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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 . Analogous to Barrow's treatment for a quantum black hole, we can estimate the motor's information processing power as
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.