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. 2019 Sep 11;9:13124. doi: 10.1038/s41598-019-49571-6

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© The Author(s) 2019

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Temporary vs. persistent interventions. (a) MAPK network for urinary bladder cancer with EGFR over-expression. Arrows and bar-headed lines represent activation and inhibition, respectively. Dotted rectangles denote input nodes of value 0 and a diamond-shaped square denotes over-expressed EGFR of value 1. The 20 nodes marked with dotted circles (“unperturbed”) have fixed values. The remaining 33 nodes (“perturbed”) are marked with solid circles (Supplementary Data 4). (b) Comparison of temporary vs. persistent interventions. The green and red colors of the 33 nodes in the center denote their undesired state values 1 and 0, respectively. The 5^th and 8^th columns on the left and right sides denote the desired attractor state, respectively. The initial and final of arrows (blue) denote the start and end of perturbations, respectively, where bars on the left side denote the end of temporary perturbation. On the left side, the 1^st state denotes a boundary state, where hexagons denote temporary target nodes and their values. We obtained the 2^nd, 3^rd, 4^th and 5^th states by substituting the boundary state into the update rules (Supplementary Data 4) as an initial state, where the 5^th state denotes the desired attractor state. On the right side, the 1^st state denotes any state such that the persistent target nodes’ values are fixed (rectangles in red or green) and the other nodes’ values can be 0 or 1 (marked with*). Substituting any state in the 1^st state into the update rules as an initial state, 9 non-persistent target nodes have fixed values at the right next time step, which are marked with circles in red or green at the 2^nd state. Similarly, substituting any state in the 2^nd state into the update rules as an initial state, 12 non-persistent target nodes have fixed values at the right next time step, which are marked with circles in red or green at the 3^rd state. Repeating this process, all nodes have fixed values by substituting any state in the 7^th state into the update rules as an initial state.