Competing hydrophobic and screened-coulomb interactions in hepatitis B virus capsid assembly

Recent experiments show that, in the range from approximately 15 to 45 degrees C, an increase in the temperature promotes the spontaneous assembly into capsids of the Escherichia coli-expressed coat proteins of hepatitis B virus. Within that temperature interval, an increase in ionic strength up to five times that of standard physiological conditions also acts to promote capsid assembly. To explain both observations we propose an interaction of mean force between the protein subunits that is the sum of an attractive hydrophobic interaction, driving the self-assembly, and a repulsive electrostatic interaction, opposing the self-assembly. We find that the binding strength of the capsid subunits increases with temperature virtually independently of the ionic strength, and that, at fixed temperature, the binding strength increases with the square root of ionic strength. Both predictions are in quantitative agreement with experiment. We point out the similarities of capsid assembly in general and the micellization of surfactants. Finally we make plausible that electrostatic repulsion between the native core subunits of a large class of virus suppresses the formation in vivo of empty virus capsids, that is, without the presence of the charge-neutralizing nucleic acid.