The complex ammonium transport and assimilation network of E. coli involves the ammonium transporter AmtB, the regulatory proteins GlnK and GlnB, and the central N-assimilating enzymes together with their highly complex interactions. The engineering and modelling of such a complex network seem impossible because functioning depends critically on a gamut of data known at patchy accuracy. We developed a way out of this predicament, which employs: (i) a constrained optimization-based technology for the simultaneous fitting of models to heterogeneous experimental data sets gathered through diverse experimental set-ups, (ii) a ‘rubber band method’ to deal with different degrees of uncertainty, both in experimentally determined or estimated parameter values and in measured transient or steady-state variables (training data sets), (iii) integration of human expertise to decide on accuracies of both parameters and variables, (iv) massive computation employing a fast algorithm and a supercomputer, (v) an objective way of quantifying the plausibility of models, which makes it possible to decide which model is the best and how much better that model is than the others. We applied the new technology to the ammonium transport and assimilation network, integrating recent and older data of various accuracies, from different expert laboratories. The kinetic model objectively ranked best, has E. coli's AmtB as an active transporter of ammonia to be assimilated with GlnK minimizing the futile cycling that is an inevitable consequence of intracellular ammonium accumulation. It is 130 times better than a model with facilitated passive transport of ammonia.