Ultracentrifugation studies on early stage polymerization of tobacco mosaic virus protein

Abstract The effects of absolute temperature (T), ionic strength (μ), and pH on the polymerization of tobacco mosaic virus protein from the 4 S form (A) to the 20 S form (D) were investigated by the method of sedimentation velocity. The loading concentration in grams per liter (C) was determined at which a just-detectable concentration (β) of 20 S material appeared. It was demonstrated experimentally that under the conditions employed herein, an equilibrium concentration of 20 S material was achieved in 3 h at the temperature of the experiment and that 20 S material dissociated again in 4 h or less to 4 S material either upon lowering the temperature or upon dilution. Thus, the use of thermodynamic equations for equilibrium processes was shown to be valid. The equation used to interpret the results, log ( C−β) = constant + ( ΔH ∗ 2.3RT ) + ( Δ W ∗ el 2.3RT ) − K′sμ + ζpH, was derived from three separate models of the process, the only difference being in the anatomy of the constant; thus, the method of analysis is essentially independent of the model. ΔH ∗ and ΔW∗el are the enthalpy and the change in electrical work per mole of A protein (the trimer of the polypeptide chain), K′s is the salting-out constant on the ionic strength basis, ζ is the number of moles of hydrogen ion bound per mole of A protein in the polymerization, and R is the gas constant. The three models leading to this equation are: a simple 11th-order equilibrium between A1 (the trimer of the polypeptide chain) and D, either the double disk or the double spiral of approximately the same molecular weight, designated model A; a second model, designated B, in which A1 was assumed to be in equilibrium with D at the same time that it is in equilibrium with A2, A3, etc., dimers and trimers, etc., of A1 in an isodesmic system; and a phase-separation model, designated model C, in which A protein is treated as a soluble material in equilibrium with D, considered as an insoluble phase. From electrical work theory, Δ W el ∗ /T was shown to be essentially independent of T; therefore, in experiments at constant μ and constant pH the equation of log (C − β) versus 1/T is linear with a slope of ΔH ∗ /2.3R . The results fit such an equation over nearly a 20 °C-temperature range with a single value of Δ H ∗ of +32 kcal/mol A1. Results obtained when T and pH were held constant but μ was varied did not fit a straight line, which shows that more than simple salting-out is involved. When the effect of ionic strength on the electrical work contribution was considered in addition to salting-out, the data were interpreted to indicate a value of Δ W ∗ el of 1.22 kcal/mol A1 at pH 6.7 and a value of 4.93 for Ks′. When μ and T were held constant but pH was varied, and when allowance was made for the effect of pH changes on the electrical work contribution, a value of 1.1 was found for ζ. This means that something like 1.1 mol of hydrogen ion must be bound per mole of A1 protein in the formation of D. When this is added to the small amount of hydrogen ion bound per A1 before polymerization, at the pH values used, it turned out that for D to be formed, 1.5 H+ ions must be bound per A1 or 0.5 per protein polypeptide chain. This amounts to 1 H+ ion per polypeptide chain for half of the protein units, presumably those in one but not the other layer of the double disk or turn of the double spiral. When polymerization goes beyond the D stage, as shown by previously published data, additional H+ ions are bound. Simultaneous osmotic pressure studies and sedimentation studies were carried out, in both cases as a function of loading concentration C. These results were in complete disagreement with models A and C but agreed reasonably well with model B. The sedimentation studies permitted evaluation of the constant, β, to be 0.33 g/liter.