Osmotic pressures of lysozyme solutions from gas-like to crystal statesElectronic supplementary information (ESI) available: Net charge of lysozyme as a function of pH (Fig. S1); reversibility of osmotic stress at 150 mM and 35 mM ionic strengths (Fig. S2 and S3); Fourier transform infrared spectra and secondary structure of lysozyme, experimental procedure and results (Fig. S4); small-angle X-ray scattering, experimental procedure and results (Fig. S5); generalized van der Waals (GVDW) model; f

We obtained osmotic pressure data of lysozyme solutions, describing their physical states over a wide concentration range, using osmotic stress for pressures between 0.05 bar and about 40 bar and volume fractions between 0.01 and 0.61. The osmotic pressure vs. volume fraction data consist of a dilute, gas-phase regime, a transition regime with a high-compressibility plateau, and a concentrated regime where the system is nearly incompressible. The first two regimes are shifted towards a higher protein volume fraction upon decreasing the strength or the range of electrostatic interactions. We describe this shift and the overall shape of the experimental data in these two regimes through a model accounting for a steric repulsion, a short-range van der Waals attraction and a screened electrostatic repulsion. The transition is caused by crystallization, as shown by small-angle X-ray scattering. We verified that our data points correspond to thermodynamic equilibria, and thus that they consist of the reference experimental counterpart of a thermodynamic equation of state. Osmotic pressures of lysozyme solutions at concentrations up to 850 g L −1 show three regimes and a clear influence of ionic strength.