We have studied the propagation of the communication signals within a population of cells by extending the theory recently developed by Kummer and Ocone [1, 2] for the cell cycle. We show how the basic framework can be extended from a cell to a collection of cells, by defining the basic thermodynamic variables such as the equivalent of the temperature, energy and pressure for the collection of cells.

For simplicity, we assume that the communication between cells in the population of cells is via propagation of ions from one cell to another. Therefore we develop a novel modelling approach by associating the thermodynamic variables with the concentration and the number of cells in the cell population. We establish a relationship between the variation in the local variables (e.g. temperature, pressure, energy and entropy) and the variation in calcium concentration and cell number. Using methods from statistical mechanics applied to a one-dimensional wave of intracellular calcium ion propagation, we derive a general expression for the pressure and explore how this relates to the pressure distribution in a biological environment.

Reference [1] A. Kummer, R. Ocone, Extension of dynamics of granular flow methodology to cell biology, Physica A, Vol:321, pp 587-597, (2003) [2] A. Kummer, R. Ocone, On the generalization of the metabolic thermodynamic theory of the cell cycle, Chem. Phys. Lett., Vol:388, pp 322-324, (2004)