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The Novak–Tyson Model is a non-linear dynamics framework developed in the context of cell-cycle control by Bela Novak and John J. Tyson. It is a prevalent theoretical model that describes a hysteretic , bistable bifurcation of which many biological systems have been shown to express.
Steps of the cell cycle. The G 2-M checkpoint occurs between the G 2 and M phases. G2-M arrest. The G 2-M DNA damage checkpoint is an important cell cycle checkpoint in eukaryotic organisms that ensures that cells don't initiate mitosis until damaged or incompletely replicated DNA is sufficiently repaired.
The eukaryotic cell cycle is very complex and is one of the most studied topics, since its misregulation leads to cancers. It is possibly a good example of a mathematical model as it deals with simple calculus but gives valid results. Two research groups [1] [2] have produced several models of the cell cycle simulating several organisms. They ...
The cell cycle is a series of complex, ordered, sequential events that control how a single cell divides into two cells, and involves several different phases. The phases include the G1 and G2 phases, DNA replication or S phase, and the actual process of cell division, mitosis or M phase. [ 1 ]
Cell cycle analysis by DNA content measurement is a method that most frequently employs flow cytometry to distinguish cells in different phases of the cell cycle.Before analysis, the cells are usually permeabilised and treated with a fluorescent dye that stains DNA quantitatively, such as propidium iodide (PI) or 4,6-diamidino-2-phenylindole (DAPI).
APC activity also causes the destruction of S and M cyclins and thus the inactivation of Cdks, which promotes the completion of mitosis and cytokinesis. APC activity is maintained in G1 until G1/S–Cdk activity rises again and commits the cell to the next cycle. This scheme serves only as a general guide and does not apply to all cell types. [1]
Cell-based models are mathematical models that represent biological cells as discrete entities. Within the field of computational biology they are often simply called agent-based models [1] of which they are a specific application and they are used for simulating the biomechanics of multicellular structures such as tissues. to study the influence of these behaviors on how tissues are organised ...
The flow across the cells is determined based on μ(k) and λ(k), two monotonic functions that uniquely define the fundamental diagram as shown in Figure 1. The density of the cells is updated based on the conservation of inflows and outflows. Thus, the flow and density are derived as: Where: and represent density and flow in cell i at time t.