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

Abstract

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.

FIGURE 1

The logarithm of the equilibrium constant, ln K, as a function of temperature, T, at various salt concentrations as indicated in the figure. Symbols are data from Ceres and Zlotnick (2002). Lines are linear fits with a fixed slope of +(5.7 ± 2.4) K⁻¹. The extrapolated values of ln K at T = T₀ = 273 K are plotted in Fig. 2.

FIGURE 2

The logarithm of the equilibrium constant, ln K, at the temperature T = T₀ = 273 K as a function of the inverse square-root of the salt concentration . The slope of the fitted line is −(253 ± 19) and its intercept is +(2317 ± 35). See the main text for an interpretation of these values.

FIGURE 3

The logarithm of the critical capsid concentration, ln c_*, versus the inverse square-root of the salt concentration, . The straight line gives our theoretical fit to the measured equilibrium constants of Ceres and Zlotnick (2002). The circles are estimates from the experimental association curves given in Fig. 1 B of Ceres and Zlotnick (2002).

FIGURE 4

The fraction of material assembled into capsids, f, versus the overall concentration of dimer subunits c, scaled to the critical capsid concentration c_*. The symbols represent the data from Ceres and Zlotnick (2002) for samples at a temperature of 25°C. Crosses, c_S = 0.7 M; triangles, c_S = 0.5 M; and squares, c_S = 0.3 M. The drawn line is the universal aggregation curve, given by Eq. 16.

FIGURE 5

Fraction of material assembled into capsids, f, as a function of the concentration of NaCl in units of mM. The symbols represent the data of Wingfield et al. (1995) on aqueous solutions of HBeAg dimer proteins that assemble into T = 3 capsids with an aggregation number of q = 90. Concentration of protein 0.5 g/l at pH = 7.0 and at near room-temperature. The drawn line is theoretical fit using Eqs. 16 and 18.