Michiki Kasai

A theory of linear and helical aggregations of macromolecules.

A theory of the helical aggregation of macromolecules is presented in comparison with simple linear aggregation. The thermodynamic analysis of the equilibrium distribution of monomers and linear and helical aggregates shows that the transition from dispersed monomers to helical aggregates takes place as a condensation phenomenon. When the concentration of macromolecules is increased, the helical aggregates begin to appear at a critical concentration determined by the solvent conditions. Above this critical concentration very long helical aggregates coexist in equilibrium with a constant concentration of dispersed monomers (and a small amount of simple linear aggregates). Theoretical analysis of the process of the helical aggregation is also made, and the relation between the aggregation rate and the monomer concentration is investigated. The theoretical results are compared with experimental data obtained for various kinds of proteins. Particularly, the equilibrium and kinetic features of the globular-to-fibrous transformation of the muscle protein actin are found to be explained reasonably by assuming that this transformation is a helical aggregation. That is to say, F-actin can be regarded as a helical aggregate of G-actin. Finally, the possible functions of intermolecular superstructures, such as helical aggregates, are discussed.

The cooperative nature of G-F transformation of actin

Abstract Experimental results are presented which suggest that the G-F transformation of actin is a cooperative phenomenon. One of these results is concerned with the relation between the initial rate of transformation and the G-actin concentration. The initial rate increases in proportion to the third to fourth power of G-actin concentration. The dephosphorylation of ATP on G-actin requires the cooperation of two or more G-actin molecules; and the formation of the nucleus of F-actin by three or four G-actins promotes the further transformation of G-actin. The addition of F-actin accelerates the transformation of G-actin and this is further evidence that the G-F transformation of actin is a cooperative phenomenon. Under various salt conditions the transformation rate increases remarkably when increasing amounts of F-actin are added. Moreover, immediately after the addition of F-actin, explosive dephosphorylation of ATP and transformation of G-actin occur.

Polymerization of actin free from nucleotide and divalent cations

Abstract EDTA-Dowex treatment of G-actin in sucrose was found to remove nucleotides and divalent cations from G-actin without loss of polymerizability. This actin could be polymerized into F-actin by the addition of a small amount of simple monovalent salts; that is, polymerization of actin was realised in the sucrose solution without participation of nucleotides and divalent cations. The bond between G-actins to form F-actin induced neither nucleotides nor divalent cations. The polymerization was accelerated by the addition of ATP or ITP, which were bound to G-actin and dephosphorylated during polymerization. The polymerizable G-actin free from nucleotides, could also be obtained by depolymerization in sucrose of the nucleotide-free F-actin prepared by a long dialysis.

The G - F equilibrium in actin solutions under various conditions

Abstract The reversible establishment of equilibrium states in actin solutions, has been investigated under various solvent conditions. In the equilibrium state F-actins coexist with G-actins, the concentration of the latter being determined by the solvent condition. The physical feature of the G - F equilibrium is expressed as a kind of condensation phenomenon. The phase diagram of the equilibrium has been obtained over wide ranges of solvent conditions, i.e. , pH, concentrations of monovalent salts, magnesium, calcium, nucleotides, and organic solvents, and temperature. It has been found that the difference in the effects on the equilibrium of magnesium and calcium increases with increasing concentration of monovalent salts, with increasing pH, and with decreasing temperature. A parallelism has been found between the equilibrium level and the G - F transformation rate and, within the range of the solvent condition here examined, the structure of F-actin is little changed by the solvent condition.

Thermodynamical aspect of G-F transformations of actin

Abstract 1. Thermodynamic analyses were made concerning the polymerization of G-actin to F-actin. The time courses of polymerization were very similar over a wide range of solvent conditions; polymerization curves obtained under varied conditions could be superposed by translation parallel to the logarithmic time axis. 2. The activation enthalpy for polymerization was 20–25 kcal/mole, while the activation enthalpy for depolymerization was about 10 kcal/mole. 3. Based on the fact that polymerization could be regarded as a condensation phenomenon, the apparent enthalpy change associated with the polymerization was estimated from the temperature dependence of the G-actin critical concentration to be about 10 kcal/mole, according to the Clausius-Clapeyron relation. This value, however, could not be directly related to the enthalpy determined by calorimetry, since the polymerization was accompanied by irreversible ATP splitting. 4. A separate calculation of the activation enthalpies in nucleation and growth, of which polymerization consists, was attempted. 5. The activation enthalpy for polymerization did not vary with changes in the ionic conditions, such as ion species, salt concentration and pH. 6. The activation enthalpy for polymerization, which was unaffected by urea, was greatly decreased by ethanol, which also changed its sign. 7. The activation enthalpy for the splitting of ATP at high temperatures and for the exchange reaction of Ca 2+ and ADP bound to F-actin was about 24 kcal/mole, while that for the splitting of ATP under sonic vibration was about 10 kcal/mole.

Behavior of divalent cations and nucleotides bound to F-actin

Abstract 1. 1. Nucleotides and divalent cations bound to F-actin were found to be slowly exchanged in the absence of any agitation such as sonic vibration; the half-life time, τ 1 2 , was about 5 h at 37°. 2. 2. The rate of exchange of divalent cation (Ca2+) was always a little faster than that of nucleotide (ADP); however, the general manner of the exchange of divalent cations was similar to that of nucleotides. 3. 3. The rate of exchange was almost independent of protein concentration. High temperature or high pH increased the rate of exchange. Activation enthalpies for the exchange of ADP and Ca2+ were both about 25 kcal/mole at neutral pH. 4. 4. The release of divalent cations or nucleotides occurred in divalent-cation- or nucleotide-free solvent. The incorporation of divalent cations and nucleotides into divalent-cation- and nucleotide-free F-actin was examined, and their binding constants were estimated. 5. 5. In the absence of ATP, the rate of exchange was decreased by myosin, H-meromyosin and tropomyosin. A large increase of Ca2+ and ADP exchange was observed with superprecipitation. 6. 6. The mechanism of exchange or release is discussed on the basis of two models: the cycle of partial destruction of the F-actin structure, and the G-F equilibrium cycle at the peripheral region of F-actin.

The Exchangeability of actin-bound calcium with various divalent cations

The exchangeability of specifically actin-bound Ca2+ with various other divalent metal ions was examined with the use of 45Ca2+. In the case of Mg2+, the exchange was examined in detail. The amount of exchange was increased by increasing the concentration of Mg2+. This was expected due to the difference in the binding constants of Ca2+ and Mg2+ to actin. The ratio of binding constants of Mg2+ and Ca2+ to G-actin was estimated to be about 1:4. In the case of various divalent cations, there was a close relationship between the ion radius and the amount of exchange. Ions with radii smaller than Ca2+ (about 1.0 A) can be exchanged, although the amount of exchange depended on their concentrations. Larger ions than Ca2+ cannot be exchanged. From these results the site on actin for binding divalent cations seems to have a radius of the order of 1.0 A. The site seems to be inflexible. The classification of divalent cations was also attempted. The binding constants of these divalent cations to actin were also estimated.

Behaviour of sonicated actin polymers: Adenosine triphosphate splitting and polymerization

Abstract The ATP splitting rate, the viscosity and other properties of actin solutions under and after sonic vibration have been investigated at various concentrations of actin and salts. It was found that under sonic vibration at low salt concentrations, G-actin coexists with short actin polymers and the equilibrium between them can be expressed as a kind of condensation phenomena, as in the case of the ordinary G-F transformation of actin. The critical concentration of G-actin for polymers under sonic vibration is almost the same as that for the ordinary Factin under the same solvent conditions. The steady and rapid ATP splitting in actin solutions under sonic vibration, which is proportional to the concentration of polymers, is interpreted as a result of the cyclic polymerization-depolymerization of G-actin taking place at a large number of ends of short polymers, where the polymerization is coupled with the ATP splitting. Sonic vibration accelerates polymerization and depolymerization probably by the increase in the number of ends of polymers. The increase in viscosity of sonicated actin after stopping vibration is mainly due to association of short polymers to form long F-actin.

ULTRAVIOLET DICHROISM OF F-ACTIN ORIENTED BY FLOW.

Ultraviolet dichroism of F-actin oriented by flow is measured. A negative dichroism (a large absorption in the direction perpendicular to the axis of F-actin filament) is observed in the region of 250 m μ to 270 m μ , where nucleotides bound to F-actin contribute to the absorption. The dichroism changes to positive between 275 m μ and 295 m μ . and to negative again between 295 m μ . and 305 m μ where tyrosine and tryptophan residues contribute. The dichroism ratios of nucleotides and amino acid residues are analysed separately. Bound nucleotides are well orientated with respect to the F-actin axis. In a comparison of dichroisms of various kinds of F-actins, it is suggested that the replacement and the removal of divalent cations and nucleotides bound to F-actin have little influence on the over-all and local structure of the F-actin filament.

Removal of nucleotides from F-actin

Abstract A partially nucleotide-free F-actin was obtained by a prolonged dialysis of a normal F-actin having bound ADP, but which maintained its polymer structure. The removal of ADP seemed to happen with equal probability everywhere in the F-actin. There was no appreciable difference in optical and rheological properties between the nucleotide-free F-actin and the normal F-actin. The nucleotide-free F-actin could not rebind nucleotide added to the solvent. However, repolymerizable G-actin was obtained from the nucleotide-free F-actin by depolymerization in the presence of ATP. The site for nucleotide binding in F-actin was not denatured by the removal of ADP. This was suggested also by the fact that the nucleotide-free F-actin had the same ATPase activity in sonic field as the normal F-actin and during this ATPase action ADP was incorporated again into F-actin. The activation of myosin ATPase (EC 3.6.1.4) at low salt concentration in the presence of Mg 2+ was caused by the nucleotide-free F-actin similarly to the normal F-actin. The nucleotide-free F-actin could be obtained only from F-actin having bound Ca 2+ . F-actin having bound Mg 2+ was destroyed in parallel with the removal of ADP. This qualitative difference came from the species of divalent cations incorporated into the structure of F-actin, not from the cations in the dialysing solvent. Some discussion is presented concerning the possible role of nucleotides in F-actin, suggested by the present experiment.