Physics – Biological Physics
Scientific paper
2009-03-29
Physics
Biological Physics
presented by Edoardo Milotti at the ECOBIOSYS 2009 conference (Milano-Italy)
Scientific paper
The network of biochemical reactions inside living organisms is characterized by an overwhelming complexity which stems from the sheer number of reactions and from the complicated topology of biochemical cycles. However the high speed of computers and the sophisticated computational methods that are available today are powerful tools that allow the numerical exploration of these exceedingly interesting dynamical systems. We are now developing a program, the Virtual Biophysics Lab (VBL), that simulates tumor spheroids, and which includes a reduced - but still quite complex - description of the biochemistry of individual cells, plus many diffusion processes that bring oxygen and nutrients into cells and metabolites into the environment. Each simulation step requires the integration of nonlinear differential equations that describe the individual cell's clockwork and the integration of the diffusion equations. These integrations are carried out under widely different conditions, in a changing environment, and for this reason they need integrators that are both unconditionally stable and that do not display unwanted algorithmic artifacts. These conditions are not always fulfilled in the existing literature, and we feel that a review of the underlying mathematical principles may be important not just for us but for other workers in the field of system biology as well.
Chignola Roberto
Fabbro Alessio Del
Milotti Edoardo
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