Force–velocity relationships in actin–myosin interactions causing cytoplasmic streaming in algal cells

Cytoplasmic streaming is widely observed in a variety of plant cells. The mechanism of cytoplasmic streaming has been studied most intensively with giant internodal cells of green algae because of their large size (diameter,approximately 500 μm; length, >10 cm). It is now well established that cytoplasmic streaming is caused by ATP-dependent interaction between well-organized actin filament arrays fixed on the rows of chloroplasts (actin cables) and `cytoplasmic' myosin molecules attached to amorphous cytoplasmic organelles. The sliding between actin and cytoplasmic myosin results in movement of the organelles in one direction, determined by the polarity of the actin cables, thus causing streaming of the surrounding cytoplasm(Kamiya and Kuroda, 1956; Kamitsubo, 1966; Nagai and Rebhum, 1966; Kersey and Wessels,1976; Kato and Tonomura,1977; Nagai and Hayama,1979; Fig.1). The direction of cytoplasmic streaming is reversed across the indifferent zone where chloroplasts are absent, reflecting the reversal of actin cable polarity across the indifferent zone. As the two indifferent zones run parallel to the cell's long axis, cytoplasmic streaming rotates longitudinally in the cell.

Although both cytoplasmic streaming and muscle contraction are caused by ATP-dependent actin–myosin interaction, they differ from each other in some properties. Contraction and relaxation in skeletal muscle is regulated by changes in intracellular Ca²⁺ concentration via regulatory proteins on actin filaments (Ebashi and Endo, 1968); a muscle is relaxed at pCa ≥7 and fully contracts at pCa ≤5. By contrast, cytoplasmic streaming occurs continuously even at pCa ≥7 and stops at pCa ≤6(Williamson, 1975; Williamson and Ashley, 1982; Tominaga et al., 1983). Latex beads coated with skeletal muscle myosin slide along actin cables when they are introduced into an internodal cell with Mg-ATP, but the bead movement is insensitive to pCa (Shimmen and Yano,1984), indicating that regulatory proteins are absent on actin cables, while cytoplasmic myosin is responsible for the Ca²⁺-induced stoppage of cytoplasmic streaming. Using the centrifuge microscope, Chaen et al.(1995) showed that the Ca²⁺-induced actin–cytoplasmic myosin linkages are stronger than their rigor linkages, suggesting that a cytoplasmic myosin head can bind with actin at two different sites. Higashi-Fujime et al.(1995) reported that proteolytic cleavage of actin impaired ATP-dependent actin filament sliding on skeletal muscle myosin but not on cytoplasmic myosin, suggesting that cytoplasmic myosin may interact with actin at sites different from those of muscle myosin.

The most striking feature of cytoplasmic streaming is that its velocity(≥50 μm s^-1; Kamiya and Kuroda, 1956) is many times larger than the maximum velocity of actin–myosin sliding in muscle (approximately 3 μm s^-1; Oiwa et al., 1990). In the presence of Mg-ATP, muscle myosin-coated beads slide on actin cables with velocities similar to the maximum unloaded velocity of actin–myosin sliding in muscle (Sheetz and Spudich,1983; Oiwa et al.,1990), whereas muscle actin filaments move on cytoplasmic myosin-coated glass surface with velocities similar to those of native cytoplasmic streaming (Higashi-Fujime et al., 1995). These results indicate that it is cytoplasmic myosin that is responsible for the rapid cytoplasmic streaming. Meanwhile, the ultrastructure of cytoplasmic myosin molecules, consisting of two heads connected to one tail, is similar to that of skeletal muscle myosin, except that the tail length is much shorter in the former than in the latter(Yamamoto et al., 1999).

Under a constant centrifugal force serving as a positive load, skeletal muscle myosin-coated beads moved with a constant velocity over a large distance (Fig. 3A), indicating the definite steady-state relationship between the load (=force generated by myosin molecules on the bead) and the velocity of actin–myosin sliding. The maximum unloaded velocity of bead movement (V_max) was 1.6–3.6 μm s^-1. The bead stopped moving when the load reached the maximum isometric force (P₀) generated by myosin molecules. The force–velocity (P–V) curve obtained was hyperbolic in shape in the low force range but deviated from the hyperbola in the high force range (Fig. 3B). The shape of the P–V curve was nearly similar to that obtained with tetanized single skeletal muscle fibres(Edman, 1988), indicating that muscle myosin molecules retain their basic kinetic properties of contracting muscle fibres despite their random orientation on the bead(Oiwa et al., 1990).

During the course of the above experiments, we made an incidental observation that, when uncoated beads suspended in Mg-ATP solution were introduced into Chara internodal cells, the bead moved along actin cables with velocities and directions similar to those of native cytoplasmic streaming. The beads stopped moving at pCa <6 or by removal of ATP from the surrounding medium. These features of bead movement indicate that it is caused by cytoplasmic myosin molecules, which remain in the cell and attach spontaneously to the bead surface to interact with actin cables. We therefore took the opportunity to determine P–V characteristics of ATP-dependent actin–myosin sliding causing cytoplasmic streaming with the centrifuge microscope system.

Under a constant centrifugal force serving as a positive load, the beads moved with a constant velocity, indicating the presence of a steady-state P–V relationship in actin–myosin interaction causing cytoplasmic streaming (Fig. 4A). V_max was 32–61 μm s^-1(mean ± S._D., 46±8.7 μm s^-1; N=14) at 24–26°C. The beads stopped moving when the load was increased to P₀, which showed a wide variation from 1.0 pN to 13 pN. The P–V curve constructed from six different beads with large P₀ (8.6–13 pN) was nearly linear(Fig. 4B) in contrast to the hyperbolic P–V curve of actin–myosin sliding causing muscle contraction (Fig. 3B). Correction of the data points for the viscous drag force against the bead movement did not alter the shape of the P–V curve(Chaen et al., 1995). The P–V curve constructed from six different beads with small P₀ (1.0–2.4 pN) was also nearly linear, although the data points showed a large scatter due to difficulties in measuring the velocity of bead movement under small centrifugal forces(Fig. 4C). Despite a large variation of P₀ from 1.0 pN to 13 pN, V_maxof the beads with small P₀ values ranged from 36 μm s^-1 to 60 μm s^-1, indicating that V_max was independent of P₀.

On the other hand, when centrifugal forces in the same direction as the bead movement were applied as negative loads, the velocity of bead movement first decreased under small negative loads and then increased with increasing negative load until the bead was finally detached from the actin cables(Fig. 4D). This puzzling phenomenon has also been seen in actin–skeletal muscle myosin sliding(Oiwa et al., 1990) and microtubule–kinesin sliding (Hall et al., 1993). As the centre of gravity of a polystyrene bead(diameter, 2.8 μm) is 1.4 μm above the actin–myosin contact,substantial torque forces around the bead would compress myosin molecules to inhibit actin–myosin sliding.

The minimum value of P₀ generated by cytoplasmic myosin molecules on the bead was 1.0 pN, which is smaller than the reported values of force spikes of single muscle myosin molecules (1–7 pN, Finer et al., 1994; 5–6 pN, Ishijima et al., 1994, 1996). In our experiments,however, the forces measured are time-averaged values against continuously applied centrifugal forces and do not contradict reported values of transient force spikes. On this basis at least, a few myosin molecules may be involved even in generating a P₀ of 1 pN if random orientation of myosin molecules on the bead is taken into consideration. On the other hand,the large V_max in actin–cytoplasmic myosin sliding indicates a large cycling rate of actin–cytoplasmic myosin interaction. Contrary to this expectation, however, the actin-activated ATPase activity of Chara cytoplasmic myosin in solution is similar to that of muscle myosin (Tanimura and Higashi-Fujime, in press). This paradox will be considered later.

In ATP-dependent actin–myosin interaction in skeletal muscle, p is approximately 0.05 (Uyeda et al., 1990; Finer et al.,1994), A is approximately 20 s^-1head^-1 (Toyoshima et al.,1987) and V_max is approximately 3 μm s^-1 (Oiwa et al.,1990). Putting these values into equation 4, we obtain a d of approximately 8 nm, a value consistent with the contraction model, in which unitary actin–myosin sliding is produced by rotation of myosin heads (Huxley and Simmons,1971). The small duty ratio in skeletal muscle myosin heads implies that at least 20 heads, working together, are necessary for continuous actin–myosin sliding.

In ATP-dependent actin–myosin interaction in cytoplasmic streaming,on the other hand, p is assumed to be 0.25, while V_max is approximately 50 μm s^-1(Chaen et al., 1995). The value of d is at present unknown but, on the basis of the Huxley–Simmons scheme, it is constrained by the size of the myosin head and may not be more than about 20 nm. In order to make d realistic(≤20 nm), it follows from equation 3 that A should be approximately 425 s^-1 head^-1. This extremely high cycling rate of actin–myosin interaction, which is likely to be associated with a very low efficiency of chemo-mechanical energy conversion,is consistent with the very large value of a/P₀ of the straight P–V curve (Fig. 4B,C; Chaen et al., 1995). This idea,however, contradicts the result that the actin-activated ATPase rate of cytoplasmic myosin in solution is similar to that of skeletal muscle myosin(20 s^-1 head^-1; Tanimura and Higashi-Fujime, in press). This paradox may be solved at least qualitatively in the following way. In the movement of cytoplasmic organelles or cytoplasmic myosin-coated beads along actin filaments, there seems to be a mechanically coupled interaction between the heads of myosin molecules attached to the same bead. Such interactions are absent in solutions where myosin molecules diffuse freely. Due to its large value of p, each cytoplasmic myosin head interacting with actin would have many chances of being `pushed forward' by sliding forces generated by the head(s) of other myosin molecules attached to the same bead. When a head interacting with actin is pushed forward, it would immediately be detached from actin to restart its sliding force generation. This would considerably reduce the time of attachment of each myosin head to actin without changing its duty ratio and would therefore result in a marked increase in its ATPase rate compared with that in solution.

The above idea of the mechanically coupled myosin head interaction comes from the report that, in single tetanized skeletal muscle fibres, the value of V_max measured by the slack test increases more than twofold in the presence of a small resting tension (≤7% of P₀) at a sarcomere length of approximately 3 μm(Edman, 1988). In the slack test, a tetanized fibre is subjected to a quick release of up to 30% of the initial fibre length. As the resting tension decreases steeply to a negligible value with decreasing sarcomere length for the first approximately 6% of sarcomere shortening following release, this indicates that the effect of resting tension to compress the stretched sarcomere (and therefore to push the myosin heads attached to actin forward) is only transient. This implies that if a myosin head is pushed forward by a transient force, the rate of actin–myosin interaction coupled with ATP hydrolysis can be markedly increased.

Meanwhile, the increase of A (from 20 s^-1head^-1 to 425 s^-1 head^-1) by the mechanically coupled myosin head interaction can be reduced if the value of d is not actually constrained by the size of the myosin head and could be as large as approximately 100 nm by a biased Brownian ratchet mechanism(Vale and Oosawa, 1990). In this case, the increase of A is reduced from 20 s^-1head^-1 to approximately 85 s^-1 head^-1. Much more experimental work is necessary to further understand the mechanisms of cytoplasmic streaming. In the Huxley contraction model(Huxley, 1957), the value of V_max is determined by the balance between positive forces generated by myosin heads and negative forces due to negative strain of myosin heads. If cytoplasmic myosin heads are assumed to detach from actin without generating appreciable negative strain forces, this would also result in a marked increase in the velocity of actin–myosin sliding in cytoplasmic streaming compared with that in muscle contraction. The myosin head negative strain is not explicitly taken into consideration in the concept of duty ratio but is implicitly included in the value of d, and in this sense d may not necessarily be constrained by the size of the myosin head.