Looking for new paradigms towards a biological-mathematical theory of complex multicellular systems

This lecture deals with the development of new paradigms based on the mathematical methods of the kinetic theory for active particles to model the dynamics of large systems of interacting cells. Interactions are ruled, not only by laws of classical mechanics, but also by some biological functions which are able to modify the above laws.
The first part of the presentation technically shows, also by reasoning on specific examples, how the theory can be applied to model large complex systems in biology. The second part deals with a critical analysis and with the indication of some research perspective concerning the challenging target of developing a biological-mathematical theory for the living matter.
The sequential steps to achieve the above outlined objectives are as follows:

(i) Integration of the concept of functional subsystems to reduce the complexity of large living systems within the approach of system biology;
(ii) Development of the mathematical kinetic and stochastic game theory for active particles;
(iii) Modelling the immune system as a large complex system;
(iv) Development of a multiscale analysis and modelling from genes to tissues.

References

N. Bellomo, Modelling Complex Living Systems-A Kinetic Theory and Stochastic Game Approach (Birkhauser, Boston, 2008).
N. Bellomo, N.K. Li, and P.K. Maini, On the foundations of cancer modelling: Selected topics, speculations, and perspectives, Mathematical Models and Methods in Applied Sciences, 18 (2008)
593-646.
N. Bellomo, C. Bianca and M. Delitala, Complexity analysis and mathematical tools towards the modelling of living systems, Physics of Life Review, 6 (2009) 144-175.