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A Glossary for Systems Biology

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DYNAMIC (BEHAVIOR) Glossary DIFFERENTIAL CONTROL

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DIFFERENTIATION

see also

differential control

Meaning

Biology:

The development of different phenotypes out of a common predecessor; also called diversification.

Systems Theory:

Refers to the mathematical operation of differentiating a variable to get the change of that variable with respect to a certain base unit.

Explanation

In the biological sense, differentiation means that different types develop out of a common predecessor. This is also called diversification. Differentiation takes place at different levels in biology: It can be seen in the development of an organism from a single cell to a complex organism (see Illustration) as well as on the evolutionary level, where species change to adapt to new conditions and new species evolve (adaptation).

The systems theoretic meaning has its roots in the definition of differential mathematics, where differentiation is explained in terms of differences of a variable $v$ with respect to infinitesimal steps of the base unit: $\frac{dv}{dt}=\frac{v(t+\Delta )-v(t)}{\Delta }$ for $\Delta \approx 0$. Usually it refers to changes with respect to time ( $\frac{dv}{dt}$), but other base units are possible as well. Differentiation with respect to direction ( $\frac{dv}{dx}$), for example, yields the change in value along a direction vector in space.

Examples

Biology:

• evolution: taxonomy (system), phylogenetic tree (hierarchy)
• development of a complex organism from a single cell (see Illustrations)

Systems Theory:

• changes in concentrations in a chemical reactor over time
• changes in concentration along a pipe (changes with respect to space)

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