Models in biology: lessons from modeling regulation of the eukaryotic cell cycle

In this essay we illustrate some general principles of mathematical modeling in biology by our experiences in studying the molecular regulatory network underlying eukaryotic cell division. We discuss how and why the models moved from simple, parsimonious cartoons to more complex, detailed mechanisms with many kinetic parameters. We describe how the mature models made surprising and informative predictions about the control system that were later confirmed experimentally. Along the way, we comment on the ‘parameter estimation problem’ and conclude with an appeal for a greater role for mathematical models in molecular cell biology.

• Publication year

  2015

• Venue

  BMC Biology

• Publication date

  2015-07-01

• Fields of study

  Biology, Mathematics, Medicine

• Identifiers
  DOI 10.1186/s12915-015-0158-9PMID 26129844PMCID 4486427
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

• Bistability, Oscillations, and Traveling Waves in Frog Egg Extracts

  2015cited by this paper
• Models in biology: ‘accurate descriptions of our pathetic thinking’

  2014influential reference
• The BEG (PP2A-B55/ENSA/Greatwall) Pathway Ensures Cytokinesis follows Chromosome Separation

  2013cited by this paper
• Greatwall is essential to prevent mitotic collapse after nuclear envelope breakdown in mammals

  2013cited by this paper
• The Cdk1–APC/C cell cycle oscillator circuit functions as a time-delayed, ultrasensitive switch

  2013cited by this paper
• Mitotic trigger waves and the spatial coordination of the Xenopus cell cycle

  2013influential reference
• Role for regulated phosphatase activity in generating mitotic oscillations in Xenopus cell-free extracts

  2013influential reference
• Adaptation to the spindle checkpoint is regulated by the interplay between Cdc28/Clbs and PP2ACdc55

  2013cited by this paper
• Sli15INCENP Dephosphorylation Prevents Mitotic Checkpoint Reengagement Due to Loss of Tension at Anaphase Onset

  2010cited by this paper
• Cohesin cleavage and Cdk inhibition trigger formation of daughter nuclei

  2010cited by this paper
• The Substrate of Greatwall Kinase, Arpp19, Controls Mitosis by Inhibiting Protein Phosphatase 2A

  2010cited by this paper
• Greatwall Phosphorylates an Inhibitor of Protein Phosphatase 2Α That Is Essential for Mitosis

  2010cited by this paper
• Structural basis for recognition of 5′-phosphotyrosine adducts by TDP2

  2009cited by this paper
• Greatwall maintains mitosis through regulation of PP2A

  2009cited by this paper
• Irreversible cell-cycle transitions are due to systems-level feedback

  2007cited by this paper
• Greatwall kinase participates in the Cdc2 autoregulatory loop in Xenopus egg extracts.

  2006cited by this paper
• Building a cell cycle oscillator: hysteresis and bistability in the activation of Cdc2

  2003cited by this paper
• Hysteresis drives cell-cycle transitions in Xenopus laevis egg extracts

  2002cited by this paper
• Testing a mathematical model of the yeast cell cycle.

  2002cited by this paper
• Kinetic analysis of a molecular model of the budding yeast cell cycle.

  2000cited by this paper
• Cytoplasmic control of nuclear behavior during meiotic maturation of frog oocytes *

  1998cited by this paper
• Modeling M-phase control in Xenopus oocyte extracts: the surveillance mechanism for unreplicated DNA.

  1998cited by this paper
• Modeling the control of DNA replication in fission yeast.

  1997cited by this paper
• Quantitative analysis of a molecular model of mitotic control in fission yeast

  1995cited by this paper
• Control of the Cdc2/cyclin B complex in Xenopus egg extracts arrested at a G2/M checkpoint with DNA synthesis inhibitors.

  1995cited by this paper
• Numerical analysis of a comprehensive model of M-phase control in Xenopus oocyte extracts and intact embryos.

  1993cited by this paper
• Modeling the Cell Division Cycle: M-phase Trigger, Oscillations, and Size Control

  1993cited by this paper
• Modeling the cell division cycle: cdc2 and cyclin interactions.

  1991influential reference
• A minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase.

  1991influential reference
• A model for the adjustment of the mitotic clock by cyclin and MPF levels.

  1991influential reference
• Cyclin is a component of maturation-promoting factor from Xenopus.

  1990cited by this paper
• Triggering of cyclin degradation in interphase extracts of amphibian eggs by cdc2 kinase

  1990influential reference
• Universal control mechanism regulating onset of M-phase

  1990influential reference
• Cyclin activation of p34cdc2.

  1990cited by this paper
• Cyclin synthesis drives the early embryonic cell cycle

  1989influential reference
• The role of cyclin synthesis and degradation in the control of maturation promoting factor activity

  1989cited by this paper
• Dominoes and clocks: the union of two views of the cell cycle.

  1989influential reference
• The Xenopus cdc2 protein is a component of MPF, a cytoplasmic regulator of mitosis.

  1988cited by this paper
• Purified maturation-promoting factor contains the product of a Xenopus homolog of the fission yeast cell cycle control gene cdc2+.

  1988cited by this paper
• Purification of maturation-promoting factor, an intracellular regulator of early mitotic events.

  1988cited by this paper
• Cell cycle dynamics of an M-phase-specific cytoplasmic factor in Xenopus laevis oocytes and eggs

  1984cited by this paper
• An amplified sensitivity arising from covalent modification in biological systems.

  1981cited by this paper
• Cytoplasmic control of nuclear behavior during meiotic maturation of frog oocytes.

  1971cited by this paper

• Systematic Analysis of Network-driven Adaptive Resistance to CDK4/6 and Estrogen Receptor Inhibition using Meta-Dynamic Network Modelling

  2025cites this paper
• 3D confinement physically regulates cell cycle progression in budding yeast

  2025cites this paper
• Dynamic modelling of cell cycle arrest through integrated single-cell and mathematical modelling approaches

  2025cites this paper
• Dynamic Modeling of Cell Cycle Arrest Through Integrated Single-Cell and Mathematical Modelling Approaches

  2025cites this paper
• Measuring Regulatory Network Inheritance in Dividing Yeast Cells Using Ordinary Differential Equations

  2025cites this paper
• Nonlinear dynamics of tumor cell cycles: From mathematical models to therapeutic insights

  2024cites this paper
• Comprehensive Parameter Space Mapping of Cell Cycle Dynamics under Network Perturbations.

  2024cites this paper
• Overview of DISCOVER22 experiment in the framework of INFN-LNGS Cosmic Silence activity: challenges and improvements in underground radiobiology

  2023cites this paper
• Modelling how plant cell-cycle progression leads to cell size regulation

  2023cites this paper
• Modeling transcriptional regulation of the cell cycle using a novel cybernetic-inspired approach

  2023cites this paper
• Modeling transcriptional regulation of the cell cycle using a novel cybernetic-inspired approach

  2023cites this paper
• A two-galectin network establishes mesenchymal condensation phenotype in limb development.

  2023cites this paper
• Patterning, From Conifers to Consciousness: Turing’s Theory and Order From Fluctuations

  2022cites this paper
• Modeling the effects of SARS-CoV-2 infection on the mTOR signaling pathway

  2022cites this paper
• Bilateral Feedback in Oscillator Model Is Required to Explain the Coupling Dynamics of Hes1 with the Cell Cycle

  2022cites this paper
• Mechanisms of cellular mRNA transcript homeostasis.

  2022cites this paper
• Long-Term Social Isolation-Induced Autophagy Inhibition and Cell Senescence Aggravate Cognitive Impairment in D(+)Galactose-Treated Male Mice

  2022cites this paper
• Mitotic spindle: lessons from theoretical modeling

  2021cites this paper
• Regulated Multiset Rewriting Systems

  2021cites this paper
• Mitotic Cycle Regulation. I. Oscillations and Bistability

  2021cites this paper
• Cell Cycle Regulation. Bifurcation Theory

  2021cites this paper
• Precartilage condensation during limb skeletogenesis occurs by tissue phase separation controlled by a bistable cell-state switch with suppressed oscillatory dynamics

  2021cites this paper
• Dynamical Modularity of the Genotype-Phenotype Map

  2021cites this paper
• New Methodologies to Study DNA Repair Processes in Space and Time Within Living Cells

  2021cites this paper
• Root locus-based stability analysis for biological systems

  2021cites this paper
• Cell cycle regulation by complex nanomachines

  2021cites this paper
• Dynamical modules in metabolism, cell and developmental biology

  2021cites this paper
• Systems-level modeling of meiotic regulatory network in fission yeast

  2021cites this paper
• Guidelines for the use and interpretation of assays for monitoring autophagy (4th edition)1

  2021cites this paper
• BCNNM: A Framework for in silico Neural Tissue Development Modeling

  2021cites this paper
• The Impact of Formal Reasoning in Computational Biology

  2020cites this paper
• Network mechanisms and dysfunction within an integrated computational model of progression through mitosis in the human cell cycle

  2020cites this paper
• CDKD-dependent activation of CDKA;1 controls microtubule dynamics and cytokinesis during meiosis

  2020cites this paper
• Modeling the Control of Meiotic Cell Divisions: Entry, Progression, and Exit.

  2020cites this paper
• Sequential adjustment of cytotoxic T lymphocyte densities improves efficacy in controlling tumor growth

  2019cites this paper
• Dissipation in Non-Steady State Regulatory Circuits

  2019cites this paper
• Cell differentiation: what have we learned in 50 years?

  2019cites this paper
• Quantitative Modelling Approaches

  2019cites this paper
• Mathematical modelling reveals unexpected inheritance and variability patterns of cell cycle parameters in mammalian cells

  2019cites this paper
• Time varying causal network reconstruction of a mouse cell cycle

  2019cites this paper
• A checkpoint-oriented cell cycle simulation model

  2019cites this paper
• Practical steps to digital organism models, from laboratory model species to 'Crops in silico.

  2019cites this paper
• Life Sciences Use Case: Initial Requirements and Scenario Definitions Work Package 1 Task 1.1-1.2 Deliverable 1.1

  2019cites this paper
• A Mathematical Model for the Effect of Low-Dose Radiation on the G2/M Transition

  2019cites this paper
• Developing context appropriate toxicity testing approaches using new alternative methods (NAMs).

  2019cites this paper
• Expression of Cyclin-D1 in Astrocytes Varies During Aging

  2018cites this paper
• A Toolbox for Discrete Modelling of Cell Signalling Dynamics

  2018cites this paper
• Bistability analysis in mathematical model of M-phase control in Xenopus oocyte extracts

  2018cites this paper
• Chemical Waves in Embryonic Cell Cycles

  2018cites this paper
• Waveforms of molecular oscillations reveal circadian timekeeping mechanisms

  2018cites this paper
• Smarten up computational intelligence to decipher time series data

  2018cites this paper
• Structural and functional characterisation of cyclin dependent kinase 1 containing complexes

  2018cites this paper
• JigCell Model Connector: building large molecular network models from components

  2018cites this paper
• Integration of Multiple Metabolic Signals Determines Cell Fate Prior to Commitment.

  2018cites this paper
• A Brief History of Eukaryotic Cell Cycle Research

  2018cites this paper
• Entrainment of a Bacterial Synthetic Gene Oscillator through Proteolytic Queueing.

  2017cites this paper
• Cell size homeostasis in animal cells

  2017cites this paper
• A minimal “push–pull” bistability model explains oscillations between quiescent and proliferative cell states

  2017cites this paper
• The dynamics of intracellular water constrains glycolytic oscillations in Saccharomyces cerevisiae

  2017cites this paper
• Multiple inputs ensure yeast cell size homeostasis during cell cycle progression

  2017cites this paper
• Bistability analysis in mathematical model of M-phase control in Xenopus oocyte extracts

  2017cites this paper
• The Design Space of the Embryonic Cell Cycle Oscillator.

  2017cites this paper
• Cell cycle proliferation decisions: the impact of single cell analyses

  2017cites this paper
• Mathematical Models for Understanding Dynamic Cellular Systems

  2017cites this paper
• PREDICTIVE COMPUTATIONAL APPROACHES FOR ANTIGROWTH SIANAL INDUCED CELL CYCLE

  2016cites this paper
• Structured population models with internal cell cycle

  2016cites this paper
• Theoretical and Computational Studies on the Dynamics and Regulation of Cell Phenotypic Transitions

  2016cites this paper
• Logical model specification aided by model-checking techniques: application to the mammalian cell cycle regulation

  2016cites this paper
• Logical Modeling and Dynamical Analysis of Cellular Networks

  2016cites this paper
• Protein sequestration versus Hill-type repression in circadian clock models.

  2016cites this paper
• Model Building by Temporal Logic Constraint Solving : Investigation of the Coupling between the Cell Cycle and the Circadian Clock

  2016cites this paper
• Phenotypic models of T cell activation

  2014cites this paper