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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 ...
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 original model proposed by Graner and Glazier contains cells of two types, with different adhesion energies for cells of the same type and cells of a different type. Each cell type also has a different contact energy with the medium, and the cell volume is assumed to remain close to a target value. The Hamiltonian is formulated as:
Creating a cellular model has been a particularly challenging task of systems biology and mathematical biology. It involves the use of computer simulations of the many cellular subsystems such as the networks of metabolites, enzymes which comprise metabolism and transcription, translation, regulation and induction of gene regulatory networks. [4]
A cellular automaton (pl. cellular automata, abbrev. CA) is a discrete model of computation studied in automata theory. Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tessellation structures, and iterative arrays. [2]
By the 1950s, cell biologists verified the existence of plasma membranes through the use of electron microscopy (which accounted for higher resolutions). J. David Robertson used this method to propose the unit membrane model. [4] Basically, he suggested that all cellular membranes share a similar underlying structure, the unit membrane. Using ...
Cell Transmission Model (CTM) is a popular numerical method proposed by Carlos Daganzo [1] to solve the kinematic wave equation. [ 2 ] [ 3 ] Lebacque [ 4 ] later showed that CTM is the first order discrete Godunov approximation.
Rule 184 can be used as a simple model for traffic flow in a single lane of a highway, and forms the basis for many cellular automaton models of traffic flow with greater sophistication. In this model, particles (representing vehicles) move in a single direction, stopping and starting depending on the cars in front of them.