Although not a traditional experimental "method," mathematical modeling can provide a powerful approach for investigating complex cell signaling networks, such as those that regulate the eukaryotic cell division cycle. We describe here one modeling approach based on expressing the rates of biochemical reactions in terms of nonlinear ordinary differential equations. We discuss the steps and challenges in assigning numerical values to model parameters and the importance of experimental testing of a mathematical model. We illustrate this approach throughout with the simple and well-characterized example of mitotic cell cycles in frog egg extracts. To facilitate new modeling efforts, we describe several publicly available modeling environments, each with a collection of integrated programs for mathematical modeling. This review is intended to justify the place of mathematical modeling as a standard method for studying molecular regulatory networks and to guide the non-expert to initiate modeling projects in order to gain a systems-level perspective for complex control systems.
Control of the Cdc2/cyclin B complex in Xenopus egg extracts arrested at a G2/M checkpoint with DNA synthesis inhibitors
Modeling M-phase control in Xenopus oocyte extracts: the surveillance mechanism for unreplicated DNA
Non-linear optimization of biochemical pathways: applications to metabolic engineering and parameter estimation
MEG (Model Extender for Gepasi): a program for the modelling of complex, heterogeneous, cellular systems
The systems biology markup language (SBML): a medium for representation and exchange of biochemical network models
Systems-level dissection of the cell-cycle oscillator: bypassing positive feedback produces damped oscillations
Mathematical formalisms based on approximated kinetic representations for modeling genetic and metabolic pathways
Mathematical modeling of fission yeast Schizosaccharomyces pombe cell cycle: exploring the role of multiple phosphatases
Effect of localization, length and orientation of chondrocytic primary cilium on murine growth plate organization
Mapping the architecture of the HIV-1 Tat circuit: A decision-making circuit that lacks bistability and exploits stochastic noise
Bridging the gap between in vitro and in vivo: Dose and schedule predictions for the ATR inhibitor AZD6738
Interoperability of time series cytometric data: a cross platform approach for modeling tumor heterogeneity
Drivers of structural features in gene regulatory networks: From biophysical constraints to biological function
An Îto stochastic differential equations model for the dynamics of the MCF-7 breast cancer cell line treated by radiotherapy
A signal transduction score flow algorithm for cyclic cellular pathway analysis, which combines transcriptome and ChIP-seq data
Network mechanisms and dysfunction within an integrated computational model of progression through mitosis in the human cell cycle
New insights into mammalian signaling pathways using microfluidic pulsatile inputs and mathematical modeling
Parameter estimation in models of biological oscillators: an automated regularised estimation approach
System modeling reveals the molecular mechanisms of HSC cell cycle alteration mediated by Maff and Egr3 under leukemia
Cell Cycle Pathways
Cell cycle is a complex process regulated by several signal transduction pathways and enzymes. Here is the latest research on regulation of cell cycle and cell cycle pathways.
Cell Checkpoints & Regulators
Cell cycle checkpoints are a series of complex checkpoint mechanisms that detect DNA abnormalities and ensure that DNA replication and repair are complete before cell division. They are primarily regulated by cyclins, cyclin-dependent kinases, and the anaphase-promoting complex/cyclosome. Here is the latest research.