a–d, Comparison of relative stabilities of ions across multiple simulation conditions. Here, stability refers to the amount of time an ion resides within 3 Å of the pre-determined centre of each binding site (see Methods). Each dot corresponds to a result from a single simulation. Closed circles indicate simulations with each cation placed in its predicted site; open circles indicate simulations with either cation swapped into the other cation’s predicted binding site. Blue circles correspond to measurements for Na+ and pink circles for K+. For a and b, we examined the relative stabilities of cations to determine whether the predicted Na+ and K+ binding sites exhibit a preference for their respective cations. a, For simulations started with all ions bound, Na+ resided longer in the Na+ site compared to K+ when K+ was initially placed within the Na+ site (‘Na+/K+/2Cl−’ vs ‘Na+/K+ swapped, 2 Cl−’). The same trend appeared for simulations with just cations initially bound within the cavity (‘Na+/K+’ vs ‘Na+/K+ swapped’). b, For simulations started with all ions bound, K+ resided for longer in the K+ site compared to Na+ when Na+ was initially placed within the K+ site (‘Na+/K+/2Cl−’ vs ‘Na+/K+ swapped, 2 Cl−’). For simulations with just cations initially bound, K+ and Na+ appeared to leave after similar amounts of time—perhaps because, particularly in the absence of Cl−, the K+ site is quite accessible to the intracellular solvent, and ions of either type could dissociate rapidly from this area. c, K+ remained within its initial position much longer compared to Na+ in the presence of two Cl− ions. In simulations with Na+ and 2 Cl− ions bound, Na+ often immediately dissociated from its site, perhaps indicating that the Na+ site on its own has a weaker affinity for binding cations in this state compared to the K+ site, the increased proximity of which to Cl− site 1 probably helps to stabilize K+ in the site. d, Chloride ions spontaneously visited and remained within 3 Å of the primary intracellular chloride site (site 2) for longer in the presence of both cations compared to in the presence of either cation alone. e, In one simulation, in which Na+ and K+ were initially placed in a swapped configuration with no Cl− ions bound, we observed escape of K+ (pink) followed by destabilization of the Na+ ion (blue) within the K+ site (123 ns) accompanied by Cl− binding. Na+ then proceeded to move down towards the intracellular side (220 ns) before rebinding for a 25-ns period within the proposed Na+-binding site.