Energy Models

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Models of Energy and Information Transfer
(click on the picture to enlarge it)

Figures courtesy of Jeffrey Satinover from his forthcoming book

    Traveling kink or boundary that emerges from the requirements of interacting ferromagnetic spins and chemical waves.
   
Tuzynski02.jpg (7917 bytes)     Double Potential Well for the tubulin dimer. The favored locations for the mobile electron is in a pocket formed by the sub-unit proteins.
   
Tuzynski03.jpg (6397 bytes)     Conformational �kink� traveling along a MT. �a� represents a domain where the mobile electron is in the a sub-unit of the tubulin proteins, orienting the dipole in the direction of travel. �b� represents a domain where the mobile electron is in the b sub-unit of the tubulin proteins, orienting the dipole roughly against the direction of travel.
   
Tuzynski04.jpg (18725 bytes)     2D Arrays forming tubes, with and without skew.
   
Tuzynski05.jpg (3392 bytes)     Two conformations of tubulin based on which subunit has the mobile electron.
   
Tuzynski06.jpg (13007 bytes)     TOP: Favored tubulin neighborhood pattern. BOTTOM: When linked, the neighborhoods form a consistent pattern, but with a skew. When wrapped, the ends will be inconsistent with the rest of the array.
   
Tuzynski07.jpg (34446 bytes)     Circumferential Frustration in a MT. TOP LEFT: Arrows represent forces between dipole sites located at the intersections of the lattice Black arrows are repulsive, white attractive. TOP RIGHT: The same lattice, wrapped, shows left-handed (black) and right-handed (white) helical lines that are symmetrical. But the purely longitudinal direction has only white lines. The black and white arrows illustrate  one sequence with minimal-energy attractive (+) and repulsive (�) dipole forces. When wrapped, these will form a closed circle of neighbor-to-neighbor forces. BOTTOM LEFT: The same arrangement of minimal-energy attractive (+) and repulsive (-) dipole forces is shown here forming a closed circle�but frustration ensues as no arrangement is perfectly consistent.

BOTTOM RIGHT: The arrangement of tubulin states that would correspond to the frustrated lattice structure and the particular closed circle path indicated previously.

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