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. 2018 Jul 16;8:10694. doi: 10.1038/s41598-018-29084-4

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© The Author(s) 2018

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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Circuit responses to amino acid inputs. (a) Amino acids (AA) stimulate the secretion of both insulin and glucagon. (b) Schematic example of coordinated behavior of insulin (blue line) and glucagon (green dashed line) over time after a step amino-acid stimulus (orange shaded area). (c) Schematic example of uncoordinated behavior of insulin (blue line) and glucagon (green dashed line) over time after a step amino-acid stimulus (red shaded area). (d) Schematics of nullclines for the T₄ circuit with a double positive interaction between the two hormones, without AA input (continuous lines) and with the AA input (dashed lines): intersections (dots) represent steady states (LL - HH). (e) Schematics of nullclines for the T₂ circuit with a double negative interaction between the two hormones without AA input (continuous lines) and with the AA input (dashed lines); intersections (dots) represent steady states (LH - HL). After the AA stimulus, nullclines shift and both steady states decrease (red dots). (f) Schematics nullclines for a negative feedback between the hormones (continuous lines); the intersection (dot) represents a single steady state; after the AA stimulus, nullclines shift (dashed lines) and both hormones increase (HH).