Extended Data Fig. 1. Osmotic potential of simple and macromolecular solutes as a function of concentration and temperature.

(a-b) The osmotic potential (mean ± SEM) of indicated macromolecules at various concentrations was determined at 27 °C by the vapour pressure method, data corresponds to Fig. 1a. Charged or hydrophilic small solutes, as well as macromolecules with predominantly hydrophilic surfaces, partake in enthalpically-compensated interactions with the solvent such that osmotic potential increases linearly with concentration. Conversely, the osmotic potential of macromolecules (BSA, PEG, Hb) with less enthalpically-favourable solvent interactions show a marked departure from linearity as concentration increases. Goodness-of-fit for a centred first order polynomial is shown. (c) A single parameter describing each solute’s effective departure from linearity (that is, its effective interaction with the solvent $I_{\mathrm{eff}}^s$, displayed with 95% confidence interval as error bars) can be derived by fitting the data to Equation 1, as proposed by Fullerton and colleagues^11,13; see methods for details. The higher the $I_{\mathrm{eff}}^s$, the more uncompensated or energetically unfavourable “structured” water is generated per unit mass of solute, and the less linear the osmometry curve is with respect to concentration. n: number of osmometry curves fitted simultaneously to evaluate $I_{\mathrm{eff}}^s$ in each condition (see supplementary discussion). (d) PEG models the effect of less enthalpically-favoured biological macromolecules with high $I_{\mathrm{eff}}^s$ on solvent thermodynamics, since it has no solubility limit and does not partition from the solvent. The osmotic potential of PEG changes as a function of concentration, molecular weight, and temperature, with a highly significant three-way interaction between the three variables. (e) $I_{\mathrm{eff}}^s$ values from the data presented in (d) illustrates how solvent thermodynamics become increasingly sensitive to temperature drop as $I_{\mathrm{eff}}^s$ increases (that is for larger PEG size). (f) As predicted by PEG, the temperature sensitivity of a less enthalpically-favoured macromolecule’s effect on solvent thermodynamics is greater for macromolecules with higher $I_{\mathrm{eff}}^s$. For example, for solutions of mucin and BSA with osmotic potential >1000 mOsm kg⁻¹ at 27 °C degrees, a 10 °C increase in temperature halves the osmotic potential of the BSA solution but has minimal effect on the osmotic potential of mucin solution. Statistics indicated. (g) $I_{\mathrm{eff}}^s$ values (±95% confidence interval) from the data presented in (f) illustrates how the temperature- sensitivity of a less enthalpically-favoured macromolecule’s effect on solvent thermodynamics is greater for those with higher $I_{\mathrm{eff}}^s$. n: number of osmometry curves measured at each temperature to evaluate $I_{\mathrm{eff}}^s$. (h,i) The concentration and temperature-dependent effect of macromolecules such as PEG on solvent thermodynamics is not attributable to macromolecular crowding or excluded volume effects, since identical concentrations of more enthalpically favourable but similarly-sized carbohydrates (h: PEG-20kDa versus dextran-20kDa; i: PEG-300Da versus Sucrose 349 Da) have more modest effects on osmotic potential that are not sensitive to temperature over this range. Two-way ANOVA for temperature versus concentration statistics are indicated. Throughout n: number of independent repeats. Please note that absolute osmotic potential is shown here, which includes 320 mOsm kg⁻¹ due to the buffer used throughout (20 mM Tris-HCl pH 7.4/150 mM KCl). Whereas, for clarity, baseline-subtracted vapour pressure measurements are presented in main figures.

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