Arne Bittig, Olaf Wolkenhauer, and Jan-Hendrik Hofmeyr (2006)
A Principal Limitation of Virtual Cell Simulations using Differential Equations
Poster, Monterey, Winter Simulation Conference.
We propose an abstract dynamic model of a cell, rooted in Mesarovic and Takahara's general systems theory, where a cell function is defined by the dynamic processes the cell can realize. We postulate the existence of a 'coordination principle', which decides upon basic cellular processes to realize cell functions, i.e., cell differentiation, proliferation etc., leading to the theorem that the coordination of cell functions is realized autonomously from within the system. Inspired by Robert Rosen's work, who introduced 'closure to efficient causation' as a nessary condition for a natural system to be an organism, we show that the mathematical model of an autonomously self-organizing cell is closed to efficient causation and that the associated category of models in cartesian closed. Our Theorem supports (in parts) Rosen's argument that living cells have non-simulable properties: Conventional computer simulations of cell models fail to capture an essential property of living systems: autonomous self-organization.