ABSTRACT
We present a statistical mechanical model based on the principle of mass action that explains the main features of the in vitro aggregation behavior of the coat protein of tobacco mosaic virus (TMV). By comparing our model to experimentally obtained stability diagrams, titration experiments, and calorimetric data, we pin down three competing factors that regulate the transitions between the different kinds of aggregated state of the coat protein. These are hydrophobic interactions, electrostatic interactions, and the formation of so-called “Caspar” carboxylate pairs. We suggest that these factors could be universal and relevant to a large class of virus coat proteins.
INTRODUCTION
The spontaneous formation of virus-like particles in aqueous solutions of the coat protein (CP) of tobacco mosaic virus (TMV) is generally seen as the paradigm for self-assembly in biology (1-3). Indeed, as was shown half a century ago, infective virus particles of helical symmetry spontaneously form upon mixing aqueous solutions of the coat protein and the RNA of the virus (4). The coat protein alone in fact exhibits, in solution, various aggregated states: mono- and oligomers, disk-like assemblies, and extended helices (5,6). The various aggregated states interconvert reversibly upon variation of the temperature, pH, and ionic strength. It appears that the propensity to form virus-like particles is an intrinsic property of the CP.
Simple mass-action models have proven quite successful in describing isolated experiments (7-11), but a theory that predicts the transitions between the various equilibrium aggregation states of TMV coat protein as a function of the external conditions is still lacking. In this work, we identify three factors of physical origin involved in the stability of the virus-like particles. These are 1), hydrophobic interactions; 2), electrostatic interactions; and 3), intersubunit carboxylate or Caspar pair interactions (7). Incorporated into a minimal statistical mechanical (mass-action) model, they explain the main features of the in vitro self-assembly behavior of the tobacco mosaic virus coat protein.
Our conclusions are based on a comparison with experimental findings, summarized in Fig. 1. Fig. 1 A gives the ranges over which the various aggregation states of the CP subunits are thought to be stable as a function of the ionic strength and pH, but at fixed temperature and concentration. It indicates that electrostatic interactions must play a role in the stability of the assemblies. The indicated stability boundaries do not demarcate true phase boundaries; they show where larger self-assembled species become detectable, yet do not imply that the smaller species actually disappear. The diagram includes both stable (reversibly formed) species and what presumably are metastable species (2,3).
The two-layered disks and the single helices form reversibly: they appear/disappear upon increasing/decreasing the proton concentration. The “lock-washer” species, on the other hand, slowly grows into larger helices, whereas the “stacked disk” structure is thought to represent an irreversible, partly protcolyzed aggregated state (see Klug (2) and Butler (3), and references cited therein). For simplicity, we shall ignore, in our model description, the appearance of cylindrical species consisting of more than two layers but discuss the implications of this idealization. Thus, in the following, only equilibria between “monomers”, disks, and helices will be considered, where the “monomers” are also thought to include oligomeric species that we do not need to explicitly include in the model.
Fig. 1 B, taken from Sturtevant et al. (11), shows the excess heat capacity associated with the reversible assembly of TMV CP as a function of the temperature, measured at three different pH values. At low temperatures, the free “monomers” are the preferred species, whereas disk and helix aggregates form upon increasing the temperature (11). A more detailed discussion of this process is presented in the Results and Discussion section. It is important to note that the excess heat capacities are larger than zero, implying that the aggregation must be endothermic and is in all likelihood driven by hydrophobic interactions. What is not shown in the figure is that at temperatures >~35°C, irreversible denaturation of the CPs takes place, a process accompanied by a large excess heat capacity.
Finally, in Fig. 1 C, typical acid-base titration curves of the TMV CP for a number of different temperatures are shown (reprinted from Butler et al. (10)). Helices form upon lowering the pH, whereby a total of approximately two protons per protein subunit are absorbed. Proton absorption seems to take place in two steps, as indicated by the large difference in slope. At low pH values, there is a steep variation of the absorbed number of protons with pH, whereas at higher pH values this variation is significantly less pronounced. We shall argue that this points to the existence of two types of proton-binding process, and that the absorption of the protons not only decreases the overall charge on the subunits but in fact also involves the formation of Caspar pairs that strongly stabilize the helical state.
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