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 that simulates tumor spheroids (VBL, Virtual Biophysics Lab), 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.
Precision and stability issues in VBL, the Virtual Biophysics Lab simulation program
CHIGNOLA, Roberto
2009-01-01
Abstract
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 that simulates tumor spheroids (VBL, Virtual Biophysics Lab), 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.
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