Complexity in Biology

We will review some of the theoretical progresses that have been in the study of complex systems in physics and of their applications to biology. 1 On the Definition of Complexity In recent years many progresses have been done in understanding the behaviour of complex systems from the physical point of view (Mèzard et al. 1987, Parisi 1992) and now we can start to reflect on the possible applications of these findings in a biological setting. Many meanings can be attached to the word complex (Peliti and Vulpiani 1988). In order to understand the precise meaning of the word complex that I use in this talk it is useful to consider a system composed by many parts at the microscopic level. Very often we can describe it also at the macroscopic level. The crucial point is the richness of this macroscopic description. Let me present two examples: if our system is water, at the macroscopic level we can only specify its temperature, pressure and normally there are no remaining ambiguities; only for particular values of the temperature and pressure there is the possibility of coexistence of more than one phase, e.g. liquid and solid at zero centigrade. In other words for a physical system the macroscopic description corresponds to state in which phase the system is (e.g. solid, liquid and gaseous). At a given temperature and pressure the number of choices is very small and consequently the macroscopic description is very poor. On the contrary, if our system is a biological system, its macroscopic description may be extremely rich (an animal may run, sleep, eat, jump.....). The variety of the macroscopic description will be taken as an indication of complexity. In other words a system is complex if its macroscopic description is rich.