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Interruption Matrix Analysis of the Chronological Order of TEs

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posted on 13.07.2007, 02:28 by Joti Giordano, Yongchao Ge, Yevgeniy Gelfand, György Abrusán, Gary Benson, Peter E Warburton

(A) A 360 × 360 adjacency matrix showing the number of times that each of the 360 human TEs interrupt each of the other 360 TEs, with values represented as a heat map as indicated. The TEs are shown in the same order on both the horizontal and vertical axes. This matrix shows a random TE order, and has an upper triangle matrix penalty score of ∼45,000.

(B) Schematic of the matrix with TEs arranged in the correct chronological order from oldest to youngest (decreasing age) on both the horizontal axis (left to right) and the vertical axis (top to bottom). The corners of this matrix will contain points that represent old into old TEs (top left), new into old TEs (bottom left), and new into new TEs (bottom right). New into old TEs (top right) are not expected. This forms the basis for the objective function, which minimizes the upper triangle matrix by element repositioning (see text).

(C) The 360 × 360 adjacency matrix after performing the repositioning algorithm. This represents one solution from one starting order, with a penalty of ∼7,800. There are 360! possible orders, which represents a state space that is far too large (∼10500 orders) to search completely.

(D) Graphical illustration of the results for three TEs of different relative ages. For each TE, the pink graph shows the amount that the TE has interrupted the other elements (interrupTER row in the matrix), and the blue graph shows the amount that the TE has been interrupted by other TEs (interrupTEE column in matrix). The TEs are arranged along the horizontal axis in the final chronological order as determined by IMA. The MLT1J element (top) is relatively old (position 32), and interrupts only a few relatively old elements (pink), but is interrupted by many newer elements (blue). The MLT1B element (middle) is of intermediate age (position 154), and gets interrupted by newer elements (blue) and interrupts older elements (pink) in similar amounts. The AluSx (bottom) is relatively new (position 317), and interrupts many older elements (pink) but is only interrupted by a few newer elements (blue). The values in these graphs have been normalized as described in Materials and Methods. A polynomial trend line of power 3 (black curve) is fitted to each set of points.