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Mathias John, Roland Ewald, and Adelinde Uhrmacher (2008)

A Spatial Extension to the Pi Calculus

In: Electronic Notes in Theoretical Computer Science, vol. 194(3), pp. 133-148, Amsterdam, The Netherlands, Elsevier Science Publishers B. V.

Spatial dynamics receive increasing attention in Systems Biology and require suitable modeling and simulation approaches. So far, modeling formalisms have focused on population-based approaches or place and move individuals relative to each other in space. SpacePi extends the Pi Calculus by time and space. Pi processes are embedded into a vector space and move individually. Only processes that are sufficiently close can communicate. The operational semantics of SpacePi defines the interplay between movement, communication, and time-triggered events. A model describing the phototaxis of the Euglena micro-organism is presented as a practical example. The formalism’s use and generality is discussed with respect to the modeling of molecular biological processes like diffusion, active transportation in cell signaling, and spatial structures.

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