Qing Nie

Do Morphogen Gradients Arise by Diffusion

Many patterns of cell and tissue organization are specified during development by gradients of morphogens, substances that assign different cell fates at different concentrations. Gradients form by morphogen transport from a localized site, but whether this occurs by simple diffusion or by more elaborate mechanisms is unclear. We attempt to resolve this controversy by analyzing recent data in ways that appropriately capture the complexity of systems in which transport, receptor interaction, endo- and exocytosis, and degradation occur together. We find that diffusive mechanisms of morphogen transport are much more plausible-and nondiffusive mechanisms much less plausible-than has generally been argued. Moreover, we show that a class of experiments, endocytic blockade, thought to effectively distinguish between diffusive and nondiffusive transport models actually fails to draw useful distinctions.

Cell Lineages and the Logic of Proliferative Control

It is widely accepted that the growth and regeneration of tissues and organs is tightly controlled. Although experimental studies are beginning to reveal molecular mechanisms underlying such control, there is still very little known about the control strategies themselves. Here, we consider how secreted negative feedback factors (“chalones”) may be used to control the output of multistage cell lineages, as exemplified by the actions of GDF11 and activin in a self-renewing neural tissue, the mammalian olfactory epithelium (OE). We begin by specifying performance objectives—what, precisely, is being controlled, and to what degree—and go on to calculate how well different types of feedback configurations, feedback sensitivities, and tissue architectures achieve control. Ultimately, we show that many features of the OE—the number of feedback loops, the cellular processes targeted by feedback, even the location of progenitor cells within the tissue—fit with expectations for the best possible control. In so doing, we also show that certain distinctions that are commonly drawn among cells and molecules—such as whether a cell is a stem cell or transit-amplifying cell, or whether a molecule is a growth inhibitor or stimulator—may be the consequences of control, and not a reflection of intrinsic differences in cellular or molecular character.

Complex Regulation of cyp26a1 Creates a Robust Retinoic Acid Gradient in the Zebrafish Embryo

Positional identities along the anterior–posterior axis of the vertebrate nervous system are assigned during gastrulation by multiple posteriorizing signals, including retinoic acid (RA), fibroblast growth factors (Fgfs), and Wnts. Experimental evidence has suggested that RA, which is produced in paraxial mesoderm posterior to the hindbrain by aldehyde dehydrogenase 1a2 (aldh1a2/raldh2), forms a posterior-to-anterior gradient across the hindbrain field, and provides the positional information that specifies the locations and fates of rhombomeres. Recently, alternative models have been proposed in which RA plays only a permissive role, signaling wherever it is not degraded. Here we use a combination of experimental and modeling tools to address the role of RA in providing long-range positional cues in the zebrafish hindbrain. Using cell transplantation and implantation of RA-coated beads into RA-deficient zebrafish embryos, we demonstrate that RA can directly convey graded positional information over long distances. We also show that expression of Cyp26a1, the major RA-degrading enzyme during gastrulation, is under complex feedback and feedforward control by RA and Fgf signaling. The predicted consequence of such control is that RA gradients will be both robust to fluctuations in RA synthesis and adaptive to changes in embryo length during gastrulation. Such control also provides an explanation for the fact that loss of an endogenous RA gradient can be compensated for by RA that is provided in a spatially uniform manner.

Robust Spatial Sensing of Mating Pheromone Gradients by Yeast Cells

Projecting or moving up a chemical gradient is a universal behavior of living organisms. We tested the ability of S. cerevisiae a-cells to sense and respond to spatial gradients of the mating pheromone α-factor produced in a microfluidics chamber; the focus was on bar1Δ strains, which do not degrade the pheromone input. The yeast cells exhibited good accuracy with the mating projection typically pointing in the correct direction up the gradient (∼80% under certain conditions), excellent sensitivity to shallow gradients, and broad dynamic range so that gradient-sensing was relatively robust over a 1000-fold range of average α-factor concentrations. Optimal directional sensing occurred at lower concentrations (5 nM) close to the Kd of the receptor and with steeper gradient slopes. Pheromone supersensitive mutations (sst2Δ and ste2300Δ) that disrupt the down-regulation of heterotrimeric G-protein signaling caused defects in both sensing and response. Interestingly, yeast cells employed adaptive mechanisms to increase the robustness of the process including filamentous growth (i.e. directional distal budding) up the gradient at low pheromone concentrations, bending of the projection to be more aligned with the gradient, and forming a more accurate second projection when the first projection was in the wrong direction. Finally, the cells were able to amplify a shallow external gradient signal of α-factor to produce a dramatic polarization of signaling proteins at the front of the cell. Mathematical modeling revealed insights into the mechanism of this amplification and how the supersensitive mutants can disrupt accurate polarization. Together, these data help to specify and elucidate the abilities of yeast cells to sense and respond to spatial gradients of pheromone.

Efficient semi-implicit schemes for stiff systems

When explicit time discretization schemes are applied to stiff reaction-diffusion equations, the stability constraint on the time step depends on two terms: the diffusion and the reaction. The part of the stability constraint due to diffusion can be totally removed if the linear diffusions are treated exactly using integration factor (IF) or exponential time differencing (ETD) methods. For systems with severely stiff reactions, those methods are not efficient because the reaction terms in IF or ETD are still approximated with explicit schemes. In this paper, we introduce a new class of semi-implicit schemes, which treats the linear diffusions exactly and explicitly, and the nonlinear reactions implicitly. A distinctive feature of the scheme is the decoupling between the exact evaluation of the diffusion terms and implicit treatment of the nonlinear reaction terms. As a result, the size of the nonlinear system arising from the implicit treatment of the reactions is independent of the number of spatial grid points; it only depends on the number of original equations, unlike the case in which standard implicit temporal schemes are directly applied to the reaction-diffusion system. The stability region for this class of methods is much larger than existing methods using an explicit treatment of reaction terms. In particular, the one with second order accuracy is unconditionally linearly stable with respect to both diffusion and reaction. Direct numerical simulations on test equations, as well as morphogen systems from developmental biology, show the new semi-implicit schemes are efficient, robust and accurate.

A theoretical framework for specificity in cell signaling

Different cellular signal transduction pathways are often interconnected, so that the potential for undesirable crosstalk between pathways exists. Nevertheless, signaling networks have evolved that maintain specificity from signal to cellular response. Here, we develop a framework for the analysis of networks containing two or more interconnected signaling pathways. We define two properties, specificity and fidelity, that all pathways in a network must possess in order to avoid paradoxical situations where one pathway activates another pathways output, or responds to another pathways input, more than its own. In unembellished networks that share components, it is impossible for all pathways to have both mutual specificity and mutual fidelity. However, inclusion of either of two related insulating mechanisms—compartmentalization or the action of a scaffold protein—allows both properties to be achieved, provided deactivation rates are fast compared to exchange rates.

Integrative multicellular biological modeling: a case study of 3D epidermal development using GPU algorithms

BackgroundSimulation of sophisticated biological models requires considerable computational power. These models typically integrate together numerous biological phenomena such as spatially-explicit heterogeneous cells, cell-cell interactions, cell-environment interactions and intracellular gene networks. The recent advent of programming for graphical processing units (GPU) opens up the possibility of developing more integrative, detailed and predictive biological models while at the same time decreasing the computational cost to simulate those models.ResultsWe construct a 3D model of epidermal development and provide a set of GPU algorithms that executes significantly faster than sequential central processing unit (CPU) code. We provide a parallel implementation of the subcellular element method for individual cells residing in a lattice-free spatial environment. Each cell in our epidermal model includes an internal gene network, which integrates cellular interaction of Notch signaling together with environmental interaction of basement membrane adhesion, to specify cellular state and behaviors such as growth and division. We take a pedagogical approach to describing how modeling methods are efficiently implemented on the GPU including memory layout of data structures and functional decomposition. We discuss various programmatic issues and provide a set of design guidelines for GPU programming that are instructive to avoid common pitfalls as well as to extract performance from the GPU architecture.ConclusionsWe demonstrate that GPU algorithms represent a significant technological advance for the simulation of complex biological models. We further demonstrate with our epidermal model that the integration of multiple complex modeling methods for heterogeneous multicellular biological processes is both feasible and computationally tractable using this new technology. We hope that the provided algorithms and source code will be a starting point for modelers to develop their own GPU implementations, and encourage others to implement their modeling methods on the GPU and to make that code available to the wider community.

Noise drives sharpening of gene expression boundaries in the zebrafish hindbrain

Morphogens provide positional information for spatial patterns of gene expression during development. However, stochastic effects such as local fluctuations in morphogen concentration and noise in signal transduction make it difficult for cells to respond to their positions accurately enough to generate sharp boundaries between gene expression domains. During development of rhombomeres in the zebrafish hindbrain, the morphogen retinoic acid (RA) induces expression of hoxb1a in rhombomere 4 (r4) and krox20 in r3 and r5. Fluorescent in situ hybridization reveals rough edges around these gene expression domains, in which cells co‐express hoxb1a and krox20 on either side of the boundary, and these sharpen within a few hours. Computational analysis of spatial stochastic models shows, surprisingly, that noise in hoxb1a/krox20 expression actually promotes sharpening of boundaries between adjacent segments. In particular, fluctuations in RA initially induce a rough boundary that requires noise in hoxb1a/krox20 expression to sharpen. This finding suggests a novel noise attenuation mechanism that relies on intracellular noise to induce switching and coordinate cellular decisions during developmental patterning.

The Measure of Success: Constraints, Objectives, and Tradeoffs in Morphogen-mediated Patterning

A large, diverse, and growing number of strategies have been proposed to explain how morphogen gradients achieve robustness and precision. We argue that, to be useful, the evaluation of such strategies must take into account the constraints imposed by competing objectives and performance tradeoffs. This point is illustrated through a mathematical and computational analysis of the strategy of self-enhanced morphogen clearance. The results suggest that the usefulness of this strategy comes less from its ability to increase robustness to morphogen source fluctuations per se, than from its ability to overcome specific kinds of noise, and to increase the fraction of a morphogen gradient within which robust threshold positions may be established. This work also provides new insights into the longstanding question of why morphogen gradients show a maximum range in vivo.

An Ovol2-Zeb1 Mutual Inhibitory Circuit Governs Bidirectional and Multi-step Transition between Epithelial and Mesenchymal States

Reversible epithelial-to-mesenchymal transition (EMT) is central to tissue development, epithelial stemness, and cancer metastasis. While many regulatory elements have been identified to induce EMT, the complex process underlying such cellular plasticity remains poorly understood. Utilizing a systems biology approach integrating modeling and experiments, we found multiple intermediate states contributing to EMT and that the robustness of the transitions is modulated by transcriptional factor Ovol2. In particular, we obtained evidence for a mutual inhibition relationship between Ovol2 and EMT inducer Zeb1, and observed that adding this regulation generates a novel four-state system consisting of two distinct intermediate phenotypes that differ in differentiation propensities and are favored in different environmental conditions. We identified epithelial cells that naturally exist in an intermediate state with bidirectional differentiation potential, and found the balance between EMT-promoting and -inhibiting factors to be critical in achieving and selecting between intermediate states. Our analysis suggests a new design principle in controlling cellular plasticity through multiple intermediate cell fates and underscores the critical involvement of Ovol2 and its associated molecular regulations.