Covalent modification of proteins as a threshold mechanism in development

Body Mass Dynamics Is Determined by the Metabolic Ohm's Law and Adipocyte-Autonomous Fat Mass Homeostasis

An ODE model integrating metabolic mechanisms with clinical data reveals an Ohm's law governing lifetime body mass dynamics, where fat and lean tissues are analogous to a parallel nonlinear capacitor and resistor, respectively. The law unexpectedly decouples weight stability (a cell-autonomous property of adipocytes) and weight change (a parabolic trajectory governed by Ohm's law). In middle age, insulin resistance causes fat accumulation to avoid excessive body shrinkage in old age. Moderate middle-age spread is thus natural, not an anomaly caused by hypothalamic defects, as proposed by lipostatic theory. These discoveries provide valuable insights into health care practices such as weight control and health assessment, explain certain observed phenomena, make testable predictions, and may help to resolve major conundrums in the field. The ODE model, which is more comprehensive than Ohm's law, is useful to study metabolism at the detailed microscopic levels.

Optogenetic approaches to investigate spatiotemporal signaling during development

Embryogenesis is coordinated by signaling pathways that pattern the developing organism. Many aspects of this process are not fully understood, including how signaling molecules spread through embryonic tissues, how signaling amplitude and dynamics are decoded, and how multiple signaling pathways cooperate to pattern the body plan. Optogenetic approaches can be used to address these questions by providing precise experimental control over a variety of biological processes. Here, we review how these strategies have provided new insights into developmental signaling and discuss how they could contribute to future investigations.

Morphogen interpretation: concentration, time, competence, and signaling dynamics

Tissue patterning during animal development is orchestrated by a handful of inductive signals. Most of these developmental cues act as morphogens, meaning they are locally produced secreted molecules that act at a distance to govern tissue patterning. The iterative use of the same signaling molecules in different developmental contexts demands that signal interpretation occurs in a highly context‐dependent manner. Hence the interpretation of signal depends on the specific competence of the receiving cells. Moreover, it has become clear that the differential interpretation of morphogens depends not only on the level of signaling but also the signaling dynamics, particularly the duration of signaling. In this review, we outline molecular mechanisms proposed in recent studies that explain how the response to morphogens is determined by differential competence, pathway intrinsic feedback, and the interpretation of signaling dynamics by gene regulatory networks. WIREs Dev Biol 2017, 6:e271. doi: 10.1002/wdev.271

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Tunable ultrasensitivity: functional decoupling and biological insights

Sensitivity has become a basic concept in biology, but much less is known about its tuning, probably because allosteric cooperativity, the best known mechanism of sensitivity, is determined by rigid conformations of interacting molecules and is thus difficult to tune. Reversible covalent modification (RCM), owing to its systems-level ingenuity, can generate concentration based, tunable sensitivity. Using a mathematical model of regulated RCM, we find sensitivity tuning can be decomposed into two orthogonal modes, which provide great insights into vital biological processes such as tissue development and cell cycle progression. We find that decoupling of the two modes of sensitivity tuning is critical to fidelity of cell fate decision; the decoupling is thus important in development. The decomposition also allows us to solve the ‘wasteful degradation conundrum’ in budding yeast cell cycle checkpoint, which further leads to discovery of a subtle but essential difference between positive feedback and double negative feedback. The latter guarantees revocability of stress-induced cell cycle arrest; while the former does not. By studying concentration conditions in the system, we extend applicability of ultrasensitivity and explain the ubiquity of reversible covalent modification.

Positional Information and Pattern Formation

The concept of positional information proposes that cells acquire positional values as in a coordinate system, which they interpret by developing in particular ways to give rise to spatial patterns. Some of the best evidence for positional information comes from regeneration experiments, and the patterning of the leg and antenna in Drosophila, and the vertebrate limb. Central problems are how positional information is set up, how it is recorded, and then how it is interpreted by the cells. A number of models have been proposed for the setting up of positional gradients, and most are based on diffusion of a morphogen and its interactions with extracellular molecules; however, diffusion may not be reliable mechanism. There are also mechanisms based on timing. There is no good evidence for the quantitative aspects of any of the proposed gradients and details how they are set up. The way in which a signaling gradient regulates differential gene expression in a concentration-dependent manner also raises several technical and quite difficult issues. A key feature of positional information being the basis for pattern formation is that there is no prepattern in the embryo.

MAPK feedback encodes a switch and timer for tunable stress adaptation in yeast

Signaling pathways can behave as switches or rheostats, generating binary or graded responses to a given cell stimulus. We evaluated whether a single signaling pathway can simultaneously encode a switch and a rheostat. We found that the kinase Hog1 mediated a bifurcated cellular response: Activation and commitment to adaptation to osmotic stress are switchlike, whereas protein induction and the resolution of this commitment are graded. Through experimentation, bioinformatics analysis, and computational modeling, we determined that graded recovery is encoded through feedback phosphorylation and a gene induction program that is both temporally staggered and variable across the population. This switch-to-rheostat signaling mechanism represents a versatile stress adaptation system, wherein a broad range of inputs generate an "all-in" response that is later tuned to allow graded recovery of individual cells over time.

A BMP-FGF morphogen toggle switch drives the ultrasensitive expression of multiple genes in the developing forebrain

Borders are important as they demarcate developing tissue into distinct functional units. A key challenge is the discovery of mechanisms that can convert morphogen gradients into tissue borders. While mechanisms that produce ultrasensitive cellular responses provide a solution, how extracellular morphogens drive such mechanisms remains poorly understood. Here, we show how Bone Morphogenetic Protein (BMP) and Fibroblast Growth Factor (FGF) pathways interact to generate ultrasensitivity and borders in the dorsal telencephalon. BMP and FGF signaling manipulations in explants produced border defects suggestive of cross inhibition within single cells, which was confirmed in dissociated cultures. Using mathematical modeling, we designed experiments that ruled out alternative cross inhibition mechanisms and identified a cross-inhibitory positive feedback (CIPF) mechanism, or "toggle switch", which acts upstream of transcriptional targets in dorsal telencephalic cells. CIPF explained several cellular phenomena important for border formation such as threshold tuning, ultrasensitivity, and hysteresis. CIPF explicitly links graded morphogen signaling in the telencephalon to switch-like cellular responses and has the ability to form multiple borders and scale pattern to size. These benefits may apply to other developmental systems.

Mathematical model of a cell size checkpoint

How cells regulate their size from one generation to the next has remained an enigma for decades. Recently, a molecular mechanism that links cell size and cell cycle was proposed in fission yeast. This mechanism involves changes in the spatial cellular distribution of two proteins, Pom1 and Cdr2, as the cell grows. Pom1 inhibits Cdr2 while Cdr2 promotes the G2 → M transition. Cdr2 is localized in the middle cell region (midcell) whereas the concentration of Pom1 is highest at the cell tips and declines towards the midcell. In short cells, Pom1 efficiently inhibits Cdr2. However, as cells grow, the Pom1 concentration at midcell decreases such that Cdr2 becomes activated at some critical size. In this study, the chemistry of Pom1 and Cdr2 was modeled using a deterministic reaction-diffusion-convection system interacting with a deterministic model describing microtubule dynamics. Simulations mimicked experimental data from wild-type (WT) fission yeast growing at normal and reduced rates; they also mimicked the behavior of a Pom1 overexpression mutant and WT yeast exposed to a microtubule depolymerizing drug. A mechanism linking cell size and cell cycle, involving the downstream action of Cdr2 on Wee1 phosphorylation, is proposed.

Cells delay division into two daughter cells until they reach a particular size. However, the molecular-level mechanisms by which they do this have remained unknown until recently. A cell-size checkpoint mechanism in rod-shaped fission yeast cells has recently been shown to involve two proteins, Pom1 and Cdr2. The concentrations of these proteins in the middle of the cell differ from that at the poles. The changing nature of these spatial gradients as the cell grows is size-sensitive. Pom1 inhibits Cdr2 while Cdr2 stimulates the cell to enter into mitosis. In short cells, the Pom1 concentration in the middle of the cell is so great that Cdr2 is inhibited. As cells grow, the Pom1 concentration in the middle of the cell declines; at some particular size, Cdr2 activates. In this study, we developed a mathematical model that mimics this checkpoint behavior.

Positional information and patterning revisited

The concept of positional information proposes that cells acquire positional values as in a coordinate system, which they interpret by developing in particular ways to give rise to spatial patterns. Some of the best evidence for positional information comes from regeneration experiments, and the patterning of the leg and antenna in Drosophila and the vertebrate limb. Central problems are how positional information is set up, how it is recorded, and then how it is interpreted by the cells. A number of models have been proposed for the setting up of positional gradients, and most are based on diffusion of a morphogen and its interactions with extracellular molecules. It is argued that diffusion may not be reliable mechanism. There are also mechanisms based on timing. There is no good evidence for the quantitative aspects of any of the gradients and details how they are set up. The way in which a signalling gradient regulates differential gene expression in a concentration-dependent manner also raises several mechanistic issues.

Robust generation and decoding of morphogen gradients

Morphogen gradients play a key role in multiple differentiation processes. Both the formation of the gradient and its interpretation by the receiving cells need to occur at high precision to ensure reproducible patterning. This need for quantitative precision is challenged by fluctuations in the environmental conditions and by variations in the genetic makeup of the developing embryos. We discuss mechanisms that buffer morphogen profiles against variations in gene dosage. Self-enhanced morphogen degradation and pre-steady-state decoding provide general means for buffering the morphogen profile against fluctuations in morphogen production rate. A more specific "shuttling" mechanism, which establishes a sharp and robust activation profile of a widely expressed morphogen, and enables the adjustment of morphogen profile with embryo size, is also described. Finally, we consider the transformation of the smooth gradient profile into sharp borders of gene expression in the signal-receiving cells. The integration theory and experiments are increasingly used, providing key insights into the system-level functioning of the developmental system.

Sharp developmental thresholds defined through bistability by antagonistic gradients of retinoic acid and FGF signaling

The establishment of thresholds along morphogen gradients in the embryo is poorly understood. Using mathematical modeling, we show that mutually inhibitory gradients can generate and position sharp morphogen thresholds in the embryonic space. Taking vertebrate segmentation as a paradigm, we demonstrate that the antagonistic gradients of retinoic acid (RA) and Fibroblast Growth Factor (FGF) along the presomitic mesoderm (PSM) may lead to the coexistence of two stable steady states. Here, we propose that this bistability is associated with abrupt switches in the levels of FGF and RA signaling, which permit the synchronized activation of segmentation genes, such as mesp2, in successive cohorts of PSM cells in response to the segmentation clock, thereby defining the future segments. Bistability resulting from mutual inhibition of RA and FGF provides a molecular mechanism for the all-or-none transitions assumed in the "clock and wavefront" somitogenesis model. Given that mutually antagonistic signaling gradients are common in development, such bistable switches could represent an important principle underlying embryonic patterning.

Single-cell zeroth-order protein degradation enhances the robustness of synthetic oscillator

In Escherichia coli, protein degradation in synthetic circuits is commonly achieved by the ssrA-tagged degradation system. In this work, we show that the degradation kinetics for the green fluorescent protein fused with the native ssrA tag in each cell exhibits the zeroth-order limit of the Michaelis–Menten kinetics, rather than the commonly assumed first-order. When measured in a population, the wide distribution of protein levels in the cells distorts the true kinetics and results in a first-order protein degradation kinetics as a population average. Using the synthetic gene-metabolic oscillator constructed previously, we demonstrated theoretically that the zeroth-order kinetics significantly enlarges the parameter space for oscillation and thus enhances the robustness of the design under parametric uncertainty.

A mechanism for the sharp transition of morphogen gradient interpretation in Xenopus

Background

One way in which positional information is established during embryonic development is through the graded distribution of diffusible morphogens. Unfortunately, little is known about how cells interpret different concentrations of morphogen to activate different genes or how thresholds are generated in a morphogen gradient.

Results

Here we show that the concentration-dependent induction of the T-box transcription factor Brachyury (Xbra) and the homeobox-containing gene Goosecoid (Gsc) by activin in Xenopus can be explained by the dynamics of a simple network consisting of three elements with a mutual negative feedback motif that can function to convert a graded signal (activin) into a binary output (Xbra on and Gsc off, or vice versa). Importantly, such a system can display sharp thresholds. Consistent with the predictions of our model, Xenopus ectodermal cells display a binary response at the single cell level after treatment with activin.

Conclusion

This kind of simple network with mutual negative feedback might provide a general mechanism for selective gene activation in response to different levels of a single external signal. It provides a mechanism by which a sharp boundary might be created between domains of different cell types in response to a morphogen gradient.

The role of modelling in identifying drug targets for diseases of the cell cycle

The cell cycle is implicated in diseases that are the leading cause of mortality and morbidity in the developed world. Until recently, the search for drug targets has focused on relatively small parts of the regulatory network under the assumption that key events can be controlled by targeting single pathways. This is valid provided the impact of couplings to the wider scale context of the network can be ignored. The resulting depth of study has revealed many new insights; however, these have been won at the expense of breadth and a proper understanding of the consequences of links between the different parts of the network. Since it is now becoming clear that these early assumptions may not hold and successful treatments are likely to employ drugs that simultaneously target a number of different sites in the regulatory network, it is timely to redress this imbalance. However, the substantial increase in complexity presents new challenges and necessitates parallel theoretical and experimental approaches. We review the current status of theoretical models for the cell cycle in light of these new challenges. Many of the existing approaches are not sufficiently comprehensive to simultaneously incorporate the required extent of couplings. Where more appropriate levels of complexity are incorporated, the models are difficult to link directly to currently available data. Further progress requires a better integration of experiment and theory. New kinds of data are required that are quantitative, have a higher temporal resolution and that allow simultaneous quantitative comparison of the concentration of larger numbers of different proteins. More comprehensive models are required and must accommodate not only substantial uncertainties in the structure and kinetic parameters of the networks, but also high levels of ignorance. The most recent results relating network complexity to robustness of the dynamics provide clues that suggest progress is possible.

Threshold responses to morphogen gradients by zero-order ultrasensitivity

Translating a graded morphogen distribution into tight response borders is central to all developmental processes. Yet, the molecular mechanisms generating such behavior are poorly understood. During patterning of the Drosophila embryonic ventral ectoderm, a graded mitogen-activated protein kinase (MAPK) activation is converted into an all-or-none degradation switch of the Yan transcriptional repressor. Replacing the cardinal phosphorylated amino acid of Yan by a phosphomimetic residue allowed its degradation in a MAPK-independent manner, consistent with Yan phosphorylation being the critical event in generating the switch. Several alternative threshold mechanisms that could, in principle, be realized by this phosphorylation, including first order, cooperativity, positive feedback and zero-order ultrasensitivity, were analyzed. We found that they can be distinguished by their kinetics and steady-state responses to Yan overexpression. In agreement with the predictions for zero-order kinetics, an increase in Yan levels did not shift the degradation border, but significantly elevated the time required to reach steady state. We propose that a reversible loop of Yan phosphorylation implements a zero-order ultrasensitivity-like threshold mechanism, with the capacity to form sharp thresholds that are independent of the level of Yan.

Roles of positive and negative feedback in biological systems

We discuss the influence of positive and negative feedback on the stability of a system, which is not clear-cut, and involves complex, mathematical problems. We show in particular that positive feedback can have a stabilising effect on some systems. We also point out the role that positive feedback plays in the digital treatment of signals required by cellular signalling, drawing on analogies from electronics, and the role that negative feedback plays in making a system robust against alteration of its parameters. Both positive and negative feedback can be seen as important enhancers of the properties of biological systems.

Transitions and new dynamical states induced by noise in a multiply regulated biochemical system

Noise-induced transitions between coexisting states, and the emergence of a new oscillatory state, are examined in a model for a multiply regulated biochemical system. For the undisturbed system, three oscillatory states, I, II, and III, coexist. It is found that noise above a critical amplitude can cause a transition between states III and II and between states III or II and state I, whereas a transition from state I to either states II or III is never observed. This indicates that the relative stability under noise perturbations is greatest for state I, and progressively less for states II and III. In addition to this transition behaviour, a purely noise-induced state is found. Under noise perturbations, the average concentration of metabolites may depend on both the time duration and amplitude of the superimposed noise. The implications of these results for understanding the in vivo behaviour of complex biochemical systems are discussed.

Growth factors as morphogens: do gradients and thresholds establish body plan?

Theories of morphogenesis have centred around gradients of morphogens interpreted by cells according to preset concentration thresholds. Growth factor proteins have been candidates for such morphogens, and experiments in the frog Xenopus, among other organisms, now show that embryonic cells are capable of interpreting growth factor concentrations according to the models. This opens up questions of whether such mechanisms are sufficient, and-if there are growth factor gradients-which factors are actually used and how.