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# Rapid prototyping a Example module for characterization (strain yCL109; β-est: β-estradiol; aTc: anhydrotetracyclin). b, c Characterization experiments, citrine fluorescence measured by flow cytometry. All flow cytometry measurements include at least 4000 cells after gating. Symbols show experimental means, ±standard deviation, and lines simulations of the maximum likelihood parameter set estimated with all seven modules. 5 μM β-estradiol were added at time 0, together with varying concentrations of α-factor (dose response at 18 h (b), dynamics after α addition (c)), or varying concentrations of aTc with 0 or 1 μM α (aTc dose response at 6 h (b)). For α-factor release (c), we removed α from the medium 18 h after induction. d Illustration of the second step of TopoDesign to infer the posterior distribution p(θ∣D)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p({\mathbf{\theta }}|D)$$\end{document} of the 20 parameters θi for parts in Fig. 1b by approximate Bayesian computation (ABC) using the likelihood p(D∣θ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p(D|{\mathbf{\theta }})$$\end{document} for data D. e Projection of the joint posterior parameter distribution on two pairs of parameters; bright contour lines indicate high probability density.

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Cells can encode information about their environment by modulating signaling dynamics and responding accordingly. Yet, the mechanisms cells use to decode these dynamics remain unknown when cells respond exclusively to transient signals. Here, we approach design principles underlying such decoding by rationally engineering a synthetic short-pulse de...

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## Citations

... Correlation between the pulses of NF-jB and differential gene expression patterns have been identified in the recent past (Lane et al., 2017;Zambrano et al., 2016). Subsequently, mathematical model studies revealed the topology of network motifs that are capable of generating pulses (Gao et al., 2018;Lormeau et al., 2021;Martinez-Corral et al., 2018;Zhang et al., 2016). Therefore, it is important to gain a systematic quantitative understanding of how various network motifs process pulsatile signals such that regulatory units process it as a true signal leaving out the small amplitude noisy signals. ...

Cells often encounter various external and internal signals in a non-sustained pulsatile manner with varying amplitude, duration and residual value. However, the effect of signal pulse on the regulatory networks is poorly understood. In order gain a quantitative understating of pulse processing by bistable switches, we investigated pulse induced population inversion kinetics in bistable switches generated either by mutual activation or by mutual inhibition motifs. We show that both a transient intense pulse and a prolonged weak pulse can induce population inversion, however by distinct mechanisms. An intense pulse facilitates the population inversion by reducing the inversion time, while a weak prolonged pulse allows more late responders to flip their steady state causing increased average transition time. Although the inversion is controlled by the pulse amplitude and duration, however the fate of the inverted state is dictated by the residual signal that determines the mean residence at the flipped state. Therefore, population inversion and its maintenance require a proper tuning of all three signal parameters. Bistable system of mutual activation motif is more prone to make a transient response to the pulse however it is less susceptible to flip its steady state. While the bistability of mutual inhibition motif does not make a transient response yet it is more prone to switch its steady state. By comparing the pulse parameters and statistical properties of associated times scales, we conclude that a bistable switch originating from mutual activation loop is less susceptible to spurious signals as compared to the mutual inhibition loop.

... The multi-output approach was previously also implemented using a transcriptional repressor in bacteria [27]. The incoherent feedforward motif has also been extended to perform more complex computations [23,28] ...

One of the most remarkable features of biological systems is their ability to adapt to the constantly changing environment. By harnessing principles of control theory, synthetic biologists are starting to mimic this adaptation in regulatory gene circuits. Doing so allows for the construction of systems that perform reliably under non-optimal conditions. Furthermore, making a system adaptive can make up for imperfect knowledge of the underlying biology and hence avoid unforeseen complications in the implementation. Here, we review recent developments in the analysis and implementation of adaptive regulatory networks in synthetic biology with a particular focus on genetic circuits that can realize perfect adaptation.

... For the commonly applied models in the form of ordinary differential equations (ODEs), both design problems can be addressed by investigating the space of model parameters to assess (predicted) circuit behaviors in relation to design objectives encoded by a reference for the desired behavior. With sampling-based methods such as (approximate) Bayesian computation, this defines a 'viable' subspace of the parameter space where the behavior is consistent with the design objective (Fig. 1A,B) [2,10,17]. ...

... Yet, for the biological implementation it is critical that a circuit functions under conditions of uncertainty (e.g., in changing environmental conditions or because the models do not capture relevant interactions between parts or with the cellular context [7]) as well as cell-to-cell variability that is present even in isogenic populations (e.g., due to extrinsic or intrinsic stochastic noise, or different cell cycle phases and ages of cells in a population [4]). One can account for uncertainty in ODE-based design, for example, via measures of robustness that quantify parameter uncertainty [10]. It is also possible to tackle cell-to-cell variability with stochastic models, where temporal logic specifications are written as Continuous Stochastic Logic (CSL) [23]. ...

... To address these limitations, here we propose a framework for robust synthetic circuit design that takes into account cell-to-cell variability, and clearly separates it from experimental noise and impact of variable environmental conditions and interacting parts. For this population design, we extend an existing algorithm for ODE-based design [10] to the NLME (NonLinear Mixed-Effect) models framework [8]. Specifically, this entails augmenting the ODE model with a statistical model at the population level that induces probability distributions over the parameter space at the individual cell level (see Fig. 1B,C). ...

Synthetic biologists use and combine diverse biological parts to build systems such as genetic circuits that perform desirable functions in, for example, biomedical or industrial applications. Computer-aided design methods have been developed to help choose appropriate network structures and biological parts for a given design objective. However, they almost always model the behavior of the network in an average cell, despite pervasive cell-to-cell variability. Here, we present a computational framework to guide the design of synthetic biological circuits while accounting for cell-to-cell variability explicitly. Our design method integrates a NonLinear Mixed-Effect (NLME) framework into an existing algorithm for design based on ordinary differential equation (ODE) models. The analysis of a recently developed transcriptional controller demonstrates first insights into design guidelines when trying to achieve reliable performance under cell-to-cell variability. We anticipate that our method not only facilitates the rational design of synthetic networks under cell-to-cell variability, but also enables novel applications by supporting design objectives that specify the desired behavior of cell populations.

Cells live in constantly changing environments and employ dynamic signaling pathways to transduce information about the signals they encounter. However, the mechanisms by which dynamic signals are decoded into appropriate gene expression patterns remain poorly understood. Here, we devise networked optogenetic pathways that achieve dynamic signal processing functions that recapitulate cellular information processing. Exploiting light-responsive transcriptional regulators with differing response kinetics, we build a falling edge pulse detector and show that this circuit can be employed to demultiplex dynamically encoded signals. We combine this demultiplexer with dCas9-based gene networks to construct pulsatile signal filters and decoders. Applying information theory, we show that dynamic multiplexing significantly increases the information transmission capacity from signal to gene expression state. Finally, we use dynamic multiplexing for precise multidimensional regulation of a heterologous metabolic pathway. Our results elucidate design principles of dynamic information processing and provide original synthetic systems capable of decoding complex signals for biotechnological applications.

Cells employ intracellular signaling pathways to sense and respond to changes in their external environment. In recent years, live-cell biosensors have revealed complex pulsatile dynamics in many pathways, but studies of these signaling dynamics are limited by the necessity of live-cell imaging at high spatiotemporal resolution. Here, we describe an approach to infer pulsatile signaling dynamics from a single measurement in fixed cells using a pulse-detecting gene circuit. We computationally screened for circuits with the capability to selectively detect signaling pulses, revealing an incoherent feedforward topology that robustly performs this computation. We implemented the motif experimentally for the Erk signaling pathway using a single engineered transcription factor and fluorescent protein reporter. Our “recorder of Erk activity dynamics” (READer) responds sensitively to spontaneous and stimulus-driven Erk pulses. READer circuits open the door to permanently labeling transient, dynamic cell populations to elucidate the mechanistic underpinnings and biological consequences of signaling dynamics.

Perfect optical vortices enable the unprecedented optical multiplexing utilizing orbital angular momentum of light, which, however, suffer from distortion when they propagate in inhomogeneous media. Herein, we report on the experimental demonstration of perfect optical vortice generation through strongly scattering media. The transmission-matrix-based point-spread-function engineering is applied to encode the targeted mask in the Fourier domain before focusing. We experimentally demonstrate the perfect optical vortice generation either through a multimode fiber or a ground glass, where the numerical results agree well with the measured one. Our results might facilitate the manipulation of orbital angular momentum of light through disordered scattering media and shed new light on the optical multiplexing utilizing perfect optical vortices.

The extracellular signal-regulated kinase (ERK) pathway governs cell proliferation, differentiation and migration, and therefore plays key roles in various developmental and regenerative processes. Recent advances in genetically encoded fluorescent biosensors have unveiled hitherto unrecognized ERK activation dynamics in space and time and their functional importance mainly in cultured cells. However, ERK dynamics during embryonic development have still only been visualized in limited numbers of model organisms, and we are far from a sufficient understanding of the roles played by developmental ERK dynamics. In this Review, we first provide an overview of the biosensors used for visualization of ERK activity in live cells. Second, we highlight the applications of the biosensors to developmental studies of model organisms and discuss the current understanding of how ERK dynamics are encoded and decoded for cell fate decision-making.

Our knowledge of how individual cells self-organize to form complex multicellular systems is being revolutionized by a data outburst, coming from high-throughput experimental breakthroughs such as single-cell RNA sequencing and spatially resolved single-molecule FISH. This information is starting to be leveraged by machine learning approaches that are helping us establish a census and timeline of cell types in developing organisms, shedding light on how biochemistry regulates cell-fate decisions. In parallel, imaging tools such as light-sheet microscopy are revealing how cells self-assemble in space and time as the organism forms, thereby elucidating the role of cell mechanics in development. Here we argue that mathematical modeling can bring together these two perspectives, by enabling us to test hypotheses about specific mechanisms, which can be further validated experimentally. We review the recent literature on this subject, focusing on representative examples that use modeling to better understand how single-cell behavior shapes multicellular organisms.