Rheology of complex fluids. Stochastic switches in the galactose signalling network

Abstract

Part I: Many biological fluids are complex fluids. Complex fluids present a particular mesoscopic structure which provides them viscoelastic effects, among others. These fluids can show viscous or solid behavior depending on the time-scale in which they are operating. These properties can have a major influence on the biological processes in which the fluids are involved. Rheological techniques can be applied in order to characterize these fluids. In the present work experiments using a cone-plane geometry rheometer will be done on a complex fluid with worm-like chain micellar structure, CPyCl-NaSal [100:60], in order to present a complete rheological characterization. In addition, a particular example of biorheology applied to blood samples will be presented. Part II: Bistability is observed in many biological processes and in particular in processes involved in cellular differentiation. It can arise from positive feedback transcription networks and can be found in a colony of cells by the coexistence of two populations with different stable concentration of a specific protein. In M. Acar, A. Becskei, A. van Oudenaarden, ¿Enhancement of cellular memory by reducing stochastic transitions¿, Letters to nature 435, 228 (2005), Yeast Saccharomyces cerevisiae cells were found to switch from one stable state to another one of the Galactose-signalling network. This network is mainly governed by a positive feedback loop and the switching rate depended on the state from which cells came. In order to describe such phenomena a deterministic model based on positive feedback loops is not sufficient. The aim of the present work is to understand from a theoretical point of view how these transitions are originated and predict the rate at which they jump between different stable states. For this purpose numerical simulations have been done based on Langevin equations with multiplicative noise and later compared to theoretical predictions derived from Fokker-Plank equations. In order to become familiar with the required numerical and theoretical techniques the Ginzburg-Landau model has been previously studied. Our results show that fluctuations in the maximal transcription rate can be responsible for this phenomenon. For the galactose network, our results predict that fluctuations in the levels of proteins Gal4p and Gal80 are crucial.