Pressure dependence of the compressibility of a micelle and a protein: insights from cavity formation analysis

Abstract

We present results from molecular dynamics simulations of a spherical micelle comprising 80 non-ionic C₈E₅ surfactants in water, a protein staphylococcal nuclease in water, and bulk n-hexane and water liquids over a range of hydrostatic pressures. We focus specifically on the pressure dependence of the volumetric properties—the partial molar volume and partial molar compressibility—of the micelle, the protein, and bulk liquids. We find that the micelle interior displays properties similar to liquid alkanes over a range of pressures and has a compressibility of ∼100−110×10⁻⁶ bar⁻¹ under ambient conditions, which is more than twice that of liquid water. In contrast, the pressure dependence of the protein interior resembles that of solid organic polymeric materials and has a compressibility of ∼ 5−10×10⁻⁶ bar⁻¹. We performed extensive analysis of cavity formation in all systems. Interestingly, it is not the average cavity size but the width of the cavity size distribution in a given medium that correlates with the compressibility of that medium over a broad range of pressures up to several kilobars. Correspondingly, the cavity size distribution is most sharply defined in protein interiors and is broadest in the micelle interior and in n-hexane. To explore the correlation between cavity formation and compressibility, we present preliminary calculations using the information theory approach in the bulk water phase. Analysis of cavity formation and, especially, the nature of the cavity size distribution may provide a sensitive probe of the compressibility and flexibility of local molecular environments in inhomogeneous condensed media.

Keywords:

• Hydrophobic effect
• Hydrophobic interactions
• Pressure denaturation
• Protein folding
• Fluctuations
• Partial molar volume

Acknowledgements

We thank Dr. Lawrence R. Pratt, Professor Michael E. Paulaitis and Professor Hank Ashbaugh for fruitful discussions over the past several years. SG is grateful for partial financial support from the ACS-PRF AC grant, NSF (CAREER, BES), and NIH-RECCR grants. BP is grateful for financial support from the NIH training grant fellowship. BP, SJ and SS contributed equally to the work described here.