Modeling the cell cycle: From deterministic models to hybrid systems

Alfieri, Roberta; Bartocci, Ezio; Merelli, Emanuela; Milanesi, Luciano

doi:10.1016/j.biosystems.2011.03.002

Cited by 14 publications

(31 citation statements)

References 31 publications

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“…We have studied the system (36) analytically and numerically. The numerical simulations confirm the criteria of cycle existence both for small ε and for ε = O (1). For small epsilon the cycle has a singular structure.…”

Section: Tropical Equilibrations and Model Reductionsupporting

confidence: 67%

“…The first method was proposed in [15] and can be applied to any rational ODE system defined by (1),(2): Definition 2. 1 We call complete tropicalization of the smooth ODE system (1),(2) the following piecewisesmooth system:…”

Section: Tropical Geometry and Hybridization 21 General Settingsmentioning

confidence: 99%

“…The model has been used to reproduce flow cytometry data. Instead of building the hybrid model from scratch, another strategy is to identify hybrid models from experimental or artificial time series [16,17,1]. The resulting cell cycle hybrid models can be used for hypothesis testing, as they are or as parts of larger, integrated models.…”

Section: Introductionmentioning

confidence: 99%

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Hybrid models of the cell cycle molecular machinery

Noël

Grigoriev

Vakulenko

et al. 2012

Electron. Proc. Theor. Comput. Sci.

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Piecewise smooth hybrid systems, involving continuous and discrete variables, are suitable models for describing the multiscale regulatory machinery of the biological cells. In hybrid models, the discrete variables can switch on and off some molecular interactions, simulating cell progression through a series of functioning modes. The advancement through the cell cycle is the archetype of such an organized sequence of events. We present an approach, inspired from tropical geometry ideas, allowing to reduce, hybridize and analyse cell cycle models consisting of polynomial or rational ordinary differential equations

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Section: Tropical Equilibrations and Model Reductionsupporting

confidence: 67%

Section: Tropical Geometry and Hybridization 21 General Settingsmentioning

confidence: 99%

See 1 more Smart Citation

Hybrid models of the cell cycle molecular machinery

Noël

Grigoriev

Vakulenko

et al. 2012

Electron. Proc. Theor. Comput. Sci.

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“…Table 1A provides a sense of the compatibility of some key analytical tools for a broad variety of model classes. To construct this table, we relied on an extensive literature survey of each model class and tool (White, 1977; Dytham, 1995; Bengtsson et al, 1996; Henzinger et al, 1997; Cozman, 1997; Ghosh and Tomlin, 2001; Alur et al, 2001; Bandini et al, 2001; Barton and Lee, 2002; Sutner, 2002, 2009; Wang et al, 2002; Antoniotti et al, 2003a,b; Shmulevich et al, 2003; Ghosh et al, 2003; Friedman and Koller, 2003; Lincoln and Tiwari, 2004; Janes et al, 2004; Friedman, 2004; Li and Chan, 2004; Kwiatkowska et al, 2004; Ihekwaba et al, 2004; Hagiya et al, 2004; Das et al, 2004; Pe’er, 2005; Fauré et al, 2006; Reeves et al, 2006; Langmead et al, 2006; Kim et al, 2006; Chaouiya, 2007; Saez-Rodriguez et al, 2007; Fränzle and Herde, 2007; Narasimhan and Biswas, 2007; Wilkinson, 2007; Sandmann, 2007; Mukherjee and Speed, 2008; Clarke et al, 2008; Sandmann and Wolf, 2008; Ryu et al, 2008; Donaldson and Gilbert, 2008; Figueirêdo et al, 2008; Yuceer et al, 2008; Qian and Dougherty, 2009; Tatyana et al, 2009; Wartlick et al, 2009; Sobie, 2009; Langmead, 2009; Didier et al, 2009; Müssel et al, 2010; Sarkar and Sobie, 2010; Campagna and Piazza, 2010; Bortolussi and Policriti, 2010; Garmaroudi et al, 2010; Yang and Lin, 2010; Donzé et al, 2010; Gunawardena, 2010; Vikram et al, 2010; Kobayashi and Hiraishi, 2010, 2011; Gong et al, 2010, 2011a,b,c; Dimitrova et al, 2011; Grosu et al, 2011; Alfieri et al, 2011; Fischer and Kaiser, 20...…”

Section: Models and Tools For Cell-autonomous Dynamic Processesmentioning

confidence: 99%

“…The HA contains discrete modes, each of whose dynamics is modeled by a simpler ODE model. This transformation has been defined and used in Alfieri et al (2011), Grosu et al (2011), and Noel et al (2011). Alternatively, the ODE dynamics may be very steep.…”

Section: Models and Tools For Heterogeneous Population Dynamicsmentioning

confidence: 99%

Systems Biology of Cancer: A Challenging Expedition for Clinical and Quantitative Biologists

Korsunsky

McGovern

LaGatta

et al. 2014

Front. Bioeng. Biotechnol.

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A systems-biology approach to complex disease (such as cancer) is now complementing traditional experience-based approaches, which have typically been invasive and expensive. The rapid progress in biomedical knowledge is enabling the targeting of disease with therapies that are precise, proactive, preventive, and personalized. In this paper, we summarize and classify models of systems biology and model checking tools, which have been used to great success in computational biology and related fields. We demonstrate how these models and tools have been used to study some of the twelve biochemical pathways implicated in but not unique to pancreatic cancer, and conclude that the resulting mechanistic models will need to be further enhanced by various abstraction techniques to interpret phenomenological models of cancer progression.

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Computationally modelling cell proliferation: A review

Barbosa

Belinha

Jorge

et al. 2023

Numer Methods Biomed Eng

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Cell proliferation is vital for the development and homeostasis of the human body. For such to occur, cells go through the cell cycle during which they replicate their genetic material and ultimately complete cellular division, when one cell divides into two new cells with equal genetic material. However, if there are some errors or abnormalities during the cell cycle that disrupt the balance between cell death and proliferation, severe problems can occur, such as tumour development, which is currently one of the leading causes of death in the world. Nowadays, mathematical and computational models are used to understand and study several biological mechanisms and processes, namely cellular proliferation. Over the last forty-five years, several models have attempted to describe cell proliferation and its regulation. Due to the complexity of the process, numerous assumptions and simplifications have been considered. This work presents a review of some of these models, focusing mainly on mammalian or generic eukaryotic models. Previously published continuum, discrete and hybrid approaches are presented and compared, in order to understand and highlight the relevance and capabilities of these models, their shortcomings and future challenges.

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Modeling the cell cycle: From deterministic models to hybrid systems

Cited by 14 publications

References 31 publications

Hybrid models of the cell cycle molecular machinery

Hybrid models of the cell cycle molecular machinery

Systems Biology of Cancer: A Challenging Expedition for Clinical and Quantitative Biologists

Computationally modelling cell proliferation: A review

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