Of cosolutes found in living cells, urea denatures and trimethylamine N-oxide (TMAO) stabilizes proteins; furthermore, these effects cancel at a 2:1 ratio of urea to TMAO. Interestingly, cartilaginous fish use urea and TMAO as osmolytes at similar ratios at the ocean surface but with increasing fractions of TMAO at increasing depths. Here, molecular dynamics simulations of aqueous solutions with different urea:TMAO ratios show that the diffusion coefficients of water in the solutions vary with pressure if the urea:TMAO ratio is constant, but strikingly, they are almost pressure independent at the ratio found in these fish as a function of depth. This suggests that this ratio may be maintaining a homeostasis of water dynamics. In addition, diffusion is determined by hydrogen-bond lifetimes of the different species in the solution. Based on these observations, a dynamical model in terms of hydrogen-bond lifetimes is developed for the hydrogen bonding propensities of cosolutes and water in an aqueous solution to proteins. This model provides an explanation for both the counteracting effects of TMAO on urea denaturation and the depth-dependent urea:TMAO ratio found in cartilaginous fish.