The pressure of economic cost and environmental constraints dictates that farmers must optimize the use of nitrogen fertilizer. Industrial uses of new wheat varieties require specific and stable grain protein concentration, which needs accurate estimation of N demand during the crop cycle. Thus breeding for high N use efficiency (NUE) and yield, whilst maintaining high grain protein concentration, is of high priority for cereal geneticists. Here, the wheat simulation model SiriusQuality1 was used to analyse the effect of variation in physiological traits on wheat NUE, grain protein composition and concentration under variable climate and conventional and limited N supply conditions. Twenty-three of the 53 parameters of SiriusQuality1 were selected for sensitivity analysis based on a literature survey four parameters were related to phenology and canopy development, seven to crop C assimilation and partitioning, eight to crop N uptake and assimilation, and four to grain development and C and N accumulation. Variations in weather and N treatments induced larger variations in NUE than most of the physiological traits considered. The simulations suggest that a single physiological trait is unlikely to break the negative correlation between the grain protein concentration and yield over a wide range of sites and seasons, especially under low N input environments. Increasing the N storage capacity of the leaves and stem and the allocation of N to non-structural proteins appeared as the more promising strategy to breaking the negative correlation between grain yield and protein concentration.