use Brownian Dynamics to describe the extracellular and intracellular regulations of cells as well as the spatial and stochastic effects influencing them. The fate of each cell depends on the number of active transcription factors in the nucleus. We use numerical simulations to investigate the individual and combined effects of mutations on the intracellular regulation of individual cells. Next, we show that the distance between active receptors increase the level of EGFR/ERK signalling. We demonstrate the usefulness of the model by quantifying the impact of mutational alterations in the EGFR/ERK pathway on the growth rate of in silico tumours.
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Affiliation(s)
- Anass Bouchnita
- Division of Scientific Computing, Department of Information Technology, Uppsala University, 75105, Uppsala, Sweden.
| | - Stefan Hellander
- Division of Scientific Computing, Department of Information Technology, Uppsala University, 75105, Uppsala, Sweden
| | - Andreas Hellander
- Division of Scientific Computing, Department of Information Technology, Uppsala University, 75105, Uppsala, Sweden
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15
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Addressing Variability and Heterogeneity of Induced Pluripotent Stem Cell-Derived Cardiomyocytes. ADVANCES IN EXPERIMENTAL MEDICINE AND BIOLOGY 2019; 1212:1-29. [DOI: 10.1007/5584_2019_350] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
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16
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Picco N, Woolley TE. Time to change your mind? Modelling transient properties of cortex formation highlights the importance of evolving cell division strategies. J Theor Biol 2018; 481:110-118. [PMID: 30121294 DOI: 10.1016/j.jtbi.2018.08.019] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/14/2018] [Revised: 08/12/2018] [Accepted: 08/13/2018] [Indexed: 11/16/2022]
Abstract
The successful development of the mammalian cerebral neocortex is linked to numerous cognitive functions such as language, voluntary movement, and episodic memory. Neocortex development occurs when neural progenitor cells divide and produce neurons. Critically, although the progenitor cells are able to self-renew they do not reproduce themselves endlessly. Hence, to fully understand the development of the neocortex we are faced with the challenge of understanding temporal changes in cell division strategy. Our approach to modelling neuronal production uses non-autonomous ordinary differential equations and allows us to use a ternary coordinate system in order to define a strategy space, through which we can visualise evolving cell division strategies. Using this strategy space, we fit the known data and use approximate Bayesian computation to predict the founding progenitor population sizes, currently unavailable in the experimental literature. Counter-intuitively, we show that humans can generate a larger number of neurons than a macaque's even when starting with a smaller number of progenitor cells. Accompanying the article is a self-contained piece of software, which provides the reader with immediate simulated results that will aid their intuition. The software can be found at www.dpag.ox.ac.uk/team/noemi-picco.
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Affiliation(s)
- Noemi Picco
- University of Oxford, Mathematical Institute, Woodstock Road, Oxford OX2 6GG, United Kingdom.
| | - Thomas E Woolley
- Cardiff School of Mathematics, Cardiff University, Senghennydd Road, Cardiff CF24 4AG, United Kingdom.
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17
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Hellander S, Petzold L. Reaction rates for reaction-diffusion kinetics on unstructured meshes. J Chem Phys 2018; 146:064101. [PMID: 28201913 DOI: 10.1063/1.4975167] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
Abstract
The reaction-diffusion master equation is a stochastic model often utilized in the study of biochemical reaction networks in living cells. It is applied when the spatial distribution of molecules is important to the dynamics of the system. A viable approach to resolve the complex geometry of cells accurately is to discretize space with an unstructured mesh. Diffusion is modeled as discrete jumps between nodes on the mesh, and the diffusion jump rates can be obtained through a discretization of the diffusion equation on the mesh. Reactions can occur when molecules occupy the same voxel. In this paper, we develop a method for computing accurate reaction rates between molecules occupying the same voxel in an unstructured mesh. For large voxels, these rates are known to be well approximated by the reaction rates derived by Collins and Kimball, but as the mesh is refined, no analytical expression for the rates exists. We reduce the problem of computing accurate reaction rates to a pure preprocessing step, depending only on the mesh and not on the model parameters, and we devise an efficient numerical scheme to estimate them to high accuracy. We show in several numerical examples that as we refine the mesh, the results obtained with the reaction-diffusion master equation approach those of a more fine-grained Smoluchowski particle-tracking model.
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Affiliation(s)
- Stefan Hellander
- Department of Computer Science, University of California, Santa Barbara, California 93106-5070, USA
| | - Linda Petzold
- Department of Computer Science, University of California, Santa Barbara, California 93106-5070, USA
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Lu H, Jiang J, Gao Y. The cloning and activity of human Hes1 gene promoter. Mol Med Rep 2017; 17:3164-3169. [PMID: 29257279 DOI: 10.3892/mmr.2017.8240] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2017] [Accepted: 09/15/2017] [Indexed: 11/06/2022] Open
Abstract
The aim of the current study was to obtain and analyze the activity of the human Hes1 gene promoter. The genomic DNA of human HeLa cell was used as template, polymerase chain reaction (PCR) was used to amplify the 5' end sequence of Hes1 gene and then the amplified segment was connected to pMD18‑T vector. Subsequently, double enzyme digestion was used for identification and the sequence was detected; the promoter with the correct sequence was inserted into pGL3‑Basic, and the sequence was identified by double enzyme digestion. The recombinant DNA with correct sequence was transiently transfected into cervical cancer cells, and the dual luciferase reporter gene assay system was used to detect the activity of the promoter. The results demonstrated that the human Hes1 gene promoter amplified by PCR was the same as that of the sequence in the gene bank, and the dual luciferase reporter gene assay system demonstrated that there was promoter activity in cervical cancer cells. In conclusion, the Hes1 luciferase reporter recombinant vector was successfully established and transfected into HeLa cells to verify that it has promoter activity, and the core area of the promoter has several tumor‑promoting and tumor suppressor genes. This provides a basis for understanding the regulatory mechanism of Hes1 transcription and translation.
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Affiliation(s)
- Hai Lu
- Department of Hepatobiliary Surgery II, Guangdong Provincial Research Center for Artificial Organ and Tissue Engineering, Guangzhou Clinical Research and Transformation Center for Artificial Liver, Institute of Regenerative Medicine, Zhujiang Hospital, Southern Medical University, Guangzhou, Guangdong 510282, P.R. China
| | - Jinqun Jiang
- Clinical Laboratory, Yuebei People's Hospital, Shaoguan, Guangdong 512026, P.R. China
| | - Yi Gao
- Department of Hepatobiliary Surgery II, Guangdong Provincial Research Center for Artificial Organ and Tissue Engineering, Guangzhou Clinical Research and Transformation Center for Artificial Liver, Institute of Regenerative Medicine, Zhujiang Hospital, Southern Medical University, Guangzhou, Guangdong 510282, P.R. China
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Bittig AT, Uhrmacher AM. ML-Space: Hybrid Spatial Gillespie and Particle Simulation of Multi-Level Rule-Based Models in Cell Biology. IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2017; 14:1339-1349. [PMID: 27514063 DOI: 10.1109/tcbb.2016.2598162] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Spatio-temporal dynamics of cellular processes can be simulated at different levels of detail, from (deterministic) partial differential equations via the spatial Stochastic Simulation algorithm to tracking Brownian trajectories of individual particles. We present a spatial simulation approach for multi-level rule-based models, which includes dynamically hierarchically nested cellular compartments and entities. Our approach ML-Space combines discrete compartmental dynamics, stochastic spatial approaches in discrete space, and particles moving in continuous space. The rule-based specification language of ML-Space supports concise and compact descriptions of models and to adapt the spatial resolution of models easily.
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Sturrock M, Li S, Shahrezaei V. The influence of nuclear compartmentalisation on stochastic dynamics of self-repressing gene expression. J Theor Biol 2017; 424:55-72. [DOI: 10.1016/j.jtbi.2017.05.003] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2016] [Revised: 04/26/2017] [Accepted: 05/03/2017] [Indexed: 01/11/2023]
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21
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Szymańska Z, Cytowski M, Mitchell E, Macnamara CK, Chaplain MAJ. Computational Modelling of Cancer Development and Growth: Modelling at Multiple Scales and Multiscale Modelling. Bull Math Biol 2017. [PMID: 28634857 DOI: 10.1007/s11538-017-0292-3] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Abstract
In this paper, we present two mathematical models related to different aspects and scales of cancer growth. The first model is a stochastic spatiotemporal model of both a synthetic gene regulatory network (the example of a three-gene repressilator is given) and an actual gene regulatory network, the NF-[Formula: see text]B pathway. The second model is a force-based individual-based model of the development of a solid avascular tumour with specific application to tumour cords, i.e. a mass of cancer cells growing around a central blood vessel. In each case, we compare our computational simulation results with experimental data. In the final discussion section, we outline how to take the work forward through the development of a multiscale model focussed at the cell level. This would incorporate key intracellular signalling pathways associated with cancer within each cell (e.g. p53-Mdm2, NF-[Formula: see text]B) and through the use of high-performance computing be capable of simulating up to [Formula: see text] cells, i.e. the tissue scale. In this way, mathematical models at multiple scales would be combined to formulate a multiscale computational model.
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Affiliation(s)
- Zuzanna Szymańska
- ICM, University of Warsaw, ul. Pawińskiego 5a, 02-106, Warsaw, Poland
| | - Maciej Cytowski
- ICM, University of Warsaw, ul. Pawińskiego 5a, 02-106, Warsaw, Poland
| | - Elaine Mitchell
- Division of Mathematics, University of Dundee, Dundee, DD1 4HN, Scotland, UK
| | - Cicely K Macnamara
- School of Mathematics and Statistics, University of St Andrews, St Andrews, KY16 9SS, Scotland, UK
| | - Mark A J Chaplain
- School of Mathematics and Statistics, University of St Andrews, St Andrews, KY16 9SS, Scotland, UK.
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Eliaš J. Positive effect of Mdm2 on p53 expression explains excitability of p53 in response to DNA damage. J Theor Biol 2017; 418:94-104. [DOI: 10.1016/j.jtbi.2017.01.038] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2016] [Revised: 09/07/2016] [Accepted: 01/21/2017] [Indexed: 11/28/2022]
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Kay SK, Harrington HA, Shepherd S, Brennan K, Dale T, Osborne JM, Gavaghan DJ, Byrne HM. The role of the Hes1 crosstalk hub in Notch-Wnt interactions of the intestinal crypt. PLoS Comput Biol 2017; 13:e1005400. [PMID: 28245235 PMCID: PMC5363986 DOI: 10.1371/journal.pcbi.1005400] [Citation(s) in RCA: 36] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2016] [Revised: 03/23/2017] [Accepted: 02/07/2017] [Indexed: 12/21/2022] Open
Abstract
The Notch pathway plays a vital role in determining whether cells in the intestinal epithelium adopt a secretory or an absorptive phenotype. Cell fate specification is coordinated via Notch's interaction with the canonical Wnt pathway. Here, we propose a new mathematical model of the Notch and Wnt pathways, in which the Hes1 promoter acts as a hub for pathway crosstalk. Computational simulations of the model can assist in understanding how healthy intestinal tissue is maintained, and predict the likely consequences of biochemical knockouts upon cell fate selection processes. Chemical reaction network theory (CRNT) is a powerful, generalised framework which assesses the capacity of our model for monostability or multistability, by analysing properties of the underlying network structure without recourse to specific parameter values or functional forms for reaction rates. CRNT highlights the role of β-catenin in stabilising the Notch pathway and damping oscillations, demonstrating that Wnt-mediated actions on the Hes1 promoter can induce dynamic transitions in the Notch system, from multistability to monostability. Time-dependent model simulations of cell pairs reveal the stabilising influence of Wnt upon the Notch pathway, in which β-catenin- and Dsh-mediated action on the Hes1 promoter are key in shaping the subcellular dynamics. Where Notch-mediated transcription of Hes1 dominates, there is Notch oscillation and maintenance of fate flexibility; Wnt-mediated transcription of Hes1 favours bistability akin to cell fate selection. Cells could therefore regulate the proportion of Wnt- and Notch-mediated control of the Hes1 promoter to coordinate the timing of cell fate selection as they migrate through the intestinal epithelium and are subject to reduced Wnt stimuli. Furthermore, mutant cells characterised by hyperstimulation of the Wnt pathway may, through coupling with Notch, invert cell fate in neighbouring healthy cells, enabling an aberrant cell to maintain its neighbours in mitotically active states.
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Affiliation(s)
- Sophie K. Kay
- Department of Computer Science, University of Oxford, Oxford, U.K.
| | | | - Sarah Shepherd
- School of Mathematical Sciences, University of Nottingham, Nottingham, U.K.
| | - Keith Brennan
- Wellcome Trust Centre for Cell Matrix Research, University of Manchester, Manchester, U.K.
| | - Trevor Dale
- School of Biosciences, Cardiff University, Cardiff, U.K.
| | - James M. Osborne
- School of Mathematics and Statistics, University of Melbourne, Melbourne, Australia
| | | | - Helen M. Byrne
- Department of Computer Science, University of Oxford, Oxford, U.K.
- Mathematical Institute, University of Oxford, Oxford, U.K.
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Macnamara CK, Chaplain MAJ. Spatio-temporal models of synthetic genetic oscillators. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2017; 14:249-262. [PMID: 27879131 DOI: 10.3934/mbe.2017016] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Signal transduction pathways play a major role in many important aspects of cellular function e.g. cell division, apoptosis. One important class of signal transduction pathways is gene regulatory networks (GRNs). In many GRNs, proteins bind to gene sites in the nucleus thereby altering the transcription rate. Such proteins are known as transcription factors. If the binding reduces the transcription rate there is a negative feedback leading to oscillatory behaviour in mRNA and protein levels, both spatially (e.g. by observing fluorescently labelled molecules in single cells) and temporally (e.g. by observing protein/mRNA levels over time). Recent computational modelling has demonstrated that spatial movement of the molecules is a vital component of GRNs and may cause the oscillations. These numerical findings have subsequently been proved rigorously i.e. the diffusion coefficient of the protein/mRNA acts as a bifurcation parameter and gives rise to a Hopf bifurcation. In this paper we first present a model of the canonical GRN (the Hes1 protein) and show the effect of varying the spatial location of gene and protein production sites on the oscillations. We then extend the approach to examine spatio-temporal models of synthetic gene regulatory networks e.g. n-gene repressilators and activator-repressor systems.
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Affiliation(s)
- Cicely K Macnamara
- School of Mathematics and Statistics, Mathematical Institute, North Haugh, University of St Andrews, St Andrews KY16 9SS, Scotland.
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26
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Richard A, Boullu L, Herbach U, Bonnafoux A, Morin V, Vallin E, Guillemin A, Papili Gao N, Gunawan R, Cosette J, Arnaud O, Kupiec JJ, Espinasse T, Gonin-Giraud S, Gandrillon O. Single-Cell-Based Analysis Highlights a Surge in Cell-to-Cell Molecular Variability Preceding Irreversible Commitment in a Differentiation Process. PLoS Biol 2016; 14:e1002585. [PMID: 28027290 PMCID: PMC5191835 DOI: 10.1371/journal.pbio.1002585] [Citation(s) in RCA: 128] [Impact Index Per Article: 16.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/06/2016] [Accepted: 09/22/2016] [Indexed: 12/31/2022] Open
Abstract
In some recent studies, a view emerged that stochastic dynamics governing the switching of cells from one differentiation state to another could be characterized by a peak in gene expression variability at the point of fate commitment. We have tested this hypothesis at the single-cell level by analyzing primary chicken erythroid progenitors through their differentiation process and measuring the expression of selected genes at six sequential time-points after induction of differentiation. In contrast to population-based expression data, single-cell gene expression data revealed a high cell-to-cell variability, which was masked by averaging. We were able to show that the correlation network was a very dynamical entity and that a subgroup of genes tend to follow the predictions from the dynamical network biomarker (DNB) theory. In addition, we also identified a small group of functionally related genes encoding proteins involved in sterol synthesis that could act as the initial drivers of the differentiation. In order to assess quantitatively the cell-to-cell variability in gene expression and its evolution in time, we used Shannon entropy as a measure of the heterogeneity. Entropy values showed a significant increase in the first 8 h of the differentiation process, reaching a peak between 8 and 24 h, before decreasing to significantly lower values. Moreover, we observed that the previous point of maximum entropy precedes two paramount key points: an irreversible commitment to differentiation between 24 and 48 h followed by a significant increase in cell size variability at 48 h. In conclusion, when analyzed at the single cell level, the differentiation process looks very different from its classical population average view. New observables (like entropy) can be computed, the behavior of which is fully compatible with the idea that differentiation is not a “simple” program that all cells execute identically but results from the dynamical behavior of the underlying molecular network. A single-cell transcriptomics analysis offers a new dynamical view of the differentiation process, involving an increase in between-cell variability prior to commitment. The differentiation process has classically been seen as a stereotyped program leading from one progenitor toward a functional cell. This vision was based upon cell population-based analyses averaged over millions of cells. However, new methods have recently emerged that allow interrogation of the molecular content at the single-cell level, challenging this view with a new model suggesting that cell-to-cell gene expression stochasticity could play a key role in differentiation. We took advantage of a physiologically relevant avian cellular model to analyze the expression level of 92 genes in individual cells collected at several time-points during differentiation. We first observed that the process analyzed at the single-cell level is very different and much less well ordered than the population-based average view. Furthermore, we showed that cell-to-cell variability in gene expression peaks transiently before strongly decreasing. This rise in variability precedes two key events: an irreversible commitment to differentiation, followed by a significant increase in cell size variability. Altogether, our results support the idea that differentiation is not a “simple” series of well-ordered molecular events executed identically by all cells in a population but likely results from dynamical behavior of the underlying molecular network.
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Affiliation(s)
- Angélique Richard
- Univ Lyon, ENS de Lyon, Univ Claude Bernard, CNRS UMR 5239, INSERM U1210, Laboratory of Biology and Modelling of the Cell, 46 allée d’Italie Site Jacques Monod, F-69007, Lyon, France
| | - Loïs Boullu
- Inria Team Dracula, Inria Center Grenoble Rhône-Alpes, France
- Université de Lyon, Université Lyon 1, CNRS UMR 5208, Institut Camille Jordan 43 blvd du 11 novembre 1918, F-69622 Villeurbanne-Cedex, France
- Département de Mathématiques et de statistiques de l’Université de Montréal, Pavillon André-Aisenstadt, 2920, chemin de la Tour, Montréal (Québec) H3T 1J4 Canada
| | - Ulysse Herbach
- Univ Lyon, ENS de Lyon, Univ Claude Bernard, CNRS UMR 5239, INSERM U1210, Laboratory of Biology and Modelling of the Cell, 46 allée d’Italie Site Jacques Monod, F-69007, Lyon, France
- Inria Team Dracula, Inria Center Grenoble Rhône-Alpes, France
- Université de Lyon, Université Lyon 1, CNRS UMR 5208, Institut Camille Jordan 43 blvd du 11 novembre 1918, F-69622 Villeurbanne-Cedex, France
| | - Arnaud Bonnafoux
- Univ Lyon, ENS de Lyon, Univ Claude Bernard, CNRS UMR 5239, INSERM U1210, Laboratory of Biology and Modelling of the Cell, 46 allée d’Italie Site Jacques Monod, F-69007, Lyon, France
- Inria Team Dracula, Inria Center Grenoble Rhône-Alpes, France
- The CoSMo company. 5 passage du Vercors – 69007 LYON – France
| | - Valérie Morin
- Univ Lyon, Univ Claude Bernard, CNRS UMR 5310 - INSERM U1217, Institut NeuroMyoGène, F-69622 Villeurbanne-Cedex, France
| | - Elodie Vallin
- Univ Lyon, ENS de Lyon, Univ Claude Bernard, CNRS UMR 5239, INSERM U1210, Laboratory of Biology and Modelling of the Cell, 46 allée d’Italie Site Jacques Monod, F-69007, Lyon, France
| | - Anissa Guillemin
- Univ Lyon, ENS de Lyon, Univ Claude Bernard, CNRS UMR 5239, INSERM U1210, Laboratory of Biology and Modelling of the Cell, 46 allée d’Italie Site Jacques Monod, F-69007, Lyon, France
| | - Nan Papili Gao
- Institute for Chemical and Bioengineering, ETH Zurich, Zurich, Switzerland
- Swiss Institute of Bioinformatics, Quartier Sorge - Batiment Genopode, 1015 Lausanne Switzerland
| | - Rudiyanto Gunawan
- Institute for Chemical and Bioengineering, ETH Zurich, Zurich, Switzerland
- Swiss Institute of Bioinformatics, Quartier Sorge - Batiment Genopode, 1015 Lausanne Switzerland
| | - Jérémie Cosette
- Genethon – Institut National de la Santé et de la Recherche Médicale – INSERM, Université d’Evry-Val-d’Essone – 1 rue de l’internationale 91000 Evry, France
| | - Ophélie Arnaud
- RIKEN - Center for Life Science Technologies (Division of Genomic Technologies)—CLST (DGT), 1-7-22 Suehiro-cho, Tsurumi-ku, Yokohama, Kanagawa 230-0045, Japan
| | | | - Thibault Espinasse
- Université de Lyon, Université Lyon 1, CNRS UMR 5208, Institut Camille Jordan 43 blvd du 11 novembre 1918, F-69622 Villeurbanne-Cedex, France
| | - Sandrine Gonin-Giraud
- Univ Lyon, ENS de Lyon, Univ Claude Bernard, CNRS UMR 5239, INSERM U1210, Laboratory of Biology and Modelling of the Cell, 46 allée d’Italie Site Jacques Monod, F-69007, Lyon, France
| | - Olivier Gandrillon
- Univ Lyon, ENS de Lyon, Univ Claude Bernard, CNRS UMR 5239, INSERM U1210, Laboratory of Biology and Modelling of the Cell, 46 allée d’Italie Site Jacques Monod, F-69007, Lyon, France
- Inria Team Dracula, Inria Center Grenoble Rhône-Alpes, France
- * E-mail:
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27
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Drawert B, Hellander A, Bales B, Banerjee D, Bellesia G, Daigle BJ, Douglas G, Gu M, Gupta A, Hellander S, Horuk C, Nath D, Takkar A, Wu S, Lötstedt P, Krintz C, Petzold LR. Stochastic Simulation Service: Bridging the Gap between the Computational Expert and the Biologist. PLoS Comput Biol 2016; 12:e1005220. [PMID: 27930676 PMCID: PMC5145134 DOI: 10.1371/journal.pcbi.1005220] [Citation(s) in RCA: 46] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2016] [Accepted: 10/24/2016] [Indexed: 01/25/2023] Open
Abstract
We present StochSS: Stochastic Simulation as a Service, an integrated development environment for modeling and simulation of both deterministic and discrete stochastic biochemical systems in up to three dimensions. An easy to use graphical user interface enables researchers to quickly develop and simulate a biological model on a desktop or laptop, which can then be expanded to incorporate increasing levels of complexity. StochSS features state-of-the-art simulation engines. As the demand for computational power increases, StochSS can seamlessly scale computing resources in the cloud. In addition, StochSS can be deployed as a multi-user software environment where collaborators share computational resources and exchange models via a public model repository. We demonstrate the capabilities and ease of use of StochSS with an example of model development and simulation at increasing levels of complexity.
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Affiliation(s)
- Brian Drawert
- Department of Computer Science, University of California, Santa Barbara, Santa Barbara, California, United States of America
- * E-mail:
| | - Andreas Hellander
- Department of Information Technology, Division of Scientific Computing, Uppsala University, Uppsala, Sweden
| | - Ben Bales
- Department of Mechanical Engineering, University of California, Santa Barbara, Santa Barbara, California, United States of America
| | - Debjani Banerjee
- Department of Computer Science, University of California, Santa Barbara, Santa Barbara, California, United States of America
| | - Giovanni Bellesia
- Department of Computer Science, University of California, Santa Barbara, Santa Barbara, California, United States of America
| | - Bernie J. Daigle
- Departments of Biological Sciences and Computer Science, The University of Memphis, Memphis, Tennessee, United States of America
| | - Geoffrey Douglas
- Department of Computer Science, University of California, Santa Barbara, Santa Barbara, California, United States of America
| | - Mengyuan Gu
- Department of Computer Science, University of California, Santa Barbara, Santa Barbara, California, United States of America
| | - Anand Gupta
- Department of Computer Science, University of California, Santa Barbara, Santa Barbara, California, United States of America
| | - Stefan Hellander
- Department of Computer Science, University of California, Santa Barbara, Santa Barbara, California, United States of America
| | - Chris Horuk
- Department of Computer Science, University of California, Santa Barbara, Santa Barbara, California, United States of America
| | - Dibyendu Nath
- Department of Computer Science, University of California, Santa Barbara, Santa Barbara, California, United States of America
| | - Aviral Takkar
- Department of Computer Science, University of California, Santa Barbara, Santa Barbara, California, United States of America
| | - Sheng Wu
- Department of Computer Science, University of California, Santa Barbara, Santa Barbara, California, United States of America
| | - Per Lötstedt
- Department of Information Technology, Division of Scientific Computing, Uppsala University, Uppsala, Sweden
| | - Chandra Krintz
- Department of Computer Science, University of California, Santa Barbara, Santa Barbara, California, United States of America
| | - Linda R. Petzold
- Department of Computer Science, University of California, Santa Barbara, Santa Barbara, California, United States of America
- Department of Mechanical Engineering, University of California, Santa Barbara, Santa Barbara, California, United States of America
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28
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Drawert B, Hellander A, Bales B, Banerjee D, Bellesia G, Daigle BJ, Douglas G, Gu M, Gupta A, Hellander S, Horuk C, Nath D, Takkar A, Wu S, Lötstedt P, Krintz C, Petzold LR. Stochastic Simulation Service: Bridging the Gap between the Computational Expert and the Biologist. PLoS Comput Biol 2016. [PMID: 27930676 DOI: 10.1371/journal.pcbi] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/11/2023] Open
Abstract
We present StochSS: Stochastic Simulation as a Service, an integrated development environment for modeling and simulation of both deterministic and discrete stochastic biochemical systems in up to three dimensions. An easy to use graphical user interface enables researchers to quickly develop and simulate a biological model on a desktop or laptop, which can then be expanded to incorporate increasing levels of complexity. StochSS features state-of-the-art simulation engines. As the demand for computational power increases, StochSS can seamlessly scale computing resources in the cloud. In addition, StochSS can be deployed as a multi-user software environment where collaborators share computational resources and exchange models via a public model repository. We demonstrate the capabilities and ease of use of StochSS with an example of model development and simulation at increasing levels of complexity.
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Affiliation(s)
- Brian Drawert
- Department of Computer Science, University of California, Santa Barbara, Santa Barbara, California, United States of America
| | - Andreas Hellander
- Department of Information Technology, Division of Scientific Computing, Uppsala University, Uppsala, Sweden
| | - Ben Bales
- Department of Mechanical Engineering, University of California, Santa Barbara, Santa Barbara, California, United States of America
| | - Debjani Banerjee
- Department of Computer Science, University of California, Santa Barbara, Santa Barbara, California, United States of America
| | - Giovanni Bellesia
- Department of Computer Science, University of California, Santa Barbara, Santa Barbara, California, United States of America
| | - Bernie J Daigle
- Departments of Biological Sciences and Computer Science, The University of Memphis, Memphis, Tennessee, United States of America
| | - Geoffrey Douglas
- Department of Computer Science, University of California, Santa Barbara, Santa Barbara, California, United States of America
| | - Mengyuan Gu
- Department of Computer Science, University of California, Santa Barbara, Santa Barbara, California, United States of America
| | - Anand Gupta
- Department of Computer Science, University of California, Santa Barbara, Santa Barbara, California, United States of America
| | - Stefan Hellander
- Department of Computer Science, University of California, Santa Barbara, Santa Barbara, California, United States of America
| | - Chris Horuk
- Department of Computer Science, University of California, Santa Barbara, Santa Barbara, California, United States of America
| | - Dibyendu Nath
- Department of Computer Science, University of California, Santa Barbara, Santa Barbara, California, United States of America
| | - Aviral Takkar
- Department of Computer Science, University of California, Santa Barbara, Santa Barbara, California, United States of America
| | - Sheng Wu
- Department of Computer Science, University of California, Santa Barbara, Santa Barbara, California, United States of America
| | - Per Lötstedt
- Department of Information Technology, Division of Scientific Computing, Uppsala University, Uppsala, Sweden
| | - Chandra Krintz
- Department of Computer Science, University of California, Santa Barbara, Santa Barbara, California, United States of America
| | - Linda R Petzold
- Department of Computer Science, University of California, Santa Barbara, Santa Barbara, California, United States of America
- Department of Mechanical Engineering, University of California, Santa Barbara, Santa Barbara, California, United States of America
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29
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Macnamara CK, Chaplain MAJ. Diffusion driven oscillations in gene regulatory networks. J Theor Biol 2016; 407:51-70. [DOI: 10.1016/j.jtbi.2016.07.021] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2015] [Revised: 06/24/2016] [Accepted: 07/16/2016] [Indexed: 10/21/2022]
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Lawson MJ, Petzold L, Hellander A. Accuracy of the Michaelis-Menten approximation when analysing effects of molecular noise. J R Soc Interface 2016; 12:rsif.2015.0054. [PMID: 25833240 DOI: 10.1098/rsif.2015.0054] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Quantitative biology relies on the construction of accurate mathematical models, yet the effectiveness of these models is often predicated on making simplifying approximations that allow for direct comparisons with available experimental data. The Michaelis-Menten (MM) approximation is widely used in both deterministic and discrete stochastic models of intracellular reaction networks, owing to the ubiquity of enzymatic activity in cellular processes and the clear biochemical interpretation of its parameters. However, it is not well understood how the approximation applies to the discrete stochastic case or how it extends to spatially inhomogeneous systems. We study the behaviour of the discrete stochastic MM approximation as a function of system size and show that significant errors can occur for small volumes, in comparison with a corresponding mass-action system. We then explore some consequences of these results for quantitative modelling. One consequence is that fluctuation-induced sensitivity, or stochastic focusing, can become highly exaggerated in models that make use of MM kinetics even if the approximations are excellent in a deterministic model. Another consequence is that spatial stochastic simulations based on the reaction-diffusion master equation can become highly inaccurate if the model contains MM terms.
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Affiliation(s)
- Michael J Lawson
- Department of Cell and Molecular Biology, Uppsala University, Box 337, Uppsala 75105, Sweden
| | - Linda Petzold
- Department of Computer Science, University of California Santa Barbara, Santa Barbara, CA 93106-5070, USA
| | - Andreas Hellander
- Department of Information Technology, Uppsala University, Box 337, Uppsala 75105, Sweden
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32
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Hellander S, Petzold L. Reaction rates for a generalized reaction-diffusion master equation. Phys Rev E 2016; 93:013307. [PMID: 26871190 DOI: 10.1103/physreve.93.013307] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2015] [Indexed: 11/07/2022]
Abstract
It has been established that there is an inherent limit to the accuracy of the reaction-diffusion master equation. Specifically, there exists a fundamental lower bound on the mesh size, below which the accuracy deteriorates as the mesh is refined further. In this paper we extend the standard reaction-diffusion master equation to allow molecules occupying neighboring voxels to react, in contrast to the traditional approach, in which molecules react only when occupying the same voxel. We derive reaction rates, in two dimensions as well as three dimensions, to obtain an optimal match to the more fine-grained Smoluchowski model and show in two numerical examples that the extended algorithm is accurate for a wide range of mesh sizes, allowing us to simulate systems that are intractable with the standard reaction-diffusion master equation. In addition, we show that for mesh sizes above the fundamental lower limit of the standard algorithm, the generalized algorithm reduces to the standard algorithm. We derive a lower limit for the generalized algorithm which, in both two dimensions and three dimensions, is of the order of the reaction radius of a reacting pair of molecules.
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Affiliation(s)
- Stefan Hellander
- Department of Computer Science, University of California, Santa Barbara, Santa Barbara, California 93106-5070, USA
| | - Linda Petzold
- Department of Computer Science, University of California, Santa Barbara, Santa Barbara, California 93106-5070, USA
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33
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Phillips NE, Manning CS, Pettini T, Biga V, Marinopoulou E, Stanley P, Boyd J, Bagnall J, Paszek P, Spiller DG, White MRH, Goodfellow M, Galla T, Rattray M, Papalopulu N. Stochasticity in the miR-9/Hes1 oscillatory network can account for clonal heterogeneity in the timing of differentiation. eLife 2016; 5:e16118. [PMID: 27700985 PMCID: PMC5050025 DOI: 10.7554/elife.16118] [Citation(s) in RCA: 38] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2016] [Accepted: 08/24/2016] [Indexed: 01/27/2023] Open
Abstract
Recent studies suggest that cells make stochastic choices with respect to differentiation or division. However, the molecular mechanism underlying such stochasticity is unknown. We previously proposed that the timing of vertebrate neuronal differentiation is regulated by molecular oscillations of a transcriptional repressor, HES1, tuned by a post-transcriptional repressor, miR-9. Here, we computationally model the effects of intrinsic noise on the Hes1/miR-9 oscillator as a consequence of low molecular numbers of interacting species, determined experimentally. We report that increased stochasticity spreads the timing of differentiation in a population, such that initially equivalent cells differentiate over a period of time. Surprisingly, inherent stochasticity also increases the robustness of the progenitor state and lessens the impact of unequal, random distribution of molecules at cell division on the temporal spread of differentiation at the population level. This advantageous use of biological noise contrasts with the view that noise needs to be counteracted.
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Affiliation(s)
- Nick E Phillips
- Faculty of Biology, Medicine and Health, University of Manchester, Manchester, United Kingdom
| | - Cerys S Manning
- Faculty of Biology, Medicine and Health, University of Manchester, Manchester, United Kingdom
| | - Tom Pettini
- Faculty of Biology, Medicine and Health, University of Manchester, Manchester, United Kingdom
| | - Veronica Biga
- Faculty of Biology, Medicine and Health, University of Manchester, Manchester, United Kingdom
| | - Elli Marinopoulou
- Faculty of Biology, Medicine and Health, University of Manchester, Manchester, United Kingdom
| | - Peter Stanley
- Faculty of Biology, Medicine and Health, University of Manchester, Manchester, United Kingdom
| | - James Boyd
- Faculty of Biology, Medicine and Health, University of Manchester, Manchester, United Kingdom
| | - James Bagnall
- Faculty of Biology, Medicine and Health, University of Manchester, Manchester, United Kingdom
| | - Pawel Paszek
- Faculty of Biology, Medicine and Health, University of Manchester, Manchester, United Kingdom
| | - David G Spiller
- Faculty of Biology, Medicine and Health, University of Manchester, Manchester, United Kingdom
| | - Michael RH White
- Faculty of Biology, Medicine and Health, University of Manchester, Manchester, United Kingdom
| | - Marc Goodfellow
- College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, United Kingdom,Centre for Biomedical Modelling and Analysis, University of Exeter, Exeter, United Kingdom,EPSRC Centre for Predictive Modelling in Healthcare, University of Exeter, Exeter, United Kingdom
| | - Tobias Galla
- Theoretical Physics, School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom
| | - Magnus Rattray
- Faculty of Biology, Medicine and Health, University of Manchester, Manchester, United Kingdom
| | - Nancy Papalopulu
- Faculty of Biology, Medicine and Health, University of Manchester, Manchester, United Kingdom,
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Is the Cell Nucleus a Necessary Component in Precise Temporal Patterning? PLoS One 2015; 10:e0134239. [PMID: 26226505 PMCID: PMC4520485 DOI: 10.1371/journal.pone.0134239] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2015] [Accepted: 07/07/2015] [Indexed: 11/30/2022] Open
Abstract
One of the functions of the cell nucleus is to help regulate gene expression by controlling molecular traffic across the nuclear envelope. Here we investigate, via stochastic simulation, what effects, if any, does segregation of a system into the nuclear and cytoplasmic compartments have on the stochastic properties of a motif with a negative feedback. One of the effects of the nuclear barrier is to delay the nuclear protein concentration, allowing it to behave in a switch-like manner. We found that this delay, defined as the time for the nuclear protein concentration to reach a certain threshold, has an extremely narrow distribution. To show this, we considered two models. In the first one, the proteins could diffuse freely from cytoplasm to nucleus (simple model); and in the second one, the proteins required assistance from a special class of proteins called importins. For each model, we generated fifty parameter sets, chosen such that the temporal profiles they effectuated were very similar, and whose average threshold time was approximately 150 minutes. The standard deviation of the threshold times computed over one hundred realizations were found to be between 1.8 and 7.16 minutes across both models. To see whether a genetic motif in a prokaryotic cell can achieve this degree of precision, we also simulated five variations on the coherent feed-forward motif (CFFM), three of which contained a negative feedback. We found that the performance of these motifs was nowhere near as impressive as the one found in the eukaryotic cell; the best standard deviation was 6.6 minutes. We argue that the significance of these results, the fact and necessity of spatio-temporal precision in the developmental stages of eukaryotes, and the absence of such a precision in prokaryotes, all suggest that the nucleus has evolved, in part, under the selective pressure to achieve highly predictable phenotypes.
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Hellander S, Hellander A, Petzold L. Reaction rates for mesoscopic reaction-diffusion kinetics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:023312. [PMID: 25768640 PMCID: PMC4854576 DOI: 10.1103/physreve.91.023312] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/01/2014] [Indexed: 05/25/2023]
Abstract
The mesoscopic reaction-diffusion master equation (RDME) is a popular modeling framework frequently applied to stochastic reaction-diffusion kinetics in systems biology. The RDME is derived from assumptions about the underlying physical properties of the system, and it may produce unphysical results for models where those assumptions fail. In that case, other more comprehensive models are better suited, such as hard-sphere Brownian dynamics (BD). Although the RDME is a model in its own right, and not inferred from any specific microscale model, it proves useful to attempt to approximate a microscale model by a specific choice of mesoscopic reaction rates. In this paper we derive mesoscopic scale-dependent reaction rates by matching certain statistics of the RDME solution to statistics of the solution of a widely used microscopic BD model: the Smoluchowski model with a Robin boundary condition at the reaction radius of two molecules. We also establish fundamental limits on the range of mesh resolutions for which this approach yields accurate results and show both theoretically and in numerical examples that as we approach the lower fundamental limit, the mesoscopic dynamics approach the microscopic dynamics. We show that for mesh sizes below the fundamental lower limit, results are less accurate. Thus, the lower limit determines the mesh size for which we obtain the most accurate results.
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Affiliation(s)
- Stefan Hellander
- Department of Computer Science, University of California, Santa Barbara, California 93106-5070, Santa Barbara, USA
| | - Andreas Hellander
- Department of Information Technology, Uppsala University, Box 337, SE-75105, Uppsala, Sweden
| | - Linda Petzold
- Department of Computer Science, University of California, Santa Barbara, California 93106-5070, Santa Barbara, USA
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36
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Rading MM, Sandmann M, Steup M, Chiarugi D, Valleriani A. Weak correlation of starch and volume in synchronized photosynthetic cells. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:012711. [PMID: 25679646 DOI: 10.1103/physreve.91.012711] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/22/2014] [Indexed: 06/04/2023]
Abstract
In cultures of unicellular algae, features of single cells, such as cellular volume and starch content, are thought to be the result of carefully balanced growth and division processes. Single-cell analyses of synchronized photoautotrophic cultures of the unicellular alga Chlamydomonas reinhardtii reveal, however, that the cellular volume and starch content are only weakly correlated. Likewise, other cell parameters, e.g., the chlorophyll content per cell, are only weakly correlated with cell size. We derive the cell size distributions at the beginning of each synchronization cycle considering growth, timing of cell division and daughter cell release, and the uneven division of cell volume. Furthermore, we investigate the link between cell volume growth and starch accumulation. This work presents evidence that, under the experimental conditions of light-dark synchronized cultures, the weak correlation between both cell features is a result of a cumulative process rather than due to asymmetric partition of biomolecules during cell division. This cumulative process necessarily limits cellular similarities within a synchronized cell population.
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Affiliation(s)
- M Michael Rading
- Department of Theory and Bio-Systems, Max Planck Institute of Colloids and Interfaces, 14476 Potsdam, Germany
| | - Michael Sandmann
- innoFSPEC, Institut für Chemie, Universität Potsdam, Physikalische Chemie, 14476 Potsdam, Germany
| | - Martin Steup
- Department of Molecular and Cellular Biology, College of Biological Science, University of Guelph, Guelph, Ontario, Canada N1G 2W1
| | - Davide Chiarugi
- Department of Theory and Bio-Systems, Max Planck Institute of Colloids and Interfaces, 14476 Potsdam, Germany
| | - Angelo Valleriani
- Department of Theory and Bio-Systems, Max Planck Institute of Colloids and Interfaces, 14476 Potsdam, Germany
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Puszynski K, Gandolfi A, d'Onofrio A. The pharmacodynamics of the p53-Mdm2 targeting drug Nutlin: the role of gene-switching noise. PLoS Comput Biol 2014; 10:e1003991. [PMID: 25504419 PMCID: PMC4263360 DOI: 10.1371/journal.pcbi.1003991] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/26/2013] [Accepted: 10/19/2014] [Indexed: 12/13/2022] Open
Abstract
In this work we investigate, by means of a computational stochastic model, how tumor cells with wild-type p53 gene respond to the drug Nutlin, an agent that interferes with the Mdm2-mediated p53 regulation. In particular, we show how the stochastic gene-switching controlled by p53 can explain experimental dose-response curves, i.e., the observed inter-cell variability of the cell viability under Nutlin action. The proposed model describes in some detail the regulation network of p53, including the negative feedback loop mediated by Mdm2 and the positive loop mediated by PTEN, as well as the reversible inhibition of Mdm2 caused by Nutlin binding. The fate of the individual cell is assumed to be decided by the rising of nuclear-phosphorylated p53 over a certain threshold. We also performed in silico experiments to evaluate the dose-response curve after a single drug dose delivered in mice, or after its fractionated administration. Our results suggest that dose-splitting may be ineffective at low doses and effective at high doses. This complex behavior can be due to the interplay among the existence of a threshold on the p53 level for its cell activity, the nonlinearity of the relationship between the bolus dose and the peak of active p53, and the relatively fast elimination of the drug. P53 is an antitumor gene regulating vital cellular functions such as repair of DNA damage, cellular suicide, and cell proliferation: in many tumors p53 is lowly expressed and/or mutated. Drugs targeting the biomolecular network of p53 are becoming important. The network includes the key proteins Mdm2 and PTEN, whose production is regulated by p53, and which, in turn, enact positive and negative feedbacks on p53. Drug Nutlin, inhibiting the p53 inhibitor Mdm2, might be important for tumors where p53 is underproduced but unmutated. We investigate the cellular mechanism of action of Nutlin. The basic concept of our mathematical model is that the experimentally observed cell-to-cell variability of Nutlin efficacy is caused by the randomness of gene activation/deactivation of Mdmd2 and PTEN. Indeed, the abundance/scarceness of p53 regulates the probability that the relative genes are active or inactive. The model reproduced the experimental cell-specific response to different doses of Nutlin (dose-response curves) in some types of tumor cells. Much clinical research focus on 'metronomic' drug delivery regimens, where instead of giving large doses with long intervals, smaller doses are frequently delivered. In our simulations, dose-splitting of Nutlin produced a response generally worse than the response to a single dose.
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Affiliation(s)
- Krzysztof Puszynski
- Silesian University of Technology, Institute of Automatic Control, Gliwice, Poland
| | - Alberto Gandolfi
- Istituto di Analisi dei Sistemi ed Informatica "A. Ruberti" - CNR, Rome, Italy
| | - Alberto d'Onofrio
- Department of Experimental Oncology, European Institute of Oncology, Milan, Italy
- International Prevention Research Institute, Lyon, France
- * E-mail:
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38
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Mathematical modeling of the intracellular protein dynamics: The importance of active transport along microtubules. J Theor Biol 2014; 363:118-28. [DOI: 10.1016/j.jtbi.2014.07.022] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/13/2014] [Revised: 06/13/2014] [Accepted: 07/22/2014] [Indexed: 01/26/2023]
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39
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Parallel solutions for voxel-based simulations of reaction-diffusion systems. BIOMED RESEARCH INTERNATIONAL 2014; 2014:980501. [PMID: 25045716 PMCID: PMC4082941 DOI: 10.1155/2014/980501] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/21/2014] [Revised: 05/12/2014] [Accepted: 05/18/2014] [Indexed: 11/25/2022]
Abstract
There is an increasing awareness of the pivotal role of noise in biochemical processes and of the effect of molecular crowding on the dynamics of biochemical systems. This necessity has given rise to a strong need for suitable and sophisticated algorithms for the simulation of biological phenomena taking into account both spatial effects and noise. However, the high computational effort characterizing simulation approaches, coupled with the necessity to simulate the models several times to achieve statistically relevant information on the model behaviours, makes such kind of algorithms very time-consuming for studying real systems. So far, different parallelization approaches have been deployed to reduce the computational time required to simulate the temporal dynamics of biochemical systems using stochastic algorithms. In this work we discuss these aspects for the spatial TAU-leaping in crowded compartments (STAUCC) simulator, a voxel-based method for the stochastic simulation of reaction-diffusion processes which relies on the Sτ-DPP algorithm. In particular we present how the characteristics of the algorithm can be exploited for an effective parallelization on the present heterogeneous HPC architectures.
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40
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Hellander A, Lawson MJ, Drawert B, Petzold L. Local error estimates for adaptive simulation of the Reaction-Diffusion Master Equation via operator splitting. JOURNAL OF COMPUTATIONAL PHYSICS 2014; 266:89-100. [PMID: 26865735 PMCID: PMC4746020 DOI: 10.1016/j.jcp.2014.02.004] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
The efficiency of exact simulation methods for the reaction-diffusion master equation (RDME) is severely limited by the large number of diffusion events if the mesh is fine or if diffusion constants are large. Furthermore, inherent properties of exact kinetic-Monte Carlo simulation methods limit the efficiency of parallel implementations. Several approximate and hybrid methods have appeared that enable more efficient simulation of the RDME. A common feature to most of them is that they rely on splitting the system into its reaction and diffusion parts and updating them sequentially over a discrete timestep. This use of operator splitting enables more efficient simulation but it comes at the price of a temporal discretization error that depends on the size of the timestep. So far, existing methods have not attempted to estimate or control this error in a systematic manner. This makes the solvers hard to use for practitioners since they must guess an appropriate timestep. It also makes the solvers potentially less efficient than if the timesteps are adapted to control the error. Here, we derive estimates of the local error and propose a strategy to adaptively select the timestep when the RDME is simulated via a first order operator splitting. While the strategy is general and applicable to a wide range of approximate and hybrid methods, we exemplify it here by extending a previously published approximate method, the Diffusive Finite-State Projection (DFSP) method, to incorporate temporal adaptivity.
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Affiliation(s)
- Andreas Hellander
- Department of Information Technology, Uppsala University, Box 337, SE-75105, Uppsala, Sweden
| | - Michael J Lawson
- Department of Computer Science, University of California Santa Barbara, Santa Barbara, CA 93106-5070, USA
| | - Brian Drawert
- Department of Computer Science, University of California Santa Barbara, Santa Barbara, CA 93106-5070, USA
| | - Linda Petzold
- Department of Computer Science, University of California Santa Barbara, Santa Barbara, CA 93106-5070, USA
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41
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Kobayashi H. Imprinting genes associated with endometriosis. EXCLI JOURNAL 2014; 13:252-64. [PMID: 26417259 PMCID: PMC4464490] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/29/2014] [Accepted: 02/19/2014] [Indexed: 11/30/2022]
Abstract
PURPOSE Much work has been carried out to investigate the genetic and epigenetic basis of endometriosis and proposed that endometriosis has been described as an epigenetic disease. The purpose of this study was to extract the imprinting genes that are associated with endometriosis development. METHODS The information on the imprinting genes can be accessed publicly from a web-based interface at http://www.geneimprint.com/site/genes-by-species. RESULTS In the current version, the database contains 150 human imprinted genes derived from the literature. We searched gene functions and their roles in particular biological processes or events, such as development and pathogenesis of endometriosis. From the genomic imprinting database, we picked 10 genes that were highly associated with female reproduction; prominent among them were paternally expressed genes (DIRAS3, BMP8B, CYP1B1, ZFAT, IGF2, MIMT1, or MIR296) and maternally expressed genes (DVL1, FGFRL1, or CDKN1C). These imprinted genes may be associated with reproductive biology such as endometriosis, pregnancy loss, decidualization process and preeclampsia. DISCUSSION This study supports the possibility that aberrant epigenetic dysregulation of specific imprinting genes may contribute to endometriosis predisposition.
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Affiliation(s)
- Hiroshi Kobayashi
- Department of Obstetrics and Gynecology, Nara Medical University, Nara, Japan
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42
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Roberts E. Cellular and molecular structure as a unifying framework for whole-cell modeling. Curr Opin Struct Biol 2014; 25:86-91. [PMID: 24509245 DOI: 10.1016/j.sbi.2014.01.005] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2013] [Accepted: 01/07/2014] [Indexed: 10/25/2022]
Abstract
Whole-cell modeling has the potential to play a major role in revolutionizing our understanding of cellular biology over the next few decades. A computational model of the entire cell would allow cellular biologists to integrate data from many disparate sources in a single consistent framework. Such a comprehensive model would be useful both for hypothesis testing and in the discovery of new behaviors that emerge from complex biological networks. Cellular and molecular structure can and should be a key organizing principle in a whole-cell model, connecting models across time and length scales in a multiscale approach. Here I present a summary of recent research centered around using molecular and cellular structure to model the behavior of cells.
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Affiliation(s)
- Elijah Roberts
- Department of Biophysics, Johns Hopkins University, Baltimore, MD 21218, USA.
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43
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Eliaš J, Dimitrio L, Clairambault J, Natalini R. The p53 protein and its molecular network: modelling a missing link between DNA damage and cell fate. BIOCHIMICA ET BIOPHYSICA ACTA-PROTEINS AND PROTEOMICS 2013; 1844:232-47. [PMID: 24113167 DOI: 10.1016/j.bbapap.2013.09.019] [Citation(s) in RCA: 44] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2013] [Revised: 09/23/2013] [Accepted: 09/25/2013] [Indexed: 12/29/2022]
Abstract
Various molecular pharmacokinetic-pharmacodynamic (PK-PD) models have been proposed in the last decades to represent and predict drug effects in anticancer chemotherapies. Most of these models are cell population based since clearly measurable effects of drugs can be seen much more easily on populations of cells, healthy and tumour, than in individual cells. The actual targets of drugs are, however, cells themselves. The drugs in use either disrupt genome integrity by causing DNA strand breaks, and consequently initiate programmed cell death, or block cell proliferation mainly by inhibiting factors that enable cells to proceed from one cell cycle phase to the next through checkpoints in the cell division cycle. DNA damage caused by cytotoxic drugs (and also cytostatic drugs at high concentrations) activates, among others, the p53 protein-modulated signalling pathways that directly or indirectly force the cell to make a decision between survival and death. The paper aims to become the first-step in a larger scale enterprise that should bridge the gap between intracellular and population PK-PD models, providing oncologists with a rationale to predict and optimise the effects of anticancer drugs in the clinic. So far, it only sticks at describing p53 activation and regulation in single cells following their exposure to DNA damaging stress agents. We show that p53 oscillations that have been observed in individual cells can be reconstructed and predicted by compartmentalising cellular events occurring after DNA damage, either in the nucleus or in the cytoplasm, and by describing network interactions, using ordinary differential equations (ODEs), between the ATM, p53, Mdm2 and Wip1 proteins, in each compartment, nucleus or cytoplasm, and between the two compartments. This article is part of a Special Issue entitled: Computational Proteomics, Systems Biology & Clinical Implications.
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Affiliation(s)
- Ján Eliaš
- UPMC, Laboratoire Jacques-Louis Lions, 4 Place Jussieu, F-75005 Paris, France; INRIA Paris-Rocquencourt, Bang project-team, Paris and Rocquencourt, France.
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Sturrock M, Hellander A, Aldakheel S, Petzold L, Chaplain MAJ. The role of dimerisation and nuclear transport in the Hes1 gene regulatory network. Bull Math Biol 2013; 76:766-98. [PMID: 23686434 DOI: 10.1007/s11538-013-9842-5] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/20/2012] [Accepted: 04/05/2013] [Indexed: 02/06/2023]
Abstract
Hes1 is a member of the family of basic helix-loop-helix transcription factors and the Hes1 gene regulatory network (GRN) may be described as the canonical example of transcriptional control in eukaryotic cells, since it involves only the Hes1 protein and its own mRNA. Recently, the Hes1 protein has been established as an excellent target for an anti-cancer drug treatment, with the design of a small molecule Hes1 dimerisation inhibitor representing a promising if challenging approach to therapy. In this paper, we extend a previous spatial stochastic model of the Hes1 GRN to include nuclear transport and dimerisation of Hes1 monomers. Initially, we assume that dimerisation occurs only in the cytoplasm, with only dimers being imported into the nucleus. Stochastic simulations of this novel model using the URDME software show that oscillatory dynamics in agreement with experimental studies are retained. Furthermore, we find that our model is robust to changes in the nuclear transport and dimerisation parameters. However, since the precise dynamics of the nuclear import of Hes1 and the localisation of the dimerisation reaction are not known, we consider a second modelling scenario in which we allow for both Hes1 monomers and dimers to be imported into the nucleus, and we allow dimerisation of Hes1 to occur everywhere in the cell. Once again, computational solutions of this second model produce oscillatory dynamics in agreement with experimental studies. We also explore sensitivity of the numerical solutions to nuclear transport and dimerisation parameters. Finally, we compare and contrast the two different modelling scenarios using numerical experiments that simulate dimer disruption, and suggest a biological experiment that could distinguish which model more faithfully captures the Hes1 GRN.
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45
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Gillespie DT, Hellander A, Petzold LR. Perspective: Stochastic algorithms for chemical kinetics. J Chem Phys 2013; 138:170901. [PMID: 23656106 PMCID: PMC3656953 DOI: 10.1063/1.4801941] [Citation(s) in RCA: 165] [Impact Index Per Article: 15.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2013] [Accepted: 03/25/2013] [Indexed: 11/14/2022] Open
Abstract
We outline our perspective on stochastic chemical kinetics, paying particular attention to numerical simulation algorithms. We first focus on dilute, well-mixed systems, whose description using ordinary differential equations has served as the basis for traditional chemical kinetics for the past 150 years. For such systems, we review the physical and mathematical rationale for a discrete-stochastic approach, and for the approximations that need to be made in order to regain the traditional continuous-deterministic description. We next take note of some of the more promising strategies for dealing stochastically with stiff systems, rare events, and sensitivity analysis. Finally, we review some recent efforts to adapt and extend the discrete-stochastic approach to systems that are not well-mixed. In that currently developing area, we focus mainly on the strategy of subdividing the system into well-mixed subvolumes, and then simulating diffusional transfers of reactant molecules between adjacent subvolumes together with chemical reactions inside the subvolumes.
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Affiliation(s)
- Daniel T Gillespie
- Dan T Gillespie Consulting, 30504 Cordoba Pl., Castaic, California 91384, USA.
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