Comment on "Molecular origin of anticooperativity in hydrophobic association".

Recently, using the TIP4P water model, Czaplewski et al.1 showed that the three-methane potential of mean force (PMF) in water at 298 K for their 2m+m system (i.e., the trimer case with isosceles-triangle geometry in their Figure 1b) is anticooperative at the contact minimum. Apparently, this conclusion is in qualitative agreement with our previous TIP4P simulation results, which have indicated anticooperativity at 25 °C for the same three-methane configuration,2-4 but contradicts their previous conclusions from TIP4P and TIP3P simulations that it is cooperative5,6 (cf. Figure 5 in ref 1 and the φ ) 0 panel of Figure 9 in ref 3, as well as Figure 8 in ref 5). Despite their new 2m+m anticooperative result at the contact minimum, Czaplewski et al.1 asserted, citing their previous TIP3P study,7 that “there is only cooperativity” in the threemethane PMF simulated in an equilateral-triangle geometry (i.e., their m+m+m system, see also the corresponding TIP4P result in Figure 7B of ref 5). By construction, however, the contactminimum three-methane configuration for the 2m+m and m+m+m systems are essentially identical. Can the cooperativity or anticooperativity of a given final three-methane configuration depend on the pathway by which it is assembled? A straightforward analysis of the simple thermodynamic cycle in Figure 1 demonstrates that this is impossible. Let W m+m (2) (êc) and W 2m+m (3) (êc) denote, respectively, the two-methane and the three-methane 2m+m PMFs at the position defined by the center-of-mass methane-methane spatial separation êc ) 3.9 Å at contact minimum. The quantity W 2m+m (3) (êc) corresponds to the free energy change of the (b) f (c) process in Figure 1. Although the separation between each of the two methanes in the methane dimer and the third methane at the 2m+m contact minimum need not be exactly equal to êc, in practice they are essentially identical. Therefore, in the present notation, the 2m+m cooperativity term at contact minimum is