**3.1 The Information Processing Power of a Molecular Motor**

The power P =E/Tmax required by any information processor can be
calculated using Wigner's second clock inequality [7]. Analogous to Barrow's
treatment for a quantum black hole, we can estimate the motor's information
processing power as

E/Tmax=h(Tmin)-2=h(v)2

where v = rmi'n is the fastest possible information processing
frequency of the motor. For a theoretical estimate of the precision Tmin ~
5xl0"l4sec, this corresponds to a power of FW ~ 4 x 10'8 J/sec.

The maximum number of computational steps carried out by the motor
can be estimated as m =Tmax/Tmin 7x1015. Note the number of computational steps
the motor performs is much larger than the number of bases (4xio4) that the
motor actually reads in the running time Tmax. Thus each base in the DNA molecule
corresponds to roughly about (2x10") computational (information
processing)steps carried out by the motor.In comparison, the power actually
generated by the motor Pom can be estimated using experimental force vs.
velocity data [4, 9] as

P = f xv ~ 5pN xlOO bases
~ 1.5x10'" JIsec (4)

If a motor molecule consumes 100 NTP (i.e. nucleotide triphosphate
fuel) molecules per second, this corresponds to an input power Pjn =~
8x10'" J/sec p and a thermodynamic efficiency £¦ = 20% . From the actual
power p generated, we can better estimate the actual precision of our motor 7\,
mW) to be 26 nsec. This suggests that the actual number of computational steps
taken by our motor during its longest running period is about which means that
3xio5 computational steps are taken (or information bits processed) for every
DNA base that the motor reads. Each of the internal microscopic states of the
motor or clock can store information. This leads to dramatically higher
information storage densities than if the information were stored solely in the
DNA molecule itself.As discussed above, the first Wigner relation imposes
constraints on the maximum timescales (and length scales) over which DNA
replication is accurate or, in other words, remains coherent. The second Wigner
inequality sets limits on the motor's precision and its information processing
power. By viewing the motor as an information processing system, we also
calculated the number of computational steps or bits required to specify the
information content of the motor-DNA system. However, in order for quantum
mechanics to play a more proactive role in the dynamics of these motors (i.e.
beyond just imposing the above constraints on their performance), it is
critical that the decoherence time (rD) of the motor-DNA complex be much longer
than the motor's base reading time (rbasereading ~ 10 milliseconds). This
decoherence time (rD) denotes a time scale over which quantum coherence is
lost.