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. 2014 Aug 19;2:27. doi: 10.3389/fbioe.2014.00027

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Copyright © 2014 Korsunsky, McGovern, LaGatta, Olde Loohuis, Grosso-Applewhite, Griffeth and Mishra.

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

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Abstraction example. (A) A concrete ODE model. Left: circuit diagram. Pointed arrows denote activation while flat head arrows denote inhibition. Right: demonstration of hysteresis in E2F concentration and the lack of it in cyclin D concentration. (B) Its reduced abstraction model. Each state is actually characterized by statistics on all species in the original model. Here, the mean and SD of E2F is used for brevity. Each edge is marked by the growth signal values (mean and SD) that cause that transition. (C) Two representative edge distributions. The left panel shows the distribution of transition time from the low E2F state to the high one when the growth signal value is 1.5. The right panel shows the same transition for a growth signal value of 2.0. In both, the green circle represents the mean. Notice that the distributions look similar but the mean transition time decreases substantially for the higher input.