Linear Engines on Tracks

The spring and ratchet systems, structurally ill-defined but clearly electrostatic in mechanism, contrast with well defined linear and rotary engines, which move in stepwise fashions, however, with mechanisms that remain unclear. In this discussion we mention the linear motors myosin and kinesin [8]; and an example of a rotary motor, suitable for driving a flagellum, in this case Ft-adenosine triphosphate synthase. In contrast to the spring systems, the energetics of these linear and rotary motors is definitely tied to the conversion (hydrolysis) of ATP to AD P. The efficiency of conversion of chemical energy to mechanical energy appears to be close to unity.

Footnote 33 to [8] states "The work efficiencies of kinesin and myosin (each 50-60% efficient) are much greater than that of an automobile (10- 15%)".

There is no quarrel with this statement, but it may not be appreciated that the biological and internal combustion engines are of entirely different types. The automobile engine is a heat engine, as described by the laws of thermodynamics, with efficiency that depends essentially on the ratio of the input and exhaust gas temperatures on the Kelvin scale, where room temperature is about 300 K. The compression ratio is a quantity to be maximized, for example, for an efficient diesel or gasoline internal combustion engine, and the mathematics for the ideal or limiting case is based on the Carnot cycle. The compression ratio has nothing to do with biological engines.

The biological motors, in contrast, provide direct conversion of chemical to mechanical energy. Temperature plays no essential role, and the system is more like a chemical battery except that the output is realized in mechanical rather than electrical terms.

The linear engines, myosin and kinesin, move along protein polymers, (actin and microtubules, respectively), in quantized steps, using up a fixed number of ATP molecules per step [8]. The actin filaments, for example, are about 5nm in diameter and 1-4 micrometers in length. The essence of the step-wise motion seems to be a change in conformation (shape or configuration) of the large motor molecule, energetically enabled by the hydrolysis of ATP, which allows the motor to move one well-defined step along its substrate. The rotary motor is less transparent in its operation. Yet it seems likely that these cases may eventually all be understood in essentially electrostatic terms.

A summary of various types of biological cellular engines is provided in Table 3.1 [6],

Table 3.1 Cellular engines of biology [6]. The performance of various cellular engines is compared with thermal energy (kT) and a typical automobile engine. Calculations for the specific power are based on the molecular weight of the smallest unit of the engine. Thus, molecular motors and polymerization-based engines are more powerful than the cellular structures in which they are found; for example, compare myosin to striated muscle

Engine Velocity Force (dynes) Specific Power

Table 3.1 Cellular engines of biology [6]. The performance of various cellular engines is compared with thermal energy (kT) and a typical automobile engine. Calculations for the specific power are based on the molecular weight of the smallest unit of the engine. Thus, molecular motors and polymerization-based engines are more powerful than the cellular structures in which they are found; for example, compare myosin to striated muscle

Engine Velocity Force (dynes) Specific Power

kT (thermal energy)

-

4 x 10 7 dyne nm

-

Actin polymerization [9]

1.0

lxlO'5

lxlO9

Microtubule polymerization [10]

0.02

4 x 10-7

5 x 108

Myosin II [11]

4.0

lxlO'6

2 x 108

Kinesin [12]

1.0

6 x 10-7

7x 107

Vorticellid spasmoneme [13]

8xl04

1 x 10-3

4xl07

Automobile engine, typical [14]

3 x 106

Striated muscle [14]

2xl06

Bacterial flagellar motor [15,16]

100 Hz

4.5 x 10"11 dyne cm

lxlO6

Thyone acrosomal reaction [17]

6-9

5 x 10-4

lxlO5

Limulus acrosome reaction

10

1 x 10~6

lxlO4

Eukaryotic flagellum [14]

-

3 x 102

Mitotic spindle [14]

2.0

1 x 10-5

Models for the movement of muscle myosin and kinesin are given in Figure 3.2 [8]. In both cases the motor moves along a strong filament which is part of the internal structure of the cell. The function of kinesin is to move material within the cell, the upward extended filament in Figure 3.2 B is attached to such a load.

Myosin

| mixrr

Kinesin

0 0

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