Mechanism of self-assembly of tobacco mosaic virus protein. I. Nucleation-controlled kinetics of polymerization.

The polymerization of tobacco mosaic virus protein has been found to proceed through metastable states under conditions where initially one of the two polymerization-linked protons is bound. These metastable polymers have been characterized and are found to be helical rods, which resemble the structure of equilibrium helical rods that form when both polymerization-linked protons are bound. At pH 6.5 and 20 °C the true equilibrium distribution of these helical rods has been shown to consist of sedimenting species that are much smaller, 24 to 34 S, than described previously, 100 to 200 S. The larger, non-equilibrium rods are produced by an overshoot in polymerization that results from the slow formation of 20 S nuclei followed by a very rapid elongation reaction. Generally, this sequence of rate processes is sensitive to the rate at which a reaction is initiated. In the present case it is the rate of heating or the rate of change of the pH that determines the reaction path and therefore the rate of attainment of equilibrium. In addition to the formation of metastable helical rods during polymerization overshoot, metastable 20 S aggregates can form when either equilibrium or non-equilibrium helical rods are depolymerized by cooling to 5 to 7 °C at pH 6.5. These 20 S aggregates are presumably two-turn disks or helices and can serve as nuclei for helical rod formation in subsequent polymerization reactions. Both helical rod and 20 S metastability are extremely sensitive to pH but, under carefully controlled conditions, the metastability is quite reproducible and reproducible nucleation-controlled polymerization kinetics can be observed even when polymerization-depolymerization cycling is carried out between branches of a hysteresis loop. Temperature- or pH-induced polymerization of tobacco mosaic virus protein can be made to proceed by the slow formation of 20 S, two-turn helix, nuclei followed by the rapid addition of one or more species comprising the 4 S protein. These results confirm a previously proposed kinetic mechanism for the non-equilibrium polymerization reaction (Scheele &; Schuster, 1974).     

Tobacco mosaic virus protein: sedimentation equilibrium studies of the initial stages of polymerization.

The lowest stages of polymerization of tobacco mosaic virus protein were studied by means of high-speed sedimentation equilibrium experiments. Several distinct modes of polymerization were found. At pH 7.1 the expected monomer-trimer-higher polymer equilibrium was observed--very little dimer was detected at this pH. At pH 7.5, however, a strong dimerization was observed--neither monomer nor trimer was detected at this pH. An octamer appeared to be the only species present other than the dimer. When 0.01 M beta-mercaptoethanol was added to the solvent pH 7.5, the dimer was dissociated, resulting in a monomer-trimer association. The dimerization may be the basis for the larger "doubled" polymers formed by the protein at alkaline pH, while the octamer may correspond to the 8S peak frequently observed in sedimentation velocity experiments at alkaline pH. On the other hand, the monomer-trimer-higher polymer equilibrium may correspond to the single helix formed by the protein at slightly acid pH and to the combination of 4S and 20S peaks seen in sedimentation velocity experiments at slightly acid pH.     

Letter: Hysteresis of proton binding to tobacco mosaic virus protein associated with metastable polymerization.

Proton binding to tobacco mosaic virus protein at 20 °C has been found to exhibit a reproducible hysteresis which results from the metastability of high molecular weight helical, virus-like rods. In a titration from pH 4 or 5 to 7, the time for depolymerization of such rods, as measured by ultracentrifugation, decreases from days to minutes over a range of about a tenth of a pH unit, near pH 6·6 at 20 °C. Relative to the extent of proton binding in the depolymerized state at 4 °C, the magnitude of the hysteresis near pH 6·2 corresponds to more than 50% of the protons bound per subunit in the equilibrium polymerized state.     

Hydrogen ion uptake upon tobacco mosaic virus protein polymerization.

To determine the stage at which H⁺ ions are bound during the entropy-driven polymerization of tobacco mosaic virus protein, acid-base titrations were carried out at a concentration of 5 mg/ml in 0.1 m-KCl from pH 8 to pH 5.2 and back to pH 8 at 4, 10, 15 and 20 °C. The titration was always completely reversible when the addition of acid or base was so slow that the experiment required seven hours in each direction. When the titration was started at pH 7 and performed down and up twice as rapidly, a hysteresis loop, indistinguishable from one previously published, was obtained at 20 °C.Ultracentrifugation experiments were carried out at selected pH values at the four temperatures. H⁺ ion uptake, as determined from the reversible titration curves, is correlated with the disappearance of the 4 S component and is independent of whether the polymerized species is in a 20 S or higher state of aggregation. At pH 7, approximately 1 mole of H⁺ ion is bound per mole of monomer. At pH values between 6.56 and 6.05, 1.5 moles of H⁺ ion are bound per mole of monomer upon polymerization. At pH 6.05, 0.5 mole of H⁺ ion is bound before any polymerization takes place.Tobacco mosaic virus protein at 20 °C in an unbuffered 0.1 m-KCl solution at pH 7.18 at a concentration of 41 mg/ml, largely in the 20 S state, was depolymerized entirely to the 4 S state by dilution with 0.1 m-KCl adjusted to the same pH. Under these conditions, there was no pH change, indicating that no H ⁺ ions are released.These seemingly contradictory findings can be explained by assuming that the 4 S component polymerizes to form either double discs without binding H⁺ ions, or, alternatively, two-turn helices accompanied by the binding of H⁺ ions. Both double discs and two-turn helices sediment at approximately 20 S. Whether polymerization in the neighborhood of pH 7 leads to helices or discs depends upon the availability of H⁺ ions.     

Physical regulation of the self-assembly of tobacco mosaic virus coat protein

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.     

Kinetics of the polymerization reaction of tobacco mosaic virus protein: transient-saturation type polymerization reaction.

The kinetics of the endothermic polymerization reaction of tobacco mosaic virus protein in the mild acid region was studied by means of temperature-jump (rising time of 6 sec)-turbidimetry, electron microscopy, and computer simulation. The time course profile of the turbidity increase changed from a normal one to an anomalous one as the size of the temperature-jump was made greater. The anomalous type polymerization profile, which we named the "transient-saturation" type, could be characterized by a rapid increase of turbidity and its transient saturation, and a slow increase to the final level. At a higher concentration of the protein, this transient-saturation effect was more marked, whereas the slow turbidity in the second phase occurred with a higher rate. This transient-saturation type polymerization profile was observed also in a pH-induced polymerization reaction. It was not observed in the case of the N-bromosuccinimide modified tobacco mosaic virus protein under a similar environmental change. By an electron microscopic study and computer simulation, it was revealed that in the first phase, a large number of short polymers were formed, and the concentration of the polymerizing units was rapidly reduced to the equilibrium value, and the polymerization reaction stopped transiently. In the second phase, polymer-polymer associations took place slowly and longer polymers were formed. The revlevance of the present study to the polymerization reaction of actin, myosin, and to a transient-overshoot type polymerization are discussed.     

Alfalfa mosaic virus protein polymerization.

The self-association of alfalfa mosaic virus coat protein was studied by sedimentation analysis and electron microscopy under a wide range of conditions. In the depolymerized state the protein exists as a molecular species with a sedimentation constant of roughly 3 S and with a molecular weight of (48.4 ± 1.1) × 10³. This value is, within experimental error, twice the value of the monomer (van Beynum, 1975). The dimer has a very stable configuration, as no evidence was found for a monomer-dimer equilibrium between pH values of 3 and 9 and values of ionic strength up to 1.0. One main type of association product (30 S) was found with a molecular weight of (1.48 ± 0.03) × 10⁶. Therefore this particle accomodates 30 dimers which are arranged according to a point group symmetry of 532. The orientation of the 30 dimers within the icosahedral lattice must be such that lattice dyads coincide with the 2-fold axes of the dimers. Micrographs of the 30 S particles show a diameter of about 123 Å; analysis of linear arrays of these particles shows that at low resolution the particle is a hollow sphere with an average coat thickness of about 40 Å.The influence of pH, ionic strength, protein concentration and the type of buffer on the polymerization was determined to some extent and is discussed. The assembly of dimers into the icosahedral particle is an entropy-driven process (Lauffer, 1975); this is concluded from studying the temperature-dependence of the free energy change. Under favourable conditions (phosphate buffer pH 5.5 and ionic strength 0.5) the average enthalpy and entropy changes for the insertion of one dimer into the lattice are about 6.4 kilocalories per mole and 50 entropy units, respectively, based on the unit mole fraction.     

Interaction of tobacco mosaic virus and tobacco mosaic virus protein with bovine serum albumin.

Bovine serum albumin (BSA) causes tobacco mosaic virus (TMV) to crystallize at pH values where both have negative charges. The amount of albumin required to precipitate the virus varies inversely with ionic strength of added electrolyte. At pH values above 5, the precipitating power is greatest when BSA has the maximum total, positive plus negative, charge. Unlike early stages of the crystallization of TMV in ammonium sulfate-phosphate solutions, which can be reversed by lowering the temperature, the precipitation of TMV by BSA is not readily reversed by changes in temperature. The logarithm of the apparent solubility of TMV in BSA solutions, at constant ionic strength of added electrolyte, decreases linearly with increasing BSA concentration. This result and the correlation of precipitating power with total BSA charge suggest that BSA acts in the manner of a salting-out agent. The effect of BSA on the reversible entropy-driven polymerization of TMV protein (TMVP) depends on BSA concentration, pH, and ionic strength. In general, BSA promotes TMVP polymerization, and this effect increases with increasing BSA concentrations. The effect is larger at pH 6.5 than at pH 6. Even though increasing ionic strength promotes polymerization of TMVP in absence of BSA, the effect of increasing ionic strength from 0.08 to 0.18 at pH 6.5 decreases the polymerization-promoting effect of BSA. Likewise, the presence of BSA decreases the polymerization-promoting effect of ionic strength. The polymerization-promoting effect of BSA can be interpreted in terms of a process akin to salting-out. The mutual suppression of the polymerization-promoting effects of BSA and of electrolytes by each other can be partially explained in terms of salting-in of BSA.     

Ultracentrifugation studies on early stage polymerization of tobacco mosaic virus protein

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 ($\text{C?β) =}\text{constant}\text{+ (}\text{ΔH}{}^1\text{2.3RT}$) + ($\text{Δ}\text{W}{}^1{}_{\mathrm{<mtext>el</mtext>}}\text{2.3RT}$) ? 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. $\text{ΔH}{}^1$ and ΔW¹_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, $\text{Δ}\text{W}{}_{\mathrm{el}}{}^1\text{/T}$ 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 $\text{ΔH}{}^1\text{/2.3R}$. The results fit such an equation over nearly a 20 °C-temperature range with a single value of $\text{Δ}\text{H}{}^1$ 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 $\text{Δ}\text{W}{}^1{}_{\mathrm{el}}$ of 1.22 kcal/mol A₁ at pH 6.7 and a value of 4.93 for K_s^′. 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.     

Entropy-driven polymerization of protein from the E66 strain of tobacco mosaic virus

Protein of the tobacco mosaic virus mutant E66 has lysine replacing asparagine of the type strain, vulgare, at position 140. Thus, E66 protein should have one more positive or one less net negative charge than vulgare at pH 6 to 7. To investigate the effect of charge, a comparative study of the polymerization of E66 and vulgare proteins at pH 6.0, 6.2, 6.4, 6.6, and 6.8 at ionic strengths 0.15, 0.10, and 0.05 was made by turbidimetry. Polymerization of E66 protein always proceeded at a lower temperature than vulgare. However, the extent of polymerization was much lower in E66, especially at the higher ionic strengths. Sedimentation velocity results paralleled those from turbidity measurements in that E66 protein polymerizes at lower temperatures than vulgare; the 20 S component is more abundant in E66 protein. Osmotic pressure measurements also show that E66 protein is more polymerized than vulgare, especially at lower pH values. Hydrogen ion titrations of E66 protein were carried out from pH 8 to 5 and back to pH 8 in 0.10 m KCl at three temperatures, 4, 10, and 15 °C. These titrations were reversible when carried out slowly. The isoionic point is near pH 5; thus the charge at pH 7.5 is ?3. The reversible titration results were correlated with the aggregates present at the various pH values and temperatures, determined from the areas under the schlieren peaks in sedimentation velocity experiments. It is found that hydrogen ion binding at the three pH values is correlated with the disappearance of the smallest aggregates and is independent of the type of higher polymer formed. To investigate the effect of ionic strength and pH on the characteristic temperature corresponding to an optical density increment of 0.01 by the method used previously for vulgare, two sets of turbidity measurements were carried out. In the first one the ionic strength was changed from 0.025 to 0.15 in increments of 0.025 at pH 6.0 and 6.4. In the other set, the ionic strength was kept constant at 0.10 and the pH changed from 5.9 to 6.7 in increments of 0.1 pH units. When the analysis of these data was carried out, $\text{Δ}\text{H}{}^1\text{= 30}\text{kcal/mol}$ was obtained. For the salting out constant a value of 1.7 was found, compared to 2.2 for vulgare, a result consistent with the fact that E66 should be less hydrophobic than vulgare. The electrical work term ΔW_el also turns out to be about one-half that for vulgare, which is expected from the lower net negative charge on E66 protein.     

Effect of dipolar ions on the entropy-driven polymerization of tobacco mosaic virus protein

The effect of the dipolar ions, glycine, glycylglycine, and glycylglycylglycine on the polymerization of tobacco mosaic virus (TMV) protein has been studied by the methods of light scattering and ultracentrifugation. All three dipolar ions promote polymerization. The major reaction in the early stage is transition from the 4 S to the 20 S state. As in the absence of dipolar ions, the polymerization is enhanced by an increase in temperature; it is endothermic and therefore entropy-driven. The effect of the dipolar ions can be understood in terms of their action as salting-out agents; they increase the activity coefficient of TMV A protein, the 4 S material, and thus shift the equilibrium toward the 20 S state. The salting-out constants, K, for the reaction in 0.10 ionic strength phosphate buffer at pH 6.7 was found by the light scattering method to be 1.6 for glycine, 2.5 for glycylglycine, and 2.5 for glycylglycylglycine. A value of 2.7 was obtained by the ultracentrifugation method for glycylglycine in phosphate buffer at 0.1 ionic strength and pH 6.8 at 10 degrees C. For both glycine and glycylglycine, K increases when the ionic strength of the phosphate buffer is decreased. This result suggests that electrolytes decrease the activity coefficient of the dipolar ions, a salting-in phenomenon. However, the salting-in constants evaluated from these results are substantially higher than those previously determined by solubility measurements. The effect of glycine and glycylglycine on polymerization was studied at pH values between 6.2 and 6.8. The effectiveness of both dipolar ions is approximately 50% greater at pH 6.8 than at pH 6.2. The variation of the extent of polymerization with pH in the presence of the dipolar ions is consistent with the interpretation that approximately one hydrogen ion is bound for half of the polypeptide units in the polymerized A protein.     

Secondary structure of tobacco mosaic virus protein

A set of rules is proposed for the prediction of α-helices in proteins. These rules lead to the correct assignment to either helical or non-helical regions of over 80% of the amino acid residues in the proteins from which they are derived. Applied to tobacco mosaic virus protein these rules lead to the prediction of five α-helical regions which may be consistent with other data.