version = 1.08 of bitt.tex 2011 Nov 12

- For a basic short lesson in information theory, see [1].
- For more terms, see “A Glossary for Molecular Information Theory and the Delila System”:

https://alum.mit.edu/www/toms/glossaryframes.html. - A PDF version of this document is at https://alum.mit.edu/www/toms/papers/bitt/bitt.pdf.
- An HTML version of this document is at https://alum.mit.edu/www/toms/papers/bitt.
^{1}

B = log_{2}M (bits) | Number of bits for M symbols | [1] |

C_{y} = dspace log_{2}(P_{y}∕N_{y} + 1) (bits/mmo) | Molecular machine capacity | [2, 3] |

D = 2dspace ≪ 3n- 6 | Dimensionality of a molecular machine coding space | [2] |

dspace = D∕2 | Number of ‘pins’ a molecular machine uses | [2, 3] |

ΔG (joules/mmo) | Free energy dissipated by a molecular machine in an operation | [2, 3] |

d.f. = 3n- 6 | Degrees of freedom for n atoms | [2] |

min = kBT ln2 (joules per bit) | A version of the Second Law of Thermodynamics that can be used as an ideal conversion factor between energy and bits | [4, 5] |

ϵ_{t} = = | Theoretical maximum molecular efficiency | [4, 5] |

ϵ_{r} ≤ ϵ_{t} | Real (or measured) molecular efficiency | [4, 5] |

kB (joules/kelvin) | Boltzmann’s constant | |

λ = R∕2 | Compressed bases: the number of bases a binding site would take up if the information of the site was compressed as small as possible. | |

M = 2^{B} | Number of symbols corresponding to B bits | |

mmo | Molecular machine operation | [2, 6] |

μ | Mean of Gaussian distribution | |

σ | Standard deviation of Gaussian distribution | |

π | Circle circumference/radius, something to eat | |

n | Number of atoms in a molecular machine. see d.f. | |

N_{y} (joules/mmo) | Thermal noise flowing through a molecular machine during an opertion | [2, 7, 8] |

P_{y} = -ΔG (joules/mmo) | Energy dissipated by a molecular machine in an opertion | [2, 3] |

p(x) = e^{-
} | Probabilty of x for a Gaussian distribution | |

quincunx | Galton’s Quincunx - a device that demonstrates the formation of a Gaussian distribution. See http://tinyurl.com/GaltonQuincunx | |

R (bits/mmo) | Information gained during a molecular machine operation, often of a binding site | [9] |

R_{energy} ≡-ΔG∘∕min (bits per mmo) | The maximum bits that can be gained for the given free energy dissipation | [4, 5] |

ρ = P_{y}∕N_{y} | Energy dissipation of a molecular machine normalized by the thermal noise flowing through the machine | |

T (K) | Absolute temperture, Kelvin | |

x | Voltage (for a communications system) or total potental and kinetic energy for a molecular machine | |

y | See x | |

[1] T. D. Schneider. Information theory primer. Published on the web at https://alum.mit.edu/www/toms/papers/primer/, 2010.

[2] T. D. Schneider. Theory of molecular machines. I. Channel capacity of molecular machines. J. Theor. Biol., 148:83–123, 1991. https://alum.mit.edu/www/toms/papers/ccmm/.

[3] T. D. Schneider. Theory of molecular machines. II. Energy dissipation from molecular machines. J. Theor. Biol., 148:125–137, 1991. https://alum.mit.edu/www/toms/papers/edmm/.

[4] T. D. Schneider. 70% efficiency of bistate molecular machines explained by information theory, high dimensional geometry and evolutionary convergence. Nucleic Acids Res., 38:5995–6006, 2010. doi:10.1093/nar/gkq389, https://alum.mit.edu/www/toms/papers/emmgeo/.

[5] T. D. Schneider. A brief review of molecular information theory. Nano Communication Networks, 1:173–180, 2010. http://dx.doi.org/10.1016/j.nancom.2010.09.002, https://alum.mit.edu/www/toms/papers/brmit/.

[6] T. D. Schneider. Sequence logos, machine/channel capacity, Maxwell’s demon, and molecular computers: a review of the theory of molecular machines. Nanotechnology, 5:1–18, 1994. https://alum.mit.edu/www/toms/papers/nano2/.

[7] J. B. Johnson. Thermal agitation of electricity in conductors. Physical Review, 32:97–109, 1928.

[8] H. Nyquist. Thermal agitation of electric charge in conductors. Physical Review, 32:110–113, 1928.

[9] T. D. Schneider, G. D. Stormo, L. Gold, and A. Ehrenfeucht. Information content of binding sites on nucleotide sequences. J. Mol. Biol., 188:415–431, 1986. https://alum.mit.edu/www/toms/papers/schneider1986/.