"Living things are too beautiful
for there not to be a mathematics
that describes them."
--- Tom Schneider
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Molecular Information Theory
the Theory of Molecular Machines

by Tom Schneider
Molecular Information Theory Group
RNA Biology Laboratory (RBL)
Center for Cancer Research, National Cancer Institute
National Institutes of Health in Frederick, MD

  Molecular information theory is the application of Claude Shannon's information theory to molecular patterns and states.
Claude Shannon said: Shannon uncertainty equation: H equals the negative
  sum from i equals 1 to M of P sub i log 2 p sub i bits per
Shannon channel capacity equation: C equals W log base
  2 of P over N plus 1 bits per second.
and so now we have reliable digital communications!
Brief overview: Tom Schneider is best known for inventing sequence logos, a computer graphic depicting patterns in DNA, RNA or protein that is now widely used by molecular biologists. Logos are only the beginning, however, as the information theory measure used to compute them gives results in bits. But why would a binding site have some number of bits? This led to a simple theory: the number of bits in the DNA binding site of a protein is the number needed to find the sites in the genome. Click on the dinosaur to see how these evolve! Next Tom asked how are bits related to binding energy? He solved this problem by using a version of the second law of thermodynamics to convert the bits to the energy needed to select them. Dividing the bits used to define a binding site by the bits that could have been selected for the given energy, he then discovered that the efficiency of DNA binding site selections is near 70% and he constructed a theory to explain this result. Schneider has a number of nanotechnology patents derived in part from this theory.
If you want to understand life, don't think about vibrant, throbbing gels and oozes, think about information technology.
--- Richard Dawkins, The Blind Watchmaker, 1986, Norton, p. 112.
The grand Question which every naturalist ought to have before him when dissecting a whale or classifying a mite, a fungus or an infusorian is "What are the Laws of Life" -- Charles Darwin B Notebook B229
NIH's mission is to seek fundamental knowledge about the nature and behavior of living systems and the application of that knowledge to enhance health, lengthen life, and reduce illness and disability.
Note: These pages use two addional windows, a glossary and references. You can use frames in the bar to the left or launch them separately by clicking on these links. Once you have launched the windows, you can instantly look up papers or get glossary definitions. You can try this with the icons to the right in the green bar.
human donor splice site sequence logo
Sequence logos
were invented here!
sequence walker for human donor splice junctions
Sequence walkers
were invented here!
head of Tyrannosaurus Rex
Evolution -
how DNA gets information!
gumball machine
Sphere packing -
biological states!
Geometry for optimal bistate molecular machines.  Two
  concentric circles are connected by a horizontal line
  segment running from the outer circle on the left, tangent
  to the inner circle in the middle and to the outer circle
  on the right.  Behind the circles are concentric colors in
  a spectrum running red at the center to purple on the edge
  representing lower to higher energy.
Molecular efficiency -
a measure of biological states


nanotechnology: molecular rotating engine
Molecular Rotation Engine
U.S. Patents 7,349,834, 8,086,432 and 8,798,980
Molecular computer circuit diagram for a NOR gate
    made from one repressor protein blocking two different
    activator proteins.
Molecular Computer
U.S. Patent 6,774,222
nanotechnology: Medusa(TM) Sequencer
MedusaTM Sequencer
U.S. Patent 7,871,777
nanotechnology: Rod-Tether Nanoprobe
Rod-Tether Nanoprobe
US Patents 8,344,121 and 8,703,734

I maintain a mailing list for announcements of changes to Delila programs and this web site. If you would like to be on the list, just ask: schneidt@mail.nih.gov

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  • Keywords for indexing: 70 percent efficiency, 70% efficiency, B-DNA, Boltzmann, Claude Shannon, DNA binding site, DNA binding, DNA sequence, DNA, Delila, Frederick, fundamental mathematics of biology, Gibbs, Herbert Schneider, MD, Maryland, Maxwell's Daemon, Maxwell's Demon, NCI, NIH, Nanobiotechnology, National Cancer Institute, National Institutes of Health, RNA, T. D. Schneider, TD Schneider, Thomas D. Schneider, Thomas Schneider, Tom Schneider, Z-DNA, bioinformatics, biological information, biologist, biology, bionet.info-theory, bit, bits, cancer, channel capacity, chowder society, consensus sequences, efficiency, entropy, evolutionary theory, genetic engineering, gumball machines, hMSH2, information entropy, information theory, isothermal efficiency, left-handed DNA, limits of computers, mathematical biology, mathematics of biology, mathematics of living things, mathematics, microarray, molecular biology, molecular information theory, molecular machines, mutation, nanotechnology, nanotechnology, polymorphism, protein, repertoires, replication, sequence logo, sequence walker, splice, splicing, statistical mechanics, theory of biology, theory of molecular machines, thermodynamics, transcription, translation, uncertainty, what is information theory, what is information

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    a scroll of paper, an ink well and a feather pen Thanks for visiting!   For comments, problems, questions or suggestions please contact Tom Schneider.
    This website is currently at:
    I have set up a permanent URL that will always point to wherever this page is:
    If you bookmark this MIT address (as opposed to where it currently points) you will always find this page. since that URL redirects to the current location of the web site.

    A tiny URL for this web page is tinyurl.com/tomschneider; it also points to the MIT web page and hence is permanent.

    You can view earlier pages with the incredible: Internet Archive WaybackMachine:

    1. WaybackMachine link for https://www-lmmb.ncifcrf.gov/~toms/
    2. WaybackMachine link for https://www-lecb.ncifcrf.gov/~toms
    3. WaybackMachine link for https://lecb.ncifcrf.gov/~toms
    4. WaybackMachine link for https://ccrnp.ncifcrf.gov/~toms
    5. WaybackMachine link for https://www.ccrnp.ncifcrf.gov/~toms
      This page USED TO BE at the above locations; they may still work but are not recommended for bookmarking.
    6. WaybackMachine link for https://schneider.ncifcrf.gov/ This is the current location.

    NIH Web Privacy Notice CCR Policies
    any browser campaign that says best viewed with any

    Disclaimers For This Web Site (From: World Wide Web NIH Guidance, April 15, 1998)

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    Small icon for Theory of Molecular Machines: physics,
chemistry, biology, molecular biology, evolutionary theory,
genetic engineering, sequence logos, information theory,
electrical engineering, thermodynamics, statistical
mechanics, hypersphere packing, gumball machines, Maxwell's
Daemon, limits of computers What's that icon?

    origin: 1995 Feb 24
    updated: version = 6.42 of home.html 2018 Jan 27

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