Tests for cycling in a signalling pathway

Summary.  Cellular signalling pathways, mediating receptor activity to nuclear gene activation, are generally regarded as feed forward cascades. We analyse measured data of a partially observed signalling pathway and address the question of possible feed-back cycling of involved biochemical components between the nucleus and cytoplasm. First we address the question of cycling in general, starting from basic assumptions about the system. We reformulate the problem as a statistical test leading to likelihood ratio tests under non-standard conditions. We find that the modelling approach without cycling is rejected. Afterwards, to differentiate two different transport mechanisms within the nucleus, we derive the appropriate dynamical models which lead to two systems of ordinary differential equations. To compare both models we apply a statistical testing procedure that is based on bootstrap distributions. We find that one of both transport mechanisms leads to a dynamical model which is rejected whereas the other model is satisfactory.