Complex biological system, mathematical model

One of the major uses of molecular simulation is to provide useful theoretical interpretation of experimental data. Before the advent of simulation this had to be done by directly comparing experiment with analytical (mathematical) models. The analytical approach has the advantage of simplicity, in that the models are derived from first principles with only a few, if any, adjustable parameters. However, the chemical complexity of biological systems often precludes the direct application of meaningful analytical models or leads to the situation where more than one model can be invoked to explain the same experimental data. 

The structure and mathematical expressions used in PBPK models significantly simplify the true complexities of biological systems. If the uptake and disposition of the chemical substance(s) is adequately described, however, this simplification is desirable because data are often unavailable for many biological processes. A simplified scheme reduces the magnitude of cumulative uncertainty. The adequacy of the model is, therefore, of great importance, and model validation is essential to the use of PBPK models in risk assessment. 

To discover and analyze the mathematical basis for the generation of complexity, one must identify simple mathematical systems that capture the essence of the process. Cellular automata are a candidate class of such systems. Cellular automata promise to provide mathematical models for a wide variety of complex phenomena, from turbulence in fluids to patterns in biological growth. 

The structure and mathematical expressions used in PBPK models significantly simplify the true complexities of biological systems. If the uptake and disposition of the chemical substance(s) is... 

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