Mathematical physiology
Elements of applied bifurcation theory (2nd ed.)
Elements of applied bifurcation theory (2nd ed.)
Membrane Computing: An Introduction
Membrane Computing: An Introduction
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We define a class of cellular interface problems (short: CIP) that mathematically model the exchange of molecules in a compartmentalised living cell. Defining and eventually solving such compartmental problems is important for several reasons. They are needed to understand the organisation of life itself, for example by exploring different 'origin of life' hypothesis based on simple metabolic pathways and their necessary division into one or more compartments. In more complex forms investigating cellular interface problems is a way to understand cellular homeostasis of different types, for example ionic fluxes and their composition between all different cellular compartments. Understanding homeostasis and its collapse is important for many physiological medical applications. This class of models is also necessary to formulate efficiently and in detail complex signalling processes taking place in different cell types, with eukaryotic cells the most complex ones in terms of sophisticated compartmentalisation. We will compare such mathematical models of signalling pathways with rule-based models as formulated in membrane computing in a final discussion. The latter is a theory that investigates computer programmes with the help of biological concepts, like a subroutine exchanging data with the environment, in this case a programme with its global variables.