Rotary Motors

Two examples of biomolecular rotary motors are Fradenosine triphosphate synthase (FrATPase) and ATP Synthase (F0Fi) [20,21]. These motors depicted in Figures 3.3 and 3.4, are similar to motors that rotate flagella in bacteria and appear to have originated in cells about a billion years ago. They have evolved and serve many different purposes. These motors occur mounted in the wall of a cell and transmit rotational torque and power across the cell wall. The cell wall is a lipid hydrophobic membrane impervious to flows of liquids and ions and generally sealing the interior of the cell from its environment. The cell is internally structured with rigid actin filaments and tubulins, which act as tracks for the linear engines mentioned above.

The F1-adenosine triphosphate synthase (FrATPase) motor is shown in Figure 3.3 [20]. This rotary engine, which is found in mitochondria and bacterial membranes, "couples with an electrochemical proton gradient and also reversibly hydro-lyzes ATP to form the gradienf [20]. It is shown in these experiments that this motor does work by rotating an attached actin filament through a viscous fluid. The work done by this motor in some biological contexts may be understood as W = e AV, where e is the charge of the proton (hydrogen ion H+) and A Vis electrostatic potential difference. In such a case we have a "proton pump".

ATP Synthase (FoFj) motors from e. coli were attached to a glass coverslip, using the His tag linked to the lower end of the a subunit (lower portion of Figure 3.3). In

Figure 3.3 Fluorescently labeled actin filament permits observation of rotation of the c subunit in ATP Synthase (F0F-|) [20]. A c subunit of Glu2 was replaced by cysteine and then biotinylated to bind streptavidin and the actin filament. The y, e, and c units are thus shown to be a rotor, while the a, ¡3, d, a, and b complex is the stator. The rotation rate of the actin filament in the viscous medium was found to depend upon its length. Rotational rates in the range 0.5 Hz - 10 Hz were measured, consistent with a torque r of40pN-nm

Figure 3.3 Fluorescently labeled actin filament permits observation of rotation of the c subunit in ATP Synthase (F0F-|) [20]. A c subunit of Glu2 was replaced by cysteine and then biotinylated to bind streptavidin and the actin filament. The y, e, and c units are thus shown to be a rotor, while the a, ¡3, d, a, and b complex is the stator. The rotation rate of the actin filament in the viscous medium was found to depend upon its length. Rotational rates in the range 0.5 Hz - 10 Hz were measured, consistent with a torque r of40pN-nm this motor, the y, e, and c units rotate together, as shown in this work. This was demonstrated by attaching the actin filament to the top of the motor, the c unit. Attachment was accomplished in an elegant fashion making use of Streptavidin as shown. The actin filament was tagged with molecules which give characteristic fluorescence when illuminated, in the fashion described above in connection with quantum dots. Video microscope pictures of the fluorescing actin filament revealed counter clockwise rotation (see arrows), when the ambient solution contained 5mM Mg ATP. The rotation rate of the actin filament in the viscous medium was found to depend upon its length. Rotational rates in the range 0.2 Hz - 3.5 Hz were measured, consistent with a torque r of 40 pN • nm.

Analysis of the rotational torque exerted in the viscous fluid was based on the expression t= (4jt/3)o>?7l3[ln(L/2r) - 0.447]-1. (3.4)

Here co is the rotation rate, rj is the viscosity 10_3Pa-s; I and r, respectively, are the length and radius of the actin filament. The actin filament radius r is taken as 5 nm. The measurements indicate a constant torque r of about 40 pN • nm.

These experiments demonstrate an accumulated virtuosity in integrating biological, chemical, and microphysical insight, experimental design, and measurements. To form the experimental structure, alone, is a great accomplishment. The "fluores-cently labeled actin filament-biotin-streptavidin complex" by which the rotation was observed in [20] is an excellent example.

The durability of such motors when harnessed as propeller-turners has been demonstrated by Soong et al [21]. It is common to use biological products in human endeavors, but certainly very uncommon to detach a molecular motor to perform work in the inanimate world.

Figure 3.4 [21] shows a biomolecular rotary motor, Fradenosine triphosphate synthase (FrATPase), harnessed to turn a nanopropeller, allowing measurement of the power output and efficiency of the motor. The motor itself is sketched in panel B of Figure 3.4, and its deployment to turn the propeller is sketched in panel D. The assembled motors are immersed in a buffer solution containing either 2mM Na2ATP (which fuels rotation), or 10 mM NaN3 (Sodium azide) which stops the motion. Panel A shows a portion of an array of nickel posts, typically 50 to 120 nm in diameter and about 200nm high, spaced by about 2.5 Jim, as deposited on a cover glass. The inset to A shows an 80 nm diameter post in a particular experiment.

The motors were mounted on the posts in order to space the propellers away from the base plane. This allows calculations of the work required to turn the propeller in the viscous fluid to be simplified.

The Ni propellers were fabricated, coated suitably to bind to the top of the rotary engines, and suspended in a buffer solution which flowed past the array of engines mounted on Ni posts. In the reported experiment [21] about 400 propellers led to observation of five that rotated continuously in a counter clockwise direction. The attachment points along the propeller length of the rotor axis showed a random distribution, but the lengths Li and I2 of the two sides from the rotor axis were mea-

Figure 3.4 Bio-molecular rotary motor powered propellers. [21] (A) 80 nm Ni post from array. (B) Schematic view of FrATPase molecular motor. (C) Array ofNi propellers, 750 nm-1400 nm in length, 150 nm in diameter. (D) Schematic view of one assembled device from array. Rotation in fluid of propeller (0.8- 8.3 rps) fueled with ATP is 50% efficient

Figure 3.4 Bio-molecular rotary motor powered propellers. [21] (A) 80 nm Ni post from array. (B) Schematic view of FrATPase molecular motor. (C) Array ofNi propellers, 750 nm-1400 nm in length, 150 nm in diameter. (D) Schematic view of one assembled device from array. Rotation in fluid of propeller (0.8- 8.3 rps) fueled with ATP is 50% efficient sured. The observed speeds of rotation depended upon the values of Lx and L2, ranging from 0.8 Hz to 8.3 Hz. It was found that some of the propellers ran for almost 2.5 hours while ATP was present in the cell. The rotation could be stopped by adding sodium azide to the cell.

An analysis of the work done by the rotating propellers was based on an expression for the force per unit length dF/dR exerted by the viscous medium on an element d# of propeller at radius R from the axis, on the assumption that the height h above a flat surface is small:

In this expression rj is the viscosity of the medium, 10_3Pa-s, co is the angular velocity of rotation, R the radius from the axis of rotation, h the pillar height (200 nm), and r half the width of the propeller (75 nm). Integration of this expression on R led to the expression for the torque t

Here Li and I2 are the lengths of the propeller sections extending from the rotational axis.

The determined values of the torque r were 20pN*nm for the 750 nm propellers (8 Hz, attached 200 nm from the end) and 19pN-nm for the 1400 nm propellers (1.1 Hz, attached 350 nm from the end). The energy for one turn of these propellers is then 119- 125 pN-nm. The energy released by hydrolysis of three ATP molecules dF/dR =A7t7]0)R[cosh~1(h/r)Y1.

is reported as about 240 pN • nm, leading to an efficiency of these motors of about 50% [21].

The experiments depicted in Figures 3.3 and 3.4 prove that engines of biology can act as stand-alone machines which function in suitably buffered environments, living or dead, if given ATP. The question: "How many pounds of muscle myosin would be needed to power a typical SUV?", if irreverent, is not entirely irrelevant. After all, large mammals, including whales and elephants, move by muscle myosin. The basic question, (solved by nature), is how to organize these tiny elemental engines to pull together.

It has been suggested that these tiny motors (available, and abundantly tested, proven over millions of years) might fill a gap in the development of nanoelectrome-chanical systems (NEMS), namely, for suitable power sources. As is pointed out in Reference [21], the typical biological rotary motor is about 8nm in diameter, 14 nm in length and is capable of producing 20- 100pN-nm of rotary torque. Its operation depends on the availability of ATP in a suitable aqueous environment.

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