  We review in this paper the use of the theory of scale relativity and fractal
space-time as a tool particularly well adapted to the possible development of a
future genuine theoretical systems biology. We emphasize in particular the
concept of quantum-type potentials, since in many situations the effect of the
fractality of space -- or of the underlying medium -- amounts to the addition
of such a potential energy to the classical equations of motion. Various
equivalent representations -- geodesic, quantum, fluid mechanical, stochastic
-- of these equations are given, as well as several forms of generalized
quantum potentials. Examples of their possible intervention in high critical
temperature superconductivity and in turbulence are also described, since some
biological processes may be analog in some aspects to these physical phenomena.
These potential energy extra contributions could have emerged in biology from
the very fractal nature of the medium, or from an evolutive advantage, since
they involve spontaneous properties of self-organization, morphogenesis
structuration and multi-scale integration.
