Processing Oscillatory Signals by Incoherent Feedforward Loops

Loss of Krüppel-like factor 9 deregulates both physiological gene expression and development

Krüppel-like factor 9 (Klf9) is a ubiquitously expressed transcription factor that is a feedforward regulator of multiple stress-responsive and endocrine signaling pathways. We previously described how loss of Klf9 function affects the transcriptome of zebrafish larvae sampled at a single time point 5 days post-fertilization (dpf). However, klf9 expression oscillates diurnally, and the sampled time point corresponded to its expression nadir. To determine if the transcriptomic effects of the klf9^-/- mutation vary with time of day, we performed bulk RNA-seq on 5 dpf zebrafish embryos sampled at three timepoints encompassing the predawn peak and midmorning nadir of klf9 expression. We found that while the major effects of the klf9^-/- mutation that we reported previously are robust to time of day, the mutation has additional effects that manifest only at the predawn time point. We used a published single-cell atlas of zebrafish development to associate the effects of the klf9^-/- mutation with different cell types and found that the mutation increased mRNA associated with digestive organs (liver, pancreas, and intestine) and decreased mRNA associated with differentiating neurons and blood. Measurements from confocally-imaged larvae suggest that overrepresentation of liver mRNA in klf9^-/- mutants is due to development of enlarged livers.

Electrifying rhythms in plant cells

Physiological oscillations (or rhythms) pervade all spatiotemporal scales of biological organization, either because they perform critical functions or simply because they can arise spontaneously and may be difficult to prevent. Regardless of the case, they reflect regulatory relationships between control points of a given system and offer insights as read-outs of the concerted regulation of a myriad of biological processes. Here we review recent advances in understanding ultradian oscillations (period < 24h) in plant cells, with a special focus on single-cell oscillations. Ion channels are at the center stage due to their involvement in electrical/excitabile phenomena associated with oscillations and cell-cell communication. We highlight the importance of quantitative approaches to measure oscillations in appropriate physiological conditions, which are essential strategies to deal with the complexity of biological rhythms. Future development of optogenetics techniques in plants will further boost research on the role of membrane potential in oscillations and waves across multiple cell types.

Generation of Realistic Gene Regulatory Networks by Enriching for Feed-Forward Loops

The regulatory relationships between genes and proteins in a cell form a gene regulatory network (GRN) that controls the cellular response to changes in the environment. A number of inference methods to reverse engineer the original GRN from large-scale expression data have recently been developed. However, the absence of ground-truth GRNs when evaluating the performance makes realistic simulations of GRNs necessary. One aspect of this is that local network motif analysis of real GRNs indicates that the feed-forward loop (FFL) is significantly enriched. To simulate this properly, we developed a novel motif-based preferential attachment algorithm, FFLatt, which outperformed the popular GeneNetWeaver network generation tool in reproducing the FFL motif occurrence observed in literature-based biological GRNs. It also preserves important topological properties such as scale-free topology, sparsity, and average in/out-degree per node. We conclude that FFLatt is well-suited as a network generation module for a benchmarking framework with the aim to provide fair and robust performance evaluation of GRN inference methods.

Glucocorticoid-Mediated Developmental Programming of Vertebrate Stress Responsivity

Glucocorticoids, vertebrate steroid hormones produced by cells of the adrenal cortex or interrenal tissue, function dynamically to maintain homeostasis under constantly changing and occasionally stressful environmental conditions. They do so by binding and thereby activating nuclear receptor transcription factors, the Glucocorticoid and Mineralocorticoid Receptors (MR and GR, respectively). The GR, by virtue of its lower affinity for endogenous glucocorticoids (cortisol or corticosterone), is primarily responsible for transducing the dynamic signals conveyed by circadian and ultradian glucocorticoid oscillations as well as transient pulses produced in response to acute stress. These dynamics are important determinants of stress responsivity, and at the systemic level are produced by feedforward and feedback signaling along the hypothalamus-pituitary-adrenal/interrenal axis. Within receiving cells, GR signaling dynamics are controlled by the GR target gene and negative feedback regulator fkpb5. Chronic stress can alter signaling dynamics via imperfect physiological adaptation that changes systemic and/or cellular set points, resulting in chronically elevated cortisol levels and increased allostatic load, which undermines health and promotes development of disease. When this occurs during early development it can "program" the responsivity of the stress system, with persistent effects on allostatic load and disease susceptibility. An important question concerns the glucocorticoid-responsive gene regulatory network that contributes to such programming. Recent studies show that klf9, a ubiquitously expressed GR target gene that encodes a Krüppel-like transcription factor important for metabolic plasticity and neuronal differentiation, is a feedforward regulator of GR signaling impacting cellular glucocorticoid responsivity, suggesting that it may be a critical node in that regulatory network.

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.

A rationally engineered decoder of transient intracellular signals

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 decoder in budding yeast. A computational method for rapid prototyping, TopoDesign, allowed us to explore 4122 possible circuit architectures, design targeted experiments, and then rationally select a single circuit for implementation. This circuit demonstrates short-pulse decoding through incoherent feedforward and positive feedback. We predict incoherent feedforward to be essential for decoding transient signals, thereby complementing proposed design principles of temporal filtering, the ability to respond to sustained signals, but not to transient signals. More generally, we anticipate TopoDesign to help designing other synthetic circuits with non-intuitive dynamics, simply by assembling available biological components.

Early Detection of Daylengths with a Feedforward Circuit Coregulated by Circadian and Diurnal Cycles

Light-entrained circadian clocks confer rhythmic dynamics of cellular and molecular activities to animals and plants. These intrinsic clocks allow stable anticipations to light-dark (diel) cycles. Many genes in the model plant Arabidopsis thaliana are regulated by diel cycles via pathways independent of the clock, suggesting that the integration of circadian and light signals is important for the fitness of plants. Previous studies of light-clock signal integrations have focused on moderate phase adjustment of the two signals. However, dynamical features of integrations across a broad range of phases remain elusive. Phosphorylation of ribosomal protein of the small subunit 6 (eS6), a ubiquitous post-translational modification across kingdoms, is influenced by the circadian clock and the light-dark (diel) cycle in an opposite manner. To understand this striking phenomenon and its underlying information processing capabilities, we built a mathematical model for the eS6 phosphorylation (eS6-P) control circuit. We found that the dynamics of eS6-P can be explained by a feedforward circuit with inputs from both circadian and diel cycles. Furthermore, the early day response of this circuit with dual rhythmic inputs is sensitive to the changes in daylength, including both transient and gradual changes observed in realistic light intervals across a year, because of weather and seasons. By analyzing published gene expression data, we found that the dynamics produced by the eS6-P control circuit can be observed in the expression profiles of a large number of genes. Our work provides mechanistic insights into the complex dynamics of a ribosomal protein, and it proposes a previously underappreciated function of the circadian clock, which not only prepares organisms for normal diel cycles but also helps to detect both transient and seasonal changes with a predictive power.

Computational Modeling Reveals Frequency Modulation of Calcium-cAMP/PKA Pathway in Dendritic Spines

Dendritic spines are the primary excitatory postsynaptic sites that act as subcompartments of signaling. Ca²⁺ is often the first and most rapid signal in spines. Downstream of calcium, the cyclic adenosine monophosphate (cAMP)/protein kinase A (PKA) pathway plays a critical role in the regulation of spine formation, morphological modifications, and ultimately, learning and memory. Although the dynamics of calcium are reasonably well-studied, calcium-induced cAMP/PKA dynamics, particularly with respect to frequency modulation, are not fully explored. In this study, we present a well-mixed model for the dynamics of calcium-induced cAMP/PKA dynamics in dendritic spines. The model is constrained using experimental observations in the literature. Further, we measured the calcium oscillation frequency in dendritic spines of cultured hippocampal CA1 neurons and used these dynamics as model inputs. Our model predicts that the various steps in this pathway act as frequency modulators for calcium, and the high frequency of calcium input is filtered by adenylyl cyclase 1 and phosphodiesterases in this pathway such that cAMP/PKA only responds to lower frequencies. This prediction has important implications for noise filtering and long-timescale signal transduction in dendritic spines. A companion manuscript presents a three-dimensional spatial model for the same pathway.

Temporal Pattern Recognition through Analog Molecular Computation

Living cells communicate information about physiological conditions by producing signaling molecules in a specific timed manner. Different conditions can result in the same total amount of a signaling molecule, differing only in the pattern of the molecular concentration over time. Such temporally coded information can be completely invisible to even state-of-the-art molecular sensors with high chemical specificity that respond only to the total amount of the signaling molecule. Here, we demonstrate design principles for circuits with temporal specificity, that is, molecular circuits that respond to specific temporal patterns in a molecular concentration. We consider pulsatile patterns in a molecular concentration characterized by three fundamental temporal features: time period, duty fraction, and number of pulses. We develop circuits that respond to each one of these features while being insensitive to the others. We demonstrate our design principles using general chemical reaction networks and with explicit simulations of DNA strand displacement reactions. In this way, our work develops building blocks for temporal pattern recognition through molecular computation.

An incoherent feed-forward loop switches the Arabidopsis clock rapidly between two hysteretic states

In higher plants (e.g., Arabidopsis thaliana), the core structure of the circadian clock is mostly governed by a repression process with very few direct activators. With a series of simplified models, we studied the underlying mechanism and found that the Arabidopsis clock consists of type-2 incoherent feed-forward loops (IFFLs), one of them creating a pulse-like expression in PRR9/7. The double-negative feedback loop between CCA1/LHY and PRR5/TOC1 generates a bistable, hysteretic behavior in the Arabidopsis circadian clock. We found that the IFFL involving PRR9/7 breaks the bistability and moves the system forward with a rapid pulse in the daytime, and the evening complex (EC) breaks it in the evening. With this illustration, we can intuitively explain the behavior of the clock under mutant conditions. Thus, our results provide new insights into the underlying network structures of the Arabidopsis core oscillator.

Network Motifs Capable of Decoding Transcription Factor Dynamics

Transcription factors (TFs) can encode the information of upstream signal in terms of its temporal activation dynamics. However, it remains unclear how different types of TF dynamics are decoded by downstream signalling networks. In this work, we studied all three-node transcriptional networks for their ability to distinguish two types of TF dynamics: amplitude modulation (AM), where the TF is activated with a constant amplitude, and frequency modulation (FM), where the TF activity displays an oscillatory behavior. We found two sets of network topologies: one set can differentially respond to AM TF signal but not to FM; the other set to FM signal but not to AM. Interestingly, there is little overlap between the two sets. We identified the prevalent topological features in each set and gave a mechanistic explanation as to why they can differentially respond to only one type of TF signal. We also found that some network topologies have a weak (not robust) ability to differentially respond to both AM and FM input signals by using different values of parameters for AM and FM cases. Our results provide a novel network mechanism for decoding different TF dynamics.

New concepts in feedback regulation of glucose metabolism

Glycolysis, the breakdown of glucose, is one of the most conserved and extensively studied biochemical pathways. Designing principles from chemistry and thermodynamics allow for energy production, biosynthesis and cellular communication. However, the kinetics or metabolic flux through the pathway also determines its function. Recently, there have been numerous developments that establish new allosteric interactions of glycolytic enzymes with small molecule metabolites and other mechanisms that may cooperate to allow for addition complex regulation of glycolysis. This review surveys these newfound sources of glycolysis regulation and discusses their possible roles in establishing kinetic design principles of glycolysis.

Late-Arriving Signals Contribute Less to Cell-Fate Decisions

Gene regulatory networks are largely responsible for cellular decision-making. These networks sense diverse external signals and respond by adjusting gene expression, enabling cells to reach environment-dependent decisions crucial for their survival or reproduction. However, information-carrying signals may arrive at variable times. Besides the intrinsic strength of these signals, their arrival time (timing) may also carry information about the environment and can influence cellular decision-making in ways that are poorly understood. For example, it is unclear how the timing of individual phage infections affects the lysis-lysogeny decision of bacteriophage λ despite variable infection times being likely in the wild and even in laboratory conditions. In this work, we combine mathematical modeling with experimentation to address this question. We develop an experimentally testable theory, which reveals that late-infecting phages contribute less to cellular decision-making. This implies that infection delays lower the probability of lysogeny compared to simultaneous infections. Furthermore, we show that infection delays reduce lysogenization by providing insufficient CII for threshold crossing during the critical decision-making period. We find evidence for a cutoff time after which subsequent infections cannot influence the cellular decision. We derive an intuitive formula that approximates the probability of lysogeny for variable infection times by a time-weighted average of probabilities for simultaneous infections. We validate these theoretical predictions experimentally. Similar concepts and simplifying modeling approaches may help elucidate the mechanisms underlying other cellular decisions.

Elements of biological oscillations in time and space

Oscillations in time and space are ubiquitous in nature and play critical roles in dynamic cellular processes. Although the molecular mechanisms underlying the generation of the dynamics are diverse, several distinct regulatory elements have been recognized as being critical in producing and modulating oscillatory dynamics. These include negative and positive feedback, time delay, nonlinearity in regulation, and random fluctuations ('noise'). Here we discuss the specific roles of these five elements in promoting or attenuating oscillatory dynamics, by drawing on insights from quantitative analyses of natural or synthetic biological networks.