A Kummer

Extension of dynamics of granular flow methodology to cell biology

In a previous paper (J. Non-Newtonian Fluid Mech. 76 (1998) 5), the analogy between the methodology typical of the dynamics of polymeric liquids and those used in granular flow theory was investigated. It was shown that such a methodology could be successfully extended to granular flow, and then it was speculated on the possibility of extending it to diverse areas. In this paper two important conclusions are reached. Firstly we show that the methodology behind the statistical theories (which starting from the microstructural element eventually leads to the formulation of constitutive equations (AICHE Symposium Series, Vol. 93, 1997, p. 103)) can be extended to an apparently completely different field, namely cell biology. We then show that classical thermodynamics, as applied to epigenetic systems, presents limitations which can be overcome following an axiomatic thermodynamic route (J. Rheol. 37 (1993) 727).

A metabolic thermodynamic theory of cell cycle

Abstract Due to its intrinsic complexity, a complete mathematical description of the cell cycle appears a difficult task. Nevertheless, a preliminary analysis, based on molecular biology, can help in clarifying what are the reliable tools for a quantitative approach. In a previous paper [Physica A 321 (3–4) (2003) 587], the steps to be followed to formulate a metabolic statistical thermodynamics have been established. Here we present a simple mathematical model for the interaction of CyclinB and Cdh1 [The Cell Cycle. An Introduction, Oxford University Press, New York, 1993], with the aim of analysing the properties of the system from a thermodynamic viewpoint. The model is shown to define the Gibbs phase integral of the system and the general Gibbs energy function is obtained. This, together with the analogue of the temperature, defines the working tools indispensable for the formulation of a metabolic statistical thermodynamic-like theory.