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.     

Preparation and properties of recombinant DNA derived tobacco mosaic virus coat protein

Recombinant DNA derived tobacco mosaic virus (vulgare strain) coat protein (r-TMVP) was obtained by cloning and expression in Escherichia coli and was purified by column chromatography, self-assembly polymerization, and precipitation. SDS-PAGE, amino terminal sequencing, and immunoblotting with polyclonal antibodies raised against TMVP confirmed the identify and purity of the recombinant protein. Isoelectric focusing in 8 M urea and fast atom bombardment mass spectrometry demonstrated that the r-TMVP is not acetylated at the amino terminus, unlike the wild-type protein isolated from the tobacco plant derived virus. The characterization of r-TMVP with regard to its self-assembly properties revealed reversible endothermic polymerization as studied by analytical ultracentrifugation, circular dichroism, and electron microscopy. However, the details of the assembly process differed from those of the wild-type protein. At neutral pH, low ionic strength, and 20 degrees C, TMVP forms a 20S two-turn helical rod that acts as a nucleus for further assembly with RNA and additional TMVP to form TMV. Under more acidic conditions, this 20S structure also acts as a nucleus for protein self-assembly to form viruslike RNA-free rods. The r-TMVP that is not acetylated carries an extra positive charge at the amino terminus and does not appear to form the 20S nucleus. Instead, it forms a 28S four-layer structure, which resembles in size and structure the dimer of the bilayer disk formed by the wild-type protein at pH 8.0, high ionic strength, and 20 degrees C.(ABSTRACT TRUNCATED AT 250 WORDS)     

The Donnan effect in tobacco mosaic virus and its components

Osmotic pressure studies were carried on tobacco mosaic virus (TMV) and its components, protein and RNA, as well as on bis(3,3′-aminopropyl)amine, reported to be present in TMV preparations. Solvents were phosphate and barbital buffers at different values of pH and ionic strength. Measurements were made at room temperature. The Donnan effect was exhibited by TMV protein in phosphate buffer of 0.01 ionic strength at pH values ranging between 5.8 and 7.5. The observed values of the Donnan effect at pH 5.8 and 5.97 were in reasonable agreement with theoretical values calculated from the charge obtained by hydrogen ion titration. TMV-RNA in phosphate buffer at pH 7.5 and ionic strength 0.01 did not exhibit more than 1% of the expected Donnan effect. This is explained tentatively as the result of firm binding of metal ions. Negative values of osmotic pressure were observed with bis(3,3′-aminopropyl)amine. Similar anomalous osmosis was sometimes observed with TMV protein and with TMV. In agreement with earlier observations, TMV did not exhibit the Donnan effect in phosphate buffer of 0.01 ionic strength at pH values ranging from 5.5 to 8.0. However, TMV dialysed extensively in the presence of EDTA at pH 8.5 and TMV produced by reconstitution of purified protein and RNA did exhibit the Donnan effect in both phosphate and barbital buffers. The magnitude was of the same order as that calculated from the net charge determined by hydrogen ion titration. When reconstituted TMV, which did exhibit Donnan effect, was treated with calcium ions, the effect was abolished.     

Structure and function of disk aggregates of the coat protein of tobacco mosaic virus

Experiments have been carried out on the coat protein of tobacco mosaic virus (TMVP) to test for the occurrence of the previously postulated RNA-induced direct switching, during in vitro assembly of tobacco mosaic virus (TMV), of the subunit packing from the cylindrical bilayer disk to the virus helical arrangement. No evidence was found for such RNA-induced switching and no evidence for the direct participation of the bilayer disk in either the nucleation or elongation phases of the in vitro virus assembly. Instead, virus assembly proceeds by an initiation step involving the binding of the RNA to the previously characterized two-plus turn helical aggregate that is formed from small oligomers of subunits. However, a bilayer disk, which has been characterized in high ionic strength crystals, has been observed in low ionic strength virus assembly solutions only as a transient species upon depolymerization of dimers of bilayer disks formed in solution at high ionic strength, and not as an equilibrium species of TMVP.     

Disk aggregates of tobacco mosaic virus protein in solution: electron microscopy observations

Previous studies of the coat protein of tobacco mosaic virus (TMVP) have shown that TMVP presumably exists as linear stacks of two-ring cylindrical disks in the 0.7 M ionic strength buffer used for crystallizing the disks for X-ray diffraction studies [Raghavendra, K., Adams, M.L., & Schuster, T.M. (1985) Biochemistry 24, 3298-3304]. The spectroscopic and sedimentation studies of solutions of TMVP under these crystallizing conditions have demonstrated a long-term metastability of these disk aggregates when they are placed in 0.1 M ionic strength buffers, as are used for reconstituting tobacco mosaic virus from TMVP and viral RNA. The present work describes an electron microscopic study of TMVP disk aggregates under the same solution conditions employed in the previous spectroscopic and sedimentation studies. The results show that in the pH 8.0 0.7 M ionic strength crystallization buffer TMVP exists as stacks of disks which range in size from about 6 to 24 layers, corresponding to 3-12 2-layer disk aggregates having 17 subunits per layer. These TMVP aggregates persist in a metastable form in 0.1 M ionic strength virus reconstitution buffer with no apparent changes in structure of the stacked disks. The results are consistent with the conclusions of the solution physical-chemical studies which suggest that the disk structure may not be related to the 20S TMVP aggregate that is the nucleation species in virus     

Polymerization studies on protein from the PM2 strain of tobacco mosaic virus: Light scattering and related studies

Light-scattering and related studies on the polymerization behavior of the protein from the PM2 strain of TMV show that in phosphate buffer of ionic strength 0.1, the maximum extent of temperature-mediated polymerization occurs at pH values lower than in the case of TMV protein. The pH range of temperature-induced polymerization is from 5.0 to 6.0, contrasted with 5.0 to 7.5 for TMV protein. Velocity sedimentation studies show that PM2 protein at room temperature in phosphate buffer (I = 0.1) has sedimentation coefficients of 174 S, 104 S, and 4.3 S at pH values of 4.89, 5.53, and 7.5. Electron microscope studies show that at room temperature in phosphate buffer of 0.1 ionic strength at pH 5.53, PM2 protein has structures resembling essentially that of stacked double discs with an occasional helical structure. Similar studies of PM2 protein in 0.1 M ammonium acetate buffer at pH 5.2 show single, double, and double-double helices.     

Phase behavior of mixtures of rods (tobacco mosaic virus) and spheres (polyethylene oxide, bovine serum albumin).

Aqueous suspensions of mixtures of the rodlike virus tobacco mosaic virus (TMV) with globular macromolecules such as polyethylene oxide (PEO) or bovine serum albumin (BSA) phase separate and exhibit rich and strikingly similar phase behavior. Isotropic, nematic, lamellar, and crystalline phases are observed as a function of the concentration of the constituents and ionic strength. The observed phase behavior is considered to arise from attractions between the two particles induced by the presence of BSA or PEO. For the TMV/BSA mixtures, the BSA adsorbs to the TMV and bridging of the BSA between TMV produces the attractions. For TMV/PEO mixtures, attractions are entropically driven via excluded volume effects known alternatively as the "depletion interaction" or "macromolecular crowding."     

Sedimentation equilibrium measurements of the intermediate-size tobacco mosaic virus protein polymers

Short-column sedimentation equilibrium methods have been applied for the first time to tobacco mosaic virus (TMV) protein (0.1 M ionic strength orthophosphate) at pH 6.5 and at pH 7.0 to estimate molecular weights. Previous sedimentation velocity experiments at pH 6.5, 20 degrees C have led to the conclusion that the major boundary with an S0(20),w value of 24.4 +/- 0.1 S consists of a distribution of polymers which are mainly three-turn, 48-51-subunit helical rod aggregates. The directly measured z-average molecular weights together with sedimentation velocity data are entirely consistent with this assignment of a three-turn aggregate. Molecular weights have also been determined under two conditions where a large mass fraction of the protein sediments with an S0(20),w value of 20.3 +/- 0.2 S. At pH 6.5, 6-8 degrees C, the aggregates in this boundary are metastable and correspond to 50-60% of the preparation. At pH 7.0, 20 degrees C at equilibrium, 65-75% of the protein sediments at 20.3 S. The 20.3S boundary is very similar under both conditions and is interpreted as being composed of a distribution of protein aggregates centered about 39 +/- 2 subunits. This result is important in the interpretation of previous kinetic measurements of TMV self-assembly. The current view is that the 34-subunit structure of TMV protein, in the form of a cylindrical disk which is made up of two 17-subunit layers and has been characterized in single-crystal X-ray diffraction studies, plays a central role in the initial binding steps with RNA. The present results are not consistent with the view that there is a significant concentration of the TMV protein disk structure in solution under the usual conditions of TMV self-assembly.     

A specific effect of calcium ion on the polymerization-depolymerization of tobacco mosaic virus protein.

Tobacco mosaic virus protein stored in the cold at low ionic strength between pH 5 and 5.5 is highly polymerized. When such protein is brought to room temperature and mixed with acetate buffer and additional electrolyte to give a final pH of 6.5 and ionic strength of 0.1, the protein is still in the polymerized state. When the temperature is dropped to about 5 °C, the protein depolymerizes rapidly, in the normal manner, if the added electrolyte is barium chloride, magnesium chloride, or potassium chloride. However, if it is 0.01 m calcium chloride, the depolymerization is slow, requiring about 12 h to reach completion. When the temperature of this depolymerized solution is raised, the protein polymerizes rapidly; when the temperature is dropped, the protein depolymerizes rapidly, just as in solutions free of calcium.Ion-binding studies show that calcium is bound to the protein during the initial step when it is brought to pH 6.5 and room temperature in the presence of calcium. The calcium is released during the slow depolymerization when the temperature is dropped and is not bound again during polymerization at pH 6.5, brought about by an increase in temperature. This means that polymerized protein at pH 5.5 has a structure capable of binding calcium ions, probably a helical structure like that of the protein in the virus. When pH is raised to pH 6.5 at room temperature, this structure remains long enough for calcium to be bound when present. These calcium ions stabilize the polymer, resulting in slow depolymerization when the temperature is lowered. When the temperature is raised at pH 6.5, a different, looser polymer structure is obtained, one not capable of binding calcium.     

Time-resolved solution X-ray scattering of tobacco mosaic virus coat protein: kinetics and structure of intermediates

The kinetics of assembly and disassembly of tobacco mosaic virus coat protein (TMVP) following temperature jumps have been studied by small-angle X-ray scattering and turbidimetry. The structures of the principal aggregates of TMVP oligomers (A protein), intermediate size (helix I) and large size helical rods (helix II), have been characterized by their average radii of gyration of thickness, cross section, and shape obtained from the corresponding regimes of the small-angle scattering pattern. This structural information was obtained within seconds after the temperature-induced initiation of either polymerization or depolymerization and allowed us to detect transient intermediates. This methodology made it possible to observe and characterize the structure of a principal intermediate. Taken together with other kinetic information, these data suggest that polymerization of TMVP under virus self-assembly conditions may proceed via a single-layered helical nucleus that contains about 20 subunits. Previous studies have shown that overshoot polymerization of TMVP can occur and results in metastable long helical viruslike rods which subsequently depolymerize and then form short helical rods, depending on the conditions of the final equilibrium state. The longer rods (helix II) are overshoot polymers which form within seconds and contain 17 1/3 subunits per turn (helix IIB), in contrast to the subunit packing arrangement of 16 1/3 subunits per turn found in the shorter helical rods (helix IA). The latter packing arrangement is the one found in TMV. An overall polymerization scheme is proposed for the formation of these two helical forms of TMVP.     

Studies on the mechanism of assembly of tobacco mosaic virus.

Sedimentation and proton binding studies on the endothermic self-association of tobacco mosaic virus (TMV) protein indicate that the so-called "20S" sedimenting protein is an interaction system involving at least the 34-subunit two-turn yield cylindrical disk aggregate and the 49-subunit three-turn helical rod. The pH dependence of this overall equilibrium suggests that disk formation is proton-linked through the binding of protons to the two-turn helix which is not present as significant concentrations near pH 7. There is a temperature-induced intramolecular conformation change in the protein leading to a difference spectrum which is complete in 5 x 10(-6) s at pH 7 and 20 degrees C and is dominated at 300 nm by tryptophan residues. Kinetics measurements of protein polymerization, from 10(-6) to 10(3) s, reveal three relaxation processes at pH 7.0, 20 degrees C, 0.10 M ionic strength K (H) PO4. The fastest relaxation time is a few milliseconds and represents reactions within the 4S protein distribution. The second fastest relaxation is 50-100 x 10(-3) s and represents elementary polymerization steps involved in the formation of the approximately 20 S protein. Analysis of the slowest relaxation, approximately 5 x 10(4) s, suggests that this very slow formation of approximately 20 S protein may be dominated by some first order process in the overall dissociation of approximately 20S protein. Sedimentation measurements of the rate of TMV reconstitution, under the same conditions, show by direct measurements of 4S and approximately 20S incorporation at various 4S to approximately 20S weight ratios that the relative rate of approximately 20S incorporation decreases almost linearly, from 0 to 50% 4S. There appears to be one or more regions of TMV-RNA, approximately 1-1.5 kilobases long, which incorporates approximately 20S protein exclusively. Solutions of approximately 95-100% approximately 20S protein have been prepared for the first time and used for reconstitution with RNA. Such protein solutions yield full size TMV, but at a slower rate than if 4S protein is added. Thus the elongation reaction in TMV assembly, following nucleation with approximately 20S protein, is not exclusively dependent upon the presence of either 4S or approximately 20S protein aggregates. The initial, maximum, rate of reconstitution increases about threefold when the protein composition is changed from 5% to 30% 4S protein, at constant total protein concentration at pH 7.0, 20 degrees C in 0.10 M ionic strength K (H)PO4. The probable binding frame at the internal assembly nucleation site of TMV-RNA has been determined by measuring the association constants for the binding of various trinucleoside diphosphates to helical TMV protein rods. The -CAG-AAG-AAG-sequence at the nucleation site is capable of providing at least 10-14 kcal/mol of sites of binding free energy for the nucleation event in TMV self-assembly.     

Polymerization studies on protein from the dahlemense strain of tobacco mosaic virus: Light scattering and related studies

Light-scattering and related studies on protein of Dahlmense strain of tobacco mosaic virus (DTMV) show that its polymerization characteristics are considerably different from those of TMV protein. At pH 6.0 in phosphate buffer (I = 0.1), the extent of polymerization of DTMV protein is greater than that of TMV protein, they are nearly the same at pH 6.25, and that of DTMV protein is less than that of TMV protein at pH 6.5. At pH 7.0 and 7.5, DTMV protein polymerizes more readily than TMV protein. Similar studies in phosphate buffer (I = 0.05) show that the extent of polymerization for DTMV protein is less than that of TMV protein at pH 6.0 and almost negligible at pH 6.25. Acid-base titration studies show that, upon temperature-mediated polymerization, about 2 H⁺ ions are bound per monomer of DTMV protein at pH 6.O.Electron microscope studies show that DTMV protein exists at room temperature as double discs and polymerized rods in phosphate buffer at pH 7.5, I = 0.1; at pH values below 6.5, DTMV protein is entirely in the form of polymerized rods. Velocity sedimentation studies of DTMV protein at room temperature are in agreement with these findings. At low temperatures, except at pH 7.5, most of the material sedimented with an s value of around 25 S. Thus, at low temperatures, except at pH 7.5, DTMV protein in solution is in the form of particles the size of double discs with an $\text{M}\text{?}{}_{\mathrm{<mtext>r</mtext>}}$ of 596,000 g/mole or even larger. Therefore, temperature-mediated polymerization of DTMV protein at pH values below 6.5 in phosphate buffer (I = 0.1) and below 6.25 in phosphate buffer (I = 0.05) involves particles at least as large as double discs as the starting material.     

Temperature dependence of the structure of aggregates of tobacco mosaic virus protein at pH 7.2. Static synchrotron small-angle X-ray scattering

The small-angle X-ray scattering (SAXS) method using a synchrotron radiation source was applied to the study of the self-aggregation process of tobacco mosaic virus protein (TMVP) at a concentration of 5.0 or 12.0 mg ml-1 in 50 mM or 100 mM-phosphate buffer (ionic strengths approx. 0.1 and 0.2, respectively) at pH 7.2 in the temperature region of 4.8 to 25.0 degrees C. This paper presents the results of static measurements of SAXS. Sedimentation velocity experiments were performed simultaneously under the same conditions. These results are qualitatively parallel to those of the SAXS measurements, although the size of stacked disks derived from the SAXS measurements is larger than that derived from the sedimentation experiments, suggesting a change in the equilibrium conditions in the centrifugal field. Qualitative analysis of the SAXS data with model simulation calculations implies that the aggregation of TMVP consists of two steps: (1) the aggregation of A-protein comprising a few subunits to form double-layered disks; and (2) the random polymerization of double-layered disks by disk-stacking. Increase in temperature, ionic strength or protein concentration induced TMVP to polymerize to form a double-layered disk or a quadruple-layered short rod with consumption of A-proteins, accompanied by a small number of multi-layered short rods. The SAXS results indicate that the A-protein and the multilayered short rods are polydisperse with respect to size and shape, i.e. the mixture of A-protein, double-layered disks and multi-layered short rods coexists in the equilibrium state without pressure-induced partial dissociation of TMPV as observed during normal ultracentrifugation, and even under solution conditions in which the formation of double-layered disks or higher-order aggregates is favored.     

Ordered association of tobacco mosaic virus in the presence of divalent metal ions

The formation of ordered aggregates of tobacco mosaic virus (TMV) in the presence of divalent metal ions has been studied in concentrated (1-25 mg/ml) solutions of the virus. The divalent metal cations Cd2+, Zn2+, Pb2+, Cu2+, and Ni2+ have been found to promote TMV precipitation from solution at a critical concentration Ccrit, which for a given metal depends on the pH and the ionic strength of the solution, but is largely independent of the virus concentration. The TMV precipitate behaves as a nematic liquid crystal and on drying at a glass surface produces highly ordered, optically birefringent films. However, precipitation is not observed with alkali-earth metals such as Ca2+ and Mg2+. The experimental data suggest that, apart from two 'internal' metal-binding sites in each TMV subunit, the virus contains metal-binding sites of a lower affinity which promote cross-linking of TMV rods via metal bridges. The latter seem to be responsible for the precipitation of TMV in the presence of divalent cations at neutral pH. We propose that the metal-induced cross-linking may be the predominant mechanism to account for the limited solubility of a variety of proteins in solution containing metal cations with valence 2 and higher.     

Proton dependence of tobacco mosaic virus dissociation by pressure

Tobacco mosaic virus (TMV) is an intensely studied model of viruses. This paper reports an investigation into the dissociation of TMV by pH and pressure up to 220 MPa. The viral solution (0.25 mg/ml) incubated at 277 K showed a significant decrease in light scattering with increasing pH, suggesting dissociation. This observation was confirmed by HPLC gel filtration and electron microscopy. The calculated volume change of dissociation (DeltaV) decreased (absolute value) from -49.7 ml/mol of subunit at pH 3.8 to -21.7 ml/mol of subunit at pH 9.0. The decrease from pH 9.0 to 3.8 caused a stabilization of 14.1 kJ/mol of TMV subunit. The estimated proton release calculated from pressure-induced dissociation curves was 0.584 mol H(+)/mol of TMV subunit. These results suggest that the degree of virus inactivation by pressure and the immunogenicity of the inactivated structures can be optimized by modulating the surrounding pH.     

A mechanism of macroscopic (amorphous) aggregation of the tobacco mosaic virus coat protein

To gain more insight into the mechanisms of heating-induced irreversible macroscopic aggregation of the tobacco mosaic virus (TMV) coat protein (CP), the effects of pH and ionic strength on this process were studied using turbidimetry, CD spectroscopy, and fluorescence spectroscopy. At 42 degrees C, the TMV CP passed very rapidly (in less than 15s) into a slightly unfolded conformation, presumably because heating disordered a segment of the subunit where the so-called hydrophobic girdle of the molecule resides. We suppose that the amino acid residues of this girdle are responsible for the aberrant hydrophobic interactions between subunits that initiate macroscopic protein aggregation. Its rate increased by several thousands of times as the phosphate buffer molarity was varied from 20 to 70 mM, suggesting that neutralization of strong repulsive electrostatic interactions of TMV CP molecules at high ionic strengths is a prerequisite for amorphous aggregation of this protein.     

Further studies on the contribution of electrostatic and hydrophobic interactions to protein adsorption on dye-ligand adsorbents.

The adsorption equilibria of bovine serum albumin (BSA), gamma-globulin, and lysozyme to three kinds of Cibacron blue 3GA (CB)-modified agarose gels, 6% agarose gel-coated steel heads (6AS), Sepharose CL-6B, and a home-made 4% agarose gel (4AB), were studied. We show that ionic strength has irregular effects on BSA adsorption to the CB-modified affinity gels by affecting the interactions between the negatively charged protein and CB as well as CB and the support matrix. At low salt concentrations, the increase in ionic strength decreases the electrostatic repulsion between negatively charged BSA and the negatively charged gel surfaces, thus resulting in the increase of BSA adsorption. This tendency depends on the pore size of the solid matrix, CB coupling density, and the net negative charges of proteins (or aqueous - phase pH value). Sepharose gel has larger average pore size, so the electrostatic repulsion-effected protein exclusion from the small gel pores is observed only for the affinity adsorbent with high CB coupling density (15.4 micromol/mL) at very low ionic strength (NaCl concentration below 0.05 M in 10 mM Tris-HCl buffer, pH 7.5). However, because CB-6AS and CB-4AB have a smaller pore size, the electrostatic exclusion effect can be found at NaCl concentrations of up to 0.2 M. The electrostatic exclusion effect is even found for CB-6AS with a CB density as low as 2.38 micromol/mL. Moreover, the electrostatic exclusion effect decreases with decreasing aqueous-phase pH due to the decrease of the net negative charges of the protein. For gamma-globulin and lysozyme with higher isoelectric points than BSA, the electrostatic exclusion effect is not observed. At higher ionic strength, protein adsorption to the CB-modified adsorbents decreases with increasing ionic strength. It is concluded that the hydrophobic interaction between CB molecules and the support matrix increases with increasing ionic strength, leading to the decrease of ligand density accessible to proteins, and then the decrease of protein adsorption. Thus, due to the hybrid effect of electrostatic and hydrophobic interactions, in most cases studied there exists a salt concentration to maximize BSA adsorption.     

The effect of ionic strength on the entropy-driven polymerization of tobacco mosaic virus protein: Contributions of electrical work and salting-out

The entropy-driven polymerization of tobacco mosaic virus protein is favored by an increase in ionic strength, μ, and by a decrease in pH. The effect of ionic strength is interpreted in terms of salting-out and electrical work, a function of charge and, therefore, of pH as well as of μ. The extent of polymerization is measured in terms of a characteristic temperature, $\text{T}{}^1$, corresponding to a characteristic value of the equilibrium constant, $\text{K}{}_{\mathrm{<mtext>c</mtext>}}{}^{\mathrm{T1}}$ is measured at an early stage in the polymerization process where the optical density increment from light scatter is 0.01. The theory developed encompassing both salting-out and electrical work terms relates $\text{1}\text{T}{}^1$ to μ approximately according to the equation, $\text{1}\text{T}{}^1\text{= C + Bμ ?}\text{A}\text{μ}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, where C is the ratio of entropy to enthalpy, B is proportional to the salting-out constant divided by enthalpy, and $\text{A}\text{μ}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ depends upon the square of the charge and is proportional to the electrical work contribution divided by the enthalpy. Data in which μ varied from 0.025 to 0.150 at three pH values, 5.95, 6.35, and 6.50, were fitted to this equation and the parameters C, B, and A were evaluated. Experiments were also carried out at a constant μ of 0.10 at pH values in increments of 0.1 between 5.9 and 6.8. The theory predicts that, at constant μ, $\text{1}\text{T}{}^1$, corrected for the electrical work contribution, is a linear function of pH with a negative slope proportional to the number of hydrogen ions bound per protein unit during polymerization, divided by the enthalpy. The data obtained fit two straight lines with different slopes above and below pH 6.3. Independent experiments carried out by the method of Stevens and Loga show that the number of hydrogen ions bound per protein unit also differs above and below pH 6.3 and the ratio of these is the same as the ratio of the above mentioned slopes. The data, therefore, make it possible to evaluate the enthalpy to be 24.8 kcal/mol of associating A protein and, with this value, the parameters C, B, and A can be interpreted. Standard entropies range from 86 e.u. at pH 6.5 to 88.5 at pH 5.95 and the salting-out constant, K_S^′, is 2.2 at all pH values studied. At μ = 0.10, the values of the electrical work contribution at pH 5.95, 6.35, and 6.50 are +0.298, +0.455, and +0.534 kcal/mol, respectively. Theoretical calculations from models predict values in agreement within a factor of less than two.     

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.