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The ultrasensitivity of a dose response function can be quantifiably defined using the generalized Hill coefficient of the function. We examined an upper bound for the Hill coefficient of the composition of two functions, namely the product of their individual Hill coefficients. We proved that this upper bound holds for compositions of Hill functions, and that there are instances of counterexamples that exist for more general sigmoidal functions. Additionally, we tested computationally other types of sigmoidal functions, such as the logistic and inverse trigonometric functions, and we provided computational evidence that in these cases the inequality also holds. We show that in large generality there is a limit to how ultrasensitive the composition of two functions can be, which has applications to understanding signaling cascades in biochemical reactions. [ABSTRACT FROM AUTHOR]

Living systems have developed control mechanisms for achieving homeostasis. Here, we propose a plausible biological feedback architecture that exploits ultrasensitivity and shows adaptive responses without requiring error detection mechanism (i.e., by measuring an external reference signal and deviation from this). While standard engineering control systems are usually based on error measurements, this is not the case for biological systems. We find that a two-state negative feedback control system, without explicit error measurements, is able to track a reference signal that is implicitly determined by the tunable threshold and slope characterizing the sigmoidal ultrasensitive relationship implemented by the control system. We design different ultrasensitive control functions (ultrasensitive up- or down-regulation, or both) and, by performing sensitivity analysis, show that increasing the sensitivity level of the control allows achieving robust adaptive responses to the effects of parameter variations and step disturbances. Finally, we show that the devised control system architecture without error detection is implemented within the yeast osmoregulatory response network and allows achieving adaptive responses to osmotic stress, by exploiting the ubiquitous ultrasensitive features of the involved biomolecular circuitry. [ABSTRACT FROM AUTHOR]

Ultrasensitive molecular detection and quantization are crucial for many applications including clinical diagnostics, functional proteomics, and drug discovery; however, conventional biochemical sensors cannot satisfy the stringent requirements, and this has resulted in a long-standing dilemma regarding sensitivity improvement. To this end, we have developed an ultrasensitive relay-type nanomechanical sensor based on a magneto lever. By establishing the link between very weak molecular interaction and five orders of magnitude larger magnetic force, analytes at ultratrace level can produce a clearly observable mechanical response. Initially, proof-of-concept studies showed an improved detection limit up to five orders of magnitude when employing the magneto lever, as compared with direct detection using probe alone. In this study, we subsequently demonstrated that the relay-type sensing mode was universal in application ranging from micromolecule to macromolecule detection, which can be easily extended to detect enzymes, DNA, proteins, cells, viruses, bacteria, chemicals, etc. Importantly, we found that, sensitivity was no longer subject to probe affinity when the magneto lever was sufficiently high, theoretically, even reaching single-molecule resolution. [ABSTRACT FROM AUTHOR]

The aryl hydrocarbon receptor (AhR) is a nuclear receptor that facilitates a wide transcriptional response and causes a variety of adaptive and maladaptive physiological functions. Such functions are entirely dependent on the type of ligand activating it, and therefore, the nuances in the activation of this receptor at the single-cell level have become a research interest for different pharmacological and toxicological applications. Here, we investigate the activation of the AhR by diverse classes of compounds in a Hepa1c1c7-based murine hepatoma cell line. The exogenous compounds analyzed produced different levels of ultrasensitivity in AhR activation as measured by XRE-coupled EGFP production and analyzed by both flow cytometric and computational simulation techniques. Interestingly, simulation experiments reported herein were able to reproduce and quantitate the natural single-cell stochasticity inherent to mammalian cell lines as well as the ligand-specific differences in ultrasensitivity. Classical AhR modulators 2,3,7,8-tetrachlorodibenzodioxin (10− 1–105 pM), PCB-126 (10− 1–107 pM), and benzo[a]pyrene (10− 1–107 pM) produced the greatest levels of single-cell ultrasensitivity and most maximal responses, while consumption-based ligands indole-3-carbinol (103–109 pM), 3,3′-diindolylmethane (103–108 pM), and cannabidiol (103–108 pM) caused low-level AhR activation in more purely graded single-cell fashions. All compounds were tested and analyzed over a 24 h period for consistency. The comparative quantitative results for each compound are presented within. This study aids in defining the disparity between different types of AhR modulators that produce distinctly different physiological outcomes. In addition, the simulation tool developed for this study can be used in future studies to predict the quantitative effects of diverse types of AhR ligands in the context of pharmacological therapies or toxicological concerns. [ABSTRACT FROM AUTHOR]

Abstract Mammalian cells can decode the concentration of extracellular transforming growth factor‐β (TGF‐β) and transduce this cue into appropriate cell fate decisions. How variable TGF‐β ligand doses quantitatively control intracellular signaling dynamics and how continuous ligand doses are translated into discontinuous cellular fate decisions remain poorly understood. Using a combined experimental and mathematical modeling approach, we discovered that cells respond differently to continuous and pulsating TGF‐β stimulation. The TGF‐β pathway elicits a transient signaling response to a single pulse of TGF‐β stimulation, whereas it is capable of integrating repeated pulses of ligand stimulation at short time interval, resulting in sustained phospho‐Smad2 and transcriptional responses. Additionally, the TGF‐β pathway displays different sensitivities to ligand doses at different time scales. While ligand‐induced short‐term Smad2 phosphorylation is graded, long‐term Smad2 phosphorylation is switch‐like to a small change in TGF‐β levels. Correspondingly, the short‐term Smad7 gene expression is graded, while long‐term PAI‐1 gene expression is switch‐like, as is the long‐term growth inhibitory response. Our results suggest that long‐term switch‐like signaling responses in the TGF‐β pathway might be critical for cell fate determination.

In this paper we study the ultrasensitive behavior of multisite phosphorylation or ligand binding systems, under site-to-site variations in the modification rates. Using computational methods and mathematical analysis, we prove that the Hill coefficient reaches its maximum value when all sites are identical to each other. This is shown for a non-cooperative multisite system with arbitrary activation function as well as for the well known MWC model. We also show that the Hill coefficient of the dose response is locally robust to variations in individual modification rates. The results suggest that maximal ultrasensitivity is reached when sites are similar to each other but not necessarily identical, a conformation found in unstructured modification domains present in many experimental systems. [ABSTRACT FROM AUTHOR]

Multisite modifications are widely recognized as an essential feature of many switch-like responses in signal transduction. It is usually assumed that the modification of one site directly or indirectly increases the rate of modification of neighboring sites. In this paper we provide a new set of assumptions for a multisite system to become highly ultrasensitive even in the absence of cooperativity or allostery. We assume that the individual sites are modified independently of each other, and that protein activity is an ultrasensitive function of the fraction of modified sites. These assumptions are particularly useful in the context of multisite systems with a large (8+) number of sites. We estimate the apparent Hill coefficient of the dose responses in the sequential and nonsequential cases, highlight their different qualitative properties, and discuss a formula to approximate dose responses in the nonsequential case. As an example we describe a model of bacterial chemotaxis that features robust ultrasensitivity and perfect adaptation over a wide range of ligand concentrations, based on non-allosteric multisite behavior at the level of receptors and flagella. We also include a model of the inactivation of the yeast pheromone protein Ste5 by cell cycle proteins. [ABSTRACT FROM AUTHOR]

GCaMP is one of the most widely used calcium indicators in neuronal imaging and calcium cell biology. The newly developed GCaMP6 shows superior brightness and ultrasensitivity to calcium concentration change. In this study, we determined crystal structures of Ca-bound GCaMP6 monomer and dimer and presented detailed structural analyses in comparison with its parent version GCaMP5G. Our analyses reveal the structural basis for the outperformance of this newly developed Ca indicator. Three substitution mutations and the resulting changes of local structure and interaction explain the ultrasensitivity and increased fluorescence intensity common to all three versions of GCaMP6. Each particular substitution in the three GCaMP6 is also structurally consistent with their differential sensitivity and intensity, maximizing the potential of using GCaMP6 in solving diverse problems in neuronal research and calcium signaling. Our studies shall also be beneficial to further structure-guided optimization of GCaMP and facilitate the design of novel calcium indicators. [ABSTRACT FROM AUTHOR]

Mammalian cells can decode the concentration of extracellular transforming growth factor‐β (TGF‐β) and transduce this cue into appropriate cell fate decisions. How variable TGF‐β ligand doses quantitatively control intracellular signaling dynamics and how continuous ligand doses are translated into discontinuous cellular fate decisions remain poorly understood. Using a combined experimental and mathematical modeling approach, we discovered that cells respond differently to continuous and pulsating TGF‐β stimulation. The TGF‐β pathway elicits a transient signaling response to a single pulse of TGF‐β stimulation, whereas it is capable of integrating repeated pulses of ligand stimulation at short time interval, resulting in sustained phospho‐Smad2 and transcriptional responses. Additionally, the TGF‐β pathway displays different sensitivities to ligand doses at different time scales. While ligand‐induced short‐term Smad2 phosphorylation is graded, long‐term Smad2 phosphorylation is switch‐like to a small change in TGF‐β levels. Correspondingly, the short‐term Smad7 gene expression is graded, while long‐term PAI‐1 gene expression is switch‐like, as is the long‐term growth inhibitory response. Our results suggest that long‐term switch‐like signaling responses in the TGF‐β pathway might be critical for cell fate determination. [ABSTRACT FROM AUTHOR]

modified Goldbeter-Koshland (GK) type model is proposed to study the open signaling cascade with forward activation. Three different regimes related to the ultrasensitivity are clearly defined. When the cascade is sufficiently long, the steady states in the downstream cycles exhibit a limiting behavior. Meanwhile, a temporal switch-like behavior is revealed in the pre-ultrasensitivity regime without any feedback circuitry. A detailed analysis of this phenomenon is provided. [ABSTRACT FROM AUTHOR]

Information processing using biochemical circuits is essential for survival and reproduction of natural organisms. As stripped-down analogs of genetic regulatory networks in cells, we engineered artificial transcriptional networks consisting of synthetic DNA switches, regulated by RNA signals acting as transcription repressors, and two enzymes, bacteriophage T7 RNA polymerase and Escherichia coli ribonuclease H. The synthetic switch design is modular with programmable connectivity and allows dynamic control of RNA signals through enzyme-mediated production and degradation. The switches support sharp and adjustable thresholds using a competitive hybridization mechanism, allowing arbitrary analog or digital circuits to be created in principle. As an example, we constructed an in vitro bistable memory by wiring together two synthetic switches and performed a systematic quantitative characterization. Good agreement between experimental data and a simple mathematical model was obtained for switch input/output functions, phase plane trajectories, and the bifurcation diagram for bistability. Construction of larger synthetic circuits provides a unique opportunity for evaluating model inference, prediction, and design of complex biochemical systems and could be used to control nanoscale devices and artificial cells. [ABSTRACT FROM AUTHOR]