Highlights d An intrinsic trade-off exists in three-node networks d Tuning timescales can partially mediate this trade-off with a cost d Sequential assembly in four-node networks can effectively decouple two functions d Biological adaptive networks are often associated with a noise attenuation module

SUMMARYIntercellular (between-cells) signals must be converted into an intracellular (within-cell) signal before it can trigger a proportionate response. How cells mount such proportionate responses within their interior remains unknown. Here we unravel the role of a coupled GTPase circuit on the Golgi membranes which enables the intracellular secretory machinery to respond proportionately to the growth factors in the extracellular space. The circuit, comprised of two species of biological switches, the Ras-superfamily monomeric GTPase Arf1, and the heterotrimeric GTPase, Giαβγ and their corresponding GAPs and GEFs, is coupled via at least one a forward and two key negative feedback loops. Interrogation of the circuit featuring such closed-loop control (CLC) using an integrated systems-based and experimental approach showed that CLC allows the two GTPases to mutually control each other and convert the expected switch-like behavior of Arf1 into an unexpected dose response aligned (DoRA) linear behavior. Such behavior translates into growth factor stimulated Giαβγ activity on Golgi membranes, temporal finiteness of Arf1 activity, and cellular secretion that is proportional to the stimuli. Findings reveal the importance of the coupled GTPase circuit in rendering concordant cellular responses via the faithful transmission of growth signals to the secretory machinery.GRAPHIC ABSTRACTHIGHLIGHTSEndo- (mono) and ectomembrane (trimeric) GTPase systems are believed to function independently.Their coupling in a closed loop system at the Golgi makes cell secretion proportionate to stimuli.Coupling enables closed-loop mutual control of both GTPases and dose response alignment (DoRA).Uncoupling creates an open loop which generates misaligned and discordant responses.

HighlightsEmergence of bivalency needs advantageous writing activity over erasing activity Emergence of bivalency is facilitated by noise and nonlinearityThe proportion of bivalent nucleosomes at bivalent chromatin is no more than 50% Bivalent chromatin facilitates chromatin state transitions

Cancers represent complex autonomous systems, displaying self‐sufficiency in growth signaling. Autonomous growth is fueled by a cancer cell's ability to “secrete‐and‐sense” growth factors (GFs): a poorly understood phenomenon. Using an integrated computational and experimental approach, here we dissect the impact of a feedback‐coupled GTPase circuit within the secretory pathway that imparts secretion‐coupled autonomy. The circuit is assembled when the Ras‐superfamily monomeric GTPase Arf1, and the heterotrimeric GTPase Giαβγ and their corresponding GAPs and GEFs are coupled by GIV/Girdin, a protein that is known to fuel aggressive traits in diverse cancers. One forward and two key negative feedback loops within the circuit create closed‐loop control, allow the two GTPases to coregulate each other, and convert the expected switch‐like behavior of Arf1‐dependent secretion into an unexpected dose–response alignment behavior of sensing and secretion. Such behavior translates into cell survival that is self‐sustained by stimulus‐proportionate secretion. Proteomic studies and protein–protein interaction network analyses pinpoint GFs (e.g., the epidermal GF) as key stimuli for such self‐sustenance. Findings highlight how the enhanced coupling of two biological switches in cancer cells is critical for multiscale feedback control to achieve secretion‐coupled autonomy of growth factors.

Oscillatory behaviors, which are ubiquitous in transcriptional regulatory networks, are often subject to inevitable biological noise. Thus, a natural question is how transcriptional regulatory networks can robustly achieve accurate oscillation in the presence of biological noise. Here, we search all two- and three-node transcriptional regulatory network topologies for those robustly capable of accurate oscillation against the parameter variability (extrinsic noise) or stochasticity of chemical reactions (intrinsic noise). We find that, no matter what source of the noise is applied, the topologies containing the repressilator with positive autoregulation show higher robustness of accurate oscillation than those containing the activator-inhibitor oscillator, and additional positive autoregulation enhances the robustness against noise. Nevertheless, the attenuation of different sources of noise is governed by distinct mechanisms: the parameter variability is buffered by the long period, while the stochasticity of chemical reactions is filtered by the high amplitude. Furthermore, we analyze the noise of a synthetic human nuclear factor κB (NF-κB) signaling network by varying three different topologies and verify that the addition of a repressilator to the activator-inhibitor oscillator, which leads to the emergence of high-robustness motif—the repressilator with positive autoregulation—improves the oscillation accuracy in comparison to the topology with only an activator-inhibitor oscillator. These design principles may be applicable to other oscillatory circuits.

Stochasticity (or noise) at cellular and molecular levels has been observed extensively as a universal feature for living systems. However, how living systems deal with noise while performing desirable biological functions remains a major mystery. Regulatory network configurations, such as their topology and timescale, are shown to be critical in attenuating noise, and noise is also found to facilitate cell fate decision. Here we review major recent findings on noise attenuation through regulatory control, the benefit of noise via noise-induced cellular plasticity during developmental patterning, and summarize key principles underlying noise control. 2 Nie Q et al. Sci China Math studies investigate how to control or utilize noise in living systems [7,10,[10][11][12][13][14][15][16][17][18]. While noise may induce heterogeneity within the cell population, contributing to diversity in cell fate choice [19][20][21], it usually causes uncertainty in information transmission in the cell and impairs robustness of cellular functions, which is one of the main reasons for the difficulty in robust circuit functions [4,22]. A natural question at hand is how cells deal with noise effectively.Since cellular functions, such as bistability, oscillation and adaptation, have been found to link to regulatory network architectures [23], the network property is naturally important in noise control [18,[24][25][26][27][28][29][30][31]. What are basic constraints on the regulatory networks for noise attenuation? How noise is controlled in function-specific systems, such as adaptive systems or oscillatory systems? In addition, can noise be utilized to achieve specific biological functions? How does noise affect spatial organization and morphogen-mediated patterning? How can a precise and robust readout be generated from the noisy spatial morphogen gradient?In this work, we first review major noise attenuation mechanisms in regulatory networks, and then explore key strategies to combat noise in morphogens during spatial patterning. We conclude by summarizing the major mechanisms in noise control.

Oscillatory behaviors, which are ubiquitous in transcriptional regulatory networks, are often subject to inevitable biological noise. Thus a natural question is how transcriptional regulatory networks can robustly achieve accurate oscillation in the presence of biological noise. Here, we search all two- and three-node transcriptional regulatory network topologies for those robustly capable of accurate oscillation against the parameter variability (extrinsic noise) or stochasticity of chemical reactions (intrinsic noise). We find that, no matter what source of the noise is applied, the topologies containing the repressilator with positive auto-regulation show higher robustness of accurate oscillation than those containing the activator-inhibitor oscillator, and additional positive auto-regulation enhances the robustness against noise. Nevertheless, the attenuation of different sources of noise is governed by distinct mechanisms: the parameter variability is buffered by the long period, while the stochasticity of chemical reactions is filtered by the high amplitude. Furthermore, we analyze the noise of a synthetic human nuclear factor κB (NF-κB) signaling network by varying three different topologies, and verify that the addition of a repressilator to the activator-inhibitor oscillator, which leads to the emergence of high-robustness motif—the repressilator with positive auto-regulation, improves the oscillation accuracy in comparison to the topology with only an activator-inhibitor oscillator. These design principles may be applicable to other oscillatory circuits.

Abstract“Dose-response alignment” (DoRA), where the downstream response of cellular signaling pathways closely matches the fraction of activated receptor, can improve the fidelity of dose information transmission. The negative feedback has been experimentally identified as a key component for DoRA, but numerical simulations indicate that negative feedback is not sufficient to achieve perfect DoRA, i.e., perfect match of downstream response and receptor activation level. Thus a natural question is whether there exist design principles for signaling motifs within only negative feedback loops to improve DoRA to near-perfect DoRA. Here, we investigated several model formulations of an experimentally validated circuit that couples two molecular switches—mGTPase (monomeric GTPase) and tGTPase (heterotrimeric GTPases) — with negative feedback loops. In the absence of feedback, the low and intermediate mGTPase activation levels benefit DoRA in mass action and Hill-function models, respectively. Adding negative feedback has versatile roles on DoRA: it may impair DoRA in the mass action model with low mGTPase activation level and Hill-function model with intermediate mGTPase activation level; in other cases, i.e., the mass action model with a high mGTPase activation level or the Hill-function model with a non-intermediate mGTPase activation level, it improves DoRA. Furthermore, we found that DoRA in a longer cascade (i.e., tGTPase) can be obtained using Hill-function kinetics under certain conditions. In summary, we show how ranges of activity of mGTPase, reaction kinetics, the negative feedback, and the cascade length affect DoRA. This work provides a framework for improving the DoRA performance in signaling motifs with negative feedback.