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An embedded graph uniquely defines cyclic orders of edges incident to the same vertex. The set of all these cyclic orders is called a rotation system.Embeddings with the same rotation system are considered to be equivalent and the corresponding equivalence class of embeddings is called combinatorial embedding (as opposed to the term topological embedding, which refers to the previous ...
Modelling biological systems is a significant task of systems biology and mathematical biology. [a] Computational systems biology [b] [1] aims to develop and use efficient algorithms, data structures, visualization and communication tools with the goal of computer modelling of biological systems.
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 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 G 1 phase, gap 1 phase, or growth 1 phase, is the first of four phases of the cell cycle that takes place in eukaryotic cell division. In this part of interphase , the cell synthesizes mRNA and proteins in preparation for subsequent steps leading to mitosis.
The concept of a combinatorial map was introduced informally by J. Edmonds for polyhedral surfaces [2] which are planar graphs.It was given its first definite formal expression under the name "Constellations" by A. Jacques [3] [4] but the concept was already extensively used under the name "rotation" by Gerhard Ringel [5] and J.W.T. Youngs in their famous solution of the Heawood map-coloring ...
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).
Cell synchronization is a process by which cells in a culture at different stages of the cell cycle are brought to the same phase. Cell synchrony is a vital process in the study of cells progressing through the cell cycle as it allows population-wide data to be collected rather than relying solely on single-cell experiments.