The bacterium Escherichia coli detects chemical attractants and repellents by means of a cluster of transmembrane receptors and associated molecules. Experiments have shown that this cluster amplifies the signal about 35-fold and current models attribute this amplification to cooperative interactions between neighbouring receptors. However, when applied to the mixed population of receptors of wild-type E. coli, these models lead to indiscriminate methylation of all receptor types rather than the selective methylation observed experimentally. In this paper, we propose that cooperative interactions occur not between receptors but in the underlying lattice of CheA molecules. In our model, each CheA molecule is stimulated by its neighbours via their flexible P1 domains and modulated by the ligand binding and methylation states of associated receptors. We test this idea with detailed, molecular-based stochastic simulations and show that it gives an accurate reproduction of signalling in this system, including ligand-specific adaptation.