Oscillatory stimuli differentiate adapting circuit topologies

Automated neuron tracking inside moving and deforming C. elegans using deep learning and targeted augmentation

Reading out neuronal activity from three-dimensional (3D) functional imaging requires segmenting and tracking individual neurons. This is challenging in behaving animals if the brain moves and deforms. The traditional approach is to train a convolutional neural network with ground-truth (GT) annotations of images representing different brain postures. For 3D images, this is very labor intensive. We introduce 'targeted augmentation', a method to automatically synthesize artificial annotations from a few manual annotations. Our method ('Targettrack') learns the internal deformations of the brain to synthesize annotations for new postures by deforming GT annotations. This reduces the need for manual annotation and proofreading. A graphical user interface allows the application of the method end-to-end. We demonstrate Targettrack on recordings where neurons are labeled as key points or 3D volumes. Analyzing freely moving animals exposed to odor pulses, we uncover rich patterns in interneuron dynamics, including switching neuronal entrainment on and off.

Phenotypic consequences of logarithmic signaling in MAPK stress response

How cells respond to dynamic environmental changes is crucial for understanding fundamental biological processes and cell physiology. In this study, we developed an experimental and quantitative analytical framework to explore how dynamic stress gradients that change over time regulate cellular volume, signaling activation, and growth phenotypes. Our findings reveal that gradual stress conditions substantially enhance cell growth compared to conventional acute stress. This growth advantage correlates with a minimal reduction in cell volume dependent on the dynamic of stress. We explain the growth phenotype with our finding of a logarithmic signal transduction mechanism in the yeast Mitogen-Activated Protein Kinase (MAPK) osmotic stress response pathway. These insights into the interplay between gradual environments, cell volume change, dynamic cell signaling, and growth, advance our understanding of fundamental cellular processes in gradual stress environments.

Multidimensional characterization of inducible promoters and a highly light-sensitive LOV-transcription factor

The ability to independently control the expression of different genes is important for quantitative biology. Using budding yeast, we characterize GAL1pr, GALL, MET3pr, CUP1pr, PHO5pr, tetOpr, terminator-tetOpr, Z₃EV, blue-light inducible optogenetic systems El222-LIP, El222-GLIP, and red-light inducible PhyB-PIF3. We report kinetic parameters, noise scaling, impact on growth, and the fundamental leakiness of each system using an intuitive unit, maxGAL1. We uncover disadvantages of widely used tools, e.g., nonmonotonic activity of MET3pr and GALL, slow off kinetics of the doxycycline- and estradiol-inducible systems tetOpr and Z₃EV, and high variability of PHO5pr and red-light activated PhyB-PIF3 system. We introduce two previously uncharacterized systems: strongLOV, a more light-sensitive El222 mutant, and ARG3pr, which is induced in the absence of arginine or presence of methionine. To demonstrate fine control over gene circuits, we experimentally tune the time between cell cycle Start and mitosis, artificially simulating near-wild-type timing. All strains, constructs, code, and data ( https://promoter-benchmark.epfl.ch/ ) are made available.

On biological networks capable of robust adaptation in the presence of uncertainties: A linear systems-theoretic approach

Biological adaptation, the tendency of every living organism to regulate its essential activities in environmental fluctuations, is a well-studied functionality in systems and synthetic biology. In this work, we present a generic methodology inspired by systems theory to discover the design principles for robust adaptation, perfect and imperfect, in two different contexts: (1) in the presence of deterministic external and parametric disturbances and (2) in a stochastic setting. In all the cases, firstly, we translate the necessary qualitative conditions for adaptation to mathematical constraints using the language of systems theory, which we then map back as design requirements for the underlying networks. Thus, contrary to the existing approaches, the proposed methodologies provide an exhaustive set of admissible network structures without resorting to computationally burdensome brute-force techniques. Further, the proposed frameworks do not assume prior knowledge about the particular rate kinetics, thereby validating the conclusions for a large class of biological networks. In the deterministic setting, we show that unlike the incoherent feed-forward network structures (IFFLP or opposer modules), the modules containing negative feedback with buffer action (NFBLB or balancer modules) are robust to parametric fluctuations when a specific part of the network is assumed to remain unaffected. To this end, we propose a sufficient condition for imperfect adaptation and show that adding negative feedback in an IFFLP topology improves the robustness concerning parametric fluctuations. Further, we propose a stricter set of necessary conditions for imperfect adaptation. Turning to the stochastic scenario, we adopt a Wiener-Kolmogorov filter strategy to tune the parameters of a given network structure towards minimum output variance. We show that both NFBLB and IFFLP can be used as a reduced-order W-K filter. Further, we define the notion of nearest neighboring motifs to compare the output variances across different network structures. We argue that the NFBLB achieves adaptation at the cost of a variance higher than its nearest neighboring motifs whereas the IFFLP topology produces locally minimum variance while compared with its nearest neighboring motifs. We present numerical simulations to support the theoretical results. Overall, our results present a generic, systematic, and robust framework for advancing the understanding of complex biological networks.

Rate thresholds in cell signaling have functional and phenotypic consequences in non-linear time-dependent environments

All cells employ signal transduction pathways to respond to physiologically relevant extracellular cytokines, stressors, nutrient levels, hormones, morphogens, and other stimuli that vary in concentration and rate in healthy and diseased states. A central unsolved fundamental question in cell signaling is whether and how cells sense and integrate information conveyed by changes in the rate of extracellular stimuli concentrations, in addition to the absolute difference in concentration. We propose that different environmental changes over time influence cell behavior in addition to different signaling molecules or different genetic backgrounds. However, most current biomedical research focuses on acute environmental changes and does not consider how cells respond to environments that change slowly over time. As an example of such environmental change, we review cell sensitivity to environmental rate changes, including the novel mechanism of rate threshold. A rate threshold is defined as a threshold in the rate of change in the environment in which a rate value below the threshold does not activate signaling and a rate value above the threshold leads to signal activation. We reviewed p38/Hog1 osmotic stress signaling in yeast, chemotaxis and stress response in bacteria, cyclic adenosine monophosphate signaling in Amoebae, growth factors signaling in mammalian cells, morphogen dynamics during development, temporal dynamics of glucose and insulin signaling, and spatio-temproral stressors in the kidney. These reviewed examples from the literature indicate that rate thresholds are widespread and an underappreciated fundamental property of cell signaling. Finally, by studying cells in non-linear environments, we outline future directions to understand cell physiology better in normal and pathophysiological conditions.

A negative feedback loop in the GPCR pathway underlies efficient coding of external stimuli

Efficient navigation based on chemical cues is an essential feature shared by all animals. These cues may be encountered in complex spatiotemporal patterns and with orders of magnitude varying intensities. Nevertheless, sensory neurons accurately extract the relevant information from such perplexing signals. Here, we show how a single sensory neuron in Caenorhabditis elegans animals can cell‐autonomously encode complex stimulus patterns composed of instantaneous sharp changes and of slowly changing continuous gradients. This encoding relies on a simple negative feedback in the G‐protein‐coupled receptor (GPCR) signaling pathway in which TAX‐6/Calcineurin plays a key role in mediating the feedback inhibition. This negative feedback supports several important coding features that underlie an efficient navigation strategy, including exact adaptation and adaptation to the magnitude of the gradient's first derivative. A simple mathematical model explains the fine neural dynamics of both wild‐type and tax‐6 mutant animals, further highlighting how the calcium‐dependent activity of TAX‐6/Calcineurin dictates GPCR inhibition and response dynamics. As GPCRs are ubiquitously expressed in all sensory neurons, this mechanism may be a general solution for efficient cell‐autonomous coding of external stimuli.

Discovering adaptation-capable biological network structures using control-theoretic approaches

Constructing biological networks capable of performing specific biological functionalities has been of sustained interest in synthetic biology. Adaptation is one such ubiquitous functional property, which enables every living organism to sense a change in its surroundings and return to its operating condition prior to the disturbance. In this paper, we present a generic systems theory-driven method for designing adaptive protein networks. First, we translate the necessary qualitative conditions for adaptation to mathematical constraints using the language of systems theory, which we then map back as ‘design requirements’ for the underlying networks. We go on to prove that a protein network with different input–output nodes (proteins) needs to be at least of third-order in order to provide adaptation. Next, we show that the necessary design principles obtained for a three-node network in adaptation consist of negative feedback or a feed-forward realization. We argue that presence of a particular class of negative feedback or feed-forward realization is necessary for a network of any size to provide adaptation. Further, we claim that the necessary structural conditions derived in this work are the strictest among the ones hitherto existed in the literature. Finally, we prove that the capability of producing adaptation is retained for the admissible motifs even when the output node is connected with a downstream system in a feedback fashion. This result explains how complex biological networks achieve robustness while keeping the core motifs unchanged in the context of a particular functionality. We corroborate our theoretical results with detailed and thorough numerical simulations. Overall, our results present a generic, systematic and robust framework for designing various kinds of biological networks.

Biological systems display a remarkable diversity of functionalities, many of which can be conceived as the response of a large network composed of small interconnecting modules. Unravelling the connection pattern, i.e. design principles, behind important biological functionalities is one of the most challenging problems in systems biology. One such phenomenon is perfect adaptation, which merits special attention owing to its universal presence ranging from chemotaxis in bacterial cells to calcium homeostasis in mammalian cells. The present work focuses on finding the design principles for perfect adaptation in the presence of a stair-case type disturbance. To this end, the current work proposes a systems-theoretic approach to deduce precise mathematical (hence structural) conditions that comply with the key performance parameters for adaptation. The approach is agnostic to the particularities of the reaction kinetics, underlining the dominant role of the topological structure on the response of the network. Notably, the design principles obtained in this work serve as the most strict necessary structural conditions for a network of any size to provide perfect adaptation.

Cyclin/Forkhead-mediated coordination of cyclin waves: an autonomous oscillator rationalizing the quantitative model of Cdk control for budding yeast

Networks of interacting molecules organize topology, amount, and timing of biological functions. Systems biology concepts required to pin down 'network motifs' or 'design principles' for time-dependent processes have been developed for the cell division cycle, through integration of predictive computer modeling with quantitative experimentation. A dynamic coordination of sequential waves of cyclin-dependent kinases (cyclin/Cdk) with the transcription factors network offers insights to investigate how incompatible processes are kept separate in time during the eukaryotic cell cycle. Here this coordination is discussed for the Forkhead transcription factors in light of missing gaps in the current knowledge of cell cycle control in budding yeast. An emergent design principle is proposed where cyclin waves are synchronized by a cyclin/Cdk-mediated feed-forward regulation through the Forkhead as a transcriptional timer. This design is rationalized by the bidirectional interaction between mitotic cyclins and the Forkhead transcriptional timer, resulting in an autonomous oscillator that may be instrumental for a well-timed progression throughout the cell cycle. The regulation centered around the cyclin/Cdk-Forkhead axis can be pivotal to timely coordinate cell cycle dynamics, thereby to actuate the quantitative model of Cdk control.

Automatic synchronisation of the cell cycle in budding yeast through closed-loop feedback control

The cell cycle is the process by which eukaryotic cells replicate. Yeast cells cycle asynchronously with each cell in the population budding at a different time. Although there are several experimental approaches to synchronise cells, these usually work only in the short-term. Here, we build a cyber-genetic system to achieve long-term synchronisation of the cell population, by interfacing genetically modified yeast cells with a computer by means of microfluidics to dynamically change medium, and a microscope to estimate cell cycle phases of individual cells. The computer implements a controller algorithm to decide when, and for how long, to change the growth medium to synchronise the cell-cycle across the population. Our work builds upon solid theoretical foundations provided by Control Engineering. In addition to providing an avenue for yeast cell cycle synchronisation, our work shows that control engineering can be used to automatically steer complex biological processes towards desired behaviours similarly to what is currently done with robots and autonomous vehicles.

Chemosensory signal transduction in Caenorhabditis elegans

Chemosensory neurons translate perception of external chemical cues, including odorants, tastants, and pheromones, into information that drives attraction or avoidance motor programs. In the laboratory, robust behavioral assays, coupled with powerful genetic, molecular and optical tools, have made Caenorhabditis elegans an ideal experimental system in which to dissect the contributions of individual genes and neurons to ethologically relevant chemosensory behaviors. Here, we review current knowledge of the neurons, signal transduction molecules and regulatory mechanisms that underlie the response of C. elegans to chemicals, including pheromones. The majority of identified molecules and pathways share remarkable homology with sensory mechanisms in other organisms. With the development of new tools and technologies, we anticipate that continued study of chemosensory signal transduction and processing in C. elegans will yield additional new insights into the mechanisms by which this animal is able to detect and discriminate among thousands of chemical cues with a limited sensory neuron repertoire.

A predictive model of gene expression reveals the role of network motifs in the mating response of yeast

Cells use signaling pathways to receive and process information about their environment. These nonlinear systems rely on feedback and feedforward regulation to respond appropriately to changing environmental conditions. Mathematical models describing signaling pathways often lack predictive power because they are not trained on data that encompass the diverse time scales on which these regulatory mechanisms operate. We addressed this limitation by measuring transcriptional changes induced by the mating response in Saccharomyces cerevisiae exposed to different dynamic patterns of pheromone. We found that pheromone-induced transcription persisted after pheromone removal and showed long-term adaptation upon sustained pheromone exposure. We developed a model of the regulatory network that captured both characteristics of the mating response. We fit this model to experimental data with an evolutionary algorithm and used the parameterized model to predict scenarios for which it was not trained, including different temporal stimulus profiles and genetic perturbations to pathway components. Our model allowed us to establish the role of four architectural elements of the network in regulating gene expression. These network motifs are incoherent feedforward, positive feedback, negative feedback, and repressor binding. Experimental and computational perturbations to these network motifs established a specific role for each in coordinating the mating response to persistent and dynamic stimulation.

Perfect adaptation of CD8+ T cell responses to constant antigen input over a wide range of affinities is overcome by costimulation

Reduced T cell responses by contrast antigen stimulation can be rescued by signals from costimulatory receptors.

A convolutional neural network segments yeast microscopy images with high accuracy

The identification of cell borders ('segmentation') in microscopy images constitutes a bottleneck for large-scale experiments. For the model organism Saccharomyces cerevisiae, current segmentation methods face challenges when cells bud, crowd, or exhibit irregular features. We present a convolutional neural network (CNN) named YeaZ, the underlying training set of high-quality segmented yeast images (>10 000 cells) including mutants, stressed cells, and time courses, as well as a graphical user interface and a web application ( www.quantsysbio.com/data-and-software ) to efficiently employ, test, and expand the system. A key feature is a cell-cell boundary test which avoids the need for fluorescent markers. Our CNN is highly accurate, including for buds, and outperforms existing methods on benchmark images, indicating it transfers well to other conditions. To demonstrate how efficient large-scale image processing uncovers new biology, we analyze the geometries of ≈2200 wild-type and cyclin mutant cells and find that morphogenesis control occurs unexpectedly early and gradually.

Processing Temporal Growth Factor Patterns by an Epidermal Growth Factor Receptor Network Dynamically Established in Space

The proto-oncogenic epidermal growth factor (EGF) receptor (EGFR) is a tyrosine kinase whose sensitivity and response to growth factor signals that vary over time and space determine cellular behavior within a developing tissue. The molecular reorganization of the receptors on the plasma membrane and the enzyme-kinetic mechanisms of phosphorylation are key determinants that couple growth factor binding to EGFR signaling. To enable signal initiation and termination while simultaneously accounting for suppression of aberrant signaling, a coordinated coupling of EGFR kinase and protein tyrosine phosphatase activity is established through space by vesicular dynamics. The dynamical operation mode of this network enables not only time-varying growth factor sensing but also adaptation of the response depending on cellular context. By connecting spatially coupled enzymatic kinase/phosphatase processes and the corresponding dynamical systems description of the EGFR network, we elaborate on the general principles necessary for processing complex growth factor signals.

Diverse Cell Stimulation Kinetics Identify Predictive Signal Transduction Models

Computationally understanding the molecular mechanisms that give rise to cell signaling responses upon different environmental, chemical, and genetic perturbations is a long-standing challenge that requires models that fit and predict quantitative responses for new biological conditions. Overcoming this challenge depends not only on good models and detailed experimental data but also on the rigorous integration of both. We propose a quantitative framework to perturb and model generic signaling networks using multiple and diverse changing environments (hereafter "kinetic stimulations") resulting in distinct pathway activation dynamics. We demonstrate that utilizing multiple diverse kinetic stimulations better constrains model parameters and enables predictions of signaling dynamics that would be impossible using traditional dose-response or individual kinetic stimulations. To demonstrate our approach, we use experimentally identified models to predict signaling dynamics in normal, mutated, and drug-treated conditions upon multitudes of kinetic stimulations and quantify which proteins and reaction rates are most sensitive to which extracellular stimulations.

A computational framework for a Lyapunov-enabled analysis of biochemical reaction networks

Complex molecular biological processes such as transcription and translation, signal transduction, post-translational modification cascades, and metabolic pathways can be described in principle by biochemical reactions that explicitly take into account the sophisticated network of chemical interactions regulating cell life. The ability to deduce the possible qualitative behaviors of such networks from a set of reactions is a central objective and an ongoing challenge in the field of systems biology. Unfortunately, the construction of complete mathematical models is often hindered by a pervasive problem: despite the wealth of qualitative graphical knowledge about network interactions, the form of the governing nonlinearities and/or the values of kinetic constants are hard to uncover experimentally. The kinetics can also change with environmental variations. This work addresses the following question: given a set of reactions and without assuming a particular form for the kinetics, what can we say about the asymptotic behavior of the network? Specifically, it introduces a class of networks that are "structurally (mono) attractive" meaning that they are incapable of exhibiting multiple steady states, oscillation, or chaos by virtue of their reaction graphs. These networks are characterized by the existence of a universal energy-like function called a Robust Lyapunov function (RLF). To find such functions, a finite set of rank-one linear systems is introduced, which form the extremals of a linear convex cone. The problem is then reduced to that of finding a common Lyapunov function for this set of extremals. Based on this characterization, a computational package, Lyapunov-Enabled Analysis of Reaction Networks (LEARN), is provided that constructs such functions or rules out their existence. An extensive study of biochemical networks demonstrates that LEARN offers a new unified framework. Basic motifs, three-body binding, and genetic networks are studied first. The work then focuses on cellular signalling networks including various post-translational modification cascades, phosphotransfer and phosphorelay networks, T-cell kinetic proofreading, and ERK signalling. The Ribosome Flow Model is also studied.

Rheostatic Control of ABA Signaling through HOS15-Mediated OST1 Degradation

Dehydrating stresses trigger the accumulation of abscisic acid (ABA), a key plant stress-signaling hormone that activates Snf1-Related Kinases (SnRK2s) to mount adaptive responses. However, the regulatory circuits that terminate the SnRK2s signal relay after acclimation or post-stress conditions remain to be defined. Here, we show that the desensitization of the ABA signal is achieved by the regulation of OST1 (SnRK2.6) protein stability via the E3-ubiquitin ligase HOS15. Upon ABA signal, HOS15-induced degradation of OST1 is inhibited and stabilized OST1 promotes the stress response. When the ABA signal terminates, protein phosphatases ABI1/2 promote rapid degradation of OST1 via HOS15. Notably, we found that even in the presence of ABA, OST1 levels are also depleted within hours of ABA signal onset. The unexpected dynamics of OST1 abundance are then resolved by systematic mathematical modeling, demonstrating a desensitizing feedback loop by which OST1-induced upregulation of ABI1/2 leads to the degradation of OST1. This model illustrates the complex rheostat dynamics underlying the ABA-induced stress response and desensitization.

Generating kinetic environments to study dynamic cellular processes in single cells

Cells of any organism are consistently exposed to changes over time in their environment. The kinetics by which these changes occur are critical for the cellular response and fate decision. It is therefore important to control the temporal changes of extracellular stimuli precisely to understand biological mechanisms in a quantitative manner. Most current cell culture and biochemical studies focus on instant changes in the environment and therefore neglect the importance of kinetic environments. To address these shortcomings, we developed two experimental methodologies to precisely control the environment of single cells. These methodologies are compatible with standard biochemistry, molecular, cell and quantitative biology assays. We demonstrate applicability by obtaining time series and time point measurements in both live and fixed cells. We demonstrate the feasibility of the methodology in yeast and mammalian cell culture in combination with widely used assays such as flow cytometry, time-lapse microscopy and single-molecule RNA Fluorescent in-situ Hybridization (smFISH). Our experimental methodologies are easy to implement in most laboratory settings and allows the study of kinetic environments in a wide range of assays and different cell culture conditions.

Scaling laws of cell-fate responses to transient stress

Analysis and modelling of dose-survival curves of cells and tissues are often used to assess therapeutic efficacy or environmental risks, much less to infer the intracellular regulatory mechanisms of cellular stress response. However, systematic measurements of how cell survival depends on the time profile of stress, such as exposure duration, provide practical means to decipher the homeostatic dynamics of stress-response regulatory networks. In this paper, we propose a dynamical framework to theoretically address the relationship between cell fate response to a transient stress and the underlying regulatory feedback mechanisms. A simple network topology that couples a homeostatic negative feedback and a death-triggering positive feedback is shown to display four response regimes for which the iso-effect relationships between duration and intensity are captured by specific power laws. These distinct response regimes define several windows of stress duration for which lethality is not merely proportional to the product of intensity and duration, and, thus, for which cells are either more tolerant or more vulnerable to a given dose. Overall, this study highlights the differential roles of feedback strength, timescale and nonlinearity in promoting survivability to particular stress profiles, providing a valuable framework for a comparative analysis of diverse stress-specific regulatory networks.

Learning: Complexities of Habituation in Escaping Zebrafish Larvae

Animals decrease responses to repeating stimuli through habituation. New research has revealed independent tuning of multiple parameters of zebrafish escape behavior during habituation.

Adaptive information processing of network modules to dynamic and spatial stimuli

BACKGROUND

Adaptation and homeostasis are basic features of information processing in cells and seen in a broad range of contexts. Much of the current understanding of adaptation in network modules/motifs is based on their response to simple stimuli. Recently, there have also been studies of adaptation in dynamic stimuli. However a broader synthesis of how different circuits of adaptation function, and which circuits enable a broader adaptive behaviour in classes of more complex and spatial stimuli is largely missing.

RESULTS

We study the response of a variety of adaptive circuits to time-varying stimuli such as ramps, periodic stimuli and static and dynamic spatial stimuli. We find that a variety of responses can be seen in ramp stimuli, making this a basis for discriminating between even similar circuits. We also find that a number of circuits adapt exactly to ramp stimuli, and dissect these circuits to pinpoint what characteristics (architecture, feedback, biochemical aspects, information processing ingredients) allow for this. These circuits include incoherent feedforward motifs, inflow-outflow motifs and transcritical circuits. We find that changes in location in such circuits where a signal acts can result in non-adaptive behaviour in ramps, even though the location was associated with exact adaptation in step stimuli. We also demonstrate that certain augmentations of basic inflow-outflow motifs can alter the behaviour of the circuit from exact adaptation to non-adaptive behaviour. When subject to periodic stimuli, some circuits (inflow-outflow motifs and transcritical circuits) are able to maintain an average output independent of the characteristics of the input. We build on this to examine the response of adaptive circuits to static and dynamic spatial stimuli. We demonstrate how certain circuits can exhibit a graded response in spatial static stimuli with an exact maintenance of the spatial mean-value. Distinct features which emerge from the consideration of dynamic spatial stimuli are also discussed. Finally, we also build on these results to show how different circuits which show any combination of presence or absence of exact adaptation in ramps, exact mainenance of time average output in periodic stimuli and exact maintenance of spatial average of output in static spatial stimuli may be realized.

CONCLUSIONS

By studying a range of network circuits/motifs on one hand and a range of stimuli on the other, we isolate characteristics of these circuits (structural) which enable different degrees of exact adaptive and homeostatic behaviour in such stimuli, how they may be combined, and also identify cases associated with non-homeostatic behaviour. We also reveal constraints associated with locations where signals may act to enable homeostatic behaviour and constraints associated with augmentations of circuits. This consideration of multiple experimentally/naturally relevant stimuli along with circuits of adaptation of relevance in natural and engineered biology, provides a platform for deepening our understanding of adaptive and homeostatic behaviour in natural systems, bridging the gap between models of adaptation and experiments and in engineering homeostatic synthetic circuits.

Fold-change Response of Photosynthesis to Step Increases of Light Level

Plants experience light intensity over several orders of magnitude. High light is stressful, and plants have several protective feedback mechanisms against this stress. Here we asked how plants respond to sudden rises at low ambient light, far below stressful levels. For this, we studied the fluorescence of excited chlorophyll a of photosystem II in Arabidopsis thaliana plants in response to step increases in light level at different background illuminations. We found a response at low-medium light with characteristics of a sensory system: fold-change detection (FCD), Weber law, and exact adaptation, in which the response depends only on relative, and not absolute, light changes. We tested various FCD circuits and provide evidence for an incoherent feedforward mechanism upstream of known stress response feedback loops. These findings suggest that plant photosynthesis may have a sensory modality for low light background that responds early to small light increases, to prepare for damaging high light levels.

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Chl a fluorescence responds to fold-change (FCD) in low-medium input light

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Identified fast feedforward (IFFL) regulation that depends on direct light input

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The direct sensing of input and FCD response are typical of sensory modules

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The IFFL precedes known feedback photoprotective regulation

Subharmonics and Chaos in Simple Periodically Forced Biomolecular Models

This article uncovers a remarkable behavior in two biochemical systems that commonly appear as components of signal transduction pathways in systems biology. These systems have globally attracting steady states when unforced, so they might have been considered uninteresting from a dynamical standpoint. However, when subject to a periodic excitation, strange attractors arise via a period-doubling cascade. Quantitative analyses of the corresponding discrete chaotic trajectories are conducted numerically by computing largest Lyapunov exponents, power spectra, and autocorrelation functions. To gain insight into the geometry of the strange attractors, the phase portraits of the corresponding iterated maps are interpreted as scatter plots for which marginal distributions are additionally evaluated. The lack of entrainment to external oscillations, in even the simplest biochemical networks, represents a level of additional complexity in molecular biology, which has previously been insufficiently recognized but is plausibly biologically important.