Page 126 - Nanotechnology an introduction

the average microtubule length diverges. The molecular origin of growth and shrinkage lies in the fact that tubulin
monomers can bind to guanosine triphosphate (GTP) and the complex can spontaneously assemble to form filaments. But the GTP slowly
hydrolyzes spontaneously to guanosine diphosphate (GDP), thereby somewhat changing the tubulin conformation such that it prefers to be
monomeric. However, the monomers can only be released from the end; disassembly can be initiated if the rate of GTP hydrolysis exceeds that of
tubulin addition for a while. The overall process is a remarkably effective way of searching a restricted volume for an object when no prior
information about the location of the object exists.

11.3.3. The Cost of Control

The force F that has to be applied to a molecular lever requires accurate knowledge of its position x if reversible work is to be performed [64].
Specifying the positional accuracy as Δx, the uncertainty principle gives the energy requirement as

(11.1)
8
where h is Planck's constant (= 6.63 × 10 −34 J s) and c the speed of light in vacuum (= 3.00 × 10 m/s). ΔE is obviously negligible for macroscopic
systems millimeters in size. The uncertainty in the force F(x) generated at x is

(11.2)
To compute the work W done by the system, equation (11.2) is integrated over the appropriate interval. The first term on the right-hand side yields

the reversible work W and the second term yields for any cycle involving j steps.
rev
The energy conversion factor ϵ is

(11.3)
where Q is the net energy input during the cycle. With the help of inequality (11.1), the ratio of this to the classical conversion factor is

(11.4)
where

(11.5)
and the relative energy cost of control is

(11.6)
The maximum possible value of the ratio ϵ/ϵ is obtained by replacing z by its optimal value z , obtained from the turning point of equation (11.4):
opt
rev
(11.7)
it is

(11.8)

If more energy than z is used, then α decreases because of the energy cost of information; if less, then ϵ decreases because of the irreversibility
opt
(dissipation, etc.).
For a macroscopic system these quantities are insignificant. But consider the myosin motor (Figure 11.2): taking F ≈ 2pN, the displacement x ≈ 10
j
nm and Q ≈ 0.067 aJ (the energy released by hydrolyzing a single ATP molecule), then the energy cost of optimum control, Qz , is equivalent to
opt
hydrolyzing almost 150 ATP molecules and . Reversible operation is evidently far from optimal; chemical to mechanical
conversion occurs at a finite rate that may essentially be uncontrolled, i.e., determined intrinsically. This analysis and conclusion allows the loose
coupling model for muscle (Section 11.3.1) to be rationalized.
11.4. DNA as Construction Material
The specific base-pairing of DNA, together with the ease of nucleotide polymerization (it can be accomplished artificially using automated
equipment) and the relative robustness of the molecule, has engendered interest in the design and construction of artificial nanoscale artifacts of
arbitrary shape made from DNA, as Nadrian Seeman was the first to point out. A drawback is that the design of the required DNA strands is a
laborious, empirical process (at least at present); but in principle both DNA and RNA could become universal construction materials (provided they
are not required to be stable under extreme conditions). The fact that enzymes constructed from RNA are known to exist in nature suggests that
ultimately devices could also be made. Once synthesized (according to what are now straightforward, routine procedures—albeit not completely
free from errors), it suffices to randomly stir a solution of the components together at an appropriate temperature; their assembly then proceeds in a
unique (if the sequences have been correctly designed) fashion (Figure 11.3). This field has recently grown enormously to encompass very
elaborate constructions. The process is connected with tile assembly and computation [76].