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. 2023 Jan 31;9:3. doi: 10.1038/s41540-023-00266-9

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© The Author(s) 2023

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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Fig. 1 — a The schematic of dose-response alignment (upper panel) and misalignment (lower panel). Dose-response alignment refers to the close match of receptor occupancy and the downstream molecules, and the misalignment the far distance between receptor occupancy and the downstream molecules. b Comparing network architectures capable of perfect DoRA to the negative feedback with general kinetics. “Perfect” means the perfect match of receptor occupancy and the downstream molecules. The naturally reoccurring negative feedback does not have so many constraints as the first three circuits, and we investigate how to improve misalignment to near-perfect DoRA in the circuit with negative feedback. c The experimentally identified coupled GTPase switches related to Arf1 (left) and the circuit without feedback (right). The adaptive response of Arf1 in³⁴ is achieved by the negative feedback loops from active tGTPase to mGAP and from tGEF to mGAP. It should be noted that the cross-talk between two negative feedback loops can be modeled using logical AND or OR operations. d The kinetic details that may affect DoRA, depending on modeling choices that are explored in this work. e Distance metric that measures the DoRA performance: the upper panel shows dose-response curves of the fractional activation for receptors $R_{s s}^{*}$ (red) and downstream GTPases $m G_{s s}^{*}$ and $t G_{s s}^{*}$ (blue: mGTPase; green: tGTPase); these curves after normalization by their activation levels (defined as the level when the stimulus goes to infinity) are denoted by $R_{s s}^{*} / R_{s s, m a x}^{*}$ and Y_ss/Y_ss,max, Y = mG^*, tG^*, as shown in the middle panel; the lower panel defines the distance metric as the weighted sum of the distance between $R_{s s}^{*} / R_{s s, m a x}^{*}$ and Y_ss/Y_ss,max. This metric is equal to the area between the Y_ss/Y_ss,max and the diagonal line in the plot Y_ss/Y_ss,max vs $R_{s s}^{*} / R_{s s, m a x}^{*}$ . The smaller value of this metric indicates better DoRA: zero means perfect DoRA, and small but non-zero value indicates a good DoRA.