Modelling spatio-temporal interactions within the cell PADMINI RANGAMANI* and RAVI IYENGAR

Cell signalling pathways make up the regulatory systems of mammalian cells. With the enormous progress in biochemistry and molecular biology of cellular processes over the past four decades and the emergence of new techniques in the last few years, an immense amount of data exists on cell signalling pathways and networks. Various groups (Bhalla and Iyengar 1999; Wiley et al 2003; Hautaniemi et al 2005; Ma’ayan et al 2005; Kowalewski et al 2006; Mayawala et al 2006; Saha and Schaffer 2006; Singh et al 2006; Stamatakis and Mantzaris 2006) have organized this data into interaction networks and models. This organization makes it possible to study the signalling networks in a modelling framework and obtain nonintuitive hypotheses based on numerical simulations. In mammalian cells, signals propagate within linear pathways in a nonlinear fashion and lead to interactions between pathways. Such interactions between pathways often lead to complex nonlinear behaviour that arises from the presence of regulatory negative and positive feedback loops (Bhalla and Iyengar 1999, 2001a, b). Feedforward motifs within networks also provide the capability to have multiple modes of controls, including the ability to have redundant pathways, and the ability to mount prolonged responses to brief input signals. To study these regulatory phenomena and follow the detailed spatial and temporal dynamics can be a daunting task given the number of components involved. However, mathematical modelling of the cell signalling networks provides us with a means to overcome this barrier and get a better understanding of the information processing capability of signalling networks. Application of mathematical modelling is not new to biological processes. Beginning from the population prey models described by the Lotka-Volterra model and the Hodgkin-Huxley model for neuron spiking (Hodgkin and Huxley 1952), many models have been proposed for various biological processes. For biochemical processes, enzyme kinetics has long been modelling by reaction engineering processes. Pharmacological systems have also been studied, using chemical kinetics and reaction engineering approaches, for ligand-receptor interactions as well as defi ne effi cacy of an antagonist or an agonist (Black and Leff 1983; Kenakin 2004; Leff et al 1997). From these models, it is clear that the specifi c formulation of the mathematical model drives the results. Cellular metabolic processes have been modelled and have provided insights into the regulatory networks (Fong et al 2005; Papin et al 2005; Thiele et al 2005). For cell signalling networks, Bhalla and Iyengar (1999, 2001a, b) have shown how the interaction of networks can Modelling spatio-temporal interactions within the cell